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import numpy as np
import scipy.signal as signal
from scipy.interpolate import interp1d
import pandas as pd
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
from astropy.io import fits
import emcee
import corner
import copy
import time
import os
import sys
import smart
def makeModel(teff, logg=5, metal=0, vsini=1, rv=0, tell_alpha=1.0, airmass=1.0, pwv=0.5, wave_offset=0, flux_offset=0,**kwargs):
"""
Return a forward model.
Parameters
----------
teff : effective temperature
data : an input science data used for continuum correction
Optional Parameters
-------------------
Returns
-------
model: a synthesized model
"""
# read in the parameters
order = kwargs.get('order', '33')
modelset = kwargs.get('modelset', 'btsettl08')
instrument = kwargs.get('instrument', 'nirspec')
veiling = kwargs.get('veiling', 0) # flux veiling parameter
lsf = kwargs.get('lsf', 4.5) # instrumental LSF
include_fringe_model = kwargs.get('include_fringe_model', False)
if instrument == 'apogee':
try:
import apogee_tools as ap
except ImportError:
print('Need to install the package "apogee_tools" (https://github.com/jbirky/apogee_tools) \n')
xlsf = kwargs.get('xlsf', np.linspace(-7.,7.,43)) # APOGEE instrumental LSF sampling
wave_off1 = kwargs.get('wave_off1') # wavelength offset for chip a
wave_off2 = kwargs.get('wave_off2') # wavelength offset for chip b
wave_off3 = kwargs.get('wave_off3') # wavelength offset for chip c
c0_1 = kwargs.get('c0_1') # constant flux offset for chip a
c0_2 = kwargs.get('c0_2') # linear flux offset for chip a
c1_1 = kwargs.get('c1_1') # constant flux offset for chip b
c1_2 = kwargs.get('c1_2') # linear flux offset for chip b
c2_1 = kwargs.get('c2_1') # constant flux offset for chip c
c2_2 = kwargs.get('c2_2') # linear flux offset for chip c
tell = kwargs.get('tell', True) # apply telluric
#tell_alpha = kwargs.get('tell_alpha', 1.0) # Telluric alpha power
binary = kwargs.get('binary', False) # make a binary model
# assume the secondary has the same metallicity
if binary:
teff2 = kwargs.get('teff2')
logg2 = kwargs.get('logg2')
rv2 = kwargs.get('rv2')
vsini2 = kwargs.get('vsini2')
flux_scale = kwargs.get('flux_scale', 0.8)
data = kwargs.get('data', None) # for continuum correction and resampling
output_stellar_model = kwargs.get('output_stellar_model', False)
if data is not None and instrument == 'nirspec':
order = data.order
# read in a model
#print('teff ',teff,'logg ',logg, 'z', z, 'order', order, 'modelset', modelset)
#print('teff ',type(teff),'logg ',type(logg), 'z', type(z), 'order', type(order), 'modelset', type(modelset))
model = smart.Model(teff=teff, logg=logg, metal=metal, order=str(order), modelset=modelset, instrument=instrument)
#elif data is not None and instrument == 'apogee':
elif instrument == 'apogee':
model = smart.Model(teff=teff, logg=logg, metal=metal, modelset=modelset, instrument=instrument)
# Dirty fix here
model.wave = model.wave[np.where(model.flux != 0)]
model.flux = model.flux[np.where(model.flux != 0)]
# apply vmicro
vmicro = 2.478 - 0.325*logg
model.flux = smart.broaden(wave=model.wave, flux=model.flux, vbroad=vmicro, rotate=False, gaussian=True)
elif data is None and instrument == 'nirspec':
model = smart.Model(teff=teff, logg=logg, metal=metal, order=str(order), modelset=modelset, instrument=instrument)
# wavelength offset
#model.wave += wave_offset
# apply vsini
model.flux = smart.broaden(wave=model.wave, flux=model.flux, vbroad=vsini, rotate=True, gaussian=False)
# apply rv (including the barycentric correction)
model.wave = rvShift(model.wave, rv=rv)
# flux veiling
model.flux += veiling
## if binary is True: make a binary model
if binary:
model2 = smart.Model(teff=teff2, logg=logg2, metal=metal, order=str(order), modelset=modelset, instrument=instrument)
# apply vsini
model2.flux = smart.broaden(wave=model2.wave, flux=model2.flux, vbroad=vsini2, rotate=True, gaussian=False)
# apply rv (including the barycentric correction)
model2.wave = rvShift(model2.wave, rv=rv2)
# linearly interpolate the model2 onto the model1 grid
fit = interp1d(model2.wave, model2.flux)
select_wavelength = np.where( (model.wave < model2.wave[-1]) & (model.wave > model2.wave[0]) )
model.flux = model.flux[select_wavelength]
model.wave = model.wave[select_wavelength]
# combine the models together and scale the secondary flux
model.flux += flux_scale * fit(model.wave)
if output_stellar_model:
stellar_model = copy.deepcopy(model)
if binary:
model2.flux = flux_scale * fit(model.wave)
# apply telluric
if tell is True:
model = smart.applyTelluric(model=model, tell_alpha=tell_alpha, airmass=airmass, pwv=pwv)
# fringe
if include_fringe_model is True:
#print('adding the fringe model')
s1, s2, s3, s4, s5 = 0, 150, 400, 600, -1
piecewise_fringe_model = [s1, s2, s3, s4, s5]
model.flux *= smart.double_sine_fringe(model, data, piecewise_fringe_model, teff, logg, vsini, rv, airmass, pwv, wave_offset, flux_offset, lsf, modelset)
# instrumental LSF
if instrument == 'nirspec':
model.flux = smart.broaden(wave=model.wave, flux=model.flux, vbroad=lsf, rotate=False, gaussian=True)
elif instrument == 'apogee':
model.flux = ap.apogee_hack.spec.lsf.convolve(model.wave, model.flux, lsf=lsf, xlsf=xlsf).flatten()
model.wave = ap.apogee_hack.spec.lsf.apStarWavegrid()
# Remove the NANs
model.wave = model.wave[~ | np.isnan(model.flux) | numpy.isnan |
import numpy as np
import pytest
from autolens.data.array import mask
from autolens.data.array import interpolation
from autolens.model.galaxy import galaxy
from autolens.model.profiles import mass_profiles
@pytest.fixture(name='scheme')
def make_scheme():
return interpolation.InterpolationScheme(shape=(3, 3), image_coords=np.array([[1.0, 1.0]]), image_pixel_scale=1.0)
@pytest.fixture(name='geometry')
def make_geometry():
return interpolation.InterpolationGeometry(y_min=-1.0, y_max=1.0, x_min=-1.0, x_max=1.0,
y_pixel_scale=1.0, x_pixel_scale=1.0)
@pytest.fixture(name='galaxy_no_profiles', scope='function')
def make_galaxy_no_profiles():
return galaxy.Galaxy()
@pytest.fixture(name="galaxy_mass_sis")
def make_galaxy_mass_sis():
sis = mass_profiles.SphericalIsothermal(einstein_radius=1.0)
return galaxy.Galaxy(mass_profile=sis)
class TestInterpolationScheme(object):
class TestConstructor:
def test__sets_up_attributes_correctly(self):
image_coords = np.array([[-1.0, -6.0], [-1.0, 0.0], [-4.0, 2.0],
[-0.0, -1.0], [0.0, 0.0], [0.0, 1.0],
[3.0, -1.0], [1.0, 0.0], [1.0, 1.0]])
interp = interpolation.InterpolationScheme(shape=(3, 3), image_coords=image_coords, image_pixel_scale=1.0)
assert interp.shape == (3, 3)
assert interp.pixels == 9
assert (interp.image_coords == image_coords).all()
assert interp.geometry.y_min == -6.0
assert interp.geometry.y_max == 2.0
assert interp.geometry.x_min == -4.0
assert interp.geometry.x_max == 3.0
assert interp.geometry.y_pixel_scale == 1.0
assert interp.geometry.x_pixel_scale == 1.0
assert interp.geometry.x_size == 7.0
assert interp.geometry.y_size == 8.0
assert interp.geometry.x_start == -4.5
assert interp.geometry.y_start == -6.5
class TestNeighbors:
def test___3x3_grid_neighbors_all_correct(self):
# |0|1|2|
# |3|4|5|
# |6|7|8|
interp = interpolation.InterpolationScheme(shape=(3, 3), image_coords=np.array([[1.0, 1.0]]),
image_pixel_scale=1.0)
assert (interp.bottom_right_neighbors[0] == np.array([1, 3, 4])).all()
assert (interp.bottom_right_neighbors[1] == np.array([2, 4, 5])).all()
assert (interp.bottom_right_neighbors[2] == np.array([-1, 5, -1])).all()
assert (interp.bottom_right_neighbors[3] == np.array([4, 6, 7])).all()
assert (interp.bottom_right_neighbors[4] == np.array([5, 7, 8])).all()
assert (interp.bottom_right_neighbors[5] == np.array([-1, 8, -1])).all()
assert (interp.bottom_right_neighbors[6] == np.array([7, -1, -1])).all()
assert (interp.bottom_right_neighbors[7] == np.array([8, -1, -1])).all()
assert (interp.bottom_right_neighbors[8] == np.array([-1, -1, -1])).all()
assert (interp.bottom_left_neighbors[0] == np.array([-1, -1, 3])).all()
assert (interp.bottom_left_neighbors[1] == np.array([0, 3, 4])).all()
assert (interp.bottom_left_neighbors[2] == np.array([1, 4, 5])).all()
assert (interp.bottom_left_neighbors[3] == np.array([-1, -1, 6])).all()
assert (interp.bottom_left_neighbors[4] == np.array([3, 6, 7])).all()
assert (interp.bottom_left_neighbors[5] == np.array([4, 7, 8])).all()
assert (interp.bottom_left_neighbors[6] == np.array([-1, -1, -1])).all()
assert (interp.bottom_left_neighbors[7] == np.array([6, -1, -1])).all()
assert (interp.bottom_left_neighbors[8] == np.array([7, -1, -1])).all()
assert (interp.top_right_neighbors[0] == np.array([-1, -1, 1])).all()
assert (interp.top_right_neighbors[1] == np.array([-1, -1, 2])).all()
assert (interp.top_right_neighbors[2] == np.array([-1, -1, -1])).all()
assert (interp.top_right_neighbors[3] == np.array([0, 1, 4])).all()
assert (interp.top_right_neighbors[4] == np.array([1, 2, 5])).all()
assert (interp.top_right_neighbors[5] == np.array([2, -1, -1])).all()
assert (interp.top_right_neighbors[6] == np.array([3, 4, 7])).all()
assert (interp.top_right_neighbors[7] == np.array([4, 5, 8])).all()
assert (interp.top_right_neighbors[8] == np.array([5, -1, -1])).all()
assert (interp.top_left_neighbors[0] == np.array([-1, -1, -1])).all()
assert (interp.top_left_neighbors[1] == np.array([-1, -1, 0])).all()
assert (interp.top_left_neighbors[2] == np.array([-1, -1, 1])).all()
assert (interp.top_left_neighbors[3] == np.array([-1, 0, -1])).all()
assert (interp.top_left_neighbors[4] == np.array([0, 1, 3])).all()
assert (interp.top_left_neighbors[5] == np.array([1, 2, 4])).all()
assert (interp.top_left_neighbors[6] == np.array([-1, 3, -1])).all()
assert (interp.top_left_neighbors[7] == np.array([3, 4, 6])).all()
assert (interp.top_left_neighbors[8] == np.array([4, 5, 7])).all()
def test___3x4_grid_neighbors_all_correct(self):
# |0|1| 2| 3|
# |4|5| 6| 7|
# |8|9|10|11|
interp = interpolation.InterpolationScheme(shape=(3, 4), image_coords=np.array([[1.0, 1.0]]),
image_pixel_scale=1.0)
assert (interp.bottom_right_neighbors[0] == np.array([1, 4, 5])).all()
assert (interp.bottom_right_neighbors[1] == np.array([2, 5, 6])).all()
assert (interp.bottom_right_neighbors[2] == np.array([3, 6, 7])).all()
assert (interp.bottom_right_neighbors[3] == np.array([-1, 7, -1])).all()
assert (interp.bottom_right_neighbors[4] == np.array([5, 8, 9])).all()
assert (interp.bottom_right_neighbors[5] == np.array([6, 9, 10])).all()
assert (interp.bottom_right_neighbors[6] == np.array([7, 10, 11])).all()
assert (interp.bottom_right_neighbors[7] == np.array([-1, 11, -1])).all()
assert (interp.bottom_right_neighbors[8] == np.array([9, -1, -1])).all()
assert (interp.bottom_right_neighbors[9] == np.array([10, -1, -1])).all()
assert (interp.bottom_right_neighbors[10] == np.array([11, -1, -1])).all()
assert (interp.bottom_right_neighbors[11] == np.array([-1, -1, -1])).all()
assert (interp.bottom_left_neighbors[0] == np.array([-1, -1, 4])).all()
assert (interp.bottom_left_neighbors[1] == np.array([0, 4, 5])).all()
assert (interp.bottom_left_neighbors[2] == np.array([1, 5, 6])).all()
assert (interp.bottom_left_neighbors[3] == np.array([2, 6, 7])).all()
assert (interp.bottom_left_neighbors[4] == np.array([-1, -1, 8])).all()
assert (interp.bottom_left_neighbors[5] == np.array([4, 8, 9])).all()
assert (interp.bottom_left_neighbors[6] == np.array([5, 9, 10])).all()
assert (interp.bottom_left_neighbors[7] == np.array([6, 10, 11])).all()
assert (interp.bottom_left_neighbors[8] == np.array([-1, -1, -1])).all()
assert (interp.bottom_left_neighbors[9] == np.array([8, -1, -1])).all()
assert (interp.bottom_left_neighbors[10] == np.array([9, -1, -1])).all()
assert (interp.bottom_left_neighbors[11] == np.array([10, -1, -1])).all()
assert (interp.top_right_neighbors[0] == np.array([-1, -1, 1])).all()
assert (interp.top_right_neighbors[1] == np.array([-1, -1, 2])).all()
assert (interp.top_right_neighbors[2] == np.array([-1, -1, 3])).all()
assert (interp.top_right_neighbors[3] == np.array([-1, -1, -1])).all()
assert (interp.top_right_neighbors[4] == np.array([0, 1, 5])).all()
assert (interp.top_right_neighbors[5] == np.array([1, 2, 6])).all()
assert (interp.top_right_neighbors[6] == np.array([2, 3, 7])).all()
assert (interp.top_right_neighbors[7] == np.array([3, -1, -1])).all()
assert (interp.top_right_neighbors[8] == np.array([4, 5, 9])).all()
assert (interp.top_right_neighbors[9] == np.array([5, 6, 10])).all()
assert (interp.top_right_neighbors[10] == np.array([6, 7, 11])).all()
assert (interp.top_right_neighbors[11] == np.array([7, -1, -1])).all()
assert (interp.top_left_neighbors[0] == np.array([-1, -1, -1])).all()
assert (interp.top_left_neighbors[1] == np.array([-1, -1, 0])).all()
assert (interp.top_left_neighbors[2] == np.array([-1, -1, 1])).all()
assert (interp.top_left_neighbors[3] == np.array([-1, -1, 2])).all()
assert (interp.top_left_neighbors[4] == np.array([-1, 0, -1])).all()
assert (interp.top_left_neighbors[5] == np.array([0, 1, 4])).all()
assert (interp.top_left_neighbors[6] == np.array([1, 2, 5])).all()
assert (interp.top_left_neighbors[7] == np.array([2, 3, 6])).all()
assert (interp.top_left_neighbors[8] == np.array([-1, 4, -1])).all()
assert (interp.top_left_neighbors[9] == np.array([4, 5, 8])).all()
assert (interp.top_left_neighbors[10] == np.array([5, 6, 9])).all()
assert (interp.top_left_neighbors[11] == np.array([6, 7, 10])).all()
def test___4x3_grid_neighbors_all_correct(self):
# |0| 1| 2|
# |3| 4| 5|
# |6| 7| 8|
# |9|10|11|
interp = interpolation.InterpolationScheme(shape=(4, 3), image_coords=np.array([[1.0, 1.0]]),
image_pixel_scale=1.0)
assert (interp.bottom_right_neighbors[0] == np.array([1, 3, 4])).all()
assert (interp.bottom_right_neighbors[1] == np.array([2, 4, 5])).all()
assert (interp.bottom_right_neighbors[2] == np.array([-1, 5, -1])).all()
assert (interp.bottom_right_neighbors[3] == np.array([4, 6, 7])).all()
assert (interp.bottom_right_neighbors[4] == np.array([5, 7, 8])).all()
assert (interp.bottom_right_neighbors[5] == np.array([-1, 8, -1])).all()
assert (interp.bottom_right_neighbors[6] == np.array([7, 9, 10])).all()
assert (interp.bottom_right_neighbors[7] == np.array([8, 10, 11])).all()
assert (interp.bottom_right_neighbors[8] == np.array([-1, 11, -1])).all()
assert (interp.bottom_right_neighbors[9] == np.array([10, -1, -1])).all()
assert (interp.bottom_right_neighbors[10] == np.array([11, -1, -1])).all()
assert (interp.bottom_right_neighbors[11] == np.array([-1, -1, -1])).all()
assert (interp.bottom_left_neighbors[0] == np.array([-1, -1, 3])).all()
assert (interp.bottom_left_neighbors[1] == np.array([0, 3, 4])).all()
assert (interp.bottom_left_neighbors[2] == np.array([1, 4, 5])).all()
assert (interp.bottom_left_neighbors[3] == np.array([-1, -1, 6])).all()
assert (interp.bottom_left_neighbors[4] == np.array([3, 6, 7])).all()
assert (interp.bottom_left_neighbors[5] == np.array([4, 7, 8])).all()
assert (interp.bottom_left_neighbors[6] == np.array([-1, -1, 9])).all()
assert (interp.bottom_left_neighbors[7] == np.array([6, 9, 10])).all()
assert (interp.bottom_left_neighbors[8] == np.array([7, 10, 11])).all()
assert (interp.bottom_left_neighbors[9] == np.array([-1, -1, -1])).all()
assert (interp.bottom_left_neighbors[10] == np.array([9, -1, -1])).all()
assert (interp.bottom_left_neighbors[11] == np.array([10, -1, -1])).all()
assert (interp.top_right_neighbors[0] == np.array([-1, -1, 1])).all()
assert (interp.top_right_neighbors[1] == np.array([-1, -1, 2])).all()
assert (interp.top_right_neighbors[2] == np.array([-1, -1, -1])).all()
assert (interp.top_right_neighbors[3] == np.array([0, 1, 4])).all()
assert (interp.top_right_neighbors[4] == np.array([1, 2, 5])).all()
assert (interp.top_right_neighbors[5] == np.array([2, -1, -1])).all()
assert (interp.top_right_neighbors[6] == np.array([3, 4, 7])).all()
assert (interp.top_right_neighbors[7] == np.array([4, 5, 8])).all()
assert (interp.top_right_neighbors[8] == np.array([5, -1, -1])).all()
assert (interp.top_right_neighbors[9] == np.array([6, 7, 10])).all()
assert (interp.top_right_neighbors[10] == np.array([7, 8, 11])).all()
assert (interp.top_right_neighbors[11] == np.array([8, -1, -1])).all()
assert (interp.top_left_neighbors[0] == np.array([-1, -1, -1])).all()
assert (interp.top_left_neighbors[1] == np.array([-1, -1, 0])).all()
assert (interp.top_left_neighbors[2] == np.array([-1, -1, 1])).all()
assert (interp.top_left_neighbors[3] == np.array([-1, 0, -1])).all()
assert (interp.top_left_neighbors[4] == np.array([0, 1, 3])).all()
assert (interp.top_left_neighbors[5] == np.array([1, 2, 4])).all()
assert (interp.top_left_neighbors[6] == np.array([-1, 3, -1])).all()
assert (interp.top_left_neighbors[7] == np.array([3, 4, 6])).all()
assert (interp.top_left_neighbors[8] == np.array([4, 5, 7])).all()
assert (interp.top_left_neighbors[9] == np.array([-1, 6, -1])).all()
assert (interp.top_left_neighbors[10] == np.array([6, 7, 9])).all()
assert (interp.top_left_neighbors[11] == np.array([7, 8, 10])).all()
def test___4x4_grid_neighbors_all_correct(self):
# | 0| 1| 2| 3|
# | 4| 5| 6| 7|
# | 8| 9|10|11|
# |12|13|14|15|
interp = interpolation.InterpolationScheme(shape=(4, 4), image_coords=np.array([[1.0, 1.0]]),
image_pixel_scale=1.0)
assert (interp.bottom_right_neighbors[0] == np.array([1, 4, 5])).all()
assert (interp.bottom_right_neighbors[1] == np.array([2, 5, 6])).all()
assert (interp.bottom_right_neighbors[2] == np.array([3, 6, 7])).all()
assert (interp.bottom_right_neighbors[3] == np.array([-1, 7, -1])).all()
assert (interp.bottom_right_neighbors[4] == np.array([5, 8, 9])).all()
assert (interp.bottom_right_neighbors[5] == np.array([6, 9, 10])).all()
assert (interp.bottom_right_neighbors[6] == np.array([7, 10, 11])).all()
assert (interp.bottom_right_neighbors[7] == np.array([-1, 11, -1])).all()
assert (interp.bottom_right_neighbors[8] == np.array([9, 12, 13])).all()
assert (interp.bottom_right_neighbors[9] == np.array([10, 13, 14])).all()
assert (interp.bottom_right_neighbors[10] == np.array([11, 14, 15])).all()
assert (interp.bottom_right_neighbors[11] == np.array([-1, 15, -1])).all()
assert (interp.bottom_right_neighbors[12] == np.array([13, -1, -1])).all()
assert (interp.bottom_right_neighbors[13] == np.array([14, -1, -1])).all()
assert (interp.bottom_right_neighbors[14] == np.array([15, -1, -1])).all()
assert (interp.bottom_right_neighbors[15] == np.array([-1, -1, -1])).all()
assert (interp.bottom_left_neighbors[0] == np.array([-1, -1, 4])).all()
assert (interp.bottom_left_neighbors[1] == np.array([0, 4, 5])).all()
assert (interp.bottom_left_neighbors[2] == np.array([1, 5, 6])).all()
assert (interp.bottom_left_neighbors[3] == np.array([2, 6, 7])).all()
assert (interp.bottom_left_neighbors[4] == np.array([-1, -1, 8])).all()
assert (interp.bottom_left_neighbors[5] == np.array([4, 8, 9])).all()
assert (interp.bottom_left_neighbors[6] == np.array([5, 9, 10])).all()
assert (interp.bottom_left_neighbors[7] == np.array([6, 10, 11])).all()
assert (interp.bottom_left_neighbors[8] == np.array([-1, -1, 12])).all()
assert (interp.bottom_left_neighbors[9] == np.array([8, 12, 13])).all()
assert (interp.bottom_left_neighbors[10] == np.array([9, 13, 14])).all()
assert (interp.bottom_left_neighbors[11] == np.array([10, 14, 15])).all()
assert (interp.bottom_left_neighbors[12] == np.array([-1, -1, -1])).all()
assert (interp.bottom_left_neighbors[13] == np.array([12, -1, -1])).all()
assert (interp.bottom_left_neighbors[14] == np.array([13, -1, -1])).all()
assert (interp.bottom_left_neighbors[15] == np.array([14, -1, -1])).all()
assert (interp.top_right_neighbors[0] == np.array([-1, -1, 1])).all()
assert (interp.top_right_neighbors[1] == np.array([-1, -1, 2])).all()
assert (interp.top_right_neighbors[2] == np.array([-1, -1, 3])).all()
assert (interp.top_right_neighbors[3] == np.array([-1, -1, -1])).all()
assert (interp.top_right_neighbors[4] == np.array([0, 1, 5])).all()
assert (interp.top_right_neighbors[5] == np.array([1, 2, 6])).all()
assert (interp.top_right_neighbors[6] == np.array([2, 3, 7])).all()
assert (interp.top_right_neighbors[7] == np.array([3, -1, -1])).all()
assert (interp.top_right_neighbors[8] == np.array([4, 5, 9])).all()
assert (interp.top_right_neighbors[9] == np.array([5, 6, 10])).all()
assert (interp.top_right_neighbors[10] == np.array([6, 7, 11])).all()
assert (interp.top_right_neighbors[11] == np.array([7, -1, -1])).all()
assert (interp.top_right_neighbors[12] == np.array([8, 9, 13])).all()
assert (interp.top_right_neighbors[13] == np.array([9, 10, 14])).all()
assert (interp.top_right_neighbors[14] == np.array([10, 11, 15])).all()
assert (interp.top_right_neighbors[15] == np.array([11, -1, -1])).all()
assert (interp.top_left_neighbors[0] == np.array([-1, -1, -1])).all()
assert (interp.top_left_neighbors[1] == np.array([-1, -1, 0])).all()
assert (interp.top_left_neighbors[2] == np.array([-1, -1, 1])).all()
assert (interp.top_left_neighbors[3] == np.array([-1, -1, 2])).all()
assert (interp.top_left_neighbors[4] == np.array([-1, 0, -1])).all()
assert (interp.top_left_neighbors[5] == np.array([0, 1, 4])).all()
assert (interp.top_left_neighbors[6] == np.array([1, 2, 5])).all()
assert (interp.top_left_neighbors[7] == | np.array([2, 3, 6]) | numpy.array |
#!/usr/bin/env python
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from astropy.coordinates import SkyCoord
from astropy import units as u
from astropy.io import fits
from astropy.nddata import Cutout2D
from astropy.wcs import WCS
from scipy.signal import fftconvolve
import argparse
# turn off runtime warnings (lots from logic on nans)
import warnings
warnings.filterwarnings("ignore", category=RuntimeWarning)
def size_limit(x,y,image):
yy,xx = image.shape
ind = ((y > 0) & (y < yy-1) & (x > 0) & (x < xx-1))
return ind
def region_cut(table,wcs):
ra = table.ra.values
dec = table.dec.values
foot = wcs.calc_footprint()
minra = min(foot[:,0])
maxra = max(foot[:,0])
mindec = min(foot[:,1])
maxdec = max(foot[:,1])
inddec = (dec < maxdec) & (dec> mindec)
indra = (ra < maxra) & (ra> minra)
ind = indra * inddec
tab = table.iloc[ind]
return tab
def circle_app(rad):
"""
makes a kinda circular aperture, probably not worth using.
"""
mask = np.zeros((int(rad*2+.5)+1,int(rad*2+.5)+1))
c = rad
x,y =np.where(mask==0)
dist = np.sqrt((x-c)**2 + (y-c)**2)
ind = (dist) < rad + .2
mask[y[ind],x[ind]]= 1
return mask
def check_table_format(table):
try:
temp = table.x
temp = table.y
temp = table.ra
temp = table.dec
temp = table.radius
temp = table.mag
temp = table.mjd_start
temp = table.mjd_end
except:
message = ("mask_table must be a csv with the following columns:\nx\ny\nra\ndec\nradius\nmag\nmjd_start\nmjd_end\n"
+ "Only a position (x,y) or (ra,dec) and size (radius) or (mag) is needed to run.")
raise ValueError()
#!/usr/bin/env python
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from astropy.coordinates import SkyCoord
from astropy import units as u
from astropy.io import fits
from astropy.nddata import Cutout2D
from astropy.wcs import WCS
from scipy.signal import fftconvolve
import argparse
# turn off runtime warnings (lots from logic on nans)
import warnings
warnings.filterwarnings("ignore", category=RuntimeWarning)
def size_limit(x,y,image):
yy,xx = image.shape
ind = ((y > 0) & (y < yy-1) & (x > 0) & (x < xx-1))
return ind
def region_cut(table,wcs):
ra = table.ra
dec = table.dec
foot = wcs.calc_footprint()
minra = min(foot[:,0])
maxra = max(foot[:,0])
mindec = min(foot[:,1])
maxdec = max(foot[:,1])
inddec = (dec < maxdec) & (dec> mindec)
indra = (ra < maxra) & (ra> minra)
ind = indra * inddec
tab = table.iloc[ind]
return tab
def circle_app(rad):
"""
makes a kinda circular aperture, probably not worth using.
"""
mask = np.zeros((int(rad*2+.5)+1,int(rad*2+.5)+1))
c = rad
x,y =np.where(mask==0)
dist = np.sqrt((x-c)**2 + (y-c)**2)
ind = (dist) < rad + .2
mask[y[ind],x[ind]]= 1
return mask
def check_table_format(table):
try:
temp = table.x
temp = table.y
temp = table.ra
temp = table.dec
temp = table.radius
temp = table.mag
temp = table.mjd_start
temp = table.mjd_end
except:
message = ("mask_table must be a csv with the following columns:\nx\ny\nra\ndec\nradius\nmag\nmjd_start\nmjd_end\n"
+ "Only a position (x,y) or (ra,dec) and size (radius) or (mag) is needed to run.")
raise ValueError()
def Spot_mask(fits_file,mask_table,ext=0):
table = pd.read_csv(mask_table)
check_table_format(table)
hdu = fits.open(fits_file)[ext]
# uses the file name to set the time, not versitile
t = float(fits_file.split('/')[-1].split('_')[1])
image = hdu.data
wcs = WCS(hdu.header)
spotmask = | np.zeros_like(image,dtype=float) | numpy.zeros_like |
#!/usr/bin/env python
# coding=utf-8
"""
Data preprocessing functions
| Option | Description |
| ------ | ----------- |
| title | prep.py |
| authors | <NAME>, <NAME>, <NAME> |
| date | 2020-03-18 |
"""
import numpy as np
import copy
import matplotlib.pyplot as plt
import mne
from autoreject import get_rejection_threshold, AutoReject
from mne.preprocessing import ICA, corrmap
def filt(raw_S: list) -> list:
"""
Filters list of raw data to remove slow drifts.
Arguments:
raw_S: list of Raw data (as an example: different occurences of
a condition for a participant). Raws are MNE objects.
Returns:
raws: list of high-pass filtered raws.
"""
# TODO: l_freq and h_freq as param
raws = []
for raw in raw_S:
raws.append(mne.io.Raw.filter(raw, l_freq=2., h_freq=None))
return raws
def ICA_choice_comp(icas: list, epochs: list) -> list:
"""
Plots Independent Components for each participant (calculated from Epochs),
let the user choose the relevant components for artifact rejection
and apply ICA on Epochs.
Arguments:
icas: list of Independent Components for each participant (IC are MNE
objects).
epochs: list of 2 Epochs objects (for each participant). Epochs_S1
and Epochs_S2 correspond to a condition and can result from the
concatenation of Epochs from different experimental realisations
of the condition.
Epochs are MNE objects: data are stored in an array of shape
(n_epochs, n_channels, n_times) and parameters information is
stored in a disctionnary.
Returns:
cleaned_epochs_ICA: list of 2 cleaned Epochs for each participant
(the chosen IC have been removed from the signal).
"""
# plotting Independant Components for each participant
for ica in icas:
ica.plot_components()
# choosing participant and its component as a template for the other participant
# if do not want to apply ICA on the data, do not fill the answer
subj_numb = input("Which participant ICA do you want"
" to use as a template for artifact rejection?"
" Index begins at zero. (If you do not want to apply"
" ICA on your data, do not enter nothing and press enter.)")
comp_number = input("Which IC do you want to use as a template?"
" Index begins at zero. (If you did not choose"
"a participant number at first question,"
"then do not enter nothing and press enter again"
"to not apply ICA on your data)")
# applying ICA
if (len(subj_numb) != 0 and len(comp_number) != 0):
cleaned_epochs_ICA = ICA_apply(icas,
int(subj_numb),
int(comp_number),
epochs)
else:
cleaned_epochs_ICA = epochs
return cleaned_epochs_ICA
def ICA_apply(icas: int, subj_number: int, comp_number: int, epochs: list) -> list:
"""
Applies ICA with template model from 1 participant in the dyad.
See ICA_choice_comp for a detailed description of the parameters and output.
"""
cleaned_epochs_ICA = []
# selecting which ICs corresponding to the template
template_eog_component = icas[subj_number].get_components()[:, comp_number]
# applying corrmap with at least 1 component detected for each subj
fig_template, fig_detected = corrmap(icas,
template=template_eog_component,
threshold=0.9,
label='blink',
ch_type='eeg')
# labeling the ICs that capture blink artifacts
print([ica.labels_ for ica in icas])
# selecting ICA components after viz
for i in icas:
i.exclude = i.labels_['blink']
epoch_all_ch = []
# applying ica on clean_epochs
# for each participant
for i, j in zip(range(0, len(epochs)), icas):
# taking all channels to apply ICA
bads = epochs[i].info['bads']
epoch_all_ch.append(mne.Epochs.copy(epochs[i]))
epoch_all_ch[i].info['bads'] = []
j.apply(epoch_all_ch[i])
epoch_all_ch[i].info['bads'] = bads
cleaned_epochs_ICA.append(epoch_all_ch[i])
return cleaned_epochs_ICA
def ICA_fit(epochs: list, n_components: int, method: str, fit_params: dict, random_state: int) -> list:
"""
Computes global Autorejection to fit Independent Components Analysis
on Epochs, for each participant.
Pre requisite : install autoreject
https://api.github.com/repos/autoreject/autoreject/zipball/master
Arguments:
epochs: list of 2 Epochs objects (for each participant).
Epochs_S1 and Epochs_S2 correspond to a condition and can result
from the concatenation of Epochs from different experimental
realisations of the condition (Epochs are MNE objects).
n_components: the number of principal components that are passed to the
ICA algorithm during fitting, int. For a first estimation,
n_components can be set to 15.
method: the ICA method used, str 'fastica', 'infomax' or 'picard'.
'Fastica' is the most frequently used. Use the fit_params argument to set
additional parameters. Specifically, if you want Extended Infomax, set
method=’infomax’ and fit_params=dict(extended=True) (this also works
for method=’picard’).
fit_params: Additional parameters passed to the ICA estimator
as specified by method. None by default.
random_state: the parameter used to compute random distributions
for ICA calulation, int or None. It can be useful to fix
random_state value to have reproducible results. For 15
components, random_state can be set to 97, for 20 components to 0
for example.
Note:
If Autoreject and ICA take too much time, change the decim value
(see MNE documentation).
Please filter the Epochs between 2 and 30 Hz before ICA fit
(mne.Epochs.filter(epoch, 2, 30, method='fir')).
Returns:
icas: list of Independant Components for each participant (IC are MNE
objects, see MNE documentation for more details).
"""
icas = []
for epoch in epochs:
# per subj
# applying AR to find global rejection threshold
reject = get_rejection_threshold(epoch, ch_types='eeg')
# if very long, can change decim value
print('The rejection dictionary is %s' % reject)
# fitting ICA on filt_raw after AR
ica = ICA(n_components=n_components,
method=method,
fit_params= fit_params,
random_state=random_state).fit(epoch)
# take bad channels into account in ICA fit
epoch_all_ch = mne.Epochs.copy(epoch)
epoch_all_ch.info['bads'] = []
icas.append(ica.fit(epoch_all_ch, reject=reject, tstep=1))
return icas
def AR_local(cleaned_epochs_ICA: list, strategy:str = 'union', threshold:float = 50.0, verbose: bool = False) -> list:
"""
Applies local Autoreject to repair or reject bad epochs.
Arguments:
clean_epochs_ICA: list of Epochs after global Autoreject and ICA.
strategy: more or less generous strategy to reject bad epochs: 'union'
or 'intersection'. 'union' rejects bad epochs from subject 1 and
subject 2 immediatly, whereas 'intersection' rejects shared bad epochs
between subjects, tries to repare remaining bad epochs per subject,
reject the non-reparable per subject and finally equalize epochs number
between subjects. Set to 'union' by default.
threshold: percentage of epochs removed that is accepted. Above
this threshold, data are considered as a too shortened sample
for further analyses. Set to 50.0 by default.
verbose: option to plot data before and after AR, boolean, set to
False by default. # use verbose = false until next Autoreject update
Note:
To reject or repair epochs, parameters are more or less conservative,
see http://autoreject.github.io/generated/autoreject.AutoReject.
Returns:
cleaned_epochs_AR: list of Epochs after local Autoreject.
dic_AR: dictionnary with the percentage of epochs rejection
for each subject and for the intersection of the them.
"""
bad_epochs_AR = []
AR = []
dic_AR = {}
dic_AR['strategy'] = strategy
dic_AR['threshold'] = threshold
# defaults values for n_interpolates and consensus_percs
n_interpolates = np.array([1, 4, 32])
consensus_percs = | np.linspace(0, 1.0, 11) | numpy.linspace |
# -*- coding: utf-8 -*-
"""
APARTADO 3
"""
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import animation
from mpl_toolkits.mplot3d import axes3d
#Dominio
u = np.linspace(0, np.pi, 25)
v = np.linspace(0, 2 * np.pi, 50)
#Esfera
x = np.outer(np.sin(u), np.sin(v))
y = np.outer(np.sin(u), np.cos(v))
z = np.outer(np.cos(u), np.ones_like(v))
#Curva
t2 = np.linspace(0.001, 1, 200)
x2 = abs(t2) * np.sin(30 * t2/2)
y2 = abs(t2) * np.cos(30 * t2/2)
z2 = np.sqrt(1-x2**2-y2**2)
c2 = x2 + y2
def animate2(t):
eps = 1e-16
#Esfera
xt = 1/((1-t) + np.abs(np.tan(-1) - np.tan(z))*t + eps)*x
yt = 1/((1-t) + np.abs(np.tan(-1) - np.tan(z))*t + eps)*y
zt = -t + z*(1-t)
#Curva
x2t = 1/((1-t) + np.abs(np.tan(-1) - np.tan(z2))*t + eps)*x2
y2t = 1/((1-t) + np.abs(np.tan(-1) - np.tan(z2))*t + eps)*y2
z2t = -t + z2*(1-t)
ax = plt.axes(projection='3d')
ax.set_xlim3d(-1,1)
ax.set_ylim3d(-1,1)
ax.set_zlim3d(-1,1)
ax.plot_surface(xt, yt, zt, rstride=1, cstride=1, cmap='viridis', edgecolor='none')
ax.plot(x2t,y2t, z2t, '-b', c="black", zorder=3)
return ax,
def init2():
return animate2(0),
animate2(0)
plt.show()
fig = plt.figure(figsize=(6,6))
ani = animation.FuncAnimation(fig, animate2, np.arange(0,1,0.05), init_func=init2,
interval=20)
ani.save("mi2ejemplo.gif", fps = 5)
def animate(t):
eps = 1e-16
#Esfera
xt = 1/(np.tan(np.pi/4 - t) + np.abs(-1-z)*np.tan(t) + eps)*x
yt = 1/(np.tan(np.pi/4 - t) + np.abs(-1-z)*np.tan(t) + eps)*y
zt = np.tan(-t) + z*np.tan(np.pi/4 - t)
#Curva
x2t = 1/(np.tan(np.pi/4 - t) + np.abs(-1-z2)*np.tan(t) + eps)*x2
y2t = 1/(np.tan(np.pi/4 - t) + np.abs(-1-z2)* | np.tan(t) | numpy.tan |
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# 3rd party imports
import numpy as np
# Local imports
from .find_closest import find_closest
__author__ = "<NAME>"
__email__ = "<EMAIL>"
__copyright__ = "Copyright 2020-2021"
__license__ = "MIT"
__version__ = "2.3.7"
__status__ = "Prototype"
def corr_deriv(inp0, inp1, flag: bool = False):
r"""Correlate the derivatives of two time series
Parameters
----------
inp0 : xarray.DataArray
Time series of the first to variable to correlate with.
inp1 : xarray.DataArray
Time series of the second to variable to correlate with.
flag : bool, Optional
Flag if False (default) returns time instants of common highest first
and second derivatives. If True returns time instants of common
highest first derivative and zeros crossings.
Returns
-------
t1_d, t2_d : ndarray
Time instants of common highest first derivatives.
t1_dd, t2_dd : ndarray
Time instants of common highest second derivatives or zero crossings.
"""
# 1st derivative
tx1 = inp0.time.data.astype(int) * 1e-9
inp0 = inp0.data
dtx1 = tx1[:-1] + 0.5 * np.diff(tx1)
dx1 = np.diff(inp0)
tx2 = inp1.time.data.astype(int) * 1e-9
inp1 = inp1.data
dtx2 = tx2[:-1] + 0.5 * np.diff(tx2)
dx2 = np.diff(inp1)
ind_zeros1 = np.where(np.sign(dx1[:-1] * dx1[1:]) < 0)[0]
if ind_zeros1 == 0:
ind_zeros1 = ind_zeros1[1:]
ind_zeros2 = np.where(np.sign(dx2[:-1] * dx2[1:]) < 0)[0]
if ind_zeros2 == 0:
ind_zeros2 = ind_zeros2[1:]
ind_zeros1_p = np.where(dx1[ind_zeros1 - 1] - dx1[ind_zeros1] > 0)[0]
ind_zeros2_p = np.where(dx2[ind_zeros2 - 1] - dx2[ind_zeros2] > 0)[0]
ind_zeros1_m = np.where(dx1[ind_zeros1 - 1] - dx1[ind_zeros1] < 0)[0]
ind_zeros2_m = np.where(dx2[ind_zeros2 - 1] - dx2[ind_zeros2] < 0)[0]
ind1_p = ind_zeros1[ind_zeros1_p]
ind1_m = ind_zeros1[ind_zeros1_m]
t_zeros1_p = dtx1[ind1_p] + (dtx1[ind1_p + 1] - dtx1[ind1_p]) / (
1 + np.abs(dx1[ind1_p + 1]) / np.abs(dx1[ind1_p]))
t_zeros1_m = dtx1[ind1_m] + (dtx1[ind1_m + 1] - dtx1[ind1_m]) / (
1 + np.abs(dx1[ind1_m + 1]) / np.abs(dx1[ind1_m]))
ind2_p = ind_zeros2[ind_zeros2_p]
ind2_m = ind_zeros2[ind_zeros2_m]
t_zeros2_p = dtx2[ind2_p] + (dtx2[ind2_p + 1] - dtx2[ind2_p]) / (
1 + np.abs(dx2[ind2_p + 1]) / np.abs(dx2[ind2_p]))
t_zeros2_m = dtx2[ind2_m] + (dtx2[ind2_m + 1] - dtx2[ind2_m]) / (
1 + np.abs(dx2[ind2_m + 1]) / np.abs(dx2[ind2_m]))
# Remove repeating points
t_zeros1_p = np.delete(t_zeros1_p, np.where(np.diff(t_zeros1_p) == 0)[0])
t_zeros2_p = np.delete(t_zeros2_p, np.where(np.diff(t_zeros2_p) == 0)[0])
# Define identical pairs of two time axis
t1_d_p, t2_d_p, _, _ = find_closest(t_zeros1_p, t_zeros2_p)
t1_d_m, t2_d_m, _, _ = find_closest(t_zeros1_m, t_zeros2_m)
t1_d = np.vstack([t1_d_p, t1_d_m])
t1_d = t1_d[t1_d[:, 0].argsort(), 0]
t2_d = np.vstack([t2_d_p, t2_d_m])
t2_d = t2_d[t2_d[:, 0].argsort(), 0]
if flag:
# zero crossings
ind_zeros1 = np.where(np.sign(inp0[:-1] * inp0[1:]) < 0)[0]
ind_zeros2 = np.where(np.sign(inp1[:-1] * inp1[1:]) < 0)[0]
ind_zeros1 = np.delete(ind_zeros1, np.where(ind_zeros1 == 1)[0])
ind_zeros2 = np.delete(ind_zeros2, np.where(ind_zeros2 == 1)[0])
ind_zeros1_p = | np.where(inp0[ind_zeros1 - 1] - inp0[ind_zeros1] > 0) | numpy.where |
import numpy as np
import matplotlib
matplotlib.rcParams.update({'font.size': 15})
import matplotlib.pyplot as plt
import pandas as pd
from scipy.optimize import leastsq
'''
# Treat ori_pref as constant.
# Double Gaussian function.
def double_gaussian(x, ori_pref, params):
(A1, A2, B, sigma) = params
ori_pref2 = (ori_pref + 180.0) % 360.0
# For a simple Gaussian, we may run into boundary effects, where x close to 360 degrees may not have the corresponding y values
# that represent properly the effect from a peak close to 0 degrees. It would be better to use a wrapped normal distribution here
# (a Gaussian on a circle), but it is an infinite series; we approximate it by just three terms, with shifts at 0 degrees,
# 360 degrees, and -360 degrees. In cases with relatively small sigma, this approximation should hold well. However, for large sigma
# it may not be quite as reasonable.
# NOTE THAT B+A1 AND B+A2 DO NOT CORRESPOND EXACTLY TO THE HEIGHTS OF THE PEAKS WITH THIS CHOICE OF THE FUNCTION.
# For small sigma, the peaks should be very close to B+A1 and B+A2, but for large sigma they will deviate from those values significantly.
r1 = A1 * np.exp( - (x - ori_pref)**2.0 / (2.0 * sigma**2.0) ) + A2 * np.exp( - (x - ori_pref2)**2.0 / (2.0 * sigma**2.0) )
r2 = A1 * np.exp( - (x - ori_pref + 360.0)**2.0 / (2.0 * sigma**2.0) ) + A2 * np.exp( - (x - ori_pref2 + 360.0)**2.0 / (2.0 * sigma**2.0) )
r3 = A1 * np.exp( - (x - ori_pref - 360.0)**2.0 / (2.0 * sigma**2.0) ) + A2 * np.exp( - (x - ori_pref2 - 360.0)**2.0 / (2.0 * sigma**2.0) )
return B + r1 + r2 + r3
def double_gaussian_fit( params, x, ori_pref, y_av ):
fit = double_gaussian( x, ori_pref, params )
return (y_av - fit)
'''
# Treat ori_pref as one of the parameters.
# Double Gaussian function.
def double_gaussian(x, params):
(ori_pref, A1, A2, B, sigma) = params
ori_pref2 = (ori_pref + 180.0) % 360.0
# For a simple Gaussian, we may run into boundary effects, where x close to 360 degrees may not have the corresponding y values
# that represent properly the effect from a peak close to 0 degrees. It would be better to use a wrapped normal distribution here
# (a Gaussian on a circle), but it is an infinite series; we approximate it by just three terms, with shifts at 0 degrees,
# 360 degrees, and -360 degrees. In cases with relatively small sigma, this approximation should hold well. However, for large sigma
# it may not be quite as reasonable.
# NOTE THAT B+A1 AND B+A2 DO NOT CORRESPOND EXACTLY TO THE HEIGHTS OF THE PEAKS WITH THIS CHOICE OF THE FUNCTION.
# For small sigma, the peaks should be very close to B+A1 and B+A2, but for large sigma they will deviate from those values significantly.
r1 = A1 * np.exp( - (x - ori_pref)**2.0 / (2.0 * sigma**2.0) ) + A2 * np.exp( - (x - ori_pref2)**2.0 / (2.0 * sigma**2.0) )
r2 = A1 * np.exp( - (x - ori_pref + 360.0)**2.0 / (2.0 * sigma**2.0) ) + A2 * | np.exp( - (x - ori_pref2 + 360.0)**2.0 / (2.0 * sigma**2.0) ) | numpy.exp |
#!/usr/bin/env python3
"""
Phonon
Only harmonic Phonon subroutines implemented
All numerically heavy computations are in f90 (f_phonon.f90)
"""
#import os
#from itertools import islice, product
from ..util.tool import my_flatten
#from ..util.string_utils import fn_available
from ..symm_kpts import HighSymmKpath
from ..interface_vasp import Poscar
#from ..structure import SupercellStructure
import numpy as np
from math import sqrt, pi
try:
# import matplotlib
# matplotlib.use('AGG')
import matplotlib.pyplot as plt
from matplotlib.backends.backend_pdf import PdfPages
except ImportError:
print("WARNING: cannot import pyplot; plotting disabled")
plt = None
pass
from f_phonon import f_phonon
#import logging
#logger = logging.getLogger(__name__)
#debug_level = 10
class NA_correction():
"""
long range non-analytic dipole-dipole correction for force-constants based phonon calculation
"""
def __init__(self, method, rho, Ncell=-1.0):
"""
method: -1 (disabled), 1 (Parlinski) or 2 (mixed-space) or 0 (dipole, FC MUST exclude dipole force)
rho: mixing parameter in Parlinski
Ncell: number of cells in the mixed-space approach
"""
self.id= method
self.rho = rho
self.Ncell = float(Ncell)
self.uniq_ijk_idx = []
@classmethod
def from_dict(cls, d):
rho = d.getfloat('NAC_rho', 0.05)
Ncell = d.getfloat('NAC_Ncell', -1.0)
return cls(d.getint('nac',-1), rho, Ncell)
class Phonon():
"""
All phonon related stuff
Note: all q-points (and hence real space coordinates) should be Cartesian unless explicitly specified
"""
def __init__(self, prim, LD, sol, pdfout, NAC=None, etafac=8.0):
"""
:param prim:
:param LD:
:param sol: solution vector
:param NAC: long range dipole-dipole non-analytic correction
:return:
"""
self.units = {'THz': (1, 'Freq. (THz)'), 'meV': (4.1356668, 'En (meV)'), 'eV': (0.0041356668, 'En (eV)'),
'cm': (33.3564227583, ' Freq. (cm^{-1})')}
self.prim = prim
self.LD = LD
#self.dim = prim.num_sites*3
if prim.intensive_properties['epsilon_inf'] is None:
NAC=None
if NAC is not None:
if (NAC.id != 0) and LD.dipole_force:
raise ValueError('Must set nac=0 when dipole forces are considered explicitly')
self.NAC = NAC
self.pdfout = pdfout
# process pair interactions
self.pairinfo = LD.get_pair_info(LD.get_full_fct(sol))
self.setup_cell(self.prim)
def setup_cell(self, cell):
from ..util.mathtool import Union
self.cell=cell
self.dim=self.cell.num_sites*3
#print("debug tralslate pair to supercell, size=", cell.num_sites)
pairinfo = self.pairinfo if cell is self.prim else self.LD.translate_pairinfo_to_supercell(cell, *self.pairinfo)
f_phonon.init(cell.lattice._matrix, cell.atomic_masses, cell.frac_coords, *pairinfo)
if (self.NAC is not None) and (self.NAC.id in [0, 1, 2]):
self.NAC.uniq_ijk_idx = Union(self.pairinfo[0], True)
if self.NAC.Ncell < 0:
self.NAC.Ncell = float(len(self.NAC.uniq_ijk_idx))
else:
if abs(self.NAC.Ncell - len(self.NAC.uniq_ijk_idx)) > 1E-6:
print("WARNING: input Ncell not equal to the given number of ijk", len(self.NAC.uniq_ijk_idx))
f_phonon.init_nac(self.NAC.id, cell.intensive_properties['epsilon_inf'],
cell.site_properties['born_charge'], self.NAC.rho,
cell.lattice.volume, self.NAC.uniq_ijk_idx, 1.0)
if (self.NAC.id==0) and (self.LD._dpcor is not None):
print(" Loading dipole correction FCM for phonon")
dpcor= self.LD._dpcor if cell is self.prim else self.LD.translate_pairinfo_to_supercell(cell, *self.LD._dpcor)
f_phonon.init_dpcor(*dpcor)
# short hand to get cartesian wave vector
def to_c(self, kpts, cart):
return np.array(kpts) if cart else self.prim.reciprocal_lattice.get_cartesian_coords(kpts)
def get_dm(self, k_in, cart=True):
"""
:param k_in: list of cartesian K-points
:return:
"""
# call fortran program
return f_phonon.get_dm(self.to_c(k_in, cart), self.dim)
def get_dmnomass(self, k_in, cart=True):
"""
Get the fourier transformed force constant matrix, without sqrt(M1,M2)
"""
mass= np.sqrt(self.cell.atomic_masses).repeat(3)
return self.get_dm(k_in, cart)* (np.outer(mass, mass)[:,:,None])
@staticmethod
def _maketicks(dist, lbl, plt):
"""
private utility method to add ticks to a band structure
"""
def _get_greek(ls):
return ["$" + l + "$" if l.startswith("\\") or l.find("_") != -1 else l for l in ls]
uniq_d = []
uniq_l = []
temp_ticks = list(map(list,zip(dist, _get_greek(lbl))))
for i in range(len(temp_ticks)):
# if (i < len(temp_ticks)-1) and (temp_ticks[i][1] != temp_ticks[i+1][1]) and abs(temp_ticks[i][0]-temp_ticks[i+1][0])<1E-7:
if (i < len(temp_ticks)-1) and abs(temp_ticks[i][0]-temp_ticks[i+1][0])<1E-7:
temp_ticks[i][1] +="|" + temp_ticks[i+1][1] if (temp_ticks[i][1] != temp_ticks[i+1][1]) else ''
temp_ticks[i+1][1] = ""
if i == 0:
uniq_d.append(temp_ticks[i][0])
uniq_l.append(temp_ticks[i][1])
# logger.debug("Adding label {l} at {d}".format(
# l=temp_ticks[i][0], d=temp_ticks[i][1]))
else:
if temp_ticks[i][1] == temp_ticks[i - 1][1]:
# logger.debug("Skipping label {i}".format(
# i=temp_ticks[i][1]))
continue
else:
# logger.debug("Adding label {l} at {d}".format(
# l=temp_ticks[i][0], d=temp_ticks[i][1]))
uniq_d.append(temp_ticks[i][0])
uniq_l.append(temp_ticks[i][1])
# logger.debug("Unique labels are %s" % list(zip(uniq_d, uniq_l)))
plt.gca().set_xticks(uniq_d)
plt.gca().set_xticklabels(uniq_l)
for i in range(len(lbl)):
if lbl[i] is not None and lbl[i]:
# don't print the same label twice
if i != 0:
if lbl[i] == lbl[i - 1]:
# logger.debug("already print label... "
# "skipping label {i}".format(
# i=ticks['label'][i]))
continue
else:
# logger.debug("Adding a line at {d}"
# " for label {l}".format(
# d=ticks['distance'][i], l=ticks['label'][i]))
plt.axvline(dist[i], color='gray', linestyle='--')
else:
# logger.debug("Adding a line at {d} for label {l}".format(
# d=ticks['distance'][i], l=ticks['label'][i]))
plt.axvline(dist[i], color='gray', linestyle='--')
plt.axhline(0, color='black')
with open('wavevec_label.txt', 'w') as f:
f.write(''.join([x[1]+'\n' for x in temp_ticks]))
return plt
#@staticmethod
def str2kpt(self, s, cart):
"""
:param s: example "[[10, [0,0,0],'\\Gamma', [0.5,0.5,0.5], 'X', [0.5,0.5,0], 'K']]"
or simply "[[10, 'X', 'K']]"
or "Auto N_pt" for automatic K-path with N_pt points on each segment
or "Auto" for default density (20)
:param cart: boolean for cartesian coordinates
:return:
"""
from csld.util.mathtool import vec_linspace
s_list = s.split()
symkp= HighSymmKpath(self.prim)
if s_list[0] == 'Auto':
kpts, lbls = symkp.get_kpoints(20 if len(s_list)<2 else int(s_list[1]))
kpts = np.array(kpts)
return kpts, lbls
d = eval(s)
lbls= []
kpts= []
kpt_dat= symkp.kpath['kpoints']
lbl_only = isinstance(d[0][1], str)
npt= d[0][0]
for x in d:
if lbl_only:
print(" found only labels in kpts specs.")
lb_line = x[1:]
kp_line = [kpt_dat[k] for k in lb_line]
else:
lb_line = x[2::2]
kp_line = x[1::2]
for i in range(len(lb_line)-1):
lbls.extend([lb_line[i]] + (['']*(npt-2)) + [lb_line[i+1]])
kpts.extend(vec_linspace(kp_line, npt))
# lbls.append(x[2])
# for y in x[4::2]:
# lbls.extend(['']*(x[0]-2))
# lbls.append(y)
# kpts = np.vstack([vec_linspace(x[1::2], x[0]) for x in d])
kpts = np.array(kpts)
if not lbl_only:
kpts = self.to_c(kpts, cart)
return kpts, lbls
def replace_gamma(self, kpts, no_gamma):
if no_gamma and self.NAC is not None:
for i in range(len(kpts)):
if not np.any(kpts[i]):
if len(kpts)<2:
kpts[i]=np.full((3),1e-6)
elif i==0:
kpts[i]=kpts[i+1]*1e-3
elif i==len(kpts)-1:
kpts[i]=kpts[i-1]*1e-3
elif np.any(kpts[i+1]):
kpts[i]=kpts[i+1]*1e-3
else:
kpts[i]=kpts[i-1]*1e-3
def get_dispersion(self, k_in_s, unit='THz', cart=True, no_gamma=False):
"""
:param k_in_s: string "Auto" or K-points definition
:return:
"""
#rec = self.prim.lattice.reciprocal_lattice
kpts, labels = self.str2kpt(k_in_s, cart)
self.replace_gamma(kpts, no_gamma)
np.savetxt('wavevec_frac_cart.txt', np.hstack([self.prim.reciprocal_lattice.get_fractional_coords(kpts), kpts]))
xval = np.zeros(len(kpts))
for i in range(1, len(kpts)):
xval[i] = xval[i-1] + (0 if labels[i-1] and labels[i] else np.linalg.norm(kpts[i:i+1] - kpts[i-1:i]))
eigE = f_phonon.get_dispersion(kpts, 1, self.dim)* self.units[unit][0]
print(np.min(eigE),np.max(eigE))
np.savetxt('phonon-dispersion.out', np.hstack((np.array([xval]).T, eigE.T)), header=
'col1: wavevector distance; col 2 ...: band 1 ...: '+self.units[unit][1])
if False:
ref_eigE= np.loadtxt('ref-dispersion.txt')[:,1:].T
print(eigE.shape, ref_eigE.shape)
else:
ref_eigE= None
if plt is not None and self.pdfout:
plt.figure()
if ref_eigE is not None:
plt.plot(*my_flatten([[xval, eigE[i,:], 'b-'] for i in range(self.dim)]+
[[xval, ref_eigE[i,:], 'r-'] for i in range(self.dim)]))
else:
plt.plot(*my_flatten([[xval, eigE[i,:], 'b-'] for i in range(self.dim)]))
plt.xlabel("Wavevector")
plt.ylabel(self.units[unit][1])
#print(xval, labels)
Phonon._maketicks(xval, labels, plt)
plt.savefig(self.pdfout, format='pdf')
plt.close()
return eigE, kpts
def get_eig_e_vec(self, k_in,unit='THz', cart=True):
"""
:param k_in: list of K-points
:return:
"""
from scipy.io import mmwrite
eigE, eigV = f_phonon.get_eig_e_vec(self.to_c(k_in, cart), self.dim)
# dm = f_phonon.get_dm(self.to_c(k_in, cart), self.dim)
# np.savetxt("eigE.txt", eigE)
# for i in range(len(k_in)):
# mmwrite("eigV_%d.mtx"%(i), eigV[:,:,i])
# mmwrite("dm_%d.mtx"%(i), dm[:,:,i])
# np.savetxt("hessian.txt", self.get_FCM())
return (eigE, eigV)
def plot_dos(self, plt, x, y, title, unit):
if plt is not None:
plt.figure()
plt.plot(x, y, 'b-')
plt.xlabel(unit)
plt.ylabel("Phonon DOS")
plt.title(title)
plt.savefig(self.pdfout, format='pdf')
plt.close()
def get_dos(self, mesh, nEdos, ismear, temp, epsilon, unit='THz', pdos=False, no_gamma=False):
"""
:param mesh: [nx ny nz]
:param ngrid_en: number of energy points
:param ismear: -1 for tetrahedron, 0 for Lorentzian smearing, 1 for Gaussian smearing
:param epsilon: width of smearing
:param unit:
:return: numpy array [[t1, dos1], [t2, dos2], ...]
"""
kgrid = np.mgrid[0:1:1./mesh[0], 0:1:1./mesh[1], 0:1:1./mesh[2]].transpose((1,2,3,0)).reshape(-1,3)
self.replace_gamma(kgrid, no_gamma)
kred, wt = zip(*self.prim.syminfo.get_ir_reciprocal_mesh(mesh))
dos, pd = f_phonon.get_dos_new(pdos, mesh, self.to_c(kgrid, False), nEdos, ismear, epsilon, self.prim.num_sites)
en = dos[:,0]* self.units[unit][0]
self.plot_dos(plt, en, dos[:,1]/self.units[unit][0], "Total", self.units[unit][1])
# returned dos always in eV per primitive cell (3 N_atom modes)
dos[:,0] *= self.units['eV'][0]
dos[:,1] /= self.units['eV'][0]
np.savetxt('phonon-total-dos'+str(temp)+'.out', dos, header='col1: energy in eV; col 2: DOS')
if pdos:
for i in range(self.prim.num_sites):
self.plot_dos(plt, en, pd[i]/self.units[unit][0], "Partial for atom %d"%(i+1), self.units[unit][1])
pd /= self.units['eV'][0]
np.savetxt('phonon-partial-dos'+str(temp)+'.out', | np.hstack((dos[:,0:1], pd.T)) | numpy.hstack |
from __future__ import division, print_function, absolute_import
import sys
import os
import tensorflow as tf
import numpy as np
from tf_layers import linear_layer
import tf_dataset as tfd
from tf_model import getNetwork
from center_loss import *
import tf_log
import sklearn.metrics
from tf_validationInfo import RSquaredResults, CenterLossAEResults, ClassificationAutoencoderResults, \
ClassifierResults, AEResults
import timeit
def getOp(args):
t = args.graph_type
if t == 'DosageDrugRegression':
print("loading DosageDrugRegression")
return DosageDrugRegression
elif t == 'AUCRegression':
print("loading AUCRegression")
return AUCRegression
elif t == 'ClassificationAutoencoder':
return ClassificationAutoencoder
elif t == 'TumorClassifier':
return TumorClassifier
elif t == 'TumorAE':
return TumorAE
elif t == 'CenterLossAutoencoder':
return CenterLossAutoencoder
elif t == 'CenterLossAutoencoder40':
return CenterLossAutoencoder40
elif t == 'ClassificationAutoencoder40':
return ClassificationAutoencoder40
elif t == 'TumorClassifier40':
return TumorClassifier40
elif t == 'TumorAE40':
return TumorAE40
elif t == 'CenterLossAutoencoder20':
return CenterLossAutoencoder20
elif t == 'ClassificationAutoencoder20':
return ClassificationAutoencoder20
elif t == 'TumorClassifier20':
return TumorClassifier20
elif t == 'TumorAE20':
return TumorAE20
else:
print("unrecognized type", t)
class Network(object):
def __init__(self, args, dataset, checkpoint=None, pretrained=None):
self.args = args
self.dataset = dataset
self.checkpoint = checkpoint
self.pretrained = pretrained
self.makePlaceholders()
self.makeNetwork()
self.makeCostFunction()
self.makeOptimizer()
# Initializing the variables
self.init = tf.group(tf.global_variables_initializer(), tf.local_variables_initializer())
self.sess = tf.Session()
self.sess.run(self.init)
self.loadWeights()
def loadWeights(self):
print("checkpoint is", self.checkpoint)
#tensorflow saver.
if os.path.exists(self.checkpoint+".index"):
# check if resuming previous run
print("restoring from previous run")
self.saver = tf.train.Saver(tf.global_variables())
self.saver.restore(self.sess, self.checkpoint)
else:
# default create saver with all variables.
self.saver = tf.train.Saver(tf.global_variables())
class EncodeDecodeOriginal:
def encoder(self):
# for MNIST. expects self.X to have 28^2 flat input vector
self.dropout_test = tf.reduce_mean(tf.layers.dropout(self.X, rate=1-self.keep_prob))
fc1 = tf.layers.dense(self.X,
5000, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="fc1")
fc2 = tf.layers.dense(tf.layers.dropout(fc1, rate=1-self.keep_prob),
3000, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="fc2")
fc3 = tf.layers.dense(tf.layers.dropout(fc2, rate=1-self.keep_prob),
2000, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="fc3")
fc4 = tf.layers.dense(tf.layers.dropout(fc3, rate=1-self.keep_prob),
943, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="fc4")
return fc4
def decoder(self):
# for MNIST. expects self.X to have 28^2 flat input vector
de_fc1 = tf.layers.dense(tf.layers.dropout(self.encoded, rate=1-self.keep_prob),
2000, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="de_fc1")
de_fc2 = tf.layers.dense(tf.layers.dropout(de_fc1, rate=1-self.keep_prob),
3000, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="de_fc2")
de_fc3 = tf.layers.dense(tf.layers.dropout(de_fc2, rate=1-self.keep_prob),
5000, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="de_fc3")
de_fc4 = tf.layers.dense(de_fc3, self.dataset.numFeatures,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
activation=tf.nn.relu,
name="de_fc4")
return de_fc4
class EncodeDecode40:
def encoder(self):
# for MNIST. expects self.X to have 28^2 flat input vector
fc1 = tf.layers.dense(self.X,
5000, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="fc1")
fc2 = tf.layers.dense(tf.layers.dropout(fc1, rate=1-self.keep_prob),
1000, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="fc2")
fc3 = tf.layers.dense(tf.layers.dropout(fc2, rate=1-self.keep_prob),
200, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="fc3")
fc4 = tf.layers.dense(tf.layers.dropout(fc3, rate=1-self.keep_prob),
40, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="fc4")
return fc4
def decoder(self):
# for MNIST. expects self.X to have 28^2 flat input vector
de_fc1 = tf.layers.dense(tf.layers.dropout(self.encoded, rate=1-self.keep_prob),
200, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="de_fc1")
de_fc2 = tf.layers.dense(tf.layers.dropout(de_fc1, rate=1-self.keep_prob),
1000, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="de_fc2")
de_fc3 = tf.layers.dense(tf.layers.dropout(de_fc2, rate=1-self.keep_prob),
5000, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="de_fc3")
de_fc4 = tf.layers.dense(de_fc3, self.dataset.numFeatures,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
activation=tf.nn.relu,
name="de_fc4")
return de_fc4
class EncodeDecode20:
def encoder(self):
# for MNIST. expects self.X to have 28^2 flat input vector
fc1 = tf.layers.dense(self.X,
2500, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="fc1")
fc2 = tf.layers.dense(tf.layers.dropout(fc1, rate=1-self.keep_prob),
500, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="fc2")
fc3 = tf.layers.dense(tf.layers.dropout(fc2, rate=1-self.keep_prob),
100, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="fc3")
fc4 = tf.layers.dense(tf.layers.dropout(fc3, rate=1-self.keep_prob),
20, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="fc4")
return fc4
def decoder(self):
# for MNIST. expects self.X to have 28^2 flat input vector
de_fc1 = tf.layers.dense(tf.layers.dropout(self.encoded, rate=1-self.keep_prob),
100, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="de_fc1")
de_fc2 = tf.layers.dense(tf.layers.dropout(de_fc1, rate=1-self.keep_prob),
500, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="de_fc2")
de_fc3 = tf.layers.dense(tf.layers.dropout(de_fc2, rate=1-self.keep_prob),
2500, activation=tf.nn.selu,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
name="de_fc3")
de_fc4 = tf.layers.dense(de_fc3, self.dataset.numFeatures,
kernel_initializer=tf.variance_scaling_initializer(scale=1.0, mode='fan_in'),
activation=tf.nn.relu,
name="de_fc4")
return de_fc4
class ClassificationAutoencoder__(Network):
@staticmethod
def buildTrainDataset(args):
# check to see which chunk we left off on
trainData = tfd.ChunkGroup(pathFeatures=[args.trainx],
pathLabels=args.trainy, batch_size=args.batch_size,
preprocessing_fn=os.path.join(args.outputFolder, 'onehot_labelencoder.pkl'))
valData = ClassificationAutoencoder.buildValidationDataset(args)
return trainData, valData
@staticmethod
def buildValidationDataset(args):
valData = tfd.ChunkGroup(pathFeatures=[args.valid],
pathLabels=args.validy, batch_size=args.valid_size, shuffle=False,
preprocessing_fn=os.path.join(args.outputFolder, 'onehot_labelencoder.pkl'))
return valData
@staticmethod
def buildSplitDataset(args):
pairs = zip(args.valid, args.validy)
datasets = []
for x, y in pairs:
datasets.append(tfd.ChunkGroup(pathFeatures=[[x]],
pathLabels=[y], batch_size=args.valid_size, shuffle=False,
preprocessing_fn=os.path.join(args.outputFolder, 'onehot_labelencoder.pkl')))
return datasets
@staticmethod
def getPreferedLogger():
return tf_log.ClassificationAutoencoderLog
def makePlaceholders(self):
# Placeholders for inputs
self.X = tf.placeholder(tf.float32, [None, self.dataset.numFeatures],
name='ph_input_tensor')
self.y_true = tf.placeholder(tf.int32, [None, self.dataset.numClasses],
name='ph_y_true')
# drop out
self.keep_prob = tf.placeholder(tf.float32, name='ph_keep_prob')
# can be used for exponential decay learning rate
self.epoch = tf.placeholder(tf.int32, name='ph_epoch')
self.learning_rate = tf.placeholder(tf.float32, name='ph_learning_rate')
def makeNetwork(self):
self.encoded = self.encoder()
self.y_pred = self.decoder()
self.logits = tf.layers.dense(self.encoded, self.dataset.numClasses)
indicies = tf.argmax(tf.nn.softmax(self.logits), axis=1)
self.class_prediction = tf.one_hot(indicies, self.dataset.numClasses)
def makeCostFunction(self):
# Targets (Labels) are the input data.
# Define loss and optimizer, minimize the squared error
self.reconstructionError = tf.sqrt(tf.reduce_mean(tf.pow(self.X - self.y_pred, 2)))
self.cross_entropy_loss = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits_v2(
logits=self.logits, labels=self.y_true))
self.cost = (1-self.args.center_loss_alpha)*self.reconstructionError + \
self.args.center_loss_alpha*self.cross_entropy_loss
def makeOptimizer(self):
#decayedLearn = tf.train.exponential_decay(self.learning_rate, \
#self.epoch, 1, .9, staircase=True)
#tf.summary.scalar("decayedLearn", decayedLearn)
#opt = tf.train.GradientDescentOptimizer(self.learning_rate)
opt = tf.train.AdamOptimizer(self.learning_rate)
self.optimizer = opt.minimize(self.cost)
def partialFit(self, data, epoch):
X, y, loop = data
feed_dict={self.X : X, self.epoch : epoch, \
self.keep_prob : self.args.keep_prob, \
self.learning_rate : self.args.learning_rate, \
self.y_true : y}
start = timeit.default_timer()
cost, y_pred, class_pred, opt, = self.sess.run([self.cost, \
self.y_pred, self.class_prediction, self.optimizer \
], feed_dict)
return timeit.default_timer()-start, \
ClassificationAutoencoderResults(X=X, y=self.dataset.inverse_transform(y),
pred_X=y_pred, pred_y=self.dataset.inverse_transform(class_pred),
cost=cost)
def validate(self, data):
X, y, loop = data
feed_dict={self.X : X, \
self.learning_rate : 0, self.epoch : 0, \
self.y_true : y}
if self.args.keep_mask_loops == 1:
feed_dict[self.keep_prob] = 1
else:
feed_dict[self.keep_prob] = self.args.keep_prob
cost, y_recon, class_pred = \
self.sess.run([self.cost, \
self.y_pred, \
self.class_prediction], \
feed_dict)
return ClassificationAutoencoderResults(X=X, y=self.dataset.inverse_transform(y),
pred_X=y_recon, pred_y=self.dataset.inverse_transform(class_pred), cost=cost)
def encode(self, data):
X, y, loop = data
feed_dict={self.X : X, \
self.learning_rate : 0, self.epoch : 0, \
self.y_true : y}
# ask for the activiations from the tensor saved as self.encoded
[encoded] = self.sess.run([self.encoded] , feed_dict)
return encoded
class ClassificationAutoencoder(ClassificationAutoencoder__, EncodeDecodeOriginal):
pass
class ClassificationAutoencoder40(ClassificationAutoencoder__, EncodeDecode40):
pass
class ClassificationAutoencoder20(ClassificationAutoencoder__, EncodeDecode20):
pass
class CenterLossAutoencoder__(ClassificationAutoencoder__):
@staticmethod
def getPreferedLogger():
return tf_log.CenterLossAELog
def makeCostFunction(self):
# center loss stuff
# calculate binary labels for center_loss, must be in one_hot encoding
self.center_loss, centers, self.centers_update_op = \
calc_center_loss(self.encoded, self.y_true, self.args.center_loss_alpha)
self.reconstruction_error = tf.sqrt(tf.reduce_mean(tf.pow(self.X - self.y_pred, 2)))
self.cross_entropy_loss = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits_v2(
logits=self.logits, labels=self.y_true))
lambdas = np.array(self.args.center_loss_lambdas)
normed_lambdas = lambdas / | np.sum(lambdas) | numpy.sum |
#################################################################################
# Example: System Identification #
#################################################################################
# #
# In this example we have a typical system identification scenario. We want #
# to estimate the filter coefficients of an unknown system given by Wo. In #
# order to accomplish this task we use an adaptive filter with the same #
# number of coefficients, N, as the unkown system. The procedure is: #
# 1) Excitate both filters (the unknown and the adaptive) with the signal #
# x. In this case, x is chosen according to the 4-QAM constellation. #
# The variance of x is normalized to 1. #
# 2) Generate the desired signal, d = Wo' x + n, which is the output of the #
# unknown system considering some disturbance (noise) in the model. The #
# noise power is given by sigma_n2. #
# 3) Choose an adaptive filtering algorithm to govern the rules of coefficient #
# updating. #
# #
# Adaptive Algorithm used here: LMS #
# #
#################################################################################
# Imports
import numpy as np
import matplotlib.pyplot as plt
import pydaptivefiltering as pdf
def LMS_example():
"""
Types:
------
None -> '(Filter, dictionary["outputs", "errors", "coefficients"])'
Example for the LMS algorithm, SignData and SignError.
"""
# Parameters
K = 70 # Number of iterations
H = np.array([0.32+0.21*1j, -0.3+0.7*1j, 0.5-0.8*1j, 0.2+0.5*1j])
Wo = H # Uknown System
sigman2 = 0.04 # Noise Power
N = 4 # Number of coefficients of the adaptative filter
mu = 0.1 # Convergence factor (step) (0 < μ < 1)
# Initializing
W = np.ones(shape=(N, K+1))
# Input at a certain iteration (tapped delay line)
X = np.zeros(N)
x = (np.random.randn(K) + np.random.randn(K)*1j)/ | np.sqrt(2) | numpy.sqrt |
# -*- coding: utf-8 -*-
import unittest
import pandas as pd
import numpy as np
# from ThymeBoost.trend_models import (linear_trend, mean_trend, median_trend,
# loess_trend, ransac_trend, ewm_trend,
# ets_trend, arima_trend, moving_average_trend,
# zero_trend, svr_trend, naive_trend)
from ThymeBoost.trend_models import *
def testing_data():
seasonality = ((np.cos(np.arange(1, 101))*10 + 50))
np.random.seed(100)
true = | np.linspace(-1, 1, 100) | numpy.linspace |
#!/usr/bin/env python
import argparse
import os
import pprint
import warnings
import time
import pickle
import random
from collections import OrderedDict
from pathlib import Path
import shutil
import sys
sys.path.append("..")
from src.training_manager import TrainingManager, get_current_time
import download_weights
import generate
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from torch.utils.data import Dataset, DataLoader
from torch.nn.utils import clip_grad_norm_
from torch.nn.utils import spectral_norm
from torch.nn.parallel import DataParallel as DP
import wandb
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
torch.multiprocessing.set_sharing_strategy("file_system")
loss_funcs = OrderedDict(
[
("G", None),
("D", None),
("RealD", None),
("FakeD", None),
("Convergence", None),
("NoiseRecon", None),
("RealRecon", None),
]
)
class VocDataset(Dataset):
def __init__(self, ids, path):
self.metadata = ids
self.path = path
def __getitem__(self, index):
id = self.metadata[index]
# voc_fp = os.path.join(self.path, id, "vocals.npy")
voc_fp = os.path.join(self.path, f"{id}.npy")
voc = np.load(voc_fp)
return voc
def __len__(self):
return len(self.metadata)
def get_voc_datasets(path, feat_type, batch_size):
dataset_fp = os.path.join(path, f"dataset.pkl")
in_dir = os.path.join(path, feat_type)
with open(dataset_fp, "rb") as f:
dataset = pickle.load(f)
dataset_ids = [x[0] for x in dataset]
random.seed(1234)
random.shuffle(dataset_ids)
split_at = int(len(dataset_ids) * 0.9)
tr_ids = dataset_ids[:split_at]
va_ids = dataset_ids[split_at:]
tr_dataset = VocDataset(tr_ids, in_dir)
va_dataset = VocDataset(va_ids, in_dir)
num_tr = len(tr_dataset)
num_va = len(va_dataset)
if num_va < batch_size:
batch_va = num_va
else:
batch_va = batch_size
iterator_tr = DataLoader(
tr_dataset,
batch_size=batch_size,
num_workers=5,
shuffle=True,
drop_last=True,
pin_memory=True,
)
iterator_va = DataLoader(
va_dataset,
batch_size=batch_va,
num_workers=0,
shuffle=False,
drop_last=True,
pin_memory=True,
)
return iterator_tr, num_tr, iterator_va, num_va
def validate(epoch, step, iterator_va, num_va):
# Store random state
cpu_rng_state_tr = torch.get_rng_state()
if device.type == "cuda":
gpu_rng_state_tr = torch.cuda.get_rng_state()
# Set random stae
torch.manual_seed(123)
# ###
sum_losses_va = OrderedDict([(loss_name, 0) for loss_name in loss_funcs])
count_all_va = num_va
# In validation, set netG.eval()
netG.eval()
netD.eval()
netE.eval()
num_batches_va = len(iterator_va)
with torch.set_grad_enabled(False):
for i_batch, batch in enumerate(iterator_va):
# voc.shape=(bs, feat_dim, num_frames)
voc = batch
voc = voc.to(device)
voc = (voc - mean) / std
bs, _, nf = voc.size()
# ### Train generator ###
z = (
torch.zeros((bs, z_dim, int(np.ceil(nf / z_total_scale_factor))))
.normal_(0, 1)
.float()
.to(device)
)
fake_voc = netG(z)
z_fake = netE(fake_voc)
z_real = netE(voc)
gloss = torch.mean(torch.abs(netD(fake_voc) - fake_voc))
noise_rloss = torch.mean(torch.abs(z_fake - z))
real_rloss = torch.mean(torch.abs(netG(z_real)[..., :nf] - voc[..., :nf]))
# ### Train discriminator ###
real_dloss = torch.mean(torch.abs(netD(voc) - voc))
fake_dloss = torch.mean(
torch.abs(netD(fake_voc.detach()) - fake_voc.detach())
)
dloss = real_dloss - k * fake_dloss
# ### Convergence ###
_, convergence = recorder(real_dloss, fake_dloss, update_k=False)
# ### Losses ###
losses = OrderedDict(
[
("G", gloss),
("D", dloss),
("RealD", real_dloss),
("FakeD", fake_dloss),
("Convergence", convergence),
("NoiseRecon", noise_rloss),
("RealRecon", real_rloss),
]
)
# ### Misc ###
# count_all_va += bs
# Accumulate losses
losses_va = OrderedDict(
[(loss_name, lo.item()) for loss_name, lo in losses.items()]
)
for loss_name, lo in losses_va.items():
sum_losses_va[loss_name] += lo * bs
if i_batch % 10 == 0:
print("{}/{}".format(i_batch, num_batches_va))
wandb.log({"loss/eval": losses, "epoch": epoch}, step=step)
mean_losses_va = OrderedDict(
[(loss_name, slo / count_all_va) for loss_name, slo in sum_losses_va.items()]
)
# Restore rng state
torch.set_rng_state(cpu_rng_state_tr)
if device.type == "cuda":
torch.cuda.set_rng_state(gpu_rng_state_tr)
return mean_losses_va
def make_inf_iterator(data_iterator):
while True:
for data in data_iterator:
yield data
class BEGANRecorder(nn.Module):
def __init__(self, lambda_k, init_k, gamma):
super().__init__()
self.lambda_k = lambda_k
self.init_k = float(init_k)
self.gamma = gamma
self.k = nn.Parameter(torch.tensor(self.init_k))
def forward(self, real_dloss, fake_dloss, update_k=False):
# convergence
diff = self.gamma * real_dloss - fake_dloss
convergence = real_dloss + torch.abs(diff)
# Update k
if update_k:
self.k.data = torch.clamp(self.k + self.lambda_k * diff, 0, 1).data
return self.k.item(), convergence
class RCBlock(nn.Module):
def __init__(self, feat_dim, ks, dilation, num_groups):
super().__init__()
ksm1 = ks - 1
mfd = feat_dim
di = dilation
self.num_groups = num_groups
self.relu = nn.LeakyReLU()
self.rec = nn.GRU(mfd, mfd, num_layers=1, batch_first=True, bidirectional=True)
self.conv = nn.Conv1d(
mfd, mfd, ks, 1, ksm1 * di // 2, dilation=di, groups=num_groups
)
self.gn = nn.GroupNorm(num_groups, mfd)
def init_hidden(self, batch_size, hidden_size):
num_layers = 1
num_directions = 2
hidden = torch.zeros(num_layers * num_directions, batch_size, hidden_size)
hidden.normal_(0, 1)
return hidden
def forward(self, x):
bs, mfd, nf = x.size()
hidden = self.init_hidden(bs, mfd).to(x.device)
r = x.transpose(1, 2)
r, _ = self.rec(r, hidden)
r = r.transpose(1, 2).view(bs, 2, mfd, nf).sum(1)
c = self.relu(self.gn(self.conv(r)))
x = x + r + c
return x
class BodyGBlock(nn.Module):
def __init__(self, input_dim, output_dim, middle_dim, num_groups):
super().__init__()
ks = 3 # kernel size
mfd = middle_dim
self.input_dim = input_dim
self.output_dim = output_dim
self.mfd = mfd
self.num_groups = num_groups
# ### Main body ###
block = [
nn.Conv1d(input_dim, mfd, 3, 1, 1),
nn.GroupNorm(num_groups, mfd),
nn.LeakyReLU(),
RCBlock(mfd, ks, dilation=1, num_groups=num_groups),
nn.Conv1d(mfd, output_dim, 3, 1, 1),
]
self.block = nn.Sequential(*block)
def forward(self, x):
# ### Main ###
x = self.block(x)
return x
class NetG(nn.Module):
def __init__(self, feat_dim, z_dim, z_scale_factors):
super().__init__()
mfd = 512
num_groups = 4
self.num_groups = num_groups
self.mfd = mfd
self.feat_dim = feat_dim
self.z_dim = z_dim
self.z_scale_factors = z_scale_factors
# ### Main body ###
self.block0 = BodyGBlock(z_dim, mfd, mfd, num_groups)
self.head0 = nn.Conv1d(mfd, feat_dim, 3, 1, 1)
blocks = []
heads = []
for scale_factor in z_scale_factors:
block = BodyGBlock(mfd, mfd, mfd, num_groups)
blocks.append(block)
head = nn.Conv1d(mfd, feat_dim, 3, 1, 1)
heads.append(head)
self.blocks = nn.ModuleList(blocks)
self.heads = nn.ModuleList(heads)
def forward(self, z):
# SBlock0
z_scale_factors = self.z_scale_factors
x_body = self.block0(z)
x_head = self.head0(x_body)
for ii, (block, head, scale_factor) in enumerate(
zip(self.blocks, self.heads, z_scale_factors)
):
x_body = F.interpolate(x_body, scale_factor=scale_factor, mode="nearest")
x_head = F.interpolate(x_head, scale_factor=scale_factor, mode="nearest")
x_body = x_body + block(x_body)
x_head = x_head + head(x_body)
return x_head
class BNSNConv2dDBlock(nn.Module):
def __init__(
self, input_dim, output_dim, kernel_size, frequency_stride, time_dilation
):
super().__init__()
ks = kernel_size
ksm1d2 = (ks - 1) // 2
self.input_dim = input_dim
self.output_dim = output_dim
self.kernel_size = kernel_size
self.time_dilation = time_dilation
self.frequency_stride = frequency_stride
block = [
spectral_norm(
nn.Conv2d(
input_dim,
output_dim,
ks,
(frequency_stride, 1),
(1, time_dilation * ksm1d2),
dilation=(1, time_dilation),
)
),
nn.BatchNorm2d(output_dim),
nn.LeakyReLU(),
]
self.block = nn.Sequential(*block)
def forward(self, x):
x = self.block(x)
return x
class BNSNConv1dDBlock(nn.Module):
def __init__(self, input_dim, output_dim, kernel_size, dilation):
super().__init__()
ks = kernel_size
ksm1d2 = (ks - 1) // 2
self.input_dim = input_dim
self.output_dim = output_dim
self.kernel_size = kernel_size
self.dilation = dilation
block = [
spectral_norm(
nn.Conv1d(
input_dim, output_dim, ks, 1, dilation * ksm1d2, dilation=dilation
)
),
nn.BatchNorm1d(output_dim),
nn.LeakyReLU(),
]
self.block = nn.Sequential(*block)
def forward(self, x):
x = self.block(x)
return x
class StridedBNSNConv1dDBlock(nn.Module):
def __init__(self, input_dim, output_dim, kernel_size, stride):
super().__init__()
ks = kernel_size
ksm1d2 = (ks - 1) // 2
self.input_dim = input_dim
self.output_dim = output_dim
self.kernel_size = kernel_size
self.stride = stride
block = [
spectral_norm(nn.Conv1d(input_dim, output_dim, ks, stride, ksm1d2)),
nn.BatchNorm1d(output_dim),
nn.LeakyReLU(),
]
self.block = nn.Sequential(*block)
def forward(self, x):
x = self.block(x)
return x
class NetD(nn.Module):
def __init__(self, input_size):
super().__init__()
ks = 3 # kernel size
mfd = 512 * int(input_size / 80)
self.mfd = mfd
self.input_size = input_size
# ### Main body ###
blocks2d = [
BNSNConv2dDBlock(1, 4, ks, 2, 2),
BNSNConv2dDBlock(4, 16, ks, 2, 4),
BNSNConv2dDBlock(16, 64, ks, 2, 8),
]
blocks1d = [
BNSNConv1dDBlock(64 * 10 * int(input_size / 80), mfd, 3, 1),
BNSNConv1dDBlock(mfd, mfd, ks, 16),
BNSNConv1dDBlock(mfd, mfd, ks, 32),
BNSNConv1dDBlock(mfd, mfd, ks, 64),
BNSNConv1dDBlock(mfd, mfd, ks, 128),
]
self.body2d = nn.Sequential(*blocks2d)
self.body1d = nn.Sequential(*blocks1d)
self.head = spectral_norm(nn.Conv1d(mfd, input_size, 3, 1, 1))
def forward(self, x):
"""
x.shape=(batch_size, feat_dim, num_frames)
cond.shape=(batch_size, cond_dim, num_frames)
"""
bs, fd, nf = x.size()
# ### Process generated ###
# shape=(bs, 1, fd, nf)
x = x.unsqueeze(1)
# shape=(bs, 64, 10, nf_)
x = self.body2d(x)
# shape=(bs, 64*10, nf_)
x = x.view(bs, -1, x.size(3))
# ### Merging ###
x = self.body1d(x)
# ### Head ###
# shape=(bs, input_size, nf)
# out = torch.sigmoid(self.head(x))
out = self.head(x)
# Pad
# out = F.pad(out, pad=(0, nf-out.size(2)))
return out
class Encoder(nn.Module):
def __init__(self, input_size, z_dim, z_scale_factors):
super().__init__()
ks = 3 # kernel size
mfd = 512
self.mfd = mfd
self.input_size = input_size
self.z_dim = z_dim
self.z_scale_factors = z_scale_factors
# ### Main body ###
blocks2d = [
BNSNConv2dDBlock(1, 4, ks, 2, 2),
BNSNConv2dDBlock(4, 16, ks, 2, 4),
BNSNConv2dDBlock(16, 64, ks, 2, 8),
]
# (input_size / 80) to make channel scalable with feat_dim/input_size .
blocks1d = [BNSNConv1dDBlock(64 * 10 * int(input_size / 80), mfd, 3, 1)]
for sf in z_scale_factors:
blocks1d.append(StridedBNSNConv1dDBlock(mfd, mfd, ks, sf))
self.body2d = nn.Sequential(*blocks2d)
self.body1d = nn.Sequential(*blocks1d)
self.head = spectral_norm(nn.Conv1d(mfd, z_dim, 3, 1, 1))
def forward(self, x):
"""
x.shape=(batch_size, feat_dim, num_frames)
cond.shape=(batch_size, cond_dim, num_frames)
"""
bs, fd, nf = x.size()
# ### Process generated ###
# shape=(bs, 1, fd, nf)
x = x.unsqueeze(1)
# shape=(bs, 64, 10, nf_)
x = self.body2d(x)
# shape=(bs, 64*10, nf_)
x = x.view(bs, -1, x.size(3))
# ### Merging ###
x = self.body1d(x)
# ### Head ###
# shape=(bs, input_size, nf)
# out = torch.sigmoid(self.head(x))
out = self.head(x)
return out
if __name__ == "__main__":
parser = argparse.ArgumentParser()
parser.add_argument("--model-id", type=str)
parser.add_argument("--audio_db_dir", type=str)
parser.add_argument("--batches-per-epoch", type=int, default=500)
parser.add_argument("--notes", type=str)
parser.add_argument(
"--wandb-dir", type=str, default="wandb", help="Directory with wandb runs"
)
# argument for log data (need to set vocoder to generate wav samples)
parser.add_argument("--melgan_run_id", default="")
parser.add_argument("--log_num_samples", type=int, default=1)
parser.add_argument("--wav_generate_dir", type=str, default="models/custom")
# new argument
parser.add_argument("--feat_dim", type=int, default=80)
parser.add_argument("--z_dim", type=int, default=20)
parser.add_argument("--z_scale_factors", default=[2, 2, 2, 2])
parser.add_argument("--num_va", type=int, default=200)
# BEGAN parameters
parser.add_argument("--gamma", type=float, default=1.0)
parser.add_argument("--lambda_k", type=float, default=0.01)
parser.add_argument("--init_k", type=float, default=0.0)
parser.add_argument("--init_lr", type=float, default=0.0001)
parser.add_argument("--num_epochs", type=int, default=1000)
parser.add_argument("--lambda_cycle", type=int, default=1)
parser.add_argument("--max_grad_norm", type=int, default=3)
parser.add_argument("--save_rate", type=int, default=20)
parser.add_argument("--batch_size", type=int, default=5)
args = parser.parse_args()
script_path = os.path.realpath(__file__)
print(script_path)
data_dir = "./training_data/exp_data"
log_num_samples = args.log_num_samples
wav_generate_dir = args.wav_generate_dir
model_id = args.model_id
if model_id:
api = wandb.Api()
previous_run = api.run(f"demiurge/unagan/{model_id}")
args = argparse.Namespace(**previous_run.config)
if hasattr(args, "log_num_samples"):
log_num_samples = args.log_num_samples
else:
args.log_num_samples = log_num_samples
if hasattr(args, "melgan_run_id"):
melgan_run_id = args.melgan_run_id
if melgan_run_id == "":
melgan_run_id = None
else:
melgan_run_id = None
if hasattr(args, "wav_generate_dir"):
wav_generate_dir = args.wav_generate_dir
else:
args.wav_generate_dir = wav_generate_dir
feat_dim = args.feat_dim
z_dim = args.z_dim
z_scale_factors = args.z_scale_factors
z_total_scale_factor = np.prod(z_scale_factors)
num_va = args.num_va
feat_type = "mel"
# BEGAN parameters
gamma = args.gamma
lambda_k = args.lambda_k
init_k = args.init_k
# #############################################################
# ### Set the validation losses that are used in evaluation ###
# #############################################################
eval_metrics = [
("Convergence", "lower_better"),
]
# #############################################################
# Training options
init_lr = args.init_lr
num_epochs = args.num_epochs
batches_per_epoch = args.batches_per_epoch
lambda_cycle = args.lambda_cycle
max_grad_norm = args.max_grad_norm
save_rate = args.save_rate
batch_size = args.batch_size
config_keys = [
"script_path",
"data_dir",
"feat_dim",
"z_dim",
"z_scale_factors",
"z_total_scale_factor",
"num_va",
"feat_type",
"gamma",
"lambda_k",
"init_k",
"init_lr",
"num_epochs",
"lambda_cycle",
"max_grad_norm",
"save_rate",
"batch_size",
]
locs = locals()
config = {**{k: locs[k] for k in config_keys}, **args.__dict__}
pprint.pprint(config)
if model_id:
print(f"Resuming wandb run ID {model_id}.")
resume_training = True
else:
print("Starting new run from scratch.")
resume_training = False
if melgan_run_id:
print(f"Downloading wandb melgan run ID {melgan_run_id} for wav generation.")
download_weights.main(
melgan_run_id=melgan_run_id,
unagan_run_id=None,
model_dir=Path("models/custom"),
)
Path(args.wandb_dir).mkdir(parents=True, exist_ok=True)
wandb.init(
dir=args.wandb_dir,
id=model_id,
entity="demiurge",
project="unagan",
config=config,
resume=resume_training,
notes=args.notes,
)
print(f"wandb: Run ID: {wandb.run.id}")
output_dir = wandb.run.dir
# XXX Saving models this way breaks torch restore functionality!
# Only use it for other files.
for files_to_save in ["record/*"]:
print(f"Registering paths matching {files_to_save} to save in wandb.")
wandb.save(files_to_save)
# Dirs and fps
iterator_tr, num_tr, iterator_va, num_va = get_voc_datasets(
data_dir, feat_type, batch_size
)
print("tr: {}, va: {}".format(num_tr, num_va))
inf_iterator_tr = make_inf_iterator(iterator_tr)
# Prepare mean and std
mean_fp = os.path.join(data_dir, f"mean.{feat_type}.npy")
std_fp = os.path.join(data_dir, f"std.{feat_type}.npy")
wandb.save(mean_fp)
wandb.save(std_fp)
# also save a copy for wav generation
if melgan_run_id:
temp_dir = Path(args.wav_generate_dir)
temp_dir.mkdir(parents=True, exist_ok=True)
shutil.copy(mean_fp, temp_dir / f"mean.{feat_type}.npy")
shutil.copy(std_fp, temp_dir / f"std.{feat_type}.npy")
mean = torch.from_numpy(np.load(mean_fp)).float().to(device).view(1, feat_dim, 1)
std = torch.from_numpy(np.load(std_fp)).float().to(device).view(1, feat_dim, 1)
# Model
if torch.cuda.device_count() > 1:
netG = DP(NetG(feat_dim, z_dim, z_scale_factors).to(device))
netD = DP(NetD(feat_dim).to(device))
netE = DP(Encoder(feat_dim, z_dim, z_scale_factors).to(device))
recorder = BEGANRecorder(lambda_k, init_k, gamma)
print(f"We have {torch.cuda.device_count()} gpus. Use data parallel.")
else:
netG = NetG(feat_dim, z_dim, z_scale_factors).to(device)
netD = NetD(feat_dim).to(device)
netE = Encoder(feat_dim, z_dim, z_scale_factors).to(device)
recorder = BEGANRecorder(lambda_k, init_k, gamma)
print(f"We have {torch.cuda.device_count()} gpu.")
# Optimizers
optimizerG = optim.Adam(netG.parameters(), lr=init_lr)
optimizerD = optim.Adam(netD.parameters(), lr=init_lr)
optimizerE = optim.Adam(netE.parameters(), lr=init_lr)
# ###################################
# ### Initialize training manager ###
# ###################################
manager = TrainingManager(
[netG, netD, netE, recorder], # networks
[optimizerG, optimizerD, optimizerE, None], # optimizers, could be None
[
"Generator",
"Discriminator",
"Encoder",
"BEGANRecorder",
], # names of the corresponding networks
output_dir,
save_rate,
script_path=script_path,
wav_generate_dir=args.wav_generate_dir,
)
# ###################################
# ### k ###
k = recorder.k.item()
# ### Resume training ###
if resume_training:
# Rolling back an unfinished epoch may cause wandb to drop logs.
# Moving to the next epoch.
init_epoch = manager.resume_training(output_dir) + 1
print(f"Resumed k: {k}")
else:
init_epoch = 1
manager.save_initial()
print(f"Initial epoch: {init_epoch}")
# ### Train ###
epoch = init_epoch
while not (epoch >= 1 + num_epochs):
# for epoch in range(init_epoch, 1 + num_epochs):
t0 = time.time()
# ### Training ###
print("Training...")
sum_losses_tr = OrderedDict([(loss_name, 0) for loss_name in loss_funcs])
count_all_tr = 0
num_batches_tr = batches_per_epoch
tt0 = time.time()
# In training, set net.train()
netG.train()
netD.train()
netE.train()
for i_batch in range(batches_per_epoch):
batch = next(inf_iterator_tr)
step = epoch * batches_per_epoch + i_batch
# voc.shape=(bs, feat_dim, num_frames)
voc = batch
voc = voc.to(device)
voc = (voc - mean) / std
bs, _, nf = voc.size()
# ### Train generator ###
z = (
torch.zeros((bs, z_dim, int(np.ceil(nf / z_total_scale_factor))))
.normal_(0, 1)
.float()
.to(device)
)
fake_voc = netG(z)
z_fake = netE(fake_voc)
z_real = netE(voc)
gloss = torch.mean(torch.abs(netD(fake_voc) - fake_voc))
noise_rloss = torch.mean(torch.abs(z_fake - z))
real_rloss = torch.mean(torch.abs(netG(z_real)[..., :nf] - voc[..., :nf]))
# Back propagation
netG.zero_grad()
netE.zero_grad()
(gloss + lambda_cycle * (noise_rloss + real_rloss)).backward(
retain_graph=True
)
if max_grad_norm is not None:
clip_grad_norm_(netG.parameters(), max_grad_norm)
clip_grad_norm_(netE.parameters(), max_grad_norm)
optimizerG.step()
optimizerE.step()
# ### Train discriminator ###
real_dloss = torch.mean(torch.abs(netD(voc) - voc))
fake_dloss = torch.mean(
torch.abs(netD(fake_voc.detach()) - fake_voc.detach())
)
dloss = real_dloss - k * fake_dloss
# Update
netD.zero_grad()
dloss.backward()
if max_grad_norm is not None:
clip_grad_norm_(netD.parameters(), max_grad_norm)
optimizerD.step()
# ### Convergence and update k ###
k, convergence = recorder(real_dloss, fake_dloss, update_k=True)
# ### Losses ###
losses = OrderedDict(
[
("G", gloss),
("D", dloss),
("RealD", real_dloss),
("FakeD", fake_dloss),
("Convergence", convergence),
("NoiseRecon", noise_rloss),
("RealRecon", real_rloss),
]
)
wandb.log({"loss/train": losses, "epoch": epoch}, step=step)
# ### Misc ###
# Accumulate losses
losses_tr = OrderedDict(
[(loss_name, lo.item()) for loss_name, lo in losses.items()]
)
for loss_name, lo in losses_tr.items():
sum_losses_tr[loss_name] += lo
count_all_tr += 1
# ### Print info ###
if i_batch % 10 == 0:
batch_info = "Epoch {}. Batch: {}/{}, T: {:.3f}, ".format(
epoch, i_batch, num_batches_tr, time.time() - tt0
) + "".join(
[
"(tr) {}: {:.5f}, ".format(loss_name, lo)
for loss_name, lo in losses_tr.items()
]
)
print(batch_info, k)
tt0 = time.time()
# check if training value NaN
detect_NaN = False
for loss_name, lo in losses_tr.items():
if np.isnan(lo):
detect_NaN = True
break
if detect_NaN:
break
# Compute average loss
mean_losses_tr = OrderedDict(
[
(loss_name, slo / count_all_tr)
for loss_name, slo in sum_losses_tr.items()
]
)
# ### Validation ###
print("")
print("Validation...")
mean_losses_va = validate(epoch, step, iterator_va, num_va)
# ###########################################################################
# ### Check the best validation losses and save information in the middle ###
# ###########################################################################
# Check and update the best validation loss
va_metrics = [
(metric_name, mean_losses_va[metric_name], higher_or_lower)
for metric_name, higher_or_lower in eval_metrics
]
best_va_metrics = manager.check_best_va_metrics(va_metrics, epoch)
# Save the record
record = {
"mean_losses_tr": mean_losses_tr,
"mean_losses_va": mean_losses_va,
"best_va_metrics": best_va_metrics,
}
# check all values in train record are not NaN.
# if NaN, resume from best_model
detect_NaN = False
for loss_name, slo in sum_losses_tr.items():
if | np.isnan(slo) | numpy.isnan |
import numpy as np
import cv2
import json, codecs
from random import *
from random import randint
import scipy.io as sio
import os
import os.path as osp
import matplotlib as mpl
if os.environ.get('DISPLAY','') == '':
print('no display found. Using non-interactive Agg backend')
mpl.use('Agg')
import matplotlib.pyplot as plt
import sys
from manage_data.utils import join_json, resize
def is_valid(X, Y, img):
return X>=0 and X<img.shape[1] and Y>=0 and Y<img.shape[0]
def json_to_string(labels):
if len(labels)==0:
return '[]'
line = '['
for i in range(len(labels)):
line += '{\"x\":'+str(labels[i]['x'])+',\"y\":'+str(labels[i]['y'])+'},'
return line[0:len(line)-1]+']'
def count_people(heads,labels,position, x_low, x_upper , y_low, y_upper):
cont =0
new_labels = []
for x in range(x_low, x_upper):
for y in range(y_low, y_upper):
if heads[y, x] == 1:
cont += 1
auxLabel = labels[int(position[y, x])].copy()
auxLabel['y'] -= y_low
auxLabel['x'] -= x_low
new_labels.append(auxLabel)
return cont,new_labels
def add_noise(image, noise_type = 's&p'):
if noise_type == "gauss":
row,col= image.shape
mean = 0
var = 0.1
sigma = var**0.5
gauss = np.random.normal(mean,sigma,(row,col))
gauss = gauss.reshape(row,col)
noisy = image + gauss
return noisy
elif noise_type == "s&p":
row,col = image.shape
s_vs_p = 0.5
amount = 0.04
out = np.copy(image)
# Salt mode
num_salt = np.ceil(amount * image.size * s_vs_p)
coords = [np.random.randint(0, i - 1, int(num_salt)) for i in image.shape]
out[coords] = 1
# Pepper mode
num_pepper = np.ceil(amount* image.size * (1. - s_vs_p))
coords = [np.random.randint(0, i - 1, int(num_pepper)) for i in image.shape]
out[coords] = 0
return out
else:
raise RuntimeError("'{}' is not a valid noise type".format(noise_type))
def noise_augmentation(out_img_dir, out_lab_dir, out_den_dir, img_id):
file_names = os.listdir(out_img_dir)
for file_name in file_names:
file_extension = file_name.split('.')[-1]
if file_extension == 'jpg':
img_id += 1
in_img_path = osp.join(out_img_dir, file_name)
in_lab_path = osp.join(out_lab_dir, file_name[:len(file_name) - len(file_extension)] + 'json')
in_den_path = osp.join(out_den_dir, file_name[:len(file_name) - len(file_extension)] + 'npy')
img = cv2.imread(in_img_path, 0)
new_den = | np.load(in_den_path) | numpy.load |
"""
The :mod:'atml.exp' module holds a set of functions to perform machine learning experiments and gather the corresponding
performances metrics.
"""
# Author: <NAME> (<EMAIL>)
# License: BSD-3
import numpy
import pandas
import openml
def get_random_split_measurement(model_instance, x, y, measure, sparse=False, cap_size=10000, test_size=0.5):
"""
Perform a random split validation experiment for a given combination of model, dataset, and evaluation measure.
Parameters
----------
model_instance: sklearn.predictor
A model instance with the sklearn.predictor template, it should have a fit() method for model training, and
a predict_proba() method to predict probability vectors on test data.
x: numpy.ndarray
The data matrix with shape (n samples, d dimensions)
y: numpy.ndarray
The label vector with shape (n samples, 1)
measure: atml.Measure
A evaluation measure selected from the atml.measure module.
sparse: boolean
To indicate whether to only use a subset of the dataset to perform the experiments.
cap_size: integer
In the case sparse=True, cap_size specifies the maximum size of the dataset to run the experiments.
test_size: float
The proportion of the dataset that is used as the testing set (validation set).
Returns
----------
measurement: float
The performance measurement on the testing set (validation set).
"""
# x : shape(n, m)
# y : shape(n, 1)
# y_vector: shape(n, k)
n = numpy.shape(x)[0]
_, y = numpy.unique(y, return_inverse=True)
k = len(numpy.unique(y))
shuffle_idx = numpy.random.permutation(numpy.arange(0, n))
x = x[shuffle_idx, :]
y = y[shuffle_idx]
y_vector = numpy.zeros((n, k))
for i in range(0, k):
y_vector[:, i] = (y == i)
if sparse & (n > cap_size):
class_count = numpy.ceil(numpy.mean(y_vector, axis=0) * cap_size).astype('int')
tmp_x = []
tmp_y = []
tmp_y_vector = []
for i in range(0, k):
idx_list = numpy.argwhere(y == i).ravel()
tmp_idx = numpy.random.choice(idx_list, class_count[i], replace=False)
tmp_x.append(x[tmp_idx, :])
tmp_y.append(y[tmp_idx])
tmp_y_vector.append(y_vector[tmp_idx, :])
x = numpy.vstack(tmp_x)
y = numpy.hstack(tmp_y)
y_vector = numpy.vstack(tmp_y_vector)
n_train = numpy.ceil(n * (1 - test_size)).astype('int')
selected_idx = numpy.zeros(n)
class_count = numpy.ceil(numpy.mean(y_vector, axis=0) * n_train).astype('int')
x_train = []
y_train = []
for j in range(0, k):
idx_list = numpy.argwhere(y == j).ravel()
tmp_idx = numpy.random.choice(idx_list, class_count[j], replace=False)
x_train.append(x[tmp_idx, :])
y_train.append(y[tmp_idx])
selected_idx[tmp_idx] = 1.0
x_train = numpy.vstack(x_train)
y_train = numpy.hstack(y_train)
x_test = x[selected_idx == 0, :]
y_test = y[selected_idx == 0]
y_train_vector = numpy.zeros((len(y_train), k))
y_test_vector = numpy.zeros((len(y_test), k))
for k in range(0, k):
y_train_vector[:, k] = (y_train == k)
y_test_vector[:, k] = (y_test == k)
mdl = model_instance
mdl.fit(x_train, y_train)
s_test = mdl.predict_proba(x_test)
s_test[~numpy.isfinite( | numpy.sum(s_test, axis=1) | numpy.sum |
import argparse
import json
import multiprocessing
import neuroglancer
import numpy as np
import os
import glob
import sys
import tempfile
import tifffile
import tqdm
import webbrowser
import time
from scipy.spatial import KDTree
from neuroglancer.server import BaseRequestHandler
from .utils.ngutils import *
from .ngreference import NGReference
viewer = None
COLOR_POINTS = "yellow"
COLOR_DETECTED_POINTS = "green"
COLOR_DELETING_POINTS = "red"
class NuggtViewer:
"""The neuroglancer viewer controller
This holds the state for displaying the current edit window.
"""
def __init__(self, img_path, alt_img_path, seg_path, points_file,
detected_points_file = None,
x0=None, x1=None, y0=None, y1=None, z0=None, z1=None,
min_distance=10):
self.viewer = neuroglancer.Viewer()
self.points_file = points_file
self.img_path = img_path
self.alt_img_path=alt_img_path
self.seg_path=seg_path
self.min_distance = min_distance
if os.path.exists(points_file):
with open(points_file) as fd:
self.points = np.array(json.load(fd))
else:
self.points = np.zeros((0, 3), np.float32)
if detected_points_file is not None:
with open(detected_points_file) as fd:
self.detected_points = json.load(fd)
else:
self.detected_points = None
self.deleting_points = None
self.box_coords = None
filenames = sorted(glob.glob(img_path))
if len(filenames) == 1:
self.z_extent, self.y_extent, self.x_extent = \
tifffile.imread(filenames[0]).shape
else:
self.y_extent, self.x_extent = tifffile.imread(filenames[0]).shape
self.z_extent = len(filenames)
if x0 is not None and x1 is not None:
self.width = x1 - x0
self.x0 = x0
self.x1 = x1
else:
self.width = self.x_extent
self.x0 = 0
self.x1 = self.x_extent
if y0 is not None and y1 is not None:
self.height = y1 - y0
self.y0 = y0
self.y1 = y1
else:
self.height = self.y_extent
self.y0 = 0
self.y1 = self.height
if z0 is not None and z1 is not None:
self.depth = z1 - z0
self.z0 = z0
self.z1 = z1
else:
self.depth = self.z_extent
self.z0 = 0
self.z1 = self.z_extent
self.display()
save_fn = lambda s: self.save()
annotate_fn = self.action_handler
delete_fn = self.delete_handler
self.viewer.actions.add("save", save_fn)
self.viewer.actions.add("annotatepts", annotate_fn)
self.viewer.actions.add("deletepts", delete_fn)
self.viewer.actions.add("start-selection",
self.start_selection_handler)
self.viewer.actions.add("extend-selection",
self.extend_selection_handler)
self.viewer.actions.add("delete-selected",
self.delete_selected_handler)
#
# Hint: this page lets you type a character and see its code
# https://developer.mozilla.org/en-US/docs/Web/API/KeyboardEvent/code
#
with self.viewer.config_state.txn() as s:
s.input_event_bindings.viewer["shift+keya"] = "annotatepts"
s.input_event_bindings.viewer["shift+keys"] = "save"
s.input_event_bindings.viewer["shift+keyd"] = "deletepts"
s.input_event_bindings.viewer["bracketleft"] = "start-selection"
s.input_event_bindings.viewer["bracketright"] = "extend-selection"
s.input_event_bindings.viewer["shift+keyx"] = "delete-selected"
@property
def shape(self):
"""The size of the potential display volume"""
return (self.z_extent, self.y_extent, self.x_extent)
def center(self):
with self.viewer.txn() as txn:
txn.position.voxel_coordinates = \
((self.x0 + self.x1) / 2,
(self.y0 + self.y1) / 2,
(self.z0 + self.z1) / 2)
def display(self):
img = load_image(self.img_path, self.x0, self.x1, self.y0, self.y1,
self.z0, self.z1)
if self.alt_img_path is not None:
alt_img = load_image(self.alt_img_path, self.x0, self.x1,
self.y0, self.y1, self.z0, self.z1)
if self.seg_path is not None:
seg = load_image(self.seg_path, self.x0, self.x1,
self.y0, self.y1, self.z0, self.z1)
with self.viewer.txn() as txn:
layer(txn, "image", img, gray_shader, 1.0,
self.x0, self.y0, self.z0)
if self.alt_img_path is not None:
layer(txn, "alt-image", alt_img, green_shader, 1.0,
self.x0, self.y0, self.z0)
if self.seg_path is not None:
seglayer(txn, "segmentation", seg, self.x0, self.y0, self.z0)
self.display_points(txn, self.points, "annotation", COLOR_POINTS)
if self.detected_points is not None:
self.display_points(txn, self.detected_points, "detected",
COLOR_DETECTED_POINTS)
elif has_layer(txn, "detected"):
del txn.layers["detected"]
if self.deleting_points is not None:
self.display_points(txn, self.deleting_points, "deleting",
COLOR_DELETING_POINTS)
elif has_layer(txn, "deleting"):
del txn.layers["deleting"]
if self.box_coords is not None:
self.display_bounding_box(txn)
elif has_layer(txn, "selection"):
del txn.layers["selection"]
self.center()
def display_bounding_box(self, txn):
box = neuroglancer.AxisAlignedBoundingBoxAnnotation()
box.point_a = self.box_coords[0]
box.point_b = self.box_coords[1]
box.id = "selection"
txn.layers["selection"] = neuroglancer.AnnotationLayer(
annotations=[box])
def display_points(self, txn, points, layer_name, color):
mask = (points[:, 0] >= self.x0) & (points[:, 0] < self.x1) & \
(points[:, 1] >= self.y0) & (points[:, 1] < self.y1) & \
(points[:, 2] >= self.z0) & (points[:, 2] < self.z1)
display_points = points[mask]
pointlayer(txn, layer_name,
display_points[:, 0], display_points[:, 1],
display_points[:, 2],
color)
def say(self, msg, category):
with self.viewer.config_state.txn() as txn:
txn.status_messages[category] = msg
def action_handler(self, s):
point = np.array(s.mouse_voxel_coordinates)
neighbors = self.find_nearby_points(point)
if len(neighbors) > 0:
self.say("Point too close to some other point!", "annotation")
return
self.points = np.vstack((self.points, point))
with self.viewer.txn() as txn:
self.display_points(txn, self.points, "annotation", COLOR_POINTS)
self.say("Added point at %.2f, %.2f, %.2f" %
(point[0], point[1], point[2]),
"annotation")
def find_nearby_points(self, point, return_index=False):
diff = self.points - point[np.newaxis, :]
distances = np.sqrt(np.sum(np.square(diff), 1))
indexes = np.where(distances < self.min_distance)[0]
if len(indexes) == 0:
if return_index:
return np.zeros((0, 3), np.float32), np.zeros(0, int)
else:
return np.zeros((0, 3), np.float32)
result = self.points[indexes]
order = np.argsort(distances[indexes])
if return_index:
return result[order], indexes[order]
else:
return result[order]
def delete_handler(self, s):
point = np.array(s.mouse_voxel_coordinates)
neighbors, indexes = self.find_nearby_points(point, return_index=True)
if len(neighbors) == 0:
self.say("No nearby point", "delete")
return
to_delete = self.points[indexes[0]]
self.points = np.delete(self.points, indexes[0], 0)
with self.viewer.txn() as txn:
self.display_points(txn, self.points, "annotation", COLOR_POINTS)
self.say("Deleting %.2f, %.2f, %.2f" %
(to_delete[0], to_delete[1], to_delete[2]), "delete")
def partition_points(self):
"""Partition points inside/outside bounding box"""
for idx in range(3):
if self.box_coords[0][idx] == self.box_coords[1][idx]:
self.box_coords[1][idx] += 1
(x0, x1), (y0, y1), (z0, z1) = [
[fn(self.box_coords[0][idx], self.box_coords[1][idx])
for fn in (min, max)] for idx in range(3)]
all_points = self.all_points
mask = (all_points[:, 0] >= x0) & (all_points[:, 0] < x1) & \
(all_points[:, 1] >= y0) & (all_points[:, 1] < y1) & \
(all_points[:, 2] >= z0) & (all_points[:, 2] < z1)
self.points, self.deleting_points = all_points[~mask], all_points[mask]
with self.viewer.txn() as txn:
self.display_points(txn, self.points, "annotation", COLOR_POINTS)
self.display_points(txn, self.deleting_points,
"deleting", COLOR_DELETING_POINTS)
self.display_bounding_box(txn)
def start_selection_handler(self, s):
point = | np.array(s.mouse_voxel_coordinates) | numpy.array |
## @package teetool
# This module contains the Visual_2d class
#
# See Visual_2d class for more details
import numpy as np
from scipy.interpolate import griddata
import matplotlib.pyplot as plt
import teetool as tt
## Visual_2d class generates the 2d output using Matplotlib
#
# Even 3-dimensional trajectories can be output in 2d (sliced)
class Visual_2d(object):
## Constructor for Visual_2d
# @param self object pointer
# @param thisWorld World object, filled with trajectory data and models
# @param kwargs additional parameters for plt.figure()
def __init__(self, thisWorld, **kwargs):
"""
<description>
"""
## figure object
self._fig = plt.figure(facecolor="white", **kwargs)
## axis object
self._ax = self._fig.gca()
# set colour of axis
#self._ax.set_axis_bgcolor('white')
#self._ax.set_facecolor('white')
## World object
self._world = thisWorld
## Labels of plots
self._labels = []
## Plot mean of trajectories
# @param self object pointer
# @param list_icluster list of clusters to plot
# @param colour if specified, overwrites distinct colours
# @param kwargs additional parameters for plotting
def plotMean(self, list_icluster=None, colour=None, **kwargs):
# check validity
list_icluster = self._world._check_list_icluster(list_icluster)
# extract data
clusters = self._world.getCluster(list_icluster)
# unique colours
colours = tt.helpers.getDistinctColours(len(self._world._clusters),
colour)
for (i, this_cluster) in enumerate(clusters):
# pass clusters
Y = this_cluster["model"].getMean()
a_line, = self._ax.plot(Y[:, 0],
Y[:, 1],
color=colours[list_icluster[i]],
**kwargs)
## Plot trajectories of cluster
# @param self object pointer
# @param list_icluster list of clusters to plot
# @param ntraj maximum number of trajectories
# @param colour if specified, overwrites distinct colours
# @param kwargs additional parameters for plotting
def plotTrajectories(self,
list_icluster=None,
ntraj=50,
colour=None,
**kwargs):
# check validity
list_icluster = self._world._check_list_icluster(list_icluster)
# extract data
clusters = self._world.getCluster(list_icluster)
# unique colours
colours = tt.helpers.getDistinctColours(len(self._world._clusters),
colour)
for (i, this_cluster) in enumerate(clusters):
# pass clusters
for itraj, (x, Y) in enumerate(this_cluster["data"]):
a_line, = self._ax.plot(Y[:, 0],
Y[:, 1],
color=colours[i],
**kwargs)
# limit number of trajectories
if itraj > ntraj:
break
self._labels.append((a_line, "data"))
## Plot trajectories of cluster
# @param self object pointer
# @param x1 point from [0,1] to visualise
# @param list_icluster list of clusters to plot
# @param ntraj maximum number of trajectories
# @param colour if specified, overwrites distinct colours
# @param kwargs additional parameters for plotting
def plotTrajectoriesPoints(self,
x1,
list_icluster=None,
ntraj=50,
colour=None,
**kwargs):
# check validity
list_icluster = self._world._check_list_icluster(list_icluster)
# obtain points
clustersP = self._world.getClusterPoints(x1, list_icluster)
# unique colours
colours = tt.helpers.getDistinctColours(len(self._world._clusters),
colour)
for (i, A) in enumerate(clustersP):
# pass clusters
for itraj, a in enumerate(A):
a_line, = self._ax.plot(a[0],
a[1],
color=colours[i],
**kwargs)
# limit number of trajectories
if itraj > ntraj:
break
self._labels.append((a_line, "data"))
## Plot time-series of trajectories
# @param self object pointer
# @param icluster select cluster to plot
# @param idim select dimension to plot
# @param ntraj maximum number of trajectories
# @param colour specificy colour of trajectories
# @param kwargs additional parameters for plotting
def plotTimeSeries(self, icluster=0, idim=0, ntraj=50,
colour='k', **kwargs):
# number of subplots, 2 or 3
ndim = self._world._ndim
# subplot
#f, axarr = plt.subplots(ndim, sharex=True)
# check validity
[icluster] = self._world._check_list_icluster([icluster])
# extract data
clusters = self._world.getCluster([icluster])
for (i, this_cluster) in enumerate(clusters):
# pass clusters
for itraj, (x, Y) in enumerate(this_cluster["data"]):
#for d in range(ndim):
x_norm = (x - x.min()) / (x.max() - x.min())
a_line, = self._ax.plot(x_norm,
Y[:,idim],
color=colour, **kwargs)
if itraj > ntraj:
break
self._labels.append((a_line, "data"))
## Plot a box based on two coordinates
# @param self object pointer
# @param coord_lowerleft lower-left coordinate (x,y)
# @param coord_upperright upper-right coordinate (x,y)
# @param kwargs additional parameters for plotting
def plotBox(self, coord_lowerleft, coord_upperright, **kwargs):
x_lo = coord_lowerleft[0]
x_hi = coord_upperright[0]
y_lo = coord_lowerleft[1]
y_hi = coord_upperright[1]
coords = np.array([[x_lo, y_lo],
[x_hi, y_lo],
[x_hi, y_hi],
[x_lo, y_hi],
[x_lo, y_lo]])
coords_x = coords[:,0]
coords_y = coords[:,1]
self._ax.plot(coords_x, coords_y, **kwargs)
## standard plotting function for Matplotlib
# @param self object pointer
# @param args additional arguments for plotting
# @param kwargs additional labeled parameters for plotting
def plot(self, *args, **kwargs):
# plot
self._ax.plot(*args, **kwargs)
## Plot samples of model
# @param self object pointer
# @param list_icluster list of clusters to plot
# @param ntraj number of trajectories
# @param colour if specified, overwrites distinct colours
# @param kwargs additional parameters for plotting
def plotSamples(self, list_icluster=None, ntraj=50, colour=None, **kwargs):
# check validity
list_icluster = self._world._check_list_icluster(list_icluster)
# unique colours
colours = tt.helpers.getDistinctColours(len(self._world._clusters),
colour)
for (i, icluster) in enumerate(list_icluster):
these_samples = self._world.getSamples(icluster,
nsamples=ntraj)
for (x, Y) in these_samples:
a_line, = self._ax.plot(Y[:, 0],
Y[:, 1],
color=colours[i],
linestyle=":",
**kwargs)
self._labels.append((a_line, "samples"))
## Add legend to plot
# @param self object pointer
def plotLegend(self):
list_lines = []
list_label = []
for (a_line, a_label) in self._labels:
list_lines.append(a_line)
list_label.append(a_label)
plt.legend(handles=list_lines, labels=list_label)
## Plots a confidence region of variance sigma
# @param self object pointer
# @param list_icluster list of clusters to plot
# @param sdwidth variance to evaluate
# @param z if specified, it evaluates the confidence region at a constant altitude for 3D trajectories
# @param resolution sets resolution for which to calculate the tube, can be a single integer, or an actual measurement [dim1 dim2] (2d) [dim1 dim2 dim3] (3d)
# @param colour if specified, overwrites distinct colours
# @param alpha opacity for the confidence region
# @param kwargs additional parameters for plotting
def plotTube(self,
list_icluster=None,
sdwidth=1,
z=None,
resolution=None,
colour=None,
alpha=.1,
**kwargs):
# check validity
list_icluster = self._world._check_list_icluster(list_icluster)
# extract
(ss_list, [xx, yy, zz]) = self._world.getTube(list_icluster,
sdwidth,
z=z,
resolution=resolution)
# unique colours
lcolours = tt.helpers.getDistinctColours(len(self._world._clusters),
colour)
for i, ss1 in enumerate(ss_list):
#plt.contourf(xx, yy, 1.*ss1, levels=[-np.inf, 1., np.inf], colors=(lcolours[i],), alpha=alpha, **kwargs)
# plot an iso surface line
plt.contour(xx,
yy,
ss1,
levels=[.5],
colors=(lcolours[list_icluster[i]], 'w'),
**kwargs)
## Plots the difference confidence region of variance sigma for two models
# @param self object pointer
# @param list_icluster list of 2 clusters to compare
# @param sdwidth variance to evaluate
# @param z if specified, it evaluates the confidence region at a constant altitude for 3D trajectories
# @param resolution specify resolution of region
# @param colour if specified, overwrites distinct colours
# @param alpha opacity for the confidence region
# @param kwargs additional parameters for plotting
def plotTubeDifference(self,
list_icluster=None,
sdwidth=1,
z=None,
resolution=None,
colour=None,
alpha=.1,
**kwargs):
# check validity
list_icluster = self._world._check_list_icluster(list_icluster)
# extract first two only!
list_icluster = list_icluster[:2]
# extract
(ss_list, [xx, yy, zz]) = self._world.getTube(list_icluster,
sdwidth, z=z,
resolution=resolution)
# to plot
ss_plot = - np.inf * np.ones_like(ss_list[0])
# 1 :: blocks added
ss_added = ((ss_list[0] - ss_list[1])==-1)
# 2 :: blocks removed
ss_removed = ((ss_list[0] - ss_list[1])==1)
# 3 :: present in both
ss_neutral = ((ss_list[0] + ss_list[1])==2)
ss_plot[ss_added] = 1.
ss_plot[ss_removed] = -1.
ss_plot[ss_neutral] = 0.
#plt.contourf(xx, yy, ss_plot, levels=[-np.inf, -1., 0., 1., np.inf], colors='none', hatches=['//', '.', '/'], **kwargs)
plt.contourf(xx,
yy,
ss_plot,
levels=[-np.inf, -1., 0., 1., np.inf],
colors=('r','b','g'),
alpha=alpha,
**kwargs)
for i in [1, 2, 3]:
if i == 1:
ss1 = 1.*ss_removed
color = 'r'
elif i == 2:
ss1 = 1.*ss_added
color = 'g'
elif i == 3:
ss1 = 1.*ss_neutral
color = 'b'
# plot an iso surface
plt.contour(xx, yy, ss1, levels=[0.5], colors=color)
## Plot the log-likehood of confidence regions -- which can be related to traffic complexity in the future
# @param self object pointer
# @param list_icluster list of clusters to compare
# @param pmin minimum value on a normalised scale
# @param pmax maximum value on a normalised scale
# @param z if specified, it evaluates the confidence region at a constant altitude for 3D trajectories
# @param resolution specify resolution of region
def plotLogLikelihood(self,
list_icluster=None,
pmin=0, pmax=1,
z=None,
resolution=None):
# check validity
list_icluster = self._world._check_list_icluster(list_icluster)
(ss_list, [xx, yy, zz]) = self._world.getLogLikelihood(list_icluster,
resolution,
z)
ss = ss_list[0] # initialise
for ss1 in ss_list:
# find those greater
mask = np.greater(ss1, ss)
# replace
ss[mask] = ss1[mask]
# normalise
ss_norm = (ss - np.min(ss)) / (np.max(ss) - np.min(ss))
# plot contours
self._ax.pcolor(xx,
yy,
ss_norm,
cmap="viridis",
vmin=pmin,
vmax=pmax)
def plotComplexityMap(self,
list_icluster=None,
complexity=1,
pmin=0, pmax=1,
z=None,
resolution=None, cmap1="Reds"):
ss, xx, yy, zz = self._world.getComplexityMap(list_icluster,
complexity,
resolution,
z)
# normalise
ss_norm = (ss - np.min(ss)) / ( | np.max(ss) | numpy.max |
import argparse
import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split
from keras.models import Sequential
from keras.layers import Dense, Dropout, Activation, Flatten
from keras.layers import Conv2D, MaxPooling2D, BatchNormalization
from keras.losses import categorical_crossentropy
from keras.optimizers import Adam
from keras.regularizers import l2
from keras.callbacks import ReduceLROnPlateau, TensorBoard, EarlyStopping, ModelCheckpoint
class TrainFER():
def __init__(self, data_path='./data/fer2013.csv', model_path='./models/model.h5'):
self.data_path = data_path
self.model_path = model_path
self.num_features = 128
self.num_labels = 7
self.batch_size = 64
self.epochs = 100
self.width, self.height = 48, 48
self.data = pd.read_csv(self.data_path)
self.model = self.build_model()
self.X_train, self.X_val,self.X_test,\
self.y_train, self.y_val, self.y_test = self.load_data()
def load_data(self):
# get label
emotions = pd.get_dummies(self.data['emotion']).values
pixels = self.data['pixels'].tolist()
faces = []
for pixel_row in pixels:
face = [int(pixel) for pixel in pixel_row.split(' ')]
face = np.asarray(face).reshape(self.width, self.height)
faces.append(face.astype('float32'))
faces = np.asarray(faces)
faces = np.expand_dims(faces, -1)
X_train, X_test, y_train, y_test = train_test_split(faces, emotions, test_size=0.1, random_state=15)
X_train, X_val, y_train, y_val = train_test_split(X_train, y_train, test_size=0.1, random_state=24)
return X_train, X_val, X_test, y_train, y_val, y_test
def build_model(self):
model = Sequential()
model.add(Conv2D(self.num_features, kernel_size=(3, 3), activation='relu', input_shape=(self.width, self.height, 1), data_format='channels_last', kernel_regularizer=l2(0.01)))
model.add(Conv2D(self.num_features, kernel_size=(3, 3), activation='relu', padding='same'))
model.add(BatchNormalization())
model.add(MaxPooling2D(pool_size=(2, 2), strides=(2, 2)))
model.add(Dropout(0.5))
model.add(Conv2D(2*self.num_features, kernel_size=(3, 3), activation='relu', padding='same'))
model.add(BatchNormalization())
model.add(Conv2D(2*self.num_features, kernel_size=(3, 3), activation='relu', padding='same'))
model.add(BatchNormalization())
model.add(MaxPooling2D(pool_size=(2, 2), strides=(2, 2)))
model.add(Dropout(0.5))
model.add(Conv2D(2*2*self.num_features, kernel_size=(3, 3), activation='relu', padding='same'))
model.add(BatchNormalization())
model.add(Conv2D(2*2*self.num_features, kernel_size=(3, 3), activation='relu', padding='same'))
model.add(BatchNormalization())
model.add(MaxPooling2D(pool_size=(2, 2), strides=(2, 2)))
model.add(Dropout(0.5))
model.add(Conv2D(2**3*self.num_features, kernel_size=(3, 3), activation='relu', padding='same'))
model.add(BatchNormalization())
model.add(Conv2D(2**3*self.num_features, kernel_size=(3, 3), activation='relu', padding='same'))
model.add(BatchNormalization())
model.add(MaxPooling2D(pool_size=(2, 2), strides=(2, 2)))
model.add(Dropout(0.5))
model.add(Flatten())
model.add(Dense(2**3*self.num_features, activation='relu'))
model.add(Dropout(0.4))
model.add(Dense(2*2*self.num_features, activation='relu'))
model.add(Dropout(0.4))
model.add(Dense(2*self.num_features, activation='relu'))
model.add(Dropout(0.5))
model.add(Dense(self.num_labels, activation='softmax'))
model.compile(loss=categorical_crossentropy,
optimizer=Adam(lr=0.001, beta_1=0.9, beta_2=0.999, epsilon=1e-7),
metrics=['accuracy'])
print(model.summary())
self.lr_reducer = ReduceLROnPlateau(monitor='val_loss', factor=0.9, patience=3, verbose=1)
self.tensorboard = TensorBoard(log_dir='./logs')
self.early_stopper = EarlyStopping(monitor='val_loss', min_delta=0, patience=8, verbose=1, mode='auto')
self.checkpointer = ModelCheckpoint(self.model_path, monitor='val_loss', verbose=1, save_best_only=True)
return model
def train(self):
self.model.fit( | np.array(self.X_train) | numpy.array |
import cv2
import numpy as np
class Threshold:
@staticmethod
def filter_bgr(img, bgr_thresh=[(0, 0, 0), (255, 255, 255)], **kwargs):
src = np.copy(img)
return cv2.inRange(src, np.uint8(bgr_thresh[0]), np.uint8(bgr_thresh[1]))
@staticmethod
def filter_hsv(img, hsv_thresh=[(0, 0, 0), (255, 255, 255)], **kwargs):
src = np.copy(img)
src = cv2.cvtColor(src, cv2.COLOR_BGR2HSV)
return cv2.inRange(src, np.uint8(hsv_thresh[0]), np.uint8(hsv_thresh[1]))
@staticmethod
def filter_hls(img, hls_thresh=[(0, 0, 0), (255, 255, 255)], **kwargs):
src = np.copy(img)
src = cv2.cvtColor(src, cv2.COLOR_BGR2HLS)
return cv2.inRange(src, np.uint8(hls_thresh[0]), np.uint8(hls_thresh[1]))
@staticmethod
def filter_lab(img, lab_thresh=[(0, 0, 0), (255, 255, 255)], **kwargs):
src = np.copy(img)
src = cv2.cvtColor(src, cv2.COLOR_BGR2LAB)
return cv2.inRange(src, np.uint8(lab_thresh[0]), np.uint8(lab_thresh[1]))
@staticmethod
def sobel(sobel_result, thresh=(0, 255), **kwargs):
# Take the absolute value of the derivative or gradient
abs_sobel = np.absolute(sobel_result)
# Scale to 8-bit (0 - 255) then convert to type = np.uint8
scaled_sobel = np.uint8(255 * abs_sobel / np.max(abs_sobel))
# Create a mask of 1's where the scaled gradient magnitude
# is > thresh_min and < thresh_max
binary_sobel = np.zeros_like(scaled_sobel, dtype=np.uint8)
binary_sobel[(scaled_sobel >= thresh[0]) & (scaled_sobel <= thresh[1])] = 1
return binary_sobel
@staticmethod
def magnitude(sobel_x, sobel_y, thresh=(0, 255), **kwargs):
sobel_mag = np.sqrt(sobel_x ** 2 + sobel_y ** 2)
# Scale to 8-bit (0 - 255) and convert to type = np.uint8
scaled_sobel = np.uint8(255 * sobel_mag / np.max(sobel_mag))
# Create a binary mask where mag thresholds are met
binary_magnitude = | np.zeros_like(scaled_sobel, dtype=np.uint8) | numpy.zeros_like |
import pandas as pd
import numpy as np
def read_goog_sp500_dataframe():
"""Returns a dataframe with the results for Google and S&P 500"""
# Point to where you've stored the CSV file on your local machine
googFile = 'data/GOOG.csv'
spFile = 'data/SP_500.csv'
goog = pd.read_csv(googFile, sep=",", usecols=[0, 5], names=['Date', 'Goog'], header=0)
sp = pd.read_csv(spFile, sep=",", usecols=[0, 5], names=['Date', 'SP500'], header=0)
goog['SP500'] = sp['SP500']
# The date object is a string, format it as a date
goog['Date'] = pd.to_datetime(goog['Date'], format='%Y-%m-%d')
goog = goog.sort_values(['Date'], ascending=[True])
returns = goog[[key for key in dict(goog.dtypes) if dict(goog.dtypes)[key] in ['float64', 'int64']]].pct_change()
return returns
def read_goog_sp500_logistic_data():
"""Returns a dataframe with the results for Google and
S&P 500 set up for logistic regression"""
returns = read_goog_sp500_dataframe()
returns['Intercept'] = 1
# Leave out the first row since it will not have a prediction for UP/DOWN
# Leave out the last row as it will not have a value for returns
# Resultant dataframe with the S&P500 and intercept values of all 1s
xData = np.array(returns[["SP500", "Intercept"]][1:-1])
yData = (returns["Goog"] > 0)[1:-1]
return (xData, yData)
def read_goog_sp500_data():
"""Returns a tuple with 2 fields, the returns for Google and the S&P 500.
Each of the returns are in the form of a 1D array"""
returns = read_goog_sp500_dataframe()
# Filter out the very first row which does not have any value for returns
xData = | np.array(returns["SP500"]) | numpy.array |
# -*- coding: utf-8 -*-
import os, sys
import numpy as np
import deepdish as dd
import math, random
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.data.dataset import Dataset
from thyroid_config import multi_class_map_dict
from thyroid_config import folder_map_dict, folder_reverse_map
from utils import aggregate_label, get_all_files
class ThyroidDataSet(Dataset):
def __init__(self, data_dir, testing=False, testing_num=128, pre_load=True):
self.data_dir = data_dir
self.pre_load = pre_load
self.testing = testing
self.testing_num = testing_num
# category configuration
self.folder_map_dict = folder_map_dict
self.folder_reverse_map = folder_reverse_map
self.class_map_dict = multi_class_map_dict
self.cur_filename = None
file_list, label_list = get_all_files(data_dir, inputext = ['.h5'],
class_map_dict=self.folder_map_dict,
pre_load=self.pre_load)
self.file_list = file_list
self.label_list = label_list
summery_label_dict = aggregate_label(label_list)
self.label_dict = summery_label_dict
self.img_num = len(self.file_list)
self.indices = list(range(self.img_num))
self.chosen_num_list = list(range(testing_num, testing_num+64))
self.max_num = testing_num+64 if not self.testing else self.testing_num
self.fixed_num = 40
self.additoinal_num = 20
def get_true_label(self, label):
new_label = self.class_map_dict[self.folder_reverse_map[label]]
return new_label
def __len__(self):
return self.img_num
def __getitem__(self, index):
if self.pre_load == True:
data = self.file_list[index]
else:
this_data_path = self.file_list[index]
data = dd.io.load(this_data_path)
self.cur_filename = os.path.basename(this_data_path)
probs, feas, bboxes = data['probs'], data['feas'], data['bboxes']
total_ind = np.array(range(0, len(probs)))
feas_placeholder = np.zeros((self.max_num, feas.shape[1]), dtype=np.float32)
box_placeholder = np.zeros((self.max_num, bboxes.shape[1]), dtype=np.int64)
if self.testing:
if len(probs) > self.testing_num:
chosen_total_ind_ = total_ind[:self.testing_num]
else:
chosen_total_ind_ = total_ind
else:
if len(probs) > self.max_num:
chosen_num = random.choice(self.chosen_num_list)
# front fixed chosen part
fixed_chosen_num = self.fixed_num+self.additoinal_num
fixed_chosen_ind = np.random.choice(total_ind[:fixed_chosen_num], self.fixed_num)
# later random chosen part
random_chosen_num = chosen_num-self.fixed_num
pos_probs = | np.sum(probs[fixed_chosen_num:, 1:], axis=1) | numpy.sum |
import pytest
import numpy as np
from Animate.Movie import Movie
from Animate.Animation import Animation
import matplotlib as mpl
def test_ratio_2():
m = Movie(dt=1.0/14, height_ratio=2)
img = np.arange(100).reshape(4, 5, 5)
m.add_image(img, style='dark_img')
a = Animation(m)
a._init_draw()
assert a.gs.get_geometry() == (1, 1)
assert a.gs.get_height_ratios() is None
m = Movie(dt=1.0/14, height_ratio=2)
img = np.arange(100).reshape(4, 5, 5)
m.add_image(img, style='dark_img')
m.add_axis('x', 'y')
m.add_trace(np.arange(4))
a = Animation(m)
a._init_draw()
assert a.gs.get_geometry() == (2, 1)
assert a.gs.get_height_ratios() == (2, 1)
m = Movie(dt=1.0 / 14, height_ratio=2)
img = np.arange(100).reshape(4, 5, 5)
m.add_image(img, style='dark_img')
m.add_axis('x', 'y')
m.add_trace(np.arange(4))
m.add_axis('x', 'y')
m.add_trace(np.arange(4), axis=1)
a = Animation(m)
a._init_draw()
assert a.gs.get_geometry() == (3, 1)
assert a.gs.get_height_ratios() == (4, 1, 1)
def test_ratio_1():
m = Movie(dt=1.0 / 14, height_ratio=1)
img = np.arange(100).reshape(4, 5, 5)
m.add_image(img, style='dark_img')
a = Animation(m)
a._init_draw()
assert a.gs.get_geometry() == (1, 1)
assert a.gs.get_height_ratios() is None
m = Movie(dt=1.0 / 14, height_ratio=1)
img = np.arange(100).reshape(4, 5, 5)
m.add_image(img, style='dark_img')
m.add_axis('x', 'y')
m.add_trace(np.arange(4))
a = Animation(m)
a._init_draw()
assert a.gs.get_geometry() == (2, 1)
assert a.gs.get_height_ratios() == (1, 1)
m = Movie(dt=1.0 / 14, height_ratio=1)
img = np.arange(100).reshape(4, 5, 5)
m.add_image(img, style='dark_img')
m.add_axis('x', 'y')
m.add_trace(np.arange(4))
m.add_axis('x', 'y')
m.add_trace(np.arange(4), axis=1)
a = Animation(m)
a._init_draw()
assert a.gs.get_geometry() == (3, 1)
assert a.gs.get_height_ratios() == (2, 1, 1)
def test_ratio_1p5():
m = Movie(dt=1.0 / 14, height_ratio=1.5)
img = np.arange(100).reshape(4, 5, 5)
m.add_image(img, style='dark_img')
a = Animation(m)
a._init_draw()
assert a.gs.get_geometry() == (1, 1)
assert a.gs.get_height_ratios() is None
m = Movie(dt=1.0 / 14, height_ratio=1.5)
img = np.arange(100).reshape(4, 5, 5)
m.add_image(img, style='dark_img')
m.add_axis('x', 'y')
m.add_trace(np.arange(4))
a = Animation(m)
a._init_draw()
assert a.gs.get_geometry() == (2, 1)
assert a.gs.get_height_ratios() == (1.5, 1)
m = Movie(dt=1.0 / 14, height_ratio=1.5)
img = np.arange(100).reshape(4, 5, 5)
m.add_image(img, style='dark_img')
m.add_axis('x', 'y')
m.add_trace( | np.arange(4) | numpy.arange |
import trimesh
from trimesh.base import Trimesh
import trimesh.creation
from trimesh.remesh import subdivide_to_size
import matplotlib.tri as mtri
import numpy as np
import torch
import quaternion
import os
from tqdm import tqdm_notebook as tqdm
from matplotlib import pyplot as plt
def plot_info(history_grad_norm, history_quad_loss,
history_smooth_loss, history_loss,
history_p_deviation, history_p_deviation_target,
history_p_deviation_mean, history_p_deviation_target_mean):
plt.figure(figsize=(10, 8))
plt.semilogy(history_grad_norm)
plt.title('Grad norm')
plt.show()
plt.figure(figsize=(10, 8))
plt.semilogy(np.array(history_quad_loss))
plt.title('Quad energy')
plt.show()
plt.figure(figsize=(10, 8))
plt.plot(np.array(history_smooth_loss))
plt.title('Smooth energy')
plt.show()
plt.figure(figsize=(10, 8))
plt.semilogy(np.array(history_loss))
plt.title('Data energy')
plt.show()
plt.figure(figsize=(10, 8))
plt.semilogy(np.array(history_p_deviation), c='b', label='from origin')
plt.semilogy(np.array(history_p_deviation_target), c='r', label='from target')
plt.legend()
plt.title('Deviation')
plt.show()
plt.figure(figsize=(10, 8))
plt.semilogy(np.array(history_p_deviation_mean), c='b', label='from origin')
plt.semilogy(np.array(history_p_deviation_target_mean), c='r', label='from target')
plt.legend()
plt.title('Mean deviation')
plt.show()
def make_M_from_tqs(t, q, s):
q = np.quaternion(q[0], q[1], q[2], q[3])
T = np.eye(4)
T[0:3, 3] = t
R = np.eye(4)
R[0:3, 0:3] = quaternion.as_rotation_matrix(q)
S = np.eye(4)
S[0:3, 0:3] = np.diag(s)
M = T.dot(R).dot(S)
return M
def two_tetrahedrons():
vertices_1 = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]])
vertices_2 = np.array([[2, 0, 0], [3, 0, 0], [2, 1, 0], [2, 0, 2]])
faces_1 = np.array([[0, 1, 2], [0, 2, 3], [0, 1, 3], [1, 2, 3],
[0, 2, 1], [0, 3, 2], [0, 3, 1], [1, 3, 2]])
faces_2 = np.array([[0, 1, 2], [0, 2, 3], [0, 1, 3], [1, 2, 3],
[0, 2, 1], [0, 3, 2], [0, 3, 1], [1, 3, 2]])
mesh_1 = Trimesh(vertices_1, faces_1)
mesh_2 = Trimesh(vertices_2, faces_2)
return mesh_1, mesh_2
def sphere(subdivisions=3, radius=1.0):
mesh = trimesh.primitives.Sphere(subdivisions=subdivisions, radius=radius)
return mesh
def plane(width=2, length=2, num_points=2500):
x = np.linspace(0, length, num=int(np.sqrt(num_points)))
y = np.linspace(0, width, num=int(np.sqrt(num_points)))
x, y = np.meshgrid(x, y)
z = np.zeros_like(x)
tri = mtri.Triangulation(x.flatten(), y.flatten())
faces = tri.triangles
faces_dual = faces[: ,[0, 2, 1]]
faces = np.vstack([faces, faces_dual])
vertices = np.array([x.flatten(), y.flatten(), z.flatten()]).T
plane = Trimesh(vertices=vertices, faces=faces)
return plane
def saddle(num_points=2500):
def f(x, y):
return x ** 2 - y ** 2
x = np.linspace(-1, 1, num=int(np.sqrt(num_points)))
y = np.linspace(-1, 1, num=int(np.sqrt(num_points)))
x, y = np.meshgrid(x, y)
z = f(x, y)
tri = mtri.Triangulation(x.flatten(), y.flatten())
faces = tri.triangles
faces_dual = faces[: ,[0, 2, 1]]
faces = np.vstack([faces, faces_dual])
vertices = np.array([x.flatten(), y.flatten(), z.flatten()]).T
saddle = Trimesh(vertices=vertices, faces=faces)
return saddle
def monkey_saddle(num_points=2500):
def f(x, y):
return x ** 3 - 3 * x * y ** 2
x = np.linspace(-1, 1, num=int(np.sqrt(num_points)))
y = np.linspace(-1, 1, num=int(np.sqrt(num_points)))
x, y = np.meshgrid(x, y)
z = f(x, y)
tri = mtri.Triangulation(x.flatten(), y.flatten())
faces = tri.triangles
faces_dual = faces[: ,[0, 2, 1]]
faces = np.vstack([faces, faces_dual])
vertices = np.array([x.flatten(), y.flatten(), z.flatten()]).T
saddle = Trimesh(vertices=vertices, faces=faces)
return saddle
def box(size=(1, 1, 1), max_edge=0.1):
box = trimesh.creation.box(extents=size)
vertices, faces = subdivide_to_size(box.vertices, box.faces, max_edge)
mesh = Trimesh(vertices, faces)
return mesh
def mesh_pcloud(points, size=0.1, color=None):
boxes = []
for point in points:
box = trimesh.creation.box(extents=(size, size, size))
box.apply_transform(translate([point - np.array([size/2, size/2, size/2])]))
if color is not None:
for facet in box.facets:
box.visual.face_colors[facet] = color
boxes += [box]
boxes = trimesh.util.concatenate(boxes)
return boxes
def set_new_mesh_vertices(mesh, vertices):
mesh_new = Trimesh(vertices=vertices.copy(), faces=mesh.faces, process=False)
return mesh_new
def affine_transform(mesh, transform):
mesh_new = mesh.copy()
mesh_new.apply_transform(transform)
return mesh_new
def rot_x(angle=0):
angle = angle * np.pi / 180
return np.array([[1, 0, 0, 0],
[0, np.cos(angle), -np.sin(angle), 0],
[0, np.sin(angle), np.cos(angle), 0],
[0, 0, 0, 1]])
def rot_y(angle=0):
angle = angle * np.pi / 180
return np.array([[np.cos(angle), 0, -np.sin(angle), 0],
[0, 1, 0, 0],
[np.sin(angle), 0, np.cos(angle), 0],
[0, 0, 0, 1]])
def rot_z(angle=0):
angle = angle * np.pi / 180
return np.array([[np.cos(angle), -np.sin(angle), 0, 0],
[np.sin(angle), np.cos(angle), 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
def translate(vector=(0, 0, 0)):
transform = np.eye(4, dtype=float)
transform[:3, 3] = np.array(vector)
return transform
def scale(scale=(1, 1, 1)):
transform = np.eye(4, dtype=float)
transform[0, 0] = np.array([scale[0]])
transform[1, 1] = np.array([scale[1]])
transform[2, 2] = np.array([scale[2]])
return transform
def compose(transforms):
identity = np.eye(4, dtype=float)
for transform in transforms:
identity = transform @ identity
return identity
def remove_duplicate_vertices(mesh):
unique_vertices, unique_inverse = np.unique(mesh.vertices, axis=0, return_inverse=True)
old2new_vertices = dict(zip(np.arange(len(mesh.vertices)), unique_inverse))
new_faces = np.copy(mesh.faces)
for i, face in enumerate(new_faces):
new_face = np.array([old2new_vertices[face[0]], old2new_vertices[face[1]], old2new_vertices[face[2]]])
new_faces[i] = new_face
new_mesh = Trimesh(unique_vertices, new_faces, process=False)
return new_mesh, old2new_vertices
def mesh_subsample(mesh, vertices):
num_vertices = len(vertices)
new_faces = []
for face in mesh.faces:
if (face[0] < num_vertices) and (face[1] < num_vertices) and (face[2] < num_vertices):
new_faces += [face]
new_mesh = Trimesh(vertices, new_faces)
return new_mesh
def pcloud_subsample(points, num=100):
if num > len(points):
num = len(points)
points = np.array(points)
new_points = [points[0]]
new_points_numpy = | np.array(new_points) | numpy.array |
#####
# some functions are borrowed from https://github.com/taigw/brats17/
#####
import nibabel
import numpy as np
import random
import os
import SimpleITK as sitk
import pickle
from scipy import ndimage
import config
import copy
def flip_lr(data):
data = copy.deepcopy(data)
img = data['images']
img = np.transpose(img, [3, 0 ,1, 2])
weight = data['weights'][:,:,:,0]
flipped_data = []
for moda in range(len(img)):
flipped_data.append(np.flip(img[moda], axis=-1))
flipped_data = np.array(flipped_data)
weight = np.flip(weight, axis=-1)
data['images'] = np.transpose(flipped_data, [1, 2, 3, 0])
data['weights'] = np.transpose(weight[np.newaxis, ...], [1, 2, 3, 0])
data['is_flipped'] = True
return data
def crop_brain_region(im, gt, with_gt=True):
mods = sorted(im.keys())
volume_list = []
for mod_idx, mod in enumerate(mods):
filename = im[mod]
volume = load_nifty_volume_as_array(filename, with_header=False)
# 155 244 244
if mod_idx == 0:
# contain whole tumor
margin = 5 # small padding value
original_shape = volume.shape
bbmin, bbmax = get_none_zero_region(volume, margin)
volume = crop_ND_volume_with_bounding_box(volume, bbmin, bbmax)
if mod_idx == 0:
weight = np.asarray(volume > 0, np.float32)
if config.INTENSITY_NORM == 'modality':
volume = itensity_normalize_one_volume(volume)
volume_list.append(volume)
## volume_list [(depth, h, w)*4]
if with_gt:
label = load_nifty_volume_as_array(gt, False)
if config.NUM_CLASS == 4:
label[label == 4] = 3
else:
label[label == 4] = 1
label[label == 2] = 1
label = crop_ND_volume_with_bounding_box(label, bbmin, bbmax)
return volume_list, label, weight, original_shape, [bbmin, bbmax]
else:
return volume_list, None, weight, original_shape, [bbmin, bbmax]
def load_pancreas_img(im, gt, with_gt=True):
volume_list = []
filename = im
volume = load_nifty_volume_as_array(filename, with_header=False)
weight = np.ones_like(volume, np.float32)
if config.INTENSITY_NORM == 'modality':
volume = itensity_rescaling_one_volume(volume)
volume_list.append(volume)
if with_gt:
label = load_nifty_volume_as_array(gt, False)
return volume_list, label, weight
else:
return volume_list, None, weight
def transpose_volumes(volumes, slice_direction):
"""
transpose a list of volumes
inputs:
volumes: a list of nd volumes
slice_direction: 'axial', 'sagittal', or 'coronal'
outputs:
tr_volumes: a list of transposed volumes
"""
if (slice_direction == 'axial'):
tr_volumes = volumes
elif(slice_direction == 'sagittal'):
if isinstance(volumes, list) or len(volumes.shape) > 3:
tr_volumes = [np.transpose(x, (2, 0, 1)) for x in volumes]
else:
tr_volumes = np.transpose(volumes, (2, 0, 1))
elif(slice_direction == 'coronal'):
if isinstance(volumes, list) or len(volumes.shape) > 3:
tr_volumes = [np.transpose(x, (1, 0, 2)) for x in volumes]
else:
tr_volumes = np.transpose(volumes, (1, 0, 2))
else:
print('undefined slice direction:', slice_direction)
tr_volumes = volumes
return tr_volumes
def remove_external_core(lab_main, lab_ext):
"""
remove the core region that is outside of whole tumor
"""
# for each component of lab_ext, compute the overlap with lab_main
s = ndimage.generate_binary_structure(3,2) # iterate structure
labeled_array, numpatches = ndimage.label(lab_ext,s) # labeling
sizes = ndimage.sum(lab_ext,labeled_array,range(1,numpatches+1))
sizes_list = [sizes[i] for i in range(len(sizes))]
new_lab_ext = np.zeros_like(lab_ext)
for i in range(len(sizes)):
sizei = sizes_list[i]
labeli = np.where(sizes == sizei)[0] + 1
componenti = labeled_array == labeli
overlap = componenti * lab_main
if((overlap.sum()+ 0.0)/sizei >= 0.5):
new_lab_ext = np.maximum(new_lab_ext, componenti)
return new_lab_ext
def get_largest_two_component(img, print_info = False, threshold = None):
"""
Get the largest two components of a binary volume
inputs:
img: the input 3D volume
threshold: a size threshold
outputs:
out_img: the output volume
"""
s = ndimage.generate_binary_structure(3,2) # iterate structure
labeled_array, numpatches = ndimage.label(img,s) # labeling
sizes = ndimage.sum(img,labeled_array,range(1,numpatches+1))
sizes_list = [sizes[i] for i in range(len(sizes))]
sizes_list.sort()
if(print_info):
print('component size', sizes_list)
if(len(sizes) == 1):
out_img = img
else:
if(threshold):
out_img = np.zeros_like(img)
for temp_size in sizes_list:
if(temp_size > threshold):
temp_lab = np.where(sizes == temp_size)[0] + 1
temp_cmp = labeled_array == temp_lab
out_img = (out_img + temp_cmp) > 0
return out_img
else:
max_size1 = sizes_list[-1]
max_size2 = sizes_list[-2]
max_label1 = np.where(sizes == max_size1)[0] + 1
max_label2 = np.where(sizes == max_size2)[0] + 1
component1 = labeled_array == max_label1
component2 = labeled_array == max_label2
if(max_size2*10 > max_size1):
component1 = (component1 + component2) > 0
out_img = component1
return out_img
def get_ND_bounding_box(label, margin):
"""
get the bounding box of the non-zero region of an ND volume
"""
input_shape = label.shape
if(type(margin) is int ):
margin = [margin]*len(input_shape)
assert(len(input_shape) == len(margin))
indxes = np.nonzero(label)
idx_min = []
idx_max = []
for i in range(len(input_shape)):
idx_min.append(indxes[i].min())
idx_max.append(indxes[i].max())
for i in range(len(input_shape)):
idx_min[i] = max(idx_min[i] - margin[i], 0)
idx_max[i] = min(idx_max[i] + margin[i], input_shape[i] - 1)
return idx_min, idx_max
def set_ND_volume_roi_with_bounding_box_range(volume, bb_min, bb_max, sub_volume):
"""
set a subregion to an nd image.
"""
dim = len(bb_min)
out = volume
if(dim == 2):
out[np.ix_(range(bb_min[0], bb_max[0] + 1),
range(bb_min[1], bb_max[1] + 1))] = sub_volume
elif(dim == 3):
out[np.ix_(range(bb_min[0], bb_max[0] + 1),
range(bb_min[1], bb_max[1] + 1),
range(bb_min[2], bb_max[2] + 1))] = sub_volume
elif(dim == 4):
out[np.ix_(range(bb_min[0], bb_max[0] + 1),
range(bb_min[1], bb_max[1] + 1),
range(bb_min[2], bb_max[2] + 1),
range(bb_min[3], bb_max[3] + 1))] = sub_volume
else:
raise ValueError("array dimension should be 2, 3 or 4")
return out
def convert_label(in_volume, label_convert_source, label_convert_target):
"""
convert the label value in a volume
inputs:
in_volume: input nd volume with label set label_convert_source
label_convert_source: a list of integers denoting input labels, e.g., [0, 1, 2, 4]
label_convert_target: a list of integers denoting output labels, e.g.,[0, 1, 2, 3]
outputs:
out_volume: the output nd volume with label set label_convert_target
"""
mask_volume = np.zeros_like(in_volume)
convert_volume = np.zeros_like(in_volume)
for i in range(len(label_convert_source)):
source_lab = label_convert_source[i]
target_lab = label_convert_target[i]
if(source_lab != target_lab):
temp_source = np.asarray(in_volume == source_lab)
temp_target = target_lab * temp_source
mask_volume = mask_volume + temp_source
convert_volume = convert_volume + temp_target
out_volume = in_volume * 1
out_volume[mask_volume>0] = convert_volume[mask_volume>0]
return out_volume
def set_roi_to_volume(volume, center, sub_volume):
"""
set the content of an roi of a 3d/4d volume to a sub volume
inputs:
volume: the input 3D/4D volume
center: the center of the roi
sub_volume: the content of sub volume
outputs:
output_volume: the output 3D/4D volume
"""
volume_shape = volume.shape
patch_shape = sub_volume.shape
output_volume = volume
for i in range(len(center)):
if(center[i] >= volume_shape[i]):
return output_volume
r0max = [int(x/2) for x in patch_shape]
r1max = [patch_shape[i] - r0max[i] for i in range(len(r0max))]
r0 = [min(r0max[i], center[i]) for i in range(len(r0max))]
r1 = [min(r1max[i], volume_shape[i] - center[i]) for i in range(len(r0max))]
patch_center = r0max
if(len(center) == 3):
output_volume[np.ix_(range(center[0] - r0[0], center[0] + r1[0]),
range(center[1] - r0[1], center[1] + r1[1]),
range(center[2] - r0[2], center[2] + r1[2]))] = \
sub_volume[np.ix_(range(patch_center[0] - r0[0], patch_center[0] + r1[0]),
range(patch_center[1] - r0[1], patch_center[1] + r1[1]),
range(patch_center[2] - r0[2], patch_center[2] + r1[2]))]
elif(len(center) == 4):
output_volume[np.ix_(range(center[0] - r0[0], center[0] + r1[0]),
range(center[1] - r0[1], center[1] + r1[1]),
range(center[2] - r0[2], center[2] + r1[2]),
range(center[3] - r0[3], center[3] + r1[3]))] = \
sub_volume[np.ix_(range(patch_center[0] - r0[0], patch_center[0] + r1[0]),
range(patch_center[1] - r0[1], patch_center[1] + r1[1]),
range(patch_center[2] - r0[2], patch_center[2] + r1[2]),
range(patch_center[3] - r0[3], patch_center[3] + r1[3]))]
else:
raise ValueError("array dimension should be 3 or 4")
return output_volume
def binary_dice3d(s,g):
"""
dice score of 3d binary volumes
inputs:
s: segmentation volume
g: ground truth volume
outputs:
dice: the dice score
"""
assert(len(s.shape)==3)
[Ds, Hs, Ws] = s.shape
[Dg, Hg, Wg] = g.shape
assert(Ds==Dg and Hs==Hg and Ws==Wg)
prod = np.multiply(s, g)
s0 = prod.sum()
s1 = s.sum()
s2 = g.sum()
dice = (2.0*s0 + 1e-10)/(s1 + s2 + 1e-10)
return dice
def load_nifty_volume_as_array(filename, with_header = False):
"""
load nifty image into numpy array, and transpose it based on the [z,y,x] axis order
The output array shape is like [Depth, Height, Width]
inputs:
filename: the input file name, should be *.nii or *.nii.gz
with_header: return affine and hearder infomation
outputs:
data: a numpy data array
"""
img = nibabel.load(filename)
data = img.get_data()
data = np.transpose(data, [2,1,0])
if(with_header):
return data, img.affine, img.header
else:
return data
def get_none_zero_region(im, margin):
"""
get the bounding box of the non-zero region of an ND volume
"""
input_shape = im.shape
if(type(margin) is int ):
margin = [margin]*len(input_shape)
assert(len(input_shape) == len(margin))
indxes = np.nonzero(im)
idx_min = []
idx_max = []
for i in range(len(input_shape)):
idx_min.append(indxes[i].min())
idx_max.append(indxes[i].max())
for i in range(len(input_shape)):
idx_min[i] = max(idx_min[i] - margin[i], 0)
idx_max[i] = min(idx_max[i] + margin[i], input_shape[i] - 1)
return idx_min, idx_max
def itensity_normalize_one_volume(volume):
"""
normalize the itensity of an nd volume based on the mean and std of nonzeor region
inputs:
volume: the input nd volume
outputs:
out: the normalized nd volume
"""
pixels = volume[volume > 0]
mean = pixels.mean()
std = pixels.std()
out = (volume - mean)/std
# random normal too slow
#out_random = np.random.normal(0, 1, size = volume.shape)
out_random = np.zeros(volume.shape)
out[volume == 0] = out_random[volume == 0]
return out
def itensity_rescaling_one_volume(volume):
"""
Rescaling the itensity of an nd volume based on max and min value
inputs:
volume: the input nd volume
outputs:
out: the normalized nd volume
"""
out = (volume + 100) / 340
return out
def crop_ND_volume_with_bounding_box(volume, min_idx, max_idx):
"""
crop/extract a subregion form an nd image.
"""
dim = len(volume.shape)
assert(dim >= 2 and dim <= 5)
if(dim == 2):
output = volume[np.ix_(range(min_idx[0], max_idx[0] + 1),
range(min_idx[1], max_idx[1] + 1))]
elif(dim == 3):
output = volume[np.ix_(range(min_idx[0], max_idx[0] + 1),
range(min_idx[1], max_idx[1] + 1),
range(min_idx[2], max_idx[2] + 1))]
elif(dim == 4):
output = volume[np.ix_(range(min_idx[0], max_idx[0] + 1),
range(min_idx[1], max_idx[1] + 1),
range(min_idx[2], max_idx[2] + 1),
range(min_idx[3], max_idx[3] + 1))]
elif(dim == 5):
output = volume[np.ix_(range(min_idx[0], max_idx[0] + 1),
range(min_idx[1], max_idx[1] + 1),
range(min_idx[2], max_idx[2] + 1),
range(min_idx[3], max_idx[3] + 1),
range(min_idx[4], max_idx[4] + 1))]
else:
raise ValueError("the dimension number shoud be 2 to 5")
return output
def get_random_roi_sampling_center(input_shape, output_shape, sample_mode='full', bounding_box = None):
"""
get a random coordinate representing the center of a roi for sampling
inputs:
input_shape: the shape of sampled volume
output_shape: the desired roi shape
sample_mode: 'valid': the entire roi should be inside the input volume
'full': only the roi centre should be inside the input volume
bounding_box: the bounding box which the roi center should be limited to
outputs:
center: the output center coordinate of a roi
"""
center = []
for i in range(len(input_shape)):
if(sample_mode[i] == 'full'):
if(bounding_box):
x0 = bounding_box[i*2]; x1 = bounding_box[i*2 + 1]
else:
x0 = 0; x1 = input_shape[i]
else:
if(bounding_box):
x0 = bounding_box[i*2] + int(output_shape[i]/2)
x1 = bounding_box[i*2+1] - int(output_shape[i]/2)
else:
x0 = int(output_shape[i]/2)
x1 = input_shape[i] - x0
if(x1 <= x0):
centeri = int((x0 + x1)/2)
else:
centeri = random.randint(x0, x1)
center.append(centeri)
return center
def extract_roi_from_volume(volume, in_center, output_shape, fill = 'random'):
"""
extract a roi from a 3d volume
inputs:
volume: the input 3D volume
in_center: the center of the roi
output_shape: the size of the roi
fill: 'random' or 'zero', the mode to fill roi region where is outside of the input volume
outputs:
output: the roi volume
"""
input_shape = volume.shape
if(fill == 'random'):
#output = np.random.normal(0, 1, size = output_shape)
output = np.random.random_sample(size = output_shape)
else:
output = | np.zeros(output_shape) | numpy.zeros |
import ctypes
from ctypes import c_int, c_uint8, c_uint16, c_uint32, c_int32, c_float, c_char_p, c_void_p, c_long, windll, CDLL, POINTER
import os
import numpy as np
import time
import logging
# add logger, to allow logging to Labber's instrument log
log = logging.getLogger('AlazarTech')
# define constants
ADMA_NPT = 0x200
ADMA_EXTERNAL_STARTCAPTURE = 0x1
sample_rate_id = {
'1 kS/s': 0x01,
'10 kS/s': 0x08,
'20 kS/s': 0x0A,
'50 kS/s': 0x0C,
'100 kS/s': 0x0E,
'200 kS/s': 0x10,
'500 kS/s': 0x12,
'1 MS/s': 0x14,
'2 MS/s': 0x18,
'5 MS/s': 0x1A,
'10 MS/s': 0x1C,
'20 MS/s': 0x1E,
'50 MS/s': 0x22,
'100 MS/s': 0x24,
'125 MS/s': 0x25,
}
try:
# For Python 3
sample_rate = {v: int(float(k.replace(" kS/s", "E3").replace(" MS/s", "E6"))) for k, v in sample_rate_id.items()}
except:
# For Python 2
sample_rate = dict((v, int(float(k.replace(" kS/s", "E3").replace(" MS/s", "E6")))) for k, v in sample_rate_id.iteritems())
input_range = {
'20 mV': 1,
'40 mV': 2,
'50 mV': 3,
'80 mV': 4,
'100 mV': 5,
'200 mV': 6,
'400 mV': 7,
'500 mV': 8,
'800 mV': 9,
'1 V': 10,
'2 V': 11,
'4 V': 12,
'5 V': 13,
'8 V': 14,
'10 V': 15,
}
class DMABuffer:
""""Buffer for DMA"""
def __init__(self, c_sample_type, size_bytes):
self.size_bytes = size_bytes
npSampleType = {
c_uint8: np.uint8,
c_uint16: np.uint16,
c_uint32: np.uint32,
c_int32: np.int32,
c_float: np.float32
}.get(c_sample_type, 0)
bytes_per_sample = {
c_uint8: 1,
c_uint16: 2,
c_uint32: 4,
c_int32: 4,
c_float: 4
}.get(c_sample_type, 0)
self.addr = None
if os.name == 'nt':
MEM_COMMIT = 0x1000
PAGE_READWRITE = 0x4
windll.kernel32.VirtualAlloc.argtypes = [c_void_p, c_long, c_long, c_long]
windll.kernel32.VirtualAlloc.restype = c_void_p
self.addr = windll.kernel32.VirtualAlloc(
0, c_long(size_bytes), MEM_COMMIT, PAGE_READWRITE)
elif os.name == 'posix':
libc = CDLL("libc.so.6")
libc.valloc.argtypes = [c_long]
libc.valloc.restype = c_void_p
self.addr = libc.valloc(size_bytes)
else:
raise Exception("Unsupported OS")
ctypes_array = (c_sample_type * (size_bytes // bytes_per_sample)).from_address(self.addr)
self.buffer = np.frombuffer(ctypes_array, dtype=npSampleType)
self.ctypes_buffer = ctypes_array
pointer, read_only_flag = self.buffer.__array_interface__['data']
def __exit__(self):
if os.name == 'nt':
MEM_RELEASE = 0x8000
windll.kernel32.VirtualFree.argtypes = [c_void_p, c_long, c_long]
windll.kernel32.VirtualFree.restype = c_int
windll.kernel32.VirtualFree(c_void_p(self.addr), 0, MEM_RELEASE)
elif os.name == 'posix':
libc = CDLL("libc.so.6")
libc.free(self.addr)
else:
raise Exception("Unsupported OS")
# error type returned by this class
class Error(Exception):
pass
class TimeoutError(Error):
pass
class Digitizer():
"""Represent the Alazartech digitizer, redefines the dll functions in python"""
_success = 512
_error_codes = {
513: 'ApiFailed',
514: 'ApiAccessDenied',
515: 'ApiDmaChannelUnavailable',
516: 'ApiDmaChannelInvalid',
517: 'ApiDmaChannelTypeError',
518: 'ApiDmaInProgress',
519: 'ApiDmaDone',
520: 'ApiDmaPaused',
521: 'ApiDmaNotPaused',
522: 'ApiDmaCommandInvalid',
523: 'ApiDmaManReady',
524: 'ApiDmaManNotReady',
525: 'ApiDmaInvalidChannelPriority',
526: 'ApiDmaManCorrupted',
527: 'ApiDmaInvalidElementIndex',
528: 'ApiDmaNoMoreElements',
529: 'ApiDmaSglInvalid',
530: 'ApiDmaSglQueueFull',
531: 'ApiNullParam',
532: 'ApiInvalidBusIndex',
533: 'ApiUnsupportedFunction',
534: 'ApiInvalidPciSpace',
535: 'ApiInvalidIopSpace',
536: 'ApiInvalidSize',
537: 'ApiInvalidAddress',
538: 'ApiInvalidAccessType',
539: 'ApiInvalidIndex',
540: 'ApiMuNotReady',
541: 'ApiMuFifoEmpty',
542: 'ApiMuFifoFull',
543: 'ApiInvalidRegister',
544: 'ApiDoorbellClearFailed',
545: 'ApiInvalidUserPin',
546: 'ApiInvalidUserState',
547: 'ApiEepromNotPresent',
548: 'ApiEepromTypeNotSupported',
549: 'ApiEepromBlank',
550: 'ApiConfigAccessFailed',
551: 'ApiInvalidDeviceInfo',
552: 'ApiNoActiveDriver',
553: 'ApiInsufficientResources',
554: 'ApiObjectAlreadyAllocated',
555: 'ApiAlreadyInitialized',
556: 'ApiNotInitialized',
557: 'ApiBadConfigRegEndianMode',
558: 'ApiInvalidPowerState',
559: 'ApiPowerDown',
560: 'ApiFlybyNotSupported',
561: 'ApiNotSupportThisChannel',
562: 'ApiNoAction',
563: 'ApiHSNotSupported',
564: 'ApiVPDNotSupported',
565: 'ApiVpdNotEnabled',
566: 'ApiNoMoreCap',
567: 'ApiInvalidOffset',
568: 'ApiBadPinDirection',
569: 'ApiPciTimeout',
570: 'ApiDmaChannelClosed',
571: 'ApiDmaChannelError',
572: 'ApiInvalidHandle',
573: 'ApiBufferNotReady',
574: 'ApiInvalidData',
575: 'ApiDoNothing',
576: 'ApiDmaSglBuildFailed',
577: 'ApiPMNotSupported',
578: 'ApiInvalidDriverVersion',
579: ('ApiWaitTimeout: operation did not finish during '
'timeout interval. Check your trigger.'),
580: 'ApiWaitCanceled',
581: 'ApiBufferTooSmall',
582: ('ApiBufferOverflow:rate of acquiring data > rate of '
'transferring data to local memory. Try reducing sample rate, '
'reducing number of enabled channels, increasing size of each '
'DMA buffer or increase number of DMA buffers.'),
583: 'ApiInvalidBuffer',
584: 'ApiInvalidRecordsPerBuffer',
585: ('ApiDmaPending:Async I/O operation was successfully started, '
'it will be completed when sufficient trigger events are '
'supplied to fill the buffer.'),
586: ('ApiLockAndProbePagesFailed:Driver or operating system was '
'unable to prepare the specified buffer for DMA transfer. '
'Try reducing buffer size or total number of buffers.'),
587: 'ApiWaitAbandoned',
588: 'ApiWaitFailed',
589: ('ApiTransferComplete:This buffer is last in the current '
'acquisition.'),
590: 'ApiPllNotLocked:hardware error, contact AlazarTech',
591: ('ApiNotSupportedInDualChannelMode:Requested number of samples '
'per channel is too large to fit in on-board memory. Try '
'reducing number of samples per channel, or switch to '
'single channel mode.')
}
_board_names = {
1: 'ATS850',
2: 'ATS310',
3: 'ATS330',
4: 'ATS855',
5: 'ATS315',
6: 'ATS335',
7: 'ATS460',
8: 'ATS860',
9: 'ATS660',
10: 'ATS665',
11: 'ATS9462',
12: 'ATS9434',
13: 'ATS9870',
14: 'ATS9350',
15: 'ATS9325',
16: 'ATS9440',
17: 'ATS9410',
18: 'ATS9351',
19: 'ATS9310',
20: 'ATS9461',
21: 'ATS9850',
22: 'ATS9625',
23: 'ATG6500',
24: 'ATS9626',
25: 'ATS9360',
26: 'AXI9870',
27: 'ATS9370',
28: 'ATU7825',
29: 'ATS9373',
30: 'ATS9416'
}
def __init__(self, systemId=1, boardId=1, timeout=10.0):
"""The init case defines a session ID, used to identify the instrument"""
# range settings; default value of 400mV for 9373;
# will be overwritten if model is 9870 and AlazarInputControl called
self.input_range = {1: 0.4, 2: 0.4}
self.buffers = []
self.timeout = timeout
# create a session id
try:
self._ATS_dll = ctypes.cdll.LoadLibrary('ATSApi')
except:
# if failure, try to open in driver folder
sPath = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'atsapi')
self._ATS_dll = ctypes.CDLL(os.path.join(sPath, 'ATSApi'))
self._handle = self._ATS_dll.AlazarGetBoardBySystemID(systemId, boardId)
if not self._handle:
raise Exception('AlazarTech_ATS not found at system {}, board {}'.format(systemId, boardId))
# func = getattr(self._ATS_dll, 'AlazarNumOfSystems')
# func.restype = c_uint32
# func = getattr(self._ATS_dll, 'AlazarGetBoardBySystemID')
# func.restype = c_void_p
# handle = func(c_uint32(systemId), c_uint32(boardId))
if self._handle is None:
raise Error('Device with system ID=%d and board ID=%d could not be found.' % (systemId, boardId))
# get mem and bitsize
(self.memorySize_samples, self.bitsPerSample) = self.get_channel_info(self._handle)
def find_boards(cls, dll_path=None):
"""
Find Alazar boards connected
Args:
dll_path: (string) path of the Alazar driver dll
Returns:
list: list of board info for each connected board
"""
system_count = cls._ATS_dll.AlazarNumOfSystems()
boards = []
for system_id in range(1, system_count + 1):
board_count = cls._ATS_dll.AlazarBoardsInSystemBySystemID(system_id)
for board_id in range(1, board_count + 1):
boards.append(cls.get_board_info(cls._ATS_dll, system_id, board_id))
return boards
def get_board_info(self, system_id, board_id):
"""
Get the information from a connected Alazar board
Args:
dll (string): path of the Alazar driver dll
system_id: id of the Alazar system
board_id: id of the board within the alazar system
Return:
Dictionary containing
- system_id
- board_id
- board_kind (as string)
- max_samples
- bits_per_sample
"""
# make a temporary instrument for this board, to make it easier
# to get its info
board_kind = self._board_names[self._ATS_dll.AlazarGetBoardKind(self._handle)]
max_s, bps = self.get_channel_info(self._handle)
return {
'system_id': system_id,
'board_id': board_id,
'board_kind': board_kind,
'max_samples': max_s,
'bits_per_sample': bps
}
def get_channel_info(self, handle):
memorySize = np.array([0], dtype=np.uint32) # memorySize memory size in samples
bitsPerSample = np.array([0], dtype=np.uint8) # bitsPerSample bits per sample
memorySize_ptr = memorySize.ctypes.data_as(POINTER(c_uint32))
bitsPerSample_ptr = bitsPerSample.ctypes.data_as(POINTER(c_uint8))
# self._ATS_dll.AlazarGetChannelInfo(handle, memorySize.ctypes.data, bitsPerSample.ctypes.data)
self._ATS_dll.AlazarGetChannelInfo(handle, memorySize_ptr, bitsPerSample_ptr)
return memorySize[0], bitsPerSample[0]
def testLED(self):
import time
self._call_dll('AlazarSetLED', self._handle, c_uint32(1))
time.sleep(0.1)
self._call_dll('AlazarSetLED', self._handle, c_uint32(0))
def _call_dll(self, func_name, *args):
"""General function caller with restype=status, also checks for errors"""
# get function from DLL
args_out = []
for arg in args:
args_out.append(arg)
func = getattr(self._ATS_dll, func_name)
return_code = func(*args_out)
# check for errors
if (return_code != self._success) and (return_code != 518):
# TODO(damazter) (C) log error
argrepr = repr(args_out)
if len(argrepr) > 100:
argrepr = argrepr[:96] + '...]'
if return_code not in self._error_codes:
raise RuntimeError(
'unknown error {} from function {} with args: {}'.format(
return_code, func_name, argrepr))
raise RuntimeError(
'error {}: {} from function {} with args: {}'.format(
return_code, self._error_codes[return_code], func_name, argrepr))
def getError(self, status):
"""Convert the error in status to a string"""
func = getattr(self._ATS_dll, 'AlazarErrorToText')
func.restype = c_char_p
# const char* AlazarErrorToText(RETURN_CODE retCode)
errorText = func(c_int(status))
return str(errorText)
def AlazarGetChannelInfo(self):
"""Get the on-board memory in samples per channel and sample size in bits per sample"""
memorySize_samples = c_uint32(0)
bitsPerSample = c_uint8(0)
self._call_dll('AlazarGetChannelInfo', self._handle)
return (int(memorySize_samples.value), int(bitsPerSample.value))
def AlazarSetCaptureClock(self, SourceId, SampleRateId, EdgeId=0, Decimation=0):
# sample_rate: {0x01: 1e3, 0x08: 10e3, 0x0A: 20e3, 0x0C: 50e3, 0x0E: 100e3, 0x10: 200e3, 0x12: 500e3, 0x14: 1e6, 0x18: 2e6, 0x1A: 5e6, 0x1C: 10e6, 0x1E: 20e6, 0x22: 50e6, 0x24: 100e6, 0x25: 125e6}
self.sample_rate = sample_rate[SampleRateId]
self._call_dll('AlazarSetCaptureClock', self._handle, c_uint32(SourceId), c_uint32(SampleRateId), c_uint32(EdgeId), c_uint32(Decimation))
def AlazarInputControl(self, Channel, Coupling, InputRange, Impedance):
# keep track of input range
dConv = {15: 10.0, 14: 8.0, 13: 5.0, 12: 4.0, 11: 2.0, 10: 1.0, 9: 0.8, 8: 0.5, 7: 0.4, 6: 0.2, 5: 0.1, 4: 0.08, 3: 0.05, 2: 0.04, 1: 0.02}
self.input_range[Channel] = dConv[InputRange]
self._call_dll('AlazarInputControl', self._handle, c_uint8(Channel), c_uint32(Coupling), c_uint32(InputRange), c_uint32(Impedance))
def AlazarSetBWLimit(self, Channel, enable):
self._call_dll('AlazarSetBWLimit', self._handle, c_uint32(Channel), c_uint32(enable))
def AlazarSetParameter(self, Channel, parameter, value):
self._call_dll('AlazarSetParameter', self._handle, c_uint8(Channel), c_uint32(parameter), c_long(value))
def AlazarSetParameterUL(self, Channel, parameter, value):
self._call_dll('AlazarSetParameter', self._handle, c_uint8(Channel), c_uint32(parameter), c_uint32(value))
def AlazarGetParameter(self, Channel, parameter):
value = c_long(0)
self._call_dll('AlazarSetParameter', self._handle, c_uint8(Channel), c_uint32(parameter), c_uint32(value))
return value.value
def AlazarSetTriggerOperation(self, TriggerOperation=0,
TriggerEngine1=0, Source1=0, Slope1=1, Level1=128,
TriggerEngine2=1, Source2=3, Slope2=1, Level2=128):
"""Configure the trigger engines of a board to use an external trigger inputand, optionally, synchronize the start of an acquisition with the next external trigger event after AlazarStartCaptureis called
Slope:
1: Positive slope
2: Nevative slope
Level: Specify a trigger level code representing the trigger level in volts that an external trigger signal connected must pass through to generate a trigger event.
"""
self._call_dll('AlazarSetTriggerOperation', self._handle, c_uint32(TriggerOperation),
c_uint32(TriggerEngine1), c_uint32(Source1), c_uint32(Slope1), c_uint32(Level1),
c_uint32(TriggerEngine2), c_uint32(Source2), c_uint32(Slope2), c_uint32(Level2))
def AlazarSetExternalTrigger(self, Coupling, Range=0):
self._call_dll('AlazarSetExternalTrigger', self._handle, c_uint32(Coupling), c_uint32(Range))
def AlazarSetTriggerDelay(self, Delay=0):
self._call_dll('AlazarSetTriggerDelay', self._handle, c_uint32(Delay))
def AlazarSetTriggerTimeOut(self, time=0.0):
tick = c_uint32(int(time * 1E5))
self._call_dll('AlazarSetTriggerTimeOut', self._handle, tick)
def AlazarSetRecordSize(self, PreSize, PostSize):
self.nPreSize = int(PreSize)
self.nPostSize = int(PostSize)
self._call_dll('AlazarSetRecordSize', self._handle, c_uint32(PreSize), c_uint32(PostSize))
def AlazarSetRecordCount(self, Count):
self.nRecord = int(Count)
self._call_dll('AlazarSetRecordCount', self._handle, c_uint32(Count))
def AlazarStartCapture(self):
self._call_dll('AlazarStartCapture', self._handle)
def AlazarAbortCapture(self):
self._call_dll('AlazarAbortCapture', self._handle)
# c_uint32 AlazarBusy( HANDLE h);
def AlazarBusy(self):
# get function from DLL
func = getattr(self._ATS_dll, 'AlazarBusy')
func.restype = c_uint32
# call function, return result
return bool(func(self._handle))
def AlazarRead(self, Channel, buffer, ElementSize, Record, TransferOffset, TransferLength):
self._call_dll('AlazarRead', self._handle,
c_uint32(Channel), buffer, c_int(ElementSize),
c_long(Record), c_long(TransferOffset), c_uint32(TransferLength))
def AlazarBeforeAsyncRead(self, channels, transferOffset, samplesPerRecord, recordsPerBuffer, recordsPerAcquisition, flags):
"""Prepares the board for an asynchronous acquisition."""
self._call_dll('AlazarBeforeAsyncRead', self._handle, channels, transferOffset, samplesPerRecord, recordsPerBuffer, recordsPerAcquisition, flags)
def AlazarAbortAsyncRead(self):
"""Cancels any asynchronous acquisition running on a board."""
self._call_dll('AlazarAbortAsyncRead', self._handle)
def AlazarPostAsyncBuffer(self, buffer, bufferLength):
"""Posts a DMA buffer to a board."""
self._call_dll('AlazarPostAsyncBuffer', self._handle, buffer, bufferLength)
def AlazarWaitAsyncBufferComplete(self, buffer, timeout_ms):
"""Blocks until the board confirms that buffer is filled with data."""
self._call_dll('AlazarWaitAsyncBufferComplete', self._handle, buffer, timeout_ms)
def readTracesDMA(self, bGetCh1, bGetCh2, nSamples, nRecord, nBuffer, nAverage=1,
bConfig=True, bArm=True, bMeasure=True,
funcStop=None, funcProgress=None, timeout=None, bufferSize=512,
firstTimeout=None, maxBuffers=1024):
"""read traces in NPT AutoDMA mode, convert to float, average to single trace"""
t0 = time.clock()
lT = []
# use global timeout if not given
timeout = self.timeout if timeout is None else timeout
# first timeout can be different in case of slow initial arming
firstTimeout = timeout if firstTimeout is None else firstTimeout
# Select the number of pre-trigger samples...not supported in NPT, keeping for consistency
preTriggerSamplesValue = 0
# change alignment to be 128
if preTriggerSamplesValue > 0:
preTriggerSamples = int(np.ceil(preTriggerSamplesValue / 128.) * 128)
else:
preTriggerSamples = 0
# Select the number of samples per record.
postTriggerSamplesValue = nSamples
# change alignment to be 128
postTriggerSamples = int(np.ceil(postTriggerSamplesValue / 128.) * 128)
samplesPerRecordValue = preTriggerSamplesValue + postTriggerSamplesValue
# Select the number of records per DMA buffer.
nRecordTotal = nRecord * nAverage
if nRecord > 1:
# if multiple records wanted, set records per buffer to match
recordsPerBuffer = nRecord
else:
# else, use 100 records per buffers
recordsPerBuffer = nBuffer
buffersPerAcquisition = int(np.ceil(nRecordTotal / float(recordsPerBuffer)))
if nRecordTotal < recordsPerBuffer:
recordsPerBuffer = nRecordTotal
# Select the active channels.
Channel1 = 1 if bGetCh1 else 0
Channel2 = 2 if bGetCh2 else 0
channels = Channel1 | Channel2
channelCount = 0
for n in range(16):
c = int(2**n)
channelCount += (c & channels == c)
# return directly if no active channels
if channelCount == 0:
return [np.array([], dtype=float), np.array([], dtype=float)]
# Compute the number of bytes per record and per buffer
bytesPerSample = (self.bitsPerSample + 7) // 8
samplesPerRecord = preTriggerSamples + postTriggerSamples
bytesPerRecord = bytesPerSample * samplesPerRecord
bytesPerBuffer = bytesPerRecord * recordsPerBuffer * channelCount
# force buffer size to be integer of 256 * 16 = 4096, not sure why
bytesPerBufferMem = int(4096 * np.ceil(bytesPerBuffer / 4096.))
recordsPerAcquisition = recordsPerBuffer * buffersPerAcquisition
# TODO: Select number of DMA buffers to allocate
MEM_SIZE = int(bufferSize * 1024 * 1024)
# force buffer count to be even number, seems faster for allocating
maxBufferCount = int(MEM_SIZE // (2 * bytesPerBufferMem))
bufferCount = max(1, 2 * maxBufferCount)
# don't allocate more buffers than needed for all data
bufferCount = min(bufferCount, buffersPerAcquisition, maxBuffers)
lT.append('Total buffers needed: %d' % buffersPerAcquisition)
lT.append('Buffer count: %d' % bufferCount)
lT.append('Buffer size: %d' % bytesPerBuffer)
lT.append('Buffer size, memory: %d' % bytesPerBufferMem)
lT.append('Records per buffer: %d' % recordsPerBuffer)
# configure board, if wanted
if bConfig:
self.AlazarSetRecordSize(preTriggerSamples, postTriggerSamples)
self.AlazarSetRecordCount(recordsPerAcquisition)
# Allocate DMA buffers
sample_type = ctypes.c_uint8
if bytesPerSample > 1:
sample_type = ctypes.c_uint16
# clear old buffers
self.removeBuffersDMA()
# create new buffers
self.buffers = []
for i in range(bufferCount):
self.buffers.append(DMABuffer(sample_type, bytesPerBufferMem))
# arm and start capture, if wanted
if bArm:
# Configure the board to make a Traditional AutoDMA acquisition
self.AlazarBeforeAsyncRead(channels,
-preTriggerSamples,
samplesPerRecord,
recordsPerBuffer,
recordsPerAcquisition,
ADMA_EXTERNAL_STARTCAPTURE | ADMA_NPT)
# Post DMA buffers to board
for buf in self.buffers:
self.AlazarPostAsyncBuffer(buf.addr, buf.size_bytes)
try:
self.AlazarStartCapture()
except:
# make sure buffers release memory if failed
self.removeBuffersDMA()
raise
# if not waiting for result, return here
if not bMeasure:
return
lT.append('Post: %.1f ms' % ((time.clock() - t0) * 1000))
try:
lT.append('Start: %.1f ms' % ((time.clock() - t0) * 1000))
buffersCompleted = 0
bytesTransferred = 0
# initialize data array
nPtsOut = samplesPerRecord * nRecord
nAvPerBuffer = recordsPerBuffer / nRecord
vData = [np.zeros(nPtsOut, dtype=float), np.zeros(nPtsOut, dtype=float)]
# range and zero for conversion to voltages
codeZero = 2 ** (float(self.bitsPerSample) - 1) - 0.5
codeRange = 2 ** (float(self.bitsPerSample) - 1) - 0.5
# range and zero for each channel, combined with bit shifting
range1 = self.input_range[1] / codeRange / 16.
range2 = self.input_range[2] / codeRange / 16.
offset = 16. * codeZero
timeout_ms = int(firstTimeout * 1000)
log.info(str(lT))
lT = []
while (buffersCompleted < buffersPerAcquisition):
# Wait for the buffer at the head of the list of available
# buffers to be filled by the board.
buf = self.buffers[buffersCompleted % len(self.buffers)]
self.AlazarWaitAsyncBufferComplete(buf.addr, timeout_ms=timeout_ms)
# lT.append('Wait: %.1f ms' % ((time.clock() - t0) * 1000))
# reset timeout time, can be different than first call
timeout_ms = int(timeout * 1000)
buffersCompleted += 1
bytesTransferred += buf.size_bytes
# break if stopped from outside
if funcStop is not None and funcStop():
break
# report progress
if funcProgress is not None:
funcProgress(float(buffersCompleted) / float(buffersPerAcquisition))
# remove extra elements for getting even 256*16 buffer sizes
if bytesPerBuffer == bytesPerBufferMem:
buf_truncated = buf.buffer
else:
buf_truncated = buf.buffer[:(bytesPerBuffer // bytesPerSample)]
# reshape, sort and average data
if nAverage > 1:
if channels == 1:
rs = buf_truncated.reshape((nAvPerBuffer, nPtsOut))
vData[0] += range1 * (np.mean(rs, 0) - offset)
elif channels == 2:
rs = buf_truncated.reshape((nAvPerBuffer, nPtsOut))
vData[1] += range2 * ( | np.mean(rs, 0) | numpy.mean |
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Aug 7 11:13:37 2019
@author: aasl
"""
import numpy as np
import matplotlib.pyplot as plt
from scipy import signal
from sklearn.cluster import DBSCAN
from scipy.io.matlab import loadmat
from os.path import dirname, join
refractory_period = 54
def mode(vec):
return np.argmax(np.bincount(vec))
def filter_output_fir(detect, prediction):
##Filtering Stage 1
Ladj = len(detect)
start_sz = np.int32(np.round(100*np.sum(detect)/Ladj))
# start_sz = 8
remainder = start_sz % 2
if remainder == 1:
filter_size = np.max([start_sz, 3])
else:
filter_size = np.max([start_sz-1, 3])
b = 1/filter_size * np.ones(filter_size)
fpred = signal.filtfilt(b, 1, detect)
# plt.figure()
# plt.stem(fpred)
# plt.show()
#
fpred2 = fpred ** 2
thr = ((np.floor(filter_size/2) - 1) / filter_size) ** 2
detect_unpad = (fpred2 > thr)
detect2 = detect_unpad
# plt.figure()
# plt.stem(detect2)
# plt.show()
#Padding
for u in range(2):
pad_val = np.pad(detect2, (1, 1), 'constant', constant_values=0)
detect2 = np.array(pad_val[2:]) + np.array(pad_val[0:-2]) + detect2
# plt.figure()
# plt.plot(detect2)
# plt.show()
##Filtering Stage 2
b2 = np.array([-1, 0, 1])
detect2_filt = signal.filtfilt(b2, 1, detect2)
# plt.figure()
# plt.plot(detect2_filt)
# plt.show()
detect6 = np.array(detect2_filt == 1)
detect4 = np.array(-detect2_filt == 1)
detect5 = np.pad(detect4, (1, 1), 'constant', constant_values=0)
detect7 = np.array(detect5[0:-2]) & detect6
detect8 = np.array(detect5[2:]) & detect6
detect3 = detect7 | detect8
positions = np.array(np.nonzero(detect3)).squeeze()
# plt.figure() este en el original
# plt.plot(positions)
# plt.show()
return positions
def filter_output_dbscan(prediction, hw_size):
detect = np.array(prediction != 2, dtype='int').squeeze()
detect2 = np.array(np.nonzero(detect)).squeeze()
detect3 = detect2.reshape(-1, 1)
db = DBSCAN(eps=10, min_samples=hw_size, metric='cityblock')
clusters = db.fit_predict(detect3)
top = np.max(clusters) + 1
class_out = np.zeros(top-1)
pos_out = | np.zeros(top-1, dtype='int') | numpy.zeros |
import os
import os.path as osp
import numpy as np
import matplotlib.pyplot as plt
from dataclasses import dataclass
from typing import List
from .xfoil_lib import read_polar, read_cp
import pandas as pd
import math
import subprocess
import time, platform, signal
import ctypes
@dataclass
class xfdata:
'''
Input structure into XFOIL
'''
airfoil_name:str
alpha_min:float
alpha_max:float
alpha_step:float
ncrit:float
Reynolds:float
Mach:float
num_nodes:int
save_airfoil_filename:str
save_polar_filename:str # save results filename
root_folder:str
xfoil_input:str
xss: np.ndarray
yss: np.ndarray
xps: np.ndarray
yps: np.ndarray
def create_psav(xfoil_data:xfdata):
"""Save the airfoil in plain coordinate format for xfoil to read
Args:
xfoil_data (xfdata): class that contains everything needed to call xfoil
"""
with open(osp.join(xfoil_data.root_folder, xfoil_data.save_airfoil_filename),'w') as f:
for i in range(len(xfoil_data.xss)):
f.write(' {0:0.7f} {1:0.7f}\n'.format(xfoil_data.xss[i],xfoil_data.yss[i]))
for i in range(len(xfoil_data.xps)):
f.write(' {0:0.7f} {1:0.7f}\n'.format(xfoil_data.xps[i],xfoil_data.yps[i]))
def run_xfoil(xfoil_data:xfdata,exe_path:str,return_cp=True,return_polars=True, check_convergence=True):
"""Runs xfoil simulation.
Args:
xfoil_data (xfdata): Class which represents the inputs to pass to xfoil
exe_path (str): path to xfoil executable
return_cp (bool, optional): Returns the cp value. Defaults to True.
return_polars (bool, optional): Returns only Cl,Cd,Cdp,Cm. Defaults to True.
check_convergence (bool, optional): Checks to see if xfoil simulation converged. Defaults to True.
Returns:
pd.dataframe or None: If simulation did not converge then None is returned otherwise a dataframe with the results is returned
"""
for item in os.listdir(xfoil_data.root_folder):
if item.endswith(".txt") or item.endswith(".cp"):
os.remove(os.path.join(xfoil_data.root_folder, item))
create_psav(xfoil_data) # Create the airfoil data
def get_cp(aoa):
# Get the Cp
with open(osp.join(xfoil_data.root_folder,xfoil_data.xfoil_input),"w") as fid:
# Add Operation
fid.write('LOAD {0}\n{1}\n'.format(str(osp.join(xfoil_data.root_folder,xfoil_data.save_airfoil_filename)),xfoil_data.airfoil_name))
fid.write('PPAR\nN\n{0}\n\n\n'.format(xfoil_data.num_nodes))
fid.write('GDES\nCADD\n\n\n\n\n'.format(xfoil_data.num_nodes))
fid.write("OPER\n")
fid.write('VPAR\n')
fid.write('N \n{0}\n'.format(xfoil_data.ncrit))
fid.write('XTR \n{0}\n{1}\n\n'.format(1.0,1.0))
fid.write('VISC {0}\n'.format(xfoil_data.Reynolds))
fid.write('MACH {0}\n'.format(xfoil_data.Mach))
fid.write('ITER {0}\n'.format(100))
fid.write('ALFA 0.0\n')
fid.write('INIT\n')
fid.write('PACC \n{0}\ntemp.dump\n'.format('temp_polar.txt'))
fid.write('ALFA {0}\n'.format(aoa))
fid.write("CPWR \n {0}.cp\n\n\n\n".format(osp.join(xfoil_data.root_folder,'Cp_'+ str(aoa))))
fid.write("QUIT" + "\n")
os.system("timeout 0.5s {0} < {1}".format(exe_path,osp.join(xfoil_data.root_folder,xfoil_data.xfoil_input)))
return osp.join(xfoil_data.root_folder,'Cp_'+str(aoa)+'.cp')
def get_polars():
# Get the Polar (Cl vs angle of attack)
with open(osp.join(xfoil_data.root_folder,xfoil_data.xfoil_input),"w") as fid:
# Add Operation
fid.write('LOAD {0}\n{1}\n'.format(str(osp.join(xfoil_data.root_folder,xfoil_data.save_airfoil_filename)),xfoil_data.save_airfoil_filename))
fid.write('PPAR\nN\n{0}\n\n\n'.format(xfoil_data.num_nodes))
fid.write('GDES\nCADD\n\n\n\n\n'.format(xfoil_data.num_nodes))
fid.write("OPER\n")
fid.write('VPAR\n')
fid.write('N \n{0}\n'.format(xfoil_data.ncrit))
fid.write('XTR \n{0}\n{1}\n\n'.format(1.0,1.0))
fid.write('VISC {0}\n'.format(xfoil_data.Reynolds))
fid.write('MACH {0}\n'.format(xfoil_data.Mach))
fid.write('ITER {0}\n'.format(1000))
fid.write('ASEQ\n')
fid.write('{0}\n'.format(xfoil_data.alpha_min))
fid.write('{0}\n'.format(xfoil_data.alpha_max))
fid.write('{0}\n'.format(xfoil_data.alpha_step))
fid.write('INIT\n')
fid.write('PACC\n{0}\ntemp.dump\n'.format(osp.join(xfoil_data.root_folder, xfoil_data.save_polar_filename)))
fid.write('ASEQ \n{0}\n{1}\n{2}\n'.format(xfoil_data.alpha_min,xfoil_data.alpha_max,xfoil_data.alpha_step))
# fid.write("CPWR \n polar_temp.cp\n\n\n\n")
fid.write("QUIT" + "\n")
# os.system("xfoil < {0}".format(xfoil_data.xfoil_input))
os.system("timeout 1s {0} < {1}".format(exe_path,osp.join(xfoil_data.root_folder,xfoil_data.xfoil_input)))
if osp.exists('temp.dump'): # delete the dump file
os.remove('temp.dump')
if osp.exists('temp_polar.txt'): # delete the temp polar file
os.remove('temp_polar.txt')
if (return_cp and return_polars):
get_polars()
df_polar = read_polar(osp.join(xfoil_data.root_folder,xfoil_data.save_polar_filename))
df_polar['x_cp'] = math.nan
df_polar['Cp'] = math.nan
df_polar['xss'] = None
df_polar['yss'] = None
df_polar['xps'] = None
df_polar['yps'] = None
df_polar=df_polar.astype(object)
if (xfoil_data.alpha_min == xfoil_data.alpha_max):
aoa_cp_file = get_cp(xfoil_data.alpha_min)
x,cp = read_cp(aoa_cp_file)
row = df_polar.index[df_polar['alpha'] == xfoil_data.alpha_min]
if len(row)>0:
row = row.values[0]
df_polar.at[row,'xss'] = np.flip(xfoil_data.xss).tolist()
df_polar.at[row,'yss'] = np.flip(xfoil_data.yss).tolist()
df_polar.at[row,'xps'] = np.flip(xfoil_data.xps)[1:].tolist() # TODO: Need to double check this for other airfoils, works with test naca foil
df_polar.at[row,'yps'] = np.flip(xfoil_data.yps)[1:].tolist()
if (x is not None and cp is not None):
df_polar.at[row,'x_cp'] = x.tolist()
df_polar.at[row,'Cp'] = cp.tolist()
else:
aoa_list = | np.arange(xfoil_data.alpha_min, xfoil_data.alpha_max,xfoil_data.alpha_step) | numpy.arange |
import argparse
import pickle
import numpy as np
import torch
from mvt.cores.metric_ops import LpDistance
def parse_args():
parser = argparse.ArgumentParser(description="evaluate emdedding")
parser.add_argument("reference", help="reference embedding file path")
parser.add_argument("query", help="query embedding file path")
args = parser.parse_args()
return args
def load_embedding(file_path):
with open(file_path, "rb") as f:
data = pickle.load(f)
return data["embeddings"], data["labels"]
def print_info(embeddings, labels):
print("Number of samples: ", embeddings.shape[0])
print("Number of classes: ", np.unique(labels).size)
def main():
args = parse_args()
ref_path = args.reference
qry_path = args.query
ref_emb, ref_labels = load_embedding(ref_path)
print("Loaded reference embeddings")
print_info(ref_emb, ref_labels)
qry_emb, qry_labels = load_embedding(qry_path)
print("Loaded query embeddings")
print_info(qry_emb, qry_labels)
valid_inds = []
valid_labels = | np.unique(ref_labels) | numpy.unique |
import cv2
import base as bs
import numpy as np
def sobel_filter(img, K_size=3, sigma=1.3):
if len(img.shape) == 3:
H, W, C = img.shape
else:
img = np.expand_dims(img, axis=-1)
H, W, C = img.shape
##padding
pad = K_size // 2
out_v = | np.zeros((H + pad * 2, W + pad * 2, C), dtype=np.float) | numpy.zeros |
__author__ = 'saeedamen' # <NAME>
#
# Copyright 2016-2020 Cuemacro
#
# Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the
# License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an
# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#
# See the License for the specific language governing permissions and limitations under the License.
#
import numpy as np
import pandas as pd
import pytz
import datetime
from datetime import timedelta
from findatapy.timeseries.calendar import Calendar
from findatapy.util.dataconstants import DataConstants
from findatapy.util.loggermanager import LoggerManager
constants = DataConstants()
class Filter(object):
"""Functions for filtering time series by dates and columns.
This class is used extensively in both findatapy and finmarketpy.
Market holidays are collected from web sources such as https://www.timeanddate.com/holidays/ and also individual
exchange websites, and is manually updated from time to time to take into account newly instituted holidays, and stored
in conf/holidays_table.parquet - if you need to add your own holidays.
"""
_time_series_cache = {} # shared across all instances of object!
def __init__(self):
self._calendar = Calendar()
def filter_time_series(self, market_data_request, data_frame, pad_columns=False):
"""Filters a time series given a set of criteria (like start/finish date and tickers)
Parameters
----------
market_data_request : MarketDataRequest
defining time series filtering
data_frame : DataFrame
time series to be filtered
pad_columns : boolean
true, non-existant columns with nan
Returns
-------
DataFrame
"""
start_date = market_data_request.start_date
finish_date = market_data_request.finish_date
data_frame = self.filter_time_series_by_date(start_date, finish_date, data_frame)
# Filter by ticker.field combinations requested
columns = self.create_tickers_fields_list(market_data_request)
if (pad_columns):
data_frame = self.pad_time_series_columns(columns, data_frame)
else:
data_frame = self.filter_time_series_by_columns(columns, data_frame)
return data_frame
def filter_time_series_by_holidays(self, data_frame, cal='FX', holidays_list=[]):
"""Removes holidays from a given time series
Parameters
----------
data_frame : DataFrame
data frame to be filtered
cal : str
business calendar to use
Returns
-------
DataFrame
"""
# Optimal case for weekdays: remove Saturday and Sunday
if (cal == 'WEEKDAY' or cal == 'WKY'):
return data_frame[data_frame.index.dayofweek <= 4]
# Select only those holidays in the sample
holidays_start = self._calendar.get_holidays(data_frame.index[0], data_frame.index[-1], cal, holidays_list=holidays_list)
if (holidays_start.size == 0):
return data_frame
holidays_end = holidays_start + np.timedelta64(1, 'D')
# floored_dates = data_frame.index.normalize()
#
# filter_by_index_start = floored_dates.searchsorted(holidays_start)
# filter_by_index_end = floored_dates.searchsorted(holidays_end)
#
# indices_to_keep = []
#
# if filter_by_index_end[0] == 0:
# counter = filter_by_index_end[0] + 1
# start_index = 1
# else:
# counter = 0
# start_index = 0
#
# for i in range(start_index, len(holidays_start)):
# indices = list(range(counter, filter_by_index_start[i] - 1))
# indices_to_keep = indices_to_keep + indices
#
# counter = filter_by_index_end[i] + 1
#
# indices = list(range(counter, len(floored_dates)))
# indices_to_keep = indices_to_keep + indices
#
# data_frame_filtered = data_frame[indices_to_keep]
if data_frame.index.tz is None:
holidays_start = holidays_start.tz_localize(None)
holidays_end = holidays_end.tz_localize(None)
data_frame_left = data_frame
data_frame_filtered = []
for i in range(0, len(holidays_start)):
data_frame_temp = data_frame_left[data_frame_left.index < holidays_start[i]]
data_frame_left = data_frame_left[data_frame_left.index >= holidays_end[i]]
data_frame_filtered.append(data_frame_temp)
data_frame_filtered.append(data_frame_left)
return pd.concat(data_frame_filtered)
def filter_time_series_by_date(self, start_date, finish_date, data_frame):
"""Filter time series by start/finish dates
Parameters
----------
start_date : DateTime
start date of calendar
finish_date : DataTime
finish date of calendar
data_frame : DataFrame
data frame to be filtered
Returns
-------
DataFrame
"""
offset = 0 # inclusive
return self.filter_time_series_by_date_offset(start_date, finish_date, data_frame, offset,
exclude_start_end=False)
def filter_time_series_by_days(self, days, data_frame):
"""Filter time series by start/finish dates
Parameters
----------
start_date : DateTime
start date of calendar
finish_date : DataTime
finish date of calendar
data_frame : DataFrame
data frame to be filtered
Returns
-------
DataFrame
"""
offset = 0 # inclusive
finish_date = datetime.datetime.utcnow()
start_date = finish_date - timedelta(days=days)
return self.filter_time_series_by_date_offset(start_date, finish_date, data_frame, offset)
def filter_time_series_by_date_exc(self, start_date, finish_date, data_frame):
"""Filter time series by start/finish dates (exclude start & finish dates)
Parameters
----------
start_date : DateTime
start date of calendar
finish_date : DataTime
finish date of calendar
data_frame : DataFrame
data frame to be filtered
Returns
-------
DataFrame
"""
offset = 1 # exclusive of start finish date
return self.filter_time_series_by_date_offset(start_date, finish_date, data_frame, offset,
exclude_start_end=True)
# try:
# # filter by dates for intraday data
# if(start_date is not None):
# data_frame = data_frame.loc[start_date <= data_frame.index]
#
# if(finish_date is not None):
# # filter by start_date and finish_date
# data_frame = data_frame.loc[data_frame.index <= finish_date]
# except:
# # filter by dates for daily data
# if(start_date is not None):
# data_frame = data_frame.loc[start_date.date() <= data_frame.index]
#
# if(finish_date is not None):
# # filter by start_date and finish_date
# data_frame = data_frame.loc[data_frame.index <= finish_date.date()]
#
# return data_frame
def filter_time_series_by_date_offset(self, start_date, finish_date, data_frame, offset, exclude_start_end=False):
"""Filter time series by start/finish dates (and an offset)
Parameters
----------
start_date : DateTime
start date of calendar
finish_date : DataTime
finish date of calendar
data_frame : DataFrame
data frame to be filtered
offset : int
offset to be applied
Returns
-------
DataFrame
"""
if hasattr(data_frame.index, 'tz'):
if data_frame.index.tz is not None:
# If the start/finish dates are timezone naive, overwrite with the DataFrame timezone
if not (isinstance(start_date, str)):
start_date = start_date.replace(tzinfo=data_frame.index.tz)
if not (isinstance(finish_date, str)):
finish_date = finish_date.replace(tzinfo=data_frame.index.tz)
else:
# Otherwise remove timezone from start_date/finish_date
if not (isinstance(start_date, str)):
try:
start_date = start_date.replace(tzinfo=None)
except:
pass
if not (isinstance(finish_date, str)):
try:
finish_date = finish_date.replace(tzinfo=None)
except:
pass
if 'int' in str(data_frame.index.dtype):
return data_frame
try:
data_frame = self.filter_time_series_aux(start_date, finish_date, data_frame, offset)
except:
# start_date = start_date.date()
# finish_date = finish_date.date()
# if isinstance(start_date, str):
# # format expected 'Jun 1 2005 01:33', '%b %d %Y %H:%M'
# try:
# start_date = datetime.datetime.strptime(start_date, '%b %d %Y %H:%M')
# except:
# i = 0
#
# if isinstance(finish_date, str):
# # format expected 'Jun 1 2005 01:33', '%b %d %Y %H:%M'
# try:
# finish_date = datetime.datetime.strptime(finish_date, '%b %d %Y %H:%M')
# except:
# i = 0
# try:
# start_date = start_date.date()
# except: pass
#
# try:
# finish_date = finish_date.date()
# except: pass
# if we have dates stored as opposed to TimeStamps (ie. daily data), we use a simple (slower) method
# for filtering daily data
if (start_date is not None):
if exclude_start_end:
data_frame = data_frame.loc[start_date < data_frame.index]
else:
data_frame = data_frame.loc[start_date <= data_frame.index]
if (finish_date is not None):
if exclude_start_end:
data_frame = data_frame.loc[data_frame.index < finish_date]
else:
# filter by start_date and finish_date
data_frame = data_frame.loc[data_frame.index <= finish_date]
return data_frame
def filter_time_series_aux(self, start_date, finish_date, data_frame, offset):
"""Filter time series by start/finish dates (and an offset)
Parameters
----------
start_date : DateTime
start date of calendar
finish_date : DataTime
finish date of calendar
data_frame : DataFrame
data frame to be filtered
offset : int (not implemented!)
offset to be applied
Returns
-------
DataFrame
"""
# start_index = 0
# finish_index = len(data_frame.index) - offset
# filter by dates for intraday data
# if(start_date is not None):
# start_index = data_frame.index.searchsorted(start_date)
#
# if (0 <= start_index + offset < len(data_frame.index)):
# start_index = start_index + offset
#
# # data_frame = data_frame[start_date < data_frame.index]
#
# if(finish_date is not None):
# finish_index = data_frame.index.searchsorted(finish_date)
#
# if (0 <= finish_index - offset < len(data_frame.index)):
# finish_index = finish_index - offset
# CAREFUL: need + 1 otherwise will only return 1 less than usual
# return data_frame.iloc[start_date:finish_date]
# Just use pandas, quicker and simpler code!
if data_frame is None:
return None
# Slower method..
# return data_frame.loc[start_date:finish_date]
# Much faster, start and finish dates are inclusive
return data_frame[(data_frame.index >= start_date) & (data_frame.index <= finish_date)]
def filter_time_series_by_time_of_day_timezone(self, hour, minute, data_frame, timezone_of_snap='UTC'):
old_tz = data_frame.index.tz
data_frame = data_frame.tz_convert(pytz.timezone(timezone_of_snap))
data_frame = data_frame[data_frame.index.minute == minute]
data_frame = data_frame[data_frame.index.hour == hour]
data_frame = data_frame.tz_convert(old_tz)
return data_frame
def filter_time_series_by_time_of_day(self, hour, minute, data_frame, in_tz=None, out_tz=None):
"""Filter time series by time of day
Parameters
----------
hour : int
hour of day
minute : int
minute of day
data_frame : DataFrame
data frame to be filtered
in_tz : str (optional)
time zone of input data frame
out_tz : str (optional)
time zone of output data frame
Returns
-------
DataFrame
"""
if out_tz is not None:
try:
if in_tz is not None:
data_frame = data_frame.tz_localize(pytz.timezone(in_tz))
except:
data_frame = data_frame.tz_convert(pytz.timezone(in_tz))
data_frame = data_frame.tz_convert(pytz.timezone(out_tz))
# change internal representation of time
data_frame.index = pd.DatetimeIndex(data_frame.index.values)
data_frame = data_frame[data_frame.index.minute == minute]
data_frame = data_frame[data_frame.index.hour == hour]
return data_frame
def filter_time_series_by_minute_of_hour(self, minute, data_frame, in_tz=None, out_tz=None):
"""Filter time series by minute of hour
Parameters
----------
minute : int
minute of hour
data_frame : DataFrame
data frame to be filtered
in_tz : str (optional)
time zone of input data frame
out_tz : str (optional)
time zone of output data frame
Returns
-------
DataFrame
"""
if out_tz is not None:
if in_tz is not None:
data_frame = data_frame.tz_localize(pytz.timezone(in_tz))
data_frame = data_frame.tz_convert(pytz.timezone(out_tz))
# change internal representation of time
data_frame.index = pd.DatetimeIndex(data_frame.index.values)
data_frame = data_frame[data_frame.index.minute == minute]
return data_frame
def filter_time_series_between_hours(self, start_hour, finish_hour, data_frame):
"""Filter time series between hours of the day
Parameters
----------
start_hour : int
start of hour filter
finish_hour : int
finish of hour filter
data_frame : DataFrame
data frame to be filtered
Returns
-------
DataFrame
"""
data_frame = data_frame[data_frame.index.hour <= finish_hour]
data_frame = data_frame[data_frame.index.hour >= start_hour]
return data_frame
def filter_time_series_by_columns(self, columns, data_frame):
"""Filter time series by certain columns
Parameters
----------
columns : list(str)
start of hour filter
data_frame : DataFrame
data frame to be filtered
Returns
-------
DataFrame
"""
if data_frame is not None and columns is not None:
return data_frame[columns]
return None
def pad_time_series_columns(self, columns, data_frame):
"""Selects time series from a dataframe and if necessary creates empty columns
Parameters
----------
columns : str
columns to be included with this keyword
data_frame : DataFrame
data frame to be filtered
Returns
-------
DataFrame
"""
old_columns = data_frame.columns.tolist()
common_columns = [val for val in columns if val in old_columns]
uncommon_columns = [val for val in columns if val not in old_columns]
uncommon_columns = [str(x) for x in uncommon_columns]
data_frame = data_frame[common_columns]
if len(uncommon_columns) > 0:
logger = LoggerManager().getLogger(__name__)
logger.info("Padding missing columns...") # " + str(uncommon_columns))
new_data_frame = pd.DataFrame(index=data_frame.index, columns=uncommon_columns)
data_frame = pd.concat([data_frame, new_data_frame], axis=1)
# Force new columns to float NaNs (not objects which causes problems with newer pandas versions)
# or to NaT if they are date columns
for u in uncommon_columns:
is_date = False
for c in constants.always_date_columns:
if c in u:
is_date = True
if is_date:
data_frame[u] = np.datetime64('NaT')
else:
data_frame[u] = np.nan
# SLOW method below
# for x in uncommon_columns: data_frame.loc[:,x] = np.nan
# Get columns in same order again
data_frame = data_frame[columns]
return data_frame
def filter_time_series_by_excluded_keyword(self, keyword, data_frame):
"""Filter time series to exclude columns which contain keyword
Parameters
----------
keyword : str
columns to be excluded with this keyword
data_frame : DataFrame
data frame to be filtered
Returns
-------
DataFrame
"""
if not (isinstance(keyword, list)):
keyword = [keyword]
columns = []
for k in keyword:
columns.append([elem for elem in data_frame.columns if k not in elem])
columns = self._calendar.flatten_list_of_lists(columns)
return self.filter_time_series_by_columns(columns, data_frame)
def filter_time_series_by_included_keyword(self, keyword, data_frame):
"""Filter time series to include columns which contain keyword
Parameters
----------
keyword : str
columns to be included with this keyword
data_frame : DataFrame
data frame to be filtered
Returns
-------
DataFrame
"""
if not (isinstance(keyword, list)):
keyword = [keyword]
columns = []
for k in keyword:
columns.append([elem for elem in data_frame.columns if k in elem])
columns = self._calendar.flatten_list_of_lists(columns)
return self.filter_time_series_by_columns(columns, data_frame)
def filter_time_series_by_minute_freq(self, freq, data_frame):
"""Filter time series where minutes correspond to certain minute filter
Parameters
----------
freq : int
minute frequency to be filtered
data_frame : DataFrame
data frame to be filtered
Returns
-------
DataFrame
"""
return data_frame.loc[data_frame.index.minute % freq == 0]
def create_tickers_fields_list(self, market_data_request):
"""Creates a list of tickers concatenated with fields from a MarketDataRequest
Parameters
----------
market_data_request : MarketDataRequest
request to be expanded
Returns
-------
list(str)
"""
tickers = market_data_request.tickers
fields = market_data_request.fields
if isinstance(tickers, str): tickers = [tickers]
if isinstance(fields, str): fields = [fields]
tickers_fields_list = []
# Create ticker.field combination for series we wish to return
for f in fields:
for t in tickers:
tickers_fields_list.append(t + '.' + f)
return tickers_fields_list
def resample_time_series(self, data_frame, freq):
return data_frame.asfreq(freq, method='pad')
def resample_time_series_frequency(self, data_frame, data_resample_freq,
data_resample_type='mean', fill_empties=False):
# Should we take the mean, first, last in our resample
if data_resample_type == 'mean':
data_frame_r = data_frame.resample(data_resample_freq).mean()
elif data_resample_type == 'first':
data_frame_r = data_frame.resample(data_resample_freq).first()
elif data_resample_type == 'last':
data_frame_r = data_frame.resample(data_resample_freq).last()
else:
# TODO implement other types
return
if fill_empties == True:
data_frame, data_frame_r = data_frame.align(data_frame_r, join='left', axis=0)
data_frame_r = data_frame_r.fillna(method='ffill')
return data_frame_r
def make_FX_1_min_working_days(self, data_frame):
data_frame = data_frame.resample('1min').mean()
data_frame = self.filter_time_series_by_holidays(data_frame, 'FX')
data_frame = data_frame.fillna(method='ffill')
data_frame = self.remove_out_FX_out_of_hours(data_frame)
return data_frame
def remove_out_FX_out_of_hours(self, data_frame):
"""Filtered a time series for FX hours (ie. excludes 22h GMT Fri - 19h GMT Sun and New Year's Day)
Parameters
----------
data_frame : DataFrame
data frame with FX prices
Returns
-------
list(str)
"""
# assume data_frame is in GMT time
# remove Fri after 22:00 GMT
# remove Sat
# remove Sun before 19:00 GMT
# Monday = 0, ..., Sunday = 6
data_frame = data_frame[~((data_frame.index.dayofweek == 4) & (data_frame.index.hour > 22))]
data_frame = data_frame[~((data_frame.index.dayofweek == 5))]
data_frame = data_frame[~((data_frame.index.dayofweek == 6) & (data_frame.index.hour < 19))]
data_frame = data_frame[~((data_frame.index.day == 1) & (data_frame.index.month == 1))]
return data_frame
def remove_duplicate_indices(self, df):
return df[~df.index.duplicated(keep='first')]
def mask_time_series_by_time(self, df, time_list, time_zone):
""" Mask a time series by time of day and time zone specified
e.g. given a time series minutes data
want to keep data at specific time periods every day with a considered time zone
Parameters
----------
df : DateTime
time series needed to be masked
time_list : list of tuples
deciding the time periods which we want to keep the data on each day
e.g. time_list = [('01:08', '03:02'),('12:24','12:55'),('17:31','19:24')]
* Note: assume no overlapping of these tuples
time_zone: str
e.g. 'Europe/London'
Returns
-------
DataFrame (which the time zone is 'UTC')
"""
# Change the time zone from 'UTC' to a given one
df.index = df.index.tz_convert(time_zone)
df_mask = pd.DataFrame(0, index=df.index, columns=['mask'])
# Mask data with each given tuple
for i in range(0, len(time_list)):
start_hour = int(time_list[i][0].split(':')[0])
start_minute = int(time_list[i][0].split(':')[1])
end_hour = int(time_list[i][1].split(':')[0])
end_minute = int(time_list[i][1].split(':')[1])
# E.g. if tuple is ('01:08', '03:02'),
# take hours in target - take values in [01:00,04:00]
narray = np.where(df.index.hour.isin(range(start_hour, end_hour + 1)), 1, 0)
df_mask_temp = pd.DataFrame(index=df.index, columns=df_mask.columns.tolist(), data=narray)
# Remove minutes not in target - remove values in [01:00,01:07], [03:03,03:59]
narray = np.where(((df.index.hour == start_hour) & (df.index.minute < start_minute)), 0, 1)
df_mask_temp = df_mask_temp * pd.DataFrame(index=df.index, columns=df_mask.columns.tolist(),
data=narray)
narray = np.where((df.index.hour == end_hour) & (df.index.minute > end_minute), 0, 1)
df_mask_temp = df_mask_temp * pd.DataFrame(index=df.index, columns=df_mask.columns.tolist(),
data=narray)
# Collect all the periods we want to keep the data
df_mask = df_mask + df_mask_temp
narray = | np.where(df_mask == 1, df, 0) | numpy.where |
# -*- coding: utf-8 -*-
#@Author: <NAME>
#@Date: 2019-11-29 01:47:58
#@Last Modified by: <NAME>
#@Last Modified time: 2019-11-29 01:47:58
import numpy as np
import os
import json
def bbox_overlaps(bboxes1, bboxes2, mode='iou'):
"""Calculate the ious between each bbox of bboxes1 and bboxes2.
Args:
bboxes1(ndarray): shape (n, 4)
bboxes2(ndarray): shape (k, 4)
mode(str): iou (intersection over union) or iof (intersection
over foreground)
Returns:
ious(ndarray): shape (n, k)
"""
assert mode in ['iou', 'iof']
bboxes1 = bboxes1.astype(np.float32)
bboxes2 = bboxes2.astype(np.float32)
rows = bboxes1.shape[0]
cols = bboxes2.shape[0]
ious = np.zeros((rows, cols), dtype=np.float32)
if rows * cols == 0:
return ious
exchange = False
if bboxes1.shape[0] > bboxes2.shape[0]:
bboxes1, bboxes2 = bboxes2, bboxes1
ious = np.zeros((cols, rows), dtype=np.float32)
exchange = True
area1 = (bboxes1[:, 2] - bboxes1[:, 0] + 1) * (
bboxes1[:, 3] - bboxes1[:, 1] + 1)
area2 = (bboxes2[:, 2] - bboxes2[:, 0] + 1) * (
bboxes2[:, 3] - bboxes2[:, 1] + 1)
for i in range(bboxes1.shape[0]):
x_start = np.maximum(bboxes1[i, 0], bboxes2[:, 0])
y_start = np.maximum(bboxes1[i, 1], bboxes2[:, 1])
x_end = np.minimum(bboxes1[i, 2], bboxes2[:, 2])
y_end = np.minimum(bboxes1[i, 3], bboxes2[:, 3])
overlap = np.maximum(x_end - x_start + 1, 0) * np.maximum(
y_end - y_start + 1, 0)
if mode == 'iou':
union = area1[i] + area2 - overlap
else:
union = area1[i] if not exchange else area2
ious[i, :] = overlap / union
if exchange:
ious = ious.T
return ious
data_path='/backdata01/KITTI/kitti/tracking'
with open(os.path.join(data_path,'kitti_train.json'),'r',encoding='utf-8') as f:
data=json.load(f)
occlusion=[]
partial_occlusion=[]
for i in data:
boxt=np.array(i['ann']['bboxes'])
if len(boxt)==0:
continue
iou=bbox_overlaps(boxt,boxt)
check= | np.sum(iou,axis=0) | numpy.sum |
import sys
import numba as nb
import numpy as np
try:
from numba.experimental import jitclass
except ImportError:
from numba import jitclass
@jitclass(
[
("__data", nb.int64[:]),
]
)
class UnionFind:
def __init__(self, n: int) -> None:
self.__data = | np.full(n, -1, np.int64) | numpy.full |
"""
Tests for the correlation function calculations.
"""
import numpy as np
from numpy.testing import (
run_module_suite,
assert_,
assert_array_almost_equal,
assert_raises,
)
from matsubara.correlation import (
sum_of_exponentials,
biexp_fit,
bath_correlation,
underdamped_brownian,
nonmatsubara_exponents,
matsubara_exponents,
matsubara_zero_analytical,
coth,
spectrum,
spectrum_matsubara,
spectrum_non_matsubara,
_S,
_A,
)
def test_sum_of_exponentials():
"""
correlation: Test the sum of exponentials.
"""
tlist = [0.0, 0.5, 1.0, 1.5, 2.0]
# Complex coefficients and frequencies.
ck1 = [0.5 + 2j, -0.1]
vk1 = [-0.5 + 3j, 1 - 1j]
corr1 = sum_of_exponentials(ck1, vk1, tlist)
y1 = np.array(
[
0.4 + 2.0j,
-1.67084356 + 0.57764922j,
-0.61828702 - 0.92938927j,
0.84201641 + 0.0170242j,
0.68968912 + 1.32694318j,
]
)
assert_array_almost_equal(corr1, y1)
# Real coefficients and frequencies.
ck2 = [0.5, -0.3]
vk2 = [-0.9, -0.3]
corr2 = sum_of_exponentials(ck2, vk2, tlist)
y2 = np.array([0.2, 0.060602, -0.018961, -0.061668, -0.081994])
assert_array_almost_equal(corr2, y2)
def test_biexp_fit():
"""
correlation: Tests biexponential fitting.
"""
tlist = np.linspace(0.0, 10, 100)
ck = [-0.21, -0.13]
vk = [-0.4, -1.5]
corr = sum_of_exponentials(ck, vk, tlist)
ck_fit, vk_fit = biexp_fit(tlist, corr)
corr_fit = sum_of_exponentials(ck_fit, vk_fit, tlist)
max_error = np.max(np.abs(corr - corr_fit))
max_amplitude = np.max( | np.abs(corr) | numpy.abs |
"""Rangeland Production Model."""
import os
import logging
import tempfile
import shutil
from builtins import range
import re
import math
import pickle
import numpy
import pandas
from osgeo import ogr
from osgeo import osr
from osgeo import gdal
import pygeoprocessing
from rangeland_production import utils
from rangeland_production import validation
LOGGER = logging.getLogger('rangeland_production.forage')
# we only have these types of soils
SOIL_TYPE_LIST = ['clay', 'silt', 'sand']
# temporary directory to store intermediate files
PROCESSING_DIR = None
# user-supplied crude protein of vegetation
CRUDE_PROTEIN = None
# state variables and parameters take their names from Century
# _SITE_STATE_VARIABLE_FILES contains state variables that are a
# property of the site, including:
# carbon in each soil compartment
# (structural, metabolic, som1, som2, som3) and layer (1=surface, 2=soil)
# e.g., som2c_2 = carbon in soil som2;
# N and P in each soil layer and compartment (1=N, 2=P)
# e.g., som2e_1_1 = N in surface som2, som2e_1_2 = P in surface som2;
# water in each soil layer, asmos_<layer>
# state variables fully described in this table:
# https://docs.google.com/spreadsheets/d/1TGCDOJS4nNsJpzTWdiWed390NmbhQFB2uUoMs9oTTYo/edit?usp=sharing
_SITE_STATE_VARIABLE_FILES = {
'metabc_1_path': 'metabc_1.tif',
'metabc_2_path': 'metabc_2.tif',
'som1c_1_path': 'som1c_1.tif',
'som1c_2_path': 'som1c_2.tif',
'som2c_1_path': 'som2c_1.tif',
'som2c_2_path': 'som2c_2.tif',
'som3c_path': 'som3c.tif',
'strucc_1_path': 'strucc_1.tif',
'strucc_2_path': 'strucc_2.tif',
'strlig_1_path': 'strlig_1.tif',
'strlig_2_path': 'strlig_2.tif',
'metabe_1_1_path': 'metabe_1_1.tif',
'metabe_2_1_path': 'metabe_2_1.tif',
'som1e_1_1_path': 'som1e_1_1.tif',
'som1e_2_1_path': 'som1e_2_1.tif',
'som2e_1_1_path': 'som2e_1_1.tif',
'som2e_2_1_path': 'som2e_2_1.tif',
'som3e_1_path': 'som3e_1.tif',
'struce_1_1_path': 'struce_1_1.tif',
'struce_2_1_path': 'struce_2_1.tif',
'metabe_1_2_path': 'metabe_1_2.tif',
'metabe_2_2_path': 'metabe_2_2.tif',
'plabil_path': 'plabil.tif',
'secndy_2_path': 'secndy_2.tif',
'parent_2_path': 'parent_2.tif',
'occlud_path': 'occlud.tif',
'som1e_1_2_path': 'som1e_1_2.tif',
'som1e_2_2_path': 'som1e_2_2.tif',
'som2e_1_2_path': 'som2e_1_2.tif',
'som2e_2_2_path': 'som2e_2_2.tif',
'som3e_2_path': 'som3e_2.tif',
'struce_1_2_path': 'struce_1_2.tif',
'struce_2_2_path': 'struce_2_2.tif',
'asmos_1_path': 'asmos_1.tif',
'asmos_2_path': 'asmos_2.tif',
'asmos_3_path': 'asmos_3.tif',
'asmos_4_path': 'asmos_4.tif',
'asmos_5_path': 'asmos_5.tif',
'asmos_6_path': 'asmos_6.tif',
'asmos_7_path': 'asmos_7.tif',
'asmos_8_path': 'asmos_8.tif',
'asmos_9_path': 'asmos_9.tif',
'avh2o_3_path': 'avh2o_3.tif',
'minerl_1_1_path': 'minerl_1_1.tif',
'minerl_2_1_path': 'minerl_2_1.tif',
'minerl_3_1_path': 'minerl_3_1.tif',
'minerl_4_1_path': 'minerl_4_1.tif',
'minerl_5_1_path': 'minerl_5_1.tif',
'minerl_6_1_path': 'minerl_6_1.tif',
'minerl_7_1_path': 'minerl_7_1.tif',
'minerl_8_1_path': 'minerl_8_1.tif',
'minerl_9_1_path': 'minerl_9_1.tif',
'minerl_10_1_path': 'minerl_10_1.tif',
'minerl_1_2_path': 'minerl_1_2.tif',
'minerl_2_2_path': 'minerl_2_2.tif',
'minerl_3_2_path': 'minerl_3_2.tif',
'minerl_4_2_path': 'minerl_4_2.tif',
'minerl_5_2_path': 'minerl_5_2.tif',
'minerl_6_2_path': 'minerl_6_2.tif',
'minerl_7_2_path': 'minerl_7_2.tif',
'minerl_8_2_path': 'minerl_8_2.tif',
'minerl_9_2_path': 'minerl_9_2.tif',
'minerl_10_2_path': 'minerl_10_2.tif',
'snow_path': 'snow.tif',
'snlq_path': 'snlq.tif',
}
# _PFT_STATE_VARIABLES contains state variables that are a
# property of a PFT, including:
# carbon, nitrogen, and phosphorous in aboveground biomass
# where 1=N, 2=P
# e.g. aglivc = C in aboveground live biomass,
# aglive_1 = N in aboveground live biomass;
# carbon, nitrogen, and phosphorous in aboveground standing dead
# biomass, stdedc and stdede;
# carbon, nitrogen and phosphorous in belowground live biomass,
# aglivc and aglive
# state variables fully described in this table:
# https://docs.google.com/spreadsheets/d/1TGCDOJS4nNsJpzTWdiWed390NmbhQFB2uUoMs9oTTYo/edit?usp=sharing
_PFT_STATE_VARIABLES = [
'aglivc', 'bglivc', 'stdedc', 'aglive_1', 'bglive_1',
'stdede_1', 'aglive_2', 'bglive_2', 'stdede_2', 'avh2o_1',
'crpstg_1', 'crpstg_2',
]
# intermediate parameters that do not change between timesteps,
# including field capacity and wilting point of each soil layer,
# coefficients describing effect of soil texture on decomposition
# rates
_PERSISTENT_PARAMS_FILES = {
'afiel_1_path': 'afiel_1.tif',
'afiel_2_path': 'afiel_2.tif',
'afiel_3_path': 'afiel_3.tif',
'afiel_4_path': 'afiel_4.tif',
'afiel_5_path': 'afiel_5.tif',
'afiel_6_path': 'afiel_6.tif',
'afiel_7_path': 'afiel_7.tif',
'afiel_8_path': 'afiel_8.tif',
'afiel_9_path': 'afiel_9.tif',
'awilt_1_path': 'awilt_1.tif',
'awilt_2_path': 'awilt_2.tif',
'awilt_3_path': 'awilt_3.tif',
'awilt_4_path': 'awilt_4.tif',
'awilt_5_path': 'awilt_5.tif',
'awilt_6_path': 'awilt_6.tif',
'awilt_7_path': 'awilt_7.tif',
'awilt_8_path': 'awilt_8.tif',
'awilt_9_path': 'awilt_9.tif',
'wc_path': 'wc.tif',
'eftext_path': 'eftext.tif',
'p1co2_2_path': 'p1co2_2.tif',
'fps1s3_path': 'fps1s3.tif',
'orglch_path': 'orglch.tif',
'fps2s3_path': 'fps2s3.tif',
'rnewas_1_1_path': 'rnewas_1_1.tif',
'rnewas_2_1_path': 'rnewas_2_1.tif',
'rnewas_1_2_path': 'rnewas_1_2.tif',
'rnewas_2_2_path': 'rnewas_2_2.tif',
'rnewbs_1_1_path': 'rnewbs_1_1.tif',
'rnewbs_1_2_path': 'rnewbs_1_2.tif',
'rnewbs_2_1_path': 'rnewbs_2_1.tif',
'rnewbs_2_2_path': 'rnewbs_2_2.tif',
'vlossg_path': 'vlossg.tif',
}
# site-level values that are updated once per year
_YEARLY_FILES = {
'annual_precip_path': 'annual_precip.tif',
'baseNdep_path': 'baseNdep.tif',
}
# pft-level values that are updated once per year
_YEARLY_PFT_FILES = ['pltlig_above', 'pltlig_below']
# intermediate values for each plant functional type that are shared
# between submodels, but do not need to be saved as output
_PFT_INTERMEDIATE_VALUES = [
'h2ogef_1', 'tgprod_pot_prod',
'cercrp_min_above_1', 'cercrp_min_above_2',
'cercrp_max_above_1', 'cercrp_max_above_2',
'cercrp_min_below_1', 'cercrp_min_below_2',
'cercrp_max_below_1', 'cercrp_max_below_2',
'tgprod', 'rtsh', 'flgrem', 'fdgrem']
# intermediate site-level values that are shared between submodels,
# but do not need to be saved as output
_SITE_INTERMEDIATE_VALUES = [
'amov_1', 'amov_2', 'amov_3', 'amov_4', 'amov_5', 'amov_6', 'amov_7',
'amov_8', 'amov_9', 'amov_10', 'snowmelt', 'bgwfunc', 'diet_sufficiency']
# fixed parameters for each grazing animal type are adapted from the GRAZPLAN
# model as described by Freer et al. 2012, "The GRAZPLAN animal biology model
# for sheep and cattle and the GrazFeed decision support tool"
_FREER_PARAM_DICT = {
'b_indicus': {
'CN1': 0.0115,
'CN2': 0.27,
'CN3': 0.4,
'CI1': 0.025,
'CI2': 1.7,
'CI8': 62,
'CI9': 1.7,
'CI15': 0.5,
'CI19': 0.416,
'CI20': 1.5,
'CR1': 0.8,
'CR2': 0.17,
'CR3': 1.7,
'CR4': 0.00078,
'CR5': 0.6,
'CR6': 0.00074,
'CR7': 0.5,
'CR12': 0.8,
'CR13': 0.35,
'CK1': 0.5,
'CK2': 0.02,
'CK3': 0.85,
'CK5': 0.4,
'CK6': 0.02,
'CK8': 0.133,
'CL0': 0.375,
'CL1': 4,
'CL2': 30,
'CL3': 0.6,
'CL5': 0.94,
'CL6': 3.1,
'CL15': 0.032,
'CM1': 0.09,
'CM2': 0.31,
'CM3': 0.00008,
'CM4': 0.84,
'CM6': 0.0025,
'CM7': 0.9,
'CM16': 0.0026,
'CRD1': 0.3,
'CRD2': 0.25,
'CRD4': 0.007,
'CRD5': 0.005,
'CRD6': 0.35,
'CRD7': 0.1,
'CA1': 0.05,
'CA2': 0.85,
'CA3': 5.5,
'CA4': 0.178,
'CA6': 1,
'CA7': 0.6,
'CP1': 285,
'CP4': 0.33,
'CP5': 1.8,
'CP6': 2.42,
'CP7': 1.16,
'CP8': 4.11,
'CP9': 343.5,
'CP10': 0.0164,
'CP15': 0.07,
},
'b_taurus': {
'CN1': 0.0115,
'CN2': 0.27,
'CN3': 0.4,
'CI1': 0.025,
'CI2': 1.7,
'CI8': 62,
'CI9': 1.7,
'CI15': 0.5,
'CI19': 0.416,
'CI20': 1.5,
'CR1': 0.8,
'CR2': 0.17,
'CR3': 1.7,
'CR4': 0.00078,
'CR5': 0.6,
'CR6': 0.00074,
'CR7': 0.5,
'CR12': 0.8,
'CR13': 0.35,
'CK1': 0.5,
'CK2': 0.02,
'CK3': 0.85,
'CK5': 0.4,
'CK6': 0.02,
'CK8': 0.133,
'CL0': 0.375,
'CL1': 4,
'CL2': 30,
'CL3': 0.6,
'CL5': 0.94,
'CL6': 3.1,
'CL15': 0.032,
'CM1': 0.09,
'CM2': 0.36,
'CM3': 0.00008,
'CM4': 0.84,
'CM6': 0.0025,
'CM7': 0.9,
'CM16': 0.0026,
'CRD1': 0.3,
'CRD2': 0.25,
'CRD4': 0.007,
'CRD5': 0.005,
'CRD6': 0.35,
'CRD7': 0.1,
'CA1': 0.05,
'CA2': 0.85,
'CA3': 5.5,
'CA4': 0.178,
'CA6': 1,
'CA7': 0.6,
'CP1': 285,
'CP4': 0.33,
'CP5': 1.8,
'CP6': 2.42,
'CP7': 1.16,
'CP8': 4.11,
'CP9': 343.5,
'CP10': 0.0164,
'CP15': 0.07,
},
'indicus_x_taurus': {
'CN1': 0.0115,
'CN2': 0.27,
'CN3': 0.4,
'CI1': 0.025,
'CI2': 1.7,
'CI8': 62,
'CI9': 1.7,
'CI15': 0.5,
'CI19': 0.416,
'CI20': 1.5,
'CR1': 0.8,
'CR2': 0.17,
'CR3': 1.7,
'CR4': 0.00078,
'CR5': 0.6,
'CR6': 0.00074,
'CR7': 0.5,
'CR12': 0.8,
'CR13': 0.35,
'CK1': 0.5,
'CK2': 0.02,
'CK3': 0.85,
'CK5': 0.4,
'CK6': 0.02,
'CK8': 0.133,
'CL0': 0.375,
'CL1': 4,
'CL2': 30,
'CL3': 0.6,
'CL5': 0.94,
'CL6': 3.1,
'CL15': 0.032,
'CM1': 0.09,
'CM2': 0.335,
'CM3': 0.00008,
'CM4': 0.84,
'CM6': 0.0025,
'CM7': 0.9,
'CM16': 0.0026,
'CRD1': 0.3,
'CRD2': 0.25,
'CRD4': 0.007,
'CRD5': 0.005,
'CRD6': 0.35,
'CRD7': 0.1,
'CA1': 0.05,
'CA2': 0.85,
'CA3': 5.5,
'CA4': 0.178,
'CA6': 1,
'CA7': 0.6,
'CP1': 285,
'CP4': 0.33,
'CP5': 1.8,
'CP6': 2.42,
'CP7': 1.16,
'CP8': 4.11,
'CP9': 343.5,
'CP10': 0.0164,
'CP15': 0.07,
},
'sheep': {
'CN1': 0.0157,
'CN2': 0.27,
'CN3': 0.4,
'CI1': 0.04,
'CI2': 1.7,
'CI8': 28,
'CI9': 1.4,
'CI12': 0.15,
'CI13': 0.02,
'CI14': 0.002,
'CI20': 1.5,
'CR1': 0.8,
'CR2': 0.17,
'CR3': 1.7,
'CR4': 0.00112,
'CR5': 0.6,
'CR6': 0.00112,
'CR7': 0,
'CR12': 0.8,
'CR13': 0.35,
'CK1': 0.5,
'CK2': 0.02,
'CK3': 0.85,
'CK5': 0.4,
'CK6': 0.02,
'CK8': 0.133,
'CL0': 0.486,
'CL1': 2,
'CL2': 22,
'CL3': 1,
'CL5': 0.94,
'CL6': 4.7,
'CL15': 0.045,
'CM1': 0.09,
'CM2': 0.26,
'CM3': 0.00008,
'CM4': 0.84,
'CM6': 0.02,
'CM7': 0.9,
'CM16': 0.0026,
'CRD1': 0.3,
'CRD2': 0.25,
'CRD4': 0.007,
'CRD5': 0.005,
'CRD6': 0.35,
'CRD7': 0.1,
'CA1': 0.05,
'CA2': 0.85,
'CA3': 5.5,
'CA4': 0.178,
'CA6': 1,
'CA7': 0.6,
'CW1': 24,
'CW2': 0.004,
'CW3': 0.7,
'CW5': 0.25,
'CW6': 0.072,
'CW7': 1.35,
'CW8': 0.016,
'CW9': 1,
'CW12': 0.025,
'CP1': 150,
'CP4': 0.33,
'CP5': 1.43,
'CP6': 3.38,
'CP7': 0.91,
'CP8': 4.33,
'CP9': 4.37,
'CP10': 0.965,
'CP15': 0.1,
},
}
# Target nodata is for general rasters that are positive, and _IC_NODATA are
# for rasters that are any range
_TARGET_NODATA = -1.0
_IC_NODATA = float(numpy.finfo('float32').min)
# SV_NODATA is for state variables
_SV_NODATA = -1.0
def execute(args):
"""InVEST Forage Model.
[model description]
Parameters:
args['workspace_dir'] (string): path to target output workspace.
args['results_suffix'] (string): (optional) string to append to any
output file names
args['starting_month'] (int): what month to start reporting where
the range 1..12 is equivalent to Jan..Dec.
args['starting_year'] (int): what year to start runs. this value is
used to notate outputs in the form [month_int]_[year]
args['n_months'] (int): number of months to run model, the model run
will start reporting in `args['starting_month']`.
args['aoi_path'] (string): path to polygon vector indicating the
desired spatial extent of the model. This has the effect of
clipping the computational area of the input datasets to be the
area intersected by this polygon.
args['management_threshold'] (float): biomass in kg/ha required to be
left standing at each model step after offtake by grazing animals
args['proportion_legume_path'] (string): path to raster containing
fraction of pasture that is legume, by weight
args['bulk_density_path'] (string): path to bulk density raster.
args['ph_path'] (string): path to soil pH raster.
args['clay_proportion_path'] (string): path to raster representing
per-pixel proportion of soil component that is clay
args['silt_proportion_path'] (string): path to raster representing
per-pixel proportion of soil component that is silt
args['sand_proportion_path'] (string): path to raster representing
per-pixel proportion of soil component that is sand
args['precip_dir'] (string): path to a directory containing monthly
precipitation rasters. The model requires at least 12 months of
precipitation and expects to find a precipitation file input for
every month of the simulation, so the number of precipitation
files should be the maximum of 12 and `n_months`. The file name of
each precipitation raster must end with the year, followed by an
underscore, followed by the month number. E.g., Precip_2016_1.tif
for January of 2016.
args['min_temp_dir'] (string): path to a directory containing monthly
minimum temperature rasters. The model requires one minimum
temperature raster for each month of the year, or each month that
the model is run, whichever is smaller. The file name of each
minimum temperature raster must end with the month number. E.g.,
Min_temperature_1.tif for January.
args['max_temp_dir'] (string): path to a directory containing monthly
maximum temperature rasters. The model requires one maximum
temperature raster for each month of the year, or each month that
the model is run, whichever is smaller. The file name of each
maximum temperature raster must end with the month number. E.g.,
Max_temperature_1.tif for January.
args['site_param_table'] (string): path to csv file giving site
parameters. This file must contain a column named "site" that
contains unique integers. These integer values correspond to site
type identifiers which are values in the site parameter spatial
index raster. Other required fields for this table are site and
"fixed" parameters from the Century model, i.e., the parameters
in the Century input files site.100 and fix.100.
args['site_param_spatial_index_path'] (string): path to a raster file
that indexes site parameters, indicating which set of site
parameter values should apply at each pixel in the raster. The
raster should be composed of integers that correspond to values in
the field "site" in `site_param_table`.
args['veg_trait_path'] (string): path to csv file giving vegetation
traits for each plant functional type available for grazing. This
file must contain a column named "PFT" that contains unique
integers. These integer values correspond to PFT identifiers of
veg spatial composition rasters. Other required fields for this
table are vegetation input parameters from the Century model, for
example maximum intrinsic growth rate, optimum temperature for
production, minimum C/N ratio, etc.
args['veg_spatial_composition_path_pattern'] (string): path to
vegetation rasters, one per plant functional type available for
grazing, where <PFT> can be replaced with an integer that is
indexed in the veg trait csv.
Example: if this value is given as `./vegetation/pft_<PFT>.tif`
and the directory `./vegetation/` contains these files:
"pft_1.tif"
"pft_12.tif"
"pft_50.tif",
then the "PFT" field in the vegetation trait table must contain
the values 1, 12, and 50.
args['animal_trait_path'] (string): path to csv file giving animal
traits for each animal type - number - duration combination. This
table must contain a column named "animal_id" that contains unique
integers. These integer values correspond to features in the
animal management layer.
Other required fields in this table are:
type (allowable values: b_indicus, b_taurus,
indicus_x_taurus, sheep, camelid, hindgut_fermenter)
sex (allowable values: entire_m, castrate, breeding_female,
NA)
age (days)
weight (kg)
SRW (standard reference weight, kg; the weight of a mature
female in median condition)
SFW (standard fleece weight, kg; the average weight of fleece
of a mature adult; for sheep only)
birth_weight (kg)
grz_months (a string of integers, separated by ','; months of
the simulation when animals are present,
relative to `starting_month`. For example, if `n_months`
is 3, and animals are present during the entire simulation
period, `grz_months` should be "1,2,3")
args['animal_grazing_areas_path'] (string): path to animal vector
inputs giving the location of grazing animals. Must have a field
named "animal_id", containing unique integers that correspond to
the values in the "animal_id" column of the animal trait csv, and
a field named "num_animal" giving the number of animals grazing
inside each polygon feature.
args['initial_conditions_dir'] (string): optional input, path to
directory containing initial conditions. If this directory is not
supplied, a site_initial_table and pft_initial_table must be
supplied. If supplied, this directory must contain a series of
rasters with initial values for each PFT and for the site.
Required rasters for each PFT:
initial variables that are a property of PFT in the table
https://docs.google.com/spreadsheets/d/1TGCDOJS4nNsJpzTWdiWed390NmbhQFB2uUoMs9oTTYo/edit?usp=sharing
e.g., aglivc_<PFT>.tif
Required for the site:
initial variables that are a property of site in the table
https://docs.google.com/spreadsheets/d/1TGCDOJS4nNsJpzTWdiWed390NmbhQFB2uUoMs9oTTYo/edit?usp=sharing
args['site_initial_table'] (string): optional input, path to table
containing initial conditions for each site state variable. If an
initial conditions directory is not supplied, this table must be
supplied. This table must contain a value for each site code and
each state variable listed in the following table:
https://docs.google.com/spreadsheets/d/1TGCDOJS4nNsJpzTWdiWed390NmbhQFB2uUoMs9oTTYo/edit?usp=sharing
args['pft_initial_table'] (string): optional input, path to table
containing initial conditions for each plant functional type state
variable. If an initial conditions directory is not supplied, this
table must be supplied. This table must contain a value for each
plant functional type index and each state variable listed in the
following table:
https://docs.google.com/spreadsheets/d/1TGCDOJS4nNsJpzTWdiWed390NmbhQFB2uUoMs9oTTYo/edit?usp=sharing
args['save_sv_rasters'] (boolean): optional input, default false.
Should rasters containing all state variables be saved for each
model time step?
args['animal_density'] (string): optional input, density of grazing
animals in animals per hectare.
args['crude_protein'] (float): optional input, crude protein
concentration of forage for the purposes of animal diet selection.
Should be a value between 0-1. If included, this value is
substituted for N content of forage when calculating digestibility
and "ingestibility" of forage, and protein content of the diet, for
grazing animals.
Returns:
None.
"""
LOGGER.info("model execute: %s", args)
starting_month = int(args['starting_month'])
starting_year = int(args['starting_year'])
n_months = int(args['n_months'])
try:
delete_sv_folders = not args['save_sv_rasters']
except KeyError:
delete_sv_folders = True
try:
global CRUDE_PROTEIN
CRUDE_PROTEIN = args['crude_protein']
except KeyError:
pass
try:
animal_density_path = args['animal_density']
except KeyError:
args['animal_density'] = None
# this set will build up the integer months that are used so we can index
# them with temperature later
temperature_month_set = set()
# this dict will be used to build the set of input rasters associated with
# a reasonable lookup ID so we can have a nice dataset to align for raster
# stack operations
base_align_raster_path_id_map = {}
precip_dir_list = [
os.path.join(args['precip_dir'], f) for f in
os.listdir(args['precip_dir'])]
for month_index in range(n_months):
month_i = (starting_month + month_index - 1) % 12 + 1
temperature_month_set.add(month_i)
year = starting_year + (starting_month + month_index - 1) // 12
year_month_match = re.compile(
r'.*[^\d]%d_%d\.[^.]+$' % (year, month_i))
file_list = [
month_file_path for month_file_path in precip_dir_list if
year_month_match.match(month_file_path)]
if len(file_list) == 0:
raise ValueError(
"No precipitation data found for year %d, month %d" %
(year, month_i))
if len(file_list) > 1:
raise ValueError(
"Ambiguous set of files found for year %d, month %d: %s" %
(year, month_i, file_list))
base_align_raster_path_id_map[
'precip_{}'.format(month_index)] = file_list[0]
# the model requires 12 months of precipitation data to calculate
# atmospheric N deposition and potential production from annual precip
n_precip_months = int(args['n_months'])
if n_precip_months < 12:
m_index = int(args['n_months'])
while n_precip_months < 12:
month_i = (starting_month + m_index - 1) % 12 + 1
year = starting_year + (starting_month + m_index - 1) // 12
year_month_match = re.compile(
r'.*[^\d]%d_%d\.[^.]+$' % (year, month_i))
file_list = [
month_file_path for month_file_path in precip_dir_list if
year_month_match.match(month_file_path)]
if len(file_list) == 0:
break
if len(file_list) > 1:
raise ValueError(
"Ambiguous set of files found for year %d, month %d: %s" %
(year, month_i, file_list))
base_align_raster_path_id_map[
'precip_%d' % m_index] = file_list[0]
n_precip_months = n_precip_months + 1
m_index = m_index + 1
if n_precip_months < 12:
raise ValueError("At least 12 months of precipitation data required")
# collect monthly temperature data
min_temp_dir_list = [
os.path.join(args['min_temp_dir'], f) for f in
os.listdir(args['min_temp_dir'])]
for month_i in temperature_month_set:
month_file_match = re.compile(r'.*[^\d]%d\.[^.]+$' % month_i)
file_list = [
month_file_path for month_file_path in min_temp_dir_list if
month_file_match.match(month_file_path)]
if len(file_list) == 0:
raise ValueError(
"No minimum temperature data found for month %d" % month_i)
if len(file_list) > 1:
raise ValueError(
"Ambiguous set of files found for month %d: %s" %
(month_i, file_list))
base_align_raster_path_id_map[
'min_temp_%d' % month_i] = file_list[0]
max_temp_dir_list = [
os.path.join(args['max_temp_dir'], f) for f in
os.listdir(args['max_temp_dir'])]
for month_i in temperature_month_set:
month_file_match = re.compile(r'.*[^\d]%d\.[^.]+$' % month_i)
file_list = [
month_file_path for month_file_path in max_temp_dir_list if
month_file_match.match(month_file_path)]
if len(file_list) == 0:
raise ValueError(
"No maximum temperature data found for month %d" % month_i)
if len(file_list) > 1:
raise ValueError(
"Ambiguous set of files found for month %d: %s" %
(month_i, file_list))
base_align_raster_path_id_map[
'max_temp_%d' % month_i] = file_list[0]
# lookup to provide path to soil percent given soil type
for soil_type in SOIL_TYPE_LIST:
base_align_raster_path_id_map[soil_type] = (
args['%s_proportion_path' % soil_type])
if not os.path.exists(base_align_raster_path_id_map[soil_type]):
raise ValueError(
"Couldn't find %s for %s" % (
base_align_raster_path_id_map[soil_type], soil_type))
base_align_raster_path_id_map['bulk_d_path'] = args['bulk_density_path']
base_align_raster_path_id_map['ph_path'] = args['ph_path']
# make sure site initial conditions and parameters exist for each site
# identifier
base_align_raster_path_id_map['site_index'] = (
args['site_param_spatial_index_path'])
n_bands = pygeoprocessing.get_raster_info(
args['site_param_spatial_index_path'])['n_bands']
if n_bands > 1:
raise ValueError(
'Site spatial index raster must contain only one band')
site_datatype = pygeoprocessing.get_raster_info(
args['site_param_spatial_index_path'])['datatype']
if site_datatype not in [1, 2, 3, 4, 5]:
raise ValueError('Site spatial index raster must be integer type')
# get unique values in site param raster
site_index_set = set()
for offset_map, raster_block in pygeoprocessing.iterblocks(
(args['site_param_spatial_index_path'], 1)):
site_index_set.update(numpy.unique(raster_block))
site_nodata = pygeoprocessing.get_raster_info(
args['site_param_spatial_index_path'])['nodata'][0]
if site_nodata in site_index_set:
site_index_set.remove(site_nodata)
site_param_table = utils.build_lookup_from_csv(
args['site_param_table'], 'site')
missing_site_index_list = list(
site_index_set.difference(site_param_table.keys()))
if missing_site_index_list:
raise ValueError(
"Couldn't find parameter values for the following site " +
"indices: %s\n\t" + ", ".join(missing_site_index_list))
# make sure plant functional type parameters exist for each pft raster
pft_dir = os.path.dirname(args['veg_spatial_composition_path_pattern'])
pft_basename = os.path.basename(
args['veg_spatial_composition_path_pattern'])
files = [
f for f in os.listdir(pft_dir) if os.path.isfile(
os.path.join(pft_dir, f))]
pft_regex = re.compile(pft_basename.replace('<PFT>', r'(\d+)'))
pft_matches = [
m for m in [pft_regex.search(f) for f in files] if m is not None]
pft_id_set = set([int(m.group(1)) for m in pft_matches])
for pft_i in pft_id_set:
pft_path = args['veg_spatial_composition_path_pattern'].replace(
'<PFT>', '%d' % pft_i)
base_align_raster_path_id_map['pft_%d' % pft_i] = pft_path
veg_trait_table = utils.build_lookup_from_csv(
args['veg_trait_path'], 'PFT')
missing_pft_trait_list = pft_id_set.difference(veg_trait_table.keys())
if missing_pft_trait_list:
raise ValueError(
"Couldn't find trait values for the following plant functional " +
"types: %s\n\t" + ", ".join(missing_pft_trait_list))
frtcindx_set = set([
pft_i['frtcindx'] for pft_i in veg_trait_table.values()])
if frtcindx_set.difference(set([0, 1])):
raise ValueError("frtcindx parameter contains invalid values")
base_align_raster_path_id_map['proportion_legume_path'] = args[
'proportion_legume_path']
# track separate state variable files for each PFT
pft_sv_dict = {}
for pft_i in pft_id_set:
for sv in _PFT_STATE_VARIABLES:
pft_sv_dict['{}_{}_path'.format(
sv, pft_i)] = '{}_{}.tif'.format(sv, pft_i)
# make sure animal traits exist for each feature in animal management
# layer
anim_id_list = []
driver = ogr.GetDriverByName('ESRI Shapefile')
datasource = driver.Open(args['animal_grazing_areas_path'], 0)
layer = datasource.GetLayer()
for feature in layer:
anim_id_list.append(feature.GetField('animal_id'))
input_animal_trait_table = utils.build_lookup_from_csv(
args['animal_trait_path'], 'animal_id')
missing_animal_trait_list = set(
anim_id_list).difference(input_animal_trait_table.keys())
if missing_animal_trait_list:
raise ValueError(
"Couldn't find trait values for the following animal " +
"ids: %s\n\t" + ", ".join(missing_animal_trait_list))
# if animal density is supplied, align inputs to match its resolution
# otherwise, match resolution of precipitation rasters
if args['animal_density']:
target_pixel_size = pygeoprocessing.get_raster_info(
args['animal_density'])['pixel_size']
base_align_raster_path_id_map['animal_density'] = args[
'animal_density']
else:
target_pixel_size = pygeoprocessing.get_raster_info(
base_align_raster_path_id_map['precip_0'])['pixel_size']
LOGGER.info(
"pixel size of aligned inputs: %s", target_pixel_size)
# temporary directory for intermediate files
global PROCESSING_DIR
PROCESSING_DIR = os.path.join(args['workspace_dir'], "temporary_files")
if not os.path.exists(PROCESSING_DIR):
os.makedirs(PROCESSING_DIR)
# set up a dictionary that uses the same keys as
# 'base_align_raster_path_id_map' to point to the clipped/resampled
# rasters to be used in raster calculations for the model.
aligned_raster_dir = os.path.join(
args['workspace_dir'], 'aligned_inputs')
if os.path.exists(aligned_raster_dir):
shutil.rmtree(aligned_raster_dir)
os.makedirs(aligned_raster_dir)
aligned_inputs = dict([(key, os.path.join(
aligned_raster_dir, 'aligned_%s' % os.path.basename(path)))
for key, path in base_align_raster_path_id_map.items()])
# align all the base inputs to be the minimum known pixel size and to
# only extend over their combined intersections
source_input_path_list = [
base_align_raster_path_id_map[k] for k in sorted(
base_align_raster_path_id_map.keys())]
aligned_input_path_list = [
aligned_inputs[k] for k in sorted(aligned_inputs.keys())]
pygeoprocessing.align_and_resize_raster_stack(
source_input_path_list, aligned_input_path_list,
['near'] * len(source_input_path_list),
target_pixel_size, 'intersection',
base_vector_path_list=[args['aoi_path']],
vector_mask_options={'mask_vector_path': args['aoi_path']})
_check_pft_fractional_cover_sum(aligned_inputs, pft_id_set)
file_suffix = utils.make_suffix_string(args, 'results_suffix')
# create animal trait spatial index raster from management polygon
aligned_inputs['animal_index'] = os.path.join(
aligned_raster_dir, 'animal_spatial_index.tif')
pygeoprocessing.new_raster_from_base(
aligned_inputs['site_index'], aligned_inputs['animal_index'],
gdal.GDT_Int32, [_TARGET_NODATA], fill_value_list=[_TARGET_NODATA])
pygeoprocessing.rasterize(
args['animal_grazing_areas_path'], aligned_inputs['animal_index'],
option_list=["ATTRIBUTE=animal_id"])
# create uniform animal density raster, if not supplied as input
if not args['animal_density']:
aligned_inputs['animal_density'] = os.path.join(
aligned_raster_dir, 'animal_density.tif')
_animal_density(aligned_inputs, args['animal_grazing_areas_path'])
# Initialization
sv_dir = os.path.join(args['workspace_dir'], 'state_variables_m-1')
os.makedirs(sv_dir)
initial_conditions_dir = None
try:
initial_conditions_dir = args['initial_conditions_dir']
except KeyError:
pass
if initial_conditions_dir:
# check that a raster for each required state variable is supplied
missing_initial_values = []
# set _SV_NODATA from initial rasters
state_var_nodata = set([])
# align initial state variables to resampled inputs
resample_initial_path_map = {}
for sv in _SITE_STATE_VARIABLE_FILES:
sv_path = os.path.join(
initial_conditions_dir, _SITE_STATE_VARIABLE_FILES[sv])
state_var_nodata.update(
set([pygeoprocessing.get_raster_info(sv_path)['nodata'][0]]))
resample_initial_path_map[sv] = sv_path
if not os.path.exists(sv_path):
missing_initial_values.append(sv_path)
for pft_i in pft_id_set:
for sv in _PFT_STATE_VARIABLES:
sv_key = '{}_{}_path'.format(sv, pft_i)
sv_path = os.path.join(
initial_conditions_dir, '{}_{}.tif'.format(sv, pft_i))
state_var_nodata.update(
set([pygeoprocessing.get_raster_info(sv_path)['nodata']
[0]]))
resample_initial_path_map[sv_key] = sv_path
if not os.path.exists(sv_path):
missing_initial_values.append(sv_path)
if missing_initial_values:
raise ValueError(
"Couldn't find the following required initial values: " +
"\n\t".join(missing_initial_values))
if len(state_var_nodata) > 1:
raise ValueError(
"Initial state variable rasters contain >1 nodata value")
global _SV_NODATA
_SV_NODATA = list(state_var_nodata)[0]
# align initial values with inputs
initial_path_list = (
[aligned_inputs['precip_0']] +
[resample_initial_path_map[key] for key in sorted(
resample_initial_path_map.keys())])
aligned_initial_path_list = (
[os.path.join(PROCESSING_DIR, 'aligned_input_template.tif')] +
[os.path.join(
sv_dir, os.path.basename(resample_initial_path_map[key])) for
key in sorted(resample_initial_path_map.keys())])
pygeoprocessing.align_and_resize_raster_stack(
initial_path_list, aligned_initial_path_list,
['near'] * len(initial_path_list),
target_pixel_size, 'intersection',
base_vector_path_list=[args['aoi_path']], raster_align_index=0,
vector_mask_options={'mask_vector_path': args['aoi_path']})
sv_reg = dict(
[(key, os.path.join(sv_dir, os.path.basename(path)))
for key, path in resample_initial_path_map.items()])
else:
# create initialization rasters from tables
try:
site_initial_conditions_table = utils.build_lookup_from_csv(
args['site_initial_table'], 'site')
except KeyError:
raise ValueError(
"If initial conditions rasters are not supplied, initial " +
"conditions tables must be supplied")
missing_site_index_list = list(
site_index_set.difference(site_initial_conditions_table.keys()))
if missing_site_index_list:
raise ValueError(
"Couldn't find initial conditions values for the following " +
"site indices: %s\n\t" + ", ".join(missing_site_index_list))
try:
pft_initial_conditions_table = utils.build_lookup_from_csv(
args['pft_initial_table'], 'PFT')
except KeyError:
raise ValueError(
"If initial conditions rasters are not supplied, initial " +
"conditions tables must be supplied")
missing_pft_index_list = pft_id_set.difference(
pft_initial_conditions_table.keys())
if missing_pft_index_list:
raise ValueError(
"Couldn't find initial condition values for the following "
"plant functional types: %s\n\t" + ", ".join(
missing_pft_index_list))
sv_reg = initial_conditions_from_tables(
aligned_inputs, sv_dir, pft_id_set, site_initial_conditions_table,
pft_initial_conditions_table)
# calculate persistent intermediate parameters that do not change during
# the simulation
persist_param_dir = os.path.join(
args['workspace_dir'], 'intermediate_parameters')
utils.make_directories([persist_param_dir])
pp_reg = utils.build_file_registry(
[(_PERSISTENT_PARAMS_FILES, persist_param_dir)], file_suffix)
# calculate derived animal traits that do not change during the simulation
freer_parameter_df = pandas.DataFrame.from_dict(
_FREER_PARAM_DICT, orient='index')
freer_parameter_df['type'] = freer_parameter_df.index
animal_trait_table = calc_derived_animal_traits(
input_animal_trait_table, freer_parameter_df)
# calculate maximum potential intake of each animal type
for animal_id in animal_trait_table.keys():
revised_animal_trait_dict = calc_max_intake(
animal_trait_table[animal_id])
animal_trait_table[animal_id] = revised_animal_trait_dict
# calculate field capacity and wilting point
LOGGER.info("Calculating field capacity and wilting point")
_afiel_awilt(
aligned_inputs['site_index'], site_param_table,
sv_reg['som1c_2_path'], sv_reg['som2c_2_path'], sv_reg['som3c_path'],
aligned_inputs['sand'], aligned_inputs['silt'],
aligned_inputs['clay'], aligned_inputs['bulk_d_path'], pp_reg)
# calculate other persistent parameters
LOGGER.info("Calculating persistent parameters")
_persistent_params(
aligned_inputs['site_index'], site_param_table,
aligned_inputs['sand'], aligned_inputs['clay'], pp_reg)
# calculate required ratios for decomposition of structural material
LOGGER.info("Calculating required ratios for structural decomposition")
_structural_ratios(
aligned_inputs['site_index'], site_param_table, sv_reg, pp_reg)
# make yearly directory for values that are updated every twelve months
year_dir = tempfile.mkdtemp(dir=PROCESSING_DIR)
year_reg = dict(
[(key, os.path.join(year_dir, path)) for key, path in
_YEARLY_FILES.items()])
for pft_i in pft_id_set:
for file in _YEARLY_PFT_FILES:
year_reg['{}_{}'.format(file, pft_i)] = os.path.join(
year_dir, '{}_{}.tif'.format(file, pft_i))
# make monthly directory for monthly intermediate parameters that are
# shared between submodels, but do not need to be saved as output
month_temp_dir = tempfile.mkdtemp(dir=PROCESSING_DIR)
month_reg = {}
for pft_i in pft_id_set:
for val in _PFT_INTERMEDIATE_VALUES:
month_reg['{}_{}'.format(
val, pft_i)] = os.path.join(
month_temp_dir, '{}_{}.tif'.format(val, pft_i))
for val in _SITE_INTERMEDIATE_VALUES:
month_reg[val] = os.path.join(month_temp_dir, '{}.tif'.format(val))
output_dir = os.path.join(args['workspace_dir'], "output")
if not os.path.exists(output_dir):
os.makedirs(output_dir)
# provisional state variable registry contains provisional biomass in
# absence of grazing
provisional_sv_dir = tempfile.mkdtemp(dir=PROCESSING_DIR)
provisional_sv_reg = utils.build_file_registry(
[(_SITE_STATE_VARIABLE_FILES, provisional_sv_dir),
(pft_sv_dict, provisional_sv_dir)], file_suffix)
intermediate_sv_dir = tempfile.mkdtemp(dir=PROCESSING_DIR)
# Main simulation loop
# for each step in the simulation
for month_index in range(n_months):
if (month_index % 12) == 0:
# Update yearly quantities
_yearly_tasks(
aligned_inputs, site_param_table, veg_trait_table, month_index,
pft_id_set, year_reg)
current_month = (starting_month + month_index - 1) % 12 + 1
current_year = starting_year + (starting_month + month_index - 1) // 12
# track state variables from previous step
prev_sv_reg = sv_reg
for animal_id in animal_trait_table.keys():
if animal_trait_table[animal_id]['sex'] == 'breeding_female':
revised_animal_trait_dict = update_breeding_female_status(
animal_trait_table[animal_id], month_index)
animal_trait_table[animal_id] = revised_animal_trait_dict
revised_animal_trait_dict = calc_max_intake(
animal_trait_table[animal_id])
animal_trait_table[animal_id] = revised_animal_trait_dict
# enforce absence of grazing as zero biomass removed
for pft_i in pft_id_set:
pygeoprocessing.new_raster_from_base(
aligned_inputs['pft_{}'.format(pft_i)],
month_reg['flgrem_{}'.format(pft_i)], gdal.GDT_Float32,
[_TARGET_NODATA], fill_value_list=[0])
pygeoprocessing.new_raster_from_base(
aligned_inputs['pft_{}'.format(pft_i)],
month_reg['fdgrem_{}'.format(pft_i)], gdal.GDT_Float32,
[_TARGET_NODATA], fill_value_list=[0])
# populate provisional_sv_reg with provisional biomass in absence of
# grazing
_potential_production(
aligned_inputs, site_param_table, current_month, month_index,
pft_id_set, veg_trait_table, prev_sv_reg, pp_reg, month_reg)
_root_shoot_ratio(
aligned_inputs, site_param_table, current_month, pft_id_set,
veg_trait_table, prev_sv_reg, year_reg, month_reg)
_soil_water(
aligned_inputs, site_param_table, veg_trait_table, current_month,
month_index, prev_sv_reg, pp_reg, pft_id_set, month_reg,
provisional_sv_reg)
_decomposition(
aligned_inputs, current_month, month_index, pft_id_set,
site_param_table, year_reg, month_reg, prev_sv_reg, pp_reg,
provisional_sv_reg)
_death_and_partition(
'stded', aligned_inputs, site_param_table, current_month,
year_reg, pft_id_set, veg_trait_table, prev_sv_reg,
provisional_sv_reg)
_death_and_partition(
'bgliv', aligned_inputs, site_param_table, current_month,
year_reg, pft_id_set, veg_trait_table, prev_sv_reg,
provisional_sv_reg)
_shoot_senescence(
pft_id_set, veg_trait_table, prev_sv_reg, month_reg, current_month,
provisional_sv_reg)
intermediate_sv_reg = copy_intermediate_sv(
pft_id_set, provisional_sv_reg, intermediate_sv_dir)
delta_agliv_dict = _new_growth(
pft_id_set, aligned_inputs, site_param_table, veg_trait_table,
month_reg, current_month, provisional_sv_reg)
_apply_new_growth(delta_agliv_dict, pft_id_set, provisional_sv_reg)
# estimate grazing offtake by animals relative to provisional biomass
# at an intermediate step, after senescence but before new growth
_calc_grazing_offtake(
aligned_inputs, args['aoi_path'], args['management_threshold'],
intermediate_sv_reg, pft_id_set, aligned_inputs['animal_index'],
animal_trait_table, veg_trait_table, current_month, month_reg)
# estimate actual biomass production for this step, integrating impacts
# of grazing
sv_dir = os.path.join(
args['workspace_dir'], 'state_variables_m%d' % month_index)
utils.make_directories([sv_dir])
sv_reg = utils.build_file_registry(
[(_SITE_STATE_VARIABLE_FILES, sv_dir),
(pft_sv_dict, sv_dir)], file_suffix)
_potential_production(
aligned_inputs, site_param_table, current_month, month_index,
pft_id_set, veg_trait_table, prev_sv_reg, pp_reg, month_reg)
_root_shoot_ratio(
aligned_inputs, site_param_table, current_month, pft_id_set,
veg_trait_table, prev_sv_reg, year_reg, month_reg)
_soil_water(
aligned_inputs, site_param_table, veg_trait_table, current_month,
month_index, prev_sv_reg, pp_reg, pft_id_set, month_reg, sv_reg)
_decomposition(
aligned_inputs, current_month, month_index, pft_id_set,
site_param_table, year_reg, month_reg, prev_sv_reg, pp_reg, sv_reg)
_death_and_partition(
'stded', aligned_inputs, site_param_table, current_month,
year_reg, pft_id_set, veg_trait_table, prev_sv_reg, sv_reg)
_death_and_partition(
'bgliv', aligned_inputs, site_param_table, current_month,
year_reg, pft_id_set, veg_trait_table, prev_sv_reg, sv_reg)
_shoot_senescence(
pft_id_set, veg_trait_table, prev_sv_reg, month_reg, current_month,
sv_reg)
delta_agliv_dict = _new_growth(
pft_id_set, aligned_inputs, site_param_table, veg_trait_table,
month_reg, current_month, sv_reg)
_animal_diet_sufficiency(
sv_reg, pft_id_set, aligned_inputs, animal_trait_table,
veg_trait_table, current_month, month_reg)
_grazing(
aligned_inputs, site_param_table, month_reg, animal_trait_table,
pft_id_set, sv_reg)
_apply_new_growth(delta_agliv_dict, pft_id_set, sv_reg)
_leach(aligned_inputs, site_param_table, month_reg, sv_reg)
_write_monthly_outputs(
aligned_inputs, provisional_sv_reg, sv_reg, month_reg, pft_id_set,
current_year, current_month, output_dir, file_suffix)
# summary results
summary_output_dir = os.path.join(output_dir, 'summary_results')
os.makedirs(summary_output_dir)
summary_shp_path = os.path.join(
summary_output_dir,
'grazing_areas_results_rpm{}.shp'.format(file_suffix))
create_vector_copy(
args['animal_grazing_areas_path'], summary_shp_path)
field_pickle_map, field_header_order_list = aggregate_and_pickle_results(
output_dir, summary_shp_path)
_add_fields_to_shapefile(
field_pickle_map, field_header_order_list, summary_shp_path)
# clean up
shutil.rmtree(persist_param_dir)
shutil.rmtree(PROCESSING_DIR)
if delete_sv_folders:
for month_index in range(-1, n_months):
shutil.rmtree(
os.path.join(
args['workspace_dir'],
'state_variables_m%d' % month_index))
def raster_multiplication(
raster1, raster1_nodata, raster2, raster2_nodata, target_path,
target_path_nodata):
"""Multiply raster1 by raster2.
Multiply raster1 by raster2 element-wise. In any pixel where raster1 or
raster2 is nodata, the result is nodata. The result is always of float
datatype.
Side effects:
modifies or creates the raster indicated by `target_path`
Returns:
None
"""
def raster_multiply_op(raster1, raster2):
"""Multiply two rasters."""
valid_mask = (
(~numpy.isclose(raster1, raster1_nodata)) &
(~numpy.isclose(raster2, raster2_nodata)))
result = numpy.empty(raster1.shape, dtype=numpy.float32)
result[:] = target_path_nodata
result[valid_mask] = raster1[valid_mask] * raster2[valid_mask]
return result
pygeoprocessing.raster_calculator(
[(path, 1) for path in [raster1, raster2]],
raster_multiply_op, target_path, gdal.GDT_Float32,
target_path_nodata)
def raster_division(
raster1, raster1_nodata, raster2, raster2_nodata, target_path,
target_path_nodata):
"""Divide raster1 by raster2.
Divide raster1 by raster2 element-wise. In any pixel where raster1 or
raster2 is nodata, the result is nodata. The result is always of float
datatype.
Side effects:
modifies or creates the raster indicated by `target_path`
Returns:
None
"""
def raster_divide_op(raster1, raster2):
"""Divide raster1 by raster2."""
valid_mask = (
(~numpy.isclose(raster1, raster1_nodata)) &
(~numpy.isclose(raster2, raster2_nodata)))
raster1 = raster1.astype(numpy.float32)
raster2 = raster2.astype(numpy.float32)
result = numpy.empty(raster1.shape, dtype=numpy.float32)
result[:] = target_path_nodata
error_mask = ((raster1 != 0) & (raster2 == 0.) & valid_mask)
zero_mask = ((raster1 == 0.) & (raster2 == 0.) & valid_mask)
nonzero_mask = ((raster2 != 0.) & valid_mask)
result[error_mask] = target_path_nodata
result[zero_mask] = 0.
result[nonzero_mask] = raster1[nonzero_mask] / raster2[nonzero_mask]
return result
pygeoprocessing.raster_calculator(
[(path, 1) for path in [raster1, raster2]],
raster_divide_op, target_path, gdal.GDT_Float32,
target_path_nodata)
def raster_list_sum(
raster_list, input_nodata, target_path, target_nodata,
nodata_remove=False):
"""Calculate the sum per pixel across rasters in a list.
Sum the rasters in `raster_list` element-wise, allowing nodata values
in the rasters to propagate to the result or treating nodata as zero. If
nodata is treated as zero, areas where all inputs are nodata will be nodata
in the output.
Parameters:
raster_list (list): list of paths to rasters to sum
input_nodata (float or int): nodata value in the input rasters
target_path (string): path to location to store the result
target_nodata (float or int): nodata value for the result raster
nodata_remove (bool): if true, treat nodata values in input
rasters as zero. If false, the sum in a pixel where any input
raster is nodata is nodata.
Side effects:
modifies or creates the raster indicated by `target_path`
Returns:
None
"""
def raster_sum_op(*raster_list):
"""Add the rasters in raster_list without removing nodata values."""
invalid_mask = numpy.any(
numpy.isclose(numpy.array(raster_list), input_nodata), axis=0)
for r in raster_list:
numpy.place(r, numpy.isclose(r, input_nodata), [0])
sum_of_rasters = numpy.sum(raster_list, axis=0)
sum_of_rasters[invalid_mask] = target_nodata
return sum_of_rasters
def raster_sum_op_nodata_remove(*raster_list):
"""Add the rasters in raster_list, treating nodata as zero."""
invalid_mask = numpy.all(
numpy.isclose(numpy.array(raster_list), input_nodata), axis=0)
for r in raster_list:
numpy.place(r, numpy.isclose(r, input_nodata), [0])
sum_of_rasters = numpy.sum(raster_list, axis=0)
sum_of_rasters[invalid_mask] = target_nodata
return sum_of_rasters
if nodata_remove:
pygeoprocessing.raster_calculator(
[(path, 1) for path in raster_list], raster_sum_op_nodata_remove,
target_path, gdal.GDT_Float32, target_nodata)
else:
pygeoprocessing.raster_calculator(
[(path, 1) for path in raster_list], raster_sum_op,
target_path, gdal.GDT_Float32, target_nodata)
def raster_sum(
raster1, raster1_nodata, raster2, raster2_nodata, target_path,
target_nodata, nodata_remove=False):
"""Add raster 1 and raster2.
Add raster1 and raster2, allowing nodata values in the rasters to
propagate to the result or treating nodata as zero.
Parameters:
raster1 (string): path to one raster operand
raster1_nodata (float or int): nodata value in raster1
raster2 (string): path to second raster operand
raster2_nodata (float or int): nodata value in raster2
target_path (string): path to location to store the sum
target_nodata (float or int): nodata value for the result raster
nodata_remove (bool): if true, treat nodata values in input
rasters as zero. If false, the sum in a pixel where any
input raster is nodata is nodata.
Side effects:
modifies or creates the raster indicated by `target_path`
Returns:
None
"""
def raster_sum_op(raster1, raster2):
"""Add raster1 and raster2 without removing nodata values."""
valid_mask = (
(~numpy.isclose(raster1, raster1_nodata)) &
(~numpy.isclose(raster2, raster2_nodata)))
result = numpy.empty(raster1.shape, dtype=numpy.float32)
result[:] = target_nodata
result[valid_mask] = raster1[valid_mask] + raster2[valid_mask]
return result
def raster_sum_op_nodata_remove(raster1, raster2):
"""Add raster1 and raster2, treating nodata as zero."""
numpy.place(raster1, numpy.isclose(raster1, raster1_nodata), [0])
numpy.place(raster2, numpy.isclose(raster2, raster2_nodata), [0])
result = raster1 + raster2
return result
if nodata_remove:
pygeoprocessing.raster_calculator(
[(path, 1) for path in [raster1, raster2]],
raster_sum_op_nodata_remove, target_path, gdal.GDT_Float32,
target_nodata)
else:
pygeoprocessing.raster_calculator(
[(path, 1) for path in [raster1, raster2]],
raster_sum_op, target_path, gdal.GDT_Float32,
target_nodata)
def raster_difference(
raster1, raster1_nodata, raster2, raster2_nodata, target_path,
target_nodata, nodata_remove=False):
"""Subtract raster2 from raster1.
Subtract raster2 from raster1 element-wise, allowing nodata values in the
rasters to propagate to the result or treating nodata as zero.
Parameters:
raster1 (string): path to raster from which to subtract raster2
raster1_nodata (float or int): nodata value in raster1
raster2 (string): path to raster which should be subtracted from
raster1
raster2_nodata (float or int): nodata value in raster2
target_path (string): path to location to store the difference
target_nodata (float or int): nodata value for the result raster
nodata_remove (bool): if true, treat nodata values in input
rasters as zero. If false, the difference in a pixel where any
input raster is nodata is nodata.
Side effects:
modifies or creates the raster indicated by `target_path`
Returns:
None
"""
def raster_difference_op(raster1, raster2):
"""Subtract raster2 from raster1 without removing nodata values."""
valid_mask = (
(~numpy.isclose(raster1, raster1_nodata)) &
(~numpy.isclose(raster2, raster2_nodata)))
result = numpy.empty(raster1.shape, dtype=numpy.float32)
result[:] = target_nodata
result[valid_mask] = raster1[valid_mask] - raster2[valid_mask]
return result
def raster_difference_op_nodata_remove(raster1, raster2):
"""Subtract raster2 from raster1, treating nodata as zero."""
numpy.place(raster1, numpy.isclose(raster1, raster1_nodata), [0])
numpy.place(raster2, numpy.isclose(raster2, raster2_nodata), [0])
result = raster1 - raster2
return result
if nodata_remove:
pygeoprocessing.raster_calculator(
[(path, 1) for path in [raster1, raster2]],
raster_difference_op_nodata_remove, target_path, gdal.GDT_Float32,
target_nodata)
else:
pygeoprocessing.raster_calculator(
[(path, 1) for path in [raster1, raster2]],
raster_difference_op, target_path, gdal.GDT_Float32,
target_nodata)
def reclassify_nodata(target_path, new_nodata_value):
"""Reclassify the nodata value of a raster to a new value.
Convert all areas of nodata in the target raster to the new nodata
value, which must be an integer.
Parameters:
target_path (string): path to target raster
new_nodata_value (integer): new value to set as nodata
Side effects:
modifies the raster indicated by `target_path`
Returns:
None
"""
def reclassify_op(target_raster):
reclassified_raster = numpy.copy(target_raster)
reclassify_mask = (target_raster == previous_nodata_value)
reclassified_raster[reclassify_mask] = new_nodata_value
return reclassified_raster
fd, temp_path = tempfile.mkstemp(dir=PROCESSING_DIR)
shutil.copyfile(target_path, temp_path)
previous_nodata_value = pygeoprocessing.get_raster_info(
target_path)['nodata'][0]
pygeoprocessing.raster_calculator(
[(temp_path, 1)], reclassify_op, target_path, gdal.GDT_Float32,
new_nodata_value)
# clean up
os.close(fd)
os.remove(temp_path)
def weighted_state_variable_sum(
sv, sv_reg, aligned_inputs, pft_id_set, weighted_sum_path):
"""Calculate weighted sum of state variable across plant functional types.
To sum a state variable across PFTs within a grid cell, the state variable
must be weighted by the fractional cover of each PFT inside the grid cell.
First multiply the state variable by its fractional cover, and then add up
the weighted products.
Parameters:
sv (string): state variable to be summed across plant functional types
sv_reg (dict): map of key, path pairs giving paths to state variables,
including sv, the state variable to be summed
aligned_inputs (dict): map of key, path pairs indicating paths
to aligned model inputs, including fractional cover of each plant
functional type
pft_id_set (set): set of integers identifying plant functional types
weighted_sum_path (string): path to raster that should contain the
weighted sum across PFTs
Side effects:
modifies or creates the raster indicated by `weighted_sum_path`
Returns:
None
"""
temp_dir = tempfile.mkdtemp(dir=PROCESSING_DIR)
temp_val_dict = {}
for pft_i in pft_id_set:
val = '{}_weighted'.format(sv)
temp_val_dict['{}_{}'.format(val, pft_i)] = os.path.join(
temp_dir, '{}_{}.tif'.format(val, pft_i))
weighted_path_list = []
for pft_i in pft_id_set:
target_path = temp_val_dict['{}_weighted_{}'.format(sv, pft_i)]
pft_nodata = pygeoprocessing.get_raster_info(
aligned_inputs['pft_{}'.format(pft_i)])['nodata'][0]
raster_multiplication(
sv_reg['{}_{}_path'.format(sv, pft_i)], _SV_NODATA,
aligned_inputs['pft_{}'.format(pft_i)], pft_nodata,
target_path, _TARGET_NODATA)
weighted_path_list.append(target_path)
raster_list_sum(
weighted_path_list, _TARGET_NODATA, weighted_sum_path, _TARGET_NODATA,
nodata_remove=True)
# clean up temporary files
shutil.rmtree(temp_dir)
def _check_pft_fractional_cover_sum(aligned_inputs, pft_id_set):
"""Check the sum of fractional cover across plant functional types.
Parameters:
aligned_inputs (dict): map of key, path pairs indicating paths
to aligned model inputs, including fractional cover of each plant
functional type
pft_id_set (set): set of integers identifying plant functional types
Raises:
ValueError if the pixel-wise sum of fractional cover values across
plant functional types exceeds 1
Returns:
None
"""
with tempfile.NamedTemporaryFile(
prefix='cover_sum', dir=PROCESSING_DIR) as cover_sum_temp_file:
cover_sum_path = cover_sum_temp_file.name
with tempfile.NamedTemporaryFile(
prefix='operand_temp', dir=PROCESSING_DIR) as operand_temp_file:
operand_temp_path = operand_temp_file.name
# initialize sum to zero
pygeoprocessing.new_raster_from_base(
aligned_inputs['site_index'], cover_sum_path, gdal.GDT_Float32,
[_TARGET_NODATA], fill_value_list=[0])
for pft_i in pft_id_set:
shutil.copyfile(cover_sum_path, operand_temp_path)
pft_nodata = pygeoprocessing.get_raster_info(
aligned_inputs['pft_{}'.format(pft_i)])['nodata'][0]
raster_sum(
aligned_inputs['pft_{}'.format(pft_i)], pft_nodata,
operand_temp_path, _TARGET_NODATA,
cover_sum_path, _TARGET_NODATA)
# get maximum sum of fractional cover
max_cover = 0.
for offset_map, raster_block in pygeoprocessing.iterblocks(
(cover_sum_path, 1)):
valid_mask = (raster_block != _TARGET_NODATA)
if raster_block[valid_mask].size > 0:
max_cover = max(max_cover, numpy.amax(raster_block[valid_mask]))
if max_cover > 1:
raise ValueError(
"Fractional cover across plant functional types exceeds 1")
# clean up
os.remove(cover_sum_path)
def initial_conditions_from_tables(
aligned_inputs, sv_dir, pft_id_set, site_initial_conditions_table,
pft_initial_conditions_table):
"""Generate initial state variable registry from initial conditions tables.
Parameters:
aligned_inputs (dict): map of key, path pairs indicating paths
to aligned model inputs, including site spatial index raster and
fractional cover of each plant functional type
sv_dir (string): path to directory where initial state variable rasters
should be stored
pft_id_set (set): set of integers identifying plant functional types
site_initial_conditions_table (dict): map of site spatial index to
dictionaries that contain initial values for site-level state
variables
pft_initial_conditions_table (dict): map of plant functional type index
to dictionaries that contain initial values for plant functional
type-level state variables
Returns:
initial_sv_reg, map of key, path pairs giving paths to initial state
variable rasters
"""
def full_masked(pft_cover, fill_val):
"""Create a constant raster masked by pft fractional cover.
Parameters:
pft_cover (numpy.ndarray): input, fractional cover of the plant
functional type
fill_val (float): constant value with which to fill raster in areas
where fractional cover > 0
Returns:
full_masked, a raster containing `fill_val` in areas where
`pft_cover` > 0
"""
valid_mask = (
(~numpy.isclose(pft_cover, _SV_NODATA)) &
(pft_cover > 0))
full_masked = numpy.empty(pft_cover.shape, dtype=numpy.float32)
full_masked[:] = _SV_NODATA
full_masked[valid_mask] = fill_val
return full_masked
initial_sv_reg = {}
# site-level state variables
# check for missing state variable values
required_site_state_var = set(
[sv_key[:-5] for sv_key in _SITE_STATE_VARIABLE_FILES.keys()])
for site_code in site_initial_conditions_table.keys():
missing_site_state_var = required_site_state_var.difference(
site_initial_conditions_table[site_code].keys())
if missing_site_state_var:
raise ValueError(
"The following state variables were not found in the site " +
"initial conditions table: \n\t" + "\n\t".join(
missing_site_state_var))
for sv_key, basename in _SITE_STATE_VARIABLE_FILES.items():
state_var = sv_key[:-5]
site_to_val = dict(
[(site_code, float(table[state_var])) for (
site_code, table) in
site_initial_conditions_table.items()])
target_path = os.path.join(sv_dir, basename)
initial_sv_reg[sv_key] = target_path
pygeoprocessing.reclassify_raster(
(aligned_inputs['site_index'], 1), site_to_val, target_path,
gdal.GDT_Float32, _SV_NODATA)
# PFT-level state variables
for pft_i in pft_id_set:
# check for missing values
missing_pft_state_var = set(_PFT_STATE_VARIABLES).difference(
pft_initial_conditions_table[pft_i].keys())
if missing_pft_state_var:
raise ValueError(
"The following state variables were not found in the plant " +
"functional type initial conditions table: \n\t" + "\n\t".join(
missing_pft_state_var))
for state_var in _PFT_STATE_VARIABLES:
fill_val = pft_initial_conditions_table[pft_i][state_var]
pft_cover_path = aligned_inputs['pft_{}'.format(pft_i)]
target_path = os.path.join(
sv_dir, '{}_{}.tif'.format(state_var, pft_i))
sv_key = '{}_{}_path'.format(state_var, pft_i)
initial_sv_reg[sv_key] = target_path
pygeoprocessing.raster_calculator(
[(pft_cover_path, 1), (fill_val, 'raw')],
full_masked, target_path, gdal.GDT_Float32, _SV_NODATA)
return initial_sv_reg
def _calc_ompc(
som1c_2_path, som2c_2_path, som3c_path, bulkd_path, edepth_path,
ompc_path):
"""Estimate total soil organic matter.
Total soil organic matter is the sum of soil carbon across
slow, active, and passive compartments, weighted by bulk
density and total modeled soil depth. Lines 220-222, Prelim.f
Parameters:
som1c_2_path (string): path to active organic soil carbon raster
som2c_2_path (string): path to slow organic soil carbon raster
som3c_path (string): path to passive organic soil carbon raster
bulkd_path (string): path to bulk density of soil raster
edepth (string): path to depth of soil raster
ompc_path (string): path to result, total soil organic matter
Side effects:
modifies or creates the raster indicated by `ompc_path`
Returns:
None
"""
def ompc_op(som1c_2, som2c_2, som3c, bulkd, edepth):
"""Estimate total soil organic matter.
Total soil organic matter is the sum of soil carbon across
slow, active, and passive compartments, weighted by bulk
density and total modeled soil depth. Lines 220-222, Prelim.f
Parameters:
som1c_2_path (string): state variable, active organic soil carbon
som2c_2_path (string): state variable, slow organic soil carbon
som3c_path (string): state variable, passive organic soil carbon
bulkd_path (string): input, bulk density of soil
edepth_path (string): parameter, depth of soil for this
calculation
Returns:
ompc, total soil organic matter weighted by bulk
density.
"""
ompc = numpy.empty(som1c_2.shape, dtype=numpy.float32)
ompc[:] = _TARGET_NODATA
valid_mask = (
(~numpy.isclose(som1c_2, _SV_NODATA)) &
(~numpy.isclose(som2c_2, _SV_NODATA)) &
(~numpy.isclose(som3c, _SV_NODATA)) &
(~numpy.isclose(bulkd, bulkd_nodata)) &
(edepth != _IC_NODATA))
ompc[valid_mask] = (
(som1c_2[valid_mask] + som2c_2[valid_mask] +
som3c[valid_mask]) * 1.724 /
(10000. * bulkd[valid_mask] * edepth[valid_mask]))
return ompc
bulkd_nodata = pygeoprocessing.get_raster_info(bulkd_path)['nodata'][0]
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
som1c_2_path, som2c_2_path, som3c_path,
bulkd_path, edepth_path]],
ompc_op, ompc_path, gdal.GDT_Float32, _TARGET_NODATA)
def _calc_afiel(
sand_path, silt_path, clay_path, ompc_path, bulkd_path, afiel_path):
"""Calculate field capacity for one soil layer.
Parameters:
sand_path (string): path to proportion sand in soil raster
silt_path (string): path to proportion silt in soil raster
clay_path (string): path to proportion clay in soil raster
ompc_path (string): path to estimated total soil organic matter raster
bulkd_path (string): path to bulk density of soil raster
afiel_path (string): path to result raster, field capacity for this
soil layer
Side effects:
creates the raster indicated by `afiel_path`
Returns:
None
"""
def afiel_op(sand, silt, clay, ompc, bulkd):
"""Calculate field capacity for one soil layer.
Field capacity, maximum soil moisture retention capacity,
from <NAME> Larson 1979, 'Estimating soil and water
retention characteristics from particle size distribution,
organic matter percent and bulk density'. Water Resources
Research 15:1633.
Parameters:
sand_path (string): input, proportion sand in soil
silt_path (string): input, proportion silt in soil
clay_path (string): input, proportion clay in soil
ompc_path (string): derived, estimated total soil organic matter
bulkd_path (string): input, bulk density of soil
Returns:
afiel, field capacity for this soil layer
"""
afiel = numpy.empty(sand.shape, dtype=numpy.float32)
afiel[:] = _TARGET_NODATA
valid_mask = (
(~numpy.isclose(sand, sand_nodata)) &
(~numpy.isclose(silt, silt_nodata)) &
(~numpy.isclose(clay, clay_nodata)) &
(ompc != _TARGET_NODATA) &
(~numpy.isclose(bulkd, bulkd_nodata)))
afiel[valid_mask] = (
0.3075 * sand[valid_mask] + 0.5886 * silt[valid_mask] +
0.8039 * clay[valid_mask] + 2.208E-03 * ompc[valid_mask] +
-0.1434 * bulkd[valid_mask])
return afiel
sand_nodata = pygeoprocessing.get_raster_info(sand_path)['nodata'][0]
silt_nodata = pygeoprocessing.get_raster_info(silt_path)['nodata'][0]
clay_nodata = pygeoprocessing.get_raster_info(clay_path)['nodata'][0]
bulkd_nodata = pygeoprocessing.get_raster_info(bulkd_path)['nodata'][0]
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
sand_path, silt_path, clay_path, ompc_path, bulkd_path]],
afiel_op, afiel_path, gdal.GDT_Float32, _TARGET_NODATA)
def _calc_awilt(
sand_path, silt_path, clay_path, ompc_path, bulkd_path, awilt_path):
"""Calculate wilting point for one soil layer.
Wilting point, minimum soil water required by plants before
wilting, from Gupta and Larson 1979, 'Estimating soil and
water retention characteristics from particle size distribution,
organic matter percent and bulk density'. Water Resources
Research 15:1633.
Parameters:
sand_path (string): path to proportion sand in soil raster
silt_path (string): path to proportion silt in soil raster
clay_path (string): path to proportion clay in soil raster
ompc_path (string): path to estimated total soil organic matter raster
bulkd_path (string): path to bulk density of soil raster
awilt_path (string): path to result raster, wilting point for this
soil layer
Side effects:
creates the raster indicated by `awilt_path`
Returns:
None
"""
def awilt_op(sand, silt, clay, ompc, bulkd):
"""Calculate wilting point for one soil layer.
Wilting point, minimum soil water required by plants before
wilting, from Gupta and Larson 1979, 'Estimating soil and
water retention characteristics from particle size distribution,
organic matter percent and bulk density'. Water Resources
Research 15:1633.
Parameters:
sand_path (string): input, proportion sand in soil
silt_path (string): input, proportion silt in soil
clay_path (string): input, proportion clay in soil
ompc_path (string): derived, estimated total soil organic matter
bulkd_path (string): input, bulk density of soil
Returns:
awilt, wilting point for this soil layer
"""
awilt = numpy.empty(sand.shape, dtype=numpy.float32)
awilt[:] = _TARGET_NODATA
valid_mask = (
(~numpy.isclose(sand, sand_nodata)) &
(~numpy.isclose(silt, silt_nodata)) &
(~numpy.isclose(clay, clay_nodata)) &
(ompc != _TARGET_NODATA) &
(~numpy.isclose(bulkd, bulkd_nodata)))
awilt[valid_mask] = (
-0.0059 * sand[valid_mask] + 0.1142 * silt[valid_mask] +
0.5766 * clay[valid_mask] + 2.228E-03 * ompc[valid_mask] +
0.02671 * bulkd[valid_mask])
return awilt
sand_nodata = pygeoprocessing.get_raster_info(sand_path)['nodata'][0]
silt_nodata = pygeoprocessing.get_raster_info(silt_path)['nodata'][0]
clay_nodata = pygeoprocessing.get_raster_info(clay_path)['nodata'][0]
bulkd_nodata = pygeoprocessing.get_raster_info(bulkd_path)['nodata'][0]
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
sand_path, silt_path, clay_path, ompc_path, bulkd_path]],
awilt_op, awilt_path, gdal.GDT_Float32, _TARGET_NODATA)
def _afiel_awilt(
site_index_path, site_param_table, som1c_2_path, som2c_2_path,
som3c_path, sand_path, silt_path, clay_path, bulk_d_path, pp_reg):
"""Calculate field capacity and wilting point for each soil layer.
Computations based on Gupta and Larson 1979, 'Estimating soil and water
retention characteristics from particle size distribution, organic
matter percent and bulk density'. Water Resources Research 15:1633.
Field capacity is calculated for -0.33 bar; wilting point is
calculated for water content at -15 bars.
Parameters:
site_index_path (string): path to site spatial index raster
site_param_table (dict): map of site spatial index to dictionaries
that contain site-level parameters including 'edepth' field
som1c_2_path (string): path to the state variable 'som1c_2',
active organic soil carbon
som2c_2_path (string): path to the state variable 'som2c_2',
slow organic soil carbon
som3c_path (string): path to the state variable 'som3c',
passive organic soil carbon
sand_path (string): path to raster containing proportion sand in soil
silt_path (string): path to raster containing proportion silt in soil
clay_path (string): path to raster containing proportion clay in soil
bulk_d_path (string): path to raster containing bulk density of soil
pp_reg (dict): map of key, path pairs giving paths to persistent
intermediate parameters that do not change over the course of
the simulation
Modifies the rasters pp_reg['afiel_<layer>'] and pp_reg['awilt_<layer>']
for all soil layers.
Returns:
None
"""
def decrement_ompc(ompc_orig_path, ompc_dec_path):
"""Decrease estimated organic matter to 85% of its value.
In each subsequent soil layer, estimated organic matter is decreased
by 15%, to 85% of its previous value.
Parameters:
ompc_orig_path (string): path to estimated soil organic matter
raster
ompc_dec_path (string): path to result raster, estimated soil
organic matter decreased to 85% of its previous value
Side effects:
modifies or creates the raster indicated by `ompc_dec_path`
Returns:
None
"""
def decrement_op(ompc_orig):
"""Reduce organic matter to 85% of its previous value."""
ompc_dec = numpy.empty(ompc_orig.shape, dtype=numpy.float32)
ompc_dec[:] = _TARGET_NODATA
valid_mask = (ompc_orig != _TARGET_NODATA)
ompc_dec[valid_mask] = ompc_orig[valid_mask] * 0.85
return ompc_dec
pygeoprocessing.raster_calculator(
[(ompc_orig_path, 1)], decrement_op, ompc_dec_path,
gdal.GDT_Float32, _TARGET_NODATA)
# temporary intermediate rasters for calculating field capacity and
# wilting point
temp_dir = tempfile.mkdtemp(dir=PROCESSING_DIR)
edepth_path = os.path.join(temp_dir, 'edepth.tif')
ompc_path = os.path.join(temp_dir, 'ompc.tif')
site_to_edepth = dict(
[(site_code, float(table['edepth'])) for
(site_code, table) in site_param_table.items()])
pygeoprocessing.reclassify_raster(
(site_index_path, 1), site_to_edepth, edepth_path, gdal.GDT_Float32,
_IC_NODATA)
# estimate total soil organic matter
_calc_ompc(
som1c_2_path, som2c_2_path, som3c_path, bulk_d_path, edepth_path,
ompc_path)
# calculate field capacity and wilting point for each soil layer,
# decreasing organic matter content by 85% with each layer
for lyr in range(1, 10):
afiel_path = pp_reg['afiel_{}_path'.format(lyr)]
awilt_path = pp_reg['awilt_{}_path'.format(lyr)]
_calc_afiel(
sand_path, silt_path, clay_path, ompc_path, bulk_d_path,
afiel_path)
_calc_awilt(
sand_path, silt_path, clay_path, ompc_path, bulk_d_path,
awilt_path)
ompc_dec_path = os.path.join(temp_dir, 'ompc{}.tif'.format(lyr))
decrement_ompc(ompc_path, ompc_dec_path)
ompc_path = ompc_dec_path
# clean up temporary files
shutil.rmtree(temp_dir)
def _persistent_params(
site_index_path, site_param_table, sand_path, clay_path, pp_reg):
"""Calculate persistent parameters.
The calculated values do not change over the course of the simulation.
Parameters:
site_index_path (string): path to site spatial index raster
site_param_table (dict): map of site spatial index to dictionaries
that contain site-level parameters
sand_path (string): path to raster containing proportion sand in soil
clay_path (string): path to raster containing proportion clay in soil
pp_reg (dict): map of key, path pairs giving paths to persistent
intermediate parameters that do not change over the course of
the simulation.
Modifies the persistent parameter rasters indexed by the following
keys:
pp_reg['wc_path']
pp_reg['eftext_path']
pp_reg['p1co2_2_path']
pp_reg['fps1s3_path']
pp_reg['fps2s3_path']
pp_reg['orglch_path']
pp_reg['vlossg_path']
Returns:
None
"""
sand_nodata = pygeoprocessing.get_raster_info(sand_path)['nodata'][0]
clay_nodata = pygeoprocessing.get_raster_info(clay_path)['nodata'][0]
# temporary intermediate rasters for persistent parameters calculation
temp_dir = tempfile.mkdtemp(dir=PROCESSING_DIR)
param_val_dict = {}
for val in[
'peftxa', 'peftxb', 'p1co2a_2', 'p1co2b_2', 'ps1s3_1',
'ps1s3_2', 'ps2s3_1', 'ps2s3_2', 'omlech_1', 'omlech_2', 'vlossg']:
target_path = os.path.join(temp_dir, '{}.tif'.format(val))
param_val_dict[val] = target_path
site_to_val = dict(
[(site_code, float(table[val])) for (
site_code, table) in site_param_table.items()])
pygeoprocessing.reclassify_raster(
(site_index_path, 1), site_to_val, target_path, gdal.GDT_Float32,
_IC_NODATA)
def calc_wc(afiel_1, awilt_1):
"""Calculate water content of soil layer 1."""
return afiel_1 - awilt_1
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
pp_reg['afiel_1_path'], pp_reg['awilt_1_path']]],
calc_wc, pp_reg['wc_path'], gdal.GDT_Float32, _TARGET_NODATA)
def calc_eftext(peftxa, peftxb, sand):
"""Calculate effect of soil texture on microbial decomposition.
Use an empirical regression to estimate the effect of soil
sand content on the microbe decomposition rate. Line 359 Prelim.f
Parameters:
peftxa (numpy.ndarray): parameter, regression intercept
peftxb (numpy.ndarray): parameter, regression slope
sand (numpy.ndarray): input, proportion sand in soil
Returns:
eftext, coefficient that modifies microbe decomposition rate.
"""
eftext = numpy.empty(sand.shape, dtype=numpy.float32)
eftext[:] = _IC_NODATA
valid_mask = (
(peftxa != _IC_NODATA) &
(peftxb != _IC_NODATA) &
(~numpy.isclose(sand, sand_nodata)))
eftext[valid_mask] = (
peftxa[valid_mask] + (peftxb[valid_mask] * sand[valid_mask]))
return eftext
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
param_val_dict['peftxa'], param_val_dict['peftxb'], sand_path]],
calc_eftext, pp_reg['eftext_path'], gdal.GDT_Float32, _IC_NODATA)
def calc_p1co2_2(p1co2a_2, p1co2b_2, sand):
"""Calculate the fraction of carbon lost to CO2 from som1c_2.
During decomposition from active organic soil carbon, a fraction
of decomposing material is lost to CO2 as the soil respires.
Line 366 Prelim.f
Parameters:
p1co2a_2 (numpy.ndarray): parameter, intercept of regression
predicting loss to CO2 from active organic soil carbon
p1co2b_2 (numpy.ndarray): parameter, slope of regression
predicting loss to CO2 from active organic soil carbon
sand (numpy.ndarray): input, proportion sand in soil
Returns:
p1co2_2, fraction of carbon that flows to CO2 from active
organic soil carbon
"""
p1co2_2 = numpy.empty(sand.shape, dtype=numpy.float32)
p1co2_2[:] = _IC_NODATA
valid_mask = (
(p1co2a_2 != _IC_NODATA) &
(p1co2b_2 != _IC_NODATA) &
(~numpy.isclose(sand, sand_nodata)))
p1co2_2[valid_mask] = (
p1co2a_2[valid_mask] + (p1co2b_2[valid_mask] * sand[valid_mask]))
return p1co2_2
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
param_val_dict['p1co2a_2'],
param_val_dict['p1co2b_2'], sand_path]],
calc_p1co2_2, pp_reg['p1co2_2_path'], gdal.GDT_Float32, _IC_NODATA)
def calc_fps1s3(ps1s3_1, ps1s3_2, clay):
"""Calculate effect of clay content on decomposition from som1c_2.
Use an empirical regression to estimate the effect of clay content
of soil on flow from soil organic matter with fast turnover to
soil organic matter with slow turnover. Line 370 Prelim.f
Parameters:
ps1s3_1 (numpy.ndarray): parameter, regression intercept
ps1s3_2 (numpy.ndarray): parameter, regression slope
clay (numpy.ndarray): input, proportion clay in soil
Returns:
fps1s3, coefficient that modifies rate of decomposition
from som1c_2
"""
fps1s3 = numpy.empty(clay.shape, dtype=numpy.float32)
fps1s3[:] = _IC_NODATA
valid_mask = (
(ps1s3_1 != _IC_NODATA) &
(ps1s3_2 != _IC_NODATA) &
(~numpy.isclose(clay, clay_nodata)))
fps1s3[valid_mask] = (
ps1s3_1[valid_mask] + (ps1s3_2[valid_mask] * clay[valid_mask]))
return fps1s3
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
param_val_dict['ps1s3_1'], param_val_dict['ps1s3_2'], clay_path]],
calc_fps1s3, pp_reg['fps1s3_path'], gdal.GDT_Float32, _IC_NODATA)
def calc_fps2s3(ps2s3_1, ps2s3_2, clay):
"""Calculate effect of clay content on decomposition from som2c_2.
Use an empirical regression to estimate the effect of clay content
of soil on flow from slow soil organic carbon to soil passive organic
carbon. Line 371 Prelim.f
Parameters:
ps2s3_1 (numpy.ndarray): parameter, regression intercept
ps2s3_2 (numpy.ndarray): parameter, regression slope
clay (numpy.ndarray): input, proportion clay in soil
Returns:
fps2s3, coefficient that modifies rate of decomposition from
som2c_2 to som3c
"""
fps2s3 = numpy.empty(clay.shape, dtype=numpy.float32)
fps2s3[:] = _IC_NODATA
valid_mask = (
(ps2s3_1 != _IC_NODATA) &
(ps2s3_2 != _IC_NODATA) &
(~numpy.isclose(clay, clay_nodata)))
fps2s3[valid_mask] = (
ps2s3_1[valid_mask] + (ps2s3_2[valid_mask] * clay[valid_mask]))
return fps2s3
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
param_val_dict['ps2s3_1'], param_val_dict['ps2s3_2'], clay_path]],
calc_fps2s3, pp_reg['fps2s3_path'], gdal.GDT_Float32, _IC_NODATA)
def calc_orglch(omlech_1, omlech_2, sand):
"""Calculate the effect of sand content on leaching from soil.
Use an empirical regression to estimate the effect of sand content
of soil on rate of organic leaching from soil when there is drainage
of soil water from soil layer 1 to soil layer 2. Line 110 Predec.f
Parameters:
omlech_1 (numpy.ndarray): parameter, regression intercept
omlech_2 (numpy.ndarray): parameter, regression slope
sand (numpy.ndarray): input, proportion sand in soil
Returns:
orglch, the fraction of organic compounds leaching from soil
with drainage from soil layer 1 to layer 2
"""
orglch = numpy.empty(sand.shape, dtype=numpy.float32)
orglch[:] = _IC_NODATA
valid_mask = (
(omlech_1 != _IC_NODATA) &
(omlech_2 != _IC_NODATA) &
(~numpy.isclose(sand, sand_nodata)))
orglch[valid_mask] = (
omlech_1[valid_mask] + (omlech_2[valid_mask] * sand[valid_mask]))
return orglch
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
param_val_dict['omlech_1'], param_val_dict['omlech_2'],
sand_path]],
calc_orglch, pp_reg['orglch_path'], gdal.GDT_Float32, _IC_NODATA)
def calc_vlossg(vlossg_param, clay):
"""Calculate proportion of gross mineralized N that is volatized.
During decomposition, some N is lost to volatilization. This is a
function of the gross mineralized N and is calculated according to this
multiplier, which varies with soil clay content.
Parameters:
vlossg (numpy.ndarray): parameter, volatilization loss multiplier
clay (numpy.ndarray): input, proportion clay in soil
Returns:
vlossg, proportion of gross mineralized N that is volatized
"""
valid_mask = (
(vlossg_param != _IC_NODATA) &
(~numpy.isclose(clay, clay_nodata)))
vlossg = numpy.empty(vlossg_param.shape, dtype=numpy.float32)
vlossg[:] = _IC_NODATA
max_mask = ((clay > 0.3) & valid_mask)
min_mask = ((clay < 0.1) & valid_mask)
vlossg[valid_mask] = -0.1 * (clay[valid_mask] - 0.3) + 0.01
vlossg[max_mask] = 0.01
vlossg[min_mask] = 0.03
vlossg[valid_mask] = vlossg[valid_mask] * vlossg_param[valid_mask]
return vlossg
pygeoprocessing.raster_calculator(
[(path, 1) for path in [param_val_dict['vlossg'], clay_path]],
calc_vlossg, pp_reg['vlossg_path'], gdal.GDT_Float32, _IC_NODATA)
# clean up temporary files
shutil.rmtree(temp_dir)
def _aboveground_ratio(anps, tca, pcemic_1, pcemic_2, pcemic_3):
"""Calculate C/<iel> ratios of decomposing aboveground material.
This ratio is used to test whether there is sufficient <iel> (N or P)
in aboveground material for the material to decompose. Agdrat.f
Parameters:
anps (numpy.ndarray): state variable, N or P in the donor material
tca (numpy.ndarray): state variable, total C in the donor material
pcemic_1 (numpy.ndarray): parameter, maximum C/<iel> of new material
pcemic_2 (numpy.ndarray): parameter, minimum C/<iel> of new material
pcemic_3 (numpy.ndarray): parameter, minimum <iel> content of
decomposing material that gives minimum C/<iel> of new material
Returns:
agdrat, the C/<iel> ratio of new material
"""
valid_mask = (
(~numpy.isclose(anps, _SV_NODATA)) &
(~numpy.isclose(tca, _SV_NODATA)) &
(pcemic_1 != _IC_NODATA) &
(pcemic_2 != _IC_NODATA) &
(pcemic_3 != _IC_NODATA))
cemicb = numpy.empty(anps.shape, dtype=numpy.float32)
cemicb[:] = _IC_NODATA
cemicb[valid_mask] = (
(pcemic_2[valid_mask] - pcemic_1[valid_mask]) /
pcemic_3[valid_mask])
econt = numpy.empty(anps.shape, dtype=numpy.float32)
econt[:] = _TARGET_NODATA
econt[valid_mask] = 0
decompose_mask = ((tca > 0.) & valid_mask)
econt[decompose_mask] = anps[decompose_mask] / (tca[decompose_mask] * 2.5)
agdrat = numpy.empty(anps.shape, dtype=numpy.float32)
agdrat[:] = _TARGET_NODATA
agdrat[valid_mask] = pcemic_2[valid_mask]
compute_mask = ((econt <= pcemic_3) & valid_mask)
agdrat[compute_mask] = (
pcemic_1[compute_mask] + econt[compute_mask] * cemicb[compute_mask])
return agdrat
def _belowground_ratio(aminrl, varat_1_iel, varat_2_iel, varat_3_iel):
"""Calculate C/<iel> ratios of decomposing belowground material.
This ratio is used to test whether there is sufficient <iel> (N or P)
in soil metabolic material to decompose. Bgdrat.f
Parameters:
aminrl (numpy.ndarray): derived, average surface mineral <iel>
varat_1_iel (numpy.ndarray): parameter, maximum C/<iel> ratio for
newly decomposed material
varat_2_iel (numpy.ndarray): parameter, minimum C/<iel> ratio
varat_3_iel (numpy.ndarray): parameter, amount of <iel> present
when minimum ratio applies
Returns:
bgdrat, the C/<iel> ratio of new material
"""
valid_mask = (
(~numpy.isclose(aminrl, _SV_NODATA)) &
(varat_1_iel != _IC_NODATA) &
(varat_2_iel != _IC_NODATA) &
(varat_3_iel != _IC_NODATA))
bgdrat = numpy.empty(aminrl.shape, dtype=numpy.float32)
bgdrat[:] = _TARGET_NODATA
bgdrat[valid_mask] = (
(1. - aminrl[valid_mask] / varat_3_iel[valid_mask]) *
(varat_1_iel[valid_mask] - varat_2_iel[valid_mask]) +
varat_2_iel[valid_mask])
max_mask = ((aminrl <= 0) & valid_mask)
bgdrat[max_mask] = varat_1_iel[max_mask]
min_mask = ((aminrl > varat_3_iel) & valid_mask)
bgdrat[min_mask] = varat_2_iel[min_mask]
return bgdrat
def _structural_ratios(site_index_path, site_param_table, sv_reg, pp_reg):
"""Calculate maximum C/N and C/P ratios for structural material.
These ratios limit decomposition of structural material (i.e., material
containing lignin). Lines 31-77 Predec.f
Parameters:
site_index_path (string): path to site spatial index raster
site_param_table (dict): map of site spatial index to dictionaries
that contain site-level parameters
sv_reg (dict): map of key, path pairs giving paths to state
variables for the current month
pp_reg (dict): map of key, path pairs giving paths to persistent
intermediate parameters that do not change over the course of
the simulation.
Modifies the persistent parameter rasters indexed by the following
keys:
pp_reg['rnewas_1_1_path']
pp_reg['rnewas_1_2_path']
pp_reg['rnewas_2_1_path']
pp_reg['rnewas_2_2_path']
pp_reg['rnewbs_1_1_path']
pp_reg['rnewbs_1_2_path']
pp_reg['rnewbs_2_1_path']
pp_reg['rnewbs_2_2_path']
Returns:
None
"""
# temporary parameter rasters for structural ratios calculations
temp_dir = tempfile.mkdtemp(dir=PROCESSING_DIR)
param_val_dict = {}
for iel in [1, 2]:
for val in[
'pcemic1_2', 'pcemic1_1', 'pcemic1_3', 'pcemic2_2',
'pcemic2_1', 'pcemic2_3', 'rad1p_1', 'rad1p_2',
'rad1p_3', 'varat1_1', 'varat22_1']:
target_path = os.path.join(temp_dir, '{}_{}.tif'.format(val, iel))
param_val_dict['{}_{}'.format(val, iel)] = target_path
site_to_val = dict(
[(site_code, float(table['{}_{}'.format(val, iel)])) for
(site_code, table) in site_param_table.items()])
pygeoprocessing.reclassify_raster(
(site_index_path, 1), site_to_val, target_path,
gdal.GDT_Float32, _IC_NODATA)
def calc_rnewas_som2(
pcemic2_2, pcemic2_1, pcemic2_3, struce_1, strucc_1, rad1p_1,
rad1p_2, rad1p_3, pcemic1_2, rnewas1):
"""Calculate C/<iel> ratio for decomposition into som2.
This ratio is calculated separately for each nutrient (i.e., N, P).
When material decomposes into the surface slow organic pool, the
C/<iel> ratio of decomposing material must be smaller than or equal to
this ratio. A portion of the ratio of material entering som1, the
surface active pool, is also added to som2 and calculated here.
Parameters:
pcemic2_2 (numpy.ndarray): parameter, minimum C/<iel> ratio for
surface slow organic pool
pcemic2_1 (numpy.ndarray): parameter, maximum C/<iel> ratio for
surface slow organic pool
pcemic2_3 (numpy.ndarray): parameter, mimimum <iel> content of
decomposing aboveground material, above which the C/<iel>
ratio of the surface slow organic pool equals pcemic1_2
struce_1 (numpy.ndarray): state variable, <iel> in surface
structural material
strucc_1 (numpy.ndarray): state variable, C in surface
structural material
rad1p_1 (numpy.ndarray): parameter, intercept of regression used
to calculate addition of <iel> from surface active pool
rad1p_2 (numpy.ndarray): parameter, slope of regression used
to calculate addition of <iel> from surface active pool
rad1p_3 (numpy.ndarray): parameter, minimum allowable C/<iel>
used to calculate addition term for C/<iel> ratio of som2
formed from surface active pool
pcemic1_2 (numpy.ndarray): parameter, minimum C/<iel> ratio for
surface active organic pool
rnewas1 (numpy.ndarray): derived, C/<iel> ratio for decomposition
into som1
Returns:
rnewas2, required ratio for decomposition of structural material
into som2 for one nutrient
"""
valid_mask = (
(pcemic2_2 != _IC_NODATA) &
(pcemic2_1 != _IC_NODATA) &
(pcemic2_3 != _IC_NODATA) &
(~numpy.isclose(struce_1, _SV_NODATA)) &
(~numpy.isclose(strucc_1, _SV_NODATA)) &
(rad1p_1 != _IC_NODATA) &
(rad1p_2 != _IC_NODATA) &
(rad1p_3 != _IC_NODATA) &
(pcemic1_2 != _IC_NODATA) &
(rnewas1 != _TARGET_NODATA))
rnewas2 = _aboveground_ratio(
struce_1, strucc_1, pcemic2_1, pcemic2_2, pcemic2_3)
radds1 = numpy.empty(strucc_1.shape, dtype=numpy.float32)
radds1[:] = _TARGET_NODATA
radds1[valid_mask] = (
rad1p_1[valid_mask] + rad1p_2[valid_mask] *
(rnewas1[valid_mask] - pcemic1_2[valid_mask]))
rnewas2[valid_mask] = rnewas1[valid_mask] + radds1[valid_mask]
rnewas2[valid_mask] = numpy.maximum(
rnewas2[valid_mask], rad1p_3[valid_mask])
return rnewas2
for iel in [1, 2]:
# calculate rnewas_iel_1 - aboveground material to SOM1
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
sv_reg['struce_1_{}_path'.format(iel)],
sv_reg['strucc_1_path'],
param_val_dict['pcemic1_1_{}'.format(iel)],
param_val_dict['pcemic1_2_{}'.format(iel)],
param_val_dict['pcemic1_3_{}'.format(iel)]]],
_aboveground_ratio, pp_reg['rnewas_{}_1_path'.format(iel)],
gdal.GDT_Float32, _TARGET_NODATA)
# calculate rnewas_iel_2 - aboveground material to SOM2
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
param_val_dict['pcemic2_2_{}'.format(iel)],
param_val_dict['pcemic2_1_{}'.format(iel)],
param_val_dict['pcemic2_3_{}'.format(iel)],
sv_reg['struce_1_{}_path'.format(iel)],
sv_reg['strucc_1_path'],
param_val_dict['rad1p_1_{}'.format(iel)],
param_val_dict['rad1p_2_{}'.format(iel)],
param_val_dict['rad1p_3_{}'.format(iel)],
param_val_dict['pcemic1_2_{}'.format(iel)],
pp_reg['rnewas_{}_1_path'.format(iel)]]],
calc_rnewas_som2, pp_reg['rnewas_{}_2_path'.format(iel)],
gdal.GDT_Float32, _TARGET_NODATA)
# calculate rnewbs_iel_1 - belowground material to SOM1
site_to_varat1_1 = dict([
(site_code, float(table['varat1_1_{}'.format(iel)])) for
(site_code, table) in site_param_table.items()])
pygeoprocessing.reclassify_raster(
(site_index_path, 1), site_to_varat1_1,
pp_reg['rnewbs_{}_1_path'.format(iel)],
gdal.GDT_Float32, _TARGET_NODATA)
# calculate rnewbs_iel_2 - belowground material to SOM2
# rnewbs(iel,2) = varat22(1,iel)
site_to_varat22_1 = dict([
(site_code, float(table['varat22_1_{}'.format(iel)])) for
(site_code, table) in site_param_table.items()])
pygeoprocessing.reclassify_raster(
(site_index_path, 1), site_to_varat22_1,
pp_reg['rnewbs_{}_2_path'.format(iel)],
gdal.GDT_Float32, _TARGET_NODATA)
# clean up temporary files
shutil.rmtree(temp_dir)
def _yearly_tasks(
aligned_inputs, site_param_table, veg_trait_table, month_index,
pft_id_set, year_reg):
"""Calculate quantities that remain static for 12 months.
These quantities are annual precipitation, annual atmospheric N
deposition, and the fraction of plant residue which is lignin for each pft.
Century also calculates non-symbiotic soil N fixation once yearly, but here
those were moved to monthly tasks. Century uses precipitation in the future
12 months (prcgrw) to predict root:shoot ratios, but here we instead use
the sum of monthly precipitation in 12 months including the current one, if
data for 12 future months are not available.
Lines 79-82, 164 Eachyr.f
Parameters:
aligned_inputs (dict): map of key, path pairs indicating paths
to aligned model inputs, including monthly precipitation and site
spatial index raster
site_param_table (dict): map of site spatial index to dictionaries
that contain site-level parameters
veg_trait_table (dict): map of pft id to dictionaries containing
plant functional type parameters
month_index (int): current monthly step, relative to 0 so that
month_index=0 at first monthly time step
pft_id_set (set): set of integers identifying plant functional types
year_reg (dict): map of key, path pairs giving paths to the annual
precipitation and N deposition rasters
Side effects:
modifies or creates the rasters indicated by:
year_reg['annual_precip_path']
year_reg['baseNdep_path']
year_reg['pltlig_above_<pft>'] for each pft
year_reg['pltlig_below_<pft>'] for each pft
Returns:
None
Raises:
ValueError if fewer than 12 monthly precipitation rasters can be found
"""
def calc_base_N_dep(epnfa_1, epnfa_2, prcann):
"""Calculate base annual atmospheric N deposition.
Parameters:
epnfa_1 (numpy.ndarray): parameter, intercept of regression
predicting atmospheric N deposition from precipitation
epnfa_2 (numpy.ndarray): parameter, slope of regression predicting
atmospheric N deposition from precipitation
prcann (numpy.ndarray): derived, annual precipitation
Returns:
baseNdep, annual atmospheric N deposition
"""
baseNdep = numpy.empty(prcann.shape, dtype=numpy.float32)
baseNdep[:] = 0.
valid_mask = (
(epnfa_1 != _IC_NODATA) &
(epnfa_2 != _IC_NODATA) &
(prcann != _TARGET_NODATA))
baseNdep[valid_mask] = (
epnfa_1[valid_mask] +
(epnfa_2[valid_mask] * numpy.minimum(prcann[valid_mask], 80.)))
baseNdep[baseNdep < 0] = 0.
return baseNdep
def calc_pltlig(fligni_1_lyr, fligni_2_lyr, prcann):
"""Calculate the fraction of residue that is lignin. Cmplig.f
This fraction is used to calculate the fraction of residue (i.e.,
incoming litter from fall of standing dead or incoming soil from death
of roots) that is partitioned to metabolic vs structural pools. It is
calculated once per year from annual precipitation and fixed
parameters.
Parameters:
fligni_1_lyr (numpy.ndarray): parameter, intercept for regression
predicting lignin content fraction from rainfall
fligni_2_lyr (numpy.ndarray): parameter, slope for regression
predicting lignin content fraction from rainfall
prcann (numpy.ndarray): derived, annual precipitation
Returns:
pltlig_lyr, fraction of residue that is lignin
"""
valid_mask = (
(fligni_1_lyr != _IC_NODATA) &
(fligni_2_lyr != _IC_NODATA) &
(prcann != _TARGET_NODATA))
pltlig = numpy.empty(fligni_1_lyr.shape, dtype=numpy.float32)
pltlig[:] = _TARGET_NODATA
pltlig[valid_mask] = (
fligni_1_lyr[valid_mask] + fligni_2_lyr[valid_mask] *
prcann[valid_mask])
pltlig[valid_mask] = numpy.clip(pltlig[valid_mask], 0.02, 0.5)
return pltlig
offset = -12
annual_precip_rasters = []
while len(annual_precip_rasters) < 12:
offset += 1
if offset == 12:
raise ValueError("Insufficient precipitation rasters were found")
precip_month = month_index + offset
try:
annual_precip_rasters.append(
aligned_inputs['precip_%d' % precip_month])
except KeyError:
continue
precip_nodata = set([])
for precip_raster in annual_precip_rasters:
precip_nodata.update(
set([pygeoprocessing.get_raster_info(precip_raster)['nodata'][0]]))
if len(precip_nodata) > 1:
raise ValueError("Precipitation rasters include >1 nodata value")
precip_nodata = list(precip_nodata)[0]
raster_list_sum(
annual_precip_rasters, precip_nodata, year_reg['annual_precip_path'],
_TARGET_NODATA)
# intermediate parameter rasters for this operation
temp_dir = tempfile.mkdtemp(dir=PROCESSING_DIR)
param_val_dict = {}
for val in['epnfa_1', 'epnfa_2']:
target_path = os.path.join(temp_dir, '{}.tif'.format(val))
param_val_dict[val] = target_path
site_to_val = dict(
[(site_code, float(table[val])) for
(site_code, table) in site_param_table.items()])
pygeoprocessing.reclassify_raster(
(aligned_inputs['site_index'], 1), site_to_val, target_path,
gdal.GDT_Float32, _IC_NODATA)
for val in ['fligni_1_1', 'fligni_2_1', 'fligni_1_2', 'fligni_2_2']:
for pft_i in pft_id_set:
target_path = os.path.join(
temp_dir, '{}_{}.tif'.format(val, pft_i))
param_val_dict['{}_{}'.format(val, pft_i)] = target_path
fill_val = veg_trait_table[pft_i][val]
pygeoprocessing.new_raster_from_base(
aligned_inputs['site_index'], target_path, gdal.GDT_Float32,
[_IC_NODATA], fill_value_list=[fill_val])
# calculate base N deposition
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
param_val_dict['epnfa_1'], param_val_dict['epnfa_2'],
year_reg['annual_precip_path']]],
calc_base_N_dep, year_reg['baseNdep_path'], gdal.GDT_Float32,
_TARGET_NODATA)
for pft_i in pft_id_set:
# fraction of surface residue that is lignin
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
param_val_dict['fligni_1_1_{}'.format(pft_i)],
param_val_dict['fligni_2_1_{}'.format(pft_i)],
year_reg['annual_precip_path']]],
calc_pltlig, year_reg['pltlig_above_{}'.format(pft_i)],
gdal.GDT_Float32, _TARGET_NODATA)
# fraction of soil residue that is lignin
pygeoprocessing.raster_calculator(
[(path, 1) for path in [
param_val_dict['fligni_1_2_{}'.format(pft_i)],
param_val_dict['fligni_2_2_{}'.format(pft_i)],
year_reg['annual_precip_path']]],
calc_pltlig, year_reg['pltlig_below_{}'.format(pft_i)],
gdal.GDT_Float32, _TARGET_NODATA)
# clean up temporary files
shutil.rmtree(temp_dir)
def calc_latitude(template_raster, latitude_raster_path):
"""Calculate latitude at the center of each pixel in a template raster."""
pygeoprocessing.new_raster_from_base(
template_raster, latitude_raster_path, gdal.GDT_Float32,
[_IC_NODATA])
latitude_raster = gdal.OpenEx(
latitude_raster_path, gdal.OF_RASTER | gdal.GA_Update)
target_band = latitude_raster.GetRasterBand(1)
base_raster_info = pygeoprocessing.get_raster_info(template_raster)
geotransform = base_raster_info['geotransform']
for offset_map, raster_block in pygeoprocessing.iterblocks(
(template_raster, 1)):
n_y_block = raster_block.shape[0]
n_x_block = raster_block.shape[1]
# offset by .5 so we're in the center of the pixel
xoff = offset_map['xoff'] + 0.5
yoff = offset_map['yoff'] + 0.5
# calculate the projected x and y coordinate bounds for the block
x_range = numpy.linspace(
geotransform[0] + geotransform[1] * xoff,
geotransform[0] + geotransform[1] * (xoff + n_x_block - 1),
n_x_block)
y_range = numpy.linspace(
geotransform[3] + geotransform[5] * yoff,
geotransform[3] + geotransform[5] * (yoff + n_y_block - 1),
n_y_block)
# we'll use this to avoid generating any nodata points
valid_mask = raster_block != base_raster_info['nodata']
# these indexes correspond to projected coordinates
# y_vector is what we want, an array of latitude coordinates
x_vector, y_vector = numpy.meshgrid(x_range, y_range)
target_band.WriteArray(
y_vector, xoff=offset_map['xoff'], yoff=offset_map['yoff'])
# Making sure the band and dataset is flushed and not in memory
target_band.FlushCache()
target_band.FlushCache()
target_band = None
gdal.Dataset.__swig_destroy__(latitude_raster)
latitude_raster = None
def _calc_daylength(template_raster, month, daylength_path):
"""Calculate estimated hours of daylength. Daylen.c.
Parameters:
template_raster (string): path to a raster in geographic coordinates
that is aligned with model inputs
month (int): current month of the year, such that month=0 indicates
January
daylength_path (string): path to shortwave radiation raster
Side effects:
modifies or creates the raster indicated by `daylength_path`
Returns:
None
"""
def daylength(month):
def _daylength(latitude):
"""Estimate hours of daylength for a given month and latitude."""
# Julian day at beginning of each month
jday_list = [
1, 32, 61, 92, 122, 153, 183, 214, 245, 275, 306, 337]
jday = jday_list[month - 1]
# Convert latitude from degrees to radians
rlatitude = latitude * (numpy.pi / 180.0)
declin = 0.4014 * numpy.sin(6.283185 * (jday - 77.0) / 365)
temp = 1.0 - (-numpy.tan(rlatitude) * numpy.tan(declin))**2
temp[temp < 0] = 0
par1 = numpy.sqrt(temp)
par2 = -numpy.tan(rlatitude) * numpy.tan(declin)
ahou = numpy.arctan2(par1, par2)
hours_of_daylength = (ahou / numpy.pi) * 24
return hours_of_daylength
return _daylength
# calculate an intermediate input, latitude at each pixel center
temp_dir = tempfile.mkdtemp(dir=PROCESSING_DIR)
latitude_raster_path = os.path.join(temp_dir, 'latitude.tif')
calc_latitude(template_raster, latitude_raster_path)
pygeoprocessing.raster_calculator(
[(latitude_raster_path, 1)], daylength(month), daylength_path,
gdal.GDT_Float32, _TARGET_NODATA)
# clean up temporary files
shutil.rmtree(temp_dir)
def _shortwave_radiation(template_raster, month, shwave_path):
"""Calculate shortwave radiation outside the atmosphere.
Shortwave radiation outside the atmosphere is calculated according to
Penman (1948), "Natural evaporation from open water, bare soil and grass",
Proc. Roy. Soc. London. The latitude of each pixel is required to
calculate radiation and is calculated as an intermediate step from the
input `template_raster`. shwave.f
Parameters:
template_raster (string): path to a raster in geographic coordinates
that is aligned with model inputs
month (int): current month of the year, such that month=0 indicates
January
shwave_path (string): path to shortwave radiation raster
Side effects:
Modifies the raster indicated by `shwave_path`
Returns:
None
"""
def shwave(month):
def _shwave(latitude):
"""Calculate shortwave radiation outside the atmosphere.
Parameters:
latitude (float): latitude of current site in degrees
month (int): current month of the year, such that month=1
indicates January
Returns:
shwave, short wave solar radiation outside the atmosphere
"""
# Julian date in middle of each month of the year
jday_list = [
16, 46, 75, 106, 136, 167, 197, 228, 259, 289, 320, 350]
jday = jday_list[month - 1]
transcof = 0.8
# Convert latitude from degrees to radians
rlatitude = latitude * (numpy.pi / 180.0)
# short wave solar radiation on a clear day
declin = 0.401426 * numpy.sin(6.283185 * (jday - 77.0) / 365.0)
temp = 1.0 - (-numpy.tan(rlatitude) * numpy.tan(declin))**2
temp[temp < 0.] = 0.
par1 = numpy.sqrt(temp)
par2 = (-numpy.tan(rlatitude) * numpy.tan(declin))
ahou = numpy.arctan2(par1, par2)
ahou[ahou < 0.] = 0.
solrad = (
917.0 * transcof * (
ahou * numpy.sin(rlatitude) * numpy.sin(declin) +
numpy.cos(rlatitude) *
numpy.cos(declin) * numpy.sin(ahou)))
# short wave radiation outside the atmosphere
shwave = solrad / transcof
return shwave
return _shwave
# calculate an intermediate input, latitude at each pixel center
temp_dir = tempfile.mkdtemp(dir=PROCESSING_DIR)
latitude_raster_path = os.path.join(temp_dir, 'latitude.tif')
calc_latitude(template_raster, latitude_raster_path)
pygeoprocessing.raster_calculator(
[(latitude_raster_path, 1)],
shwave(month), shwave_path,
gdal.GDT_Float32, _TARGET_NODATA)
# clean up temporary files
shutil.rmtree(temp_dir)
def _reference_evapotranspiration(
max_temp_path, min_temp_path, shwave_path, fwloss_4_path,
pevap_path):
"""Calculate reference evapotranspiration.
Reference evapotranspiration from the FAO Penman-Monteith equation in
"Guidelines for computing crop water requirements", FAO Irrigation and
drainage paper 56 (http://www.fao.org/docrep/X0490E/x0490e08.htm),
modified by the parameter fwloss(4).
Parameters:
max_temp_path (string): path to maximum monthly temperature
min_temp_path (string): path to minimum monthly temperature
shwave_path (string): path to shortwave radiation outside the
atmosphere
fwloss_4_path (string): path to parameter, scaling factor for
reference evapotranspiration
pevap_path (string): path to result, reference evapotranspiration
raster
Side effects:
modifies or creates the raster indicated by `pevap_path`
Returns:
None
"""
def _calc_pevap(max_temp, min_temp, shwave, fwloss_4):
"""Calculate reference evapotranspiration.
Pevap.f
Parameters:
max_temp (numpy.ndarray): input, maximum monthly temperature
min_temp (numpy.ndarray): input, minimum monthly temperature
shwave (numpy.ndarray): derived, shortwave radiation outside the
atmosphere
fwloss_4 (numpy.ndarray): parameter, scaling factor for reference
evapotranspiration
Returns:
pevap, reference evapotranspiration
"""
const1 = 0.0023
const2 = 17.8
langleys2watts = 54.0
valid_mask = (
(~numpy.isclose(max_temp, maxtmp_nodata)) &
(~numpy.isclose(min_temp, mintmp_nodata)) &
(shwave != _TARGET_NODATA) &
(fwloss_4 != _IC_NODATA))
trange = numpy.empty(fwloss_4.shape, dtype=numpy.float32)
trange[:] = _TARGET_NODATA
trange[valid_mask] = max_temp[valid_mask] - min_temp[valid_mask]
tmean = numpy.empty(fwloss_4.shape, dtype=numpy.float32)
tmean[:] = _IC_NODATA
tmean[valid_mask] = (max_temp[valid_mask] + min_temp[valid_mask]) / 2.0
# daily reference evapotranspiration
daypet = numpy.empty(fwloss_4.shape, dtype=numpy.float32)
daypet[:] = _TARGET_NODATA
in1 = const1 * (tmean[valid_mask] + const2)
in2 = numpy.sqrt(trange[valid_mask])
in3 = (shwave[valid_mask] / langleys2watts)
daypet[valid_mask] = (
const1 * (tmean[valid_mask] + const2) *
numpy.sqrt(trange[valid_mask]) *
(shwave[valid_mask] / langleys2watts))
# monthly reference evapotranspiration, from mm to cm,
# bounded to be at least 0.5
monpet = (daypet * 30.) / 10.
monpet[monpet <= 0.5] = 0.5
pevap = | numpy.empty(fwloss_4.shape, dtype=numpy.float32) | numpy.empty |
import logging
from pathlib import Path
import numpy as np
from keras import backend as K
from keras.callbacks import Callback, EarlyStopping, CSVLogger, ModelCheckpoint, TensorBoard, LearningRateScheduler
from sklearn.metrics import f1_score, precision_score, recall_score, classification_report, confusion_matrix
import setting
from .tools import init_path
LOGGER = logging.getLogger(setting.LOGGING_NAME)
class MetricCallback(Callback):
def __init__(self, predict_batch_size=64, include_on_batch=False):
super(MetricCallback, self).__init__()
self.predict_batch_size = predict_batch_size
self.include_on_batch = include_on_batch
def on_batch_end(self, batch, logs=None):
if self.include_on_batch:
logs['val_recall'] = np.float32('-inf')
logs['val_precision'] = np.float32('-inf')
logs['val_f1'] = np.float32('-inf')
if self.validation_data:
y_true = np.argmax(self.validation_data[1], axis=1)
y_pred = np.argmax(self.model.predict(self.validation_data[0], batch_size=self.predict_batch_size),
axis=1)
self.set_scores(y_true, y_pred, logs)
def on_train_begin(self, logs=None):
if 'val_recall' not in self.params['metrics']:
self.params['metrics'].append('val_recall')
if 'val_precision' not in self.params['metrics']:
self.params['metrics'].append('val_precision')
if 'val_f1' not in self.params['metrics']:
self.params['metrics'].append('val_f1')
if 'val_auc' not in self.params['metrics']:
self.params['metrics'].append('val_auc')
def on_epoch_end(self, epoch, logs=None):
logs['val_recall'] = np.float32('-inf')
logs['val_precision'] = | np.float32('-inf') | numpy.float32 |
import numpy as np
def random_policy(env):
counter = 0
total_rewards = 0
reward = None
while reward != 20:
env.render()
state, reward, done, info = env.step(env.action_space.sample())
counter += 1
total_rewards += reward
print("Solved in {} Steps with a total reward of {}".format(counter, total_rewards))
# random_policy() # result : Solved in 3768 Steps with a total reward of -14556
def q_learning(env, episodes=1000, reward_decay=0.9, alpha=0.618):
reward_tracker = []
n_states = env.observation_space.n
n_actions = env.action_space.n
Q = np.zeros([n_states, n_actions])
total_rewards = 0
for episode in range(1, episodes + 1):
done = False
total_rewards, reward = 0, 0
state = env.reset()
while not done:
action = | np.argmax(Q[state]) | numpy.argmax |
import gmsh
import numpy as np
from .mesher import Mesher
def removeSurfaceMeshes(model: Mesher) -> None:
"""
In order to assign face based boundary conditions to surfaces (e.g. flux, convection), the surface mesh is compared
to the volumetric mesh to identify the actual surface mesh. This is then removed afterwards.
:param model: Mesher: The GMSH model
"""
tags = model.getPhysicalGroups(2)
for tag in tags:
# Remove all tri group surfaces
print('removing surface {:s}'.format(model.getPhysicalName(2, tag[1])))
model.removePhysicalGroups(tag)
def getNodesFromVolume(volumeName : str, model: Mesher):
"""
Gets the nodes for a specified volume
:param volumeName: str - The volume domain in the model to obtain the nodes from
:param model: Mesher: The GMSH model
:return:
"""
vols = model.getPhysicalGroups(3)
names = [(model.getPhysicalName(3, x[1]), x[1]) for x in vols]
volTagId = -1
for name in names:
if name[0] == volumeName:
volTagId = name[1]
if volTagId == -1:
raise ValueError('Volume region ({:s}) was not found'.format(volumeName))
return model.mesh.getNodesForPhysicalGroup(3, volTagId)[0]
def getNodesFromRegion(surfaceRegionName: str, model : Mesher):
"""
Gets the nodes for a specified surface region
:param surfaceRegionName: str - The volume domain in the model to obtain the nodes from
:param model: Mesher: The GMSH model
:return:
"""
surfs = model.getPhysicalGroups(2)
names = [(model.getPhysicalName(2, x[1]), x[1]) for x in surfs]
surfTagId = -1
for name in names:
if name[0] == surfaceRegionName:
surfTagId = name[1]
if surfTagId == -1:
raise ValueError('Surface region ({:s}) was not found'.format(surfaceRegionName))
return model.mesh.getNodesForPhysicalGroup(2, surfTagId)[0]
def getSurfaceFacesFromRegion(regionName, model):
"""
Gets the faces from a surface region, which are compatible with GMSH in order to apply surface BCs to.
:param surfaceRegionName: str - The volume domain in the model to obtain the nodes from
:param model: Mesher: The GMSH model
:return:
"""
surfs = model.getPhysicalGroups(2)
names = [(model.getPhysicalName(2, x[1]), x[1]) for x in surfs]
surfTagId = -1
for name in names:
if name[0] == regionName:
surfTagId = name[1]
if surfTagId == -1:
raise ValueError('Surface region ({:s}) was not found'.format(regionName))
mesh = model.mesh
surfNodeList2 = mesh.getNodesForPhysicalGroup(2, surfTagId)[0]
# Get tet elements
tetElList = mesh.getElementsByType(4)
tetNodes = tetElList[1].reshape(-1, 4)
tetMinEl = np.min(tetElList[0])
mask = np.isin(tetNodes, surfNodeList2) # Mark nodes which are on boundary
ab = | np.sum(mask, axis=1) | numpy.sum |
import pandas as pd
import numpy as np
import scipy as sp
import os
import errno
from sklearn.decomposition import PCA
import umap.distances as dist
from sklearn.utils.extmath import svd_flip
from sklearn.utils import check_array, check_random_state
from scipy import sparse
import sklearn.utils.sparsefuncs as sf
from umap.umap_ import nearest_neighbors
__version__ = "0.8.7"
def find_corr_genes(sam, input_gene):
"""Rank genes by their spatially averaged expression pattern correlations to
a desired gene.
Parameters
----------
sam - SAM
The analyzed SAM object
input_gene - string
The gene ID with respect to which correlations will be computed.
Returns
-------
A ranked list of gene IDs based on correlation to the input gene.
"""
all_gene_names = np.array(list(sam.adata.var_names))
D_avg = sam.adata.layers["X_knn_avg"]
input_gene = np.where(all_gene_names == input_gene)[0]
if input_gene.size == 0:
print(
"Gene note found in the filtered dataset. Note "
"that genes are case sensitive."
)
return
pw_corr = generate_correlation_map(D_avg.T.A, D_avg[:, input_gene].T.A)
return all_gene_names[np.argsort(-pw_corr.flatten())]
def _pca_with_sparse(X, npcs, solver='arpack', mu=None, seed=0):
random_state = check_random_state(seed)
np.random.set_state(random_state.get_state())
random_init = np.random.rand(np.min(X.shape))
X = check_array(X, accept_sparse=['csr', 'csc'])
if mu is None:
mu = X.mean(0).A.flatten()[None, :]
mdot = mu.dot
mmat = mdot
mhdot = mu.T.dot
mhmat = mu.T.dot
Xdot = X.dot
Xmat = Xdot
XHdot = X.T.conj().dot
XHmat = XHdot
ones = np.ones(X.shape[0])[None, :].dot
def matvec(x):
return Xdot(x) - mdot(x)
def matmat(x):
return Xmat(x) - mmat(x)
def rmatvec(x):
return XHdot(x) - mhdot(ones(x))
def rmatmat(x):
return XHmat(x) - mhmat(ones(x))
XL = sp.sparse.linalg.LinearOperator(
matvec=matvec,
dtype=X.dtype,
matmat=matmat,
shape=X.shape,
rmatvec=rmatvec,
rmatmat=rmatmat,
)
u, s, v = sp.sparse.linalg.svds(XL, solver=solver, k=npcs, v0=random_init)
u, v = svd_flip(u, v)
idx = np.argsort(-s)
v = v[idx, :]
X_pca = (u * s)[:, idx]
ev = s[idx] ** 2 / (X.shape[0] - 1)
total_var = sf.mean_variance_axis(X, axis=0)[1].sum()
ev_ratio = ev / total_var
output = {
'X_pca': X_pca,
'variance': ev,
'variance_ratio': ev_ratio,
'components': v,
}
return output
def nearest_neighbors_wrapper(X,n_neighbors=15,metric='correlation',metric_kwds={},angular=True,random_state=0):
random_state=np.random.RandomState(random_state)
return nearest_neighbors(X,n_neighbors,metric,metric_kwds,angular,random_state)[:2]
def knndist(nnma):
x, y = nnma.nonzero()
data = nnma.data
knn = y.reshape((nnma.shape[0], nnma[0, :].data.size))
val = data.reshape(knn.shape)
return knn, val
def save_figures(filename, fig_IDs=None, **kwargs):
"""
Save figures.
Parameters
----------
filename - str
Name of output file
fig_IDs - int, numpy.array, list, optional, default None
A list of open figure IDs or a figure ID that will be saved to a
pdf/png file respectively.
**kwargs -
Extra keyword arguments passed into 'matplotlib.pyplot.savefig'.
"""
import matplotlib.pyplot as plt
if fig_IDs is not None:
if type(fig_IDs) is list:
savetype = "pdf"
else:
savetype = "png"
else:
savetype = "pdf"
if savetype == "pdf":
from matplotlib.backends.backend_pdf import PdfPages
if len(filename.split(".")) == 1:
filename = filename + ".pdf"
else:
filename = ".".join(filename.split(".")[:-1]) + ".pdf"
pdf = PdfPages(filename)
if fig_IDs is None:
figs = [plt.figure(n) for n in plt.get_fignums()]
else:
figs = [plt.figure(n) for n in fig_IDs]
for fig in figs:
fig.savefig(pdf, format="pdf", **kwargs)
pdf.close()
elif savetype == "png":
plt.figure(fig_IDs).savefig(filename, **kwargs)
def weighted_PCA(mat, do_weight=True, npcs=None, solver="auto",seed = 0):
# mat = (mat - np.mean(mat, axis=0))
if do_weight:
if min(mat.shape) >= 10000 and npcs is None:
print(
"More than 10,000 cells. Running with 'npcs' set to < 1000 is"
" recommended."
)
if npcs is None:
ncom = min(mat.shape)
else:
ncom = min((min(mat.shape), npcs))
pca = PCA(svd_solver=solver, n_components=ncom,random_state=check_random_state(seed))
reduced = pca.fit_transform(mat)
scaled_eigenvalues = pca.explained_variance_
scaled_eigenvalues = scaled_eigenvalues / scaled_eigenvalues.max()
reduced_weighted = reduced * scaled_eigenvalues[None, :] ** 0.5
else:
pca = PCA(n_components=npcs, svd_solver=solver,random_state=check_random_state(seed))
reduced = pca.fit_transform(mat)
if reduced.shape[1] == 1:
pca = PCA(n_components=2, svd_solver=solver,random_state=check_random_state(seed))
reduced = pca.fit_transform(mat)
reduced_weighted = reduced
return reduced_weighted, pca
def transform_wPCA(mat, pca):
mat = mat - pca.mean_
reduced = mat.dot(pca.components_.T)
v = pca.explained_variance_ # .var(0)
scaled_eigenvalues = v / v.max()
reduced_weighted = np.array(reduced) * scaled_eigenvalues[None, :] ** 0.5
return reduced_weighted
def search_string(vec, s, case_sensitive=False, invert=False):
vec = np.array(vec)
if isinstance(s,list):
S = s
else:
S = [s]
V=[]; M=[]
for s in S:
m = []
if not case_sensitive:
s = s.lower()
for i in range(len(vec)):
if case_sensitive:
st = vec[i]
else:
st = vec[i].lower()
b = st.find(s)
if not invert and b != -1 or invert and b == -1:
m.append(i)
if len(m) > 0:
V.append(vec[np.array(m)]); M.append(np.array(m))
if len(V)>0:
i = len(V)
if not invert:
V = np.concatenate(V); M = np.concatenate(M);
if i > 1:
ix = np.sort(np.unique(M,return_index=True)[1])
V=V[ix]; M=M[ix];
else:
for i in range(len(V)):
V[i]=list(set(V[i]).intersection(*V))
V = vec[np.in1d(vec,np.unique(np.concatenate(V)))]
M = np.array([np.where(vec==x)[0][0] for x in V])
return V,M
else:
return -1,-1
def distance_matrix_error(dist1, dist2):
s = 0
for k in range(dist1.shape[0]):
s += np.corrcoef(dist1[k, :], dist2[k, :])[0, 1]
return 1 - s / dist1.shape[0]
def generate_euclidean_map(A, B):
a = (A ** 2).sum(1).flatten()
b = (B ** 2).sum(1).flatten()
x = a[:, None] + b[None, :] - 2 * np.dot(A, B.T)
x[x < 0] = 0
return np.sqrt(x)
def generate_correlation_map(x, y):
mu_x = x.mean(1)
mu_y = y.mean(1)
n = x.shape[1]
if n != y.shape[1]:
raise ValueError("x and y must " + "have the same number of timepoints.")
s_x = x.std(1, ddof=n - 1)
s_y = y.std(1, ddof=n - 1)
s_x[s_x == 0] = 1
s_y[s_y == 0] = 1
cov = np.dot(x, y.T) - n * np.dot(mu_x[:, None], mu_y[None, :])
return cov / np.dot(s_x[:, None], s_y[None, :])
def extract_annotation(cn, x, c="_"):
m = []
if x is not None:
for i in range(cn.size):
f = cn[i].split(c)
x = min(len(f) - 1, x)
m.append(f[x])
return np.array(m)
else:
ms = []
ls = []
for i in range(cn.size):
f = cn[i].split(c)
m = []
for x in range(len(f)):
m.append(f[x])
ms.append(m)
ls.append(len(m))
ml = max(ls)
for i in range(len(ms)):
ms[i].extend([""] * (ml - len(ms[i])))
if ml - len(ms[i]) > 0:
ms[i] = np.concatenate(ms[i])
ms = np.vstack(ms)
MS = []
for i in range(ms.shape[1]):
MS.append(ms[:, i])
return MS
def isolate(dt, x1, x2, y1, y2):
return np.where(
np.logical_and(
np.logical_and(dt[:, 0] > x1, dt[:, 0] < x2),
np.logical_and(dt[:, 1] > y1, dt[:, 1] < y2),
)
)[0]
def to_lower(y):
x = y.copy().flatten()
for i in range(x.size):
x[i] = x[i].lower()
return x
def to_upper(y):
x = y.copy().flatten()
for i in range(x.size):
x[i] = x[i].upper()
return x
def create_folder(path):
try:
os.makedirs(path)
except OSError as exception:
if exception.errno != errno.EEXIST:
raise
def convert_annotations(A):
x = np.unique(A)
y = np.zeros(A.size)
z = 0
for i in x:
y[A == i] = z
z += 1
return y.astype("int")
def nearest_neighbors_hnsw(x,ef=200,M=48,n_neighbors = 100):
import hnswlib
labels = np.arange(x.shape[0])
p = hnswlib.Index(space = 'cosine', dim = x.shape[1])
p.init_index(max_elements = x.shape[0], ef_construction = ef, M = M)
p.add_items(x, labels)
p.set_ef(ef)
idx, dist = p.knn_query(x, k = n_neighbors)
return idx,dist
def calc_nnm(g_weighted, k, distance=None):
if g_weighted.shape[0] > 0:
if distance == 'cosine':
nnm, dists = nearest_neighbors_hnsw(g_weighted, n_neighbors=k)
else:
nnm, dists = nearest_neighbors_wrapper(g_weighted, n_neighbors=k, metric=distance)
EDM = gen_sparse_knn(nnm, dists)
EDM = EDM.tocsr()
return EDM
def compute_distances(A, dm):
if dm == "euclidean":
m = np.dot(A, A.T)
h = np.diag(m)
x = h[:, None] + h[None, :] - 2 * m
x[x < 0] = 0
dist = | np.sqrt(x) | numpy.sqrt |
"""
Implement a Vanilla NBP and NRW model for MC simulation of the NTE.
Code for the article "Monte Carlo Methods for the Neutron Transport Equation.
By <NAME>, <NAME>, <NAME>, <NAME>.
Thi sfile contains the code to produce the plots in the case of the 2D version
of the NTE.
MIT License
Copyright (c) <NAME>, 2020.
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.
"""
import numpy as np
import math
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from scipy.ndimage.filters import gaussian_filter
class circle:
"""Shape to determine area of scatter/branching."""
def __init__(self, centre, radius):
self.centre = centre
self.radius = radius
def time_in_circle(self, pos, theta, v):
"""Compute entry, exit times in circle for given trajectory."""
a = v**2
b = 2*v*((pos[0] - self.centre[0])*np.cos(theta)
+ (pos[1] - self.centre[1])*np.sin(theta))
c = ((pos[0] - self.centre[0])**2 + (pos[1] - self.centre[1])**2
- self.radius**2)
det = b**2 - 4*a*c
if det < 0:
self.entry_time = -100
self.exit_time = -100
elif det == 0:
self.entry_time = (-b - np.sqrt(det))/(2*a)
self.exit_time = self.entry_time
else:
if -b - np.sqrt(det) < 0:
if -b + np.sqrt(det) > 0:
self.entry_time = 0
self.exit_time = (-b + np.sqrt(det))/(2*a)
else:
self.entry_time = -100
self.exit_time = -100
else:
self.entry_time = (-b - np.sqrt(det))/(2*a)
self.exit_time = (-b + np.sqrt(det))/(2*a)
return self.entry_time, self.exit_time
def interval_in_circle(self, traj, max_time):
"""Compute entry, exit times for a given "stick"."""
en, ex = self.time_in_circle(traj[1], traj[2], traj[3])
if (en >= 0 and en < (max_time-traj[0])):
return traj[0]+en, min(traj[0]+ex, max_time)
else:
return None
def in_circle(self, pos):
"""Return true if the position is in the circle."""
return ((pos[0]-self.centre[0])**2. + (pos[1]-self.centre[1])**2.
<= self.radius**2.)
class domain:
"""Define a spatial domain (in 2d) with Scattering rates and boundaries."""
def __init__(self, L=1, A=np.array([[-1, 0], [1, 0], [0, 1], [0, -1]]),
b=np.array([1.0, 1.0, 1.0, 1.0])):
# L is outer box size. Might be used to discretize space in e.g.
# plotting.
# A, b define the domain, so x is in the domain if and only if
# |x_i| <= L and A x \le b for each coordinate.
# The default is the box [-1,1] x [-1,1]
# List of scatter locations
self.A = A
self.b = b
self.L = L
def is_in_domain(self, pos):
"""Is the position pos in the Domain."""
return np.all((self.b - self.A@pos >= 0))
def exit_time(self, pos, theta, v=1.0):
"""When does the particle exit the Domain."""
z = np.array([np.cos(theta), np.sin(theta)])
return min(filter(lambda x: x >= 0, (self.b-self.A@pos)/(v*self.A@z)))
def exit_time_reverse(self, pos, theta, v=1.0):
"""When does the particle exit the domain, travelling in reverse."""
z = np.array([np.cos(theta), np.sin(theta)])
return min(filter(lambda x: x >= 0,
(self.A@pos - self.b)/(v*self.A@z)))
class SubPathCircles:
"""Define a subpath of a 2D-neutron trajectory through domain with circles.
Note that in circle, rates are for additional branching/scattering
over base rate of domain.
"""
def __init__(self, tstart, xstart, thetastart, vstart, tfin, srate_dom,
srate_circ, brate_dom, brate_circ):
self.tstart = tstart
self.xstart = xstart
self.thetastart = thetastart
self.vstart = vstart
self.tfin = tfin
self.drate = srate_dom
self.crate = srate_circ
self.drate_b = brate_dom
self.crate_b = brate_circ
self.alive = True
self.c1 = circle(np.array([0.5, 0.5]), 0.25)
self.c2 = circle(np.array([0.5, -0.5]), 0.25)
self.c3 = circle(np.array([-0.5, 0.5]), 0.25)
self.c4 = circle(np.array([-0.5, -0.5]), 0.25)
self.c = [self.c1, self.c2, self.c3, self.c4]
self.d = domain()
self.circle_time = []
self.turn = [[self.tstart, self.xstart, self.thetastart, self.vstart]]
self.scatter(self.tfin, self.drate, self.crate, self.drate_b,
self.crate_b)
# self.time_in_circle(self.c)
def in_circle(self, time_in, time_out, event_time):
"""Return true if particle is in any circle at event time.
Expects time_in, time_out to be entry/exit times of circle. Event
time is time after the entry.
"""
return (time_in + event_time <= time_out)
def scatter(self, tfin, srate_dom, srate_circ, brate_dom, brate_circ):
"""
Generate paths up to time tfin.
Parameters
----------
tfin : TYPE real
Time to generate paths up to.
srate_dom : TYPE
Scatter rate in the domain.
srate_circ : TYPE
Extra scatter rate observed in circles.
brate_dom : TYPE
Branch rate in domain.
brate_circ : TYPE
Extra scatter observed in circles.
Returns
-------
TYPE list
List of times and places of scatter events up to tfin, or death.
If particle survives, last location is not a scatter.
"""
zeta = self.d.exit_time(self.xstart, self.thetastart, self.vstart)
temp = self.tstart
position = self.xstart
angle = self.thetastart
speed = self.vstart
while temp < tfin and self.alive:
circle_times = [circ.time_in_circle(position, angle, speed)
for circ in self.c]
if (srate_dom+brate_dom) > 0:
d_exp = -np.log(np.random.uniform())/(srate_dom+brate_dom)
else:
d_exp = math.inf
if (srate_circ+brate_circ) > 0:
c_exp = (-np.log(np.random.uniform(size=len(self.c))) /
(srate_circ + brate_circ)).tolist()
Exp = min(d_exp,
min([math.inf] +
[(circle_times[c_exp.index(stime)][0]
+ stime)
for stime in c_exp if
self.in_circle(
circle_times[c_exp.index(stime)][0],
circle_times[c_exp.index(stime)][1],
stime)]))
else:
Exp = d_exp
# if (Exp == math.inf) and (temp + zeta < tfin):
# self.alive = False
# self.tfin = temp + zeta
# self.turn.append([self.tfin,
# [position[0]+speed*np.cos(angle)*zeta,
# position[1]+speed*np.sin(angle)*zeta],
# angle, speed])
# temp += Exp
if np.min([temp + Exp, temp + zeta]) < tfin:
if Exp >= zeta:
# Hits Boundary before tfin
self.alive = False
self.tfin = temp + zeta
self.turn.append([temp + zeta,
[position[0] +
speed * np.cos(angle) * zeta,
position[1] +
speed * np.sin(angle) * zeta],
angle, speed])
temp = temp + zeta
else:
# Scatter before tfin
position = [position[0] + np.cos(angle) * speed * Exp,
position[1] + np.sin(angle) * speed * Exp]
angle = np.random.uniform(0, 2 * np.pi)-np.pi
speed = self.vstart
zeta = self.d.exit_time(position, angle, speed)
self.tfin = temp + Exp
temp = temp + Exp
self.turn.append([temp, position, angle, speed])
else:
# reach tfin:
position = [position[0] + | np.cos(angle) | numpy.cos |
"""
====================================
SDE INTEGRATION AND
REALIZATIONS OF STOCHASTIC PROCESSES
====================================
* ``paths_generator``, ``integrator``, ``SDE`` and ``SDEs`` classes,
* ``integrate`` decorator,
* realization of stochastic processes.
"""
import numpy as np
from numpy import sqrt, exp, log
from .infrastructure import (
process,
wiener_source, poisson_source, cpoisson_source,
norm_rv, double_exp_rv
)
########################################
# Private functions for recurring tasks
########################################
from .infrastructure import (
_get_default_rng,
_shape_setup,
_const_param_setup,
_variable_param_setup,
_source_setup,
_signature,
_empty
)
############################
# The paths_generator class
############################
class paths_generator:
"""
Step by step generation of stochastic simulations across multiple
paths, intended for subclassing.
Given a number of requested paths, shapes and output timeline,
encapsulates the low level tasks of memory allocation and step by step
iteration along the timeline.
The definition of the target iteration steps (``pace`` method),
initialization (``begin`` method),
computation of next step (``next`` method),
storing results at points on the requested timeline (``store`` method),
cleaning up (``end`` method) and
evaluation of a final result to be returned (``exit`` method),
are delegated to subclasses.
Instances are callables with signature ``(timeline)`` that iterate
subclass methods along the given timeline, using the configuration
set out at instantiation.
Parameters
----------
paths : int
Size of last axis of the allocated arrays
(number of paths of the simulation).
xshape : int or tuple of int
Shape of values that will be stored at each point
of the output timeline.
wshape : int or tuple of int
Shape of working space used for step by step iteration.
dtype : data-type
Data-type of the output and working space.
steps : iterable, or int, or None
Specification of the time points to be touched during the simulation
(as defined by the ``pace`` method). Default behaviour is:
- if ``None``, the simulated steps coincide with the timeline;
- if ``int``, the simulated steps touch all timeline points,
as well as ``steps`` equally spaced points between the minimum
and maximum point in the timeline;
- if iterable, the simulated steps touch all timeline points,
as well as all values in ``steps`` between the minimum and maximum
points in the timeline.
i0 : int
Index along the timeline at which the simulation starts. The timeline
is assumed to be in ascending order. The simulation is performed
backwards from ``timeline[i0]`` to ``timeline[0]``, and forwards
from ``timeline[i0]`` to ``timeline[-1]``.
info : dict, or None
Diagnostic information about the simulation is stored in this
dictionary and is accessible as the ``info`` attribute.
If ``None``, a new empty ``dict`` is used.
getinfo : bool
If ``True`` (default), records basic information in the ``info``
attribute about the last performed simulation (if the simulation is
both backwards and forwards, the information pertains to the forwards
part only). Used by subclasses to enable/disable diagnostic
info generation.
Returns
-------
simulation results
Once instantiated as ``p``, ``p(timeline)`` runs the simulation
along the given timeline, based on parameters of instantiation,
returning results as determined by subclass methods.
Defaults to ``(tt, xx)`` where ``tt`` is a reference to ``timeline``
and ``xx`` is an array of ``numpy.nan`` of the requested shape.
See Also
--------
integrator
SDE
SDEs
Notes
-----
All initialization parameters are stored as attributes of the same name,
and may be accessed by subclasses.
During the simulation, a ``itervars`` attribute is present,
pointing to a dictionary that contains the following items,
to be used by subclass methods (double letters refer to values
along the entire timeline, single letters refer to single time points):
* ``steps_tt`` : an array of all time points to be touched
by the simulation. It consolidates the output timeline
and the time points to be touched, as specified by ``steps``.
* ``tt``: the output timeline.
* ``xx``: simulation output, an array of shape
``tt.shape + xshape + (paths,)``. ``xx[i]`` is the simulated value
at time ``tt[i]``.
* ``sw``: working space for time points, an array
of shape ``(depth,)``.
* ``xw``: working space for paths generation, an array of objects
of shape ``(depth,)``, where each of ``xw[k]`` is an array
of shape ``wshape + (paths,)``.
* ``reverse`` : ``True`` if the simulation runs backwards,
``False`` otherwise. If ``True``, ``steps_tt`` and ``tt`` are
in descending order.
* ``i`` : such that ``tt[i]`` is the next point
along the timeline that will be reached (when invoking ``next``),
or the point that was just reached (when invoking ``store``).
Note that:
* ``sw`` and ``xw`` are rolled at each iteration: subclass methods
should not rely on storing references to their elements
across iterations.
* ``xw[k][...] = value`` broadcasts ``value`` into the allocated
memory of ``xw[k]`` (this is usually what you want),
``xw[k] = value`` stores ``value``, as an object, in ``xw[k]``
(avoid).
* ``xx`` and ``xw[k]`` are initialized to arrays filled
with ``numpy.nan``.
Attributes
----------
depth : int
Number of time points to be stored in the working space. Defaults to 2.
Methods
-------
__call__
pace
begin
next
store
end
exit
"""
def __init__(self, *, paths=1,
xshape=(), wshape=(),
dtype=None, steps=None, i0=0,
info=None, getinfo=True):
self.paths = paths
self.xshape = _shape_setup(xshape)
self.wshape = _shape_setup(wshape)
self.dtype = dtype
self.steps, self.i0 = steps, i0
self.info = {} if info is None else info
self.getinfo = getinfo
super().__init__()
# public interface vs subclasses
# ------------------------------
depth = 2 # should be set in subclasses to be an integer >= 2
def pace(self, timeline):
"""
Target integration steps for the current integration.
Parameters
----------
timeline : array
Requested simulation timeline, cast as an array of float data-type.
Returns
-------
array
Target time points to be touched during the simulation
(typically, more thinly spaced than the output time
points in ``timeline``, based on the ``steps`` parameter),
to be merged with ``timeline``.
May be overridden by subclasses. For default behaviour,
see paths_generator class documentation.
"""
steps = self.steps
ttype = timeline.dtype
if timeline.size == 1:
return timeline
elif steps is None:
return np.array((), dtype=ttype)
elif np.isscalar(steps):
return np.linspace(timeline[0], timeline[-1], steps, dtype=ttype)
else:
return np.fromiter(steps, dtype=ttype)
def begin(self):
"""
Set initial conditions.
Given the time points ``sw[0], ..., sw[depth - 2]``,
should define and store in the working space
the corresponding initial values ``xw[0], ..., xw[depth - 2]``.
Note that when ``begin`` gets called,
``sw[depth - 1]`` and ``xw[depth - 1]`` are undefined and will be
respectively set, and computed, at the first iteration.
Notes
-----
It is called once for each backwards and forwards simulation,
after memory allocation and before starting the iteration along
the time points in ``steps_tt``.
Outline of expected code for ``depth=2``::
# access itervars
iv = self.itervars
sw, xw = iv['sw'], iv['xw']
# this is the initial time, taken from the
# simulation timeline
t0 = sw[0]
assert t0 == iv['steps_tt'][0] == iv['tt'][0]
# store the initial condition
xw[0][...] = 1.
Must be provided by subclasses.
"""
pass
def next(self):
"""
Numerical simulation step.
Given the points ``sw[0], ..., sw[depth - 2]``
and the corresponding values ``xw[0], ..., xw[depth - 2]``,
should:
1. Optionally modify the target next time point ``sw[depth - 1]``,
to a value between ``sw[depth - 2]`` and ``sw[depth - 1]``
(this allows for adaptive time steps, with the constraint of
touching all point specified by the output timeline and the
``steps`` parameter).
2. Compute the corresponding value ``xw[depth - 1]``
Notes
-----
It is called once per iteration step.
Outline of expected code for ``depth=2``::
# access itervars
iv = self.itervars
sw, xw = iv['sw'], iv['xw']
# get starting values, and time step to be taken
s0, x0 = sw[0], xw[0]
ds = sw[1] - sw[0]
# compute and store the next step
xw[1][...] = x0 + ds
Must be provided by subclasses.
"""
pass
def store(self, i, k):
"""
Store the current integration step into the integration output.
Should take the k-th value in the working space ``xw``,
transform it if need be, and store it as the output
``xx[i]`` at the output time point ``tt[i]``.
Parameters
----------
i : int
Index of the output timeline point to set as output.
k : int
Index of the working space point to use as input.
Notes
-----
It is called initially to store the initial values that belong
to the output timeline, among those put into the working space
by ``begin``, and later during the iteration, each time the simulation
touches a point on the output timeline.
Outline of expected code for ``xshape == wshape`` and
an exponentiation transformation::
# access itervars
iv = self.itervars
sw, xw = iv['sw'], iv['xw']
xx = iv['xx']
# this is the current time, also found
# along the output timeline
s = sw[k]
assert s == iv['tt'][i]
# transform and store
np.exp(xw[k], out=xx[i])
Must be provided by subclasses.
"""
pass
def end(self):
"""
End of iteration optional tasks.
It is called once for each backwards and forwards simulation,
once the final point in the output timeline has been reached
and the simulation ends.
After it is called, ``itervars`` are deleted.
May be provided by subclasses.
"""
pass
def exit(self, tt, xx):
"""
Final tasks and construction of the output value(s).
Parameters
----------
tt : array
Output timeline. It is the timeline passed to the ``__call__``
method, cast as an array, with its original data-type
(if the data-type is of integer kind, the simulation
is carried out using floats).
xx : array
Output values along the timeline, as computed by ``next``
and stored by ``store`` methods.
Notes
-----
It is called once, after backwards and/or forwards simulations
have been completed, and its return value is returned.
Default implementation::
return tt, xx
May be provided by subclasses.
"""
return tt, xx
# private methods
# ---------------
def _store_if_reached(self, i, k):
iv = self.itervars
tt, sw, reverse = iv['tt'], iv['sw'], iv['reverse']
diff = (tt[i] - sw[k]) * (-1 if reverse else 1)
if diff < 0: # should never occur
raise RuntimeError(
'invalid path generation step encountered in {}: '
'realized s={} is beyond target value t={}'
.format(self, sw[k], tt[i]))
elif tt[i] == sw[k]:
self.store(i, k)
return 1
else:
return 0
def _generate_paths(self, steps_tt, tt, xx, sw, xw, reverse):
K = self.depth
# set itervars to be used by subclass methods
# -------------------------------------------
self.itervars = dict(steps_tt=steps_tt, tt=tt, xx=xx,
sw=sw, xw=xw, reverse=reverse)
# set steps iterator
# ------------------
st = iter(steps_tt)
# initialize working space
# ------------------------
# set sw[0] ... sw[K-2]
for k in range(K-1):
sw[k] = next(st)
# invoke cooperative subclass method 'being'
# (should initialize xw[0:K-1], given sw[0:K-1])
self.begin()
# store initial condition x[0] at t[0] == sw[0], and possibly
# other output values if any of the sw[1], ..., sw[K-1] is
# part of the requested timeline t
i = 0
for k in range(K-1):
# invoke cooperative subclass method 'store'
i += self._store_if_reached(i, k)
# MAIN LOOP
# ---------
target_s = current_s = sw[-2] # any same value will do
while i < tt.size:
# when the iteration begins:
# sw[0:K-1], xw[0:K-1] refer to the last stored K-1 steps
# s[K-1] == s[-1], xw[K-1] == xw[-1] are undefined
# and will be used to store the next computed step
# i is such that x[i] is the last stored output value
# ------------------------------------------------------
# if the previous step reached target_s, get next time point
if current_s == target_s:
target_s = next(st)
# set sw[-1] to the target time point
sw[-1] = target_s
self.itervars['i'] = i
# call cooperative subclass method 'next'
# (should decrease or leave unchanged, but not
# increase, the time point sw[-1], and compute the
# corresponding xw[-1])
self.next()
# check the adjusted step size is within permitted bounds
order_ok = (sw[-2] > sw[-1] >= target_s
if reverse else sw[-2] < sw[-1] <= target_s)
if not order_ok:
raise RuntimeError(
'invalid path generation step encountered in {}: '
's={} was followed by s+ds={}, beyond requested s+ds={}'
.format(self, sw[-2], sw[-1], target_s))
# invoke cooperative subclass method 'store'
di = self._store_if_reached(i=i, k=-1)
# update diagnostic info
if self.getinfo:
self.info['computed_steps'] += 1
self.info['stored_steps'] += di
# prepare next iteration
current_s = sw[-1]
sw[...] = np.roll(sw, -1)
xw[...] = np.roll(xw, -1)
i += di
# invoke cooperative subclass method 'end'
self.end()
# clean up temporary variables
del self.itervars
def __call__(self, timeline):
"""
Run the simulation along the given timeline.
Parameters
----------
timeline : array-like
A one dimensional array of strictly increasing numbers,
defining the timeline of the simulation.
Returns
-------
Simulation results, as specified by subclass methods.
"""
paths, xshape, wshape = self.paths, self.xshape, self.wshape
dtype, i0 = self.dtype, self.i0
K = self.depth
# set dtype default
if dtype is None:
dtype = float
# enforce depth >= 2
if K < 2:
raise ValueError(
'the depth of the integrator algorithm should be '
'>= 2, not {}'.format(K))
# preprocess and validate the result's timeline
# ---------------------------------------------
tt = np.asarray(timeline)
if tt.shape != (tt.size,):
raise ValueError(
'the integration timeline should be a one-dimensional array, '
'not an array of shape {}'.format(tt.shape))
if not np.array_equal(tt, np.unique(tt)):
raise ValueError(
'the integration timeline sholud be '
'an array of strictly increasing numbers, '
'but {} was given'
.format(tt))
try:
if not np.isscalar(tt[i0]):
raise IndexError()
except IndexError:
raise IndexError(
'i0 should be an integer indexing an element of the '
'integration timeline, but {} was given'
.format(i0))
# NOTE:
# if tt is an integer type, the use of floats is forced in
# computations. the integer tt is finally passed to self.exit
# to be set as the timeline of the returned process
ttype = float if tt.dtype.kind == 'i' else tt.dtype
tt, tt_asis = tt.astype(ttype), tt
# built the integration steps
# ---------------------------
tmin, tmax = tt[0], tt[-1]
target_tt = self.pace(tt)
target_tt = target_tt[np.logical_and(target_tt >= tmin,
target_tt <= tmax)]
steps_tt = np.unique(np.concatenate((target_tt, tt)))
if len(steps_tt) < K-1:
raise ValueError(
'at least {} time points are needed '
'for a paths_generator with depth {}'
.format(K-1, K)
)
# steps_tt consolidates all target integration points and all points
# in the timeline to be returned
# memory allocation
# -----------------
xx = np.full(tt.shape + xshape + (paths,), np.nan,
dtype=dtype)
xw = np.empty(K, dtype=object)
sw = np.full(K, np.nan, dtype=ttype)
for k in range(K):
xw[k] = np.full(wshape + (paths,), np.nan, dtype=dtype)
# store/initialize info
# ---------------------
if self.getinfo:
self.info.update(
t0=tt[i0], tmin=tt[0], tmax=tt[-1],
computed_steps=0, stored_steps=0
)
# MAIN LOOP
# ---------
# get integration timeline and locate tt[i0] into it
j0 = np.where(steps_tt == tt[i0])
assert len(j0) == 1 and j0[0].shape == (1,)
j0 = j0[0][0]
# integrate backwards if not starting from the first point
if i0 != 0:
self._generate_paths(steps_tt[j0::-1], tt[i0::-1], xx[i0::-1],
sw, xw, reverse=True)
# integrate forwards if not starting from last point
# (if tt.size==1, integrates only forwards)
if i0 == 0 or i0 not in (-1, tt.size - 1):
self._generate_paths(steps_tt[j0:], tt[i0:], xx[i0:],
sw, xw, reverse=False)
# Postprocess and exit
# --------------------
return self.exit(tt_asis, xx)
############################################
# SDE integration frameword:
# the integraor and SDE cooperating classes
############################################
# -------------------------
# The integrator class
# -------------------------
class integrator(paths_generator):
"""
Step by step numerical integration of Ito Stochastic Differential
Equations (SDEs), intended for subclassing.
For usage, see the ``SDE`` class documentation.
This class encapsulates SDE integration methods, and cooperates
with the ``SDE`` class, that should always have precedence in
method resolution order. As long as the respective
APIs are complied with, a new integrator stated as an
``integrator`` subclass will interoperate with existing
SDEs (as described by ``SDE`` subclasses), and a new SDE
will interoperate with existing integrators.
Parameters
----------
paths, xshape, wshape, dtype, steps, i0, info, getinfo
See ``paths_generator`` class documentation.
method : string
Integration method. Defaults to ``'euler'``, for the
Euler-Maruyama method (at present, this single method
is supported). It is stored as an attribute of the same name.
Returns
-------
process
Once instantiated as ``p``, ``p(timeline)`` performs the integration
along the given timeline, based on parameters of instantiation,
returning the resulting process as determined by the cooperating
``SDE`` subclass and the chosen integration method.
Defaults to a process of ``numpy.nan`` along the given timeline.
See Also
--------
paths_generator
SDE
SDEs
Notes
-----
The equation to be integrated is exposed to the integration
algorithm in a standardized form, via methods ``A`` and ``dZ``
delegated to a cooperating ``SDE`` class. The latter should take care
of equation parameters, initial conditions, expected paths and shapes,
and should instantiate all necessary stochasticity sources.
The integration method is exposed as the ``next`` method to the
``paths_generator`` parent class.
If the ``getinfo`` attribute is set to ``True``, at each integration
step the following items are added to the ``itervars`` dictionary,
made available to subclasses to track the integration progress:
* ``last_t``: starting time point of the last integration step.
* ``last_dt``: time increment of the last integration step.
* ``last_x`` : starting value of the process, at time ``last_t``.
* ``last_A``: dictionary of the last computed values of the SDE
terms, at time ``last_t``.
* ``last_dZ``: dictionary of the last realized SDE stochasticity
source values, cumulated in the interval from ``last_t``
to ``last_t + last_dt``.
* ``new_x`` : computed value of the process, at time
``last_t + last_dt``.
This becomes relevant in case the output timeline is coarse
(e.g. just the initial and final time) but diagnostic information
is needed about all integration steps performed
(e.g., to track how often the process has changed sign, or to
count the number of realized jumps).
Methods
-------
A
dZ
next
euler_next
"""
def _check_integration_method(self, id):
if not hasattr(self, id + '_next'):
raise ValueError(
'unrecognized integration method {}: '
"use 'euler' "
'or provide a properly defined '
'`{}_next` integrator class method'
.format(id, id))
def _get_integration_method(self, id):
return getattr(self, id + '_next')
def __init__(self, *, paths=1,
xshape=(), wshape=(),
dtype=None, steps=None, i0=0,
info=None, getinfo=True,
method='euler'):
# setup the required integration method
self.method = method
self._check_integration_method(method)
self._method_next = self._get_integration_method(method)
# set up the paths_generator parent class
super().__init__(paths=paths,
xshape=xshape, wshape=wshape,
dtype=dtype, steps=steps, i0=i0,
info=info, getinfo=getinfo)
# integration methods
# -------------------
def euler_next(self):
"""
Euler-Maruyama integration step.
"""
iv = self.itervars
sw, xw = iv['sw'], iv['xw']
s, ds = sw[0], sw[1] - sw[0]
x = xw[0]
# compute A, dZ and make them available as attributes
A, dZ = self.A(s, x), self.dZ(s, ds)
xw[1][...] = x + sum(A.get(id, 0)*dZ[id] for id in A.keys())
if self.getinfo:
iv.update(last_t=s, last_dt=ds,
last_x=xw[0], last_A=A,
last_dZ=dZ, new_x=xw[1])
# interface vs parent paths_generator class, and
# delegation to cooperating class methods
# ----------------------------------------------
depth = 2
def next(self):
"""Perform an integration step with the requested method."""
super().next()
self._method_next()
def exit(self, tt, xx):
"""See documentation of paths_generator.exit"""
return process(t=tt, x=xx)
# interface vs cooperating SDE class
# ----------------------------------
def A(self, t, x):
"""Value of the SDE terms at time t and process value x.
Example of expected code for the SDE ``dx = (1 - x)*dt + 2*dw(t)``::
return {
'dt': (1 - x),
'dw': 2
}
The ``SDE`` class takes care of casting user-specified
equations into this format.
"""
return {'dt': x + np.nan}
def dZ(self, t, dt):
"""Value of the SDE differentials at time t, for
time increment dt.
Example of expected code for the SDE ``dx = (1 - x)*dt + 2*dw(t)``,
where ``x`` has two components::
shape = (2, self.paths)
return {
'dt': dt,
'dw': wiener_source(vshape=2, paths=self.paths)(0, dt)
}
The ``SDE`` class takes care of instantiating user-specified
stochasticity sources and casting them into this format.
"""
return {'dt': dt + np.nan}
# ------------------------------------------------------------
# The SDE (one equation) and SDEs (multiple equations) classes
# ------------------------------------------------------------
class SDE:
"""
Class representation of a user defined Stochastic Differential
Equation (SDE), intended for subclassing.
This class aims to provide an easy to use and flexible interface,
allowing to specify user-defined SDEs and expose them in a standardized
form to the cooperating ``integrator`` class (the latter should
always follow in method resolution order). A minimal
definition of an Ornstein-Uhlenbeck process is as follows:
>>> from sdepy import SDE, integrator
>>> class my_process(SDE, integrator):
... def sde(self, t, x, theta=1., k=1., sigma=1.):
... return {'dt': k*(theta - x), 'dw': sigma}
An SDE is stated as a dictionary, containing for each differential
the value of the corresponding coefficient::
dx = f(t, x)*dt + g(t, x)*dw + h(t, x)*dj
translates to::
{'dt': f(t, x), 'dw': g(t, x), 'dj': h(t, x)}
Instances are callables with signature ``(timeline)`` that integrate
the SDE along the given timeline, using the configuration set out in
the instantiation parameters:
>>> P = my_process(x0=1, sigma=0.5, paths=100*1000, steps=100)
>>> x = P(timeline=(0., 0.5, 1.))
>>> x.shape
(3, 100000)
Subclasses can specify or customize:
the equation and its parameters (``sde`` method),
initial conditions and preprocessing (``init`` method and
``log`` attribute), shape of the values to be computed and stored
(``shapes`` method), stochastic differentials appearing in the equation
(``sources`` attribute) and their parameters and initialization (methods
``source_dt``, ``source_dw``, ``source_dn``, ``source_dj``, or any custom
``source_{id}`` method for a corresponding differential ``'{id}'``
declared in ``sources`` and used as a key in ``sde`` return values),
optional non array-like parameters (``more`` method), how to store results
at points on the requested timeline (``let`` method), and
postprocessing (``result`` method and ``log`` attribute).
Parameters
----------
paths : int
Number of paths of the process.
vshape : int or tuple of int
Shape of the values of the process.
dtype : data-type, optional
Data-type of the process. Defaults to the numpy default.
rng : numpy.random.Generator, or numpy.random.RandomState, or None
Random numbers generator used to instantiate sources.
If ``None``, defaults to
``sdepy.infrastructure.default_rng``, a global variabile
initialized on import to ``numpy.random.default_rng()``.
steps : iterable, or int, or None
Specification of the time points to be touched during integration
(as accepted by a cooperating ``integrator`` class).
Default behaviour is:
- if ``None``, the simulated steps coincide with the timeline;
- if ``int``, the simulated steps touch all timeline points,
as well as ``steps`` equally spaced points between the minimum
and maximum point in the timeline;
- if iterable, the simulated steps touch all timeline points,
as well as all values in ``steps`` between the minimum and maximum
points in the timeline.
i0 : int
Index along the timeline at which the integration starts. The timeline
is assumed to be in ascending order. Initial conditions are set
at ``timeline[i0]``, the integration is performed
backwards from ``timeline[i0]`` to ``timeline[0]``, and forwards
from ``timeline[i0]`` to ``timeline[-1]``.
info : dict, optional
Diagnostic information about the integration is stored in this
dictionary and is accessible as the ``info`` attribute.
Defaults to a new empty ``dict``.
getinfo : bool
If ``True``, subclass methods ``info_begin``, ``info_next``,
``info_store``, ``info_end`` are invoked during integration.
Defaults to ``True``.
method : str
Integration method, as accepted by the ``integrator``
cooperating class.
**args : SDE-specific parameters
SDE parameters and initial conditions, as implied by the signature
of ``sde``, ``init`` and ``more`` methods, and stochasticity sources
parameters, as implied by the signature of ``source_{id}`` methods.
Each keyword should be used once (e.g. ``corr``, a ``source_dw``
parameter, should not be used as the name of a SDE parameter) or,
if repeated, must have consistent default values.
Returns
-------
process
Once instantiated as ``p``, ``p(timeline)`` performs the integration
along the given timeline, based on parameters of instantiation,
and returns the resulting process as defined by subclass methods.
Defaults to a process of ``numpy.nan`` along the given timeline.
See Also
--------
paths_generator
integrator
SDEs
Notes
-----
Custom stochastic differentials used in the SDE should be recognized,
and treated appropriately, by the chosen integration method. This
may require customization of the ``next`` method of the ``integrator``
class.
All named initialization parameters (``paths``, ``steps`` etc.)
are stored as attributes.
Notes on SDE-specific parameters:
* ``init`` parameters are converted to arrays via ``np.asarray``.
* ``sde`` and source quantitative parameters may be array-like,
or time dependent with signature ``(t)``.
* both are converted to arrays via ``np.asarray``, and
for both, their constant value, or values at each time point,
should be broadcastable to a shape ``wshape + (paths,)``.
* ``more`` parameters undergo no further initialization, before
being made available to the ``shapes`` and ``more`` methods.
If ``getinfo`` is ``True``, the invoked info subclass methods
may initialize and cumulate diagnostic information in items
of the ``info`` dictionary, based on read-only access of the
internal variables set during integration by ``paths_generator``
and ``integrator`` cooperating classes, as exposed in the ``itervars``
attribute.
Attributes
----------
sources : set or dict
As a class attribute, holds the names of the differentials ``'dz'``
expected to appear in the equation. As an instance attribute,
``sources['dz']`` is an object, complying with the ``source`` protocol,
that instantiates the differential ``'dz'`` used during integration.
``sources['dz'](t, dt)`` is computed at every step for each
``'dz' in sources``, as required by the chosen integration method.
args : dict
Stores parameters passed as ``**args`` upon initialization
of the SDE. Should be used by subclass methods to access
and modify their values.
log : bool
If True, the natural logarithm of the initial values set by the
``init`` method is taken as the initial value of the integration,
and the result of the integration is exponentiated back before
serving it to the ``result`` method. The ``sde`` should expose
the appropriate equation for integrating the logarithm of the
intended process.
Methods
-------
sde
shapes
source_dt
source_dw
source_dn
source_dj
more
init
let
result
info_begin
info_next
info_store
info_end
"""
# public attributes
# -----------------
sources = {'dt', 'dw'}
log = False
q = None
addaxis = None
# q and addaxis are not used in this class
# (inserted for consistency with subclass SDEs)
# private methods and attributes
# ------------------------------
def _check_source_id(self, id):
if not hasattr(self, 'source_' + id):
raise ValueError(
'unrecognized source {}: '
"use one of 'dt', 'dw', 'dn', 'dj', "
'or provide a properly defined '
'SDE class method `source_{}`'
.format(id, id))
def _get_source_setup_method(self, id):
return getattr(self, 'source_' + id)
def _get_args(self, keys):
return {k: z for k, z in self._args.items()
if k in keys}
def _inspect_args_defaults(self, sde_nvars=1):
# inspect signatures to find expected args and defaults,
# apply user-defined defaults if any
expected_source_args = {}
for id in self.sources:
self._check_source_id(id)
source_setup_method = self._get_source_setup_method(id)
expected_source_args[id] = \
dict(_signature(source_setup_method))
# first two parameters of sde.init are expected to be t and out_x
expected_init_args = dict(_signature(self.init)[2:])
# first two parameters of sde callable are expected to be t and x,
# (for SDEs, first 1+q parameters are t, x1, x2, ... xq)
expected_sde_args = dict(_signature(self.sde)[1+sde_nvars:])
expected_more_args = dict(_signature(self.more))
# consolidate
expected_args = {}
for D in (tuple(expected_source_args.values()) +
(expected_init_args, expected_sde_args,
expected_more_args)):
expected_args.update(D)
# check for multiple occurrencies of the same expected arg,
# with different defaults
defaults = {k: [] for k in expected_args}
for D in (tuple(expected_source_args.values()) +
(expected_init_args, expected_sde_args,
expected_more_args)):
for k, z in D.items():
defaults[k].append(z)
repeated = {k for k in defaults
if len(set(defaults[k])) > 1}
if repeated:
raise TypeError(
'two or more incompatible defaults found '
'for SDE parameter(s) {}'
.format(repeated))
# store arg keys for later use in self._get_args()
self._source_args_keys = {}
for id in self.sources:
self._source_args_keys[id] = set(expected_source_args[id])
self._init_args_keys = set(expected_init_args)
self._sde_args_keys = set(expected_sde_args)
self._more_args_keys = set(expected_more_args)
# store args defaults for later use by _consolidate_args
self._expected_args = expected_args
def _consolidate_args(self, **args):
expected_args = self._expected_args
# consolidate given args with expected defaults and check
all_args = {**expected_args, **args}
unexpected = set(all_args).difference(expected_args)
missing = {k for (k, v) in all_args.items()
if v is _empty}
if unexpected:
raise TypeError(
'unexpected keyword(s): {}'
.format(unexpected))
if missing:
raise TypeError(
'no value and no default found for sde parameter(s) {}'
.format(missing))
# return a unique dict with all args
return all_args
def _sde_args_setup(self, sde_args):
# convert to array all sde args, preserving optional
# time dependence
new_sde_args = {k: _variable_param_setup(z)
for (k, z) in sde_args.items()}
return new_sde_args
def _init_args_setup(self, init_args):
# initialize and convert to array all init args
new_init_args = {k: _const_param_setup(z)
for (k, z) in init_args.items()}
return new_init_args
def _sources_setup(self):
# initialize stochasticity sources
sources = {id:
self._get_source_setup_method(id)(
**self._get_args(self._source_args_keys[id]))
for id in self.sources}
return sources
# initialization
# --------------
def __init__(self, *, paths=1, vshape=(), dtype=None, rng=None,
steps=None, i0=0,
info=None, getinfo=True,
method='euler',
**args):
if not isinstance(self, integrator):
raise TypeError(
'cannot instantiate SDE subclass {} that is not a subclass '
'of a cooperating integrator class'
.format(type(self)))
elif hasattr(self, 'method'):
raise TypeError(
'improper method resolution order in class {}: '
'the integrator class cannot precede the the SDE class'
.format(type(self)))
# self.vshape is used by SDEs subclass
# to force self.addaxis in case vshape == ()
self.vshape = _shape_setup(vshape)
# get default args by inspection
# (stored as private attributes)
self._inspect_args_defaults()
# consolidate given args with defaults
self._args = self._consolidate_args(**args)
# preprocess sde and init args
init_args = self._init_args_setup(self._get_args(self._init_args_keys))
self._args.update(init_args)
sde_args = self._sde_args_setup(self._get_args(self._sde_args_keys))
self._args.update(sde_args)
# compute shapes
(self.vshape,
self.xshape,
self.wshape) = self.shapes(self.vshape)
# set paths and dtype
self.paths = paths
self.dtype = dtype
# set rng passed upon source instantiation
# (needed for compatibility with legacy numpy versions,
# for which sources accept only rng=None)
self._rng_asis = rng
# set rng accessed via the rng attribute (in case rng is None,
# should be the default_rng at the time of instantiation)
self._rng = _get_default_rng() if (rng is None) else rng
# setup stochasticity sources
# (this uses paths, shapes and dtype attributes)
self.sources = self._sources_setup()
self._ordered_source_ids = sorted(list(self.sources))
# optional further initializations delegated to subclasses
# (may include read or write access to _args items
# via the 'args' property)
self.more(**self._get_args(self._more_args_keys))
# further initialization by a superclass
# (should be an integrator)
super().__init__(paths=self.paths,
xshape=self.xshape, wshape=self.wshape,
dtype=self.dtype, steps=steps, i0=i0,
info=info, getinfo=getinfo,
method=method)
# public interface vs the integrator and
# paths_generator classes
# --------------------------------------
def begin(self):
"""See documentation of paths_generator.begin"""
super().begin()
iv = self.itervars
t0 = iv['sw'][0]
out_x = iv['xw'][0]
assert t0 == iv['steps_tt'][0] == iv['tt'][0]
init_args = self._get_args(self._init_args_keys)
self.init(t0, out_x, **init_args)
if self.log:
log(out_x, out=out_x)
if self.getinfo:
self.info_begin()
def next(self):
"""See documentation of paths_generator.next"""
super().next()
if self.getinfo:
self.info_next()
def store(self, i, k):
"""See documentation of paths_generator.store"""
super().store(i, k)
iv = self.itervars
t = iv['sw'][k]
x = iv['xw'][k]
out_x = iv['xx'][i]
assert iv['tt'][i] == t
self.let(t, out_x, x)
if self.getinfo:
self.info_store()
def end(self):
"""See documentation of paths_generator.end"""
super().end()
if self.getinfo:
self.info_end()
def exit(self, tt, xx):
"""See documentation paths_generator.exit"""
if self.log:
exp(xx, out=xx)
return self.result(tt, xx)
# public interface vs the integration
# algorithm of the integrator class
# -----------------------------------
def _check_sde_values(self, A):
if not isinstance(A, dict):
raise TypeError(
'invalid {} return values: a dict, not a {} object expected'
.format(self.sde, type(A))
)
if not set(A.keys()).issubset(self.sources):
raise KeyError(
'invalid {} return values: {} entries expected (one per '
'stochasticity source), not {}'
.format(self.sde, set(self.sources), set(A.keys()))
)
def A(self, t, x):
"""See documentation integrator.A"""
sde_args_eval = {
k: (z(t) if callable(z) else z)
for (k, z) in self._get_args(self._sde_args_keys).items()
}
# get and check sde values
A_ = self.sde(t, x, **sde_args_eval)
self._check_sde_values(A_)
return A_
def dZ(self, t, dt):
"""See documentation of integrator.dZ"""
sources = self.sources
# sources are evaluated in order of ascending id
# (safeguards reproduciblility of outcomes after
# seeding numpy.random)
return {id: sources[id](t, dt)
for id in self._ordered_source_ids}
# public interface vs subclasses
# ------------------------------
@property
def rng(self):
"""Read-only access to the random number generator used
to instantiate stochasticity sources.
"""
# prevent modifications of the `rng` attribute (changes would silently
# fail to propagate to sources).
return self._rng
@property
def args(self):
"""
Stores parameters passed as ``**args`` upon initialization
of the SDE. Should be used by subclass methods to access
and modify their values.
"""
return self._args
def shapes(self, vshape):
"""
Shape of the values to be computed and stored
upon integration of the SDE.
Parameters
----------
vshape : int or tuple of int
Shape of the values of the integration result,
as requested upon instantiation of ``SDE``.
Returns
-------
vshape : int or tuple of int
Confirms or overrides the given ``vshape``.
xshape : int or tuple of int
Shape of the values stored during integration
at the output time points. ``out_x`` array
passed to the ``let`` method has shape
``xshape + (paths,)``. Defaults to ``vshape``.
wshape : int or tuple of int
Shape of the working space used during integration.
``x`` values passed to the ``sde`` and ``let`` methods
have shape ``wshape + (paths,)``. Defaults to ``vshape``.
Notes
-----
``xshape`` and ``wshape`` are passed to the
parent ``paths_generator`` class.
``hull_white_SDE`` and ``heston_SDE`` classes illustrate
use cases for different values of ``vshape``, ``xshape``
and/or ``wshape``.
"""
xshape = wshape = vshape
return vshape, xshape, wshape
def source_dt(self):
"""
Setup a source of deterministic increments, to be used
as 'dt' during integration.
Returns
-------
An object ``z`` complying with the ``source`` protocol,
such that ``z(t, dt) == dt``.
"""
def dt(s, ds):
return ds
dt.paths = self.paths
dt.vshape = self.wshape
return dt
def source_dw(self,
dw=None, corr=None, rho=None):
"""Setup a source of standard Wiener process (Brownian motion)
increments, to be used as 'dw' during integration.
Parameters
----------
dw : source, or source subclass, or None
If an object complying with the ``source`` protocol,
it is returned (``corr`` and ``rho``, as well as
``self.dtype`` and ``self.rng``, are ignored).
If a source subclass, it is instantiated with the
given parameters, and returned. If None, a
new instance of ``wiener_source`` is returned, with
the given parameters.
corr, rho : see ``wiener_source`` documentation
Returns
-------
An object complying with the ``source`` protocol,
instantiating the requested stochasticity source.
The shape and paths of source values are set to
``self.paths``, ``self.wshape`` respectively.
If instantiated, ``dtype=self.dtype`` and ``rng=self.rng``
keywords are used upon instantiation.
See Also
--------
wiener_source
"""
return _source_setup(dw, wiener_source,
paths=self.paths, vshape=self.wshape,
dtype=self.dtype, rng=self._rng_asis,
corr=corr, rho=rho)
def source_dn(self,
dn=None, ptype=int, lam=1.):
"""
Setup a source of Poisson process increments,
to be used as 'dn' during integration.
Parameters
----------
dn : source, or source subclass, or None
If an object complying with the ``source`` protocol,
it is returned (``ptype`` and ``lam``, as well as
``self.rng``, are ignored).
If a source subclass, it is instantiated with the
given parameters, and returned. If None, a
new instance of ``poisson_source`` is returned, with
the given parameters.
ptype, lam : see ``poisson_source`` documentation
Returns
-------
An object complying with the ``source`` protocol,
instantiating the requested stochasticity source.
The shape and paths of source values are set to
``self.paths``, ``self.wshape`` respectively.
If instantiated, ``rng=self.rng`` keyword is used
upon instantiation.
See Also
--------
poisson_source
"""
return _source_setup(dn, poisson_source,
paths=self.paths, vshape=self.wshape,
# dtype of the poisson source is ptype
dtype=ptype, rng=self._rng_asis,
lam=lam)
def source_dj(self,
dj=None,
dn=None, ptype=int, lam=1.,
y=None):
"""
Set up a source of compound Poisson process increments
(jumps), to be used as 'dj' during integration.
Parameters
----------
dj : source, or source subclass, or None
If an object complying with the ``source`` protocol,
it is returned (``ptype``, ``lam`` and ``y``, as well as
``self.dtype`` and ``self.rng``, are ignored).
If a source subclass, it is instantiated with the
given parameters, and returned. If None, a
new instance of ``cpoisson_source`` is returned, with
the given parameters.
ptype, lam, y : see ``cpoisson_source`` documentation
Returns
-------
An object complying with the ``source`` protocol,
instantiating the requested stochasticity source.
The shape and paths of source values are set to
``self.paths``, ``self.wshape`` respectively.
If instantiated, ``dtype=self.dtype`` and ``rng=self.rng``
keywords are used upon instantiation.
See Also
--------
cpoisson_source
"""
return _source_setup(dj, cpoisson_source,
paths=self.paths, vshape=self.wshape,
dtype=self.dtype, # dtype of the source
rng=self._rng_asis,
dn=dn,
ptype=ptype, # dtype of underlying poisson source
lam=lam,
y=y)
def more(self):
"""
Further optional non array parameters,
and initializations.
Parameters
----------
more_args : zero or more keyword arguments
Further, possibly non array-like, SDE parameters, as implied
by the ``more`` method signature. Passed upon instantiation
of the ``SDE`` class, are served to the ``more`` method
and made available to other methods as items in the ``args``
attribute.
Notes
-----
The ``factors`` parameter of ``hull_white_SDE`` illustrates
a use case for the ``more`` method.
"""
pass
def init(self, t, out_x, x0=1.):
"""
Set initial conditions for SDE integration.
Parameters
----------
t : float
Time point at which initial conditions should be
imposed.
out_x : array
Array, shaped ``wshape + (paths,)``, where initial
conditions are to be stored.
init_args : zero or more arrays, as keyword arguments
Initialization parameters, as implied by the ``init`` method
signature. Passed upon instantiation of the ``SDE`` class
as array-like, these parameters are served to the ``init`` method
converted to arrays via ``np.asarray``.
Notes
-----
The default implementation has a single ``x0`` parameter,
and sets ``out_x[...] = x0``.
"""
out_x[...] = x0
def sde(self, t, x):
"""
Stochastic Differential Equation (SDE) to be integrated.
Parameters
----------
t : float
Time point at which the SDE should be evaluated.
x : array
Values that the stochastic process takes at time ``t``.
sde_args : zero or more arrays, as keyword arguments
SDE parameters, as implied by the
``sde`` method signature. Passed upon
instantiation of the ``SDE`` class as possibly time-dependent
array-like, these parameters are served to the ``sde`` method
once evaluated at ``t`` and converted to arrays via ``np.asarray``.
Returns
-------
sde_terms : dict of arrays
Contains, for each differential stated in the ``source``
attribute, the value of the corresponding coefficient
in the represented SDE.
Notes
-----
``x`` should be treated as read-only.
"""
return {'dt': x + np.nan}
def let(self, t, out_x, x):
"""
Store the value of the integrated process at
time point ``t`` belonging to the requested output timeline.
Parameters
----------
t : float
Time point to which the integration result ``x`` refers.
out_x : array
Array, shaped ``xshape + (paths,)``, where the result
``x`` is to be stored.
x : array
Integration result at time ``t``, shaped
``wshape + (paths,)``
Notes
-----
The default implementation sets ``out_x[...] = x``.
In case ``xshape != wshape``, this method should operate as needed
in order to store in ``out_x`` a value broadcastable to its shape
(e.g. it might store in ``out_x`` only some of the components of
``x``).
``x`` should be treated as read-only.
"""
out_x[...] = x
def result(self, tt, xx):
"""
Compute the integration output.
Parameters
----------
tt : array
Output integration timeline.
xx : array
Integration result, shaped ``tt.shape + xshape + (paths,)``.
Returns
-------
result
Final result, returned to the user.
Notes
-----
The default implementation returns ``sdepy.process(t=tt, x=xx)``.
In case ``vshape != xshape``, this method should operate as needed
in order to return a process with values shaped as ``vshape``
(e.g. it might return a function of the components of ``xx``).
"""
return process(t=tt, x=xx)
def info_begin(self):
"""
Optional diagnostic information logging function,
called before the integration begins.
"""
pass
def info_next(self):
"""
Optional diagnostic information logging function,
called after each integration step.
"""
pass
def info_store(self):
"""
Optional diagnostic information logging function,
called after each invocation of the let method.
"""
pass
def info_end(self):
"""
Optional diagnostic information logging function,
called after the integration has been completed.
"""
pass
class SDEs(SDE):
"""
Class representation of a user defined system of Stochastic Differential
Equations (SDEs), intended for subclassing.
The parent ``SDE`` class represents a single SDE, scalar
or multidimensional: by an appropriate choice of the ``vshape`` parameter,
and composition of equation values, it suffices to describe
any system of SDEs.
Its ``SDEs`` subclass is added for convenience of representation: it allows
to state each equation separately and to retrieve separate processes
as a result. The number of equations must be stated as the ``q`` attribute.
The ``vshape`` parameter is taken as the common shape of values in each
equation in the system.
A minimal definition of a lognormal process ``x`` with stochastic
volatility ``y`` is as follows::
>>> from sdepy import SDEs, integrator
>>> class my_process(SDEs, integrator):
... q = 2
... def sde(self, t, x, y, mu=0., sigma=1., xi=1.):
... return ({'dt': mu*x, 'dw': y*x},
... {'dt': 0, 'dw': xi*y})
>>> P = my_process(x0=(1., 2.), xi=0.5, vshape=5,
... paths=100*1000, steps=100, )
>>> x, y = P(timeline=(0., 0.5, 1.))
>>> x.shape, y.shape
((3, 5, 100000), (3, 5, 100000))
See Also
--------
SDE
integrator
paths_generator
Notes
-----
By default, the stochasticity sources of each component equation
are realized independently, even if represented in the ``sde`` output
by the same key (``'dw'`` in the example above).
The way stochasticity sources are instantiated and dispatched to
each equation, and how correlations of the Wiener source are set
via the ``corr`` parameter, depend on the value of the ``addaxis``
attribute:
* If ``True``, source values have shape ``vshape + (q,)``,
and the ``[kk, i]`` component of source values
is dispatched to the ``kk`` component of equation ``i``
(``kk`` is a multiindex spanning shape ``vshape``).
If given, ``corr`` must be of shape ``(q, q)`` and correlates
corresponding components across equations.
* If ``addaxis`` is ``False`` (default) and ``N`` is the size
of the last axis of ``vshape``, the values of the sources have shape
``vshape[:-1] + (N*q,)``, and the ``[kk, i*N + h]`` component
of the source values is dispatched to the ``[kk, h]`` component
of equation ``i`` (``kk`` is a multiindex spanning
shape ``vshape[:-1]``, and ``h`` is in ``range(N)``).
If given, ``corr`` must be of shape ``(N*q, N*q)``, and correlates
all last components of all equations to each other.
After instantiation, stochasticity sources and correlation matrices
may be inspected as follows::
>>> P = my_process(vshape=(), rho=0.5)
>>> P.sources['dw'].vshape
(2,)
>>> P.sources['dw'].corr.shape
(2, 2)
>>> P.sources['dw'].corr[0, 1]
0.5
Attributes
----------
q : int
Number of equations.
addaxis : bool
Affects the internal representation of the equations: if ``True``,
a last axis of size ``q`` is added to ``vshape``, if ``False``,
components are stacked onto the last axis of ``vshape``.
Defaults to ``False``. It is forced to ``True`` if the process
components have scalar values.
Methods
-------
pack
unpack
"""
# public attributes
# -----------------
q = 1
addaxis = False
# private methods and attributes
# ------------------------------
def _inspect_args_defaults(self):
if self.q < 1:
raise ValueError(
'the number of equations q should be positive, but '
'{} was given'.format(self.q))
if self.vshape == ():
# force adding an axis for equations
self.addaxis = True
super()._inspect_args_defaults(sde_nvars=self.q)
# public interface vs the integration
# algorithm of the integrator class
# -----------------------------------
def _check_sde_values(self, As):
if not isinstance(As, (list, tuple)):
raise TypeError(
'invalid {} return values: a list or tuple of {} dict '
'(one per equation) expected, not a {} object'
.format(self.sde, self.q, type(As))
)
if len(As) != self.q:
raise ValueError(
'invalid {} return values: {} equations expected, '
'not {}'.format(self.sde, self.q, len(As)))
for a in As:
super()._check_sde_values(a)
def A(self, t, X):
"""See documentation of integrator.A"""
sde_args_eval = {
k: (z(t) if callable(z) else z)
for (k, z) in self._get_args(self._sde_args_keys).items()
}
# unpack X, as feeded by integrator.next, in a list
# of arrays (one per equation)
xs = self.unpack(X)
# get and check sde values
As = self.sde(t, *xs, **sde_args_eval)
self._check_sde_values(As)
A_ids = set()
for a in As:
A_ids.update(a.keys())
A = {id: self.pack(tuple(a.get(id, 0) for a in As))
for id in A_ids}
return A
# public interface vs subclasses
# ------------------------------
def unpack(self, X):
"""Unpacks the given array into multiple arrays
(one per equation).
Parameters
----------
X : array
Array with a last dimension enumerating paths, and a second
last dimension to be unpacked according to the ``addaxis``
attribute setting.
Returns
-------
x, y, ... : list of arrays
List of ``self.q`` arrays, unpacking the given ``X``.
"""
q = self.q
if self.addaxis:
xs = tuple(X[..., k, :] for k in range(q))
else:
d = self.vshape[-1]
xs = tuple(X[..., k*d:(k+1)*d, :] for k in range(q))
return xs
def pack(self, xs):
"""Packs the given arrays (one per equation) into a single array.
Parameters
----------
xs : list of arrays
List of ``self.q`` arrays to be packed according to the ``addaxis``
attribute setting.
Returns
-------
X : array
Array packing the given ``xs`` along its second-last dimension
(the last dimension enumerates paths).
"""
target_shape = self.vshape + (self.paths,)
if self.addaxis:
i = np.index_exp[..., np.newaxis, :]
else:
i = np.index_exp[...]
X = np.concatenate(tuple(
np.broadcast_to(x, target_shape)[i]
for x in xs
), axis=-2)
return X
def shapes(self, vshape):
"""See documentation of SDE.shapes"""
q = self.q
if self.addaxis:
xshape = wshape = vshape + (q,)
else:
xshape = wshape = vshape[:-1] + (vshape[-1]*q,)
return vshape, xshape, wshape
def init(self, t, out_X, x0=1.):
"""See documentation of SDE.init"""
x0s = x0
# in init's calling signature, x0 is kept for compatibility with SDE;
# should be a list or tuple or array of the q initial conditions
if x0s.shape == (): # scalar values are broadcasted to all equations
x0s = (x0s,)*self.q
X0 = self.pack(x0s)
super().init(t, out_X, X0)
def sde(self, t, x):
"""Stochastic Differential Equations (SDEs) to be integrated.
Parameters
----------
t : float
Time point at which the SDE should be evaluated.
x, y, ... : arrays
Values that each equation variable takes at time ``t``.
There should be as many parameters as the number of
equations stated in ``self.q``.
sde_args : zero or more arrays, as keyword arguments
See documentation of ``SDE.sde``.
Returns
-------
sde_terms : list or tuple of dict of arrays
A list or tuple of dictionaries, one per equation.
See documentation of ``SDE.sde``.
Notes
-----
``x, y, ...`` should be treated as read-only.
"""
return ({'dt': x + np.nan},)
def result(self, tt, XX):
"""See documentation of SDE.result"""
if self.log:
exp(XX, out=XX)
xxs = self.unpack(XX)
return tuple(process(t=tt, x=xx) for xx in xxs)
# -----------------------
# integration interface:
# the integrate decorator
# -----------------------
def _SDE_from_function(f, q=None, sources=None, log=False, addaxis=False):
if q is not None and sources is not None:
neq = q
ids = set(sources)
SDE_class = SDE if neq == 0 else SDEs
else:
# perform a test evaluation of f
try:
try:
test_val = f()
except Exception:
test_val = f(np.array(1.), np.array(1.))
except Exception:
raise TypeError(
'test evaluation of {} failed'
.format(f))
# infer neq, ids and SDE_class from test_val
if isinstance(test_val, (tuple, list)):
neq = len(test_val)
if neq == 0:
raise ValueError('non empty list or tuple expected')
SDE_class = SDEs
else:
neq = 0
SDE_class = SDE
test_val = (test_val,)
ids = set()
for z in test_val:
ids.update(z.keys())
# consistency check
if ((q is not None and neq != q) or
(sources is not None and set(sources) != ids)):
raise TypeError(
'test evaluation of {} inconsistent with given '
"'q' or 'sources'".format(f))
# avoid namespace conflicts inside SDE_wrapper
log_flag = log
addaxis_flag = addaxis
class SDE_wrapper(SDE_class):
q = neq
sources = ids
log = log_flag
addaxis = addaxis_flag
sde = staticmethod(f)
return SDE_wrapper
def integrate(sde=None, *, q=None, sources=None, log=False, addaxis=False):
"""Decorator for Ito Stochastic Differential Equation (SDE)
integration.
Decorates a function representing the SDE or SDEs into the corresponding
``sdepy`` integrator.
Parameters
----------
sde : function
Function to be wrapped. Its signature and values should be
as expected for the ``sde`` method of the ``sdepy.SDE`` or
``sdepy.SDEs`` classes.
q : int
Number of equations. If ``None``, attempts a test evaluation
of ``sde`` to find out. ``q=0`` indicates a single equation.
sources : set
Stochasticity sources used in the equation. If ``None``,
attempts a test evaluation of ``sde`` to find out.
log : bool
Sets the ``log`` attribute for the wrapping class.
addaxis : bool
Sets the ``addaxis`` attribute for the wrapping class.
Returns
-------
A subclass of ``sdepy.SDE`` or ``sdepy.SDEs`` as appropriate,
and of ``sdepy.integrator``, with the given ``sde``
cast as its ``sde`` method.
Notes
-----
To prevent a test evaluation of ``sde``, explicitly provide
the intended ``q`` and ``sources`` as keyword arguments to ``integrate()``.
The test evaluation is attempted as ``sde()`` and, upon failure,
again as ``sde(1., 1.)``.
Examples
--------
>>> from sdepy import integrate
>>> @integrate
... def my_process(t, x, theta=1., k=1., sigma=1.):
... return {'dt': k*(theta - x), 'dw': sigma}
>>> P = my_process(x0=1, sigma=0.5, paths=100*1000, steps=100)
>>> x = P(timeline=(0., 0.5, 1.))
>>> x.shape
(3, 100000)
"""
if sde is None:
def decorator(sde):
return integrate(sde, q=q, sources=sources,
log=log, addaxis=addaxis)
return decorator
else:
SDE_class = _SDE_from_function(sde, q=q, sources=sources,
log=log, addaxis=addaxis)
class sde_integrator(SDE_class, integrator):
pass
return sde_integrator
#############################################
# Process generators withoud SDE integration
#############################################
# THIS CODE HAS BEEN REMOVED AND NOT KEPT UP TO DATE
# all the point was to gain speed, and as of april 2018
# the cumsum operation on which const_wiener_process and
# const_lognorm_process rely takes longer than step by step
# integration with lognorm_process and wiener_process
# (tested on 1000 time steps and 10000 paths)
#
# the code is frozen as a string in case one might
# consider re-inclusion in the future
'''
class const_wiener_process:
"""
Wiener process (Brownian motion), with time-independent parameters.
"""
def __init__(self, paths=1, vshape=(), dtype=None,
dw=None, corr=None, rho=None,
x0=0., mu=0., sigma=1.
):
self.paths = paths
self.vshape = vshape = _shape_setup(vshape)
self.xshape = self.wshape = vshape
self.dtype = dtype
args = {'x0': x0, 'mu': mu, 'sigma': sigma}
args = {k: _const_param_setup(z) for (k, z) in args.items()}
self._args = args
# the setup of corr, rho is delegated to 'wiener'
self.sources = {'dt': lambda t, dt: dt,
'dw': _dw_source_setup(
dw, paths, vshape, dtype,
corr, rho)}
@property
def params(self):
return self._args.copy()
def __call__(self, t):
paths, vshape, dtype = self.paths, self.vshape, self.dtype
# timeline and time increments setup
t = np.asarray(t)
if t.shape != (t.size,):
raise ValueError(
'the process timeline should be a '
'one-dimensional array, not an array of shape {}'
.format(t.shape))
dt = np.concatenate((0*t[:1], np.diff(t))) # dt[0] == 0
shifted_t = np.concatenate((t[:1], t[:-1]))
tx = t.reshape((-1,) + (1,)*len(vshape) + (1,)) \
# initial condition and parameters setup
x0, mu, sigma = [self._args[k]
for k in ('x0', 'mu', 'sigma')]
# generate process
dw = self.sources['dw'](shifted_t, dt)
x = np.empty(t.shape + vshape + (paths,), dtype=dtype)
x[...] = x0 + mu * (tx - tx[0]) + sigma * dw.cumsum(axis=0)
return process(t, x=x)
class const_lognorm_process(const_wiener_process):
"""
Lognormal process, with time-independent parameters.
"""
def __init__(self, paths=1, vshape=(), dtype=None,
dw=None, corr=None, rho=None,
x0=1., mu=0., sigma=1.
):
super().__init__(paths=paths, vshape=vshape, dtype=dtype,
dw=dw, corr=corr, rho=rho,
x0=x0, mu=mu, sigma=sigma)
def __call__(self, t):
x0, mu, sigma = [self._args[k] for k in ('x0', 'mu', 'sigma')]
wp = const_wiener_process(
paths=self.paths, vshape=self.vshape, dtype=self.dtype,
dw=self.sources['dw'],
x0=log(x0), mu=mu - sigma*sigma/2, sigma=sigma)(t)
exp(wp, out=wp)
return wp
'''
##########################################
# Process generators with SDE integration
##########################################
class wiener_SDE(SDE):
"""
SDE for a Wiener process (Brownian motion) with drift.
See Also
--------
wiener_process
"""
# set x0 default value to 0.
def init(self, s, out_x, x0=0.):
super().init(s, out_x, x0)
def sde(self, t, x, mu=0., sigma=1.):
return {'dt': mu, 'dw': sigma}
class wiener_process(wiener_SDE, integrator):
"""
wiener_process(paths=1, vshape=(), dtype=None, rng=None,
steps=None, i0=0, info=None, getinfo=True, method='euler',
x0=0., mu=0., sigma=1., dw=None, corr=None, rho=None)
Wiener process (Brownian motion) with drift.
Generates a process ``x(t)`` that solves the following SDE::
dx(t) = mu(t)*dt + sigma(t)*dw(t, dt)
where ``dw(t, dt)`` are standard Wiener process increments with
correlation matrix specified by ``corr(t)`` or ``rho(t)``.
``x0``, SDE parameters and ``dw(t, dt)`` should broadcast to
``vshape + (paths,)``.
Parameters
----------
paths, vshape, dtype, rng, steps, i0, info, getinfo, method
See ``SDE`` class documentation.
x0 : array-like
Initial condition.
mu, sigma : array-like, or callable
SDE parameters.
dw, corr, rho
Specification of stochasticity source of Wiener process increments.
See ``SDE.source_dw`` documentation.
Returns
-------
x : process
Once instantiated as ``p``, ``p(timeline)`` performs the integration
along the given timeline, based on parameters of instantiation,
and returns the resulting process.
See also
--------
SDE
SDE.source_dw
wiener_source
wiener_SDE
"""
pass
class lognorm_SDE(SDE):
"""
SDE for a lognormal process with drift.
See Also
--------
lognorm_process
"""
log = True
def sde(self, t, x, mu=0., sigma=1.):
return {'dt': mu - sigma*sigma/2, 'dw': sigma}
class lognorm_process(lognorm_SDE, integrator):
"""
lognorm_process(paths=1, vshape=(), dtype=None, rng=None,
steps=None, i0=0, info=None, getinfo=True, method='euler',
x0=1., mu=0., sigma=1., dw=None, corr=None, rho=None)
Lognormal process.
Generates a process ``x(t)`` that solves the following SDE::
dx(t) = mu(t)*x(t)*dt + sigma(t)*x(t)*dw(t, dt)
where ``dw(t, dt)`` are standard Wiener process increments with
correlation matrix specified by ``corr(t)`` or ``rho(t)``.
``x0``, SDE parameters and ``dw(t, dt)`` should broadcast to
``vshape + (paths,)``. ``x0`` should be positive.
Parameters
----------
paths, vshape, dtype, rng, steps, i0, info, getinfo, method
See ``SDE`` class documentation.
x0 : array-like
Initial condition.
mu, sigma : array-like, or callable
SDE parameters.
dw, corr, rho
Specification of stochasticity source of Wiener process increments.
See ``SDE.source_dw`` documentation.
Returns
-------
x : process
Once instantiated as ``p``, ``p(timeline)`` performs the integration
along the given timeline, based on parameters of instantiation,
and returns the resulting process.
See also
--------
SDE
SDE.source_dw
wiener_source
wiener_SDE
Notes
-----
``x(t)`` is obtained via Euler-Maruyama numerical integration of the
following equivalent SDE for ``a(t) = log(x(t))``::
da(t) = (mu(t) - sigma(t)**2/2)*dt + sigma(t)*dw(t, dt)
"""
class ornstein_uhlenbeck_SDE(SDE):
"""
SDE for an Ornstein-Uhlenbeck process.
See Also
--------
ornstein_uhlenbeck_process
"""
# set x0 default value to 0.
def init(self, s, out_x, x0=0.):
super().init(s, out_x, x0)
def sde(self, s, x, theta=0., k=1., sigma=1.):
return {'dt': k*(theta - x), 'dw': sigma}
class ornstein_uhlenbeck_process(ornstein_uhlenbeck_SDE, integrator):
"""
ornstein_uhlenbeck_process(paths=1, vshape=(), dtype=None, rng=None,
steps=None, i0=0, info=None, getinfo=True, method='euler',
x0=0., theta=0., k=1., sigma=1., dw=None, corr=None, rho=None)
Ornstein-Uhlenbeck process (mean-reverting Brownian motion).
Generates a process ``x(t)`` that solves the following SDE::
dx(t) = k(t)*(theta(t) - x(t))*dt + sigma(t)*dw(t, dt)
where ``dw(t, dt)`` are standard Wiener process increments with
correlation matrix specified by ``corr(t)`` or ``rho(t)``.
``x0``, SDE parameters and ``dw(t, dt)`` should broadcast to
``vshape + (paths,)``.
Parameters
----------
paths, vshape, dtype, rng, steps, i0, info, getinfo, method
See ``SDE`` class documentation.
x0 : array-like
Initial condition.
theta, k, sigma : array-like, or callable
SDE parameters.
dw, corr, rho
Specification of stochasticity source of Wiener process increments.
See ``SDE.source_dw`` documentation.
Returns
-------
x : process
Once instantiated as ``p``, ``p(timeline)`` performs the integration
along the given timeline, based on parameters of instantiation,
and returns the resulting process.
See also
--------
SDE
SDE.source_dw
wiener_source
ornstein_uhlenbeck_SDE
"""
class hull_white_SDE(SDE):
"""
SDE for an F-factors Hull White process.
See Also
--------
hull_white_process
"""
# set x0 default value to 0.
def init(self, s, out_x, x0=0.):
super().init(s, out_x, x0)
def more(self, factors=1):
pass
def shapes(self, vshape):
xshape = vshape
wshape = vshape + (self.args['factors'],)
return vshape, xshape, wshape
def sde(self, s, x, theta=0., k=1., sigma=1.):
return {'dt': k*(theta - x), 'dw': sigma}
def let(self, s, out_x, x):
out_x[...] = x.sum(axis=-2)
class hull_white_process(hull_white_SDE, integrator):
"""
hull_white_process(paths=1, vshape=(), dtype=None, rng=None,
steps=None, i0=0, info=None, getinfo=True, method='euler',
factors=1, x0=0., theta=0., k=1., sigma=1., dw=None, corr=None, rho=None)
F-factors Hull-White process (sum of F correlated mean-reverting Brownian
motions).
Generates a process x(t) that solves the following SDE::
x(t) = y_1(t) + ... + y_F(t)
dy_i(t) = k_i(t)*(theta_i(t) - y_i(t))*dt +
+ sigma_i(t)*dw_i(t, dt)
where ``dw_i(t, dt)`` are standard Wiener process increments with
correlations ``dw_i(t, dt)*dw_j(t, dt) = corr(t)[i, j]``.
``x0``, SDE parameters and ``dw(t, dt)`` should broadcast to
``vshape + (factors, paths)``.
Parameters
----------
paths, vshape, dtype, rng, steps, i0, info, getinfo, method
See ``SDE`` class documentation.
x0 : array-like
Initial condition.
theta, k, sigma : array-like, or callable
SDE parameters.
dw, corr, rho
Specification of stochasticity source of Wiener process increments.
See ``SDE.source_dw`` documentation.
See also
--------
SDE
SDE.source_dw
wiener_source
hull_white_SDE
ornstein_uhlenbeck_process
"""
pass
class hull_white_1factor_process(ornstein_uhlenbeck_process):
"""
hull_white_1factor_process(paths=1, vshape=(), dtype=None, rng=None,
steps=None, i0=0, info=None, getinfo=True, method='euler',
x0=0., theta=0., k=1., sigma=1., dw=None, corr=None, rho=None)
1-factor Hull-White process (F=1 Hull-White process with F-index
collapsed to a scalar). See ``hull_white_process`` class documentation.
See Also
--------
hull_white_process
ornstein_uhlenbeck_process
Notes
-----
Class added for naming convenience. Differs from a ``hull_white_process``
with ``factors=1`` in that the last index of the process parameters has not
been reserved to enumerate factors, and no ``factors`` parameter is
present. Synonymous with ``ornstein_uhlenbeck_process``.
"""
pass
class cox_ingersoll_ross_SDE(SDE):
"""
SDE for a Cox-Ingersoll-Ross mean reverting process.
See Also
--------
cox_ingersoll_ross_process
"""
def sde(self, s, x, theta=1., k=1., xi=1.):
x_plus = np.maximum(x, 0.)
return {'dt': k*(theta - x_plus),
'dw': xi * sqrt(x_plus)}
class cox_ingersoll_ross_process(cox_ingersoll_ross_SDE, integrator):
"""
cox_ingersoll_ross_process(paths=1, vshape=(), dtype=None, rng=None,
steps=None, i0=0, info=None, getinfo=True, method='euler',
x0=1., theta=1., k=1., xi=1., dw=None, corr=None, rho=None)
Cox-Ingersoll-Ross mean reverting process.
Generates a process ``x(t)`` that solves the following SDE::
dx(t) = k(t)*(theta(t) - x(t))*dt + xi(t)*sqrt(x(t))*dw(t, dt)
where ``dw(t, dt)`` are standard Wiener process increments with
correlation matrix specified by ``corr(t)`` or ``rho(t)``.
``x0``, SDE parameters and ``dw(t, dt)`` should broadcast to
``vshape + (paths,)``. ``x0, theta, k`` should be positive.
Parameters
----------
paths, vshape, dtype, rng, steps, i0, info, getinfo, method
See ``SDE`` class documentation.
x0 : array-like
Initial condition.
theta, k, xi : array-like, or callable
SDE parameters.
dw, corr, rho
Specification of stochasticity source of Wiener process increments.
See ``SDE.source_dw`` documentation.
Returns
-------
x : process
Once instantiated as ``p``, ``p(timeline)`` performs the integration
along the given timeline, based on parameters of instantiation,
and returns the resulting process.
See also
--------
SDE
SDE.source_dw
wiener_source
cox_ingersoll_ross_SDE
"""
pass
class full_heston_SDE(SDEs):
"""
SDE for a Heston stochastic volatility process.
See Also
--------
full_heston_process
heston_process
"""
q = 2
addaxis = False
log = False
def init(self, s, out_X, x0=1., y0=1.):
out_x, out_y = self.unpack(out_X)
out_x[...] = log(x0)
out_y[...] = y0
def info_begin(self):
self.info['negative_y_count'] = np.zeros(
self.vshape + (self.paths,), dtype=int)
def sde(self, t, x, y, mu=0., sigma=1.,
theta=1., k=1., xi=1.):
y_plus = | np.maximum(y, 0.) | numpy.maximum |
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright 1999-2020 Alibaba Group Holding Ltd.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import numpy as np
import scipy.sparse as sps
import pandas as pd
from mars import dataframe as md
from mars import tensor as mt
from mars.core import get_tiled
from mars.tensor.base import copyto, transpose, moveaxis, broadcast_to, broadcast_arrays, where, \
expand_dims, rollaxis, atleast_1d, atleast_2d, atleast_3d, argwhere, array_split, split, \
hsplit, vsplit, dsplit, roll, squeeze, diff, ediff1d, flip, flipud, fliplr, repeat, tile, \
isin, searchsorted, unique, sort, argsort, partition, argpartition, topk, argtopk, \
trapz, shape, to_gpu, to_cpu, swapaxes
from mars.tensor.datasource import tensor, ones, zeros, arange
from mars.tests.core import require_cupy, TestBase
class Test(TestBase):
def setUp(self):
self.ctx, self.executor = self._create_test_context()
def testRechunkExecution(self):
raw = np.random.RandomState(0).random((11, 8))
arr = tensor(raw, chunk_size=3)
arr2 = arr.rechunk(4)
res = self.executor.execute_tensor(arr2)
self.assertTrue(np.array_equal(res[0], raw[:4, :4]))
self.assertTrue(np.array_equal(res[1], raw[:4, 4:]))
self.assertTrue(np.array_equal(res[2], raw[4:8, :4]))
self.assertTrue(np.array_equal(res[3], raw[4:8, 4:]))
self.assertTrue(np.array_equal(res[4], raw[8:, :4]))
self.assertTrue(np.array_equal(res[5], raw[8:, 4:]))
def testCopytoExecution(self):
a = ones((2, 3), chunk_size=1)
b = tensor([3, -1, 3], chunk_size=2)
copyto(a, b, where=b > 1)
res = self.executor.execute_tensor(a, concat=True)[0]
expected = np.array([[3, 1, 3], [3, 1, 3]])
np.testing.assert_equal(res, expected)
a = ones((2, 3), chunk_size=1)
b = tensor(np.asfortranarray(np.random.rand(2, 3)), chunk_size=2)
copyto(b, a)
res = self.executor.execute_tensor(b, concat=True)[0]
expected = np.asfortranarray(np.ones((2, 3)))
np.testing.assert_array_equal(res, expected)
self.assertTrue(res.flags['F_CONTIGUOUS'])
self.assertFalse(res.flags['C_CONTIGUOUS'])
def testAstypeExecution(self):
raw = np.random.random((10, 5))
arr = tensor(raw, chunk_size=3)
arr2 = arr.astype('i8')
res = self.executor.execute_tensor(arr2, concat=True)
np.testing.assert_array_equal(res[0], raw.astype('i8'))
raw = sps.random(10, 5, density=.2)
arr = tensor(raw, chunk_size=3)
arr2 = arr.astype('i8')
res = self.executor.execute_tensor(arr2, concat=True)
self.assertTrue(np.array_equal(res[0].toarray(), raw.astype('i8').toarray()))
raw = np.asfortranarray(np.random.random((10, 5)))
arr = tensor(raw, chunk_size=3)
arr2 = arr.astype('i8', order='C')
res = self.executor.execute_tensor(arr2, concat=True)[0]
np.testing.assert_array_equal(res, raw.astype('i8'))
self.assertTrue(res.flags['C_CONTIGUOUS'])
self.assertFalse(res.flags['F_CONTIGUOUS'])
def testTransposeExecution(self):
raw = np.random.random((11, 8, 5))
arr = tensor(raw, chunk_size=3)
arr2 = transpose(arr)
res = self.executor.execute_tensor(arr2, concat=True)
np.testing.assert_array_equal(res[0], raw.T)
arr3 = transpose(arr, axes=(-2, -1, -3))
res = self.executor.execute_tensor(arr3, concat=True)
np.testing.assert_array_equal(res[0], raw.transpose(1, 2, 0))
raw = sps.random(11, 8)
arr = tensor(raw, chunk_size=3)
arr2 = transpose(arr)
self.assertTrue(arr2.issparse())
res = self.executor.execute_tensor(arr2, concat=True)
np.testing.assert_array_equal(res[0].toarray(), raw.T.toarray())
# test order
raw = np.asfortranarray(np.random.random((11, 8, 5)))
arr = tensor(raw, chunk_size=3)
arr2 = transpose(arr)
res = self.executor.execute_tensor(arr2, concat=True)[0]
expected = np.transpose(raw).copy(order='A')
np.testing.assert_array_equal(res, expected)
self.assertEqual(res.flags['C_CONTIGUOUS'], expected.flags['C_CONTIGUOUS'])
self.assertEqual(res.flags['F_CONTIGUOUS'], expected.flags['F_CONTIGUOUS'])
arr = tensor(raw, chunk_size=3)
arr2 = transpose(arr, (1, 2, 0))
res = self.executor.execute_tensor(arr2, concat=True)[0]
expected = np.transpose(raw, (1, 2, 0)).copy(order='A')
np.testing.assert_array_equal(res, expected)
self.assertEqual(res.flags['C_CONTIGUOUS'], expected.flags['C_CONTIGUOUS'])
self.assertEqual(res.flags['F_CONTIGUOUS'], expected.flags['F_CONTIGUOUS'])
df = md.DataFrame(mt.random.rand(10, 5, chunk_size=5))
df = df[df[0] < 1]
# generate tensor with unknown shape
t = df.to_tensor()
t2 = transpose(t)
res = self.executor.execute_tensor(t2, concat=True)[0]
self.assertEqual(res.shape, (5, 10))
def testSwapaxesExecution(self):
raw = np.random.random((11, 8, 5))
arr = swapaxes(raw, 2, 0)
res = self.executor.execute_tensor(arr, concat=True)
np.testing.assert_array_equal(res[0], raw.swapaxes(2, 0))
raw = np.random.random((11, 8, 5))
arr = tensor(raw, chunk_size=3)
arr2 = arr.swapaxes(2, 0)
res = self.executor.execute_tensor(arr2, concat=True)
np.testing.assert_array_equal(res[0], raw.swapaxes(2, 0))
raw = sps.random(11, 8, density=.2)
arr = tensor(raw, chunk_size=3)
arr2 = arr.swapaxes(1, 0)
res = self.executor.execute_tensor(arr2, concat=True)
np.testing.assert_array_equal(res[0].toarray(), raw.toarray().swapaxes(1, 0))
# test order
raw = np.asfortranarray(np.random.rand(11, 8, 5))
arr = tensor(raw, chunk_size=3)
arr2 = arr.swapaxes(2, 0)
res = self.executor.execute_tensor(arr2, concat=True)[0]
expected = raw.swapaxes(2, 0).copy(order='A')
np.testing.assert_array_equal(res, expected)
self.assertEqual(res.flags['C_CONTIGUOUS'], expected.flags['C_CONTIGUOUS'])
self.assertEqual(res.flags['F_CONTIGUOUS'], expected.flags['F_CONTIGUOUS'])
arr = tensor(raw, chunk_size=3)
arr2 = arr.swapaxes(0, 2)
res = self.executor.execute_tensor(arr2, concat=True)[0]
expected = raw.swapaxes(0, 2).copy(order='A')
np.testing.assert_array_equal(res, expected)
self.assertEqual(res.flags['C_CONTIGUOUS'], expected.flags['C_CONTIGUOUS'])
self.assertEqual(res.flags['F_CONTIGUOUS'], expected.flags['F_CONTIGUOUS'])
arr = tensor(raw, chunk_size=3)
arr2 = arr.swapaxes(1, 0)
res = self.executor.execute_tensor(arr2, concat=True)[0]
expected = raw.swapaxes(1, 0).copy(order='A')
np.testing.assert_array_equal(res, expected)
self.assertEqual(res.flags['C_CONTIGUOUS'], expected.flags['C_CONTIGUOUS'])
self.assertEqual(res.flags['F_CONTIGUOUS'], expected.flags['F_CONTIGUOUS'])
def testMoveaxisExecution(self):
x = zeros((3, 4, 5), chunk_size=2)
t = moveaxis(x, 0, -1)
res = self.executor.execute_tensor(t, concat=True)[0]
self.assertEqual(res.shape, (4, 5, 3))
t = moveaxis(x, -1, 0)
res = self.executor.execute_tensor(t, concat=True)[0]
self.assertEqual(res.shape, (5, 3, 4))
t = moveaxis(x, [0, 1], [-1, -2])
res = self.executor.execute_tensor(t, concat=True)[0]
self.assertEqual(res.shape, (5, 4, 3))
t = moveaxis(x, [0, 1, 2], [-1, -2, -3])
res = self.executor.execute_tensor(t, concat=True)[0]
self.assertEqual(res.shape, (5, 4, 3))
def testBroadcastToExecution(self):
raw = np.random.random((10, 5, 1))
arr = tensor(raw, chunk_size=2)
arr2 = broadcast_to(arr, (5, 10, 5, 6))
res = self.executor.execute_tensor(arr2, concat=True)[0]
np.testing.assert_array_equal(res, np.broadcast_to(raw, (5, 10, 5, 6)))
# test chunk with unknown shape
arr1 = mt.random.rand(3, 4, chunk_size=2)
arr2 = mt.random.permutation(arr1)
arr3 = broadcast_to(arr2, (2, 3, 4))
res = self.executor.execute_tensor(arr3, concat=True)[0]
self.assertEqual(res.shape, (2, 3, 4))
def testBroadcastArraysExecutions(self):
x_data = [[1, 2, 3]]
x = tensor(x_data, chunk_size=1)
y_data = [[1], [2], [3]]
y = tensor(y_data, chunk_size=2)
a = broadcast_arrays(x, y)
res = [self.executor.execute_tensor(arr, concat=True)[0] for arr in a]
expected = np.broadcast_arrays(x_data, y_data)
for r, e in zip(res, expected):
np.testing.assert_equal(r, e)
def testWhereExecution(self):
raw_cond = np.random.randint(0, 2, size=(4, 4), dtype='?')
raw_x = np.random.rand(4, 1)
raw_y = np.random.rand(4, 4)
cond, x, y = tensor(raw_cond, chunk_size=2), tensor(raw_x, chunk_size=2), tensor(raw_y, chunk_size=2)
arr = where(cond, x, y)
res = self.executor.execute_tensor(arr, concat=True)
self.assertTrue(np.array_equal(res[0], np.where(raw_cond, raw_x, raw_y)))
raw_cond = sps.csr_matrix(np.random.randint(0, 2, size=(4, 4), dtype='?'))
raw_x = sps.random(4, 1, density=.1)
raw_y = sps.random(4, 4, density=.1)
cond, x, y = tensor(raw_cond, chunk_size=2), tensor(raw_x, chunk_size=2), tensor(raw_y, chunk_size=2)
arr = where(cond, x, y)
res = self.executor.execute_tensor(arr, concat=True)[0]
self.assertTrue(np.array_equal(res.toarray(),
np.where(raw_cond.toarray(), raw_x.toarray(), raw_y.toarray())))
# GH 2009
raw_x = np.arange(9.).reshape(3, 3)
x = arange(9.).reshape(3, 3)
arr = where(x < 5, 2, -1)
res = self.executor.execute_tensor(arr, concat=True)[0]
np.testing.assert_array_equal(res, np.where(raw_x < 5, 2, -1))
def testReshapeExecution(self):
raw_data = np.random.rand(10, 20, 30)
x = tensor(raw_data, chunk_size=6)
y = x.reshape(-1, 30)
res = self.executor.execute_tensor(y, concat=True)
np.testing.assert_array_equal(res[0], raw_data.reshape(-1, 30))
y2 = x.reshape(10, -1)
res = self.executor.execute_tensor(y2, concat=True)
np.testing.assert_array_equal(res[0], raw_data.reshape(10, -1))
y3 = x.reshape(-1)
res = self.executor.execute_tensor(y3, concat=True)
np.testing.assert_array_equal(res[0], raw_data.reshape(-1))
y4 = x.ravel()
res = self.executor.execute_tensor(y4, concat=True)
np.testing.assert_array_equal(res[0], raw_data.ravel())
raw_data = np.random.rand(30, 100, 20)
x = tensor(raw_data, chunk_size=6)
y = x.reshape(-1, 20, 5, 5, 4)
res = self.executor.execute_tensor(y, concat=True)
np.testing.assert_array_equal(res[0], raw_data.reshape(-1, 20, 5, 5, 4))
y2 = x.reshape(3000, 10, 2)
res = self.executor.execute_tensor(y2, concat=True)
np.testing.assert_array_equal(res[0], raw_data.reshape(3000, 10, 2))
y3 = x.reshape(60, 25, 40)
res = self.executor.execute_tensor(y3, concat=True)
np.testing.assert_array_equal(res[0], raw_data.reshape(60, 25, 40))
y4 = x.reshape(60, 25, 40)
y4.op.extra_params['_reshape_with_shuffle'] = True
size_res = self.executor.execute_tensor(y4, mock=True)
res = self.executor.execute_tensor(y4, concat=True)
self.assertEqual(res[0].nbytes, sum(v[0] for v in size_res))
self.assertTrue(np.array_equal(res[0], raw_data.reshape(60, 25, 40)))
y5 = x.ravel(order='F')
res = self.executor.execute_tensor(y5, concat=True)[0]
expected = raw_data.ravel(order='F')
np.testing.assert_array_equal(res, expected)
self.assertEqual(res.flags['C_CONTIGUOUS'], expected.flags['C_CONTIGUOUS'])
self.assertEqual(res.flags['F_CONTIGUOUS'], expected.flags['F_CONTIGUOUS'])
def testExpandDimsExecution(self):
raw_data = np.random.rand(10, 20, 30)
x = tensor(raw_data, chunk_size=6)
y = expand_dims(x, 1)
res = self.executor.execute_tensor(y, concat=True)
self.assertTrue(np.array_equal(res[0], np.expand_dims(raw_data, 1)))
y = expand_dims(x, 0)
res = self.executor.execute_tensor(y, concat=True)
self.assertTrue(np.array_equal(res[0], np.expand_dims(raw_data, 0)))
y = expand_dims(x, 3)
res = self.executor.execute_tensor(y, concat=True)
self.assertTrue(np.array_equal(res[0], np.expand_dims(raw_data, 3)))
y = expand_dims(x, -1)
res = self.executor.execute_tensor(y, concat=True)
self.assertTrue(np.array_equal(res[0], np.expand_dims(raw_data, -1)))
y = expand_dims(x, -4)
res = self.executor.execute_tensor(y, concat=True)
self.assertTrue(np.array_equal(res[0], np.expand_dims(raw_data, -4)))
with self.assertRaises(np.AxisError):
expand_dims(x, -5)
with self.assertRaises(np.AxisError):
expand_dims(x, 4)
def testRollAxisExecution(self):
x = ones((3, 4, 5, 6), chunk_size=1)
y = rollaxis(x, 3, 1)
res = self.executor.execute_tensor(y, concat=True)
self.assertTrue(np.array_equal(res[0], np.rollaxis(np.ones((3, 4, 5, 6)), 3, 1)))
def testAtleast1dExecution(self):
x = 1
y = ones(3, chunk_size=2)
z = ones((3, 4), chunk_size=2)
t = atleast_1d(x, y, z)
res = [self.executor.execute_tensor(i, concat=True)[0] for i in t]
self.assertTrue(np.array_equal(res[0], np.array([1])))
self.assertTrue(np.array_equal(res[1], np.ones(3)))
self.assertTrue(np.array_equal(res[2], np.ones((3, 4))))
def testAtleast2dExecution(self):
x = 1
y = ones(3, chunk_size=2)
z = ones((3, 4), chunk_size=2)
t = atleast_2d(x, y, z)
res = [self.executor.execute_tensor(i, concat=True)[0] for i in t]
self.assertTrue(np.array_equal(res[0], np.array([[1]])))
self.assertTrue(np.array_equal(res[1], np.atleast_2d(np.ones(3))))
self.assertTrue(np.array_equal(res[2], np.ones((3, 4))))
def testAtleast3dExecution(self):
x = 1
y = ones(3, chunk_size=2)
z = ones((3, 4), chunk_size=2)
t = atleast_3d(x, y, z)
res = [self.executor.execute_tensor(i, concat=True)[0] for i in t]
self.assertTrue(np.array_equal(res[0], np.atleast_3d(x)))
self.assertTrue(np.array_equal(res[1], np.atleast_3d(np.ones(3))))
self.assertTrue(np.array_equal(res[2], np.atleast_3d(np.ones((3, 4)))))
def testArgwhereExecution(self):
x = arange(6, chunk_size=2).reshape(2, 3)
t = argwhere(x > 1)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.argwhere(np.arange(6).reshape(2, 3) > 1)
np.testing.assert_array_equal(res, expected)
data = np.asfortranarray(np.random.rand(10, 20))
x = tensor(data, chunk_size=10)
t = argwhere(x > 0.5)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.argwhere(data > 0.5)
np.testing.assert_array_equal(res, expected)
self.assertTrue(res.flags['F_CONTIGUOUS'])
self.assertFalse(res.flags['C_CONTIGUOUS'])
def testArraySplitExecution(self):
x = arange(48, chunk_size=3).reshape(2, 3, 8)
ss = array_split(x, 3, axis=2)
res = [self.executor.execute_tensor(i, concat=True)[0] for i in ss]
expected = np.array_split(np.arange(48).reshape(2, 3, 8), 3, axis=2)
self.assertEqual(len(res), len(expected))
[np.testing.assert_equal(r, e) for r, e in zip(res, expected)]
ss = array_split(x, [3, 5, 6, 10], axis=2)
res = [self.executor.execute_tensor(i, concat=True)[0] for i in ss]
expected = np.array_split(np.arange(48).reshape(2, 3, 8), [3, 5, 6, 10], axis=2)
self.assertEqual(len(res), len(expected))
[np.testing.assert_equal(r, e) for r, e in zip(res, expected)]
def testSplitExecution(self):
for a in ((1, 1, 1, 2, 2, 3), [1, 1, 1, 2, 2, 3]):
splits = split(a, (3, 5))
self.assertEqual(len(splits), 3)
splits0 = self.executor.execute_tensor(splits[0], concat=True)[0]
np.testing.assert_array_equal(splits0, (1, 1, 1))
splits1 = self.executor.execute_tensor(splits[1], concat=True)[0]
np.testing.assert_array_equal(splits1, (2, 2))
splits2 = self.executor.execute_tensor(splits[2], concat=True)[0]
np.testing.assert_array_equal(splits2, (3,))
x = arange(48, chunk_size=3).reshape(2, 3, 8)
ss = split(x, 4, axis=2)
res = [self.executor.execute_tensor(i, concat=True)[0] for i in ss]
expected = np.split(np.arange(48).reshape(2, 3, 8), 4, axis=2)
self.assertEqual(len(res), len(expected))
[np.testing.assert_equal(r, e) for r, e in zip(res, expected)]
ss = split(x, [3, 5, 6, 10], axis=2)
res = [self.executor.execute_tensor(i, concat=True)[0] for i in ss]
expected = np.split(np.arange(48).reshape(2, 3, 8), [3, 5, 6, 10], axis=2)
self.assertEqual(len(res), len(expected))
[np.testing.assert_equal(r, e) for r, e in zip(res, expected)]
# hsplit
x = arange(120, chunk_size=3).reshape(2, 12, 5)
ss = hsplit(x, 4)
res = [self.executor.execute_tensor(i, concat=True)[0] for i in ss]
expected = np.hsplit(np.arange(120).reshape(2, 12, 5), 4)
self.assertEqual(len(res), len(expected))
[np.testing.assert_equal(r, e) for r, e in zip(res, expected)]
# vsplit
x = arange(48, chunk_size=3).reshape(8, 3, 2)
ss = vsplit(x, 4)
res = [self.executor.execute_tensor(i, concat=True)[0] for i in ss]
expected = np.vsplit(np.arange(48).reshape(8, 3, 2), 4)
self.assertEqual(len(res), len(expected))
[np.testing.assert_equal(r, e) for r, e in zip(res, expected)]
# dsplit
x = arange(48, chunk_size=3).reshape(2, 3, 8)
ss = dsplit(x, 4)
res = [self.executor.execute_tensor(i, concat=True)[0] for i in ss]
expected = np.dsplit(np.arange(48).reshape(2, 3, 8), 4)
self.assertEqual(len(res), len(expected))
[np.testing.assert_equal(r, e) for r, e in zip(res, expected)]
x_data = sps.random(12, 8, density=.1)
x = tensor(x_data, chunk_size=3)
ss = split(x, 4, axis=0)
res = [self.executor.execute_tensor(i, concat=True)[0] for i in ss]
expected = np.split(x_data.toarray(), 4, axis=0)
self.assertEqual(len(res), len(expected))
[np.testing.assert_equal(r.toarray(), e) for r, e in zip(res, expected)]
def testRollExecution(self):
x = arange(10, chunk_size=2)
t = roll(x, 2)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.roll(np.arange(10), 2)
np.testing.assert_equal(res, expected)
x2 = x.reshape(2, 5)
t = roll(x2, 1)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.roll(np.arange(10).reshape(2, 5), 1)
np.testing.assert_equal(res, expected)
t = roll(x2, 1, axis=0)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.roll(np.arange(10).reshape(2, 5), 1, axis=0)
np.testing.assert_equal(res, expected)
t = roll(x2, 1, axis=1)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.roll(np.arange(10).reshape(2, 5), 1, axis=1)
np.testing.assert_equal(res, expected)
def testSqueezeExecution(self):
data = np.array([[[0], [1], [2]]])
x = tensor(data, chunk_size=1)
t = squeeze(x)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.squeeze(data)
np.testing.assert_equal(res, expected)
t = squeeze(x, axis=2)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.squeeze(data, axis=2)
np.testing.assert_equal(res, expected)
def testDiffExecution(self):
data = np.array([1, 2, 4, 7, 0])
x = tensor(data, chunk_size=2)
t = diff(x)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.diff(data)
np.testing.assert_equal(res, expected)
t = diff(x, n=2)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.diff(data, n=2)
np.testing.assert_equal(res, expected)
data = np.array([[1, 3, 6, 10], [0, 5, 6, 8]])
x = tensor(data, chunk_size=2)
t = diff(x)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.diff(data)
np.testing.assert_equal(res, expected)
t = diff(x, axis=0)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.diff(data, axis=0)
np.testing.assert_equal(res, expected)
x = mt.arange('1066-10-13', '1066-10-16', dtype=mt.datetime64)
t = diff(x)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.diff(np.arange('1066-10-13', '1066-10-16', dtype=np.datetime64))
np.testing.assert_equal(res, expected)
def testEdiff1d(self):
data = np.array([1, 2, 4, 7, 0])
x = tensor(data, chunk_size=2)
t = ediff1d(x)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.ediff1d(data)
np.testing.assert_equal(res, expected)
to_begin = tensor(-99, chunk_size=2)
to_end = tensor([88, 99], chunk_size=2)
t = ediff1d(x, to_begin=to_begin, to_end=to_end)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.ediff1d(data, to_begin=-99, to_end=np.array([88, 99]))
np.testing.assert_equal(res, expected)
data = [[1, 2, 4], [1, 6, 24]]
t = ediff1d(tensor(data, chunk_size=2))
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.ediff1d(data)
np.testing.assert_equal(res, expected)
def testFlipExecution(self):
a = arange(8, chunk_size=2).reshape((2, 2, 2))
t = flip(a, 0)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.flip(np.arange(8).reshape(2, 2, 2), 0)
np.testing.assert_equal(res, expected)
t = flip(a, 1)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.flip(np.arange(8).reshape(2, 2, 2), 1)
np.testing.assert_equal(res, expected)
t = flipud(a)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.flipud(np.arange(8).reshape(2, 2, 2))
np.testing.assert_equal(res, expected)
t = fliplr(a)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.fliplr(np.arange(8).reshape(2, 2, 2))
np.testing.assert_equal(res, expected)
def testRepeatExecution(self):
a = repeat(3, 4)
res = self.executor.execute_tensor(a)[0]
expected = np.repeat(3, 4)
np.testing.assert_equal(res, expected)
x_data = np.random.randn(20, 30)
x = tensor(x_data, chunk_size=(3, 4))
t = repeat(x, 2)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.repeat(x_data, 2)
np.testing.assert_equal(res, expected)
t = repeat(x, 3, axis=1)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.repeat(x_data, 3, axis=1)
np.testing.assert_equal(res, expected)
t = repeat(x, np.arange(20), axis=0)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.repeat(x_data, np.arange(20), axis=0)
np.testing.assert_equal(res, expected)
t = repeat(x, arange(20, chunk_size=5), axis=0)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.repeat(x_data, np.arange(20), axis=0)
np.testing.assert_equal(res, expected)
x_data = sps.random(20, 30, density=.1)
x = tensor(x_data, chunk_size=(3, 4))
t = repeat(x, 2, axis=1)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.repeat(x_data.toarray(), 2, axis=1)
np.testing.assert_equal(res.toarray(), expected)
def testTileExecution(self):
a_data = np.array([0, 1, 2])
a = tensor(a_data, chunk_size=2)
t = tile(a, 2)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tile(a_data, 2)
np.testing.assert_equal(res, expected)
t = tile(a, (2, 2))
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tile(a_data, (2, 2))
np.testing.assert_equal(res, expected)
t = tile(a, (2, 1, 2))
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tile(a_data, (2, 1, 2))
np.testing.assert_equal(res, expected)
b_data = np.array([[1, 2], [3, 4]])
b = tensor(b_data, chunk_size=1)
t = tile(b, 2)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tile(b_data, 2)
np.testing.assert_equal(res, expected)
t = tile(b, (2, 1))
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tile(b_data, (2, 1))
np.testing.assert_equal(res, expected)
c_data = np.array([1, 2, 3, 4])
c = tensor(c_data, chunk_size=3)
t = tile(c, (4, 1))
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tile(c_data, (4, 1))
np.testing.assert_equal(res, expected)
def testIsInExecution(self):
element = 2 * arange(4, chunk_size=1).reshape((2, 2))
test_elements = [1, 2, 4, 8]
mask = isin(element, test_elements)
res = self.executor.execute_tensor(mask, concat=True)[0]
expected = np.isin(2 * np.arange(4).reshape((2, 2)), test_elements)
np.testing.assert_equal(res, expected)
res = self.executor.execute_tensor(element[mask], concat=True)[0]
expected = np.array([2, 4])
np.testing.assert_equal(res, expected)
mask = isin(element, test_elements, invert=True)
res = self.executor.execute_tensor(mask, concat=True)[0]
expected = np.isin(2 * np.arange(4).reshape((2, 2)), test_elements, invert=True)
np.testing.assert_equal(res, expected)
res = self.executor.execute_tensor(element[mask], concat=True)[0]
expected = np.array([0, 6])
np.testing.assert_equal(res, expected)
test_set = {1, 2, 4, 8}
mask = isin(element, test_set)
res = self.executor.execute_tensor(mask, concat=True)[0]
expected = np.isin(2 * np.arange(4).reshape((2, 2)), test_set)
np.testing.assert_equal(res, expected)
def testRavelExecution(self):
arr = ones((10, 5), chunk_size=2)
flat_arr = mt.ravel(arr)
res = self.executor.execute_tensor(flat_arr, concat=True)[0]
self.assertEqual(len(res), 50)
np.testing.assert_equal(res, np.ones(50))
def testSearchsortedExecution(self):
raw = np.sort(np.random.randint(100, size=(16,)))
# test different chunk_size, 3 will have combine, 6 will skip combine
for chunk_size in (3, 6):
arr = tensor(raw, chunk_size=chunk_size)
# test scalar, with value in the middle
t1 = searchsorted(arr, 20)
res = self.executor.execute_tensor(t1, concat=True)[0]
expected = np.searchsorted(raw, 20)
np.testing.assert_array_equal(res, expected)
# test scalar, with value larger than 100
t2 = searchsorted(arr, 200)
res = self.executor.execute_tensor(t2, concat=True)[0]
expected = np.searchsorted(raw, 200)
np.testing.assert_array_equal(res, expected)
# test scalar, side left, with value exact in the middle of the array
t3 = searchsorted(arr, raw[10], side='left')
res = self.executor.execute_tensor(t3, concat=True)[0]
expected = np.searchsorted(raw, raw[10], side='left')
np.testing.assert_array_equal(res, expected)
# test scalar, side right, with value exact in the middle of the array
t4 = searchsorted(arr, raw[10], side='right')
res = self.executor.execute_tensor(t4, concat=True)[0]
expected = np.searchsorted(raw, raw[10], side='right')
np.testing.assert_array_equal(res, expected)
# test scalar, side left, with value exact in the end of the array
t5 = searchsorted(arr, raw[15], side='left')
res = self.executor.execute_tensor(t5, concat=True)[0]
expected = np.searchsorted(raw, raw[15], side='left')
np.testing.assert_array_equal(res, expected)
# test scalar, side right, with value exact in the end of the array
t6 = searchsorted(arr, raw[15], side='right')
res = self.executor.execute_tensor(t6, concat=True)[0]
expected = np.searchsorted(raw, raw[15], side='right')
np.testing.assert_array_equal(res, expected)
# test scalar, side left, with value exact in the start of the array
t7 = searchsorted(arr, raw[0], side='left')
res = self.executor.execute_tensor(t7, concat=True)[0]
expected = np.searchsorted(raw, raw[0], side='left')
np.testing.assert_array_equal(res, expected)
# test scalar, side right, with value exact in the start of the array
t8 = searchsorted(arr, raw[0], side='right')
res = self.executor.execute_tensor(t8, concat=True)[0]
expected = np.searchsorted(raw, raw[0], side='right')
np.testing.assert_array_equal(res, expected)
raw2 = np.random.randint(100, size=(3, 4))
# test tensor, side left
t9 = searchsorted(arr, tensor(raw2, chunk_size=2), side='left')
res = self.executor.execute_tensor(t9, concat=True)[0]
expected = np.searchsorted(raw, raw2, side='left')
np.testing.assert_array_equal(res, expected)
# test tensor, side right
t10 = searchsorted(arr, tensor(raw2, chunk_size=2), side='right')
res = self.executor.execute_tensor(t10, concat=True)[0]
expected = np.searchsorted(raw, raw2, side='right')
np.testing.assert_array_equal(res, expected)
# test one chunk
arr = tensor(raw, chunk_size=16)
# test scalar, tensor to search has 1 chunk
t11 = searchsorted(arr, 20)
res = self.executor.execute_tensor(t11, concat=True)[0]
expected = np.searchsorted(raw, 20)
np.testing.assert_array_equal(res, expected)
# test tensor with 1 chunk, tensor to search has 1 chunk
t12 = searchsorted(arr, tensor(raw2, chunk_size=4))
res = self.executor.execute_tensor(t12, concat=True)[0]
expected = np.searchsorted(raw, raw2)
np.testing.assert_array_equal(res, expected)
# test tensor with more than 1 chunk, tensor to search has 1 chunk
t13 = searchsorted(arr, tensor(raw2, chunk_size=2))
res = self.executor.execute_tensor(t13, concat=True)[0]
expected = np.searchsorted(raw, raw2)
np.testing.assert_array_equal(res, expected)
# test sorter
raw3 = np.random.randint(100, size=(16,))
arr = tensor(raw3, chunk_size=3)
order = np.argsort(raw3)
order_arr = tensor(order, chunk_size=4)
t14 = searchsorted(arr, 20, sorter=order_arr)
res = self.executor.execute_tensor(t14, concat=True)[0]
expected = np.searchsorted(raw3, 20, sorter=order)
np.testing.assert_array_equal(res, expected)
def testUniqueExecution(self):
rs = np.random.RandomState(0)
raw = rs.randint(10, size=(10,))
for chunk_size in (10, 3):
x = tensor(raw, chunk_size=chunk_size)
y = unique(x)
res = self.executor.execute_tensor(y, concat=True)[0]
expected = np.unique(raw)
np.testing.assert_array_equal(res, expected)
y, indices = unique(x, return_index=True)
res = self.executor.execute_tensors([y, indices])
expected = np.unique(raw, return_index=True)
self.assertEqual(len(res), 2)
self.assertEqual(len(expected), 2)
np.testing.assert_array_equal(res[0], expected[0])
np.testing.assert_array_equal(res[1], expected[1])
y, inverse = unique(x, return_inverse=True)
res = self.executor.execute_tensors([y, inverse])
expected = np.unique(raw, return_inverse=True)
self.assertEqual(len(res), 2)
self.assertEqual(len(expected), 2)
np.testing.assert_array_equal(res[0], expected[0])
np.testing.assert_array_equal(res[1], expected[1])
y, counts = unique(x, return_counts=True)
res = self.executor.execute_tensors([y, counts])
expected = np.unique(raw, return_counts=True)
self.assertEqual(len(res), 2)
self.assertEqual(len(expected), 2)
np.testing.assert_array_equal(res[0], expected[0])
np.testing.assert_array_equal(res[1], expected[1])
y, indices, inverse, counts = unique(x, return_index=True,
return_inverse=True, return_counts=True)
res = self.executor.execute_tensors([y, indices, inverse, counts])
expected = np.unique(raw, return_index=True,
return_inverse=True, return_counts=True)
self.assertEqual(len(res), 4)
self.assertEqual(len(expected), 4)
np.testing.assert_array_equal(res[0], expected[0])
np.testing.assert_array_equal(res[1], expected[1])
np.testing.assert_array_equal(res[2], expected[2])
np.testing.assert_array_equal(res[3], expected[3])
y, indices, counts = unique(x, return_index=True, return_counts=True)
res = self.executor.execute_tensors([y, indices, counts])
expected = np.unique(raw, return_index=True, return_counts=True)
self.assertEqual(len(res), 3)
self.assertEqual(len(expected), 3)
np.testing.assert_array_equal(res[0], expected[0])
np.testing.assert_array_equal(res[1], expected[1])
np.testing.assert_array_equal(res[2], expected[2])
raw2 = rs.randint(10, size=(4, 5, 6))
x2 = tensor(raw2, chunk_size=chunk_size)
y2 = unique(x2)
res = self.executor.execute_tensor(y2, concat=True)[0]
expected = np.unique(raw2)
np.testing.assert_array_equal(res, expected)
y2 = unique(x2, axis=1)
res = self.executor.execute_tensor(y2, concat=True)[0]
expected = np.unique(raw2, axis=1)
np.testing.assert_array_equal(res, expected)
y2 = unique(x2, axis=2)
res = self.executor.execute_tensor(y2, concat=True)[0]
expected = np.unique(raw2, axis=2)
np.testing.assert_array_equal(res, expected)
raw = rs.randint(10, size=(10, 20))
raw[:, 0] = raw[:, 11] = rs.randint(10, size=(10,))
x = tensor(raw, chunk_size=2)
y, ind, inv, counts = unique(x, aggregate_size=3, axis=1, return_index=True,
return_inverse=True, return_counts=True)
res_unique, res_ind, res_inv, res_counts = self.executor.execute_tensors((y, ind, inv, counts))
exp_unique, exp_ind, exp_counts = np.unique(raw, axis=1, return_index=True, return_counts=True)
raw_res_unique = res_unique
res_unique_df = pd.DataFrame(res_unique)
res_unique_ind = np.asarray(res_unique_df.sort_values(list(range(res_unique.shape[0])),
axis=1).columns)
res_unique = res_unique[:, res_unique_ind]
res_ind = res_ind[res_unique_ind]
res_counts = res_counts[res_unique_ind]
np.testing.assert_array_equal(res_unique, exp_unique)
np.testing.assert_array_equal(res_ind, exp_ind)
np.testing.assert_array_equal(raw_res_unique[:, res_inv], raw)
np.testing.assert_array_equal(res_counts, exp_counts)
x = (mt.random.RandomState(0).rand(1000, chunk_size=20) > 0.5).astype(np.int32)
y = unique(x)
res = np.sort(self.executor.execute_tensor(y, concat=True)[0])
np.testing.assert_array_equal(res, np.array([0, 1]))
# test sparse
sparse_raw = sps.random(10, 3, density=0.1, format='csr', random_state=rs)
x = tensor(sparse_raw, chunk_size=2)
y = unique(x)
res = np.sort(self.executor.execute_tensor(y, concat=True)[0])
np.testing.assert_array_equal(res, np.unique(sparse_raw.data))
# test empty
x = tensor([])
y = unique(x)
res = self.executor.execute_tensor(y, concat=True)[0]
np.testing.assert_array_equal(res, np.unique([]))
x = tensor([[]])
y = unique(x)
res = self.executor.execute_tensor(y, concat=True)[0]
np.testing.assert_array_equal(res, np.unique([[]]))
@require_cupy
def testToGPUExecution(self):
raw = np.random.rand(10, 10)
x = tensor(raw, chunk_size=3)
gx = to_gpu(x)
res = self.executor.execute_tensor(gx, concat=True)[0]
np.testing.assert_array_equal(res.get(), raw)
@require_cupy
def testToCPUExecution(self):
raw = np.random.rand(10, 10)
x = tensor(raw, chunk_size=3, gpu=True)
cx = to_cpu(x)
res = self.executor.execute_tensor(cx, concat=True)[0]
np.testing.assert_array_equal(res, raw)
def testSortExecution(self):
# only 1 chunk when axis = -1
raw = np.random.rand(100, 10)
x = tensor(raw, chunk_size=10)
sx = sort(x)
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw))
# 1-d chunk
raw = np.random.rand(100)
x = tensor(raw, chunk_size=10)
sx = sort(x)
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw))
# test force need_align=True
sx = sort(x)
sx.op._need_align = True
res = self.executor.execute_tensor(sx, concat=True)[0]
self.assertEqual(get_tiled(sx).nsplits, get_tiled(x).nsplits)
np.testing.assert_array_equal(res, np.sort(raw))
# test psrs_kinds
sx = sort(x, psrs_kinds=[None, None, 'quicksort'])
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw))
# structured dtype
raw = np.empty(100, dtype=[('id', np.int32), ('size', np.int64)])
raw['id'] = np.random.randint(1000, size=100, dtype=np.int32)
raw['size'] = np.random.randint(1000, size=100, dtype=np.int64)
x = tensor(raw, chunk_size=10)
sx = sort(x, order=['size', 'id'])
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw, order=['size', 'id']))
# test psrs_kinds with structured dtype
sx = sort(x, order=['size', 'id'], psrs_kinds=[None, None, 'quicksort'])
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw, order=['size', 'id']))
# test flatten case
raw = np.random.rand(10, 10)
x = tensor(raw, chunk_size=5)
sx = sort(x, axis=None)
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw, axis=None))
# test multi-dimension
raw = np.random.rand(10, 100)
x = tensor(raw, chunk_size=(2, 10))
sx = sort(x, psrs_kinds=['quicksort'] * 3)
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw))
sx = sort(x, psrs_kinds=[None, None, 'quicksort'])
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw))
raw = np.random.rand(10, 99)
x = tensor(raw, chunk_size=(2, 10))
sx = sort(x)
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw))
# test 3-d
raw = np.random.rand(20, 25, 28)
x = tensor(raw, chunk_size=(10, 5, 7))
sx = sort(x)
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw))
sx = sort(x, psrs_kinds=[None, None, 'quicksort'])
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw))
sx = sort(x, axis=0)
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw, axis=0))
sx = sort(x, axis=0, psrs_kinds=[None, None, 'quicksort'])
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw, axis=0))
sx = sort(x, axis=1)
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw, axis=1))
sx = sort(x, axis=1, psrs_kinds=[None, None, 'quicksort'])
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw, axis=1))
# test multi-dimension with structured type
raw = np.empty((10, 100), dtype=[('id', np.int32), ('size', np.int64)])
raw['id'] = np.random.randint(1000, size=(10, 100), dtype=np.int32)
raw['size'] = np.random.randint(1000, size=(10, 100), dtype=np.int64)
x = tensor(raw, chunk_size=(3, 10))
sx = sort(x)
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw))
sx = sort(x, order=['size', 'id'])
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw, order=['size', 'id']))
sx = sort(x, order=['size'])
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw, order=['size']))
sx = sort(x, axis=0, order=['size', 'id'])
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw, axis=0, order=['size', 'id']))
sx = sort(x, axis=0, order=['size', 'id'],
psrs_kinds=[None, None, 'quicksort'])
res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw, axis=0, order=['size', 'id']))
# test inplace sort
raw = np.random.rand(10, 12)
a = tensor(raw, chunk_size=(5, 4))
a.sort(axis=1)
res = self.executor.execute_tensor(a, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw, axis=1))
a.sort(axis=0)
res = self.executor.execute_tensor(a, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(np.sort(raw, axis=1), axis=0))
# test with empty chunk
raw = np.random.rand(20, 10)
raw[:, :8] = 1
a = tensor(raw, chunk_size=5)
filtered = a[a < 1]
filtered.sort()
res = self.executor.execute_tensor(filtered, concat=True)[0]
np.testing.assert_array_equal(res, np.sort(raw[raw < 1]))
def testSortIndicesExecution(self):
# only 1 chunk when axis = -1
raw = np.random.rand(100, 10)
x = tensor(raw, chunk_size=10)
r = sort(x, return_index=True)
sr, si = self.executor.execute_tensors(r)
np.testing.assert_array_equal(sr, np.take_along_axis(raw, si, axis=-1))
x = tensor(raw, chunk_size=(22, 4))
r = sort(x, return_index=True)
sr, si = self.executor.execute_tensors(r)
np.testing.assert_array_equal(sr, np.take_along_axis(raw, si, axis=-1))
raw = np.random.rand(100)
x = tensor(raw, chunk_size=23)
r = sort(x, axis=0, return_index=True)
sr, si = self.executor.execute_tensors(r)
np.testing.assert_array_equal(sr, raw[si])
def testArgsort(self):
# only 1 chunk when axis = -1
raw = np.random.rand(100, 10)
x = tensor(raw, chunk_size=10)
xa = argsort(x)
r = self.executor.execute_tensor(xa, concat=True)[0]
np.testing.assert_array_equal(np.sort(raw), np.take_along_axis(raw, r, axis=-1))
x = tensor(raw, chunk_size=(22, 4))
xa = argsort(x)
r = self.executor.execute_tensor(xa, concat=True)[0]
np.testing.assert_array_equal(np.sort(raw), np.take_along_axis(raw, r, axis=-1))
raw = np.random.rand(100)
x = tensor(raw, chunk_size=23)
xa = argsort(x, axis=0)
r = self.executor.execute_tensor(xa, concat=True)[0]
np.testing.assert_array_equal(np.sort(raw, axis=0), raw[r])
def testPartitionExecution(self):
# only 1 chunk when axis = -1
raw = np.random.rand(100, 10)
x = tensor(raw, chunk_size=10)
px = partition(x, [1, 8])
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(res, np.partition(raw, [1, 8]))
# 1-d chunk
raw = np.random.rand(100)
x = tensor(raw, chunk_size=10)
kth = np.random.RandomState(0).randint(-100, 100, size=(10,))
px = partition(x, kth)
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(res[kth], np.partition(raw, kth)[kth])
# structured dtype
raw = np.empty(100, dtype=[('id', np.int32), ('size', np.int64)])
raw['id'] = np.random.randint(1000, size=100, dtype=np.int32)
raw['size'] = np.random.randint(1000, size=100, dtype=np.int64)
x = tensor(raw, chunk_size=10)
px = partition(x, kth, order=['size', 'id'])
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(
res[kth], np.partition(raw, kth, order=['size', 'id'])[kth])
# test flatten case
raw = np.random.rand(10, 10)
x = tensor(raw, chunk_size=5)
px = partition(x, kth, axis=None)
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(res[kth], np.partition(raw, kth, axis=None)[kth])
# test multi-dimension
raw = np.random.rand(10, 100)
x = tensor(raw, chunk_size=(2, 10))
kth = np.random.RandomState(0).randint(-10, 10, size=(3,))
px = partition(x, kth)
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(res[:, kth], np.partition(raw, kth)[:, kth])
raw = np.random.rand(10, 99)
x = tensor(raw, chunk_size=(2, 10))
px = partition(x, kth)
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(res[:, kth], np.partition(raw, kth)[:, kth])
# test 3-d
raw = np.random.rand(20, 25, 28)
x = tensor(raw, chunk_size=(10, 5, 7))
kth = np.random.RandomState(0).randint(-28, 28, size=(3,))
px = partition(x, kth)
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(
res[:, :, kth], np.partition(raw, kth)[:, :, kth])
kth = np.random.RandomState(0).randint(-20, 20, size=(3,))
px = partition(x, kth, axis=0)
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(res[kth], np.partition(raw, kth, axis=0)[kth])
kth = np.random.RandomState(0).randint(-25, 25, size=(3,))
px = partition(x, kth, axis=1)
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(
res[:, kth], np.partition(raw, kth, axis=1)[:, kth])
# test multi-dimension with structured type
raw = np.empty((10, 100), dtype=[('id', np.int32), ('size', np.int64)])
raw['id'] = np.random.randint(1000, size=(10, 100), dtype=np.int32)
raw['size'] = np.random.randint(1000, size=(10, 100), dtype=np.int64)
x = tensor(raw, chunk_size=(3, 10))
kth = np.random.RandomState(0).randint(-100, 100, size=(10,))
px = partition(x, kth)
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(res[:, kth], np.partition(raw, kth)[:, kth])
px = partition(x, kth, order=['size', 'id'])
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(
res[:, kth], np.partition(raw, kth, order=['size', 'id'])[:, kth])
px = partition(x, kth, order=['size'])
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(
res[:, kth], np.partition(raw, kth, order=['size'])[:, kth])
kth = np.random.RandomState(0).randint(-10, 10, size=(5,))
px = partition(x, kth, axis=0, order=['size', 'id'])
res = self.executor.execute_tensor(px, concat=True)[0]
np.testing.assert_array_equal(
res[kth], np.partition(raw, kth, axis=0, order=['size', 'id'])[kth])
raw = np.random.rand(10, 12)
a = tensor(raw, chunk_size=(5, 4))
kth = np.random.RandomState(0).randint(-12, 12, size=(2,))
a.partition(kth, axis=1)
res = self.executor.execute_tensor(a, concat=True)[0]
np.testing.assert_array_equal(
res[:, kth], np.partition(raw, kth, axis=1)[:, kth])
kth = np.random.RandomState(0).randint(-10, 10, size=(2,))
a.partition(kth, axis=0)
raw_base = res
res = self.executor.execute_tensor(a, concat=True)[0]
np.testing.assert_array_equal(
res[kth], np.partition(raw_base, kth, axis=0)[kth])
# test kth which is tensor
raw = np.random.rand(10, 12)
a = tensor(raw, chunk_size=(3, 5))
kth = (mt.random.rand(5) * 24 - 12).astype(int)
px = partition(a, kth)
sx = sort(a)
res = self.executor.execute_tensor(px, concat=True)[0]
kth_res = self.executor.execute_tensor(kth, concat=True)[0]
sort_res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res[:, kth_res], sort_res[:, kth_res])
a = tensor(raw, chunk_size=(10, 12))
kth = (mt.random.rand(5) * 24 - 12).astype(int)
px = partition(a, kth)
sx = sort(a)
res = self.executor.execute_tensor(px, concat=True)[0]
kth_res = self.executor.execute_tensor(kth, concat=True)[0]
sort_res = self.executor.execute_tensor(sx, concat=True)[0]
np.testing.assert_array_equal(res[:, kth_res], sort_res[:, kth_res])
def testPartitionIndicesExecution(self):
# only 1 chunk when axis = -1
raw = np.random.rand(100, 10)
x = tensor(raw, chunk_size=10)
kth = [2, 5, 9]
r = partition(x, kth, return_index=True)
pr, pi = self.executor.execute_tensors(r)
np.testing.assert_array_equal(pr, np.take_along_axis(raw, pi, axis=-1))
np.testing.assert_array_equal(np.sort(raw)[:, kth], pr[:, kth])
x = tensor(raw, chunk_size=(22, 4))
r = partition(x, kth, return_index=True)
pr, pi = self.executor.execute_tensors(r)
np.testing.assert_array_equal(pr, np.take_along_axis(raw, pi, axis=-1))
np.testing.assert_array_equal(np.sort(raw)[:, kth], pr[:, kth])
raw = np.random.rand(100)
x = tensor(raw, chunk_size=23)
r = partition(x, kth, axis=0, return_index=True)
pr, pi = self.executor.execute_tensors(r)
np.testing.assert_array_equal(pr, np.take_along_axis(raw, pi, axis=-1))
np.testing.assert_array_equal(np.sort(raw)[kth], pr[kth])
def testArgpartitionExecution(self):
# only 1 chunk when axis = -1
raw = np.random.rand(100, 10)
x = tensor(raw, chunk_size=10)
kth = [6, 3, 8]
pa = argpartition(x, kth)
r = self.executor.execute_tensor(pa, concat=True)[0]
np.testing.assert_array_equal(np.sort(raw)[:, kth], np.take_along_axis(raw, r, axis=-1)[:, kth])
x = tensor(raw, chunk_size=(22, 4))
pa = argpartition(x, kth)
r = self.executor.execute_tensor(pa, concat=True)[0]
np.testing.assert_array_equal(np.sort(raw)[:, kth], np.take_along_axis(raw, r, axis=-1)[:, kth])
raw = np.random.rand(100)
x = tensor(raw, chunk_size=23)
pa = argpartition(x, kth, axis=0)
r = self.executor.execute_tensor(pa, concat=True)[0]
np.testing.assert_array_equal(np.sort(raw, axis=0)[kth], raw[r][kth])
@staticmethod
def _topk_slow(a, k, axis, largest, order):
if axis is None:
a = a.flatten()
axis = 0
a = np.sort(a, axis=axis, order=order)
if largest:
a = a[(slice(None),) * axis + (slice(None, None, -1),)]
return a[(slice(None),) * axis + (slice(k),)]
@staticmethod
def _handle_result(result, axis, largest, order):
result = np.sort(result, axis=axis, order=order)
if largest:
ax = axis if axis is not None else 0
result = result[(slice(None),) * ax + (slice(None, None, -1),)]
return result
def testTopkExecution(self):
raw1, order1 = np.random.rand(5, 6, 7), None
raw2 = np.empty((5, 6, 7), dtype=[('a', np.int32), ('b', np.float64)])
raw2['a'] = np.random.randint(1000, size=(5, 6, 7), dtype=np.int32)
raw2['b'] = np.random.rand(5, 6, 7)
order2 = ['b', 'a']
for raw, order in [(raw1, order1), (raw2, order2)]:
for chunk_size in [7, 4]:
a = tensor(raw, chunk_size=chunk_size)
for axis in [0, 1, 2, None]:
size = raw.shape[axis] if axis is not None else raw.size
for largest in [True, False]:
for to_sort in [True, False]:
for parallel_kind in ['tree', 'psrs']:
for k in [2, size - 2, size, size + 2]:
r = topk(a, k, axis=axis, largest=largest, sorted=to_sort,
order=order, parallel_kind=parallel_kind)
result = self.executor.execute_tensor(r, concat=True)[0]
if not to_sort:
result = self._handle_result(result, axis, largest, order)
expected = self._topk_slow(raw, k, axis, largest, order)
np.testing.assert_array_equal(result, expected)
r = topk(a, k, axis=axis, largest=largest,
sorted=to_sort, order=order,
parallel_kind=parallel_kind,
return_index=True)
ta, ti = self.executor.execute_tensors(r)
raw2 = raw
if axis is None:
raw2 = raw.flatten()
np.testing.assert_array_equal(ta, np.take_along_axis(raw2, ti, axis))
if not to_sort:
ta = self._handle_result(ta, axis, largest, order)
np.testing.assert_array_equal(ta, expected)
def testArgtopk(self):
# only 1 chunk when axis = -1
raw = np.random.rand(100, 10)
x = tensor(raw, chunk_size=10)
pa = argtopk(x, 3, parallel_kind='tree')
r = self.executor.execute_tensor(pa, concat=True)[0]
np.testing.assert_array_equal(np.sort(raw)[:, -1:-4:-1], np.take_along_axis(raw, r, axis=-1))
pa = argtopk(x, 3, parallel_kind='psrs')
r = self.executor.execute_tensor(pa, concat=True)[0]
np.testing.assert_array_equal(np.sort(raw)[:, -1:-4:-1], np.take_along_axis(raw, r, axis=-1))
x = tensor(raw, chunk_size=(22, 4))
pa = argtopk(x, 3, parallel_kind='tree')
r = self.executor.execute_tensor(pa, concat=True)[0]
np.testing.assert_array_equal(np.sort(raw)[:, -1:-4:-1], np.take_along_axis(raw, r, axis=-1))
pa = argtopk(x, 3, parallel_kind='psrs')
r = self.executor.execute_tensor(pa, concat=True)[0]
np.testing.assert_array_equal(np.sort(raw)[:, -1:-4:-1], np.take_along_axis(raw, r, axis=-1))
raw = np.random.rand(100)
x = tensor(raw, chunk_size=23)
pa = argtopk(x, 3, axis=0, parallel_kind='tree')
r = self.executor.execute_tensor(pa, concat=True)[0]
np.testing.assert_array_equal(np.sort(raw, axis=0)[-1:-4:-1], raw[r])
pa = argtopk(x, 3, axis=0, parallel_kind='psrs')
r = self.executor.execute_tensor(pa, concat=True)[0]
np.testing.assert_array_equal(np.sort(raw, axis=0)[-1:-4:-1], raw[r])
def testCopy(self):
x = tensor([1, 2, 3])
y = mt.copy(x)
z = x
x[0] = 10
y_res = self.executor.execute_tensor(y)[0]
np.testing.assert_array_equal(y_res, np.array([1, 2, 3]))
z_res = self.executor.execute_tensor(z)[0]
np.testing.assert_array_equal(z_res, np.array([10, 2, 3]))
def testTrapzExecution(self):
raws = [
np.random.rand(10),
np.random.rand(10, 3)
]
for raw in raws:
for chunk_size in (4, 10):
for dx in (1.0, 2.0):
t = tensor(raw, chunk_size=chunk_size)
r = trapz(t, dx=dx)
result = self.executor.execute_tensor(r, concat=True)[0]
expected = np.trapz(raw, dx=dx)
np.testing.assert_almost_equal(result, expected,
err_msg=f'failed when raw={raw}, '
f'chunk_size={chunk_size}, dx={dx}')
# test x not None
raw_ys = [np.random.rand(10),
np.random.rand(10, 3)]
raw_xs = [np.random.rand(10),
| np.random.rand(10, 3) | numpy.random.rand |
# Copyright 2019 Xanadu Quantum Technologies Inc.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
r"""Unit tests for the poly_quad_expectations method in the states.py submodule"""
import pytest
import numpy as np
from scipy.stats import multivariate_normal
from scipy.integrate import simps
from scipy.linalg import block_diag
from strawberryfields import backends
from strawberryfields import utils
from strawberryfields.backends.shared_ops import rotation_matrix as R, changebasis
# some tests require a higher cutoff for accuracy
CUTOFF = 12
a = 0.3 + 0.1j
r = 0.23
phi = 0.123
qphi = 0.78
@pytest.mark.backends("fock", "gaussian")
class TestSingleModePolyQuadratureExpectations:
"""Test single mode poly_quad_expectation methods"""
@pytest.fixture
def gaussian_state(self, hbar):
"""A test Gaussian state to use in testing"""
# quadrature rotation
# construct the expected vector of means and covariance matrix
mu = R(qphi).T @ np.array([a.real, a.imag]) * np.sqrt(2 * hbar)
cov = R(qphi).T @ utils.squeezed_cov(r, phi, hbar=hbar) @ R(qphi)
return mu, cov
@pytest.fixture
def sample_normal_expectations(self, gaussian_state):
"""Returns the expectation value E(f) and the variance var(f)
for some normal distribution X~N(mu, cov).
Args:
mu (array): means vector
cov (array): covariance matrix
func (function): function acting on the random variables X, P, XP,
returning a second order polynomial
Returns:
tuple: tuple of expectation value and variance.
"""
def _sample(func, correction=0, mu=None, cov=None):
"""wrapped function"""
if mu is None:
mu = gaussian_state[0]
if cov is None:
cov = gaussian_state[1]
X, P = np.mgrid[-7:7:0.01, -7:7:0.01]
grid = np.dstack((X, P))
XP = np.prod(grid, axis=2)
poly = func(X, P, XP)
PDF = multivariate_normal.pdf(grid, mu, cov)
Ex = simps(simps(poly * PDF, P[0]), X.T[0])
ExSq = simps(simps(poly ** 2 * PDF, P[0]), X.T[0])
var = ExSq - Ex ** 2 + correction
return Ex, var
return _sample
def test_no_expectation(self, setup_backend, tol):
"""Test the case E(0), var(0)"""
backend = setup_backend(3)
state = backend.state()
A = np.zeros([6, 6])
d = np.zeros([6])
k = 0
mean, var = state.poly_quad_expectation(A, d, k)
assert np.allclose(mean, 0, atol=tol, rtol=0)
assert np.allclose(var, 0, atol=tol, rtol=0)
def test_constant(self, setup_backend, tol):
"""Test the case E(k), var(k)"""
backend = setup_backend(3)
state = backend.state()
A = np.zeros([6, 6])
d = np.zeros([6])
k = 0.543
mean, var = state.poly_quad_expectation(A, d, k)
assert np.allclose(mean, k, atol=tol, rtol=0)
assert np.allclose(var, 0, atol=tol, rtol=0)
def test_linear_vacuum(self, setup_backend, tol, hbar):
"""Test that the correct results are returned for the vacuum state."""
backend = setup_backend(3)
state = backend.state()
A = np.zeros([6, 6])
# create an arbitrary linear combination
d = np.array([1, 1, 0, 1, 0, 0])
k = 0
mean, var = state.poly_quad_expectation(A, d, k, phi=qphi)
assert np.allclose(mean, 0, atol=tol, rtol=0)
assert np.allclose(var, len(d) * hbar / 4, atol=tol, rtol=0)
def test_x_squeezed(self, setup_backend, tol, pure, hbar):
"""Test that the correct E(x) is returned for the squeezed state."""
backend = setup_backend(3)
backend.reset(cutoff_dim=CUTOFF, pure=pure)
A = None
d = np.array([1, 0, 0, 0, 0, 0])
k = 0
# prepare a squeezed state
backend.squeeze(r, 0)
state = backend.state()
mean, var = state.poly_quad_expectation(A, d, k, phi=0)
assert np.allclose(mean, 0, atol=tol, rtol=0)
assert np.allclose(var, np.exp(-2 * r)*hbar/2, atol=tol, rtol=0)
def test_x_displaced(self, setup_backend, tol, hbar):
"""Test that the correct E(x) is returned for a displaced state."""
backend = setup_backend(3)
A = None
d = np.array([1, 0, 0, 0, 0, 0])
k = 0
# prepare a displaced state
backend.displacement(a, 0)
state = backend.state()
mean, var = state.poly_quad_expectation(A, d, k, phi=0)
assert np.allclose(mean, a.real * np.sqrt(2 * hbar), atol=tol, rtol=0)
assert np.allclose(var, hbar / 2, atol=tol, rtol=0)
def test_x_displaced_squeezed(self, setup_backend, tol, gaussian_state):
"""Test that the correct E(x) is returned for the displaced squeezed state."""
backend = setup_backend(3)
mu, cov = gaussian_state
A = None
d = np.array([1, 0, 0, 0, 0, 0])
k = 0
# prepare a displaced squeezed state
backend.prepare_displaced_squeezed_state(a, r, phi, 0)
state = backend.state()
mean, var = state.poly_quad_expectation(A, d, k, phi=qphi)
assert np.allclose(mean, mu[0], atol=tol, rtol=0)
assert np.allclose(var, cov[0, 0], atol=tol, rtol=0)
def test_p_displaced_squeezed(self, setup_backend, tol, gaussian_state):
"""Test that the correct E(p) is returned for the displaced squeezed state."""
backend = setup_backend(3)
mu, cov = gaussian_state
A = None
d = np.array([0, 0, 0, 1, 0, 0])
k = 0
# prepare a displaced squeezed state
backend.prepare_displaced_squeezed_state(a, r, phi, 0)
state = backend.state()
mean, var = state.poly_quad_expectation(A, d, k, phi=qphi)
assert np.allclose(mean, mu[1], atol=tol, rtol=0)
assert np.allclose(var, cov[1, 1], atol=tol, rtol=0)
def test_linear_combination(self, setup_backend, tol, gaussian_state):
"""Test that the correct result is returned for E(ax+bp)"""
backend = setup_backend(3)
mu, cov = gaussian_state
A = None
d = np.array([0.4234, 0, 0, 0.1543, 0, 0])
k = 0
# prepare a displaced squeezed state
backend.prepare_displaced_squeezed_state(a, r, phi, 0)
state = backend.state()
mean, var = state.poly_quad_expectation(A, d, k, phi=qphi)
# E(ax+bp) = aE(x) + bE(p)
mean_expected = d[0] * mu[0] + d[3] * mu[1]
assert np.allclose(mean, mean_expected, atol=tol, rtol=0)
# var(ax+bp) = a**2 var(x)+b**2 var(p)+2ab cov(x,p)
var_expected = (
cov[0, 0] * d[0] ** 2 + cov[1, 1] * d[3] ** 2 + 2 * d[0] * d[3] * cov[0, 1]
)
assert np.allclose(var, var_expected, atol=tol, rtol=0)
def test_n_thermal(self, setup_backend, tol, hbar, pure):
"""Test expectation and variance of the number operator on a thermal state"""
backend = setup_backend(3)
backend.reset(cutoff_dim=CUTOFF, pure=pure)
nbar = 0.423
backend.prepare_thermal_state(nbar, 0)
state = backend.state()
# n = a^\dagger a = (X^2 +P^2)/2\hbar - I/2
A = np.zeros([6, 6])
A[0, 0] = 1 / (2 * hbar)
A[3, 3] = 1 / (2 * hbar)
k = -0.5
mean, var = state.poly_quad_expectation(A, d=None, k=k, phi=0)
assert np.allclose(mean, nbar, atol=tol, rtol=0)
assert np.allclose(var, nbar * (nbar + 1), atol=tol, rtol=0)
def test_n_squeeze(self, setup_backend, tol, hbar, pure):
"""Test expectation and variance of the number operator on a squeezed state"""
backend = setup_backend(3)
backend.reset(cutoff_dim=CUTOFF, pure=pure)
backend.prepare_squeezed_state(r, phi, 0)
state = backend.state()
# n = a^\dagger a = (X^2 +P^2)/2\hbar - I/2
A = np.zeros([6, 6])
A[0, 0] = 1 / (2 * hbar)
A[3, 3] = 1 / (2 * hbar)
k = -0.5
mean, var = state.poly_quad_expectation(A, None, k, phi=qphi)
mean_ex = np.sinh(r) ** 2
var_ex = 0.5 * np.sinh(2 * r) ** 2
assert np.allclose(mean, mean_ex, atol=tol, rtol=0)
assert np.allclose(var, var_ex, atol=tol, rtol=0)
def test_x_squared(self, setup_backend, tol, pure, sample_normal_expectations):
"""Test that the correct result is returned for E(x^2)"""
backend = setup_backend(3)
backend.reset(cutoff_dim=CUTOFF, pure=pure)
A = np.zeros([6, 6])
A[0, 0] = 1
d = None
k = 0
# prepare a displaced squeezed state
backend.prepare_displaced_squeezed_state(a, r, phi, 0)
state = backend.state()
mean, var = state.poly_quad_expectation(A, d, k, phi=qphi)
mean_ex, var_ex = sample_normal_expectations(lambda X, P, XP: A[0, 0] * X ** 2)
assert np.allclose(mean, mean_ex, atol=tol, rtol=0)
assert np.allclose(var, var_ex, atol=tol, rtol=0)
def test_p_squared(self, setup_backend, tol, pure, sample_normal_expectations):
"""Test that the correct result is returned for E(p^2)"""
backend = setup_backend(3)
backend.reset(cutoff_dim=CUTOFF, pure=pure)
A = np.zeros([6, 6])
A[3, 3] = 1
d = None
k = 0
# prepare a displaced squeezed state
backend.prepare_displaced_squeezed_state(a, r, phi, 0)
state = backend.state()
mean, var = state.poly_quad_expectation(A, d, k, phi=qphi)
mean_ex, var_ex = sample_normal_expectations(lambda X, P, XP: P ** 2)
assert np.allclose(mean, mean_ex, atol=tol, rtol=0)
assert np.allclose(var, var_ex, atol=tol, rtol=0)
def test_xp_vacuum(self, setup_backend, tol, sample_normal_expectations, hbar):
"""Test that the correct result is returned for E(xp) on the vacuum state"""
backend = setup_backend(3)
# set quadratic coefficient
A = np.zeros([6, 6])
A[3, 0] = A[0, 3] = 0.5
d = None
k = 0
state = backend.state()
mean, var = state.poly_quad_expectation(A, d, k, phi=0)
mean_ex, var_ex = sample_normal_expectations(
lambda X, P, XP: XP,
correction=-np.linalg.det(hbar * A[:, [0, 3]][[0, 3]]),
mu=np.zeros([2]),
cov=np.identity(2)*hbar/2,
)
assert np.allclose(mean, mean_ex, atol=tol, rtol=0)
assert np.allclose(var, var_ex, atol=tol, rtol=0)
def test_xp_displaced_squeezed(
self, setup_backend, tol, pure, sample_normal_expectations, hbar
):
"""Test that the correct result is returned for E(xp) on a displaced squeezed state"""
backend = setup_backend(3)
backend.reset(cutoff_dim=CUTOFF, pure=pure)
# set quadratic coefficient
A = np.zeros([6, 6])
A[3, 0] = A[0, 3] = 0.5
d = None
k = 0
# prepare a displaced squeezed state
backend.prepare_displaced_squeezed_state(a, r, phi, 0)
state = backend.state()
mean, var = state.poly_quad_expectation(A, d, k, phi=qphi)
mean_ex, var_ex = sample_normal_expectations(
lambda X, P, XP: XP, correction=-np.linalg.det(hbar * A[:, [0, 3]][[0, 3]])
)
assert np.allclose(mean, mean_ex, atol=tol, rtol=0)
assert np.allclose(var, var_ex, atol=tol, rtol=0)
def test_arbitrary_quadratic(
self, setup_backend, tol, pure, sample_normal_expectations, hbar
):
"""Test that the correct result is returned for E(c0 x^2 + c1 p^2 + c2 xp + c3 x + c4 p + k) on a displaced squeezed state"""
backend = setup_backend(3)
backend.reset(cutoff_dim=CUTOFF, pure=pure)
c0 = 1 / np.sqrt(2)
c1 = 3
c2 = 0.53
c3 = 1 / 3.0
c4 = -1
# define the arbitrary quadratic
A = | np.zeros([6, 6]) | numpy.zeros |
#!/usr/bin/env python
"""Tests for the linalg.isolve.gcrotmk module
"""
from numpy.testing import (assert_, assert_allclose, assert_equal,
suppress_warnings)
import numpy as np
from numpy import zeros, array, allclose
from scipy.linalg import norm
from scipy.sparse import csr_matrix, eye, rand
from scipy.sparse.linalg.interface import LinearOperator
from scipy.sparse.linalg import splu
from scipy.sparse.linalg.isolve import gcrotmk, gmres
Am = csr_matrix(array([[-2,1,0,0,0,9],
[1,-2,1,0,5,0],
[0,1,-2,1,0,0],
[0,0,1,-2,1,0],
[0,3,0,1,-2,1],
[1,0,0,0,1,-2]]))
b = array([1,2,3,4,5,6])
count = [0]
def matvec(v):
count[0] += 1
return Am*v
A = LinearOperator(matvec=matvec, shape=Am.shape, dtype=Am.dtype)
def do_solve(**kw):
count[0] = 0
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x0, flag = gcrotmk(A, b, x0=zeros(A.shape[0]), tol=1e-14, **kw)
count_0 = count[0]
assert_(allclose(A*x0, b, rtol=1e-12, atol=1e-12), norm(A*x0-b))
return x0, count_0
class TestGCROTMK(object):
def test_preconditioner(self):
# Check that preconditioning works
pc = splu(Am.tocsc())
M = LinearOperator(matvec=pc.solve, shape=A.shape, dtype=A.dtype)
x0, count_0 = do_solve()
x1, count_1 = do_solve(M=M)
assert_equal(count_1, 3)
assert_(count_1 < count_0/2)
assert_(allclose(x1, x0, rtol=1e-14))
def test_arnoldi(self):
np.random.seed(1)
A = eye(2000) + rand(2000, 2000, density=5e-4)
b = np.random.rand(2000)
# The inner arnoldi should be equivalent to gmres
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x0, flag0 = gcrotmk(A, b, x0=zeros(A.shape[0]), m=15, k=0, maxiter=1)
x1, flag1 = gmres(A, b, x0=zeros(A.shape[0]), restart=15, maxiter=1)
assert_equal(flag0, 1)
| assert_equal(flag1, 1) | numpy.testing.assert_equal |
import numpy as np
from scipy.special import loggamma, gammaln, gamma
from matplotlib import pyplot as plt
from scipy.optimize import minimize
from scipy.optimize import root
from mpl_toolkits import mplot3d
np.seterr(divide = 'raise')
logmoments = np.load("logmoments_Harmonic_4.npy")
moments = np.load("moments_Harmonic_4.npy")
s_values = np.load("s_values_Harmonic_4.npy")
N_base = 7
N_constant = 0
N_plus = 0
N_minus = 0
PPT = 2
N_params_shift = N_base + N_constant + PPT*N_plus + PPT*N_minus
## Scaled
def func(sr,si, *q):
p=list(q)
s = sr+1j*si
base = loggamma(p[3] + p[2]*s) + np.log(p[0]**2) + s*np.log(p[1]**2) #+ s**2 * np.log(p[2]**2) + s**3 * np.log(p[3]**2) + s**4 * np.log(p[4]**2)
polynom = np.log(p[4] + p[5]*s + p[6]*s**2)
#constant = loggamma(p[2]) - loggamma(p[3])
off = N_base + N_constant
plus = np.sum([ loggamma(p[off + PPT*k + 0]+ p[off + PPT*k + 1]*s) for k in range(N_plus)])
off = N_base + N_constant + PPT*N_plus
minus = np.sum([ -loggamma(p[off + PPT*k + 0]+p[off + PPT*k + 1]*s) for k in range(N_minus)])
return base + polynom + plus - minus
## Allow for nearby branches in the solution
def spc(m,sr,si,*p):
qq = np.imag(func(sr,si,*p))
## Allow for 5 branches
a = [(m - qq + k*2*np.pi)**2 for k in range(-2,3)]
return np.amin(a)
## The difference to minimize
def diff(p,S_R,S_I,M_R,M_I):
## Add a regularisation term to force real inputs (s) to have real outputs (i.e. zero imaginary part)
loss_real = np.sum([ (m - np.real(func(sr,si,*p)))**2 for sr,si,m in zip(S_R,S_I,M_R)])
loss_imag = np.sum([ spc(m,sr,si,*p) for sr,si,m in zip(S_R,S_I,M_I)])
ret = loss_real + loss_imag
print(p)
print(ret)
return ret
p0 = np.random.rand(N_params_shift)
p0 = np.ones(N_params_shift) + 0.2 * np.random.rand(N_params_shift)
## Chop up
real_s = np.real(s_values)
imag_s = np.imag(s_values)
real_logm = np.real(logmoments)
imag_logm = np.imag(logmoments)
real_m = np.real(moments)
imag_m = np.imag(moments)
if(True):
res = minimize(diff,p0,args = (real_s,imag_s,real_logm,imag_logm),method = 'BFGS')
print(res)
popt=res.x
fit = np.array([ func(sr,si,*popt) for sr,si in zip(real_s,imag_s)])
loss_real = np.sum([ (m - np.real(func(sr,si,*popt)))**2 for sr,si,m in zip(real_s,imag_s,real_m)])
loss_imag = np.sum([ spc(m,sr,si,*popt) for sr,si,m in zip(real_s,imag_s,imag_m)])
print("Final Loss:",loss_real+loss_imag)
if(False):
ax = plt.axes(projection='3d')
# Data for three-dimensional scattered points
ax.scatter3D(real_s, imag_s, real_m, c=real_m, cmap='Reds', label = "Numeric")
ax.scatter3D(real_s, imag_s, np.real(fit), c=np.real(fit), cmap='Greens', label = "Theoretical")
ax.set_xlabel('Re(s)')
ax.set_ylabel('Im(s)')
ax.set_zlabel('$Re(E[x^{s-1}])$')
plt.legend()
plt.show()
ax = plt.axes(projection='3d')
# Data for three-dimensional scattered points
ax.scatter3D(real_s, imag_s, imag_m, c=imag_m, cmap='Reds', label = "Numeric")
ax.scatter3D(real_s, imag_s, np.imag(fit), c= | np.imag(fit) | numpy.imag |
import pytest
import numpy as np
import os
from ansys import dpf
from ansys.dpf import core
from ansys.dpf.core.common import shell_layers, locations
from ansys.dpf.core import FieldDefinition
from ansys.dpf.core import operators as ops
from conftest import local_server
@pytest.fixture()
def stress_field(allkindofcomplexity):
model = dpf.core.Model(allkindofcomplexity)
stress = model.results.stress()
return stress.outputs.fields_container()[0]
def test_create_field():
field = dpf.core.Field()
assert field._message.id != 0
def test_create_field_from_helper_scalar():
data = np.random.random(10)
field_a = dpf.core.field_from_array(data)
assert np.allclose(field_a.data, data)
def test_create_field_from_helper_vector():
data = np.random.random((10, 3))
field_a = dpf.core.field_from_array(data)
assert np.allclose(field_a.data, data)
def test_createbycopy_field():
field = dpf.core.Field()
field2 = dpf.core.Field(field=field._message)
assert field._message.id == field2._message.id
def test_set_get_scoping():
field = dpf.core.Field()
scoping = dpf.core.Scoping()
ids=[1,2,3,5,8,9,10]
scoping.ids=ids
field.scoping = scoping
assert field.scoping.ids == ids
def test_set_get_data_field():
field = dpf.core.Field(nentities=20, nature=dpf.core.natures.scalar)
scoping = dpf.core.Scoping()
ids = []
data= []
for i in range(0, 20):
ids.append(i+1)
data.append(i+0.001)
scoping.ids = ids
field.scoping = scoping
field.data = data
assert np.allclose(field.data,data)
def test_set_get_data_array_field():
field= dpf.core.Field(nentities=20, nature=dpf.core.natures.vector)
scoping = dpf.core.Scoping()
ids =[]
data=[]
for i in range(0, 20):
ids.append(i+1)
data.append(i+0.001)
data.append(i+0.001)
data.append(i+0.001)
data = np.array(data)
data =data.reshape((20,3))
scoping.ids = ids
field.scoping = scoping
field.data = data
assert np.allclose(field.data,data)
def test_append_data_field():
field= dpf.core.Field(nentities=20, nature=dpf.core.natures.vector)
for i in range(0,20):
scopingid= i+1
scopingindex=i
data = [0.01+i,0.02+i,0.03+i]
field.append(data, scopingid)
scopingOut = field.scoping
assert scopingOut.ids == list(range(1,21))
for i in range(0,20):
scopingid= i+1
scopingindex=i
datain = [0.01+i,0.02+i,0.03+i]
dataout = field.get_entity_data(scopingindex)
assert np.allclose(dataout,datain)
def test_set_get_entity_data_array_field():
field= dpf.core.Field(nentities=20, nature=dpf.core.natures.vector)
for i in range(0,20):
scopingid= i+1
scopingindex=i
data = [0.01+i,0.02+i,0.03+i]
data = np.array(data)
data =data.reshape((1,3))
field.append(data,scopingid)
scopingOut = field.scoping
assert scopingOut.ids == list(range(1,21))
for i in range(0,20):
scopingid= i+1
scopingindex=i
datain = [0.01+i,0.02+i,0.03+i]
dataout = field.get_entity_data(scopingindex)
assert np.allclose(dataout,datain)
dataout = field.get_entity_data_by_id(scopingid)
assert np.allclose(dataout,datain)
#def test_get_data_ptr_field():
# field= dpf.core.Field(nentities=3, nature=dpf.core.natures.scalar,
# location=dpf.core.locations.elemental_nodal)
# data = [0.01,0.02,0.03]
# field.set_entity_data(data,0,1)
# data = [0.01,0.02,0.03,0.01,0.02,0.03]
# field.set_entity_data(data,1,2)
# data = [0.01,0.02,0.03,0.01]
# field.set_entity_data(data,2,3)
# scopingOut = field.scoping
# assert scopingOut.ids == [1,2,3]
# dataptr = field.data_ptr
# assert dataptr == [0,3,9]
def test_set_get_data_property_field():
field= core.Field(nentities=20, nature=dpf.core.natures.scalar)
scoping = core.Scoping()
ids = []
data= []
for i in range(0, 20):
ids.append(i+1)
data.append(i+0.001)
scoping.ids = ids
field.scoping = scoping
field.data = data
assert np.allclose(field.data,data)
def test_count_field():
field= dpf.core.Field(nentities=20, nature=dpf.core.natures.scalar)
scoping = dpf.core.Scoping()
ids = []
data= []
for i in range(0, 20):
ids.append(i+1)
data.append(i+0.001)
scoping.ids = ids
field.scoping = scoping
field.data = data
assert field.component_count == 1
assert field.elementary_data_count == 20
assert field.size == 20
def test_resize_field():
field= dpf.core.Field(nentities=1, nature=dpf.core.natures.scalar)
scoping = dpf.core.Scoping()
ids = []
data= []
for i in range(0, 20):
ids.append(i+1)
data.append(i+0.001)
field.resize(20,20)
scoping.ids = ids
field.scoping = scoping
field.data = data
assert field.component_count == 1
assert field.elementary_data_count == 20
assert field.size == 20
def test_fromarray_field():
data = np.empty((100, 6))
f = dpf.core.field_from_array(data)
assert f.shape == (100, 6)
def test_field_definition_field(allkindofcomplexity):
dataSource = dpf.core.DataSources()
dataSource.set_result_file_path(allkindofcomplexity)
op = dpf.core.Operator("U")
op.connect(4, dataSource)
fcOut = op.get_output(0, dpf.core.types.fields_container)
f = fcOut[0]
assert f.unit == "m"
assert f.location == dpf.core.locations.nodal
def test_field_definition_modif_field(allkindofcomplexity):
dataSource = dpf.core.DataSources()
dataSource.set_result_file_path(allkindofcomplexity)
op = dpf.core.Operator("U")
op.connect(4, dataSource)
fcOut = op.get_output(0, dpf.core.types.fields_container)
f = fcOut[0]
fielddef = f.field_definition
assert fielddef.unit == "m"
assert fielddef.location == dpf.core.locations.nodal
assert fielddef.dimensionality.nature == dpf.core.natures.vector
assert fielddef.dimensionality.dim == [3]
assert fielddef.shell_layers == dpf.core.shell_layers.layerindependent
fielddef.unit = "mm"
assert fielddef.unit == "mm"
fielddef.location = dpf.core.locations.elemental
assert fielddef.location == dpf.core.locations.elemental
fielddef.dimensionality = dpf.core.Dimensionality.scalar_dim()
assert fielddef.dimensionality.nature == dpf.core.natures.scalar
assert fielddef.dimensionality.dim == [1]
fielddef.dimensionality = dpf.core.Dimensionality.tensor_dim()
assert fielddef.dimensionality.nature == dpf.core.natures.symmatrix
assert fielddef.dimensionality.dim == [3,3]
fielddef.dimensionality = dpf.core.Dimensionality.vector_3d_dim()
assert fielddef.dimensionality.nature == dpf.core.natures.vector
assert fielddef.dimensionality.dim == [3]
fielddef.dimensionality = dpf.core.Dimensionality.vector_dim(4)
assert fielddef.dimensionality.nature == dpf.core.natures.vector
assert fielddef.dimensionality.dim == [4]
fielddef.shell_layers = dpf.core.shell_layers.bottom
assert fielddef.shell_layers == dpf.core.shell_layers.bottom
def test_field_definition_set_in_field(allkindofcomplexity):
dataSource = dpf.core.DataSources()
dataSource.set_result_file_path(allkindofcomplexity)
op = dpf.core.Operator("U")
op.connect(4, dataSource)
fcOut = op.get_output(0, dpf.core.types.fields_container)
f = fcOut[0]
fielddef = f.field_definition
fielddef.unit = "mm"
fielddef.location = dpf.core.locations.elemental
fielddef.dimensionality = dpf.core.Dimensionality.scalar_dim()
fielddef.shell_layers = dpf.core.shell_layers.bottom
f.field_definition = fielddef
fielddef = f.field_definition
assert fielddef.unit == "mm"
assert fielddef.location == dpf.core.locations.elemental
assert fielddef.dimensionality.nature == dpf.core.natures.scalar
assert fielddef.dimensionality.dim == [1]
assert fielddef.shell_layers == dpf.core.shell_layers.bottom
assert f.unit == "mm"
assert f.location == dpf.core.locations.elemental
assert f.dimensionality.nature == dpf.core.natures.scalar
assert f.dimensionality.dim == [1]
assert f.shell_layers == dpf.core.shell_layers.bottom
def test_change_field_definition_in_field(allkindofcomplexity):
dataSource = dpf.core.DataSources()
dataSource.set_result_file_path(allkindofcomplexity)
op = dpf.core.Operator("U")
op.connect(4, dataSource)
fcOut = op.get_output(0, dpf.core.types.fields_container)
f = fcOut[0]
f.unit = "mm"
f.location = dpf.core.locations.elemental
f.dimensionality = dpf.core.Dimensionality.scalar_dim()
f.shell_layers = dpf.core.shell_layers.bottom
fielddef = f.field_definition
assert fielddef.unit == "mm"
assert fielddef.location == dpf.core.locations.elemental
assert fielddef.dimensionality.nature == dpf.core.natures.scalar
assert fielddef.dimensionality.dim == [1]
assert fielddef.shell_layers == dpf.core.shell_layers.bottom
assert f.unit == "mm"
assert f.location == dpf.core.locations.elemental
assert f.dimensionality.nature == dpf.core.natures.scalar
assert f.dimensionality.dim == [1]
assert f.shell_layers == dpf.core.shell_layers.bottom
def test_create_overall_field():
field_overall = dpf.core.Field(nentities=1, location="overall", nature="vector")
field_overall.scoping.location = "overall"
field_overall.scoping.ids =[0]
field_overall.data = [1.0, 2.0, 3.0]
field = dpf.core.Field(nentities=5, location="nodal")
field.scoping.location = "nodal"
field.scoping.ids = list(range(1,6))
data =[float(i) for i in range(0,15)]
field.data = data
add = dpf.core.Operator("add")
add.inputs.fieldA(field)
add.inputs.fieldB(field_overall)
field_added= add.outputs.field()
data_added = field_added.data
for i in range(0,5):
assert np.allclose(data_added[i],[i*3.0+1.0,i*3.0+3.0,i*3.0+5.0])
def test_data_pointer_field(allkindofcomplexity):
dataSource = dpf.core.DataSources()
dataSource.set_result_file_path(allkindofcomplexity)
op = dpf.core.Operator("S")
op.connect(4, dataSource)
fcOut = op.get_output(0, dpf.core.types.fields_container)
data_pointer = fcOut[0]._data_pointer
assert len(data_pointer)==len(fcOut[0].scoping)
assert data_pointer[0] == 0
assert data_pointer[1] == 72
f = fcOut[0]
data_pointer[1] = 40
f._data_pointer = data_pointer
data_pointer = fcOut[0]._data_pointer
assert len(data_pointer)==len(fcOut[0].scoping)
assert data_pointer[0] == 0
assert data_pointer[1] == 40
def test_data_pointer_prop_field():
pfield = dpf.core.PropertyField()
pfield.append([1,2,3],1)
pfield.append([1,2,3,4],2)
pfield.append([1,2,3],3)
data_pointer = pfield._data_pointer
assert len(data_pointer)==3
assert data_pointer[0] == 0
assert data_pointer[1] == 3
assert data_pointer[2] == 7
data_pointer[1]=4
pfield._data_pointer = data_pointer
data_pointer = pfield._data_pointer
assert len(data_pointer)==3
assert data_pointer[0] == 0
assert data_pointer[1] == 4
assert data_pointer[2] == 7
def test_append_data_elemental_nodal_field(allkindofcomplexity):
model = dpf.core.Model(allkindofcomplexity)
stress = model.results.stress()
f = stress.outputs.fields_container()[0]
assert f.location == "ElementalNodal"
f_new= dpf.core.Field(f.scoping.size, nature=dpf.core.natures.symmatrix, location=dpf.core.locations.elemental_nodal)
for i in range(0,int(f.scoping.size/10)):
f_new.append(f.get_entity_data(i),f.scoping.id(i))
for i in range(0,int(f.scoping.size/10)):
assert np.allclose(f_new.get_entity_data(i), f.get_entity_data(i))
def test_str_field(stress_field):
assert 'Location' in str(stress_field)
assert 'ElementalNodal' in str(stress_field)
assert 'Unit'in str(stress_field)
assert 'Pa' in str(stress_field)
assert '9255' in str(stress_field)
assert '40016' in str(stress_field)
assert '6' in str(stress_field)
def test_to_nodal(stress_field):
assert stress_field.location == 'ElementalNodal'
field_out = stress_field.to_nodal()
assert field_out.location == 'Nodal'
def test_mesh_support_field(stress_field):
mesh = stress_field.meshed_region
assert len(mesh.nodes.scoping) == 15129
assert len(mesh.elements.scoping) == 10292
def test_shell_layers_1(allkindofcomplexity):
model = dpf.core.Model(allkindofcomplexity)
stress = model.results.stress()
f = stress.outputs.fields_container()[0]
assert f.shell_layers == shell_layers.topbottommid
model = dpf.core.Model(allkindofcomplexity)
disp = model.results.displacement()
f = disp.outputs.fields_container()[0]
assert f.shell_layers == shell_layers.layerindependent
def test_shell_layers_2(velocity_acceleration):
model = dpf.core.Model(velocity_acceleration)
stress = model.results.stress()
f = stress.outputs.fields_container()[0]
assert f.shell_layers == shell_layers.nonelayer
def test_mesh_support_field_model(allkindofcomplexity):
model = dpf.core.Model(allkindofcomplexity)
stress = model.results.stress()
f = stress.outputs.fields_container()[0]
mesh =f.meshed_region
assert len(mesh.nodes.scoping)==15129
assert len(mesh.elements.scoping)==10292
def test_delete_auto_field():
field = dpf.core.Field()
field2 = dpf.core.Field(field=field)
del field
with pytest.raises(Exception):
field2.get_ids()
def test_create_and_update_field_definition():
fieldDef = FieldDefinition()
assert fieldDef is not None
with pytest.raises(Exception):
assert fieldDef.location is None
fieldDef.location = locations.nodal
assert fieldDef.location == locations.nodal
def test_set_support_timefreq(simple_bar):
tfq = dpf.core.TimeFreqSupport()
time_frequencies = dpf.core.Field(nature=dpf.core.natures.scalar, location=dpf.core.locations.time_freq)
time_frequencies.scoping.location = dpf.core.locations.time_freq_step
time_frequencies.append([0.1, 0.32, 0.4], 1)
tfq.time_frequencies = time_frequencies
model = dpf.core.Model(simple_bar)
disp = model.results.displacement()
fc = disp.outputs.fields_container()
field = fc[0]
# initial_support = field.time_freq_support
# assert initial_support is None
field.time_freq_support = tfq
tfq_to_check = field.time_freq_support
assert np.allclose(tfq.time_frequencies.data, tfq_to_check.time_frequencies.data)
def test_set_support_mesh(simple_bar):
mesh = dpf.core.MeshedRegion()
mesh.nodes.add_node(1, [0.0,0.0,0.0])
model = dpf.core.Model(simple_bar)
disp = model.results.displacement()
fc = disp.outputs.fields_container()
field = fc[0]
field.meshed_region = mesh
mesh_to_check = field.meshed_region
assert mesh_to_check.nodes.n_nodes == 1
assert mesh_to_check.elements.n_elements == 0
mesh.nodes.add_node(2, [1.0,0.0,0.0])
mesh.nodes.add_node(3, [1.0,1.0,0.0])
mesh.nodes.add_node(4,[0.0,1.0,0.0])
field.meshed_region = mesh
mesh_to_check_2 = field.meshed_region
assert mesh_to_check_2.nodes.n_nodes == 4
assert mesh_to_check_2.elements.n_elements == 0
def test_local_field_append():
num_entities = 400
field_to_local = dpf.core.fields_factory.create_3d_vector_field(num_entities)
with field_to_local.as_local_field() as f:
for i in range(1,num_entities+1):
f.append([0.1*i,0.2*i, 0.3*i],i)
field = dpf.core.fields_factory.create_3d_vector_field(num_entities)
for i in range(1,num_entities+1):
field.append([0.1*i,0.2*i, 0.3*i],i)
assert np.allclose(field.data, field_to_local.data)
assert np.allclose(field.scoping.ids, field_to_local.scoping.ids)
assert len(field_to_local._data_pointer)==0
def test_local_elemental_nodal_field_append():
num_entities = 100
field_to_local = dpf.core.fields_factory.create_3d_vector_field(num_entities, location=dpf.core.locations.elemental_nodal)
with field_to_local.as_local_field() as f:
for i in range(1,num_entities+1):
f.append([[0.1*i,0.2*i, 0.3*i],[0.1*i,0.2*i, 0.3*i]],i)
field = dpf.core.fields_factory.create_3d_vector_field(num_entities)
for i in range(1,num_entities+1):
field.append([[0.1*i,0.2*i, 0.3*i],[0.1*i,0.2*i, 0.3*i]],i)
assert np.allclose(field.data, field_to_local.data)
assert np.allclose(field.scoping.ids, field_to_local.scoping.ids)
assert len(field_to_local._data_pointer)==num_entities
#flat data
field_to_local = dpf.core.fields_factory.create_3d_vector_field(num_entities, location=dpf.core.locations.elemental_nodal)
with field_to_local.as_local_field() as f:
for i in range(1,num_entities+1):
f.append([0.1*i,0.2*i, 0.3*i,0.1*i,0.2*i, 0.3*i],i)
assert np.allclose(field.data, field_to_local.data)
assert np.allclose(field.scoping.ids, field_to_local.scoping.ids)
assert len(field_to_local._data_pointer)==num_entities
def test_local_array_field_append():
num_entities = 400
field_to_local = dpf.core.fields_factory.create_3d_vector_field(num_entities)
with field_to_local.as_local_field() as f:
for i in range(1,num_entities+1):
f.append(np.array([0.1*i,0.2*i, 0.3*i]),i)
field = dpf.core.fields_factory.create_3d_vector_field(num_entities)
for i in range(1,num_entities+1):
field.append(np.array([0.1*i,0.2*i, 0.3*i]),i)
assert np.allclose(field.data, field_to_local.data)
assert np.allclose(field.scoping.ids, field_to_local.scoping.ids)
assert len(field_to_local._data_pointer)==0
def test_local_elemental_nodal_array_field_append():
num_entities = 100
field_to_local = dpf.core.fields_factory.create_3d_vector_field(num_entities, location=dpf.core.locations.elemental_nodal)
with field_to_local.as_local_field() as f:
for i in range(1,num_entities+1):
f.append(np.array([[0.1*i,0.2*i, 0.3*i],[0.1*i,0.2*i, 0.3*i]]),i)
field = dpf.core.fields_factory.create_3d_vector_field(num_entities)
for i in range(1,num_entities+1):
field.append(np.array([[0.1*i,0.2*i, 0.3*i],[0.1*i,0.2*i, 0.3*i]]),i)
assert np.allclose(field.data, field_to_local.data)
assert np.allclose(field.scoping.ids, field_to_local.scoping.ids)
assert len(field_to_local._data_pointer)==num_entities
#flat data
field_to_local = dpf.core.fields_factory.create_3d_vector_field(num_entities, location=dpf.core.locations.elemental_nodal)
with field_to_local.as_local_field() as f:
for i in range(1,num_entities+1):
f.append(np.array([0.1*i,0.2*i, 0.3*i,0.1*i,0.2*i, 0.3*i]),i)
assert np.allclose(field.data, field_to_local.data)
assert | np.allclose(field.scoping.ids, field_to_local.scoping.ids) | numpy.allclose |
# This module has been generated automatically from space group information
# obtained from the Computational Crystallography Toolbox
#
"""
Space groups
This module contains a list of all the 230 space groups that can occur in
a crystal. The variable space_groups contains a dictionary that maps
space group numbers and space group names to the corresponding space
group objects.
.. moduleauthor:: <NAME> <<EMAIL>>
"""
#-----------------------------------------------------------------------------
# Copyright (C) 2013 The Mosaic Development Team
#
# Distributed under the terms of the BSD License. The full license is in
# the file LICENSE.txt, distributed as part of this software.
#-----------------------------------------------------------------------------
import numpy as N
class SpaceGroup(object):
"""
Space group
All possible space group objects are created in this module. Other
modules should access these objects through the dictionary
space_groups rather than create their own space group objects.
"""
def __init__(self, number, symbol, transformations):
"""
:param number: the number assigned to the space group by
international convention
:type number: int
:param symbol: the Hermann-Mauguin space-group symbol as used
in PDB and mmCIF files
:type symbol: str
:param transformations: a list of space group transformations,
each consisting of a tuple of three
integer arrays (rot, tn, td), where
rot is the rotation matrix and tn/td
are the numerator and denominator of the
translation vector. The transformations
are defined in fractional coordinates.
:type transformations: list
"""
self.number = number
self.symbol = symbol
self.transformations = transformations
self.transposed_rotations = N.array([N.transpose(t[0])
for t in transformations])
self.phase_factors = N.exp(N.array([(-2j*N.pi*t[1])/t[2]
for t in transformations]))
def __repr__(self):
return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol))
def __len__(self):
"""
:return: the number of space group transformations
:rtype: int
"""
return len(self.transformations)
def symmetryEquivalentMillerIndices(self, hkl):
"""
:param hkl: a set of Miller indices
:type hkl: Scientific.N.array_type
:return: a tuple (miller_indices, phase_factor) of two arrays
of length equal to the number of space group
transformations. miller_indices contains the Miller
indices of each reflection equivalent by symmetry to the
reflection hkl (including hkl itself as the first element).
phase_factor contains the phase factors that must be applied
to the structure factor of reflection hkl to obtain the
structure factor of the symmetry equivalent reflection.
:rtype: tuple
"""
hkls = N.dot(self.transposed_rotations, hkl)
p = N.multiply.reduce(self.phase_factors**hkl, -1)
return hkls, p
space_groups = {}
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(1, 'P 1', transformations)
space_groups[1] = sg
space_groups['P 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(2, 'P -1', transformations)
space_groups[2] = sg
space_groups['P -1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(3, 'P 1 2 1', transformations)
space_groups[3] = sg
space_groups['P 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(4, 'P 1 21 1', transformations)
space_groups[4] = sg
space_groups['P 1 21 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(5, 'C 1 2 1', transformations)
space_groups[5] = sg
space_groups['C 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(6, 'P 1 m 1', transformations)
space_groups[6] = sg
space_groups['P 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(7, 'P 1 c 1', transformations)
space_groups[7] = sg
space_groups['P 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(8, 'C 1 m 1', transformations)
space_groups[8] = sg
space_groups['C 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(9, 'C 1 c 1', transformations)
space_groups[9] = sg
space_groups['C 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(10, 'P 1 2/m 1', transformations)
space_groups[10] = sg
space_groups['P 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(11, 'P 1 21/m 1', transformations)
space_groups[11] = sg
space_groups['P 1 21/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(12, 'C 1 2/m 1', transformations)
space_groups[12] = sg
space_groups['C 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(13, 'P 1 2/c 1', transformations)
space_groups[13] = sg
space_groups['P 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(14, 'P 1 21/c 1', transformations)
space_groups[14] = sg
space_groups['P 1 21/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(15, 'C 1 2/c 1', transformations)
space_groups[15] = sg
space_groups['C 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(16, 'P 2 2 2', transformations)
space_groups[16] = sg
space_groups['P 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(17, 'P 2 2 21', transformations)
space_groups[17] = sg
space_groups['P 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(18, 'P 21 21 2', transformations)
space_groups[18] = sg
space_groups['P 21 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(19, 'P 21 21 21', transformations)
space_groups[19] = sg
space_groups['P 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(20, 'C 2 2 21', transformations)
space_groups[20] = sg
space_groups['C 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(21, 'C 2 2 2', transformations)
space_groups[21] = sg
space_groups['C 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(22, 'F 2 2 2', transformations)
space_groups[22] = sg
space_groups['F 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(23, 'I 2 2 2', transformations)
space_groups[23] = sg
space_groups['I 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(24, 'I 21 21 21', transformations)
space_groups[24] = sg
space_groups['I 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(25, 'P m m 2', transformations)
space_groups[25] = sg
space_groups['P m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(26, 'P m c 21', transformations)
space_groups[26] = sg
space_groups['P m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(27, 'P c c 2', transformations)
space_groups[27] = sg
space_groups['P c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(28, 'P m a 2', transformations)
space_groups[28] = sg
space_groups['P m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(29, 'P c a 21', transformations)
space_groups[29] = sg
space_groups['P c a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(30, 'P n c 2', transformations)
space_groups[30] = sg
space_groups['P n c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(31, 'P m n 21', transformations)
space_groups[31] = sg
space_groups['P m n 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(32, 'P b a 2', transformations)
space_groups[32] = sg
space_groups['P b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(33, 'P n a 21', transformations)
space_groups[33] = sg
space_groups['P n a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(34, 'P n n 2', transformations)
space_groups[34] = sg
space_groups['P n n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(35, 'C m m 2', transformations)
space_groups[35] = sg
space_groups['C m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(36, 'C m c 21', transformations)
space_groups[36] = sg
space_groups['C m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(37, 'C c c 2', transformations)
space_groups[37] = sg
space_groups['C c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(38, 'A m m 2', transformations)
space_groups[38] = sg
space_groups['A m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(39, 'A b m 2', transformations)
space_groups[39] = sg
space_groups['A b m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(40, 'A m a 2', transformations)
space_groups[40] = sg
space_groups['A m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(41, 'A b a 2', transformations)
space_groups[41] = sg
space_groups['A b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(42, 'F m m 2', transformations)
space_groups[42] = sg
space_groups['F m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(43, 'F d d 2', transformations)
space_groups[43] = sg
space_groups['F d d 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(44, 'I m m 2', transformations)
space_groups[44] = sg
space_groups['I m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(45, 'I b a 2', transformations)
space_groups[45] = sg
space_groups['I b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(46, 'I m a 2', transformations)
space_groups[46] = sg
space_groups['I m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(47, 'P m m m', transformations)
space_groups[47] = sg
space_groups['P m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(48, 'P n n n :2', transformations)
space_groups[48] = sg
space_groups['P n n n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(49, 'P c c m', transformations)
space_groups[49] = sg
space_groups['P c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(50, 'P b a n :2', transformations)
space_groups[50] = sg
space_groups['P b a n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(51, 'P m m a', transformations)
space_groups[51] = sg
space_groups['P m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(52, 'P n n a', transformations)
space_groups[52] = sg
space_groups['P n n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(53, 'P m n a', transformations)
space_groups[53] = sg
space_groups['P m n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(54, 'P c c a', transformations)
space_groups[54] = sg
space_groups['P c c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(55, 'P b a m', transformations)
space_groups[55] = sg
space_groups['P b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(56, 'P c c n', transformations)
space_groups[56] = sg
space_groups['P c c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(57, 'P b c m', transformations)
space_groups[57] = sg
space_groups['P b c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(58, 'P n n m', transformations)
space_groups[58] = sg
space_groups['P n n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(59, 'P m m n :2', transformations)
space_groups[59] = sg
space_groups['P m m n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(60, 'P b c n', transformations)
space_groups[60] = sg
space_groups['P b c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(61, 'P b c a', transformations)
space_groups[61] = sg
space_groups['P b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(62, 'P n m a', transformations)
space_groups[62] = sg
space_groups['P n m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(63, 'C m c m', transformations)
space_groups[63] = sg
space_groups['C m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(64, 'C m c a', transformations)
space_groups[64] = sg
space_groups['C m c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(65, 'C m m m', transformations)
space_groups[65] = sg
space_groups['C m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(66, 'C c c m', transformations)
space_groups[66] = sg
space_groups['C c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(67, 'C m m a', transformations)
space_groups[67] = sg
space_groups['C m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(68, 'C c c a :2', transformations)
space_groups[68] = sg
space_groups['C c c a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(69, 'F m m m', transformations)
space_groups[69] = sg
space_groups['F m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(70, 'F d d d :2', transformations)
space_groups[70] = sg
space_groups['F d d d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(71, 'I m m m', transformations)
space_groups[71] = sg
space_groups['I m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(72, 'I b a m', transformations)
space_groups[72] = sg
space_groups['I b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(73, 'I b c a', transformations)
space_groups[73] = sg
space_groups['I b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(74, 'I m m a', transformations)
space_groups[74] = sg
space_groups['I m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(75, 'P 4', transformations)
space_groups[75] = sg
space_groups['P 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(76, 'P 41', transformations)
space_groups[76] = sg
space_groups['P 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(77, 'P 42', transformations)
space_groups[77] = sg
space_groups['P 42'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(78, 'P 43', transformations)
space_groups[78] = sg
space_groups['P 43'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(79, 'I 4', transformations)
space_groups[79] = sg
space_groups['I 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(80, 'I 41', transformations)
space_groups[80] = sg
space_groups['I 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(81, 'P -4', transformations)
space_groups[81] = sg
space_groups['P -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(82, 'I -4', transformations)
space_groups[82] = sg
space_groups['I -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(83, 'P 4/m', transformations)
space_groups[83] = sg
space_groups['P 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(84, 'P 42/m', transformations)
space_groups[84] = sg
space_groups['P 42/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(85, 'P 4/n :2', transformations)
space_groups[85] = sg
space_groups['P 4/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(86, 'P 42/n :2', transformations)
space_groups[86] = sg
space_groups['P 42/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(87, 'I 4/m', transformations)
space_groups[87] = sg
space_groups['I 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(88, 'I 41/a :2', transformations)
space_groups[88] = sg
space_groups['I 41/a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(89, 'P 4 2 2', transformations)
space_groups[89] = sg
space_groups['P 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(90, 'P 4 21 2', transformations)
space_groups[90] = sg
space_groups['P 4 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(91, 'P 41 2 2', transformations)
space_groups[91] = sg
space_groups['P 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(92, 'P 41 21 2', transformations)
space_groups[92] = sg
space_groups['P 41 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(93, 'P 42 2 2', transformations)
space_groups[93] = sg
space_groups['P 42 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(94, 'P 42 21 2', transformations)
space_groups[94] = sg
space_groups['P 42 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(95, 'P 43 2 2', transformations)
space_groups[95] = sg
space_groups['P 43 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(96, 'P 43 21 2', transformations)
space_groups[96] = sg
space_groups['P 43 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(97, 'I 4 2 2', transformations)
space_groups[97] = sg
space_groups['I 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(98, 'I 41 2 2', transformations)
space_groups[98] = sg
space_groups['I 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(99, 'P 4 m m', transformations)
space_groups[99] = sg
space_groups['P 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(100, 'P 4 b m', transformations)
space_groups[100] = sg
space_groups['P 4 b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(101, 'P 42 c m', transformations)
space_groups[101] = sg
space_groups['P 42 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(102, 'P 42 n m', transformations)
space_groups[102] = sg
space_groups['P 42 n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(103, 'P 4 c c', transformations)
space_groups[103] = sg
space_groups['P 4 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(104, 'P 4 n c', transformations)
space_groups[104] = sg
space_groups['P 4 n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(105, 'P 42 m c', transformations)
space_groups[105] = sg
space_groups['P 42 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(106, 'P 42 b c', transformations)
space_groups[106] = sg
space_groups['P 42 b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(107, 'I 4 m m', transformations)
space_groups[107] = sg
space_groups['I 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(108, 'I 4 c m', transformations)
space_groups[108] = sg
space_groups['I 4 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(109, 'I 41 m d', transformations)
space_groups[109] = sg
space_groups['I 41 m d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(110, 'I 41 c d', transformations)
space_groups[110] = sg
space_groups['I 41 c d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(111, 'P -4 2 m', transformations)
space_groups[111] = sg
space_groups['P -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(112, 'P -4 2 c', transformations)
space_groups[112] = sg
space_groups['P -4 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(113, 'P -4 21 m', transformations)
space_groups[113] = sg
space_groups['P -4 21 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(114, 'P -4 21 c', transformations)
space_groups[114] = sg
space_groups['P -4 21 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(115, 'P -4 m 2', transformations)
space_groups[115] = sg
space_groups['P -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(116, 'P -4 c 2', transformations)
space_groups[116] = sg
space_groups['P -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(117, 'P -4 b 2', transformations)
space_groups[117] = sg
space_groups['P -4 b 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(118, 'P -4 n 2', transformations)
space_groups[118] = sg
space_groups['P -4 n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(119, 'I -4 m 2', transformations)
space_groups[119] = sg
space_groups['I -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(120, 'I -4 c 2', transformations)
space_groups[120] = sg
space_groups['I -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(121, 'I -4 2 m', transformations)
space_groups[121] = sg
space_groups['I -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(122, 'I -4 2 d', transformations)
space_groups[122] = sg
space_groups['I -4 2 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(123, 'P 4/m m m', transformations)
space_groups[123] = sg
space_groups['P 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(124, 'P 4/m c c', transformations)
space_groups[124] = sg
space_groups['P 4/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(125, 'P 4/n b m :2', transformations)
space_groups[125] = sg
space_groups['P 4/n b m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(126, 'P 4/n n c :2', transformations)
space_groups[126] = sg
space_groups['P 4/n n c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(127, 'P 4/m b m', transformations)
space_groups[127] = sg
space_groups['P 4/m b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(128, 'P 4/m n c', transformations)
space_groups[128] = sg
space_groups['P 4/m n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(129, 'P 4/n m m :2', transformations)
space_groups[129] = sg
space_groups['P 4/n m m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(130, 'P 4/n c c :2', transformations)
space_groups[130] = sg
space_groups['P 4/n c c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(131, 'P 42/m m c', transformations)
space_groups[131] = sg
space_groups['P 42/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(132, 'P 42/m c m', transformations)
space_groups[132] = sg
space_groups['P 42/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(133, 'P 42/n b c :2', transformations)
space_groups[133] = sg
space_groups['P 42/n b c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(134, 'P 42/n n m :2', transformations)
space_groups[134] = sg
space_groups['P 42/n n m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(135, 'P 42/m b c', transformations)
space_groups[135] = sg
space_groups['P 42/m b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(136, 'P 42/m n m', transformations)
space_groups[136] = sg
space_groups['P 42/m n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(137, 'P 42/n m c :2', transformations)
space_groups[137] = sg
space_groups['P 42/n m c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(138, 'P 42/n c m :2', transformations)
space_groups[138] = sg
space_groups['P 42/n c m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(139, 'I 4/m m m', transformations)
space_groups[139] = sg
space_groups['I 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(140, 'I 4/m c m', transformations)
space_groups[140] = sg
space_groups['I 4/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(141, 'I 41/a m d :2', transformations)
space_groups[141] = sg
space_groups['I 41/a m d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(142, 'I 41/a c d :2', transformations)
space_groups[142] = sg
space_groups['I 41/a c d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(143, 'P 3', transformations)
space_groups[143] = sg
space_groups['P 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(144, 'P 31', transformations)
space_groups[144] = sg
space_groups['P 31'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(145, 'P 32', transformations)
space_groups[145] = sg
space_groups['P 32'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(146, 'R 3 :H', transformations)
space_groups[146] = sg
space_groups['R 3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(147, 'P -3', transformations)
space_groups[147] = sg
space_groups['P -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(148, 'R -3 :H', transformations)
space_groups[148] = sg
space_groups['R -3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(149, 'P 3 1 2', transformations)
space_groups[149] = sg
space_groups['P 3 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(150, 'P 3 2 1', transformations)
space_groups[150] = sg
space_groups['P 3 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(151, 'P 31 1 2', transformations)
space_groups[151] = sg
space_groups['P 31 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(152, 'P 31 2 1', transformations)
space_groups[152] = sg
space_groups['P 31 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(153, 'P 32 1 2', transformations)
space_groups[153] = sg
space_groups['P 32 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(154, 'P 32 2 1', transformations)
space_groups[154] = sg
space_groups['P 32 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(155, 'R 3 2 :H', transformations)
space_groups[155] = sg
space_groups['R 3 2 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(156, 'P 3 m 1', transformations)
space_groups[156] = sg
space_groups['P 3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(157, 'P 3 1 m', transformations)
space_groups[157] = sg
space_groups['P 3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(158, 'P 3 c 1', transformations)
space_groups[158] = sg
space_groups['P 3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(159, 'P 3 1 c', transformations)
space_groups[159] = sg
space_groups['P 3 1 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(160, 'R 3 m :H', transformations)
space_groups[160] = sg
space_groups['R 3 m :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(161, 'R 3 c :H', transformations)
space_groups[161] = sg
space_groups['R 3 c :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(162, 'P -3 1 m', transformations)
space_groups[162] = sg
space_groups['P -3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(163, 'P -3 1 c', transformations)
space_groups[163] = sg
space_groups['P -3 1 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(164, 'P -3 m 1', transformations)
space_groups[164] = sg
space_groups['P -3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(165, 'P -3 c 1', transformations)
space_groups[165] = sg
space_groups['P -3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(166, 'R -3 m :H', transformations)
space_groups[166] = sg
space_groups['R -3 m :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(167, 'R -3 c :H', transformations)
space_groups[167] = sg
space_groups['R -3 c :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(168, 'P 6', transformations)
space_groups[168] = sg
space_groups['P 6'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(169, 'P 61', transformations)
space_groups[169] = sg
space_groups['P 61'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(170, 'P 65', transformations)
space_groups[170] = sg
space_groups['P 65'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(171, 'P 62', transformations)
space_groups[171] = sg
space_groups['P 62'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(172, 'P 64', transformations)
space_groups[172] = sg
space_groups['P 64'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(173, 'P 63', transformations)
space_groups[173] = sg
space_groups['P 63'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(174, 'P -6', transformations)
space_groups[174] = sg
space_groups['P -6'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(175, 'P 6/m', transformations)
space_groups[175] = sg
space_groups['P 6/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(176, 'P 63/m', transformations)
space_groups[176] = sg
space_groups['P 63/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(177, 'P 6 2 2', transformations)
space_groups[177] = sg
space_groups['P 6 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(178, 'P 61 2 2', transformations)
space_groups[178] = sg
space_groups['P 61 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(179, 'P 65 2 2', transformations)
space_groups[179] = sg
space_groups['P 65 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(180, 'P 62 2 2', transformations)
space_groups[180] = sg
space_groups['P 62 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(181, 'P 64 2 2', transformations)
space_groups[181] = sg
space_groups['P 64 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(182, 'P 63 2 2', transformations)
space_groups[182] = sg
space_groups['P 63 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(183, 'P 6 m m', transformations)
space_groups[183] = sg
space_groups['P 6 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(184, 'P 6 c c', transformations)
space_groups[184] = sg
space_groups['P 6 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(185, 'P 63 c m', transformations)
space_groups[185] = sg
space_groups['P 63 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(186, 'P 63 m c', transformations)
space_groups[186] = sg
space_groups['P 63 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(187, 'P -6 m 2', transformations)
space_groups[187] = sg
space_groups['P -6 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(188, 'P -6 c 2', transformations)
space_groups[188] = sg
space_groups['P -6 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(189, 'P -6 2 m', transformations)
space_groups[189] = sg
space_groups['P -6 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(190, 'P -6 2 c', transformations)
space_groups[190] = sg
space_groups['P -6 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(191, 'P 6/m m m', transformations)
space_groups[191] = sg
space_groups['P 6/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(192, 'P 6/m c c', transformations)
space_groups[192] = sg
space_groups['P 6/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(193, 'P 63/m c m', transformations)
space_groups[193] = sg
space_groups['P 63/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(194, 'P 63/m m c', transformations)
space_groups[194] = sg
space_groups['P 63/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(195, 'P 2 3', transformations)
space_groups[195] = sg
space_groups['P 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(196, 'F 2 3', transformations)
space_groups[196] = sg
space_groups['F 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(197, 'I 2 3', transformations)
space_groups[197] = sg
space_groups['I 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(198, 'P 21 3', transformations)
space_groups[198] = sg
space_groups['P 21 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(199, 'I 21 3', transformations)
space_groups[199] = sg
space_groups['I 21 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(200, 'P m -3', transformations)
space_groups[200] = sg
space_groups['P m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(201, 'P n -3 :2', transformations)
space_groups[201] = sg
space_groups['P n -3 :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(202, 'F m -3', transformations)
space_groups[202] = sg
space_groups['F m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(203, 'F d -3 :2', transformations)
space_groups[203] = sg
space_groups['F d -3 :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(204, 'I m -3', transformations)
space_groups[204] = sg
space_groups['I m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(205, 'P a -3', transformations)
space_groups[205] = sg
space_groups['P a -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(206, 'I a -3', transformations)
space_groups[206] = sg
space_groups['I a -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(207, 'P 4 3 2', transformations)
space_groups[207] = sg
space_groups['P 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(208, 'P 42 3 2', transformations)
space_groups[208] = sg
space_groups['P 42 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(209, 'F 4 3 2', transformations)
space_groups[209] = sg
space_groups['F 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(210, 'F 41 3 2', transformations)
space_groups[210] = sg
space_groups['F 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(211, 'I 4 3 2', transformations)
space_groups[211] = sg
space_groups['I 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(212, 'P 43 3 2', transformations)
space_groups[212] = sg
space_groups['P 43 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(213, 'P 41 3 2', transformations)
space_groups[213] = sg
space_groups['P 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(214, 'I 41 3 2', transformations)
space_groups[214] = sg
space_groups['I 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(215, 'P -4 3 m', transformations)
space_groups[215] = sg
space_groups['P -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(216, 'F -4 3 m', transformations)
space_groups[216] = sg
space_groups['F -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(217, 'I -4 3 m', transformations)
space_groups[217] = sg
space_groups['I -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(218, 'P -4 3 n', transformations)
space_groups[218] = sg
space_groups['P -4 3 n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(219, 'F -4 3 c', transformations)
space_groups[219] = sg
space_groups['F -4 3 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(220, 'I -4 3 d', transformations)
space_groups[220] = sg
space_groups['I -4 3 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(221, 'P m -3 m', transformations)
space_groups[221] = sg
space_groups['P m -3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(222, 'P n -3 n :2', transformations)
space_groups[222] = sg
space_groups['P n -3 n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = | N.array([0,0,0]) | numpy.array |
# coding: utf-8
#
# This code is part of lattpy.
#
# Copyright (c) 2021, <NAME>
#
# This code is licensed under the MIT License. The copyright notice in the
# LICENSE file in the root directory and this permission notice shall
# be included in all copies or substantial portions of the Software.
import numpy as np
import lattpy as lp
from numpy.testing import assert_array_equal, assert_array_almost_equal
from lattpy import Lattice
PI = np.pi
TWOPI = 2 * np.pi
chain = Lattice.chain(a=1.0)
rchain = Lattice(TWOPI)
square = Lattice.square(a=1.0)
rsquare = Lattice(TWOPI * np.eye(2))
rect = Lattice.rectangular(a1=2.0, a2=1.0)
rrect = Lattice(PI * np.array([[1, 0], [0, 2]]))
hexagonal = Lattice.hexagonal(a=1)
rhexagonal = Lattice(np.array([[+2.0943951, +3.62759873],
[+2.0943951, -3.62759873]]))
sc = Lattice.sc(a=1.0)
rsc = Lattice(TWOPI * np.eye(3))
fcc = Lattice.fcc(a=1.0)
rfcc = Lattice(TWOPI * np.array([[+1, +1, -1],
[+1, -1, +1],
[-1, +1, +1]]))
bcc = Lattice.bcc(a=1.0)
rbcc = Lattice(TWOPI * np.array([[+1, +1, 0],
[0, -1, +1],
[-1, 0, +1]]))
def test_is_reciprocal():
# Chain
rvecs = rchain.vectors
assert chain.is_reciprocal(rvecs)
assert not chain.is_reciprocal(-1 * rvecs)
assert not chain.is_reciprocal(+2 * rvecs)
assert not chain.is_reciprocal(0.5 * rvecs)
assert not chain.is_reciprocal(0.0 * rvecs)
# Square
rvecs = rsquare.vectors
assert square.is_reciprocal(rvecs)
assert not square.is_reciprocal(-1 * rvecs)
assert not square.is_reciprocal(+2 * rvecs)
assert not square.is_reciprocal(0.5 * rvecs)
assert not square.is_reciprocal(0.0 * rvecs)
# Rectangular
rvecs = rrect.vectors
assert rect.is_reciprocal(rvecs)
assert not rect.is_reciprocal(-1 * rvecs)
assert not rect.is_reciprocal(+2 * rvecs)
assert not rect.is_reciprocal(0.5 * rvecs)
assert not rect.is_reciprocal(0.0 * rvecs)
# Hexagonal
rvecs = rhexagonal.vectors
assert hexagonal.is_reciprocal(rvecs)
assert not hexagonal.is_reciprocal(-1 * rvecs)
assert not hexagonal.is_reciprocal(+2 * rvecs)
assert not hexagonal.is_reciprocal(0.5 * rvecs)
assert not hexagonal.is_reciprocal(0.0 * rvecs)
# Cubic
rvecs = rsc.vectors
assert sc.is_reciprocal(rvecs)
assert not sc.is_reciprocal(-1 * rvecs)
assert not sc.is_reciprocal(+2 * rvecs)
assert not sc.is_reciprocal(0.5 * rvecs)
assert not sc.is_reciprocal(0.0 * rvecs)
# Face-centerec-cudic (fcc)
rvecs = rfcc.vectors
assert fcc.is_reciprocal(rvecs)
assert not fcc.is_reciprocal(-1 * rvecs)
assert not fcc.is_reciprocal(+2 * rvecs)
assert not fcc.is_reciprocal(0.5 * rvecs)
assert not fcc.is_reciprocal(0.0 * rvecs)
# Body-centerec-cudic (bcc)
rvecs = rbcc.vectors
assert bcc.is_reciprocal(rvecs)
assert not bcc.is_reciprocal(-1 * rvecs)
assert not bcc.is_reciprocal(+2 * rvecs)
assert not bcc.is_reciprocal(0.5 * rvecs)
assert not bcc.is_reciprocal(0.0 * rvecs)
def test_reciprocal_vectors():
# Chain
expected = rchain.vectors
actual = chain.reciprocal_vectors()
assert_array_equal(expected, actual)
# Square
expected = rsquare.vectors
actual = square.reciprocal_vectors()
assert_array_equal(expected, actual)
# Rectangular
expected = rrect.vectors
actual = rect.reciprocal_vectors()
assert_array_equal(expected, actual)
# Hexagonal
expected = rhexagonal.vectors
actual = hexagonal.reciprocal_vectors()
assert_array_almost_equal(expected, actual)
# Cubic
expected = rsc.vectors
actual = sc.reciprocal_vectors()
assert_array_equal(expected, actual)
# Face-centerec-cudic (fcc)
expected = rfcc.vectors
actual = fcc.reciprocal_vectors()
assert_array_equal(expected, actual)
# Body-centerec-cudic (bcc)
expected = rbcc.vectors
actual = bcc.reciprocal_vectors()
assert_array_equal(expected, actual)
def test_reciprocal_vectors_double():
# Chain
expected = chain.vectors
actual = chain.reciprocal_lattice().reciprocal_vectors()
assert_array_equal(expected, actual)
# Square
expected = square.vectors
actual = square.reciprocal_lattice().reciprocal_vectors()
assert_array_equal(expected, actual)
# Rectangular
expected = rect.vectors
actual = rect.reciprocal_lattice().reciprocal_vectors()
assert_array_equal(expected, actual)
# Hexagonal
expected = hexagonal.vectors
actual = hexagonal.reciprocal_lattice().reciprocal_vectors()
assert_array_equal(expected, actual)
# Cubic
expected = sc.vectors
actual = sc.reciprocal_lattice().reciprocal_vectors()
assert_array_equal(expected, actual)
# Face-centerec-cudic (fcc)
expected = fcc.vectors
actual = fcc.reciprocal_lattice().reciprocal_vectors()
assert_array_equal(expected, actual)
# Body-centerec-cudic (bcc)
expected = bcc.vectors
actual = bcc.reciprocal_lattice().reciprocal_vectors()
assert_array_equal(expected, actual)
def test_translate():
# Square lattice
expected = [2.0, 0.0]
actual = square.translate([2, 0], [0.0, 0.0])
assert_array_equal(expected, actual)
expected = [0.0, 2.0]
actual = square.translate([0, 2], [0.0, 0.0])
assert_array_equal(expected, actual)
expected = [1.0, 2.0]
actual = square.translate([1, 2], [0.0, 0.0])
assert_array_equal(expected, actual)
# Rectangular lattice
expected = [4.0, 0.0]
actual = rect.translate([2, 0], [0.0, 0.0])
assert_array_equal(expected, actual)
expected = [0.0, 2.0]
actual = rect.translate([0, 2], [0.0, 0.0])
assert_array_equal(expected, actual)
expected = [2.0, 2.0]
actual = rect.translate([1, 2], [0.0, 0.0])
assert_array_equal(expected, actual)
def test_itranslate():
# Square lattice
expected = [2, 0], [0.0, 0.0]
actual = square.itranslate([2.0, 0.0])
assert_array_equal(expected, actual)
expected = [0, 2], [0.0, 0.0]
actual = square.itranslate([0.0, 2.0])
assert_array_equal(expected, actual)
expected = [1, 2], [0.0, 0.0]
actual = square.itranslate([1.0, 2.0])
assert_array_equal(expected, actual)
# Rectangular lattice
expected = [1, 0], [0.0, 0.0]
actual = rect.itranslate([2.0, 0.0])
| assert_array_equal(expected, actual) | numpy.testing.assert_array_equal |
import numpy as np
import csv
def get_model(model_name, power, test_window_size, power_window_size):
"""
get score of model
Args:
model_name: str, we use model_name to find the folder
power: ndarray, power of each fold to fuse
test_window_size: list, the window_size we selected to fuse
power_window_size: ndarray, power of each window_size to fuse
Returns:
score: score of model
"""
out = np.zeros((634, 30), dtype='float32')
power = power / power.sum()
power_window_size = power_window_size / power_window_size.sum()
for i in range(0, 5):
for j in range(0, len(test_window_size)):
path = "./output/%s_fold%s/score_%s.npy" % (model_name, i, test_window_size[j])
print(path)
data = np.load(path)
out = out + data * power[i] * power_window_size[j]
return out
def get_agcn():
model_name = 'AGCN'
power = np.array([1.5, 1, 1.5, 1, 2], dtype='float32')
test_window_size = [300, 350, 500]
power_window_size = np.array([1, 1, 1], dtype='float32')
return get_model(model_name, power, test_window_size, power_window_size)
def get_ctrgcn():
model_name = 'CTRGCN'
power = np.array([1, 1, 2, 2, 3], dtype='float32')
test_window_size = [300, 350, 450]
power_window_size = np.array([1, 1, 1], dtype='float32')
return get_model(model_name, power, test_window_size, power_window_size)
def get_ctrgcn2():
model_name = 'CTRGCN2'
power = np.array([1, 1, 2, 2, 3], dtype='float32')
test_window_size = [350]
power_window_size = np.array([1], dtype='float32')
return get_model(model_name, power, test_window_size, power_window_size)
def get_stgcn():
model_name = 'STGCN'
power = np.array([1, 1, 2, 1, 2], dtype='float32')
test_window_size = [350]
power_window_size = | np.array([1], dtype='float32') | numpy.array |
# Name: <NAME>
# Date: 2 March 2020
# Program: biot_helix.py
import numpy as np
import matplotlib.pyplot as plt
import time as time
from matplotlib.patches import Circle
def biot(Rvec, wire, I):
mu_4pi = 10
dB = np.zeros((len(wire), 3))
R = Rvec - wire
Rsqr = np.sum( R**2, axis = 1 )
dL = (np.roll(wire, -1, axis = 0) - np.roll(wire, +1, axis = 0))/2
cr = np.cross(dL, R, axis = 1 )
dB = mu_4pi * I * cr/Rsqr[:,None]**(3/2)
dB = np.concatenate((dB, [dB[0,:]]), axis = 0)
Btot = np.array([simpson(dB[:,0], 1), simpson(dB[:,1], 1), simpson(dB[:,2], 1)])
return Btot
def simpson(f, dr):
total = dr/3*(np.sum(f[1:] + f[:-1]) + 2*np.sum(f[1::2]))
return total
def trapz(f, dL):
return dL/2*np.sum(f[1:] + f[:-1])
# setting up the square loop of wire
I = 0.01 # current, in amperes
L = 0.20 # length of helix in m
N = 500 # number of segments per side of square
segL = L/N # segment length in m
turns = 20 # number of loops in helix
radius = 0.03
# some useful segments to build a position array of the segments in helical wire
helix_x = np.arange(-L/2, L/2, segL)
helix_y, helix_z = np.zeros(helix_x.size), np.zeros(helix_x.size)
theta_steps = N/turns
dtheta = 2*np.pi/theta_steps
for i in range (N):
helix_y[i] = -np.sin(i*dtheta)*radius
helix_z[i] = np.cos(i*dtheta)*radius
helix = np.column_stack((helix_x, helix_y, helix_z))
# test the biot function for a single point (the origin)
pointCalc = True
if pointCalc:
# choose a point in space at which to calculate B
point = np.array([0.1,0.0,0.0])
Ti = time.time()
# call the biot function to calculate B
B = biot(point, helix,I)
print(point)
print(B)
print("duration: %5f" % (time.time()-Ti) )
# Create a 2D grid of x, y points using numpy's meshgrid function
gridstep=50
nx, ny, nz = gridstep,gridstep,gridstep
x = np.linspace(-0.2, 0.2, nx)
y = np.linspace(-0.2, 0.2, ny)
z = np.linspace(-0.2, 0.2, nz)
fig = plt.figure(figsize = (18,6))
ax1 = fig.add_subplot(2, 3, 1)
ax2 = fig.add_subplot(2, 3, 2)
ax3 = fig.add_subplot(2, 3, 3)
# Set up meshgrid as needed for the particular 2D streamplot
X, Z = np.meshgrid(x,z)
# Set up 3D array, Bgrid, for x,y,z-components of B at points in space
Bgrid = np.zeros([nx,nz,3])
Ti = time.time()
# Use for loops to populate Bgrid array with relevant B-field values
# XZ Plane
for i in range(nx):
for k in range(nz):
Bgrid[k,i, :] = biot(np.array([x[i],0.,z[k]]),helix,I)
# XY Plane
for i in range(nx):
for k in range(nz):
Bgrid[k,i, :] = biot( | np.array([x[i],y[k],0.0]) | numpy.array |
"""
Revised by <NAME>
Code reference
<NAME>, <NAME>, <NAME>, and <NAME>. Inducing Domain-Specific Sentiment Lexicons from
Unlabeled Corpora. Proceedings of EMNLP. 2016. (to appear; arXiv:1606.02820).
"""
import random
import time
import codecs
import numpy as np
import config
import embedding
import base_words
from transformation_method import densify
from sklearn.metrics import roc_auc_score, average_precision_score
start_time = time.time()
DEFAULT_ARGUMENTS = dict(
# for iterative graph algorithms
similarity_power=1,
arccos=True,
max_iter=50,
epsilon=1e-6,
sym=True,
# for learning embeddings transformation
n_epochs=50,
force_orthogonal=False,
batch_size=100,
cosine=False,
## bootstrap
num_boots=1,
n_procs=1,
)
def generate_random_seeds(lexicon, num=10):
items = lexicon.items()
pos_items = [item for item in items if item[1] == 1]
neg_items = [item for item in items if item[1] == -1]
pos_seeds, _ = zip(*(random.sample(pos_items, num)))
neg_seeds, _ = zip(*(random.sample(neg_items, num)))
return pos_seeds, neg_seeds
def generate_random_seeds_imbalanced(lexicon, num=10, num2=10):
items = lexicon.items()
pos_items = [item for item in items if item[1] == 1]
neg_items = [item for item in items if item[1] == -1]
pos_seeds, _ = zip(*(random.sample(pos_items, num)))
neg_seeds, _ = zip(*(random.sample(neg_items, num2)))
return pos_seeds, neg_seeds
def top_n_words(score_dict, eval_words, scope, n=10):
sorted_list = sorted(score_dict.items(),
key=lambda item: -item[1]) # not use np.linalg.norm(item[1]). polarities are ignored.
top_n_pos, top_n_neg = [], []
count = 0
for i, (word, value) in enumerate(sorted_list):
if count < n and word in eval_words:
top_n_pos.append((word, value))
count += 1
count = 0
for i, (word, value) in enumerate(sorted_list[::-1]):
if count < n and word in eval_words:
top_n_neg.append((word, value))
count += 1
print("top{} {} / {}: {} / {}".format(n, scope[0], scope[1], top_n_pos, top_n_neg))
def mitigate_embedding():
print("Getting evaluation words and embeddings... in {:.2f} sec".format(config.whattime()))
print("Input: {} / Output: {}".format(config.WORD_EMBEDDING_NAME, config.MITIGATED_EMBEDDING_NAME))
lexicon = config.load_sent_lexicon()
eval_words = set(lexicon.keys())
lexicon2, lexicon2_vocab = config.load_entity_lexicon()
eval_words2 = set(lexicon2.keys())
num = int(config.BASE_WORD_NUM)
if not config.RANDOM_BASE_WORDS:
positive_seeds, negative_seeds = base_words.sent_seeds(num)
entity_seeds, notity_seeds = base_words.entity_seeds(num)
else:
positive_seeds, negative_seeds = generate_random_seeds(lexicon, num=num)
if config.UNBALANCED_BASE_WORDS:
entity_seeds, notity_seeds = generate_random_seeds_imbalanced(lexicon2, num=num, num2=3 * num)
else:
entity_seeds, notity_seeds = generate_random_seeds(lexicon2, num=num)
print('pos / neg = {} / {}'.format(positive_seeds, negative_seeds))
print('entity / notity = {} / {}'.format(entity_seeds, notity_seeds))
common_embed = embedding.WordEmbedding(config.WORD_EMBEDDING_NAME,
eval_words.union(positive_seeds).union(negative_seeds).union(eval_words2))
print("Complete to load original embedding... in {:.2f} sec".format(config.whattime()))
common_words = set(common_embed.iw)
eval_words = eval_words.intersection(common_words)
eval_words2 = eval_words2.intersection(common_words)
eval_words = [word for word in eval_words if not word in positive_seeds and not word in negative_seeds]
eval_words2 = [word for word in eval_words2 if not word in entity_seeds and not word in notity_seeds]
print("Generate a word embedding... in {:.2f} sec".format(time.time() - start_time))
polarities, entities = run_method(positive_seeds, negative_seeds, entity_seeds, notity_seeds,
common_embed.get_subembed(
set(eval_words).union(negative_seeds).union(positive_seeds).union(
eval_words2).union(entity_seeds).union(notity_seeds)),
method=densify,
lr=0.001, regularization_strength=0.001, lexicon2_vocab=lexicon2_vocab,
**DEFAULT_ARGUMENTS)
with codecs.open(config.MITIGATED_EMBEDDING_INFO, "w", encoding='utf-8', errors='ignore') as f:
evaluate(polarities, lexicon, eval_words, f, scope=('pos', 'neg'))
evaluate(entities, lexicon2, eval_words2, f, scope=('entity', 'notity'))
print("Program end... in {:.2f} sec".format(config.whattime()))
def run_method(positive_seeds, negative_seeds, entity_seeds, notity_seeds, embeddings,
method=densify, lexicon2_vocab={}, **kwargs):
positive_seeds = [s for s in positive_seeds if s in embeddings]
negative_seeds = [s for s in negative_seeds if s in embeddings]
entity_seeds = [s for s in entity_seeds if s in embeddings]
notity_seeds = [s for s in notity_seeds if s in embeddings]
return method(embeddings, positive_seeds, negative_seeds, entity_seeds, notity_seeds, lexicon2_vocab=lexicon2_vocab,
**kwargs)
def evaluate(polarities, lexicon, eval_words, f, scope=('pos', 'neg')):
acc, auc, avg_prec, cutoff = binary_metrics(polarities, lexicon, eval_words)
space_order = 1
if auc < 0.5:
polarities = {word: -1 * polarities[word] for word in polarities}
acc, auc, avg_prec, cutoff = binary_metrics(polarities, lexicon, eval_words)
space_order = -1
top_n_words(polarities, eval_words, scope)
f.write('{} / {} cutoff:{} with space_order: {}\n'.format(scope[0], scope[1], cutoff, space_order))
print("{} / {} cutoff: {} with space_order: {}".format(scope[0], scope[1], cutoff, space_order))
print("Binary metrics:")
print("==============")
print("Accuracy with optimal threshold: {:.4f}".format(acc))
print("ROC AUC Score: {:.4f}".format(auc))
print("Average Precision Score: {:.4f}".format(avg_prec))
def binary_metrics(polarities, lexicon, eval_words, top_perc=None):
eval_words = [word for word in eval_words if lexicon[word] != 0]
y_prob, y_true = [], []
if top_perc:
polarities = {word: polarities[word] for word in
sorted(eval_words, key=lambda w: abs(polarities[w] - 0.5), reverse=True)[
:int(top_perc * len(polarities))]}
else:
polarities = {word: polarities[word] for word in eval_words}
for w in polarities:
y_prob.append(polarities[w])
y_true.append((1 + lexicon[w]) / 2)
n = len(y_true)
ordered_labels = [y_true[i] for i in sorted(range(n), key=lambda i: y_prob[i])]
positive = sum(ordered_labels)
cumsum = | np.cumsum(ordered_labels) | numpy.cumsum |
#!/usr/bin/env python
# coding:utf-8
"""
Author : <NAME>
Contact : <EMAIL>
"""
import os
import sys
import cv2
import time
# import gtts
import numpy as np
import pandas as pd
import mediapipe as mp
import tensorflow as tf
from datetime import datetime
from playsound import playsound
from goprocam import GoProCamera, constants
from PySide6.QtCore import QThread, Signal, Slot, QAbstractTableModel, Qt, QModelIndex
from PySide6.QtGui import QAction, QImage, QKeySequence, QPixmap
from PySide6.QtWidgets import (QApplication, QComboBox, QGroupBox, QHBoxLayout, QLabel, QMainWindow, QPushButton,
QSizePolicy, QVBoxLayout, QWidget, QStatusBar, QToolBar, QTableView, QHeaderView)
class KeepAliveThread(QThread):
def __init__(self, parent=None):
QThread.__init__(self, parent)
self.gopro = GoProCamera.GoPro()
def run(self):
self.gopro.stream("udp://127.0.0.1:10000")
class InferThread(QThread):
updateFrame = Signal(QImage)
updateText = Signal(str)
updateTable = Signal(dict)
def __init__(self, parent=None):
QThread.__init__(self, parent)
self.interpreter = None
self.signatures = None
self.input_index = None
self.output_index = None
self.status = True
self.cap = True
self.actions = {0: 'None', 1: 'Start', 2: 'Stop'}
self.goproCamera = GoProCamera.GoPro()
self.tracking = False
# tts = gtts.gTTS("Enregistrement", lang="fr")
# tts.save("tts.mp3")
def print_config(self):
info = self.goproCamera.infoCamera()
self.updateText.emit("Streaming {} ({})".format(info['model_name'], info['serial_number']))
def print_message(self, message):
self.updateText.emit(message)
def set_file(self, fname):
self.interpreter = tf.lite.Interpreter(model_path=fname)
self.interpreter.allocate_tensors()
self.signatures = self.interpreter.get_signature_list()
self.input_index = self.interpreter.get_input_details()[0]["index"]
self.output_index = self.interpreter.get_output_details()[0]["index"]
self.updateText.emit("Model loaded: {}".format(fname))
def run(self):
self.cap = cv2.VideoCapture("udp://127.0.0.1:10000?overrun_nonfatal=1&fifo_size=300000", cv2.CAP_FFMPEG)
while self.status:
tracking_start = None
with mp.solutions.hands.Hands(model_complexity=0, min_detection_confidence=0.5,
min_tracking_confidence=0.5) as hands:
while self.cap.isOpened():
success, image = self.cap.read()
if not success:
print("Ignoring empty camera frame.")
else:
image.flags.writeable = False
image = cv2.cvtColor(image, cv2.COLOR_BGR2RGB)
results = hands.process(image)
image.flags.writeable = True
image = cv2.cvtColor(image, cv2.COLOR_RGB2BGR)
h, w, c = image.shape
frame_landmarks = np.zeros(shape=(42, 3))
if results.multi_hand_landmarks:
if 0 < len(results.multi_hand_landmarks) < 3:
for j, hand in enumerate(results.multi_hand_landmarks):
for i, landmark in enumerate(hand.landmark):
frame_landmarks[21 * j + i][0] = int(landmark.x * w)
frame_landmarks[21 * j + i][1] = int(landmark.y * h)
frame_landmarks[21 * j + i][2] = landmark.z * w
_max = np.amax(frame_landmarks, axis=0)
_min = np.amin(frame_landmarks, axis=0)
frame_landmarks[:, -1] = 255 * ((frame_landmarks[:, -1] - _min[-1]
) / (_max[-1] - _min[-1]))
for lm in frame_landmarks:
cv2.circle(image, (int(lm[0]), int(lm[1])), 8, thickness=-1, color=[lm[2]] * 3)
_max1 = np.amax(frame_landmarks[:21], axis=0)
_min1 = np.amin(frame_landmarks[:21], axis=0)
cv2.rectangle(image, (int(_min1[0]), int(_min1[1])), (int(_max1[0]), int(_max1[1])),
(255, 0, 0), 3)
_max2 = np.amax(frame_landmarks[21:], axis=0)
_min2 = np.amin(frame_landmarks[21:], axis=0)
cv2.rectangle(image, (int(_min2[0]), int(_min2[1])), (int(_max2[0]), int(_max2[1])),
(255, 0, 0), 3)
frame_landmarks -= frame_landmarks[0]
to_predict = frame_landmarks[:21, :2].flatten()
self.interpreter.set_tensor(self.input_index, np.expand_dims(to_predict,
axis=0).astype(np.float32))
self.interpreter.invoke()
predict_result = self.interpreter.get_tensor(self.output_index)[0]
cv2.putText(image, self.actions[np.argmax(predict_result)], _min1[:2].astype(np.uint16),
cv2.FONT_HERSHEY_SIMPLEX, 1, (0, 255, 0), 3)
to_predict = frame_landmarks[21:, :2].flatten()
self.interpreter.set_tensor(self.input_index,
np.expand_dims(to_predict, axis=0).astype(np.float32))
self.interpreter.invoke()
predict_result2 = self.interpreter.get_tensor(self.output_index)[0]
cv2.putText(image, self.actions[np.argmax(predict_result2)], _min2[:2].astype(np.uint16),
cv2.FONT_HERSHEY_SIMPLEX, 1, (0, 255, 0), 3)
if (np.argmax(predict_result2) == 1 or np.argmax(predict_result) == 1) and not self.tracking:
playsound("resources/tts.mp3", block=False)
tracking_start = datetime.now()
self.print_message("Tracking started at {}".format(tracking_start))
self.tracking = True
elif (np.argmax(predict_result2) == 2 or | np.argmax(predict_result) | numpy.argmax |
"""
Linear mixed effects models for Statsmodels
The data are partitioned into disjoint groups. The probability model
for group i is:
Y = X*beta + Z*gamma + epsilon
where
* n_i is the number of observations in group i
* Y is a n_i dimensional response vector
* X is a n_i x k_fe design matrix for the fixed effects
* beta is a k_fe-dimensional vector of fixed effects slopes
* Z is a n_i x k_re design matrix for the random effects
* gamma is a k_re-dimensional random vector with mean 0
and covariance matrix Psi; note that each group
gets its own independent realization of gamma.
* epsilon is a n_i dimensional vector of iid normal
errors with mean 0 and variance sigma^2; the epsilon
values are independent both within and between groups
Y, X and Z must be entirely observed. beta, Psi, and sigma^2 are
estimated using ML or REML estimation, and gamma and epsilon are
random so define the probability model.
The mean structure is E[Y|X,Z] = X*beta. If only the mean structure
is of interest, GEE is a good alternative to mixed models.
The primary reference for the implementation details is:
<NAME>, <NAME> (1988). "Newton Raphson and EM algorithms for
linear mixed effects models for repeated measures data". Journal of
the American Statistical Association. Volume 83, Issue 404, pages
1014-1022.
See also this more recent document:
http://econ.ucsb.edu/~doug/245a/Papers/Mixed%20Effects%20Implement.pdf
All the likelihood, gradient, and Hessian calculations closely follow
Lindstrom and Bates.
The following two documents are written more from the perspective of
users:
http://lme4.r-forge.r-project.org/lMMwR/lrgprt.pdf
http://lme4.r-forge.r-project.org/slides/2009-07-07-Rennes/3Longitudinal-4.pdf
Notation:
* `cov_re` is the random effects covariance matrix (referred to above
as Psi) and `scale` is the (scalar) error variance. For a single
group, the marginal covariance matrix of endog given exog is scale*I
+ Z * cov_re * Z', where Z is the design matrix for the random
effects in one group.
Notes:
1. Three different parameterizations are used here in different
places. The regression slopes (usually called `fe_params`) are
identical in all three parameterizations, but the variance parameters
differ. The parameterizations are:
* The "natural parameterization" in which cov(endog) = scale*I + Z *
cov_re * Z', as described above. This is the main parameterization
visible to the user.
* The "profile parameterization" in which cov(endog) = I +
Z * cov_re1 * Z'. This is the parameterization of the profile
likelihood that is maximized to produce parameter estimates.
(see Lindstrom and Bates for details). The "natural" cov_re is
equal to the "profile" cov_re1 times scale.
* The "square root parameterization" in which we work with the
Cholesky factor of cov_re1 instead of cov_re1 directly.
All three parameterizations can be "packed" by concatenating fe_params
together with the lower triangle of the dependence structure. Note
that when unpacking, it is important to either square or reflect the
dependence structure depending on which parameterization is being
used.
2. The situation where the random effects covariance matrix is
singular is numerically challenging. Small changes in the covariance
parameters may lead to large changes in the likelihood and
derivatives.
3. The optimization strategy is to first use OLS to get starting
values for the mean structure. Then we optionally perform a few EM
steps, followed by optionally performing a few steepest ascent steps.
This is followed by conjugate gradient optimization using one of the
scipy gradient optimizers. The EM and steepest ascent steps are used
to get adequate starting values for the conjugate gradient
optimization, which is much faster.
"""
import numpy as np
import statsmodels.base.model as base
from scipy.optimize import fmin_ncg, fmin_cg, fmin_bfgs, fmin
from statsmodels.tools.decorators import cache_readonly
from scipy.stats.distributions import norm
import pandas as pd
import patsy
from statsmodels.compat.collections import OrderedDict
from statsmodels.compat import range
import warnings
from statsmodels.tools.sm_exceptions import ConvergenceWarning
from statsmodels.base._penalties import Penalty
from statsmodels.compat.numpy import np_matrix_rank
from pandas import DataFrame
def _get_exog_re_names(exog_re):
if isinstance(exog_re, (pd.Series, pd.DataFrame)):
return exog_re.columns.tolist()
return ["Z{0}".format(k + 1) for k in range(exog_re.shape[1])]
class MixedLMParams(object):
"""
This class represents a parameter state for a mixed linear model.
Parameters
----------
k_fe : integer
The number of covariates with fixed effects.
k_re : integer
The number of covariates with random effects.
use_sqrt : boolean
If True, the covariance matrix is stored using as the lower
triangle of its Cholesky square root, otherwise it is stored
as the lower triangle of the covariance matrix.
Notes
-----
This object represents the parameter state for the model in which
the scale parameter has been profiled out.
"""
def __init__(self, k_fe, k_re, use_sqrt=True):
self.k_fe = k_fe
self.k_re = k_re
self.k_re2 = k_re * (k_re + 1) / 2
self.k_tot = self.k_fe + self.k_re2
self.use_sqrt = use_sqrt
self._ix = np.tril_indices(self.k_re)
self._params = np.zeros(self.k_tot)
def from_packed(params, k_fe, use_sqrt):
"""
Factory method to create a MixedLMParams object based on the
given packed parameter vector.
Parameters
----------
params : array-like
The mode parameters packed into a single vector.
k_fe : integer
The number of covariates with fixed effects
use_sqrt : boolean
If True, the random effects covariance matrix is stored as
its Cholesky factor, otherwise the lower triangle of the
covariance matrix is stored.
Returns
-------
A MixedLMParams object.
"""
k_re2 = len(params) - k_fe
k_re = (-1 + np.sqrt(1 + 8*k_re2)) / 2
if k_re != int(k_re):
raise ValueError("Length of `packed` not compatible with value of `fe`.")
k_re = int(k_re)
pa = MixedLMParams(k_fe, k_re, use_sqrt)
pa.set_packed(params)
return pa
from_packed = staticmethod(from_packed)
def from_components(fe_params, cov_re=None, cov_re_sqrt=None,
use_sqrt=True):
"""
Factory method to create a MixedLMParams object from given
values for each parameter component.
Parameters
----------
fe_params : array-like
The fixed effects parameter (a 1-dimensional array).
cov_re : array-like
The random effects covariance matrix (a square, symmetric
2-dimensional array).
cov_re_sqrt : array-like
The Cholesky (lower triangular) square root of the random
effects covariance matrix.
use_sqrt : boolean
If True, the random effects covariance matrix is stored as
the lower triangle of its Cholesky factor, otherwise the
lower triangle of the covariance matrix is stored.
Returns
-------
A MixedLMParams object.
"""
k_fe = len(fe_params)
k_re = cov_re.shape[0]
pa = MixedLMParams(k_fe, k_re, use_sqrt)
pa.set_fe_params(fe_params)
pa.set_cov_re(cov_re)
return pa
from_components = staticmethod(from_components)
def copy(self):
"""
Returns a copy of the object.
"""
obj = MixedLMParams(self.k_fe, self.k_re, self.use_sqrt)
obj.set_packed(self.get_packed().copy())
return obj
def get_packed(self, use_sqrt=None):
"""
Returns the model parameters packed into a single vector.
Parameters
----------
use_sqrt : None or bool
If None, `use_sqrt` has the value of this instance's
`use_sqrt`. Otherwise it is set to the given value.
"""
if (use_sqrt is None) or (use_sqrt == self.use_sqrt):
return self._params
pa = self._params.copy()
cov_re = self.get_cov_re()
if use_sqrt:
L = np.linalg.cholesky(cov_re)
pa[self.k_fe:] = L[self._ix]
else:
pa[self.k_fe:] = cov_re[self._ix]
return pa
def set_packed(self, params):
"""
Sets the packed parameter vector to the given vector, without
any validity checking.
"""
self._params = params
def get_fe_params(self):
"""
Returns the fixed effects paramaters as a ndarray.
"""
return self._params[0:self.k_fe]
def set_fe_params(self, fe_params):
"""
Set the fixed effect parameters to the given vector.
"""
self._params[0:self.k_fe] = fe_params
def set_cov_re(self, cov_re=None, cov_re_sqrt=None):
"""
Set the random effects covariance matrix to the given value.
Parameters
----------
cov_re : array-like
The random effects covariance matrix.
cov_re_sqrt : array-like
The Cholesky square root of the random effects covariance
matrix. Only the lower triangle is read.
Notes
-----
The first of `cov_re` and `cov_re_sqrt` that is not None is
used.
"""
if cov_re is not None:
if self.use_sqrt:
cov_re_sqrt = np.linalg.cholesky(cov_re)
self._params[self.k_fe:] = cov_re_sqrt[self._ix]
else:
self._params[self.k_fe:] = cov_re[self._ix]
elif cov_re_sqrt is not None:
if self.use_sqrt:
self._params[self.k_fe:] = cov_re_sqrt[self._ix]
else:
cov_re = np.dot(cov_re_sqrt, cov_re_sqrt.T)
self._params[self.k_fe:] = cov_re[self._ix]
def get_cov_re(self):
"""
Returns the random effects covariance matrix.
"""
pa = self._params[self.k_fe:]
cov_re = np.zeros((self.k_re, self.k_re))
cov_re[self._ix] = pa
if self.use_sqrt:
cov_re = np.dot(cov_re, cov_re.T)
else:
cov_re = (cov_re + cov_re.T) - np.diag(np.diag(cov_re))
return cov_re
# This is a global switch to use direct linear algebra calculations
# for solving factor-structured linear systems and calculating
# factor-structured determinants. If False, use the
# Sherman-Morrison-Woodbury update which is more efficient for
# factor-structured matrices. Should be False except when testing.
_no_smw = False
def _smw_solve(s, A, AtA, B, BI, rhs):
"""
Solves the system (s*I + A*B*A') * x = rhs for x and returns x.
Parameters
----------
s : scalar
See above for usage
A : square symmetric ndarray
See above for usage
AtA : square ndarray
A.T * A
B : square symmetric ndarray
See above for usage
BI : square symmetric ndarray
The inverse of `B`. Can be None if B is singular
rhs : ndarray
See above for usage
Returns
-------
x : ndarray
See above
If the global variable `_no_smw` is True, this routine uses direct
linear algebra calculations. Otherwise it uses the
Sherman-Morrison-Woodbury identity to speed up the calculation.
"""
# Direct calculation
if _no_smw or BI is None:
mat = np.dot(A, np.dot(B, A.T))
# Add constant to diagonal
mat.flat[::mat.shape[0]+1] += s
return np.linalg.solve(mat, rhs)
# Use SMW identity
qmat = BI + AtA / s
u = np.dot(A.T, rhs)
qmat = np.linalg.solve(qmat, u)
qmat = np.dot(A, qmat)
rslt = rhs / s - qmat / s**2
return rslt
def _smw_logdet(s, A, AtA, B, BI, B_logdet):
"""
Use the matrix determinant lemma to accelerate the calculation of
the log determinant of s*I + A*B*A'.
Parameters
----------
s : scalar
See above for usage
A : square symmetric ndarray
See above for usage
AtA : square matrix
A.T * A
B : square symmetric ndarray
See above for usage
BI : square symmetric ndarray
The inverse of `B`; can be None if B is singular.
B_logdet : real
The log determinant of B
Returns
-------
The log determinant of s*I + A*B*A'.
"""
p = A.shape[0]
if _no_smw or BI is None:
mat = np.dot(A, np.dot(B, A.T))
# Add constant to diagonal
mat.flat[::p+1] += s
_, ld = np.linalg.slogdet(mat)
return ld
ld = p * np.log(s)
qmat = BI + AtA / s
_, ld1 = np.linalg.slogdet(qmat)
return B_logdet + ld + ld1
class MixedLM(base.LikelihoodModel):
"""
An object specifying a linear mixed effects model. Use the `fit`
method to fit the model and obtain a results object.
Parameters
----------
endog : 1d array-like
The dependent variable
exog : 2d array-like
A matrix of covariates used to determine the
mean structure (the "fixed effects" covariates).
groups : 1d array-like
A vector of labels determining the groups -- data from
different groups are independent
exog_re : 2d array-like
A matrix of covariates used to determine the variance and
covariance structure (the "random effects" covariates). If
None, defaults to a random intercept for each group.
use_sqrt : bool
If True, optimization is carried out using the lower
triangle of the square root of the random effects
covariance matrix, otherwise it is carried out using the
lower triangle of the random effects covariance matrix.
missing : string
The approach to missing data handling
Notes
-----
The covariates in `exog` and `exog_re` may (but need not)
partially or wholly overlap.
`use_sqrt` should almost always be set to True. The main use case
for use_sqrt=False is when complicated patterns of fixed values in
the covariance structure are set (using the `free` argument to
`fit`) that cannot be expressed in terms of the Cholesky factor L.
"""
def __init__(self, endog, exog, groups, exog_re=None,
use_sqrt=True, missing='none', **kwargs):
self.use_sqrt = use_sqrt
# Some defaults
self.reml = True
self.fe_pen = None
self.re_pen = None
# If there is one covariate, it may be passed in as a column
# vector, convert these to 2d arrays.
# TODO: Can this be moved up in the class hierarchy?
# yes, it should be done up the hierarchy
if exog is not None and exog.ndim == 1:
exog = exog[:,None]
if exog_re is not None and exog_re.ndim == 1:
exog_re = exog_re[:,None]
# Calling super creates self.endog, etc. as ndarrays and the
# original exog, endog, etc. are self.data.endog, etc.
super(MixedLM, self).__init__(endog, exog, groups=groups,
exog_re=exog_re, missing=missing,
**kwargs)
self.k_fe = exog.shape[1] # Number of fixed effects parameters
if exog_re is None:
# Default random effects structure (random intercepts).
self.k_re = 1
self.k_re2 = 1
self.exog_re = np.ones((len(endog), 1), dtype=np.float64)
self.data.exog_re = self.exog_re
self.data.param_names = self.exog_names + ['Intercept']
else:
# Process exog_re the same way that exog is handled
# upstream
# TODO: this is wrong and should be handled upstream wholly
self.data.exog_re = exog_re
self.exog_re = np.asarray(exog_re)
if not self.data._param_names:
# HACK: could've been set in from_formula already
# needs refactor
(self.data.param_names,
self.data.exog_re_names) = self._make_param_names(exog_re)
# Model dimensions
# Number of random effect covariates
self.k_re = exog_re.shape[1]
# Number of covariance parameters
self.k_re2 = self.k_re * (self.k_re + 1) // 2
self.k_params = self.k_fe + self.k_re2
# Convert the data to the internal representation, which is a
# list of arrays, corresponding to the groups.
group_labels = list(set(groups))
group_labels.sort()
row_indices = dict((s, []) for s in group_labels)
for i,g in enumerate(groups):
row_indices[g].append(i)
self.row_indices = row_indices
self.group_labels = group_labels
self.n_groups = len(self.group_labels)
# Split the data by groups
self.endog_li = self.group_list(self.endog)
self.exog_li = self.group_list(self.exog)
self.exog_re_li = self.group_list(self.exog_re)
# Precompute this.
self.exog_re2_li = [np.dot(x.T, x) for x in self.exog_re_li]
# The total number of observations, summed over all groups
self.n_totobs = sum([len(y) for y in self.endog_li])
# why do it like the above?
self.nobs = len(self.endog)
# Set the fixed effects parameter names
if self.exog_names is None:
self.exog_names = ["FE%d" % (k + 1) for k in
range(self.exog.shape[1])]
def _make_param_names(self, exog_re):
exog_names = list(self.exog_names)
exog_re_names = _get_exog_re_names(exog_re)
param_names = []
jj = self.k_fe
for i in range(exog_re.shape[1]):
for j in range(i + 1):
if i == j:
param_names.append(exog_re_names[i] + " RE")
else:
param_names.append(exog_re_names[j] + " x " +
exog_re_names[i] + " RE")
jj += 1
return exog_names + exog_re_names, exog_re_names
@classmethod
def from_formula(cls, formula, data, re_formula=None, subset=None,
*args, **kwargs):
"""
Create a Model from a formula and dataframe.
Parameters
----------
formula : str or generic Formula object
The formula specifying the model
data : array-like
The data for the model. See Notes.
re_formula : string
A one-sided formula defining the variance structure of the
model. The default gives a random intercept for each
group.
subset : array-like
An array-like object of booleans, integers, or index
values that indicate the subset of df to use in the
model. Assumes df is a `pandas.DataFrame`
args : extra arguments
These are passed to the model
kwargs : extra keyword arguments
These are passed to the model with one exception. The
``eval_env`` keyword is passed to patsy. It can be either a
:class:`patsy:patsy.EvalEnvironment` object or an integer
indicating the depth of the namespace to use. For example, the
default ``eval_env=0`` uses the calling namespace. If you wish
to use a "clean" environment set ``eval_env=-1``.
Returns
-------
model : Model instance
Notes
------
`data` must define __getitem__ with the keys in the formula
terms args and kwargs are passed on to the model
instantiation. E.g., a numpy structured or rec array, a
dictionary, or a pandas DataFrame.
If `re_formula` is not provided, the default is a random
intercept for each group.
This method currently does not correctly handle missing
values, so missing values should be explicitly dropped from
the DataFrame before calling this method.
"""
if "groups" not in kwargs.keys():
raise AttributeError("'groups' is a required keyword argument in MixedLM.from_formula")
# If `groups` is a variable name, retrieve the data for the
# groups variable.
if type(kwargs["groups"]) == str:
kwargs["groups"] = np.asarray(data[kwargs["groups"]])
if re_formula is not None:
eval_env = kwargs.get('eval_env', None)
if eval_env is None:
eval_env = 1
elif eval_env == -1:
from patsy import EvalEnvironment
eval_env = EvalEnvironment({})
exog_re = patsy.dmatrix(re_formula, data, eval_env=eval_env)
exog_re_names = exog_re.design_info.column_names
exog_re = np.asarray(exog_re)
else:
exog_re = np.ones((data.shape[0], 1),
dtype=np.float64)
exog_re_names = ["Intercept RE"]
mod = super(MixedLM, cls).from_formula(formula, data,
subset=None,
exog_re=exog_re,
*args, **kwargs)
mod.data.param_names = mod.exog_names + exog_re_names
mod.data.exog_re_names = exog_re_names
return mod
def group_list(self, array):
"""
Returns `array` split into subarrays corresponding to the
grouping structure.
"""
if array.ndim == 1:
return [np.array(array[self.row_indices[k]])
for k in self.group_labels]
else:
return [np.array(array[self.row_indices[k], :])
for k in self.group_labels]
def fit_regularized(self, start_params=None, method='l1', alpha=0,
ceps=1e-4, ptol=1e-6, maxit=200, **fit_kwargs):
"""
Fit a model in which the fixed effects parameters are
penalized. The dependence parameters are held fixed at their
estimated values in the unpenalized model.
Parameters
----------
method : string of Penalty object
Method for regularization. If a string, must be 'l1'.
alpha : array-like
Scalar or vector of penalty weights. If a scalar, the
same weight is applied to all coefficients; if a vector,
it contains a weight for each coefficient. If method is a
Penalty object, the weights are scaled by alpha. For L1
regularization, the weights are used directly.
ceps : positive real scalar
Fixed effects parameters smaller than this value
in magnitude are treaded as being zero.
ptol : positive real scalar
Convergence occurs when the sup norm difference
between successive values of `fe_params` is less than
`ptol`.
maxit : integer
The maximum number of iterations.
fit_kwargs : keywords
Additional keyword arguments passed to fit.
Returns
-------
A MixedLMResults instance containing the results.
Notes
-----
The covariance structure is not updated as the fixed effects
parameters are varied.
The algorithm used here for L1 regularization is a"shooting"
or cyclic coordinate descent algorithm.
If method is 'l1', then `fe_pen` and `cov_pen` are used to
obtain the covariance structure, but are ignored during the
L1-penalized fitting.
References
----------
<NAME>., <NAME>. and <NAME>. Regularized
Paths for Generalized Linear Models via Coordinate
Descent. Journal of Statistical Software, 33(1) (2008)
http://www.jstatsoft.org/v33/i01/paper
http://statweb.stanford.edu/~tibs/stat315a/Supplements/fuse.pdf
"""
if type(method) == str and (method.lower() != 'l1'):
raise ValueError("Invalid regularization method")
# If method is a smooth penalty just optimize directly.
if isinstance(method, Penalty):
# Scale the penalty weights by alpha
method.alpha = alpha
fit_kwargs.update({"fe_pen": method})
return self.fit(**fit_kwargs)
if np.isscalar(alpha):
alpha = alpha * np.ones(self.k_fe, dtype=np.float64)
# Fit the unpenalized model to get the dependence structure.
mdf = self.fit(**fit_kwargs)
fe_params = mdf.fe_params
cov_re = mdf.cov_re
scale = mdf.scale
try:
cov_re_inv = np.linalg.inv(cov_re)
except np.linalg.LinAlgError:
cov_re_inv = None
for itr in range(maxit):
fe_params_s = fe_params.copy()
for j in range(self.k_fe):
if abs(fe_params[j]) < ceps:
continue
# The residuals
fe_params[j] = 0.
expval = np.dot(self.exog, fe_params)
resid_all = self.endog - expval
# The loss function has the form
# a*x^2 + b*x + pwt*|x|
a, b = 0., 0.
for k, lab in enumerate(self.group_labels):
exog = self.exog_li[k]
ex_r = self.exog_re_li[k]
ex2_r = self.exog_re2_li[k]
resid = resid_all[self.row_indices[lab]]
x = exog[:,j]
u = _smw_solve(scale, ex_r, ex2_r, cov_re,
cov_re_inv, x)
a += np.dot(u, x)
b -= 2 * np.dot(u, resid)
pwt1 = alpha[j]
if b > pwt1:
fe_params[j] = -(b - pwt1) / (2 * a)
elif b < -pwt1:
fe_params[j] = -(b + pwt1) / (2 * a)
if np.abs(fe_params_s - fe_params).max() < ptol:
break
# Replace the fixed effects estimates with their penalized
# values, leave the dependence parameters in their unpenalized
# state.
params_prof = mdf.params.copy()
params_prof[0:self.k_fe] = fe_params
scale = self.get_scale(fe_params, mdf.cov_re_unscaled)
# Get the Hessian including only the nonzero fixed effects,
# then blow back up to the full size after inverting.
hess = self.hessian_full(params_prof)
pcov = np.nan * np.ones_like(hess)
ii = np.abs(params_prof) > ceps
ii[self.k_fe:] = True
ii = np.flatnonzero(ii)
hess1 = hess[ii, :][:, ii]
pcov[np.ix_(ii,ii)] = np.linalg.inv(-hess1)
results = MixedLMResults(self, params_prof, pcov / scale)
results.fe_params = fe_params
results.cov_re = cov_re
results.scale = scale
results.cov_re_unscaled = mdf.cov_re_unscaled
results.method = mdf.method
results.converged = True
results.cov_pen = self.cov_pen
results.k_fe = self.k_fe
results.k_re = self.k_re
results.k_re2 = self.k_re2
return MixedLMResultsWrapper(results)
def _reparam(self):
"""
Returns parameters of the map converting parameters from the
form used in optimization to the form returned to the user.
Returns
-------
lin : list-like
Linear terms of the map
quad : list-like
Quadratic terms of the map
Notes
-----
If P are the standard form parameters and R are the
modified parameters (i.e. with square root covariance),
then P[i] = lin[i] * R + R' * quad[i] * R
"""
k_fe, k_re, k_re2 = self.k_fe, self.k_re, self.k_re2
k_tot = k_fe + k_re2
ix = np.tril_indices(self.k_re)
lin = []
for k in range(k_fe):
e = np.zeros(k_tot)
e[k] = 1
lin.append(e)
for k in range(k_re2):
lin.append(np.zeros(k_tot))
quad = []
for k in range(k_tot):
quad.append(np.zeros((k_tot, k_tot)))
ii = np.tril_indices(k_re)
ix = [(a,b) for a,b in zip(ii[0], ii[1])]
for i1 in range(k_re2):
for i2 in range(k_re2):
ix1 = ix[i1]
ix2 = ix[i2]
if (ix1[1] == ix2[1]) and (ix1[0] <= ix2[0]):
ii = (ix2[0], ix1[0])
k = ix.index(ii)
quad[k_fe+k][k_fe+i2, k_fe+i1] += 1
for k in range(k_tot):
quad[k] = 0.5*(quad[k] + quad[k].T)
return lin, quad
def hessian_sqrt(self, params):
"""
Returns the Hessian matrix of the log-likelihood evaluated at
a given point, calculated with respect to the parameterization
in which the random effects covariance matrix is represented
through its Cholesky square root.
Parameters
----------
params : MixedLMParams or array-like
The model parameters. If array-like, must contain packed
parameters that are compatible with this model.
Returns
-------
The Hessian matrix of the profile log likelihood function,
evaluated at `params`.
Notes
-----
If `params` is provided as a MixedLMParams object it may be of
any parameterization.
"""
if type(params) is not MixedLMParams:
params = MixedLMParams.from_packed(params, self.k_fe,
self.use_sqrt)
score0 = self.score_full(params)
hess0 = self.hessian_full(params)
params_vec = params.get_packed(use_sqrt=True)
lin, quad = self._reparam()
k_tot = self.k_fe + self.k_re2
# Convert Hessian to new coordinates
hess = 0.
for i in range(k_tot):
hess += 2 * score0[i] * quad[i]
for i in range(k_tot):
vi = lin[i] + 2*np.dot(quad[i], params_vec)
for j in range(k_tot):
vj = lin[j] + 2*np.dot(quad[j], params_vec)
hess += hess0[i, j] * np.outer(vi, vj)
return hess
def loglike(self, params):
"""
Evaluate the (profile) log-likelihood of the linear mixed
effects model.
Parameters
----------
params : MixedLMParams, or array-like.
The parameter value. If array-like, must be a packed
parameter vector compatible with this model.
Returns
-------
The log-likelihood value at `params`.
Notes
-----
This is the profile likelihood in which the scale parameter
`scale` has been profiled out.
The input parameter state, if provided as a MixedLMParams
object, can be with respect to any parameterization.
"""
if type(params) is not MixedLMParams:
params = MixedLMParams.from_packed(params, self.k_fe,
self.use_sqrt)
fe_params = params.get_fe_params()
cov_re = params.get_cov_re()
try:
cov_re_inv = np.linalg.inv(cov_re)
except np.linalg.LinAlgError:
cov_re_inv = None
_, cov_re_logdet = np.linalg.slogdet(cov_re)
# The residuals
expval = np.dot(self.exog, fe_params)
resid_all = self.endog - expval
likeval = 0.
# Handle the covariance penalty
if self.cov_pen is not None:
likeval -= self.cov_pen.func(cov_re, cov_re_inv)
# Handle the fixed effects penalty
if self.fe_pen is not None:
likeval -= self.fe_pen.func(fe_params)
xvx, qf = 0., 0.
for k, lab in enumerate(self.group_labels):
exog = self.exog_li[k]
ex_r = self.exog_re_li[k]
ex2_r = self.exog_re2_li[k]
resid = resid_all[self.row_indices[lab]]
# Part 1 of the log likelihood (for both ML and REML)
ld = _smw_logdet(1., ex_r, ex2_r, cov_re, cov_re_inv,
cov_re_logdet)
likeval -= ld / 2.
# Part 2 of the log likelihood (for both ML and REML)
u = _smw_solve(1., ex_r, ex2_r, cov_re, cov_re_inv, resid)
qf += np.dot(resid, u)
# Adjustment for REML
if self.reml:
mat = _smw_solve(1., ex_r, ex2_r, cov_re, cov_re_inv,
exog)
xvx += np.dot(exog.T, mat)
if self.reml:
likeval -= (self.n_totobs - self.k_fe) * np.log(qf) / 2.
_,ld = np.linalg.slogdet(xvx)
likeval -= ld / 2.
likeval -= (self.n_totobs - self.k_fe) * np.log(2 * np.pi) / 2.
likeval += ((self.n_totobs - self.k_fe) *
np.log(self.n_totobs - self.k_fe) / 2.)
likeval -= (self.n_totobs - self.k_fe) / 2.
else:
likeval -= self.n_totobs * np.log(qf) / 2.
likeval -= self.n_totobs * np.log(2 * np.pi) / 2.
likeval += self.n_totobs * np.log(self.n_totobs) / 2.
likeval -= self.n_totobs / 2.
return likeval
def _gen_dV_dPsi(self, ex_r, max_ix=None):
"""
A generator that yields the derivative of the covariance
matrix V (=I + Z*Psi*Z') with respect to the free elements of
Psi. Each call to the generator yields the index of Psi with
respect to which the derivative is taken, and the derivative
matrix with respect to that element of Psi. Psi is a
symmetric matrix, so the free elements are the lower triangle.
If max_ix is not None, the iterations terminate after max_ix
values are yielded.
"""
jj = 0
for j1 in range(self.k_re):
for j2 in range(j1 + 1):
if max_ix is not None and jj > max_ix:
return
mat = np.outer(ex_r[:,j1], ex_r[:,j2])
if j1 != j2:
mat += mat.T
yield jj,mat
jj += 1
def score(self, params):
"""
Returns the score vector of the profile log-likelihood.
Notes
-----
The score vector that is returned is computed with respect to
the parameterization defined by this model instance's
`use_sqrt` attribute. The input value `params` can be with
respect to any parameterization.
"""
if self.use_sqrt:
return self.score_sqrt(params)
else:
return self.score_full(params)
def hessian(self, params):
"""
Returns the Hessian matrix of the profile log-likelihood.
Notes
-----
The Hessian matrix that is returned is computed with respect
to the parameterization defined by this model's `use_sqrt`
attribute. The input value `params` can be with respect to
any parameterization.
"""
if self.use_sqrt:
return self.hessian_sqrt(params)
else:
return self.hessian_full(params)
def score_full(self, params):
"""
Calculates the score vector for the profiled log-likelihood of
the mixed effects model with respect to the parameterization
in which the random effects covariance matrix is represented
in its full form (not using the Cholesky factor).
Parameters
----------
params : MixedLMParams or array-like
The parameter at which the score function is evaluated.
If array-like, must contain packed parameter values that
are compatible with the current model.
Returns
-------
The score vector, calculated at `params`.
Notes
-----
The score vector that is returned is taken with respect to the
parameterization in which `cov_re` is represented through its
lower triangle (without taking the Cholesky square root).
The input, if provided as a MixedLMParams object, can be of
any parameterization.
"""
if type(params) is not MixedLMParams:
params = MixedLMParams.from_packed(params, self.k_fe,
self.use_sqrt)
fe_params = params.get_fe_params()
cov_re = params.get_cov_re()
try:
cov_re_inv = np.linalg.inv(cov_re)
except np.linalg.LinAlgError:
cov_re_inv = None
score_fe = np.zeros(self.k_fe, dtype=np.float64)
score_re = np.zeros(self.k_re2, dtype=np.float64)
# Handle the covariance penalty.
if self.cov_pen is not None:
score_re -= self.cov_pen.grad(cov_re, cov_re_inv)
# Handle the fixed effects penalty.
if self.fe_pen is not None:
score_fe -= self.fe_pen.grad(fe_params)
# resid' V^{-1} resid, summed over the groups (a scalar)
rvir = 0.
# exog' V^{-1} resid, summed over the groups (a k_fe
# dimensional vector)
xtvir = 0.
# exog' V^{_1} exog, summed over the groups (a k_fe x k_fe
# matrix)
xtvix = 0.
# V^{-1} exog' dV/dQ_jj exog V^{-1}, where Q_jj is the jj^th
# covariance parameter.
xtax = [0.,] * self.k_re2
# Temporary related to the gradient of log |V|
dlv = np.zeros(self.k_re2, dtype=np.float64)
# resid' V^{-1} dV/dQ_jj V^{-1} resid (a scalar)
rvavr = np.zeros(self.k_re2, dtype=np.float64)
for k in range(self.n_groups):
exog = self.exog_li[k]
ex_r = self.exog_re_li[k]
ex2_r = self.exog_re2_li[k]
# The residuals
expval = np.dot(exog, fe_params)
resid = self.endog_li[k] - expval
if self.reml:
viexog = _smw_solve(1., ex_r, ex2_r, cov_re,
cov_re_inv, exog)
xtvix += np.dot(exog.T, viexog)
# Contributions to the covariance parameter gradient
jj = 0
vex = _smw_solve(1., ex_r, ex2_r, cov_re, cov_re_inv,
ex_r)
vir = _smw_solve(1., ex_r, ex2_r, cov_re, cov_re_inv,
resid)
for jj,mat in self._gen_dV_dPsi(ex_r):
dlv[jj] = np.trace(_smw_solve(1., ex_r, ex2_r, cov_re,
cov_re_inv, mat))
rvavr[jj] += np.dot(vir, np.dot(mat, vir))
if self.reml:
xtax[jj] += np.dot(viexog.T, np.dot(mat, viexog))
# Contribution of log|V| to the covariance parameter
# gradient.
score_re -= 0.5 * dlv
# Needed for the fixed effects params gradient
rvir += np.dot(resid, vir)
xtvir += np.dot(exog.T, vir)
fac = self.n_totobs
if self.reml:
fac -= self.exog.shape[1]
score_fe += fac * xtvir / rvir
score_re += 0.5 * fac * rvavr / rvir
if self.reml:
for j in range(self.k_re2):
score_re[j] += 0.5 * np.trace(np.linalg.solve(
xtvix, xtax[j]))
score_vec = np.concatenate((score_fe, score_re))
if self._freepat is not None:
return self._freepat.get_packed() * score_vec
else:
return score_vec
def score_sqrt(self, params):
"""
Returns the score vector with respect to the parameterization
in which the random effects covariance matrix is represented
through its Cholesky square root.
Parameters
----------
params : MixedLMParams or array-like
The model parameters. If array-like must contain packed
parameters that are compatible with this model instance.
Returns
-------
The score vector.
Notes
-----
The input, if provided as a MixedLMParams object, can be of
any parameterization.
"""
if type(params) is not MixedLMParams:
params = MixedLMParams.from_packed(params, self.k_fe,
self.use_sqrt)
score_full = self.score_full(params)
params_vec = params.get_packed(use_sqrt=True)
lin, quad = self._reparam()
scr = 0.
for i in range(len(params_vec)):
v = lin[i] + 2 * np.dot(quad[i], params_vec)
scr += score_full[i] * v
if self._freepat is not None:
return self._freepat.get_packed() * scr
else:
return scr
def hessian_full(self, params):
"""
Calculates the Hessian matrix for the mixed effects model with
respect to the parameterization in which the covariance matrix
is represented directly (without square-root transformation).
Parameters
----------
params : MixedLMParams or array-like
The model parameters at which the Hessian is calculated.
If array-like, must contain the packed parameters in a
form that is compatible with this model instance.
Returns
-------
hess : 2d ndarray
The Hessian matrix, evaluated at `params`.
Notes
-----
Tf provided as a MixedLMParams object, the input may be of
any parameterization.
"""
if type(params) is not MixedLMParams:
params = MixedLMParams.from_packed(params, self.k_fe,
self.use_sqrt)
fe_params = params.get_fe_params()
cov_re = params.get_cov_re()
try:
cov_re_inv = np.linalg.inv(cov_re)
except np.linalg.LinAlgError:
cov_re_inv = None
# Blocks for the fixed and random effects parameters.
hess_fe = 0.
hess_re = np.zeros((self.k_re2, self.k_re2), dtype=np.float64)
hess_fere = np.zeros((self.k_re2, self.k_fe),
dtype=np.float64)
fac = self.n_totobs
if self.reml:
fac -= self.exog.shape[1]
rvir = 0.
xtvix = 0.
xtax = [0.,] * self.k_re2
B = np.zeros(self.k_re2, dtype=np.float64)
D = np.zeros((self.k_re2, self.k_re2), dtype=np.float64)
F = [[0.,]*self.k_re2 for k in range(self.k_re2)]
for k in range(self.n_groups):
exog = self.exog_li[k]
ex_r = self.exog_re_li[k]
ex2_r = self.exog_re2_li[k]
# The residuals
expval = np.dot(exog, fe_params)
resid = self.endog_li[k] - expval
viexog = _smw_solve(1., ex_r, ex2_r, cov_re, cov_re_inv,
exog)
xtvix += np.dot(exog.T, viexog)
vir = _smw_solve(1., ex_r, ex2_r, cov_re, cov_re_inv,
resid)
rvir += np.dot(resid, vir)
for jj1,mat1 in self._gen_dV_dPsi(ex_r):
hess_fere[jj1,:] += np.dot(viexog.T,
| np.dot(mat1, vir) | numpy.dot |
#!/usr/bin/env python
# -*- coding=utf-8 -*-
###########################################################################
# Copyright (C) 2013-2016 by Caspar. All rights reserved.
# File Name: txtclf.py
# Author: <NAME>
# E-mail: <EMAIL>
# Created Time: 2016-07-05 14:39:18
###########################################################################
#
import os, sys, difflib, itertools
from time import time
import numpy as np
import scipy as sp
import scipy.stats as stats
import pandas as pd
from sklearn.base import clone
from sklearn.preprocessing import MinMaxScaler, LabelBinarizer, label_binarize, normalize
from sklearn.multiclass import OneVsRestClassifier
from sklearn.pipeline import Pipeline
from sklearn.model_selection import StratifiedShuffleSplit, StratifiedKFold, KFold, GridSearchCV, RandomizedSearchCV
from sklearn import metrics
from .util import io, func, plot
from .util import math as imath
common_cfg = {}
def init(plot_cfg={}, plot_common={}):
if (len(plot_cfg) > 0 and plot_cfg['MON'] is not None):
plot.MON = plot_cfg['MON']
global common_cfg
if (len(plot_common) > 0):
common_cfg = plot_common
def get_featw(pipeline, feat_num):
feat_w_dict, sub_feat_w = [{} for i in range(2)]
filt_feat_idx = feature_idx = np.arange(feat_num)
for component in ('featfilt', 'clf'):
if (type(pipeline) != Pipeline):
if (component == 'featfilt'):
continue
else:
cmpn = pipeline
elif (component in pipeline.named_steps):
cmpn = pipeline.named_steps[component]
else:
continue
if (hasattr(cmpn, 'estimators_')):
for i, estm in enumerate(cmpn.estimators_):
filt_subfeat_idx = feature_idx[:]
if (hasattr(estm, 'get_support')):
filt_subfeat_idx = feature_idx[estm.get_support()]
for measure in ('feature_importances_', 'coef_', 'scores_'):
if (hasattr(estm, measure)):
filt_subfeat_w = getattr(estm, measure)
subfeat_w = (filt_subfeat_w.min() - 1) * np.ones_like(feature_idx)
# subfeat_w[filt_subfeat_idx] = normalize(estm.feature_importances_, norm='l1')
subfeat_w[filt_subfeat_idx] = filt_subfeat_w
# print 'Sub FI shape: (%s)' % ','.join([str(x) for x in filt_subfeat_w.shape])
# print 'Feature Importance inside %s Ensemble Method: %s' % (component, filt_subfeat_w)
sub_feat_w[(component, i)] = subfeat_w
if (hasattr(component, 'get_support')):
filt_feat_idx = feature_idx[component.get_support()]
for measure in ('feature_importances_', 'coef_', 'scores_'):
if (hasattr(cmpn, measure)):
filt_feat_w = getattr(cmpn, measure)
# print '*' * 80 + '\n%s\n'%filt_feat_w + '*' * 80
feat_w = (filt_feat_w.min() - 1) * np.ones_like(feature_idx)
# feat_w[filt_feat_idx] = normalize(filt_feat_w, norm='l1')
feat_w[filt_feat_idx] = filt_feat_w
# print '*' * 80 + '\n%s\n'%feat_w + '*' * 80
feat_w_dict[(component, measure)] = feat_w
print('FI shape: (%s)' % ','.join([str(x) for x in feat_w_dict[(component, measure)].shape]))
print('Sample 10 Feature from %s.%s: %s' % (component, measure, feat_w[feat_w > 0][:10]))
# print 'Feature Importance from %s.%s: %s' % (component, measure, feat_w)
return feat_w_dict, sub_feat_w
def get_score(pipeline, X_test, mltl=False):
if ((not isinstance(pipeline, Pipeline) and hasattr(pipeline, 'predict_proba')) or(isinstance(pipeline.named_steps['clf'], OneVsRestClassifier) and hasattr(pipeline.named_steps['clf'].estimators_[0], 'predict_proba')) or (not isinstance(pipeline.named_steps['clf'], OneVsRestClassifier) and hasattr(pipeline, 'predict_proba'))):
if (mltl):
return pipeline.predict_proba(X_test)
else:
# return pipeline.predict_proba(X_test)[:, 1]
return pipeline.predict_proba(X_test)
elif (hasattr(pipeline, 'decision_function')):
return pipeline.decision_function(X_test)
else:
print('Neither probability estimate nor decision function is supported in the classification model!')
return [0] * Y_test.shape[0]
# Benchmark
def benchmark(pipeline, X_train, Y_train, X_test, Y_test, mltl=False, signed=False, average='micro'):
print('+' * 80)
print('Training Model: ')
print(pipeline)
t0 = time()
pipeline.fit(X_train, Y_train)
train_time = time() - t0
print('train time: %0.3fs' % train_time)
t0 = time()
orig_pred = pred = pipeline.predict(X_test)
orig_prob = prob = pipeline.predict_proba(X_test) if hasattr(pipeline, 'predict_proba') else pipeline.decision_function(X_test)
test_time = time() - t0
print('+' * 80)
print('Testing: ')
print('test time: %0.3fs' % test_time)
is_mltl = mltl
if (signed):
Y_test = np.column_stack([np.abs(Y_test).reshape((Y_test.shape[0],-1))] + [label_binarize(lb, classes=[-1,1,0])[:,1] for lb in (np.sign(Y_test).astype('int8').reshape((Y_test.shape[0],-1))).T]) if (len(Y_test.shape) < 2 or Y_test.shape[1] == 1 or np.where(Y_test<0)[0].shape[0]>0) else Y_test
pred = np.column_stack([np.abs(pred).reshape((pred.shape[0],-1))] + [label_binarize(lb, classes=[-1,1,0])[:,1] for lb in (np.sign(pred).astype('int8').reshape((pred.shape[0],-1))).T]) if (len(pred.shape) < 2 or pred.shape[1] == 1 or np.where(pred<0)[0].shape[0]>0) else pred
is_mltl = True
try:
accuracy = metrics.accuracy_score(Y_test, pred)
except ValueError as e:
print(e)
Y_test, pred = Y_test.ravel(), pred.ravel()
accuracy = metrics.accuracy_score(Y_test, pred)
print('accuracy: %0.3f' % accuracy)
if (is_mltl and average == 'all'):
micro_precision = metrics.precision_score(Y_test, pred, average='micro')
print('micro-precision: %0.3f' % micro_precision)
micro_recall = metrics.recall_score(Y_test, pred, average='micro')
print('micro-recall: %0.3f' % micro_recall)
micro_fscore = metrics.fbeta_score(Y_test, pred, beta=1, average='micro')
print('micro-fscore: %0.3f' % micro_fscore)
macro_precision = metrics.precision_score(Y_test, pred, average='macro')
print('macro-precision: %0.3f' % macro_precision)
macro_recall = metrics.recall_score(Y_test, pred, average='macro')
print('macro-recall: %0.3f' % macro_recall)
macro_fscore = metrics.fbeta_score(Y_test, pred, beta=1, average='macro')
print('macro-fscore: %0.3f' % macro_fscore)
else:
precision = metrics.precision_score(Y_test, pred, average=average if is_mltl else 'binary')
print('precision: %0.3f' % precision)
recall = metrics.recall_score(Y_test, pred, average=average if is_mltl else 'binary')
print('recall: %0.3f' % recall)
fscore = metrics.fbeta_score(Y_test, pred, beta=1, average=average if is_mltl else 'binary')
print('fscore: %0.3f' % fscore)
print('classification report:')
# print metrics.classification_report(Y_test, pred)
metric_df = pd.DataFrame(metrics.classification_report(Y_test, pred, output_dict=True)).T[['precision', 'recall', 'f1-score', 'support']]
print(metric_df)
print('confusion matrix:')
if (is_mltl):
pass
else:
print(metrics.confusion_matrix(Y_test, pred))
print('+' * 80)
clf = pipeline.named_steps['clf'] if (type(pipeline) is Pipeline) else pipeline
if ((isinstance(clf, OneVsRestClassifier) and hasattr(clf.estimators_[0], 'predict_proba')) or (not isinstance(clf, OneVsRestClassifier) and hasattr(pipeline, 'predict_proba'))):
if (mltl):
scores = pipeline.predict_proba(X_test)
if (type(scores) == list):
scores = np.concatenate([score[:, -1].reshape((-1, 1)) for score in scores], axis=1)
else:
scores = pipeline.predict_proba(X_test)[:, -1]
elif (hasattr(pipeline, 'decision_function')):
scores = pipeline.decision_function(X_test)
else:
print('Neither probability estimate nor decision function is supported in the classification model! ROC and PRC figures will be invalid.')
scores = [0] * Y_test.shape[0]
if (signed and (len(scores.shape) < 2 or scores.shape[1] < pred.shape[1])):
scores = np.concatenate([np.abs(scores).reshape((scores.shape[0],-1))] + [label_binarize(lb, classes=[-1,1,0])[:,:2] for lb in (np.sign(scores).astype('int8').reshape((scores.shape[0],-1))).T], axis=1)
if (is_mltl):
if ((len(Y_test.shape) == 1 or Y_test.shape[1] == 1) and len(np.unique(Y_test)) > 2):
lbz = LabelBinarizer()
Y_test = lbz.fit_transform(Y_test)
def micro():
# Micro-average ROC curve
y_true = np.array(Y_test)
s_array = np.array(scores)
if (len(s_array.shape) == 3):
s_array = s_array[:,:,1].reshape((s_array.shape[0],s_array.shape[1],))
if (y_true.shape[0] == s_array.shape[1] and y_true.shape[1] == s_array.shape[0]):
s_array = s_array.T
return metrics.roc_curve(y_true.ravel(), s_array.ravel())
def macro():
# Macro-average ROC curve
n_classes = Y_test.shape[1]
fpr, tpr = [dict() for i in range(2)]
for i in range(n_classes):
fpr[i], tpr[i], _ = metrics.roc_curve(Y_test[:, i], scores[:, i])
# First aggregate all false positive rates
all_fpr = np.unique(np.concatenate([fpr[i] for i in range(n_classes)]))
# Then interpolate all ROC curves at this points
mean_tpr = np.zeros_like(all_fpr)
for i in range(n_classes):
mean_tpr += np.interp(all_fpr, fpr[i], tpr[i])
# Finally average it and compute AUC
mean_tpr /= n_classes
return all_fpr, mean_tpr, _
if (average == 'micro'):
roc = micro()
elif (average == 'macro'):
roc = macro()
elif (average == 'all'):
micro_roc = micro()
macro_roc = macro()
if (type(scores) == list):
scores = np.array(scores)[:,:,0]
prc = metrics.precision_recall_curve(Y_test.ravel(), scores.ravel()) # Only micro-prc is supported
else:
roc = metrics.roc_curve(Y_test, scores)
prc = metrics.precision_recall_curve(Y_test, scores)
# print 'ROC:\n%s\n%s' % (roc[0], roc[1])
# print 'PRC:\n%s\n%s' % (prc[0], prc[1])
print('Training and Testing X shape: %s; %s' % (', '.join(['(%s)' % ','.join([str(x) for x in X.shape]) for X in X_train]) if type(X_train) is list else '(%s)' % ','.join([str(x) for x in X_train.shape]), ', '.join(['(%s)' % ','.join([str(x) for x in X.shape]) for X in X_test]) if type(X_test) is list else '(%s)' % ','.join([str(x) for x in X_test.shape])))
feat_w_dict, sub_feat_w = [{} for i in range(2)]
filt_feat_idx = feature_idx = np.arange(X_train[0].shape[1] if type(X_train) is list else X_train.shape[1])
for component in ('featfilt', 'clf'):
if (type(pipeline) != Pipeline):
if (component == 'featfilt'):
continue
else:
cmpn = pipeline
elif (component in pipeline.named_steps):
cmpn = pipeline.named_steps[component]
else:
continue
if (hasattr(cmpn, 'estimators_')):
for i, estm in enumerate(cmpn.estimators_):
filt_subfeat_idx = filt_feat_idx[:]
if (hasattr(estm, 'get_support')):
filt_subfeat_idx = filt_feat_idx[estm.get_support()]
for measure in ('feature_importances_', 'coef_', 'scores_'):
if (hasattr(estm, measure)):
filt_subfeat_w = getattr(estm, measure)
subfeat_w = (filt_subfeat_w.min() - 1) * np.ones_like(feature_idx)
# subfeat_w[filt_subfeat_idx][:len(estm.feature_importances_)] = normalize(estm.feature_importances_, norm='l1')
subfeat_w[filt_subfeat_idx][:len(filt_subfeat_w)] = filt_subfeat_w
# print 'Sub FI shape: (%s)' % ','.join([str(x) for x in filt_subfeat_w.shape])
# print 'Feature Importance inside %s Ensemble Method: %s' % (component, filt_subfeat_w)
sub_feat_w[(component, i)] = subfeat_w
for measure in ('feature_importances_', 'coef_', 'scores_'):
if (hasattr(cmpn, measure)):
filt_feat_w = getattr(cmpn, measure)
# print '*' * 80 + '\n%s\n'%filt_feat_w + '*' * 80
feat_w = (filt_feat_w.min() - 1) * np.ones_like(feature_idx)
# feat_w[filt_feat_idx][:filt_feat_w.shape[1] if len(filt_feat_w.shape) > 1 else len(filt_feat_w)] = normalize(filt_feat_w[1,:] if len(filt_feat_w.shape) > 1 else filt_feat_w, norm='l1')
feat_w[filt_feat_idx][:filt_feat_w.shape[1] if len(filt_feat_w.shape) > 1 else len(filt_feat_w)] = filt_feat_w[1,:] if len(filt_feat_w.shape) > 1 else filt_feat_w
# print '*' * 80 + '\n%s\n'%feat_w + '*' * 80
feat_w_dict[(component, measure)] = feat_w
print('FI shape: (%s)' % ','.join([str(x) for x in feat_w_dict[(component, measure)].shape]))
print('Sample 10 Feature from %s.%s: %s' % (component, measure, feat_w[feat_w > 0][:10]))
# print 'Feature Importance from %s.%s: %s' % (component, measure, feat_w)
if (hasattr(cmpn, 'get_support')):
filt_feat_idx = filt_feat_idx[cmpn.get_support()]
print('\n')
if (is_mltl and average == 'all'):
return {'accuracy':accuracy, 'micro-precision':micro_precision, 'micro-recall':micro_recall, 'micro-fscore':micro_fscore, 'macro-precision':macro_precision, 'macro-recall':macro_recall, 'macro-fscore':macro_fscore, 'train_time':train_time, 'test_time':test_time, 'micro-roc':micro_roc, 'macro-roc':macro_roc, 'prc':prc, 'feat_w':feat_w_dict, 'sub_feat_w':sub_feat_w, 'pred_lb':orig_pred, 'metrics':metric_df}
else:
return {'accuracy':accuracy, 'precision':precision, 'recall':recall, 'fscore':fscore, 'train_time':train_time, 'test_time':test_time, 'roc':roc, 'prc':prc, 'feat_w':feat_w_dict, 'sub_feat_w':sub_feat_w, 'pred_lb':orig_pred, 'pred_prob':orig_prob, 'metrics':metric_df}
# Calculate the venn digram overlaps
def pred_ovl(preds, pred_true=None, axis=1):
if (axis == 0):
preds = preds.T
if (pred_true is not None):
pred_true = pred_true.reshape((-1,))
# Row represents feature, column represents instance
var_num, dim = preds.shape[0], preds.shape[1]
orig_idx = np.arange(var_num)
if (len(preds.shape) < 2 or preds.shape[1] == 1):
if (pred_true is None):
return np.ones(shape=(1,), dtype='int')
else:
overlap_mt = np.ones(shape=(1,2), dtype='int')
overlap_mt[0,1] = orig_idx[preds.reshape((-1,)) == pred_true].shape[0]
return overlap_mt
# Calculate possible subsets of all the instance indices
subset_idx = list(imath.subset(list(range(dim)), min_crdnl=1))
# Initialize result matrix
if (pred_true is None):
overlap_mt = np.zeros(shape=(len(subset_idx),), dtype='int')
else:
overlap_mt = np.zeros(shape=(len(subset_idx), 2), dtype='int')
# Calculate overlap for each subset
for i, idx in enumerate(subset_idx):
rmn_idx = set(range(dim)) - set(idx)
# Select the positions of the target instance that without any overlap with other instances
pred_sum, chsn_sum, rmn_sum = preds.sum(axis=1), preds[:,idx].sum(axis=1), preds[:,list(rmn_idx)].sum(axis=1)
condition = np.all([np.logical_or(chsn_sum == 0, chsn_sum == len(idx)), np.logical_or(rmn_sum == 0, rmn_sum == len(rmn_idx)), np.logical_or(pred_sum == len(idx), pred_sum == len(rmn_idx))], axis=0)
if (pred_true is None):
overlap_mt[i] = orig_idx[condition].shape[0]
else:
# And the selected positions should be true
true_cond = np.logical_and(condition, preds[:,idx[0]] == pred_true)
overlap_mt[i,0] = orig_idx[condition].shape[0]
overlap_mt[i,1] = orig_idx[true_cond].shape[0]
return overlap_mt
def save_featw(features, crsval_featw, crsval_subfeatw, cfg_param={}, lbid=''):
lbidstr = ('_' + (str(lbid) if lbid != -1 else 'all')) if lbid is not None and lbid != '' else ''
for k, v in crsval_featw.items():
measure_str = k.replace(' ', '_').strip('_').lower()
feat_w_mt = np.column_stack(v)
mms = MinMaxScaler()
feat_w_mt = mms.fit_transform(feat_w_mt)
feat_w_avg = feat_w_mt.mean(axis=1)
feat_w_std = feat_w_mt.std(axis=1)
sorted_idx = np.argsort(feat_w_avg, axis=-1)[::-1]
# sorted_idx = sorted(range(feat_w_avg.shape[0]), key=lambda k: feat_w_avg[k])[::-1]
sorted_feat_w = np.column_stack((features[sorted_idx], feat_w_avg[sorted_idx], feat_w_std[sorted_idx]))
feat_w_df = pd.DataFrame(sorted_feat_w, index=sorted_idx, columns=['Feature Name', 'Importance Mean', 'Importance Std'])
if (cfg_param.setdefault('save_featw', False)):
feat_w_df.to_excel('featw%s_%s.xlsx' % (lbidstr, measure_str))
if (cfg_param.setdefault('save_featw_npz', False)):
io.write_df(feat_w_df, 'featw%s_%s' % (lbidstr, measure_str), with_idx=True)
if (cfg_param.setdefault('plot_featw', False)):
plot.plot_bar(feat_w_avg[sorted_idx[:10]].reshape((1,-1)), feat_w_std[sorted_idx[:10]].reshape((1,-1)), features[sorted_idx[:10]], labels=None, title='Feature importances', fname='fig_featw%s_%s' % (lbidstr, measure_str), plot_cfg=common_cfg)
for k, v in crsval_subfeatw.items():
measure_str = k.replace(' ', '_').strip('_').lower()
subfeat_w_mt = np.column_stack(v)
mms = MinMaxScaler()
subfeat_w_mt = mms.fit_transform(subfeat_w_mt)
subfeat_w_avg = subfeat_w_mt.mean(axis=1)
subfeat_w_std = subfeat_w_mt.std(axis=1)
sorted_idx = np.argsort(subfeat_w_avg, axis=-1)[::-1]
sorted_subfeat_w = np.column_stack((features[sorted_idx], subfeat_w_avg[sorted_idx], subfeat_w_std[sorted_idx]))
subfeat_w_df = pd.DataFrame(sorted_subfeat_w, index=sorted_idx, columns=['Feature Name', 'Importance Mean', 'Importance Std'])
if (cfg_param.setdefault('save_subfeatw', False)):
subfeat_w_df.to_excel('subfeatw%s_%s.xlsx' % (lbidstr, measure_str))
if (cfg_param.setdefault('save_subfeatw_npz', False)):
io.write_df(subfeat_w_df, 'subfeatw%s_%s' % (lbidstr, measure_str), with_idx=True)
if (cfg_param.setdefault('plot_subfeatw', False)):
plot.plot_bar(subfeat_w_avg[sorted_idx[:10]].reshape((1,-1)), subfeat_w_std[sorted_idx[:10]].reshape((1,-1)), features[sorted_idx[:10]], labels=None, title='Feature importances', fname='fig_subfeatw_%s' % measure_str, plot_cfg=common_cfg)
# Classification
def classification(X_train, Y_train, X_test, model_iter, model_param={}, cfg_param={}, global_param={}, lbid=''):
print('Classifing...')
global common_cfg
FILT_NAMES, CLF_NAMES, PL_NAMES, PL_SET = model_param['glb_filtnames'], model_param['glb_clfnames'], global_param['pl_names'], global_param['pl_set']
lbidstr = ('_' + (str(lbid) if lbid != -1 else 'all')) if lbid is not None and lbid != '' else ''
to_hdf, hdf5_fpath = cfg_param.setdefault('to_hdf', False), '%s' % 'crsval_dataset.h5' if cfg_param.setdefault('hdf5_fpath', 'crsval_dataset.h5') is None else cfg_param['hdf5_fpath']
# Format the data
if (type(X_train) == list):
assert all([len(x) == len(X_train[0]) for x in X_train[1:]])
X_train = [pd.DataFrame(x) if (type(x) != pd.io.parsers.TextFileReader and type(x) != pd.DataFrame) else x for x in X_train]
X_train = [pd.concat(x) if (type(x) == pd.io.parsers.TextFileReader and not to_hdf) else x for x in X_train]
else:
if (type(X_train) != pd.io.parsers.TextFileReader and type(X_train) != pd.DataFrame):
X_train = pd.DataFrame(X_train)
X_train = pd.concat(X_train) if (type(X_train) == pd.io.parsers.TextFileReader and not to_hdf) else X_train
if (type(X_test) == list):
assert all([len(x) == len(X_test[0]) for x in X_test[1:]])
X_test = [pd.DataFrame(x) if (type(x) != pd.io.parsers.TextFileReader and type(x) != pd.DataFrame) else x for x in X_test]
X_test = [pd.concat(x) if (type(x) == pd.io.parsers.TextFileReader and not to_hdf) else x for x in X_test]
else:
if (type(X_test) != pd.io.parsers.TextFileReader and type(X_test) != pd.DataFrame):
X_test = pd.DataFrame(X_test)
X_test = pd.concat(X_test) if (type(X_test) == pd.io.parsers.TextFileReader and not to_hdf) else X_test
if (type(Y_train) != pd.io.parsers.TextFileReader and type(Y_train) != pd.DataFrame):
Y_train = pd.DataFrame(Y_train)
Y_train_mt = Y_train.values.reshape((Y_train.shape[0],)) if (len(Y_train.shape) == 1 or Y_train.shape[1] == 1) else Y_train.values
mltl=True if len(Y_train_mt.shape) > 1 and Y_train_mt.shape[1] > 1 or 2 in Y_train_mt else False
print('Classification is starting...')
preds, probs, scores = [[] for i in range(3)]
crsval_featw, crsval_subfeatw = [{} for i in range(2)]
for vars in model_iter(**model_param):
if (global_param['comb']):
mdl_name, mdl = [vars[x] for x in range(2)]
else:
filt_name, filter, clf_name, clf= [vars[x] for x in range(4)]
print('#' * 80)
# Assemble a pipeline
if ('filter' in locals() and filter != None):
model_name = '%s [Ft Filt] & %s [CLF]' % (filt_name, clf_name)
pipeline = Pipeline([('featfilt', clone(filter)), ('clf', clf)])
elif ('clf' in locals() and clf != None):
model_name = '%s [CLF]' % clf_name
pipeline = Pipeline([('clf', clf)])
else:
model_name = mdl_name
pipeline = mdl if (type(mdl) is Pipeline) else Pipeline([('clf', mdl)])
if (model_name in PL_SET): continue
PL_NAMES.append(model_name)
PL_SET.add(model_name)
print(model_name)
# Build the model
print('+' * 80)
print('Training Model: ')
print(pipeline)
t0 = time()
pipeline.fit(X_train, Y_train_mt)
train_time = time() - t0
print('train time: %0.3fs' % train_time)
t0 = time()
pred = pipeline.predict(X_test)
prob = pipeline.predict_proba(X_test)
test_time = time() - t0
print('+' * 80)
print('Testing: ')
print('test time: %0.3fs' % test_time)
preds.append(pred)
probs.append(prob)
scores.append(get_score(pipeline, X_test, mltl))
# Save predictions and model
if (cfg_param.setdefault('save_pred', True)):
io.write_npz(dict(pred_lb=pred, pred_prob=prob), 'clf_pred_%s%s' % (model_name.replace(' ', '_').lower(), lbidstr))
if (cfg_param.setdefault('save_model', True)):
mdl_name = '%s' % model_name.replace(' ', '_').lower()
if (all([hasattr(pipeline.steps[i][1], 'save') for i in range(len(pipeline.steps))])):
for sub_mdl_name, mdl in pipeline.steps:
mdl.save('%s_%s%s' % (mdl_name, sub_mdl_name.replace(' ', '_').lower(), lbidstr), **global_param.setdefault('mdl_save_kwargs', {}))
else:
io.write_obj(pipeline, '%s%s' % (mdl_name, lbidstr))
# Feature importances
feat_w, sub_feat_w = get_featw(pipeline, X_train[0].shape[1] if (type(X_train) is list) else X_train.shape[1])
for k, v in feat_w.items():
key = '%s_%s_%s' % (model_name, k[0], k[1])
crsval_featw.setdefault(key, []).append(v)
for k, v in sub_feat_w.items():
key = '%s_%s_%s' % (model_name, k[0], k[1])
crsval_subfeatw.setdefault(key, []).append(v)
print('\n')
if (len(preds) > 1):
# Prediction overlap
preds_mt = np.column_stack([x.ravel() for x in preds])
povl = np.array(pred_ovl(preds_mt))
# Spearman's rank correlation
spmnr, spmnr_pval = stats.spearmanr(preds_mt)
# Kendall rank correlation
# kendalltau = stats.kendalltau(preds_mt)[0]
# Pearson correlation
# pearson = tats.pearsonr(preds_mt)[0]
## Save performance data
povl_idx = [' & '.join(x) for x in imath.subset(PL_NAMES, min_crdnl=1)]
povl_df = pd.DataFrame(povl, index=povl_idx, columns=['pred_ovl'])
spmnr_df = pd.DataFrame(spmnr, index=PL_NAMES, columns=PL_NAMES)
spmnr_pval_df = pd.DataFrame(spmnr_pval, index=PL_NAMES, columns=PL_NAMES)
if (cfg_param.setdefault('save_povl', False)):
povl_df.to_excel('cpovl_clf%s.xlsx' % lbidstr)
if (cfg_param.setdefault('save_povl_npz', False)):
io.write_df(povl_df, 'povl_clf%s.npz' % lbidstr, with_idx=True)
if (cfg_param.setdefault('save_spmnr', False)):
spmnr_df.to_excel('spmnr_clf%s.xlsx' % lbidstr)
if (cfg_param.setdefault('save_spmnr_npz', False)):
io.write_df(spmnr_df, 'spmnr_clf%s.npz' % lbidstr, with_idx=True)
if (cfg_param.setdefault('save_spmnr_pval', False)):
spmnr_pval_df.to_excel('spmnr_pval_clf%s.xlsx' % lbidstr)
if (cfg_param.setdefault('save_spmnr_pval_npz', False)):
io.write_df(spmnr_pval_df, 'spmnr_pval_clf%s.npz' % lbidstr, with_idx=True)
save_featw(X_train[0].columns.values if (type(X_train) is list) else X_train.columns.values, crsval_featw, crsval_subfeatw, cfg_param=cfg_param, lbid=lbid)
return preds, scores
def kf2data(kf, X, Y, to_hdf=False, hdf5_fpath='crsval_dataset.h5'):
if (to_hdf):
import h5py
from keras.utils.io_utils import HDF5Matrix
hdf5_fpath = hdf5_fpath if hdf5_fpath else os.path.abspath('crsval_dataset.h5')
for i, (train_idx, test_idx) in enumerate(kf):
if (type(X)==list):
if (type(X[0]) == pd.io.parsers.TextFileReader):
pass
assert all([len(x) == len(X[0]) for x in X[1:]])
X_train, X_test = [x[train_idx,:] for x in X] if to_hdf and type(X[0]) == HDF5Matrix or type(X[0]) != pd.DataFrame else [x.iloc[train_idx,:] for x in X], [x[test_idx,:] for x in X] if to_hdf and type(X[0]) == HDF5Matrix or type(X[0]) != pd.DataFrame else [x.iloc[test_idx,:] for x in X]
train_idx_df, test_idx_df = pd.DataFrame(np.arange(X_train[0].shape[0]), index=X[0].index[train_idx]), pd.DataFrame(np.arange(X_test[0].shape[0]), index=X[0].index[test_idx])
else:
if (type(X) == pd.io.parsers.TextFileReader):
pass
X_train, X_test = X[train_idx] if to_hdf and type(X) == HDF5Matrix or type(X) != pd.DataFrame else X.iloc[train_idx,:], X[test_idx] if to_hdf and type(X) == HDF5Matrix or type(X) != pd.DataFrame else X.iloc[test_idx,:]
train_idx_df, test_idx_df = pd.DataFrame(np.arange(X_train.shape[0]), index=None if to_hdf and type(X) == HDF5Matrix or type(X) != pd.DataFrame else X.index[train_idx]), pd.DataFrame(np.arange(X_test.shape[0]), index=None if to_hdf and type(X) == HDF5Matrix or type(X) != pd.DataFrame else X.index[test_idx])
Y_train, Y_test = Y[train_idx], Y[test_idx]
# Y_train = Y_train.reshape((Y_train.shape[0],)) if (len(Y_train.shape) > 1 and Y_train.shape[1] == 1) else Y_train
# Y_test = Y_test.reshape((Y_test.shape[0],)) if (len(Y_test.shape) > 1 and Y_test.shape[1] == 1) else Y_test
if (to_hdf):
with h5py.File(hdf5_fpath, 'w') as hf:
if (type(X_train) == list):
for idx, x_train in enumerate(X_train):
hf.create_dataset('X_train%i' % idx, data=x_train.values if type(X) != HDF5Matrix else x_train[:])
else:
hf.create_dataset('X_train', data=X_train.values if type(X) != HDF5Matrix else X_train[:])
if (type(X_test) == list):
for idx, x_test in enumerate(X_test):
hf.create_dataset('X_test%i' % idx, data=x_test.values if type(X) != HDF5Matrix else x_test[:])
else:
hf.create_dataset('X_test', data=X_test.values if type(X) != HDF5Matrix else X_test[:])
hf.create_dataset('Y_train', data=Y_train if type(Y) != HDF5Matrix else Y_train[:])
hf.create_dataset('Y_test', data=Y_test if type(Y) != HDF5Matrix else Y_test[:])
yield i, [HDF5Matrix(hdf5_fpath, 'X_train%i' % idx) for idx in range(len(X_train))] if (type(X_train) == list) else HDF5Matrix(hdf5_fpath, 'X_train'), [HDF5Matrix(hdf5_fpath, 'X_test%i' % idx) for idx in range(len(X_test))] if (type(X_test) == list) else HDF5Matrix(hdf5_fpath, 'X_test'), HDF5Matrix(hdf5_fpath, 'Y_train'), HDF5Matrix(hdf5_fpath, 'Y_test'), train_idx_df, test_idx_df
# The implementation of HDF5Matrix is not good since it keep all the hdf5 file opened, so we need to manually close them.
remove_hfps = []
for hfpath, hf in HDF5Matrix.refs.items():
if (hfpath.startswith(hdf5_fpath)):
hf.close()
remove_hfps.append(hfpath)
for hfpath in remove_hfps:
HDF5Matrix.refs.pop(hfpath, None)
else:
yield i, [x.values for x in X_train] if (type(X_train) == list) else X_train.values, [x.values for x in X_test] if (type(X_test) == list) else X_test.values, Y_train, Y_test, train_idx_df, test_idx_df
# Evaluation
def evaluate(X_train, Y_train, X_test, Y_test, model_iter, model_param={}, avg='micro', kfold=5, cfg_param={}, global_param={}, lbid=''):
print('Evaluating...')
from keras.utils.io_utils import HDF5Matrix
global common_cfg
FILT_NAMES, CLF_NAMES, PL_NAMES, PL_SET = model_param['glb_filtnames'], model_param['glb_clfnames'], global_param['pl_names'], global_param['pl_set']
lbidstr = ('_' + (str(lbid) if lbid != -1 else 'all')) if lbid is not None and lbid != '' else ''
# Format the data
if (type(X_train) == list):
assert all([len(x) == len(X_train[0]) for x in X_train[1:]])
X_train = [pd.DataFrame(x) if (type(x) != pd.io.parsers.TextFileReader and type(x) != pd.DataFrame) else x for x in X_train]
X_train = [pd.concat(x) if (type(x) == pd.io.parsers.TextFileReader and not to_hdf) else x for x in X_train]
else:
if (type(X_train) != pd.io.parsers.TextFileReader and type(X_train) != pd.DataFrame):
X_train = pd.DataFrame(X_train) if type(X_train) != HDF5Matrix else X_train
X_train = pd.concat(X_train) if (type(X_train) == pd.io.parsers.TextFileReader and not to_hdf) else X_train
if (type(Y_train) != pd.io.parsers.TextFileReader and type(Y_train) != pd.DataFrame):
Y_train = pd.DataFrame(Y_train) if (type(Y_train) == pd.io.parsers.TextFileReader and not to_hdf) else Y_train
if (type(Y_train) != HDF5Matrix):
Y_train = Y_train.values.reshape((Y_train.shape[0],)) if (len(Y_train.shape) == 1 or Y_train.shape[1] == 1) else Y_train.values
else:
Y_train = Y_train
if (type(X_test) == list):
assert all([len(x) == len(X_test[0]) for x in X_test[1:]])
X_test = [pd.DataFrame(x) if (type(x) != pd.io.parsers.TextFileReader and type(x) != pd.DataFrame) else x for x in X_test]
X_test = [pd.concat(x) if (type(x) == pd.io.parsers.TextFileReader and not to_hdf) else x for x in X_test]
else:
if (type(X_test) != pd.io.parsers.TextFileReader and type(X_test) != pd.DataFrame):
X_test = pd.DataFrame(X_test) if type(X_test) != HDF5Matrix else X_test
X_test = pd.concat(X_test) if (type(X_test) == pd.io.parsers.TextFileReader and not to_hdf) else X_test
if (type(Y_test) != pd.io.parsers.TextFileReader and type(Y_test) != pd.DataFrame):
Y_test = pd.DataFrame(Y_test) if (type(Y_test) == pd.io.parsers.TextFileReader and not to_hdf) else Y_test
if (type(Y_test) != HDF5Matrix):
Y_test = Y_test.values.reshape((Y_test.shape[0],)) if (len(Y_test.shape) == 1 or Y_test.shape[1] == 1) else Y_test.values
else:
Y_test = Y_test
is_mltl = True if len(Y_train.shape) > 1 and Y_train.shape[1] > 1 or 2 in Y_train else False
print('Benchmark is starting...')
mean_fpr = np.linspace(0, 1, 100)
mean_recall = np.linspace(0, 1, 100)
xdf = X_train[0] if type(X_train)==list else X_train
roc_dict, prc_dict, featw_data, subfeatw_data = [{} for i in range(4)]
## Copy from cross_validate function Start ##
del PL_NAMES[:]
PL_SET.clear()
if (cfg_param.setdefault('npg_ratio', None) is not None):
npg_ratio = cfg_param['npg_ratio']
Y_train = np.array(Y_train) # HDF5Matrix is not working in matrix slicing and boolean operation
y = Y_train[:,0] if (len(Y_train.shape) > 1) else Y_train
if (1.0 * np.abs(y).sum() / Y_train.shape[0] < 1.0 / (npg_ratio + 1)):
all_true = np.arange(Y_train.shape[0])[y > 0].tolist()
all_false = np.arange(Y_train.shape[0])[y <= 0].tolist()
true_id = np.random.choice(len(all_true), size=int(1.0 / npg_ratio * len(all_false)), replace=True)
true_idx = [all_true[i] for i in true_id]
all_train_idx = sorted(set(true_idx + all_false))
X_train = [x.iloc[all_train_idx] if type(x) != HDF5Matrix else x[all_train_idx] for x in X_train] if (type(X_train) is list) else X_train.iloc[all_train_idx] if type(x) != HDF5Matrix else X_train[all_train_idx]
Y_train = Y_train[all_train_idx,:] if (len(Y_train.shape) > 1) else Y_train[all_train_idx]
results, preds = [[] for x in range(2)]
# Y_test = np.column_stack([np.abs(Y_test).reshape((Y_test.shape[0],-1))] + [label_binarize(lb, classes=[-1,1,0])[:,1] for lb in (np.sign(Y_test).astype('int8').reshape((Y_test.shape[0],-1))).T]) if (len(Y_test.shape) < 2 or Y_test.shape[1] == 1 or np.where(Y_test<0)[0].shape[0]>0) else Y_test
for vars in model_iter(**model_param):
if (global_param['comb']):
mdl_name, mdl = [vars[x] for x in range(2)]
else:
filt_name, filter, clf_name, clf= [vars[x] for x in range(4)]
print('#' * 80)
# Assemble a pipeline
if ('filter' in locals() and filter != None):
model_name = '%s [Ft Filt] & %s [CLF]' % (filt_name, clf_name)
pipeline = Pipeline([('featfilt', clone(filter)), ('clf', clf)])
elif ('clf' in locals() and clf != None):
model_name = '%s [CLF]' % clf_name
pipeline = Pipeline([('clf', clf)])
else:
model_name = mdl_name
pipeline = mdl
if (model_name in PL_SET): continue
PL_NAMES.append(model_name)
PL_SET.add(model_name)
print(model_name)
# Benchmark results
bm_results = benchmark(pipeline, X_train, Y_train, X_test, Y_test, mltl=is_mltl, signed=global_param.setdefault('signed', True if np.where(Y_train<0)[0].shape[0]>0 else False), average=avg)
# Clear the model environment (e.g. GPU resources)
del pipeline
# if (type(pipeline) is Pipeline):
# for cmpn in pipeline.named_steps.values():
# if (getattr(cmpn, "clear", None)): cmpn.clear()
# else:
# if (getattr(pipeline, "clear", None)):
# pipeline.clear()
# Obtain the results
if (is_mltl and avg == 'all'):
results.append([bm_results[x] for x in ['accuracy', 'micro-precision', 'micro-recall', 'micro-fscore', 'macro-precision', 'macro-recall', 'macro-fscore', 'train_time', 'test_time']])
else:
results.append([bm_results[x] for x in ['accuracy', 'precision', 'recall', 'fscore', 'train_time', 'test_time']])
preds.append(bm_results['pred_lb'])
if (cfg_param.setdefault('save_pred', False)):
io.write_npz(dict(pred_lb=bm_results['pred_lb'], pred_prob=bm_results['pred_prob'], true_lb=Y_test), 'pred_%s%s' % (model_name.replace(' ', '_').lower(), lbidstr))
if (is_mltl and avg == 'all'):
micro_id, macro_id = '-'.join([model_name,'micro']), '-'.join([model_name,'macro'])
roc_dict[micro_id] = roc_dict.setdefault(micro_id, 0) + np.interp(mean_fpr, bm_results['micro-roc'][0], bm_results['micro-roc'][1])
roc_dict[macro_id] = roc_dict.setdefault(macro_id, 0) + np.interp(mean_fpr, bm_results['macro-roc'][0], bm_results['macro-roc'][1])
else:
roc_dict[model_name] = roc_dict.setdefault(model_name, 0) + np.interp(mean_fpr, bm_results['roc'][0], bm_results['roc'][1])
prc_dict[model_name] = prc_dict.setdefault(model_name, 0) + np.interp(mean_recall, bm_results['prc'][0], bm_results['prc'][1])
for k, v in bm_results['feat_w'].items():
key = '%s_%s_%s' % (model_name, k[0], k[1])
featw_data[key] = v
for k, v in bm_results['sub_feat_w'].items():
key = '%s_%s_%s' % (model_name, k[0], k[1])
subfeatw_data[key] = v
print('\n')
# Prediction overlap
if (True if len(Y_train.shape) > 1 and Y_train.shape[1] > 1 else False):
preds_mt = np.column_stack([x.ravel() for x in preds])
else:
preds_mt = np.column_stack(preds)
preds.append(Y_test)
tpreds_mt = np.column_stack([x.ravel() for x in preds])
## Copy from cross_validate function End ##
povl = pred_ovl(preds_mt, Y_test)
# Spearman's rank correlation
spearman = stats.spearmanr(tpreds_mt)
# Kendall rank correlation
# kendalltau = stats.kendalltau(preds_mt)
# Pearson correlation
# pearson = stats.pearsonr(preds_mt)
## Save performance data
if (is_mltl and avg == 'all'):
metric_idx = ['Accuracy', 'Micro Precision', 'Micro Recall', 'Micro F score', 'Macro Precision', 'Macro Recall', 'Macro F score', 'Train time', 'Test time']
else:
metric_idx = ['Accuracy', 'Precision', 'Recall', 'F score', 'Train time', 'Test time']
perf_df = pd.DataFrame(np.array(results).T, index=metric_idx, columns=PL_NAMES)
povl_idx = [' & '.join(x) for x in imath.subset(PL_NAMES, min_crdnl=1)]
povl_df = pd.DataFrame(np.array(povl), index=povl_idx, columns=['pred_ovl', 'tpred_ovl'])
spmnr_val_df = pd.DataFrame(spearman[0], index=PL_NAMES+['Annotations'], columns=PL_NAMES+['Annotations'])
spmnr_pval_df = pd.DataFrame(spearman[1], index=PL_NAMES+['Annotations'], columns=PL_NAMES+['Annotations'])
if (cfg_param.setdefault('save_tpred', True)):
io.write_npz(tpreds_mt, 'tpred_clf%s' % lbidstr)
if (cfg_param.setdefault('save_perf', True)):
perf_df.to_excel('perf_clf%s.xlsx' % lbidstr)
if (cfg_param.setdefault('save_perf_npz', False)):
io.write_df(perf_df, 'perf_clf%s.npz' % lbidstr, with_idx=True)
if (cfg_param.setdefault('save_povl', False)):
povl_df.to_excel('povl_clf%s.xlsx' % lbidstr)
if (cfg_param.setdefault('save_povl_npz', False)):
io.write_df(povl_df, 'povl_clf%s.npz' % lbidstr, with_idx=True)
if (cfg_param.setdefault('save_spmnr', False)):
spmnr_val_df.to_excel('spmnr_clf%s.xlsx' % lbidstr)
if (cfg_param.setdefault('save_spmnr_npz', False)):
io.write_df(spmnr_val_df, 'spmnr_clf%s.npz' % lbidstr, with_idx=True)
if (cfg_param.setdefault('save_spmnr_pval', False)):
spmnr_pval_df.to_excel('spmnr_pval_clf%s.xlsx' % lbidstr)
if (cfg_param.setdefault('save_spmnr_pval_npz', False)):
io.write_df(spmnr_pval_df, 'spmnr_pval_clf%s.npz' % lbidstr, with_idx=True)
# Feature importances
try:
save_featw(xdf.columns.values if type(xdf) != HDF5Matrix else np.arange(xdf.shape[1]), featw_data, subfeatw_data, cfg_param=cfg_param, lbid=lbid)
except Exception as e:
print(e)
## Plot figures
if (is_mltl and avg == 'all'):
micro_roc_data, micro_roc_labels, micro_roc_aucs, macro_roc_data, macro_roc_labels, macro_roc_aucs = [[] for i in range(6)]
else:
roc_data, roc_labels, roc_aucs = [[] for i in range(3)]
prc_data, prc_labels, prc_aucs = [[] for i in range(3)]
for pl in PL_NAMES:
if (is_mltl and avg == 'all'):
micro_id, macro_id = '-'.join([pl,'micro']), '-'.join([pl,'macro'])
micro_mean_tpr, macro_mean_tpr = roc_dict[micro_id], roc_dict[macro_id]
micro_roc_auc = metrics.auc(mean_fpr, micro_mean_tpr)
macro_roc_auc = metrics.auc(mean_fpr, macro_mean_tpr)
micro_roc_data.append([mean_fpr, micro_mean_tpr])
micro_roc_aucs.append(micro_roc_auc)
micro_roc_labels.append('%s (AUC=%0.2f)' % (pl, micro_roc_auc))
macro_roc_data.append([mean_fpr, macro_mean_tpr])
macro_roc_aucs.append(macro_roc_auc)
macro_roc_labels.append('%s (AUC=%0.2f)' % (pl, macro_roc_auc))
else:
mean_tpr = roc_dict[pl]
mean_roc_auc = metrics.auc(mean_fpr, mean_tpr)
roc_data.append([mean_fpr, mean_tpr])
roc_aucs.append(mean_roc_auc)
roc_labels.append('%s (AUC=%0.2f)' % (pl, mean_roc_auc))
mean_prcn = prc_dict[pl]
mean_prc_auc = metrics.auc(mean_recall, mean_prcn)
prc_data.append([mean_recall, mean_prcn])
prc_aucs.append(mean_prc_auc)
prc_labels.append('%s (AUC=%0.2f)' % (pl, mean_prc_auc))
group_dict = {}
for i, pl in enumerate(PL_NAMES):
group_dict.setdefault(tuple(set(difflib.get_close_matches(pl, PL_NAMES))), []).append(i)
if (not cfg_param.setdefault('group_by_name', False) or len(group_dict) == len(PL_NAMES)):
groups = None
else:
group_array = np.array(group_dict.values())
group_array.sort()
groups = group_array.tolist()
if (is_mltl and avg == 'all'):
aucs_df = pd.DataFrame([micro_roc_aucs, macro_roc_aucs, prc_aucs], index=['Micro ROC AUC', 'Macro ROC AUC', 'PRC AUC'], columns=PL_NAMES)
if (cfg_param.setdefault('plot_roc', True)):
plot.plot_roc(micro_roc_data, micro_roc_labels, groups=groups, fname='micro_roc%s'%lbidstr, plot_cfg=common_cfg)
plot.plot_roc(macro_roc_data, macro_roc_labels, groups=groups, fname='macro_roc%s'%lbidstr, plot_cfg=common_cfg)
else:
aucs_df = pd.DataFrame([roc_aucs, prc_aucs], index=['ROC AUC', 'PRC AUC'], columns=PL_NAMES)
if (cfg_param.setdefault('plot_roc', True)):
plot.plot_roc(roc_data, roc_labels, groups=groups, fname='roc%s'%lbidstr, plot_cfg=common_cfg)
if (cfg_param.setdefault('plot_prc', True)):
plot.plot_prc(prc_data, prc_labels, groups=groups, fname='prc%s'%lbidstr, plot_cfg=common_cfg)
if (cfg_param.setdefault('save_auc', False)):
aucs_df.to_excel('auc%s.xlsx' % lbidstr)
filt_num, clf_num = len(FILT_NAMES), len(CLF_NAMES)
if (cfg_param.setdefault('plot_metric', False)):
for mtrc in metric_idx:
mtrc_avg_list, mtrc_std_list = [[] for i in range(2)]
if (global_param['comb']):
mtrc_avg = perf_avg_df.ix[mtrc,:].values.reshape((1,-1))
mtrc_std = perf_std_df.ix[mtrc,:].values.reshape((1,-1))
plot.plot_bar(mtrc_avg, mtrc_std, xlabels=PL_NAMES, labels=None, title='%s by Classifier and Feature Selection' % mtrc, fname='%s_clf_ft%s' % (mtrc.replace(' ', '_').lower(), lbidstr), plot_cfg=common_cfg)
else:
for i in range(filt_num):
offset = i * clf_num
mtrc_avg_list.append(perf_avg_df.ix[mtrc,offset:offset+clf_num].values.reshape((1,-1)))
mtrc_std_list.append(perf_std_df.ix[mtrc,offset:offset+clf_num].values.reshape((1,-1)))
mtrc_avg = np.concatenate(mtrc_avg_list)
mtrc_std = np.concatenate(mtrc_std_list)
plot.plot_bar(mtrc_avg, mtrc_std, xlabels=CLF_NAMES, labels=FILT_NAMES, title='%s by Classifier and Feature Selection' % mtrc, fname='%s_clf_ft%s' % (mtrc.replace(' ', '_').lower(), lbidstr), plot_cfg=common_cfg)
# Cross validation
def cross_validate(X, Y, model_iter, model_param={}, avg='micro', kfold=5, cfg_param={}, split_param={}, global_param={}, lbid=''):
print('Cross validating...')
from keras.utils.io_utils import HDF5Matrix
global common_cfg
FILT_NAMES, CLF_NAMES, PL_NAMES, PL_SET = model_param['glb_filtnames'], model_param['glb_clfnames'], global_param['pl_names'], global_param['pl_set']
lbidstr = ('_' + (str(lbid) if lbid != -1 else 'all')) if lbid is not None and lbid != '' else ''
to_hdf, hdf5_fpath = cfg_param.setdefault('to_hdf', False), 'crsval_dataset%s.h5' % lbidstr if cfg_param.setdefault('hdf5_fpath', 'crsval_dataset%s.h5' % lbidstr) is None else cfg_param['hdf5_fpath']
# Format the data
if (type(X) == list):
assert all([len(x) == len(X[0]) for x in X[1:]])
X = [pd.DataFrame(x) if (type(x) != pd.io.parsers.TextFileReader and type(x) != pd.DataFrame) else x for x in X]
X = [pd.concat(x) if (type(x) == pd.io.parsers.TextFileReader and not to_hdf) else x for x in X]
else:
if (type(X) != pd.io.parsers.TextFileReader and type(X) != pd.DataFrame):
X = pd.DataFrame(X) if type(X) != HDF5Matrix else X
X = pd.concat(X) if (type(X) == pd.io.parsers.TextFileReader and not to_hdf) else X
if (type(Y) != pd.io.parsers.TextFileReader and type(Y) != pd.DataFrame):
Y = pd.DataFrame(Y) if (type(Y) == pd.io.parsers.TextFileReader and not to_hdf) else Y
if (type(Y) != HDF5Matrix):
Y_mt = Y.values.reshape((Y.shape[0],)) if (len(Y.shape) == 1 or Y.shape[1] == 1) else Y.values
else:
Y_mt = Y
is_mltl = True if len(Y_mt.shape) > 1 and Y_mt.shape[1] > 1 or 2 in Y_mt else False
print('Benchmark is starting...')
mean_fpr = np.linspace(0, 1, 100)
mean_recall = np.linspace(0, 1, 100)
xdf = X[0] if type(X)==list else X
if (len(split_param) == 0):
if (type(xdf) != HDF5Matrix):
kf = list(KFold(n_splits=kfold, shuffle=True, random_state=0).split(xdf, Y_mt)) if (len(Y_mt.shape) == 1) else list(KFold(n_splits=kfold, shuffle=True, random_state=0).split(xdf, Y_mt[:,0].reshape((Y_mt.shape[0],))))
else:
kf = list(KFold(n_splits=kfold, shuffle=False, random_state=0).split(xdf[:], Y_mt[:])) if (len(Y_mt.shape) == 1) else list(KFold(n_splits=kfold, shuffle=False, random_state=0).split(xdf[:], Y_mt[:].reshape((-1,)))) # HDF5Matrix is not working in shuffle indices
else:
split_param['shuffle'] = True if type(xdf) != HDF5Matrix else False
# To-do: implement the split method for multi-label data
if ('train_size' in split_param and 'test_size' in split_param):
kf = list(StratifiedShuffleSplit(n_splits=kfold, train_size=split_param['train_size'], test_size=split_param['test_size'], random_state=0).split(xdf, Y_mt)) if (len(Y_mt.shape) == 1) else list(StratifiedShuffleSplit(n_splits=kfold, train_size=split_param['train_size'], test_size=split_param['test_size'], random_state=0).split(xdf, Y_mt[:,0].reshape((Y_mt.shape[0],))))
else:
kf = list(StratifiedKFold(n_splits=kfold, shuffle=split_param.setdefault('shuffle', True), random_state=0).split(xdf, Y_mt)) if (len(Y_mt.shape) == 1) else list(StratifiedKFold(n_splits=kfold, shuffle=split_param.setdefault('shuffle', True), random_state=0).split(xdf, Y_mt[:,0].reshape((Y_mt.shape[0],))))
crsval_results, crsval_tpreds, crsval_povl, crsval_spearman, crsval_kendalltau, crsval_pearson = [[] for i in range(6)]
crsval_roc, crsval_prc, crsval_featw, crsval_subfeatw = [{} for i in range(4)]
# for i, (train_idx, test_idx) in enumerate(kf):
for i, X_train, X_test, Y_train, Y_test, train_idx_df, test_idx_df in kf2data(kf, X, Y_mt, to_hdf=to_hdf, hdf5_fpath=hdf5_fpath):
del PL_NAMES[:]
PL_SET.clear()
print('\n' + '-' * 80 + '\n' + '%s time validation' % imath.ordinal(i+1) + '\n' + '-' * 80 + '\n')
if (cfg_param.setdefault('save_crsval_idx', False)):
io.write_df(train_idx_df, 'train_idx_crsval_%s%s.npz' % (i, lbidstr), with_idx=True)
io.write_df(test_idx_df, 'test_idx_crsval_%s%s.npz' % (i, lbidstr), with_idx=True)
if (cfg_param.setdefault('npg_ratio', None) is not None):
npg_ratio = cfg_param['npg_ratio']
Y_train = np.array(Y_train) # HDF5Matrix is not working in matrix slicing and boolean operation
y = Y_train[:,0] if (len(Y_train.shape) > 1) else Y_train
if (1.0 * np.abs(y).sum() / Y_train.shape[0] < 1.0 / (npg_ratio + 1)):
all_true = | np.arange(Y_train.shape[0]) | numpy.arange |
"""Test function to rotate vector onto vector."""
from __future__ import absolute_import, division, print_function
import unittest
import numpy as np
import rowan
class TestVectorVector(unittest.TestCase):
"""Test rotation of a vector onto another vector."""
def test_simple(self):
"""Test finding quaternion to rotate a vector onto another vector."""
vec1 = np.array([1, 0, 0])
vec2 = np.array([0, 1, 0])
vec3 = np.array([0, 0, 1])
quat = rowan.vector_vector_rotation(vec1, vec2)
self.assertTrue(
np.allclose(quat, np.array([[0, np.sqrt(2) / 2, np.sqrt(2) / 2, 0]]))
)
quat = rowan.vector_vector_rotation(vec1, vec3)
self.assertTrue(
np.allclose(quat, np.array([[0, np.sqrt(2) / 2, 0, np.sqrt(2) / 2]]))
)
def test_ap(self):
"""Test finding quaternion to rotate antiparallel vectors onto each other."""
# For this test, there are multiple quaternions that would effect the
# correct rotation, so rather than checking for a specific one we check
# that the appropriate rotation results from applying the quaternion
vec1 = np.array([1, 0, 0])
vec2 = np.array([0, 1, 0])
quat = rowan.vector_vector_rotation(vec1, vec2)
self.assertTrue(
np.allclose(rowan.rotate(quat, vec1), vec2 / np.linalg.norm(vec2, axis=-1))
)
vec1 = np.array([1, 0, 0])
vec2 = np.array([[0, 1, 0], [2, 0, 0], [-2, 0, 0]])
quat = rowan.vector_vector_rotation(vec1, vec2)
self.assertTrue(
np.allclose(
rowan.rotate(quat, vec1),
vec2 / np.linalg.norm(vec2, axis=-1)[:, np.newaxis],
)
)
vec1 = np.array([0, 1, 0])
vec2 = np.array([[0, 0, 1], [0, 2, 0], [0, -2, 0]])
quat = rowan.vector_vector_rotation(vec1, vec2)
self.assertTrue(
np.allclose(
rowan.rotate(quat, vec1),
vec2 / np.linalg.norm(vec2, axis=-1)[:, np.newaxis],
)
)
def test_broadcast(self):
"""Test broadcasting."""
vec1 = np.array([1, 0, 0])
vec2 = np.array([0, 1, 0])
vec3 = np.array([0, 0, 1])
arr1 = np.stack((vec2, vec3), axis=0)
output = np.array(
[
[0, np.sqrt(2) / 2, np.sqrt(2) / 2, 0],
[0, | np.sqrt(2) | numpy.sqrt |
################################################################################
# Peach - Computational Intelligence for Python
# <NAME>
#
# This file: optm/optm.py
# Basic definitions and base class
################################################################################
# Doc string, reStructuredText formatted:
__doc__ = """
Basic definitons and base class for optimizers
This sub-package exports some auxiliary functions to work with cost functions,
namely, a function to calculate gradient vectors and hessian matrices, which are
extremely important in optimization.
Also, a base class, ``Optimizer``, for all optimizers. Sub-class this class if
you want to create your own optmizer, and follow the interface. This will allow
easy configuration of your own scripts and comparison between methods.
"""
################################################################################
from numpy import array, zeros
################################################################################
# Auxiliary functions
################################################################################
def gradient(f, dx=1e-5):
'''
Creates a function that calculates the gradient vector of a scalar field.
This function takes as a parameter a scalar function and creates a new
function that is able to calculate the derivative (in case of single
variable functions) or the gradient vector (in case of multivariable
functions. Please, note that this function takes as a parameter a
*function*, and returns as a result *another function*. Calling the returned
function on a point will give the gradient vector of the original function
at that point::
>>> def f(x):
return x^2
>>> df = gradient(f)
>>> df(1)
2
In the above example, ``df`` is a generated function which will return the
result of the expression ``2*x``, the derivative of the original function.
In the case ``f`` is a multivariable function, it is assumed that its
argument is a line vector.
:Parameters:
f
Any function, one- or multivariable. The function must be an scalar
function, though there is no checking at the moment the function is
created. If ``f`` is not an scalar function, an exception will be
raised at the moment the returned function is used.
dx
Optional argument that gives the precision of the calculation. It is
recommended that ``dx = sqrt(D)``, where ``D`` is the machine precision.
It defaults to ``1e-5``, which usually gives a good estimate.
:Returns:
A new function which, upon calling, gives the derivative or gradient
vector of the original function on the analised point. The parameter of
the returned function is a real number or a line vector where the gradient
should be calculated.
'''
def _df(x):
try:
x = float(x)
return (f(x+dx) - f(x-dx)) / (2.*dx)
except TypeError:
n = x.size
df = zeros((n, ))
for i in xrange(n):
xl = array(x)
xl[i] = xl[i] - dx
xr = array(x)
xr[i] = xr[i] + dx
df[i] = (f(xr) - f(xl)) / (2.*dx)
return df
return _df
def hessian(f, dx=1e-5):
'''
Creates a function that calculates the hessian matrix of a scalar field.
This function takes as a parameter a scalar function and creates a new
function that is able to calculate the second derivative (in case of single
variable functions) or the hessian matrix (in case of multivariable
functions. Please, note that this function takes as a parameter a
*function*, and returns as a result *another function*. Calling the returned
function on a point will give the hessian matrix of the original function
at that point::
>>> def f(x):
return x^4
>>> ddf = hessian(f)
>>> ddf(1)
12
In the above example, ``ddf`` is a generated function which will return the
result of the expression ``12*x**2``, the second derivative of the original
function. In the case ``f`` is a multivariable function, it is assumed that
its argument is a line vector.
:Parameters:
f
Any function, one- or multivariable. The function must be an scalar
function, though there is no checking at the moment the function is
created. If ``f`` is not an scalar function, an exception will be
raised at the moment the returned function is used.
dx
Optional argument that gives the precision of the calculation. It is
recommended that ``dx = sqrt(D)``, where ``D`` is the machine precision.
It defaults to ``1e-5``, which usually gives a good estimate.
:Returns:
A new function which, upon calling, gives the second derivative or hessian
matrix of the original function on the analised point. The parameter of
the returned function is a real number or a line vector where the hessian
should be calculated.
'''
def _hf(x):
try:
x = float(x)
return (f(x+dx) - 2*f(x) + f(x-dx)) / (4.*dx*dx)
except TypeError:
n = x.size
hf = zeros((n, n))
for i in range(n):
for j in range(n):
xll = array(x)
xll[i] = xll[i] - dx
xll[j] = xll[j] - dx
xul = | array(x) | numpy.array |
from . import GeneExpressionDataset
from .anndataset import AnnDatasetFromAnnData, DownloadableAnnDataset
import torch
import pickle
import os
import numpy as np
import pandas as pd
import anndata
class AnnDatasetKeywords(GeneExpressionDataset):
def __init__(self, data, select_genes_keywords=[]):
super().__init__()
if isinstance(data, str):
anndataset = anndata.read(data)
else:
anndataset = data
idx_and_gene_names = [
(idx, gene_name) for idx, gene_name in enumerate(list(anndataset.var.index))
]
for keyword in select_genes_keywords:
idx_and_gene_names = [
(idx, gene_name)
for idx, gene_name in idx_and_gene_names
if keyword.lower() in gene_name.lower()
]
gene_indices = | np.array([idx for idx, _ in idx_and_gene_names]) | numpy.array |
"""
Evaluate NPL posterior samples predictive performance/time
"""
import numpy as np
import pickle
import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd
from tqdm import tqdm
import scipy as sp
import importlib
import npl.sk_gaussian_mixture as skgm
from npl.evaluate import gmm_ll as gll
from sklearn.mixture.gaussian_mixture import _compute_precision_cholesky
from joblib import Parallel, delayed
def IS_lppd(y,pi,mu,sigma,K,logweights_is): #calculate posterior predictive of test
model = skgm.GaussianMixture(K, covariance_type = 'diag')
B = np.shape(mu)[0]
N_test = np.shape(y)[0]
ll_test = | np.zeros(N_test) | numpy.zeros |
# -*- coding: utf-8 -*-
"""
Created on Dec 21 14:57:02 2019
@author: Learning Deep Kernels for Two-sample Test
@Implementation of Deep-kernel ME (selecting test locations) on CIFAR dataset (Interpretability experiments).
BEFORE USING THIS CODE:
1. This code requires PyTorch 1.1.0, which can be found in
https://pytorch.org/get-started/previous-versions/ (CUDA version is 10.1).
2. This code also requires freqopttest repo (interpretable nonparametric two-sample test)
to implement ME and SCF tests, which can be installed by
pip install git+https://github.com/wittawatj/interpretable-test
3. Numpy, Sklearn, Matplotlib are also required. Users can install
Python via Anaconda (Python 3.7.3) to obtain both packages. Anaconda
can be found in https://www.anaconda.com/distribution/#download-section .
"""
import argparse
import os
import numpy as np
import torchvision.transforms as transforms
from torch.utils.data import DataLoader
from torchvision import datasets
from torch.autograd import Variable
import torch.nn as nn
import torch
import matplotlib.pyplot as plt
from utils_HD import compute_ME_stat, MatConvert, MMDu, TST_ME_DK_per
# Setup seeds
os.makedirs("images", exist_ok=True)
np.random.seed(819)
torch.manual_seed(819)
torch.cuda.manual_seed(819)
torch.backends.cudnn.deterministic = True
is_cuda = True
# parameters setting
parser = argparse.ArgumentParser()
parser.add_argument("--n_epochs", type=int, default=1000, help="number of epochs of training")
parser.add_argument("--batch_size", type=int, default=100, help="size of the batches")
parser.add_argument("--lr", type=float, default=0.0002, help="adam: learning rate")
parser.add_argument("--img_size", type=int, default=64, help="size of each image dimension")
parser.add_argument("--channels", type=int, default=3, help="number of image channels")
parser.add_argument("--n", type=int, default=1000, help="number of samples")
opt = parser.parse_args()
print(opt)
dtype = torch.float
device = torch.device("cuda:0")
cuda = True if torch.cuda.is_available() else False
N_per = 100 # permutation times
alpha = 0.05 # test threshold
N1 = opt.n # number of samples in one set
K = 10 # number of trails
J = 1 # number of test locations
N = 100 # number of test sets
N_f = 100.0 # number of test sets (float)
# Loss function
adversarial_loss = torch.nn.CrossEntropyLoss()
# Naming variables
ep_OPT = np.zeros([K])
s_OPT = np.zeros([K])
s0_OPT = np.zeros([K])
T_org_OPT = torch.zeros([K,J,3,64,64]) # Record test locations obtained by MMD-D
Results = np.zeros([1,K])
# Define the deep network for distinguishing two sets of samples
class Discriminator(nn.Module):
def __init__(self):
super(Discriminator, self).__init__()
def discriminator_block(in_filters, out_filters, bn=True):
block = [nn.Conv2d(in_filters, out_filters, 3, 2, 1), nn.LeakyReLU(0.2, inplace=True), nn.Dropout2d(0)]
if bn:
block.append(nn.BatchNorm2d(out_filters, 0.8))
return block
self.model = nn.Sequential(
*discriminator_block(opt.channels, 16, bn=False),
*discriminator_block(16, 32),
*discriminator_block(32, 64),
*discriminator_block(64, 128),
)
# The height and width of downsampled image
ds_size = opt.img_size // 2 ** 4
self.adv_layer = nn.Sequential(
nn.Linear(128 * ds_size ** 2, 300),
nn.ReLU(),
nn.Linear(300, 2),
nn.Softmax())
def forward(self, img):
out = self.model(img)
out = out.view(out.shape[0], -1)
validity = self.adv_layer(out)
return validity
# Define the deep network for MMD-D
class Featurizer(nn.Module):
def __init__(self):
super(Featurizer, self).__init__()
def discriminator_block(in_filters, out_filters, bn=True):
block = [nn.Conv2d(in_filters, out_filters, 3, 2, 1), nn.LeakyReLU(0.2, inplace=True), nn.Dropout2d(0)] #0.25
if bn:
block.append(nn.BatchNorm2d(out_filters, 0.8))
return block
self.model = nn.Sequential(
*discriminator_block(opt.channels, 16, bn=False),
*discriminator_block(16, 32),
*discriminator_block(32, 64),
*discriminator_block(64, 128),
)
# The height and width of downsampled image
ds_size = opt.img_size // 2 ** 4
self.adv_layer = nn.Sequential(
nn.Linear(128 * ds_size ** 2, 300))
def forward(self, img):
out = self.model(img)
out = out.view(out.shape[0], -1)
feature = self.adv_layer(out)
return feature
# Configure data loader
dataset_test = datasets.CIFAR10(root='./data/cifar10', download=True,train=False,
transform=transforms.Compose([
transforms.Resize(opt.img_size),
transforms.ToTensor(),
transforms.Normalize((0.5, 0.5, 0.5), (0.5, 0.5, 0.5)),
]))
dataloader_test = torch.utils.data.DataLoader(dataset_test, batch_size=10000,
shuffle=False, num_workers=1)
dataset_test_org = datasets.CIFAR10(root='./data/cifar10', download=True,train=False, transform=transforms.Compose([transforms.ToTensor()]))
dataloader_test_org = torch.utils.data.DataLoader(dataset_test_org, batch_size=10000,
shuffle=False, num_workers=1)
# Obtain CIFAR10 images
for i, (imgs, Labels) in enumerate(dataloader_test):
data_all = imgs
label_all = Labels
for i, (imgs, Labels) in enumerate(dataloader_test_org):
data_all_org= imgs
label_all_org = Labels
print(data_all_org.shape)
Ind_all = np.arange(len(data_all))
# Obtain CIFAR10.1 images
data_new = np.load('./cifar10.1_v4_data.npy')
data_T = np.transpose(data_new, [0,3,1,2])
TT = transforms.Compose([transforms.Resize(opt.img_size),transforms.ToTensor(),
transforms.Normalize((0.5, 0.5, 0.5), (0.5, 0.5, 0.5))])
TT_org = transforms.Compose([transforms.ToTensor()])
trans = transforms.ToPILImage()
data_trans = torch.zeros([len(data_T),3,opt.img_size,opt.img_size])
data_trans_org = torch.zeros([len(data_T),3,32,32])
data_T_tensor = torch.from_numpy(data_T)
for i in range(len(data_T)):
d0 = trans(data_T_tensor[i])
data_trans[i] = TT(d0)
for i in range(len(data_T)):
d0 = trans(data_T_tensor[i])
data_trans_org[i] = TT_org(d0)
print(data_trans_org.shape)
Ind_v4_all = np.arange(len(data_T))
# Repeat experiments K times (K = 10) and report average test power (rejection rate)
for kk in range(K):
print(kk)
torch.manual_seed(kk * 19 + N1)
torch.cuda.manual_seed(kk * 19 + N1)
np.random.seed(seed=1102 * (kk + 10) + N1)
# Initialize deep networks for MMD-D
featurizer = Featurizer()
discriminator = Discriminator()
# Initialize parameters
epsilonOPT = torch.log(MatConvert(np.random.rand(1) * 10 ** (-10), device, dtype))
epsilonOPT.requires_grad = True
sigmaOPT = MatConvert(np.ones(1) * np.sqrt(2 * 32 * 32), device, dtype)
sigmaOPT.requires_grad = True
sigma0OPT = MatConvert(np.ones(1) * np.sqrt(0.005), device, dtype)
sigma0OPT.requires_grad = True
TT_org = MatConvert(np.random.randn(J,3,64,64), device, dtype)
TT_org.requires_grad = True
print(epsilonOPT.item())
if cuda:
featurizer.cuda()
discriminator.cuda()
adversarial_loss.cuda()
# Collect CIFAR10 images
Ind_tr = np.random.choice(len(data_all), N1, replace=False)
Ind_te = np.delete(Ind_all, Ind_tr)
train_data = []
for i in Ind_tr:
train_data.append([data_all[i], label_all[i]])
print(len(train_data))
dataloader = torch.utils.data.DataLoader(
train_data,
batch_size=opt.batch_size,
shuffle=False,
)
# Collect CIFAR10.1 images
np.random.seed(seed=819 * (kk + 9) + N1)
Ind_tr_v4 = np.random.choice(len(data_T), N1, replace=False)
Ind_te_v4 = np.delete(Ind_v4_all, Ind_tr_v4)
Fake_MNIST_tr = data_trans[Ind_tr_v4]
Fake_MNIST_te = data_trans[Ind_te_v4]
# Optimizers
optimizer_F = torch.optim.Adam(list(featurizer.parameters()) + [epsilonOPT] + [sigmaOPT] + [sigma0OPT],
lr=opt.lr) # optimizer for training deep kernel
optimizer_T = torch.optim.Adam([sigmaOPT] + [sigma0OPT] + [TT_org],
lr=opt.lr) # optimizer for training test location
optimizer_D = torch.optim.Adam(discriminator.parameters(),
lr=opt.lr) # optimizer for training deep networks to distinguish two sets of samples
Tensor = torch.cuda.FloatTensor if cuda else torch.FloatTensor
# ---------------------
# Training deep kernel
# ---------------------
np.random.seed(seed=1102)
torch.manual_seed(1102)
torch.cuda.manual_seed(1102)
for epoch in range(opt.n_epochs):
for i, (imgs, _) in enumerate(dataloader):
if True:
ind = np.random.choice(N1, imgs.shape[0], replace=False)
Fake_imgs = Fake_MNIST_tr[ind]
# Adversarial ground truths
valid = Variable(Tensor(imgs.shape[0], 1).fill_(1.0), requires_grad=False)
fake = Variable(Tensor(imgs.shape[0], 1).fill_(0.0), requires_grad=False)
# Configure input
real_imgs = Variable(imgs.type(Tensor))
Fake_imgs = Variable(Fake_imgs.type(Tensor))
X = torch.cat([real_imgs, Fake_imgs], 0)
Y = torch.cat([valid, fake], 0).squeeze().long()
# ------------------------------
# Train deep network for MMD-D
# ------------------------------
# Initialize optimizer
optimizer_F.zero_grad()
# Compute output of deep network
modelu_output = featurizer(X)
# Compute epsilon, sigma and sigma_0
ep = torch.exp(epsilonOPT) / (1 + torch.exp(epsilonOPT))
sigma = sigmaOPT ** 2
sigma0_u = sigma0OPT ** 2
# Compute Compute J (STAT_u)
TEMP = MMDu(modelu_output, imgs.shape[0], X.view(X.shape[0], -1), sigma, sigma0_u, ep)
mmd_value_temp = -1 * (TEMP[0])
mmd_std_temp = torch.sqrt(TEMP[1] + 10 ** (-8))
STAT_u_F = torch.div(mmd_value_temp, mmd_std_temp)
# Compute gradient
STAT_u_F.backward()
# Update weights using gradient descent
optimizer_F.step()
# ------------------------------------------------------
# Train deep network to distinguish two sets of samples
# ------------------------------------------------------
# Initialize optimizer
optimizer_D.zero_grad()
# Compute Cross-Entropy (loss_C) loss between two samples
loss_C = adversarial_loss(discriminator(X), Y)
# Compute gradient
loss_C.backward()
# Update weights using gradient descent
optimizer_D.step()
if (epoch + 1) % 100 == 0:
print(
"[Epoch %d/%d] [Batch %d/%d] [D loss: %f] [Stat: %f]"
% (epoch, opt.n_epochs, i, len(dataloader), loss_C.item(), -STAT_u_F.item())
)
batches_done = epoch * len(dataloader) + i
else:
break
# -------------------------------
# SELECT the best test location
# -------------------------------
# Fetch training data
s1 = data_all[Ind_tr]
s2 = data_trans[Ind_tr_v4]
S = torch.cat([s1.cpu(), s2.cpu()], 0).cuda()
print(S.shape)
Sv = S.view(2 * N1, -1)
# Select the best test location
max_stat = 0
for ti in range(2*N1):
stat__me = compute_ME_stat(featurizer(S[:N1, :]), featurizer(S[N1:, :]), featurizer(S[ti, :].unsqueeze(0)),
S[:N1, :].view(N1, -1), S[N1:, :].view(N1, -1),
S[ti, :].view(J, -1), sigma, sigma0_u, ep)
if stat__me > max_stat:
max_stat = stat__me
T_org = S[ti, :].unsqueeze(0)
if ti < N1:
test_locs = data_all_org[Ind_tr[ti]]
else:
test_locs = data_trans_org[Ind_tr_v4[ti-N1]]
print("Maximum statistics", max_stat)
# Run two-sample test based on deep-kernel ME
h_u, threshold_u, mmd_value_u = TST_ME_DK_per(featurizer(S[:N1, :]), featurizer(S[N1:, :]), featurizer(T_org),
S[:N1, :].view(N1, -1), S[N1:, :].view(N1, -1),
T_org.view(J, -1), alpha, sigma, sigma0_u, ep)
print("h:", h_u, "Threshold:", threshold_u, "MMD_value:", mmd_value_u, "stats:", stat__me)
# Record the best epsilon, sigma, sigma_0 and test location
ep_OPT[kk] = ep.item()
s_OPT[kk] = sigma.item()
s0_OPT[kk] = sigma0_u.item()
T_org_OPT[kk] = T_org
# Compute test power of MMD-D
H_u = np.zeros(N)
T_u = np.zeros(N)
M_u = | np.zeros(N) | numpy.zeros |
# -*- coding: utf-8 -*-
"""
Created on Wed Oct 22 11:35:00 2014
@author: <NAME>
"""
import os
import inspect
import warnings
import sympy as sp
from sympy import sin, cos, exp
import numpy as np
import scipy as sc
import scipy.integrate
import symbtools as st
from symbtools import lzip
try:
import control
except ImportError:
control = None
from symbtools.test import unittesthelper as uth
import unittest
from symbtools.test import test_core1
from symbtools.test import test_time_deriv
from symbtools.test import test_pickle_tools
uth.inject_tests_into_namespace(globals(), test_time_deriv)
uth.inject_tests_into_namespace(globals(), test_core1)
def make_abspath(*args):
"""
returns new absolute path, basing on the path of this module
"""
current_dir = os.path.dirname(os.path.abspath(inspect.getfile(inspect.currentframe())))
return os.path.join(current_dir, *args)
# Avoid warnings of undefined symbols from the IDE,
# but still make use of st.make_global
x1 = x2 = x3 = x4 = None
y1 = y2 = y3 = None
a1 = z4 = z7 = z10 = None
# noinspection PyShadowingNames,PyPep8Naming,PySetFunctionToLiteral
class InteractiveConvenienceTest(unittest.TestCase):
def setUp(self):
pass
def test_no_IPS_call(self):
"""
test whether there is some call to interactive IPython (legacy from debugging)
"""
srclines = inspect.getsourcelines(st)[0]
def filter_func(tup):
idx, line = tup
return 'IPS()' in line and not line.strip()[0] == '#'
res = list(filter(filter_func, enumerate(srclines, 1)))
self.assertEqual(res, [])
def test_symbol_atoms(self):
a, b, t = sp.symbols("a, b, t")
x1 = a + b
x2 = a + b - 3 + sp.pi
M1 = sp.Matrix([x2, t, a**2])
M2 = sp.ImmutableDenseMatrix(M1)
self.assertEqual(set([a]), a.s)
self.assertEqual(x1.atoms(), x1.s)
self.assertEqual(x2.atoms(sp.Symbol), x2.s)
self.assertEqual(set([a, b, t]), M1.s)
self.assertEqual(set([a, b, t]), M2.s)
def test_count_ops(self):
a, b, t = sp.symbols("a, b, t")
x1 = a + b
x2 = a + b - 3 + sp.pi
M1 = sp.Matrix([x2, t, a**2])
M2 = sp.ImmutableDenseMatrix(M1)
self.assertEqual(st.count_ops(a), a.co)
self.assertEqual(st.count_ops(x1), x1.co)
self.assertEqual(st.count_ops(x2), x2.co)
self.assertEqual(st.count_ops(M1), M1.co)
self.assertEqual(st.count_ops(M2), M2.co)
def test_count_ops2(self):
a, b, t = sp.symbols("a, b, t")
x1 = a + b
x2 = a + b - 3 + sp.pi
M1 = sp.Matrix([x2, t, a**2, 0, 1])
M2 = sp.ImmutableDenseMatrix(M1)
self.assertEqual(st.count_ops(0), 0)
self.assertEqual(st.count_ops(a), 1)
self.assertEqual(st.count_ops(1.3), 1)
self.assertEqual(st.count_ops(x1), 2)
self.assertEqual(st.count_ops(x2), 4)
self.assertEqual(st.count_ops(M1), sp.Matrix([4, 1, 2, 0, 1]))
self.assertEqual(st.count_ops(M2), sp.Matrix([4, 1, 2, 0, 1]))
def test_srn(self):
x, y, z = xyz = st.symb_vector('x, y, z')
st.random.seed(3319)
self.assertAlmostEqual(x.srn01, 0.843044195656457)
st.random.seed(3319)
x_srn = x.srn
self.assertNotAlmostEqual(x_srn, 8.59)
self.assertAlmostEqual(x_srn, 8.58739776090811)
# now apply round
st.random.seed(3319)
self.assertAlmostEqual(x.srnr, 8.59)
# test compatibility with sp.Matrix
# the order might depend on the platform (due to dict ordering)
expected_res = [5.667115517927374668261109036393463611602783203125,
7.76957198624519962404377793063758872449398040771484375,
8.58739776090810946751474830307415686547756195068359375]
st.random.seed(3319)
xyz_srn = list(xyz.srn)
xyz_srn.sort()
for a, b in zip(xyz_srn, expected_res):
self.assertAlmostEqual(a, b)
# should live in a separate test !!
st.random.seed(3319)
# ensure that application to matrix does raise exception
_ = xyz.srnr
test_matrix = sp.Matrix(expected_res)
rounded_res = sp.Matrix([[5.667], [ 7.77], [8.587]])
self.assertNotEqual(test_matrix, rounded_res)
self.assertEqual(test_matrix.ar, rounded_res)
def test_subz(self):
x1, x2, x3 = xx = sp.Matrix(sp.symbols("x1, x2, x3"))
y1, y2, y3 = yy = sp.symbols("y1, y2, y3")
a = x1 + 7*x2*x3
M1 = sp.Matrix([x2, x1*x2, x3**2])
M2 = sp.ImmutableDenseMatrix(M1)
self.assertEqual(x1.subs(lzip(xx, yy)), x1.subz(xx, yy))
self.assertEqual(a.subs(lzip(xx, yy)), a.subz(xx, yy))
self.assertEqual(M1.subs(lzip(xx, yy)), M1.subz(xx, yy))
self.assertEqual(M2.subs(lzip(xx, yy)), M2.subz(xx, yy))
def test_smplf(self):
x1, x2, x3 = xx = sp.Matrix(sp.symbols("x1, x2, x3"))
y1, y2, y3 = yy = sp.symbols("y1, y2, y3")
a = x1**2*(x2/x1 + 7) - x1*x2
M1 = sp.Matrix([sin(x1)**2 + cos(x1)**2, a, x3])
self.assertEqual(M1.smplf, sp.simplify(M1))
self.assertEqual(a.smplf, sp.simplify(a))
def test_subz0(self):
x1, x2, x3 = xx = st.symb_vector("x1, x2, x3")
y1, y2, y3 = yy = st.symb_vector("y1, y2, y3")
XX = (x1, x2)
a = x1 + 7*x2*x3
M1 = sp.Matrix([x2, x1*x2, x3**2])
M2 = sp.ImmutableDenseMatrix(M1)
self.assertEqual(x1.subs(st.zip0(XX)), x1.subz0(XX))
self.assertEqual(a.subs(st.zip0(XX)), a.subz0(XX))
self.assertEqual(M1.subs(st.zip0(XX)), M1.subz0(XX))
self.assertEqual(M2.subs(st.zip0(XX)), M2.subz0(XX))
konst = sp.Matrix([1,2,3])
zz = konst + xx + 5*yy
self.assertEqual(zz.subz0(xx, yy), konst)
# noinspection PyShadowingNames,PyPep8Naming,PySetFunctionToLiteral
class LieToolsTest(unittest.TestCase):
def setUp(self):
pass
def test_involutivity_test(self):
x1, x2, x3 = xx = st.symb_vector('x1:4')
st.make_global(xx)
# not involutive
f1 = sp.Matrix([x2*x3 + x1**2, 3*x1, 4 + x2*x3])
f2 = sp.Matrix([x3 - 2*x1*x3, x2 - 5, 3 + x1*x2])
dist1 = st.col_stack(f1, f2)
# involutive
f3 = sp.Matrix([-x2, x1, 0])
f4 = sp.Matrix([0, -x3, x2])
dist2 = st.col_stack(f3, f4)
res, fail = st.involutivity_test(dist1, xx)
self.assertFalse(res)
self.assertEqual(fail, (0, 1))
res2, fail2 = st.involutivity_test(dist2, xx)
self.assertTrue(res2)
self.assertEqual(fail2, [])
def test_lie_deriv_cartan(self):
x1, x2, x3 = xx = sp.symbols('x1:4')
u1, u2 = uu = sp.Matrix(sp.symbols('u1:3'))
# ordinary lie_derivative
# source: inspired by the script of Prof. Kugi (TU-Wien)
f = sp.Matrix([-x1**3, cos(x1)*cos(x2), x2])
g = sp.Matrix([cos(x2), 1, exp(x1)])
h = x3
Lfh = x2
Lf2h = f[1]
Lgh = exp(x1)
res1 = st.lie_deriv_cartan(h, f, xx)
res2 = st.lie_deriv_cartan(h, f, xx, order=2)
self.assertEqual(res1, Lfh)
self.assertEqual(res2, Lf2h)
# incorporating the input
h2 = u1
udot1, udot2 = uudot = st.time_deriv(uu, uu, order=1)
uddot1, uddot2 = st.time_deriv(uu, uu, order=2)
res_a1 = st.lie_deriv_cartan(h2, f, xx, uu, order=1)
res_a2 = st.lie_deriv_cartan(h2, f, xx, uu, order=2)
self.assertEqual(res_a1, udot1)
self.assertEqual(res_a2, uddot1)
res_a3 = st.lie_deriv_cartan(udot1, f, xx, [uu, uudot], order=1)
self.assertEqual(res_a3, uddot1)
# more complex examples
h3 = x3 + u1
fg = f + g * u2
res_b1 = st.lie_deriv_cartan(h3, fg, xx, uu, order=1)
res_b2 = st.lie_deriv_cartan(h3, fg, xx, uu, order=2)
res_b3 = st.lie_deriv_cartan(res_b1, fg, xx, [uu, uudot], order=1)
self.assertEqual(res_b1, Lfh + Lgh*u2 + udot1)
self.assertEqual(sp.expand(res_b2 - res_b3), 0)
h4 = x3 * sin(x2)
fg = f + g * u2
res_c1 = st.lie_deriv_cartan(h4, fg, xx, uu, order=1)
res_c2 = st.lie_deriv_cartan(res_c1, fg, xx, uu, order=1)
res_c3 = st.lie_deriv_cartan(h4, fg, xx, uu, order=2)
self.assertEqual(sp.expand(res_c2 - res_c3), 0)
def test_lie_deriv(self):
xx = st.symb_vector('x1:4')
st.make_global(xx)
f = sp.Matrix([x1 + x3*x2, 7*exp(x1), cos(x2)])
h1 = x1**2 + sin(x3)*x2
res1 = st.lie_deriv(h1, f, xx)
eres1 = 2*x1**2 + 2*x1*x2*x3 + 7*exp(x1)*sin(x3) + x2*cos(x2)*cos(x3)
self.assertEqual(res1.expand(), eres1)
res2a = st.lie_deriv(h1, f, xx, order=2).expand()
res2b = st.lie_deriv(h1, f, xx, 2).expand()
eres2 = st.lie_deriv(eres1, f, xx).expand()
self.assertEqual(res2a, eres2)
self.assertEqual(res2b, eres2)
res2c = st.lie_deriv(h1, f, f, xx).expand()
res2d = st.lie_deriv(h1, f, f, xx=xx).expand()
self.assertEqual(res2c, eres2)
self.assertEqual(res2d, eres2)
F = f[:-1, :]
with self.assertRaises(ValueError) as cm:
# different lengths of vectorfields:
res1 = st.lie_deriv(h1, F, f, xx)
# noinspection PyTypeChecker
def test_lie_bracket(self):
xx = st.symb_vector('x1:4')
st.make_global(xx)
fx = sp.Matrix([[(x2 - 1)**2 + 1/x3], [x1 + 7], [-x3**2*(x2 - 1)]])
v = sp.Matrix([[0], [0], [-x3**2]])
dist = st.col_stack(v, st.lie_bracket(-fx, v, xx), st.lie_bracket(-fx, v, xx, order=2))
v0, v1, v2 = st.col_split(dist)
self.assertEqual(v1, sp.Matrix([1, 0, 0]))
self.assertEqual(v2, sp.Matrix([0, 1, 0]))
self.assertEqual(st.lie_bracket(fx, fx, xx), sp.Matrix([0, 0, 0]))
def test_lie_deriv_covf(self):
xx = st.symb_vector('x1:4')
st.make_global(xx)
# we test this by building the observability matrix with two different but equivalent approaches
f = sp.Matrix([x1 + x3*x2, 7*exp(x1), cos(x2)])
y = x1**2 + sin(x3)*x2
ydot = st.lie_deriv(y, f, xx)
yddot = st.lie_deriv(ydot, f, xx)
cvf1 = st.gradient(y, xx)
cvf2 = st.gradient(ydot, xx)
cvf3 = st.gradient(yddot, xx)
# these are the rows of the observability matrix
# second approach
dh0 = cvf1
dh1 = st.lie_deriv_covf(dh0, f, xx)
dh2a = st.lie_deriv_covf(dh1, f, xx)
dh2b = st.lie_deriv_covf(dh0, f, xx, order=2)
zero = dh0*0
self.assertEqual((dh1 - cvf2).expand(), zero)
self.assertEqual((dh2a - cvf3).expand(), zero)
self.assertEqual((dh2b - cvf3).expand(), zero)
# noinspection PyShadowingNames,PyPep8Naming,PySetFunctionToLiteral
class TestSupportFunctions(unittest.TestCase):
"""
Test functionality which is used indirectly by other functions
"""
def setUp(self):
pass
def test_recursive_function_decorator(self):
@st.recursive_function
def myfactorial(thisfunc, x):
if x == 0:
return 1
else:
return x*thisfunc(x-1)
nn = [0, 1, 3, 5, 10]
res1 = [sp.factorial(x) for x in nn]
res2 = [myfactorial(x) for x in nn]
self.assertEqual(res1, res2)
def test_get_custom_attr_map(self):
t = st.t
x1, x2 = xx = st.symb_vector("x1, x2")
xdot1, xdot2 = xxd = st.time_deriv(xx, xx)
xddot1, xddot2 = xxdd = st.time_deriv(xx, xx, order=2)
m1 = st.get_custom_attr_map("ddt_child")
em1 = [(x1, xdot1), (x2, xdot2), (xdot1, xddot1), (xdot2, xddot2)]
# convert to set because sorting might depend on plattform
self.assertEqual(set(m1), set(em1))
m2 = st.get_custom_attr_map("ddt_parent")
em2 = [(xdot1, x1), (xdot2, x2), (xddot1, xdot1), (xddot2, xdot2)]
self.assertEqual(set(m2), set(em2))
m3 = st.get_custom_attr_map("ddt_func")
# ensure unique sorting
m3.sort(key=lambda x: "{}_{}".format(x[0].difforder, str(x[0])))
self.assertEqual(len(m3), 6)
x2_func = sp.Function(x2.name)(t)
self.assertEqual(type(type(m3[0][1])), sp.function.UndefinedFunction)
self.assertEqual(m3[-1][1], x2_func.diff(t, t))
# noinspection PyShadowingNames,PyPep8Naming,PySetFunctionToLiteral
class SymbToolsTest2(unittest.TestCase):
def setUp(self):
pass
def test_solve_scalar_ode_1sto(self):
a, b = sp.symbols("a, b", nonzero=True)
t, x1, x2 = sp.symbols("t, x1, x2")
# x1_dot = <rhs>
rhs1 = sp.S(0)
rhs2 = sp.S(2.5)
rhs3 = x1
rhs5 = x1*(3-t)
rhs6 = cos(b*t) # coeff must be nonzero to prevent case distinction
res1 = st.solve_scalar_ode_1sto(rhs1, x1, t)
self.assertEqual(res1.diff(t), rhs1.subs(x1, res1))
res2 = st.solve_scalar_ode_1sto(rhs2, x1, t)
self.assertEqual(res2.diff(t), rhs2.subs(x1, res2))
res3, iv3 = st.solve_scalar_ode_1sto(rhs3, x1, t, return_iv=True)
self.assertEqual(res3.diff(t), rhs3.subs(x1, res3))
self.assertEqual(res3, iv3*exp(t))
res5 = st.solve_scalar_ode_1sto(rhs5, x1, t)
test_difference5 = res5.diff(t) - rhs5.subs(x1, res5)
self.assertEqual(test_difference5.expand(), 0)
res6 = st.solve_scalar_ode_1sto(rhs6, x1, t)
self.assertEqual(res6.diff(t), rhs6.subs(x1, res6).expand())
@uth.skip_slow
def test_solve_scalar_ode_1sto_2(self):
a, b = sp.symbols("a, b", nonzero=True)
t, x1, x2 = sp.symbols("t, x1, x2")
rhs4 = sin(a*x1)
# this test works but is slow
with st.warnings.catch_warnings(record=True) as cm:
res4 = st.solve_scalar_ode_1sto(rhs4, x1, t)
self.assertEqual(len(cm), 1)
self.assertTrue('multiple solutions' in str(cm[0].message))
test_difference4 = res4.diff(t) - rhs4.subs(x1, res4)
self.assertEqual(test_difference4.simplify(), 0)
def test_calc_flow_from_vectorfield(self):
a, b = sp.symbols("a, b", nonzero=True)
t, x1, x2, x3, x4 = sp.symbols("t, x1, x2, x3, x4")
xx = x1, x2, x3, x4
vf1 = sp.Matrix([0, 1, x3])
vf2 = sp.Matrix([0, 1, x3, sin(a*x2)])
res1, fp, iv1 = st.calc_flow_from_vectorfield(vf1, xx[:-1], flow_parameter=t)
vf1_sol = vf1.subs(lzip(xx[:-1], res1))
self.assertEqual(fp, t)
self.assertEqual(res1.diff(t), vf1_sol)
res2, fp, iv2 = st.calc_flow_from_vectorfield(vf2, xx, flow_parameter=t)
vf2_sol = vf2.subs(lzip(xx[:-1], res2))
self.assertEqual(fp, t)
self.assertEqual(res2.diff(t), vf2_sol)
res3, fp, iv3 = st.calc_flow_from_vectorfield(sp.Matrix([x1, 1, x1]), xx[:-1])
t = fp
x1_0, x2_0, x3_0 = iv3
ref3 = sp.Matrix([[x1_0*sp.exp(t)], [t + x2_0], [x1_0*sp.exp(t) - x1_0 + x3_0]])
self.assertEqual(res3, ref3)
def test_create_simfunction(self):
x1, x2, x3, x4 = xx = sp.Matrix(sp.symbols("x1, x2, x3, x4"))
u1, u2 = uu = sp.Matrix(sp.symbols("u1, u2")) # inputs
p1, p2, p3, p4 = pp = sp.Matrix(sp.symbols("p1, p2, p3, p4")) # parameter
t = sp.Symbol('t')
A = A0 = sp.randMatrix(len(xx), len(xx), -10, 10, seed=704)
B = B0 = sp.randMatrix(len(xx), len(uu), -10, 10, seed=705)
v1 = A[0, 0]
A[0, 0] = p1
v2 = A[2, -1]
A[2, -1] = p2
v3 = B[3, 0]
B[3, 0] = p3
v4 = B[2, 1]
B[2, 1] = p4
par_vals = lzip(pp, [v1, v2, v3, v4])
f = A*xx
G = B
fxu = (f + G*uu).subs(par_vals)
# some random initial values
x0 = st.to_np( sp.randMatrix(len(xx), 1, -10, 10, seed=706) ).squeeze()
# Test handling of unsubstituted parameters
mod = st.SimulationModel(f, G, xx, model_parameters=par_vals[1:])
with self.assertRaises(ValueError) as cm:
rhs0 = mod.create_simfunction()
self.assertTrue("unexpected symbols" in cm.exception.args[0])
# create the model and the rhs-function
mod = st.SimulationModel(f, G, xx, par_vals)
rhs0 = mod.create_simfunction()
self.assertFalse(mod.compiler_called)
self.assertFalse(mod.use_sp2c)
res0_1 = rhs0(x0, 0)
dres0_1 = st.to_np(fxu.subs(lzip(xx, x0) + st.zip0(uu))).squeeze()
bin_res01 = np.isclose(res0_1, dres0_1) # binary array
self.assertTrue( np.all(bin_res01) )
# difference should be [0, 0, ..., 0]
self.assertFalse( np.any(rhs0(x0, 0) - rhs0(x0, 3.7) ) )
# simulate
tt = np.linspace(0, 0.5, 100) # simulation should be short due to instability
res1 = sc.integrate.odeint(rhs0, x0, tt)
# create and try sympy_to_c bridge (currently only works on linux
# and if sympy_to_c is installed (e.g. with `pip install sympy_to_c`))
# until it is not available for windows we do not want it as a requirement
# see also https://stackoverflow.com/a/10572833/333403
try:
import sympy_to_c
except ImportError:
# noinspection PyUnusedLocal
sympy_to_c = None
sp2c_available = False
else:
sp2c_available = True
if sp2c_available:
rhs0_c = mod.create_simfunction(use_sp2c=True)
self.assertTrue(mod.compiler_called)
res1_c = sc.integrate.odeint(rhs0_c, x0, tt)
self.assertTrue(np.all(np.isclose(res1_c, res1)))
mod.compiler_called = None
rhs0_c = mod.create_simfunction(use_sp2c=True)
self.assertTrue(mod.compiler_called is None)
# proof calculation
# x(t) = x0*exp(A*t)
Anum = st.to_np(A.subs(par_vals))
Bnum = st.to_np(G.subs(par_vals))
# noinspection PyUnresolvedReferences
xt = [ np.dot( sc.linalg.expm(Anum*T), x0 ) for T in tt ]
xt = np.array(xt)
# test whether numeric results are close within given tolerance
bin_res1 = np.isclose(res1, xt, rtol=2e-5) # binary array
self.assertTrue( np.all(bin_res1) )
# test handling of parameter free models:
mod2 = st.SimulationModel(Anum*xx, Bnum, xx)
rhs2 = mod2.create_simfunction()
res2 = sc.integrate.odeint(rhs2, x0, tt)
self.assertTrue(np.allclose(res1, res2))
# test input functions
des_input = st.piece_wise((0, t <= 1 ), (t, t < 2), (0.5, t < 3), (1, True))
des_input_func_scalar = st.expr_to_func(t, des_input)
des_input_func_vec = st.expr_to_func(t, sp.Matrix([des_input, des_input]) )
# noinspection PyUnusedLocal
with self.assertRaises(TypeError) as cm:
mod2.create_simfunction(input_function=des_input_func_scalar)
rhs3 = mod2.create_simfunction(input_function=des_input_func_vec)
# noinspection PyUnusedLocal
res3_0 = rhs3(x0, 0)
rhs4 = mod2.create_simfunction(input_function=des_input_func_vec, time_direction=-1)
res4_0 = rhs4(x0, 0)
self.assertTrue(np.allclose(res3_0, np.array([119., -18., -36., -51.])))
self.assertTrue(np.allclose(res4_0, - res3_0))
def test_create_simfunction2(self):
x1, x2, x3, x4 = xx = sp.Matrix(sp.symbols("x1, x2, x3, x4"))
u1, u2 = uu = sp.Matrix(sp.symbols("u1, u2")) # inputs
p1, p2, p3, p4 = pp = sp.Matrix(sp.symbols("p1, p2, p3, p4")) # parameter
t = sp.Symbol('t')
A = A0 = sp.randMatrix(len(xx), len(xx), -10, 10, seed=704)
B = B0 = sp.randMatrix(len(xx), len(uu), -10, 10, seed=705)
v1 = A[0, 0]
A[0, 0] = p1
v2 = A[2, -1]
A[2, -1] = p2
v3 = B[3, 0]
B[3, 0] = p3
v4 = B[2, 1]
B[2, 1] = p4
par_vals = lzip(pp, [v1, v2, v3, v4])
f = A*xx
G = B
fxu = (f + G*uu).subs(par_vals)
# some random initial values
x0 = st.to_np( sp.randMatrix(len(xx), 1, -10, 10, seed=706) ).squeeze()
u0 = st.to_np( sp.randMatrix(len(uu), 1, -10, 10, seed=2257) ).squeeze()
# create the model and the rhs-function
mod = st.SimulationModel(f, G, xx, par_vals)
rhs_xx_uu = mod.create_simfunction(free_input_args=True)
res0_1 = rhs_xx_uu(x0, u0, 0)
dres0_1 = st.to_np(fxu.subs(lzip(xx, x0) + lzip(uu, u0))).squeeze()
bin_res01 = np.isclose(res0_1, dres0_1) # binary array
self.assertTrue( np.all(bin_res01) )
def test_num_trajectory_compatibility_test(self):
x1, x2, x3, x4 = xx = sp.Matrix(sp.symbols("x1, x2, x3, x4"))
u1, u2 = uu = sp.Matrix(sp.symbols("u1, u2")) # inputs
t = sp.Symbol('t')
# we want to create a random but stable matrix
np.random.seed(2805)
diag = np.diag( np.random.random(len(xx))*-10 )
T = sp.randMatrix(len(xx), len(xx), -10, 10, seed=704)
Tinv = T.inv()
A = Tinv*diag*T
B = B0 = sp.randMatrix(len(xx), len(uu), -10, 10, seed=705)
x0 = st.to_np( sp.randMatrix(len(xx), 1, -10, 10, seed=706) ).squeeze()
tt = np.linspace(0, 5, 2000)
des_input = st.piece_wise((2-t, t <= 1 ), (t, t < 2), (2*t-2, t < 3), (4, True))
des_input_func_vec = st.expr_to_func(t, sp.Matrix([des_input, des_input]) )
mod2 = st.SimulationModel(A*xx, B, xx)
rhs3 = mod2.create_simfunction(input_function=des_input_func_vec)
XX = sc.integrate.odeint(rhs3, x0, tt)
UU = des_input_func_vec(tt)
res1 = mod2.num_trajectory_compatibility_test(tt, XX, UU)
self.assertTrue(res1)
# slightly different input signal -> other results
res2 = mod2.num_trajectory_compatibility_test(tt, XX, UU*1.1)
self.assertFalse(res2)
def test_expr_to_func(self):
x1, x2 = xx = sp.Matrix(sp.symbols("x1, x2"))
t, = sp.symbols("t,")
r_ = np.r_
f1 = st.expr_to_func(x1, 2*x1)
self.assertEqual(f1(5.1), 10.2)
XX1 = np.r_[1, 2, 3.7]
res1 = f1(XX1) == 2*XX1
self.assertTrue(res1.all)
f2 = st.expr_to_func(x1, sp.Matrix([x1*2, x1+5, 4]))
res2 = f2(3) == r_[6, 8, 4]
self.assertTrue(res2.all())
res2b = f2(r_[3, 10, 0]) == np.array([[6, 8, 4], [20, 15, 4], [0, 5, 4]])
self.assertTrue(res2b.all())
f3 = st.expr_to_func(xx, sp.Matrix([x1*2, x2+5, 4]))
res3 = np.allclose(f3(-3.1, 4), r_[-6.2, 9, 4])
self.assertTrue(res3)
# test compatibility with Piecewise Expressions
des_input = st.piece_wise((0, t <= 1 ), (t, t < 2), (0.5, t < 3), (1, True))
f4s = st.expr_to_func(t, des_input)
f4v = st.expr_to_func(t, sp.Matrix([des_input, des_input]) )
self.assertEqual(f4s(2.7), 0.5)
sol = r_[0, 1.6, 0.5, 1, 1]
res4a = f4s(r_[0.3, 1.6, 2.2, 3.1, 500]) == sol
self.assertTrue(res4a.all())
res4b = f4v(r_[0.3, 1.6, 2.2, 3.1, 500])
col1, col2 = res4b.T
self.assertTrue(np.array_equal(col1, sol))
self.assertTrue(np.array_equal(col2, sol))
spmatrix = sp.Matrix([[x1, x1*x2], [0, x2**2]])
fnc1 = st.expr_to_func(xx, spmatrix, keep_shape=False)
fnc2 = st.expr_to_func(xx, spmatrix, keep_shape=True)
res1 = fnc1(1.0, 2.0)
res2 = fnc2(1.0, 2.0)
self.assertEqual(res1.shape, (4, ))
self.assertEqual(res2.shape, (2, 2))
# noinspection PyTypeChecker
self.assertTrue(np.all(res1 == [1, 2, 0, 4]))
# noinspection PyTypeChecker
self.assertTrue(np.all(res1 == res2.flatten()))
fnc = st.expr_to_func(xx, x1 + x2)
self.assertEqual(fnc(1, 3), 4)
xx_res = np.array([1, 3, 1.1, 3, 1.2, 3.0]).reshape(3, -1)
self.assertTrue(np.allclose(fnc(*xx_res.T), np.array([4, 4.1, 4.2])))
fnc1 = st.expr_to_func(xx, 3*xx)
fnc2 = st.expr_to_func(xx, 3*xx, allow_kwargs=True)
self.assertTrue(np.allclose(fnc1(10, 100), fnc2(x2=100, x1=10)))
def test_reformulate_Integral(self):
t = sp.Symbol('t')
c = sp.Symbol('c')
F = sp.Function('F')
x = sp.Function('x')(t)
a = sp.Function('a')
i1 = sp.Integral(F(t), t)
j1 = st.reformulate_integral_args(i1)
self.assertEqual(j1.subs(t, 0).doit(), 0)
ode = x.diff(t) + x -a(t)*x**c
sol = sp.dsolve(ode, x).rhs
# the solution contains an undetemined integral
self.assertTrue( len(sol.atoms(sp.Integral)) == 1)
# extract the integration constant (not necessary for test)
# C1 = list(sol.atoms(sp.Symbol)-ode.atoms(sp.Symbol))[0]
sol2 = st.reformulate_integral_args(sol)
self.assertTrue( len(sol2.atoms(sp.Integral)) == 1)
sol2_at_0 = sol2.subs(t, 0).doit()
self.assertTrue( len(sol2_at_0.atoms(sp.Integral)) == 0)
# noinspection PyShadowingNames,PyPep8Naming,PySetFunctionToLiteral
class SymbToolsTest3(unittest.TestCase):
def setUp(self):
st.init_attribute_store(reinit=True)
def test_get_symbols_by_name(self):
c1, C1, x, a, t, Y = sp.symbols('c1, C1, x, a, t, Y')
F = sp.Function('F')
expr1 = c1*(C1+x**x)/(sp.sin(a*t))
expr2 = sp.Matrix([sp.Integral(F(x), x)*sp.sin(a*t) - \
1/F(x).diff(x)*C1*Y])
res1 = st.get_symbols_by_name(expr1, 'c1')
self.assertEqual(res1, c1)
res2 = st.get_symbols_by_name(expr1, 'C1')
self.assertEqual(res2, C1)
res3 = st.get_symbols_by_name(expr1, *'c1 x a'.split())
self.assertEqual(res3, [c1, x, a])
with self.assertRaises(ValueError) as cm:
st.get_symbols_by_name(expr1, 'Y')
with self.assertRaises(ValueError) as cm:
st.get_symbols_by_name(expr1, 'c1', 'Y')
res4 = st.get_symbols_by_name(expr2, 'Y')
self.assertEqual(res4, Y)
res5 = st.get_symbols_by_name(expr2, 'C1')
self.assertEqual(res5, C1)
res6 = st.get_symbols_by_name(expr2, *'C1 x a'.split())
self.assertEqual(res6, [C1, x, a])
def test_general_attribute(self):
st.register_new_attribute_for_sp_symbol("foo", save_setter=False)
st.register_new_attribute_for_sp_symbol("bar", getter_default="__self__")
x1 = sp.Symbol('x1')
self.assertEqual(x1.foo, None)
self.assertEqual(x1.bar, x1)
x1.foo = 7
self.assertEqual(x1.foo, 7)
x1.foo = "some string"
self.assertEqual(x1.foo, "some string")
x1.foo = x1
self.assertEqual(x1.foo, x1)
x1.bar = 12
# noinspection PyUnusedLocal
with self.assertRaises(ValueError) as cm:
x1.bar = 13
def test_difforder_attribute(self):
x1 = sp.Symbol('x1')
self.assertEqual(x1.difforder, 0)
xddddot1 = st.time_deriv(x1, [x1], order=4)
self.assertEqual(xddddot1.difforder, 4)
xx = sp.Matrix(sp.symbols("x1, x2, x3"))
xxd = st.time_deriv(xx, xx)
xxdd = st.time_deriv(xx, xx, order=2)
for xdd in xxdd:
self.assertEqual(xdd.difforder, 2)
# once, this was a bug
y = sp.Symbol('y')
ydot = st.time_deriv(y, [y])
yddot = st.time_deriv(ydot, [y, ydot])
self.assertEqual(yddot.difforder, 2)
z = sp.Symbol('z')
zdot_false = sp.Symbol('zdot')
st.global_data.attribute_store[(zdot_false, 'difforder')] = -7
with self.assertRaises(ValueError) as cm:
st.time_deriv( z, [z])
# ensure that difforder is not changed after value_set
z2 = sp.Symbol('z2')
z2.difforder = 3
z2.difforder = 3 # same value is allowed
with self.assertRaises(ValueError) as cm:
z2.difforder = 4 # not allowed
def test_introduce_abreviations(self):
x1, x2, x3 = xx = st.symb_vector('x1:4')
a1, a2, a3 = aa = st.symb_vector('a1:4')
P1 = sp.eye(3)
P2 = sp.Matrix([x1**2, a1+a2, a3*x2, 13.7, 1, 0])
res1 = st.introduce_abreviations(P1)
res2 = st.introduce_abreviations(P1, time_dep_symbs=xx)
res3 = st.introduce_abreviations(P2, time_dep_symbs=xx)
self.assertEqual(res1[0], P1)
self.assertEqual(res2[0], P1)
# test subs_tuples
self.assertNotEqual(res3[0], P2)
self.assertEqual(res3[0].subs(res3[1]), P2)
# time dependend symbols
tds = res3[2]
original_expressions = tds.subs(res3[1])
self.assertEqual(original_expressions, sp.Matrix([x1**2, a3*x2]))
def _test_make_global(self):
xx = st.symb_vector('x1:4')
yy = st.symb_vector('y1:4')
st.make_global(xx)
self.assertEqual(x1 + x2, xx[0] + xx[1])
# test if set is accepted
st.make_global(yy.atoms(sp.Symbol))
self.assertEqual(y1 + y2, yy[0] + yy[1])
with self.assertRaises(TypeError) as cm:
st.make_global(dict())
def test_make_global(self):
aa = tuple(st.symb_vector('a1:4'))
xx = st.symb_vector('x1:4')
yy = st.symb_vector('y1:4')
zz = st.symb_vector('z1:11').reshape(2, 5)
# tollerate if there are numbers in the sequences:
zz[0] = 0
zz[1] = 10
st.make_global(xx, yy, zz, aa)
res = a1 + x2 + y3 + z4 + z7 + z10
res2 = aa[0] + xx[1] + yy[2] + zz[3] + zz[6] + zz[9]
self.assertEqual(res, res2)
# noinspection PyShadowingNames,PyPep8Naming,PySetFunctionToLiteral
class SymbToolsTest4(unittest.TestCase):
def setUp(self):
st.init_attribute_store(reinit=True)
def test_re_im(self):
x, y = sp.symbols('x, y', real=True)
M1 = sp.Matrix([[x, 0], [sp.pi, 5*x**2]])
M2 = sp.Matrix([[y, 3], [sp.exp(1), 7/y]])
M = M1 + 1j*M2
R = st.re(M)
I = st.im(M)
self.assertEqual(R-M1, R*0)
self.assertEqual(I-M2, R*0)
def test_is_number(self):
x1, x2, x3 = xx = st.symb_vector('x1:4')
self.assertTrue(st.is_number(x1/x1))
self.assertTrue(st.is_number(5))
self.assertTrue(st.is_number(5.3))
self.assertTrue(st.is_number(sp.pi))
self.assertTrue(st.is_number(sp.Rational(2, 7)))
self.assertTrue(st.is_number(sp.Rational(2, 7).evalf(30)))
self.assertTrue(st.is_number(sin(7)))
self.assertTrue(st.is_number(np.float(9000)))
self.assertFalse(st.is_number(x1))
self.assertFalse(st.is_number(sin(x1)))
with self.assertRaises(TypeError) as cm:
st.is_number( sp.eye(3) )
with self.assertRaises(TypeError) as cm:
st.is_number( "567" )
def test_is_scalar(self):
x1, x2, x3 = xx = st.symb_vector('x1:4')
self.assertTrue(st.is_scalar(x1/x1))
self.assertTrue(st.is_scalar(5))
self.assertTrue(st.is_scalar(5.3))
self.assertTrue(st.is_scalar(sp.pi))
self.assertTrue(st.is_scalar(sp.Rational(2, 7)))
self.assertTrue(st.is_scalar(sp.Rational(2, 7).evalf(30)))
self.assertTrue(st.is_scalar(sin(7)))
self.assertTrue(st.is_scalar(np.float(9000)))
self.assertTrue(st.is_scalar(x1**2 + x3))
self.assertFalse(st.is_scalar( sp.eye(3)*x2 ))
self.assertFalse(st.is_scalar( sp.zeros(2, 4)*x2 ))
self.assertFalse(st.is_scalar( sp.eye(0)*x2 ))
def test_is_scalar2(self):
x1, x2, x3 = xx = st.symb_vector('x1:4')
a1, a2, a3 = aa = st.symb_vector('a1:4')
M1 = sp.Matrix([[0, 0], [a1, a2], [0, a3]])
M2 = sp.ImmutableDenseMatrix(M1)
iss = st.is_scalar
self.assertTrue(iss(x1))
self.assertTrue(iss(x1 ** 2 + sp.sin(x2)))
self.assertTrue(iss(0))
self.assertTrue(iss(0.1))
self.assertTrue(iss(7.5 - 23j))
self.assertTrue(iss(np.float64(0.1)))
self.assertFalse(iss(M1))
self.assertFalse(iss(M2))
self.assertFalse(iss(M1[:1, :1]))
self.assertFalse(iss( | np.arange(5) | numpy.arange |
#!/usr/bin/env python
# -*- coding: utf-8 -*-
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from mhmcmc import MHMCMCSampler, GaussianStep
from mhmcmc import display_trace, autocorrelation
table = pd.read_csv('../../data/mcmc/exercise_linear_regression.csv')
def log_likelihood(x):
delta = table.logM_B - (x[0] + x[1]*(table.logsig-np.log10(200)))
sigma = table.logM_B_err
return -np.sum(delta**2/sigma**2/2)
step = GaussianStep(np.array([0.02, 0.15]))
model = MHMCMCSampler(log_likelihood, step)
x0 = np.array([7.0, 8.0])
model.initialize(x0)
sample = model.generate(1000)
x = np.linspace(-0.5,0.5,50)
a,b = sample[400:].mean(axis=0)
fig = plt.figure(figsize=(8,6))
def update(i, sample):
fig.clf()
ax = fig.add_subplot()
ax.errorbar(
x = table.logsig- | np.log10(200) | numpy.log10 |
import sys
sys.path.append('../lib')
import exchange
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import datetime
from scipy.optimize import minimize
from sklearn.linear_model import LinearRegression
from scipy.stats import norm
def moving_average(a, n=1000) :
ret = np.cumsum(a, dtype=float)
ret[n:] = ret[n:] - ret[:-n]
return ret[n - 1:] / n
def main():
e = exchange.Exchange('../lib/binance.db')
times = [datetime.datetime(2018, 4, 1) + i * datetime.timedelta(hours=1) for i in range(10000)]
variances = []
prices = []
average_distances = []
order_average = 25
for start, end in zip(times[:-1], times[1:]):
print(start)
it = e.get_orders('BTCUSDT', start.timestamp() * 1000, end.timestamp() * 1000)
trades = {'price': [], 'time': []}
for order in it:
trades['time'].append(order.time)
trades['price'].append(order.average_price)
trades = pd.DataFrame(trades)
if trades['time'].values.shape[0] == 0:
continue
price_changes = | np.diff(trades['price']) | numpy.diff |
# -*- coding: utf-8 -*-
import numpy as np
def sortAngles(vis_cors_row,norm_n,norm_e,norm_d,terrain):
'''
This function sorts the visible points in the histogram by camera viewing angle
This lets us specify that points must be covered from a variety of angles
INPUTS
vis_cors: Contains one row of the visibility histogram matrix, and the
orientation of the corresponding camera [-3:]
norm_n: North component of surface normals
norm_e: East component of surface normals
norm_d: Vertical component of surface normals
OUTPUTS
visibilityRowAngles: Histogram row duplicated to account for each angle bin
'''
# Camera location vector
cam = vis_cors_row[-6:-3]
# Camera orientation vector
cor = vis_cors_row[-3:]
# Visibility for the camera
vis = vis_cors_row[:-6]
# Flatten 2D grids to 1D vectors
nu = np.ravel(terrain.nn)
eu = | np.ravel(terrain.ee) | numpy.ravel |
import numpy as np
import numpy.linalg as LA
import scipy.sparse as sp
from scipy.stats.mstats import gmean
from time import time
from multiprocessing import Process, Pipe
import sys, os, warnings
from a2dr.precondition import precondition
from a2dr.acceleration import aa_weights
from a2dr.utilities import get_version
sys_stdout_origin = sys.stdout
def map_g(p_list,A,b,v,t,dk,n_list_cumsum):
N=len(p_list)
#
v_list = [v[n_list_cumsum[i]:n_list_cumsum[i+1]] for i in range(N) ]
x_list = [p_list[i](v_list[i],t) for i in range(N)]
x_half = np.concatenate(x_list, axis=0)
v_half = 2*x_half-v
dk = sp.linalg.lsqr(A, A.dot(v_half) - b, atol=1e-10, btol=1e-10, x0=dk)[0]
x_new = v_half - dk
f = x_new - x_half
v_new = v + f
return v_new, f, dk, x_half, x_half - v
def lmaa(p_list, A_list=[], b=np.array([]), v_init=None, n_list=None, *args, **kwargs):
start = time()
# Problem parameters.
max_iter = kwargs.pop("max_iter", 1000)
t_init = kwargs.pop("t_init", 1 / 10) # Step size.
eps_abs = kwargs.pop("eps_abs", 1e-6) # Absolute stopping tolerance.
eps_rel = kwargs.pop("eps_rel", 1e-8) # Relative stopping tolerance.
precond = kwargs.pop("precond", True) # Precondition A and b?
ada_reg = kwargs.pop("ada_reg", True) # Adaptive regularization?
# AA-II parameters.
anderson = kwargs.pop("anderson", True)
m_accel = int(kwargs.pop("m_accel", 10)) # Maximum past iterations to keep (>= 0).
lam_accel = kwargs.pop("lam_accel", 1e-8) # AA-II regularization weight.
aa_method = kwargs.pop("aa_method", "lstsq") # Algorithm for solving AA LS problem.
# Safeguarding parameters.
D_safe = kwargs.pop("D_safe", 1e6)
eps_safe = kwargs.pop("eps_safe", 1e-6)
M_safe = kwargs.pop("M_safe", int(max_iter / 100))
c = kwargs.pop("c", 1-1e-6)
# Printout parameters
verbose = kwargs.pop("verbose", True)
# Validate parameters.
if max_iter <= 0:
raise ValueError("max_iter must be a positive integer.")
if t_init <= 0:
raise ValueError("t_init must be a positive scalar.")
if eps_abs < 0:
raise ValueError("eps_abs must be a non-negative scalar.")
if eps_rel < 0:
raise ValueError("eps_rel must be a non-negative scalar.")
if m_accel <= 0:
raise ValueError("m_accel must be a positive integer.")
if lam_accel < 0:
raise ValueError("lam_accel must be a non-negative scalar.")
if not aa_method in ["lstsq", "lsqr"]:
raise ValueError("aa_method must be either 'lstsq' or 'lsqr'.")
# if D_safe < 0:
# raise ValueError("D_safe must be a non-negative scalar.")
# if eps_safe < 0:
# raise ValueError("eps_safe must be a non-negative scalar.")
# if M_safe <= 0:
# raise ValueError("M_safe must be a positive integer.")
# DRS parameters.
N = len(p_list) # Number of subproblems.
has_constr = len(A_list) != 0
if len(A_list) == 0:
if b.size != 0:
raise ValueError("Dimension mismatch: nrow(A_i) != nrow(b)")
if n_list is not None:
if len(n_list) != N:
raise ValueError("n_list must have exactly {} entries".format(N))
A_list = [sp.csr_matrix((0, ni)) for ni in n_list]
elif v_init is not None:
if len(v_init) != N:
raise ValueError("v_init must be None or contain exactly {} entries".format(N))
A_list = [sp.csr_matrix((0, vi.shape[0])) for vi in v_init]
else:
raise ValueError("n_list or v_init must be defined if A_list and b are empty")
if len(A_list) != N:
raise ValueError("A_list must be empty or contain exactly {} entries".format(N))
if v_init is None:
# v_init = [np.random.randn(A.shape[1]) for A in A_list]
v_init = [np.zeros(A.shape[1]) for A in A_list]
# v_init = [sp.csc_matrix((A.shape[1],1)) for A in A_list]
if len(v_init) != N:
raise ValueError("v_init must be None or contain exactly {} entries".format(N))
# Variable size list.
if n_list is None:
n_list = [A_list[i].shape[1] for i in range(N)]
if len(n_list) != N:
raise ValueError("n_list must be None or contain exactly {} entries".format(N))
n_list_cumsum = np.insert(np.cumsum(n_list), 0, 0)
for i in range(N):
if A_list[i].shape[0] != b.shape[0]:
raise ValueError("Dimension mismatch: nrow(A_i) != nrow(b)")
elif A_list[i].shape[1] != v_init[i].shape[0]:
raise ValueError("Dimension mismatch: ncol(A_i) != nrow(v_i)")
elif A_list[i].shape[1] != n_list[i]:
raise ValueError("Dimension mismatch: ncol(A_i) != n_i")
if not sp.issparse(A_list[i]):
A_list[i] = sp.csr_matrix(A_list[i])
if verbose:
version = get_version("__init__.py")
line_solver = "a2dr v" + version + " - Prox-Affine Distributed Convex Optimization Solver"
dashes = "-" * len(line_solver)
ddashes = "=" * len(line_solver)
line_authors = "(c) <NAME>, <NAME>"
num_spaces_authors = (len(line_solver) - len(line_authors)) // 2
line_affil = "Stanford University 2019"
num_spaces_affil = (len(line_solver) - len(line_affil)) // 2
print(dashes)
print(line_solver)
print(" " * num_spaces_authors + line_authors)
print(" " * num_spaces_affil + line_affil)
print(dashes)
# Precondition data.
if precond and has_constr:
if verbose:
print('### Preconditioning starts ... ###')
p_list, A_list, b, e_pre = precondition(p_list, A_list, b)
t_init = 1 / gmean(e_pre) ** 2 / 10
if verbose:
print('### Preconditioning finished. ###')
sigma0 = kwargs.pop("sigma0", 1e-10)
sigma1 = kwargs.pop("sigma1", 1)
c=max((t_init*sigma1-1)/(t_init*sigma1+1),(1-t_init*sigma0)/(1+t_init*sigma0))
c=np.sqrt((3+c**2))/2
if verbose:
print("max_iter = {}, t_init (after preconditioning) = {:.2f}".format(
max_iter, t_init))
print("eps_abs = {:.2e}, eps_rel = {:.2e}, precond = {!r}".format(
eps_abs, eps_rel, precond))
print("ada_reg = {!r}, anderson = {!r}, m_accel = {}".format(
ada_reg, anderson, m_accel))
print("lam_accel = {:.2e}, aa_method = {}, D_safe = {:.2e}".format(
lam_accel, aa_method, D_safe))
print("eps_safe = {:.2e}, M_safe = {:d}".format(
eps_safe, M_safe))
# Store constraint matrix for projection step.
A = sp.csr_matrix(sp.hstack(A_list))
if verbose:
print("variables n = {}, constraints m = {}".format(A.shape[1], A.shape[0]))
print("nnz(A) = {}".format(A.nnz))
print("Setup time: {:.2e}".format(time() - start))
# Check linear feasibility
sys.stdout = open(os.devnull, 'w')
r1norm = sp.linalg.lsqr(A, b)[3]
sys.stdout.close()
sys.stdout = sys_stdout_origin
if r1norm >= np.sqrt(eps_abs): # infeasible
if verbose:
print('Infeasible linear equality constraint: minimum constraint violation = {:.2e}'.format(r1norm))
print('Status: Terminated due to linear infeasibility')
print("Solve time: {:.2e}".format(time() - start))
return {"x_vals": None, "primal": None, "dual": None, "num_iters": None, "solve_time": None}
if verbose:
print("----------------------------------------------------")
print(" iter | total res | primal res | dual res | time (s)")
print("----------------------------------------------------")
# Set up the workers.
# Initialize AA-II variables.
if anderson: # TODO: Store and update these efficiently as arrays.
n_sum = np.sum([np.prod(v.shape) for v in v_init])
g_vec = np.zeros(n_sum) # g^(k) = v^(k) - F(v^(k)).
s_hist = [] # History of s^(j) = v^(j+1) - v^(j), kept in S^(k) = [s^(k-m_k) ... s^(k-1)].
y_hist = [] # History of y^(j) = g^(j+1) - g^(j), kept in Y^(k) = [y^(k-m_k) ... y^(k-1)].
n_AA = M_AA = 0 # Safeguarding counters.
# A2DR loop.
k = 0
finished = False
safeguard = True
r_primal = np.zeros(max_iter)
r_dual = np.zeros(max_iter)
r_dr = np.zeros(max_iter)
time_iter = np.zeros(max_iter)
r_best = np.inf
# Warm start terms.
dk = np.zeros(A.shape[1])
sol = np.zeros(A.shape[0])
v =np.concatenate(v_init)
f_list = np.zeros((A.shape[1],m_accel+1))
g_list = np.zeros((A.shape[1],m_accel+1))
x_list = np.zeros((A.shape[1],m_accel+1))
F_norm = np.zeros((m_accel+1))
M = np.zeros((m_accel+1,m_accel+1))
idx = 0
eta0 = 2
eta1 = 0.25
mu = 1e-8
delta = 2
p1 = 0.01
p2 = 0.25
curr_dk = dk.copy()
while not finished:
if k==0:
x_list[:,0] = v
curr_g, curr_f, curr_dk, curr_x_half, curr_xvdiff =map_g(p_list,A,b,v,t_init,curr_dk,n_list_cumsum)
g_list[:,0] = curr_g
F_norm[0] = np.sum(curr_f**2)
f_list[:, 0] = curr_f/np.sqrt(F_norm[0])
M[0,0] = 1
Ax_half = A.dot(curr_x_half)
r_primal_vec = (Ax_half) - b
r_primal[k] = LA.norm(r_primal_vec, ord=2)
subgrad = curr_xvdiff / t_init
# sol = LA.lstsq(A.T, subgrad, rcond=None)[0]
sys.stdout = open(os.devnull, 'w')
sol = sp.linalg.lsqr(A.T, subgrad, atol=1e-10, btol=1e-10, x0=sol)[0]
sys.stdout.close()
sys.stdout = sys_stdout_origin
r_dual_vec = A.T.dot(sol) - subgrad
r_dual[k] = LA.norm(r_dual_vec, ord=2)
# Save x_i^(k+1/2) if residual norm is smallest so far.
r_all = LA.norm(np.concatenate([r_primal_vec, r_dual_vec]), ord=2)
# Store ||r^0||_2 for stopping criterion.
r_all_0 = r_all
x_final = curr_x_half
r_best = r_all
k_best = k
r_dr[k] = np.sqrt(F_norm[0])
time_iter[k] = time() - start
v = curr_g.copy()
curr_g, curr_f, curr_dk, curr_x_half, curr_xvdiff = map_g(p_list,A,b,v,t_init,curr_dk,n_list_cumsum)
idx += 1
m_hat = min(idx, m_accel)
id = np.mod(idx,m_accel+1)
x_list[:,id] = v
g_list[:,id] = curr_g
F_norm[id] = np.sum(curr_f ** 2)
f_list[:, id] = curr_f / np.sqrt(F_norm[id])
k += 1
continue
if id>0:
M[0:id,id] = (f_list[:,0:id]).T @ f_list[:,id]
if id<m_hat:
M[id+1:m_hat+1,id]= (f_list[:,id+1:m_hat+1]).T @ f_list[:,id]
M[id,id] = 1
M[id, 0:m_hat+1] = (M[0:m_hat+1,id]).T
k0=np.argmin(F_norm[0:m_hat+1])
normal_Fnorm= np.sqrt(F_norm[0:m_hat+1])/np.sqrt(F_norm[k0])
lam = mu
tM = np.diag(normal_Fnorm)@ M[0:m_hat+1,0:m_hat+1] @ np.diag(normal_Fnorm)
bb = tM[:,k0]
B = np.repeat(np.array([bb]).T,m_hat+1,axis=1)
D = tM + 1 - B - B.T
D = np.delete(D, k0, axis=0)
D = np.delete(D, k0, axis=1)
tb = 1 - bb
tb = np.delete(tb,k0)
tA = D + lam*np.eye(m_hat)
alpha = np.linalg.lstsq(tA,tb,rcond=None)[0]
gamma = 1e-4*np.ones((m_hat+1));
gamma[k0] =1 - 1e-4 * (m_hat);
sum_f =np.dot( F_norm[0:m_hat+1] , gamma)
g_k0=g_list[:,k0]
temp_alpha= np.concatenate((alpha[0:k0],[1-np.sum(alpha)],alpha[k0:]))
g_hat= np.dot(g_list[:,0:m_hat+1],temp_alpha)
descent = alpha.T @ D @ alpha -2 * np.dot(tb, alpha)
normf_hat = F_norm[k0]*(1+descent)
trial_g, trial_f, trial_dk, trial_x_half, trial_xvdiff=map_g(p_list,A,b,g_hat,t_init,curr_dk,n_list_cumsum)
trial_Fnorm = np.sum(trial_f**2)
pred = sum_f - c*c*normf_hat
ared = sum_f - trial_Fnorm
rho = ared/pred
if rho<p1:
mu = eta0 * mu
elif rho>p2:
mu = eta1 * mu
if rho<p1:
v = g_k0.copy()
curr_g, curr_f, curr_dk, curr_x_half, curr_xvdiff = map_g(p_list,A,b,v,t_init,curr_dk,n_list_cumsum)
idx = idx + 1
m_hat = min(idx, m_accel)
id = np.mod(idx, m_accel+1)
x_list[:,id] = v
g_list[:,id] = curr_g
F_norm[id] = np.sum(curr_f**2)
f_list[:,id] = curr_f/(np.sqrt(F_norm[id]))
else:
v = g_hat.copy()
curr_g = trial_g.copy()
curr_f = trial_f.copy()
curr_dk, curr_x_half, curr_xvdiff = trial_dk.copy(),trial_x_half.copy(),trial_xvdiff.copy()
idx = idx + 1
m_hat = min(idx, m_accel)
id = np.mod(idx, m_accel + 1)
x_list[:, id] = v
g_list[:, id] = curr_g
F_norm[id] = | np.sum(curr_f ** 2) | numpy.sum |
# -*- coding: utf-8 -*-
"""
Created on Mon Sep 4 21:44:21 2017
@author: wangronin
"""
import pdb
import warnings
import numpy as np
from numpy import sqrt, exp, pi
from scipy.stats import norm
from abc import ABCMeta, abstractmethod
# warnings.filterwarnings("error")
# TODO: perphas also enable acquisition function engineering here?
# meaning the combination of the acquisition functions
class InfillCriteria:
__metaclass__ = ABCMeta
def __init__(self, model, plugin=None, minimize=True):
assert hasattr(model, 'predict')
self.model = model
self.minimize = minimize
# change maximization problem to minimization
self.plugin = plugin if self.minimize else -plugin
if self.plugin is None:
self.plugin = np.min(model.y) if minimize else -np.max(self.model.y)
@abstractmethod
def __call__(self, X):
raise NotImplementedError
def _predict(self, X):
y_hat, sd2 = self.model.predict(X, eval_MSE=True)
sd = sqrt(sd2)
if not self.minimize:
y_hat = -y_hat
return y_hat, sd
def _gradient(self, X):
y_dx, sd2_dx = self.model.gradient(X)
if not self.minimize:
y_dx = -y_dx
return y_dx, sd2_dx
def check_X(self, X):
"""Keep input as '2D' object
"""
return np.atleast_2d(X)
# return [X] if not hasattr(X[0], '__iter__') else X
# TODO: test UCB implementation
class UCB(InfillCriteria):
"""
Upper Confidence Bound
"""
def __init__(self, model, plugin=None, minimize=True, alpha=1e-10):
super(EpsilonPI, self).__init__(model, plugin, minimize)
self.alpha = alpha
def __call__(self, X, dx=False):
X = self.check_X(X)
y_hat, sd = self._predict(X)
try:
f_value = y_hat + self.alpha * sd
except Exception: # in case of numerical errors
f_value = 0
if dx:
y_dx, sd2_dx = self._gradient(X)
sd_dx = sd2_dx / (2. * sd)
try:
f_dx = y_dx + self.alpha * sd_dx
except Exception:
f_dx = np.zeros((len(X[0]), 1))
return f_value, f_dx
return f_value
class EI(InfillCriteria):
"""
Expected Improvement
"""
# perhaps separate the gradient computation here
def __call__(self, X, dx=False):
X = self.check_X(X)
y_hat, sd = self._predict(X)
# if the Kriging variance is to small
# TODO: check the rationale of 1e-6 and why the ratio if intended
# TODO: implement a counterpart of 'sigma2' for randomforest
if hasattr(self.model, 'sigma2'):
if sd / np.sqrt(self.model.sigma2) < 1e-6:
return (np.array([0.]), np.zeros((len(X[0]), 1))) if dx else 0.
try:
# TODO: I have save xcr_ becasue xcr * sd != xcr_ numerically
# find out the cause of such an error, probably representation error...
xcr_ = self.plugin - y_hat
xcr = xcr_ / sd
xcr_prob, xcr_dens = norm.cdf(xcr), norm.pdf(xcr)
f_value = xcr_ * xcr_prob + sd * xcr_dens
except Exception: # in case of numerical errors
# IMPORTANT: always keep the output in the same type
f_value = np.array([0.])
if dx:
y_dx, sd2_dx = self._gradient(X)
sd_dx = sd2_dx / (2. * sd)
try:
f_dx = -y_dx * xcr_prob + sd_dx * xcr_dens
except Exception:
f_dx = np.zeros((len(X[0]), 1))
return f_value, f_dx
return f_value
class EpsilonPI(InfillCriteria):
"""
epsilon-Probability of Improvement
# TODO: verify the implementation
"""
def __init__(self, model, plugin=None, minimize=True, epsilon=1e-10):
super(EpsilonPI, self).__init__(model, plugin, minimize)
self.epsilon = epsilon
def __call__(self, X, dx=False):
X = self.check_X(X)
y_hat, sd = self._predict(X)
coef = 1 - self.epsilon if y_hat > 0 else (1 + self.epsilon)
try:
xcr_ = self.plugin - coef * y_hat
xcr = xcr_ / sd
f_value = norm.cdf(xcr)
except Exception:
f_value = 0.
if dx:
y_dx, sd2_dx = self._gradient(X)
sd_dx = sd2_dx / (2. * sd)
try:
f_dx = -(coef * y_dx + xcr * sd_dx) * norm.pdf(xcr) / sd
except Exception:
f_dx = np.zeros((len(X[0]), 1))
return f_value, f_dx
return f_value
class PI(EpsilonPI):
"""
Probability of Improvement
"""
def __init__(self, model, plugin=None, minimize=True):
super(PI, self).__init__(model, plugin, minimize, epsilon=0)
class MGFI(InfillCriteria):
"""
Moment-Generating Function of Improvement
My new acquisition function proposed in SMC'17 paper
"""
def __init__(self, model, plugin=None, minimize=True, t=1):
super(MGFI, self).__init__(model, plugin, minimize)
self.t = t
def __call__(self, X, dx=False):
X = self.check_X(X)
y_hat, sd = self._predict(X)
# if the Kriging variance is to small
# TODO: check the rationale of 1e-6 and why the ratio if intended
if np.isclose(sd, 0):
return (np.array([0.]), np.zeros((len(X[0]), 1))) if dx else 0.
try:
y_hat_p = y_hat - self.t * sd ** 2.
beta_p = (self.plugin - y_hat_p) / sd
term = self.t * (self.plugin - y_hat - 1)
f_ = norm.cdf(beta_p) * exp(term + self.t ** 2. * sd ** 2. / 2.)
except Exception: # in case of numerical errors
f_ = np.array([0.])
if np.isinf(f_):
f_ = np.array([0.])
if dx:
y_dx, sd2_dx = self._gradient(X)
sd_dx = sd2_dx / (2. * sd)
try:
term = exp(self.t * (self.plugin + self.t * sd ** 2. / 2 - y_hat - 1))
m_prime_dx = y_dx - 2. * self.t * sd * sd_dx
beta_p_dx = -(m_prime_dx + beta_p * sd_dx) / sd
f_dx = term * (norm.pdf(beta_p) * beta_p_dx + \
norm.cdf(beta_p) * ((self.t ** 2) * sd * sd_dx - self.t * y_dx))
except Exception:
f_dx = np.zeros((len(X[0]), 1))
return f_, f_dx
return f_
class GEI(InfillCriteria):
"""
Generalized Expected Improvement
"""
def __init__(self, model, plugin=None, minimize=True, g=1):
super(GEI, self).__init__(model, plugin, minimize)
self.g = g
def __call__(self, X, dx=False):
pass
if __name__ == '__main__':
# TODO: diagnostic plot for the gradient of Infill-Criteria
# goes to unittest
from GaussianProcess.trend import linear_trend, constant_trend
from GaussianProcess import GaussianProcess
from GaussianProcess.utils import plot_contour_gradient
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
from deap import benchmarks
np.random.seed(123)
plt.ioff()
fig_width = 16
fig_height = 16
noise_var = 0.
def fitness(X):
X = np.atleast_2d(X)
return np.array([benchmarks.schwefel(x)[0] for x in X]) + \
np.sqrt(noise_var) * np.random.randn(X.shape[0])
dim = 2
n_init_sample = 10
x_lb = | np.array([-5] * dim) | numpy.array |
import time
import inspect
import logging
import json
import functools
from abc import abstractmethod
from typing import Dict, Union, List
from pathlib import Path
from collections import OrderedDict
import numpy as np
import torch as th
from numpy.random import randint
from torch.utils.data import Dataset
from typeguard import typechecked
import data_loader
from utils.util import ensure_tensor, expert_tensor_storage
from zsvision.zs_utils import memcache
# For SLURM usage, buffering makes it difficult to see events as they happen, so we set
# the global print statement to enforce flushing
print = functools.partial(print, flush=True)
class BaseDataset(Dataset):
@staticmethod
@abstractmethod
@typechecked
def dataset_paths() -> Dict[str, Union[Path, str]]:
"""Generates a datastructure containing all the paths required to load features
"""
raise NotImplementedError
@abstractmethod
def sanity_checks(self):
"""Run sanity checks on loaded data
"""
raise NotImplementedError
@abstractmethod
def load_features(self):
"""Load features from disk
"""
raise NotImplementedError
@typechecked
def __init__(
self,
data_dir: Path,
fuse_captions: bool,
spatial_feats: bool,
challenge_mode: bool,
eval_only: bool,
use_zeros_for_missing: bool,
task: str,
text_agg: str,
text_feat: str,
split_name: str,
cls_partition: str,
root_feat_folder: str,
challenge_test_root_feat_folder: str,
subsample_training_data_fraction: float,
text_dim: int,
num_test_captions: int,
restrict_train_captions: int,
max_tokens: Dict[str, int],
text_dropout: float,
logger: logging.Logger,
raw_input_dims: Dict[str, int],
feat_aggregation: Dict[str, Dict],
):
self.task = task
self.eval_only = eval_only
self.logger = logger
self.challenge_mode = challenge_mode
self.text_feat = text_feat
self.data_dir = data_dir
self.text_dim = text_dim
self.spatial_feats = spatial_feats
self.text_dropout = text_dropout
self.restrict_train_captions = restrict_train_captions
self.subsample_training_data_fraction = subsample_training_data_fraction
self.max_tokens = max_tokens
self.cls_partition = cls_partition
self.fuse_captions = fuse_captions
self.num_test_captions = num_test_captions
self.feat_aggregation = feat_aggregation
self.root_feat = data_dir / root_feat_folder
self.challenge_test_root_feat_folder = data_dir / challenge_test_root_feat_folder
self.experts = set(raw_input_dims.keys())
# This attributes can be overloaded by different datasets, so it must be set
# before the `load_features() method call`
self.restrict_test_captions = None
self.text_features = None
self.label_features = None
self.video_labels = None
self.raw_captions = None
self.features = None
# Use a single caption per video when forming training minibatches (different
# captions from the same video may still be used across different minibatches)
self.captions_per_video = 1
# TODO(Samuel) - is a global fixed ordering still necessary?
self.ordered_experts = list(raw_input_dims.keys())
# Training and test lists are set by dataset-specific subclasses
self.partition_lists = {}
self.configure_train_test_splits(split_name=split_name)
# All retrieval-based tasks use a single dataloader (and handle the retrieval
# data separately), whereas for classification we use one dataloader for
# training and one for validation.
self.logger.info("The current task is {}".format(self.task))
self.sample_list = self.partition_lists["train"]
if self.subsample_training_data_fraction < 1:
num_train = len(self.sample_list)
num_keep = int(self.subsample_training_data_fraction * num_train)
sampled_train = np.random.choice(self.sample_list, num_keep, replace=False)
self.logger.info(f"Sampling training samples [{num_train} -> {num_keep}]")
self.sample_list = sampled_train.tolist()
self.num_samples = len(self.sample_list)
num_val = len(self.partition_lists["val"])
if self.task == "classification":
self.sample_list = self.partition_lists[self.cls_partition]
self.num_samples = len(self.sample_list)
self.logger.info("The current cls_partition is {}".format(self.cls_partition))
# The number of classes and class type (i.e. single or multi-label) must be
# overriden in the subclass
self.num_classes = None
self.class_type = None
self.raw_input_dims = raw_input_dims
# we store default paths to enable visualisations (this can be overloaded by
# dataset-specific classes)
self.video_path_retrieval = [f"videos/{x}.mp4" for x
in self.partition_lists["val"]]
# NOTE: We use nans rather than zeros to indicate missing faces, unless we wish
# to test single modality strength, which requires passing zeroed features for
# missing videos
if use_zeros_for_missing:
self.MISSING_VAL = 0
else:
self.MISSING_VAL = np.nan
# load the dataset-specific features into memory
self.load_features()
if text_agg == "avg":
self.logger.info("averaging the text features...")
for key, val in self.text_features.items():
self.text_features[key] = [np.mean(x, 0, keepdims=1) for x in val]
self.logger.info("finished averaging the text features")
self.trn_config = {}
self.raw_config = {}
self.tensor_storage = expert_tensor_storage(self.experts, self.feat_aggregation)
for static_expert in self.tensor_storage["fixed"]:
if static_expert in self.feat_aggregation:
if "trn_seg" in self.feat_aggregation[static_expert].keys():
self.trn_config[static_expert] = \
self.feat_aggregation[static_expert]["trn_seg"]
if "raw" in self.feat_aggregation[static_expert]["temporal"]:
self.raw_config[static_expert] = 1
if self.task == "classification":
# for classification we don't need to preload additional features
return
retrieval = {
expert: np.zeros((num_val, self.max_tokens[expert], raw_input_dims[expert]))
for expert in self.tensor_storage["variable"]
}
retrieval.update({expert: np.zeros((num_val, raw_input_dims[expert]))
for expert in self.tensor_storage["fixed"]})
self.retrieval = retrieval
self.test_ind = {expert: th.ones(num_val) for expert in self.experts}
self.raw_captions_retrieval = [None] * num_val
if self.task == "retrieval-as-classification":
# Treat each category label as a query
num_labels = len(self.label_features)
self.text_retrieval = np.zeros((num_labels, 1, 1, self.text_dim))
self.query_masks = np.zeros((num_labels, num_val))
for ii, video_name in enumerate(self.partition_lists["val"]):
labels = self.video_labels[video_name]
self.query_masks[ | np.array(labels) | numpy.array |
# ******************************************************************************
# Copyright 2017-2020 Intel Corporation
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ******************************************************************************
import numpy as np
import pytest
import ngraph as ng
@pytest.fixture()
def _proposal_node():
attributes = {
"base_size": np.uint16(1),
"pre_nms_topn": np.uint16(20),
"post_nms_topn": np.uint16(64),
"nms_thresh": np.float64(0.34),
"feat_stride": np.uint16(16),
"min_size": np.uint16(32),
"ratio": np.array([0.1, 1.5, 2.0, 2.5], dtype=np.float64),
"scale": np.array([2, 3, 3, 4], dtype=np.float64),
}
batch_size = 7
class_probs = ng.parameter([batch_size, 12, 34, 62], np.float64, "class_probs")
bbox_deltas = ng.parameter([batch_size, 24, 34, 62], np.float64, "bbox_deltas")
image_shape = ng.parameter([3], np.float64, "image_shape")
return ng.proposal(class_probs, bbox_deltas, image_shape, attributes)
def test_dynamic_attributes_softmax():
axis = 2
data = ng.parameter([1, 2, 3, 4], np.float32, "data_in")
node = ng.softmax(data, axis)
assert node.get_axis() == axis
node.set_axis(3)
assert node.get_axis() == 3
@pytest.mark.parametrize(
"int_dtype, fp_dtype",
[
(np.int8, np.float32),
(np.int16, np.float32),
(np.int32, np.float32),
(np.int64, np.float32),
(np.uint8, np.float32),
(np.uint16, np.float32),
(np.uint32, np.float32),
(np.uint64, np.float32),
(np.int32, np.float16),
(np.int32, np.float64),
],
)
def test_dynamic_get_attribute_value(int_dtype, fp_dtype):
attributes = {
"attrs.num_classes": int_dtype(85),
"attrs.background_label_id": int_dtype(13),
"attrs.top_k": int_dtype(16),
"attrs.variance_encoded_in_target": True,
"attrs.keep_top_k": np.array([64, 32, 16, 8], dtype=int_dtype),
"attrs.code_type": "pytorch.some_parameter_name",
"attrs.share_location": False,
"attrs.nms_threshold": fp_dtype(0.645),
"attrs.confidence_threshold": fp_dtype(0.111),
"attrs.clip_after_nms": True,
"attrs.clip_before_nms": False,
"attrs.decrease_label_id": True,
"attrs.normalized": True,
"attrs.input_height": int_dtype(86),
"attrs.input_width": int_dtype(79),
"attrs.objectness_score": fp_dtype(0.77),
}
box_logits = ng.parameter([4, 1, 5, 5], fp_dtype, "box_logits")
class_preds = ng.parameter([2, 1, 4, 5], fp_dtype, "class_preds")
proposals = ng.parameter([2, 1, 4, 5], fp_dtype, "proposals")
aux_class_preds = ng.parameter([2, 1, 4, 5], fp_dtype, "aux_class_preds")
aux_box_preds = ng.parameter([2, 1, 4, 5], fp_dtype, "aux_box_preds")
node = ng.detection_output(box_logits, class_preds, proposals, attributes, aux_class_preds, aux_box_preds)
assert node.get_num_classes() == int_dtype(85)
assert node.get_background_label_id() == int_dtype(13)
assert node.get_top_k() == int_dtype(16)
assert node.get_variance_encoded_in_target()
assert np.all(np.equal(node.get_keep_top_k(), np.array([64, 32, 16, 8], dtype=int_dtype)))
assert node.get_code_type() == "pytorch.some_parameter_name"
assert not node.get_share_location()
assert np.isclose(node.get_nms_threshold(), fp_dtype(0.645))
assert np.isclose(node.get_confidence_threshold(), fp_dtype(0.111))
assert node.get_clip_after_nms()
assert not node.get_clip_before_nms()
assert node.get_decrease_label_id()
assert node.get_normalized()
assert node.get_input_height() == int_dtype(86)
assert node.get_input_width() == int_dtype(79)
assert np.isclose(node.get_objectness_score(), fp_dtype(0.77))
assert node.get_num_classes() == int_dtype(85)
@pytest.mark.parametrize(
"int_dtype, fp_dtype",
[
(np.uint8, np.float32),
(np.uint16, np.float32),
(np.uint32, np.float32),
(np.uint64, np.float32),
(np.uint32, np.float16),
(np.uint32, np.float64),
],
)
def test_dynamic_set_attribute_value(int_dtype, fp_dtype):
attributes = {
"base_size": int_dtype(1),
"pre_nms_topn": int_dtype(20),
"post_nms_topn": int_dtype(64),
"nms_thresh": fp_dtype(0.34),
"feat_stride": int_dtype(16),
"min_size": int_dtype(32),
"ratio": np.array([0.1, 1.5, 2.0, 2.5], dtype=fp_dtype),
"scale": np.array([2, 3, 3, 4], dtype=fp_dtype),
}
batch_size = 7
class_probs = ng.parameter([batch_size, 12, 34, 62], fp_dtype, "class_probs")
bbox_deltas = ng.parameter([batch_size, 24, 34, 62], fp_dtype, "bbox_deltas")
image_shape = ng.parameter([3], fp_dtype, "image_shape")
node = ng.proposal(class_probs, bbox_deltas, image_shape, attributes)
node.set_base_size(int_dtype(15))
node.set_pre_nms_topn(int_dtype(7))
node.set_post_nms_topn(int_dtype(33))
node.set_nms_thresh(fp_dtype(1.55))
node.set_feat_stride(int_dtype(8))
node.set_min_size(int_dtype(123))
node.set_ratio(np.array([1.1, 2.5, 3.0, 4.5], dtype=fp_dtype))
node.set_scale(np.array([2.1, 3.2, 3.3, 4.4], dtype=fp_dtype))
node.set_clip_before_nms(True)
node.set_clip_after_nms(True)
node.set_normalize(True)
node.set_box_size_scale(fp_dtype(1.34))
node.set_box_coordinate_scale(fp_dtype(0.88))
node.set_framework("OpenVINO")
assert node.get_base_size() == int_dtype(15)
assert node.get_pre_nms_topn() == int_dtype(7)
assert node.get_post_nms_topn() == int_dtype(33)
assert np.isclose(node.get_nms_thresh(), fp_dtype(1.55))
assert node.get_feat_stride() == int_dtype(8)
assert node.get_min_size() == int_dtype(123)
assert np.allclose(node.get_ratio(), np.array([1.1, 2.5, 3.0, 4.5], dtype=fp_dtype))
assert np.allclose(node.get_scale(), np.array([2.1, 3.2, 3.3, 4.4], dtype=fp_dtype))
assert node.get_clip_before_nms()
assert node.get_clip_after_nms()
assert node.get_normalize()
assert np.isclose(node.get_box_size_scale(), fp_dtype(1.34))
assert np.isclose(node.get_box_coordinate_scale(), fp_dtype(0.88))
assert node.get_framework() == "OpenVINO"
def test_dynamic_attr_cache(_proposal_node):
node = _proposal_node
assert not node._attr_cache_valid
node.set_nms_thresh(1.3453678102)
assert not node._attr_cache_valid
assert np.isclose(node.get_nms_thresh(), np.float64(1.3453678102))
assert node._attr_cache_valid
def test_dynamic_attr_transitivity(_proposal_node):
node = _proposal_node
node2 = node
node.set_ratio(np.array([1.1, 2.5, 3.0, 4.5], dtype=np.float64))
assert np.allclose(node.get_ratio(), np.array([1.1, 2.5, 3.0, 4.5], dtype=np.float64))
assert np.allclose(node2.get_ratio(), np.array([1.1, 2.5, 3.0, 4.5], dtype=np.float64))
node2.set_scale(np.array([2.1, 3.2, 3.3, 4.4], dtype=np.float64))
assert np.allclose(node2.get_scale(), | np.array([2.1, 3.2, 3.3, 4.4], dtype=np.float64) | numpy.array |
import subprocess as sp
import numpy as np
from sk import SK,get_speech_ts_adaptive
from pdb import set_trace
CHUNK_SIZE = 4000
def video_frames_ffmpeg(url):
iterator = 0
cmd = f'ffmpeg -loglevel quiet -re -i {url} -acodec pcm_f32le -f f32le -vn -sn -dn -ar 16000 -ac 1 -'.split(" ")
p = sp.Popen(cmd, stdout=sp.PIPE)
asr = SK(model="silero_en_large")
buffer = []
current_text = ""
current_len = 0
skip = False
repeated = 0
while True:
data = p.stdout.read(CHUNK_SIZE*10)
data = | np.frombuffer(data, dtype=np.float32) | numpy.frombuffer |
#!/usr/bin/env python
u"""
read_cryosat_L1b.py
Written by <NAME> (02/2020)
Reads CryoSat Level-1b data products from baselines A, B and C
Reads CryoSat Level-1b netCDF4 data products from baseline D
Supported CryoSat Modes: LRM, SAR, SARin, FDM, SID, GDR
INPUTS:
full_filename: full path of CryoSat .DBL or .nc file
OUTPUTS:
Location: Time and Orbit Group
Data: Measurements Group
Geometry: External Corrections Group
Waveform_1Hz: Average Waveforms Group
Waveform_20Hz: Waveforms Group (with SAR/SARIN Beam Behavior Parameters)
METADATA: MPH, SPH and DSD Header data
PYTHON DEPENDENCIES:
numpy: Scientific Computing Tools For Python
https://numpy.org
https://numpy.org/doc/stable/user/numpy-for-matlab-users.html
netCDF4: Python interface to the netCDF C library
https://unidata.github.io/netcdf4-python/netCDF4/index.html
UPDATE HISTORY:
Updated 02/2020: tilde-expansion of cryosat-2 files before opening
add scale factors function for converting packed units in binary files
convert from hard to soft tabulation
Updated 11/2019: empty placeholder dictionary for baseline D DSD headers
Updated 09/2019: added netCDF4 read function for baseline D
will output with same variable names as the binary read functions
Updated 04/2019: USO correction signed 32 bit int
Updated 10/2018: updated header read functions for python3
Updated 05/2016: using __future__ print and division functions
Written 03/2016
"""
from __future__ import print_function
from __future__ import division
import os
import re
import netCDF4
import numpy as np
#-- PURPOSE: Initiate L1b MDS variables for CryoSat Baselines A and B
def cryosat_baseline_AB(fid, n_records, MODE):
n_SARIN_RW = 512
n_SAR_RW = 128
n_LRM_RW = 128
n_blocks = 20
n_BeamBehaviourParams = 50
#-- CryoSat-2 Time and Orbit Group
Location = {}
#-- Time: day part
Location['Day'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Time: second part
Location['Second'] = np.zeros((n_records,n_blocks),dtype=np.uint32)
#-- Time: microsecond part
Location['Micsec'] = np.zeros((n_records,n_blocks),dtype=np.uint32)
#-- USO correction factor
Location['USO_Corr'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Mode ID
Location['Mode_ID'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Source sequence counter
Location['SSC'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Instrument configuration
Location['Inst_config'] = np.zeros((n_records,n_blocks),dtype=np.uint32)
#-- Record Counter
Location['Rec_Count'] = np.zeros((n_records,n_blocks),dtype=np.uint32)
#-- Lat: packed units (0.1 micro-degree, 1e-7 degrees)
Location['Lat'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Lon: packed units (0.1 micro-degree, 1e-7 degrees)
Location['Lon'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Alt: packed units (mm, 1e-3 m)
#-- Altitude of COG above reference ellipsoid (interpolated value)
Location['Alt'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Instantaneous altitude rate derived from orbit: packed units (mm/s, 1e-3 m/s)
Location['Alt_rate'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Satellite velocity vector. In ITRF: packed units (mm/s, 1e-3 m/s)
#-- ITRF= International Terrestrial Reference Frame
Location['Sat_velocity'] = np.zeros((n_records,n_blocks,3),dtype=np.int32)
#-- Real beam direction vector. In CRF: packed units (micro-m, 1e-6 m)
#-- CRF= CryoSat Reference Frame.
Location['Real_beam'] = np.zeros((n_records,n_blocks,3),dtype=np.int32)
#-- Interferometric baseline vector. In CRF: packed units (micro-m, 1e-6 m)
Location['Baseline'] = np.zeros((n_records,n_blocks,3),dtype=np.int32)
#-- Measurement Confidence Data Flags
#-- Generally the MCD flags indicate problems when set
#-- If MCD is 0 then no problems or non-nominal conditions were detected
#-- Serious errors are indicated by setting bit 31
Location['MCD'] = np.zeros((n_records,n_blocks),dtype=np.uint32)
#-- CryoSat-2 Measurement Group
#-- Derived from instrument measurement parameters
Data_20Hz = {}
#-- Window Delay reference (two-way) corrected for instrument delays
Data_20Hz['TD'] = np.zeros((n_records,n_blocks),dtype=np.int64)
#-- H0 Initial Height Word from telemetry
Data_20Hz['H_0'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- COR2 Height Rate: on-board tracker height rate over the radar cycle
Data_20Hz['COR2'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Coarse Range Word (LAI) derived from telemetry
Data_20Hz['LAI'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Fine Range Word (FAI) derived from telemetry
Data_20Hz['FAI'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Automatic Gain Control Channel 1: AGC gain applied on Rx channel 1.
#-- Gain calibration corrections are applied (Sum of AGC stages 1 and 2
#-- plus the corresponding corrections) (dB/100)
Data_20Hz['AGC_CH1'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Automatic Gain Control Channel 2: AGC gain applied on Rx channel 2.
#-- Gain calibration corrections are applied (dB/100)
Data_20Hz['AGC_CH2'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Total Fixed Gain On Channel 1: gain applied by the RF unit. (dB/100)
Data_20Hz['TR_gain_CH1'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Total Fixed Gain On Channel 2: gain applied by the RF unit. (dB/100)
Data_20Hz['TR_gain_CH2'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Transmit Power in microWatts
Data_20Hz['TX_Power'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Doppler range correction: Radial component (mm)
#-- computed for the component of satellite velocity in the nadir direction
Data_20Hz['Doppler_range'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Instrument Range Correction: transmit-receive antenna (mm)
#-- Calibration correction to range on channel 1 computed from CAL1.
Data_20Hz['TR_inst_range'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Instrument Range Correction: receive-only antenna (mm)
#-- Calibration correction to range on channel 2 computed from CAL1.
Data_20Hz['R_inst_range'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Instrument Gain Correction: transmit-receive antenna (dB/100)
#-- Calibration correction to gain on channel 1 computed from CAL1
Data_20Hz['TR_inst_gain'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Instrument Gain Correction: receive-only (dB/100)
#-- Calibration correction to gain on channel 2 computed from CAL1
Data_20Hz['R_inst_gain'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Internal Phase Correction (microradians)
Data_20Hz['Internal_phase'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- External Phase Correction (microradians)
Data_20Hz['External_phase'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Noise Power measurement (dB/100): converted from telemetry units to be
#-- the noise floor of FBR measurement echoes.
#-- Set to -9999.99 when the telemetry contains zero.
Data_20Hz['Noise_power'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Phase slope correction (microradians)
#-- Computed from the CAL-4 packets during the azimuth impulse response
#-- amplitude (SARIN only). Set from the latest available CAL-4 packet.
Data_20Hz['Phase_slope'] = np.zeros((n_records,n_blocks),dtype=np.int32)
Data_20Hz['Spares1'] = np.zeros((n_records,n_blocks,4),dtype=np.int8)
#-- CryoSat-2 External Corrections Group
Geometry = {}
#-- Dry Tropospheric Correction packed units (mm, 1e-3 m)
Geometry['dryTrop'] = np.zeros((n_records),dtype=np.int32)
#-- Wet Tropospheric Correction packed units (mm, 1e-3 m)
Geometry['wetTrop'] = np.zeros((n_records),dtype=np.int32)
#-- Inverse Barometric Correction packed units (mm, 1e-3 m)
Geometry['InvBar'] = np.zeros((n_records),dtype=np.int32)
#-- Delta Inverse Barometric Correction packed units (mm, 1e-3 m)
Geometry['DAC'] = np.zeros((n_records),dtype=np.int32)
#-- GIM Ionospheric Correction packed units (mm, 1e-3 m)
Geometry['Iono_GIM'] = np.zeros((n_records),dtype=np.int32)
#-- Model Ionospheric Correction packed units (mm, 1e-3 m)
Geometry['Iono_model'] = np.zeros((n_records),dtype=np.int32)
#-- Ocean tide Correction packed units (mm, 1e-3 m)
Geometry['ocTideElv'] = np.zeros((n_records),dtype=np.int32)
#-- Long period equilibrium ocean tide Correction packed units (mm, 1e-3 m)
Geometry['lpeTideElv'] = np.zeros((n_records),dtype=np.int32)
#-- Ocean loading tide Correction packed units (mm, 1e-3 m)
Geometry['olTideElv'] = np.zeros((n_records),dtype=np.int32)
#-- Solid Earth tide Correction packed units (mm, 1e-3 m)
Geometry['seTideElv'] = np.zeros((n_records),dtype=np.int32)
#-- Geocentric Polar tide Correction packed units (mm, 1e-3 m)
Geometry['gpTideElv'] = np.zeros((n_records),dtype=np.int32)
#-- Surface Type: enumerated key to classify surface at nadir
#-- 0 = Open Ocean
#-- 1 = Closed Sea
#-- 2 = Continental Ice
#-- 3 = Land
Geometry['Surf_type'] = np.zeros((n_records),dtype=np.uint32)
Geometry['Spare1'] = np.zeros((n_records,4),dtype=np.int8)
#-- Corrections Status Flag
Geometry['Corr_status'] = np.zeros((n_records),dtype=np.uint32)
#-- Correction Error Flag
Geometry['Corr_error'] = np.zeros((n_records),dtype=np.uint32)
Geometry['Spare2'] = np.zeros((n_records,4),dtype=np.int8)
#-- CryoSat-2 Average Waveforms Groups
Waveform_1Hz = {}
if (MODE == 'LRM'):
#-- Low-Resolution Mode
#-- Data Record Time (MDSR Time Stamp)
Waveform_1Hz['Day'] = np.zeros((n_records),dtype=np.int32)
Waveform_1Hz['Second'] = np.zeros((n_records),dtype=np.uint32)
Waveform_1Hz['Micsec'] = np.zeros((n_records),dtype=np.uint32)
#-- Lat: packed units (0.1 micro-degree, 1e-7 degrees)
Waveform_1Hz['Lat'] = np.zeros((n_records),dtype=np.int32)
#-- Lon: packed units (0.1 micro-degree, 1e-7 degrees)
Waveform_1Hz['Lon'] = np.zeros((n_records),dtype=np.int32)
#-- Alt: packed units (mm, 1e-3 m)
#-- Altitude of COG above reference ellipsoid (interpolated value)
Waveform_1Hz['Alt'] = np.zeros((n_records),dtype=np.int32)
#-- Window Delay (two-way) corrected for instrument delays
Waveform_1Hz['TD'] = np.zeros((n_records),dtype=np.int64)
#-- 1 Hz Averaged Power Echo Waveform
Waveform_1Hz['Waveform'] = np.zeros((n_records,n_LRM_RW),dtype=np.uint16)
#-- Echo Scale Factor (to scale echo to watts)
Waveform_1Hz['Linear_Wfm_Multiplier'] = np.zeros((n_records),dtype=np.int32)
#-- Echo Scale Power (a power of 2)
Waveform_1Hz['Power2_Wfm_Multiplier'] = np.zeros((n_records),dtype=np.int32)
#-- Number of echoes averaged
Waveform_1Hz['N_avg_echoes'] = np.zeros((n_records),dtype=np.uint16)
Waveform_1Hz['Flags'] = np.zeros((n_records),dtype=np.uint16)
elif (MODE == 'SAR'):
#-- SAR Mode
#-- Data Record Time (MDSR Time Stamp)
Waveform_1Hz['Day'] = np.zeros((n_records),dtype=np.int32)
Waveform_1Hz['Second'] = np.zeros((n_records),dtype=np.uint32)
Waveform_1Hz['Micsec'] = np.zeros((n_records),dtype=np.uint32)
#-- Lat: packed units (0.1 micro-degree, 1e-7 degrees)
Waveform_1Hz['Lat'] = np.zeros((n_records),dtype=np.int32)
#-- Lon: packed units (0.1 micro-degree, 1e-7 degrees)
Waveform_1Hz['Lon'] = np.zeros((n_records),dtype=np.int32)
#-- Alt: packed units (mm, 1e-3 m)
#-- Altitude of COG above reference ellipsoid (interpolated value)
Waveform_1Hz['Alt'] = np.zeros((n_records),dtype=np.int32)
#-- Window Delay (two-way) corrected for instrument delays
Waveform_1Hz['TD'] = np.zeros((n_records),dtype=np.int64)
#-- 1 Hz Averaged Power Echo Waveform
Waveform_1Hz['Waveform'] = np.zeros((n_records,n_SAR_RW),dtype=np.uint16)
#-- Echo Scale Factor (to scale echo to watts)
Waveform_1Hz['Linear_Wfm_Multiplier'] = np.zeros((n_records),dtype=np.int32)
#-- Echo Scale Power (a power of 2)
Waveform_1Hz['Power2_Wfm_Multiplier'] = np.zeros((n_records),dtype=np.int32)
#-- Number of echoes averaged
Waveform_1Hz['N_avg_echoes'] = np.zeros((n_records),dtype=np.uint16)
Waveform_1Hz['Flags'] = np.zeros((n_records),dtype=np.uint16)
elif (MODE == 'SIN'):
#-- SARIN Mode
#-- Same as the LRM/SAR groups but the waveform array is 512 bins instead of
#-- 128 and the number of echoes averaged is different.
#-- Data Record Time (MDSR Time Stamp)
Waveform_1Hz['Day'] = np.zeros((n_records),dtype=np.int32)
Waveform_1Hz['Second'] = np.zeros((n_records),dtype=np.uint32)
Waveform_1Hz['Micsec'] = np.zeros((n_records),dtype=np.uint32)
#-- Lat: packed units (0.1 micro-degree, 1e-7 degrees)
Waveform_1Hz['Lat'] = np.zeros((n_records),dtype=np.int32)
#-- Lon: packed units (0.1 micro-degree, 1e-7 degrees)
Waveform_1Hz['Lon'] = np.zeros((n_records),dtype=np.int32)
#-- Alt: packed units (mm, 1e-3 m)
#-- Altitude of COG above reference ellipsoid (interpolated value)
Waveform_1Hz['Alt'] = np.zeros((n_records),dtype=np.int32)
#-- Window Delay (two-way) corrected for instrument delays
Waveform_1Hz['TD'] = np.zeros((n_records),dtype=np.int64)
#-- 1 Hz Averaged Power Echo Waveform
Waveform_1Hz['Waveform'] = np.zeros((n_records,n_SARIN_RW),dtype=np.uint16)
#-- Echo Scale Factor (to scale echo to watts)
Waveform_1Hz['Linear_Wfm_Multiplier'] = np.zeros((n_records),dtype=np.int32)
#-- Echo Scale Power (a power of 2)
Waveform_1Hz['Power2_Wfm_Multiplier'] = np.zeros((n_records),dtype=np.int32)
#-- Number of echoes averaged
Waveform_1Hz['N_avg_echoes'] = np.zeros((n_records),dtype=np.uint16)
Waveform_1Hz['Flags'] = np.zeros((n_records),dtype=np.uint16)
#-- CryoSat-2 Waveforms Groups
#-- Beam Behavior Parameters
Beam_Behavior = {}
#-- Standard Deviation of Gaussian fit to range integrated stack power.
Beam_Behavior['SD'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Stack Center: Mean of Gaussian fit to range integrated stack power.
Beam_Behavior['Center'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Stack amplitude parameter scaled in dB/100.
Beam_Behavior['Amplitude'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- 3rd moment: providing the degree of asymmetry of the range integrated
#-- stack power distribution.
Beam_Behavior['Skewness'] = np.zeros((n_records,n_blocks),dtype=np.int16)
#-- 4th moment: Measure of peakiness of range integrated stack power distribution.
Beam_Behavior['Kurtosis'] = np.zeros((n_records,n_blocks),dtype=np.int16)
Beam_Behavior['Spare'] = np.zeros((n_records,n_blocks,n_BeamBehaviourParams-5),dtype=np.int16)
#-- CryoSat-2 mode specific waveforms
Waveform_20Hz = {}
if (MODE == 'LRM'):
#-- Low-Resolution Mode
#-- Averaged Power Echo Waveform [128]
Waveform_20Hz['Waveform'] = np.zeros((n_records,n_blocks,n_LRM_RW),dtype=np.uint16)
#-- Echo Scale Factor (to scale echo to watts)
Waveform_20Hz['Linear_Wfm_Multiplier'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Echo Scale Power (a power of 2 to scale echo to Watts)
Waveform_20Hz['Power2_Wfm_Multiplier'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Number of echoes averaged
Waveform_20Hz['N_avg_echoes'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
Waveform_20Hz['Flags'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
elif (MODE == 'SAR'):
#-- SAR Mode
#-- Averaged Power Echo Waveform [128]
Waveform_20Hz['Waveform'] = np.zeros((n_records,n_blocks,n_SAR_RW),dtype=np.uint16)
#-- Echo Scale Factor (to scale echo to watts)
Waveform_20Hz['Linear_Wfm_Multiplier'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Echo Scale Power (a power of 2 to scale echo to Watts)
Waveform_20Hz['Power2_Wfm_Multiplier'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Number of echoes averaged
Waveform_20Hz['N_avg_echoes'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
Waveform_20Hz['Flags'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Beam behaviour parameters
Waveform_20Hz['Beam'] = Beam_Behavior
elif (MODE == 'SIN'):
#-- SARIN Mode
#-- Averaged Power Echo Waveform [512]
Waveform_20Hz['Waveform'] = np.zeros((n_records,n_blocks,n_SARIN_RW),dtype=np.uint16)
#-- Echo Scale Factor (to scale echo to watts)
Waveform_20Hz['Linear_Wfm_Multiplier'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Echo Scale Power (a power of 2 to scale echo to Watts)
Waveform_20Hz['Power2_Wfm_Multiplier'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Number of echoes averaged
Waveform_20Hz['N_avg_echoes'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
Waveform_20Hz['Flags'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Beam behaviour parameters
Waveform_20Hz['Beam'] = Beam_Behavior
#-- Coherence [512]: packed units (1/1000)
Waveform_20Hz['Coherence'] = np.zeros((n_records,n_blocks,n_SARIN_RW),dtype=np.int16)
#-- Phase Difference [512]: packed units (microradians)
Waveform_20Hz['Phase_diff'] = np.zeros((n_records,n_blocks,n_SARIN_RW),dtype=np.int32)
#-- for each record in the CryoSat file
for r in range(n_records):
#-- CryoSat-2 Time and Orbit Group
for b in range(n_blocks):
Location['Day'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Second'][r,b] = np.fromfile(fid,dtype='>u4',count=1)
Location['Micsec'][r,b] = np.fromfile(fid,dtype='>u4',count=1)
Location['USO_Corr'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Mode_ID'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Location['SSC'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Location['Inst_config'][r,b] = np.fromfile(fid,dtype='>u4',count=1)
Location['Rec_Count'][r,b] = np.fromfile(fid,dtype='>u4',count=1)
Location['Lat'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Lon'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Alt'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Alt_rate'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Sat_velocity'][r,b,:] = np.fromfile(fid,dtype='>i4',count=3)
Location['Real_beam'][r,b,:] = np.fromfile(fid,dtype='>i4',count=3)
Location['Baseline'][r,b,:] = np.fromfile(fid,dtype='>i4',count=3)
Location['MCD'][r,b] = np.fromfile(fid,dtype='>u4',count=1)
#-- CryoSat-2 Measurement Group
#-- Derived from instrument measurement parameters
for b in range(n_blocks):
Data_20Hz['TD'][r,b] = np.fromfile(fid,dtype='>i8',count=1)
Data_20Hz['H_0'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['COR2'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['LAI'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['FAI'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['AGC_CH1'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['AGC_CH2'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['TR_gain_CH1'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['TR_gain_CH2'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['TX_Power'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['Doppler_range'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['TR_inst_range'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['R_inst_range'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['TR_inst_gain'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['R_inst_gain'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['Internal_phase'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['External_phase'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['Noise_power'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['Phase_slope'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['Spares1'][r,b,:] = np.fromfile(fid,dtype='>i1',count=4)
#-- CryoSat-2 External Corrections Group
Geometry['dryTrop'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['wetTrop'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['InvBar'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['DAC'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['Iono_GIM'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['Iono_model'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['ocTideElv'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['lpeTideElv'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['olTideElv'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['seTideElv'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['gpTideElv'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['Surf_type'][r] = np.fromfile(fid,dtype='>u4',count=1)
Geometry['Spare1'][r,:] = np.fromfile(fid,dtype='>i1',count=4)
Geometry['Corr_status'][r] = np.fromfile(fid,dtype='>u4',count=1)
Geometry['Corr_error'][r] = np.fromfile(fid,dtype='>u4',count=1)
Geometry['Spare2'][r,:] = np.fromfile(fid,dtype='>i1',count=4)
#-- CryoSat-2 Average Waveforms Groups
if (MODE == 'LRM'):
#-- Low-Resolution Mode
Waveform_1Hz['Day'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Second'][r] = np.fromfile(fid,dtype='>u4',count=1)
Waveform_1Hz['Micsec'][r] = np.fromfile(fid,dtype='>u4',count=1)
Waveform_1Hz['Lat'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Lon'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Alt'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['TD'][r] = np.fromfile(fid,dtype='>i8',count=1)
Waveform_1Hz['Waveform'][r,:] = np.fromfile(fid,dtype='>u2',count=n_LRM_RW)
Waveform_1Hz['Linear_Wfm_Multiplier'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Power2_Wfm_Multiplier'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['N_avg_echoes'][r] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_1Hz['Flags'][r] = np.fromfile(fid,dtype='>u2',count=1)
elif (MODE == 'SAR'):
#-- SAR Mode
Waveform_1Hz['Day'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Second'][r] = np.fromfile(fid,dtype='>u4',count=1)
Waveform_1Hz['Micsec'][r] = np.fromfile(fid,dtype='>u4',count=1)
Waveform_1Hz['Lat'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Lon'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Alt'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['TD'][r] = np.fromfile(fid,dtype='>i8',count=1)
Waveform_1Hz['Waveform'][r,:] = np.fromfile(fid,dtype='>u2',count=n_SAR_RW)
Waveform_1Hz['Linear_Wfm_Multiplier'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Power2_Wfm_Multiplier'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['N_avg_echoes'][r] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_1Hz['Flags'][r] = np.fromfile(fid,dtype='>u2',count=1)
elif (MODE == 'SIN'):
#-- SARIN Mode
Waveform_1Hz['Day'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Second'][r] = np.fromfile(fid,dtype='>u4',count=1)
Waveform_1Hz['Micsec'][r] = np.fromfile(fid,dtype='>u4',count=1)
Waveform_1Hz['Lat'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Lon'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Alt'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['TD'][r] = np.fromfile(fid,dtype='>i8',count=1)
Waveform_1Hz['Waveform'][r,:] = np.fromfile(fid,dtype='>u2',count=n_SARIN_RW)
Waveform_1Hz['Linear_Wfm_Multiplier'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Power2_Wfm_Multiplier'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['N_avg_echoes'][r] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_1Hz['Flags'][r] = np.fromfile(fid,dtype='>u2',count=1)
#-- CryoSat-2 Waveforms Groups
if (MODE == 'LRM'):
#-- Low-Resolution Mode
for b in range(n_blocks):
Waveform_20Hz['Waveform'][r,b,:] = np.fromfile(fid,dtype='>u2',count=n_LRM_RW)
Waveform_20Hz['Linear_Wfm_Multiplier'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_20Hz['Power2_Wfm_Multiplier'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_20Hz['N_avg_echoes'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Flags'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
elif (MODE == 'SAR'):
#-- SAR Mode
for b in range(n_blocks):
Waveform_20Hz['Waveform'][r,b,:] = np.fromfile(fid,dtype='>u2',count=n_SAR_RW)
Waveform_20Hz['Linear_Wfm_Multiplier'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_20Hz['Power2_Wfm_Multiplier'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_20Hz['N_avg_echoes'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Flags'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['SD'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['Center'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['Amplitude'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['Skewness'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['Kurtosis'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['Spare'][r,b,:] = np.fromfile(fid,dtype='>i2',count=(n_BeamBehaviourParams-5))
elif (MODE == 'SIN'):
#-- SARIN Mode
for b in range(n_blocks):
Waveform_20Hz['Waveform'][r,b,:] = np.fromfile(fid,dtype='>u2',count=n_SARIN_RW)
Waveform_20Hz['Linear_Wfm_Multiplier'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_20Hz['Power2_Wfm_Multiplier'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_20Hz['N_avg_echoes'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Flags'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['SD'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['Center'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['Amplitude'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['Skewness'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['Kurtosis'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['Spare'][r,b,:] = np.fromfile(fid,dtype='>i2',count=(n_BeamBehaviourParams-5))
Waveform_20Hz['Coherence'][r,b,:] = np.fromfile(fid,dtype='>i2',count=n_SARIN_RW)
Waveform_20Hz['Phase_diff'][r,b,:] = np.fromfile(fid,dtype='>i4',count=n_SARIN_RW)
#-- Bind all the bits of the l1b_mds together into a single dictionary
CS_l1b_mds = {}
CS_l1b_mds['Location'] = Location
CS_l1b_mds['Data'] = Data_20Hz
CS_l1b_mds['Geometry'] = Geometry
CS_l1b_mds['Waveform_1Hz'] = Waveform_1Hz
CS_l1b_mds['Waveform_20Hz'] = Waveform_20Hz
#-- return the output dictionary
return CS_l1b_mds
#-- PURPOSE: Initiate L1b MDS variables for CryoSat Baseline C
def cryosat_baseline_C(fid, n_records, MODE):
n_SARIN_BC_RW = 1024
n_SARIN_RW = 512
n_SAR_BC_RW = 256
n_SAR_RW = 128
n_LRM_RW = 128
n_blocks = 20
n_BeamBehaviourParams = 50
#-- CryoSat-2 Time and Orbit Group
Location = {}
#-- Time: day part
Location['Day'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Time: second part
Location['Second'] = np.zeros((n_records,n_blocks),dtype=np.uint32)
#-- Time: microsecond part
Location['Micsec'] = np.zeros((n_records,n_blocks),dtype=np.uint32)
#-- USO correction factor
Location['USO_Corr'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Mode ID
Location['Mode_ID'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Source sequence counter
Location['SSC'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Instrument configuration
Location['Inst_config'] = np.zeros((n_records,n_blocks),dtype=np.uint32)
#-- Record Counter
Location['Rec_Count'] = np.zeros((n_records,n_blocks),dtype=np.uint32)
#-- Lat: packed units (0.1 micro-degree, 1e-7 degrees)
Location['Lat'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Lon: packed units (0.1 micro-degree, 1e-7 degrees)
Location['Lon'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Alt: packed units (mm, 1e-3 m)
#-- Altitude of COG above reference ellipsoid (interpolated value)
Location['Alt'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Instantaneous altitude rate derived from orbit: packed units (mm/s, 1e-3 m/s)
Location['Alt_rate'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Satellite velocity vector. In ITRF: packed units (mm/s, 1e-3 m/s)
#-- ITRF= International Terrestrial Reference Frame
Location['Sat_velocity'] = np.zeros((n_records,n_blocks,3),dtype=np.int32)
#-- Real beam direction vector. In CRF: packed units (micro-m/s, 1e-6 m/s)
#-- CRF= CryoSat Reference Frame.
Location['Real_beam'] = np.zeros((n_records,n_blocks,3),dtype=np.int32)
#-- Interferometric baseline vector. In CRF: packed units (micro-m/s, 1e-6 m/s)
Location['Baseline'] = np.zeros((n_records,n_blocks,3),dtype=np.int32)
#-- Star Tracker ID
Location['ST_ID'] = np.zeros((n_records,n_blocks),dtype=np.int16)
#-- Antenna Bench Roll Angle (Derived from star trackers)
#-- packed units (0.1 micro-degree, 1e-7 degrees)
Location['Roll'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Antenna Bench Pitch Angle (Derived from star trackers)
#-- packed units (0.1 micro-degree, 1e-7 degrees)
Location['Pitch'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Antenna Bench Yaw Angle (Derived from star trackers)
#-- packed units (0.1 micro-degree, 1e-7 degrees)
Location['Yaw'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Measurement Confidence Data Flags
#-- Generally the MCD flags indicate problems when set
#-- If MCD is 0 then no problems or non-nominal conditions were detected
#-- Serious errors are indicated by setting bit 31
Location['MCD'] = np.zeros((n_records,n_blocks),dtype=np.uint32)
Location['Spares'] = np.zeros((n_records,n_blocks,2),dtype=np.int16)
#-- CryoSat-2 Measurement Group
#-- Derived from instrument measurement parameters
Data_20Hz = {}
#-- Window Delay reference (two-way) corrected for instrument delays
Data_20Hz['TD'] = np.zeros((n_records,n_blocks),dtype=np.int64)
#-- H0 Initial Height Word from telemetry
Data_20Hz['H_0'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- COR2 Height Rate: on-board tracker height rate over the radar cycle
Data_20Hz['COR2'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Coarse Range Word (LAI) derived from telemetry
Data_20Hz['LAI'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Fine Range Word (FAI) derived from telemetry
Data_20Hz['FAI'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Automatic Gain Control Channel 1: AGC gain applied on Rx channel 1.
#-- Gain calibration corrections are applied (Sum of AGC stages 1 and 2
#-- plus the corresponding corrections) (dB/100)
Data_20Hz['AGC_CH1'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Automatic Gain Control Channel 2: AGC gain applied on Rx channel 2.
#-- Gain calibration corrections are applied (dB/100)
Data_20Hz['AGC_CH2'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Total Fixed Gain On Channel 1: gain applied by the RF unit. (dB/100)
Data_20Hz['TR_gain_CH1'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Total Fixed Gain On Channel 2: gain applied by the RF unit. (dB/100)
Data_20Hz['TR_gain_CH2'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Transmit Power in microWatts
Data_20Hz['TX_Power'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Doppler range correction: Radial component (mm)
#-- computed for the component of satellite velocity in the nadir direction
Data_20Hz['Doppler_range'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Instrument Range Correction: transmit-receive antenna (mm)
#-- Calibration correction to range on channel 1 computed from CAL1.
Data_20Hz['TR_inst_range'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Instrument Range Correction: receive-only antenna (mm)
#-- Calibration correction to range on channel 2 computed from CAL1.
Data_20Hz['R_inst_range'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Instrument Gain Correction: transmit-receive antenna (dB/100)
#-- Calibration correction to gain on channel 1 computed from CAL1
Data_20Hz['TR_inst_gain'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Instrument Gain Correction: receive-only (dB/100)
#-- Calibration correction to gain on channel 2 computed from CAL1
Data_20Hz['R_inst_gain'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Internal Phase Correction (microradians)
Data_20Hz['Internal_phase'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- External Phase Correction (microradians)
Data_20Hz['External_phase'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Noise Power measurement (dB/100)
Data_20Hz['Noise_power'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Phase slope correction (microradians)
#-- Computed from the CAL-4 packets during the azimuth impulse response
#-- amplitude (SARIN only). Set from the latest available CAL-4 packet.
Data_20Hz['Phase_slope'] = np.zeros((n_records,n_blocks),dtype=np.int32)
Data_20Hz['Spares1'] = np.zeros((n_records,n_blocks,4),dtype=np.int8)
#-- CryoSat-2 External Corrections Group
Geometry = {}
#-- Dry Tropospheric Correction packed units (mm, 1e-3 m)
Geometry['dryTrop'] = np.zeros((n_records),dtype=np.int32)
#-- Wet Tropospheric Correction packed units (mm, 1e-3 m)
Geometry['wetTrop'] = np.zeros((n_records),dtype=np.int32)
#-- Inverse Barometric Correction packed units (mm, 1e-3 m)
Geometry['InvBar'] = np.zeros((n_records),dtype=np.int32)
#-- Delta Inverse Barometric Correction packed units (mm, 1e-3 m)
Geometry['DAC'] = np.zeros((n_records),dtype=np.int32)
#-- GIM Ionospheric Correction packed units (mm, 1e-3 m)
Geometry['Iono_GIM'] = np.zeros((n_records),dtype=np.int32)
#-- Model Ionospheric Correction packed units (mm, 1e-3 m)
Geometry['Iono_model'] = np.zeros((n_records),dtype=np.int32)
#-- Ocean tide Correction packed units (mm, 1e-3 m)
Geometry['ocTideElv'] = np.zeros((n_records),dtype=np.int32)
#-- Long period equilibrium ocean tide Correction packed units (mm, 1e-3 m)
Geometry['lpeTideElv'] = np.zeros((n_records),dtype=np.int32)
#-- Ocean loading tide Correction packed units (mm, 1e-3 m)
Geometry['olTideElv'] = np.zeros((n_records),dtype=np.int32)
#-- Solid Earth tide Correction packed units (mm, 1e-3 m)
Geometry['seTideElv'] = np.zeros((n_records),dtype=np.int32)
#-- Geocentric Polar tide Correction packed units (mm, 1e-3 m)
Geometry['gpTideElv'] = np.zeros((n_records),dtype=np.int32)
#-- Surface Type: enumerated key to classify surface at nadir
#-- 0 = Open Ocean
#-- 1 = Closed Sea
#-- 2 = Continental Ice
#-- 3 = Land
Geometry['Surf_type'] = np.zeros((n_records),dtype=np.uint32)
Geometry['Spare1'] = np.zeros((n_records,4),dtype=np.int8)
#-- Corrections Status Flag
Geometry['Corr_status'] = np.zeros((n_records),dtype=np.uint32)
#-- Correction Error Flag
Geometry['Corr_error'] = np.zeros((n_records),dtype=np.uint32)
Geometry['Spare2'] = np.zeros((n_records,4),dtype=np.int8)
#-- CryoSat-2 Average Waveforms Groups
Waveform_1Hz = {}
if (MODE == 'LRM'):
#-- Low-Resolution Mode
#-- Data Record Time (MDSR Time Stamp)
Waveform_1Hz['Day'] = np.zeros((n_records),dtype=np.int32)
Waveform_1Hz['Second'] = np.zeros((n_records),dtype=np.uint32)
Waveform_1Hz['Micsec'] = np.zeros((n_records),dtype=np.uint32)
#-- Lat: packed units (0.1 micro-degree, 1e-7 degrees)
Waveform_1Hz['Lat'] = np.zeros((n_records),dtype=np.int32)
#-- Lon: packed units (0.1 micro-degree, 1e-7 degrees)
Waveform_1Hz['Lon'] = np.zeros((n_records),dtype=np.int32)
#-- Alt: packed units (mm, 1e-3 m)
#-- Altitude of COG above reference ellipsoid (interpolated value)
Waveform_1Hz['Alt'] = np.zeros((n_records),dtype=np.int32)
#-- Window Delay (two-way) corrected for instrument delays
Waveform_1Hz['TD'] = np.zeros((n_records),dtype=np.int64)
#-- 1 Hz Averaged Power Echo Waveform
Waveform_1Hz['Waveform'] = np.zeros((n_records,n_LRM_RW),dtype=np.uint16)
#-- Echo Scale Factor (to scale echo to watts)
Waveform_1Hz['Linear_Wfm_Multiplier'] = np.zeros((n_records),dtype=np.int32)
#-- Echo Scale Power (a power of 2 to scale echo to Watts)
Waveform_1Hz['Power2_Wfm_Multiplier'] = np.zeros((n_records),dtype=np.int32)
#-- Number of echoes averaged
Waveform_1Hz['N_avg_echoes'] = np.zeros((n_records),dtype=np.uint16)
Waveform_1Hz['Flags'] = np.zeros((n_records),dtype=np.uint16)
elif (MODE == 'SAR'):
#-- SAR Mode
#-- Data Record Time (MDSR Time Stamp)
Waveform_1Hz['Day'] = np.zeros((n_records),dtype=np.int32)
Waveform_1Hz['Second'] = np.zeros((n_records),dtype=np.uint32)
Waveform_1Hz['Micsec'] = np.zeros((n_records),dtype=np.uint32)
#-- Lat: packed units (0.1 micro-degree, 1e-7 degrees)
Waveform_1Hz['Lat'] = np.zeros((n_records),dtype=np.int32)
#-- Lon: packed units (0.1 micro-degree, 1e-7 degrees)
Waveform_1Hz['Lon'] = np.zeros((n_records),dtype=np.int32)
#-- Alt: packed units (mm, 1e-3 m)
#-- Altitude of COG above reference ellipsoid (interpolated value)
Waveform_1Hz['Alt'] = np.zeros((n_records),dtype=np.int32)
#-- Window Delay (two-way) corrected for instrument delays
Waveform_1Hz['TD'] = np.zeros((n_records),dtype=np.int64)
#-- 1 Hz Averaged Power Echo Waveform
Waveform_1Hz['Waveform'] = np.zeros((n_records,n_SAR_RW),dtype=np.uint16)
#-- Echo Scale Factor (to scale echo to watts)
Waveform_1Hz['Linear_Wfm_Multiplier'] = np.zeros((n_records),dtype=np.int32)
#-- Echo Scale Power (a power of 2 to scale echo to Watts)
Waveform_1Hz['Power2_Wfm_Multiplier'] = np.zeros((n_records),dtype=np.int32)
#-- Number of echoes averaged
Waveform_1Hz['N_avg_echoes'] = np.zeros((n_records),dtype=np.uint16)
Waveform_1Hz['Flags'] = np.zeros((n_records),dtype=np.uint16)
elif (MODE == 'SIN'):
#-- SARIN Mode
#-- Same as the LRM/SAR groups but the waveform array is 512 bins instead of
#-- 128 and the number of echoes averaged is different.
#-- Data Record Time (MDSR Time Stamp)
Waveform_1Hz['Day'] = np.zeros((n_records),dtype=np.int32)
Waveform_1Hz['Second'] = np.zeros((n_records),dtype=np.uint32)
Waveform_1Hz['Micsec'] = np.zeros((n_records),dtype=np.uint32)
#-- Lat: packed units (0.1 micro-degree, 1e-7 degrees)
Waveform_1Hz['Lat'] = np.zeros((n_records),dtype=np.int32)
#-- Lon: packed units (0.1 micro-degree, 1e-7 degrees)
Waveform_1Hz['Lon'] = np.zeros((n_records),dtype=np.int32)
#-- Alt: packed units (mm, 1e-3 m)
#-- Altitude of COG above reference ellipsoid (interpolated value)
Waveform_1Hz['Alt'] = np.zeros((n_records),dtype=np.int32)
#-- Window Delay (two-way) corrected for instrument delays
Waveform_1Hz['TD'] = np.zeros((n_records),dtype=np.int64)
#-- 1 Hz Averaged Power Echo Waveform
Waveform_1Hz['Waveform'] = np.zeros((n_records,n_SARIN_RW),dtype=np.uint16)
#-- Echo Scale Factor (to scale echo to watts)
Waveform_1Hz['Linear_Wfm_Multiplier'] = np.zeros((n_records),dtype=np.int32)
#-- Echo Scale Power (a power of 2 to scale echo to Watts)
Waveform_1Hz['Power2_Wfm_Multiplier'] = np.zeros((n_records),dtype=np.int32)
#-- Number of echoes averaged
Waveform_1Hz['N_avg_echoes'] = np.zeros((n_records),dtype=np.uint16)
Waveform_1Hz['Flags'] = np.zeros((n_records),dtype=np.uint16)
#-- CryoSat-2 Waveforms Groups
#-- Beam Behavior Parameters
Beam_Behavior = {}
#-- Standard Deviation of Gaussian fit to range integrated stack power.
Beam_Behavior['SD'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Stack Center: Mean of Gaussian fit to range integrated stack power.
Beam_Behavior['Center'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Stack amplitude parameter scaled in dB/100.
Beam_Behavior['Amplitude'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- 3rd moment: providing the degree of asymmetry of the range integrated
#-- stack power distribution.
Beam_Behavior['Skewness'] = np.zeros((n_records,n_blocks),dtype=np.int16)
#-- 4th moment: Measure of peakiness of range integrated stack power distribution.
Beam_Behavior['Kurtosis'] = np.zeros((n_records,n_blocks),dtype=np.int16)
#-- Standard deviation as a function of boresight angle (microradians)
Beam_Behavior['SD_boresight_angle'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Stack Center angle as a function of boresight angle (microradians)
Beam_Behavior['Center_boresight_angle'] = np.zeros((n_records,n_blocks),dtype=np.int16)
Beam_Behavior['Spare'] = np.zeros((n_records,n_blocks,n_BeamBehaviourParams-7),dtype=np.int16)
#-- CryoSat-2 mode specific waveform variables
Waveform_20Hz = {}
if (MODE == 'LRM'):
#-- Low-Resolution Mode
#-- Averaged Power Echo Waveform [128]
Waveform_20Hz['Waveform'] = np.zeros((n_records,n_blocks,n_LRM_RW),dtype=np.uint16)
#-- Echo Scale Factor (to scale echo to watts)
Waveform_20Hz['Linear_Wfm_Multiplier'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Echo Scale Power (a power of 2)
Waveform_20Hz['Power2_Wfm_Multiplier'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Number of echoes averaged
Waveform_20Hz['N_avg_echoes'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
Waveform_20Hz['Flags'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
elif (MODE == 'SAR'):
#-- SAR Mode
#-- Averaged Power Echo Waveform [256]
Waveform_20Hz['Waveform'] = np.zeros((n_records,n_blocks,n_SAR_BC_RW),dtype=np.uint16)
#-- Echo Scale Factor (to scale echo to watts)
Waveform_20Hz['Linear_Wfm_Multiplier'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Echo Scale Power (a power of 2)
Waveform_20Hz['Power2_Wfm_Multiplier'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Number of echoes averaged
Waveform_20Hz['N_avg_echoes'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
Waveform_20Hz['Flags'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Beam behaviour parameters
Waveform_20Hz['Beam'] = Beam_Behavior
elif (MODE == 'SIN'):
#-- SARIN Mode
#-- Averaged Power Echo Waveform [1024]
Waveform_20Hz['Waveform'] = np.zeros((n_records,n_blocks,n_SARIN_BC_RW),dtype=np.uint16)
#-- Echo Scale Factor (to scale echo to watts)
Waveform_20Hz['Linear_Wfm_Multiplier'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Echo Scale Power (a power of 2)
Waveform_20Hz['Power2_Wfm_Multiplier'] = np.zeros((n_records,n_blocks),dtype=np.int32)
#-- Number of echoes averaged
Waveform_20Hz['N_avg_echoes'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
Waveform_20Hz['Flags'] = np.zeros((n_records,n_blocks),dtype=np.uint16)
#-- Beam behaviour parameters
Waveform_20Hz['Beam'] = Beam_Behavior
#-- Coherence [1024]: packed units (1/1000)
Waveform_20Hz['Coherence'] = np.zeros((n_records,n_blocks,n_SARIN_BC_RW),dtype=np.int16)
#-- Phase Difference [1024]: packed units (microradians)
Waveform_20Hz['Phase_diff'] = np.zeros((n_records,n_blocks,n_SARIN_BC_RW),dtype=np.int32)
#-- for each record in the CryoSat file
for r in range(n_records):
#-- CryoSat-2 Time and Orbit Group
for b in range(n_blocks):
Location['Day'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Second'][r,b] = np.fromfile(fid,dtype='>u4',count=1)
Location['Micsec'][r,b] = np.fromfile(fid,dtype='>u4',count=1)
Location['USO_Corr'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Mode_ID'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Location['SSC'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Location['Inst_config'][r,b] = np.fromfile(fid,dtype='>u4',count=1)
Location['Rec_Count'][r,b] = np.fromfile(fid,dtype='>u4',count=1)
Location['Lat'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Lon'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Alt'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Alt_rate'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Sat_velocity'][r,b,:] = np.fromfile(fid,dtype='>i4',count=3)
Location['Real_beam'][r,b,:] = np.fromfile(fid,dtype='>i4',count=3)
Location['Baseline'][r,b,:] = np.fromfile(fid,dtype='>i4',count=3)
Location['ST_ID'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Location['Roll'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Pitch'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['Yaw'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Location['MCD'][r,b] = np.fromfile(fid,dtype='>u4',count=1)
Location['Spares'][r,b,:] = np.fromfile(fid,dtype='>i2',count=2)
#-- CryoSat-2 Measurement Group
#-- Derived from instrument measurement parameters
for b in range(n_blocks):
Data_20Hz['TD'][r,b] = np.fromfile(fid,dtype='>i8',count=1)
Data_20Hz['H_0'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['COR2'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['LAI'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['FAI'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['AGC_CH1'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['AGC_CH2'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['TR_gain_CH1'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['TR_gain_CH2'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['TX_Power'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['Doppler_range'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['TR_inst_range'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['R_inst_range'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['TR_inst_gain'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['R_inst_gain'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['Internal_phase'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['External_phase'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['Noise_power'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['Phase_slope'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Data_20Hz['Spares1'][r,b,:] = np.fromfile(fid,dtype='>i1',count=4)
#-- CryoSat-2 External Corrections Group
Geometry['dryTrop'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['wetTrop'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['InvBar'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['DAC'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['Iono_GIM'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['Iono_model'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['ocTideElv'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['lpeTideElv'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['olTideElv'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['seTideElv'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['gpTideElv'][r] = np.fromfile(fid,dtype='>i4',count=1)
Geometry['Surf_type'][r] = np.fromfile(fid,dtype='>u4',count=1)
Geometry['Spare1'][r,:] = np.fromfile(fid,dtype='>i1',count=4)
Geometry['Corr_status'][r] = np.fromfile(fid,dtype='>u4',count=1)
Geometry['Corr_error'][r] = np.fromfile(fid,dtype='>u4',count=1)
Geometry['Spare2'][r,:] = np.fromfile(fid,dtype='>i1',count=4)
#-- CryoSat-2 Average Waveforms Groups
if (MODE == 'LRM'):
#-- Low-Resolution Mode
Waveform_1Hz['Day'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Second'][r] = np.fromfile(fid,dtype='>u4',count=1)
Waveform_1Hz['Micsec'][r] = np.fromfile(fid,dtype='>u4',count=1)
Waveform_1Hz['Lat'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Lon'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Alt'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['TD'][r] = np.fromfile(fid,dtype='>i8',count=1)
Waveform_1Hz['Waveform'][r,:] = np.fromfile(fid,dtype='>u2',count=n_LRM_RW)
Waveform_1Hz['Linear_Wfm_Multiplier'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Power2_Wfm_Multiplier'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['N_avg_echoes'][r] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_1Hz['Flags'][r] = np.fromfile(fid,dtype='>u2',count=1)
elif (MODE == 'SAR'):
#-- SAR Mode
Waveform_1Hz['Day'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Second'][r] = np.fromfile(fid,dtype='>u4',count=1)
Waveform_1Hz['Micsec'][r] = np.fromfile(fid,dtype='>u4',count=1)
Waveform_1Hz['Lat'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Lon'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Alt'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['TD'][r] = np.fromfile(fid,dtype='>i8',count=1)
Waveform_1Hz['Waveform'][r,:] = np.fromfile(fid,dtype='>u2',count=n_SAR_RW)
Waveform_1Hz['Linear_Wfm_Multiplier'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Power2_Wfm_Multiplier'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['N_avg_echoes'][r] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_1Hz['Flags'][r] = np.fromfile(fid,dtype='>u2',count=1)
elif (MODE == 'SIN'):
#-- SARIN Mode
Waveform_1Hz['Day'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Second'][r] = np.fromfile(fid,dtype='>u4',count=1)
Waveform_1Hz['Micsec'][r] = np.fromfile(fid,dtype='>u4',count=1)
Waveform_1Hz['Lat'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Lon'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Alt'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['TD'][r] = np.fromfile(fid,dtype='>i8',count=1)
Waveform_1Hz['Waveform'][r,:] = np.fromfile(fid,dtype='>u2',count=n_SARIN_RW)
Waveform_1Hz['Linear_Wfm_Multiplier'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['Power2_Wfm_Multiplier'][r] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_1Hz['N_avg_echoes'][r] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_1Hz['Flags'][r] = np.fromfile(fid,dtype='>u2',count=1)
#-- CryoSat-2 Waveforms Groups
if (MODE == 'LRM'):
#-- Low-Resolution Mode
for b in range(n_blocks):
Waveform_20Hz['Waveform'][r,b,:] = np.fromfile(fid,dtype='>u2',count=n_LRM_RW)
Waveform_20Hz['Linear_Wfm_Multiplier'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_20Hz['Power2_Wfm_Multiplier'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_20Hz['N_avg_echoes'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Flags'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
elif (MODE == 'SAR'):
#-- SAR Mode
for b in range(n_blocks):
Waveform_20Hz['Waveform'][r,b,:] = np.fromfile(fid,dtype='>u2',count=n_SAR_BC_RW)
Waveform_20Hz['Linear_Wfm_Multiplier'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_20Hz['Power2_Wfm_Multiplier'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_20Hz['N_avg_echoes'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Flags'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['SD'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['Center'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['Amplitude'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['Skewness'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['Kurtosis'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['SD_boresight_angle'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['Center_boresight_angle'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['Spare'][r,b,:] = np.fromfile(fid,dtype='>i2',count=(n_BeamBehaviourParams-7))
elif (MODE == 'SIN'):
#-- SARIN Mode
for b in range(n_blocks):
Waveform_20Hz['Waveform'][r,b,:] = np.fromfile(fid,dtype='>u2',count=n_SARIN_BC_RW)
Waveform_20Hz['Linear_Wfm_Multiplier'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_20Hz['Power2_Wfm_Multiplier'][r,b] = np.fromfile(fid,dtype='>i4',count=1)
Waveform_20Hz['N_avg_echoes'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Flags'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['SD'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['Center'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['Amplitude'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['Skewness'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['Kurtosis'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['SD_boresight_angle'][r,b] = np.fromfile(fid,dtype='>u2',count=1)
Waveform_20Hz['Beam']['Center_boresight_angle'][r,b] = np.fromfile(fid,dtype='>i2',count=1)
Waveform_20Hz['Beam']['Spare'][r,b,:] = np.fromfile(fid,dtype='>i2',count=(n_BeamBehaviourParams-7))
Waveform_20Hz['Coherence'][r,b,:] = np.fromfile(fid,dtype='>i2',count=n_SARIN_BC_RW)
Waveform_20Hz['Phase_diff'][r,b,:] = np.fromfile(fid,dtype='>i4',count=n_SARIN_BC_RW)
#-- Bind all the bits of the l1b_mds together into a single dictionary
CS_l1b_mds = {}
CS_l1b_mds['Location'] = Location
CS_l1b_mds['Data'] = Data_20Hz
CS_l1b_mds['Geometry'] = Geometry
CS_l1b_mds['Waveform_1Hz'] = Waveform_1Hz
CS_l1b_mds['Waveform_20Hz'] = Waveform_20Hz
#-- return the output dictionary
return CS_l1b_mds
#-- PURPOSE: Initiate L1b MDS variables for CryoSat Baseline D (netCDF4)
def cryosat_baseline_D(full_filename, MODE, UNPACK=False):
#-- open netCDF4 file for reading
fid = netCDF4.Dataset(os.path.expanduser(full_filename),'r')
#-- use original unscaled units unless UNPACK=True
fid.set_auto_scale(UNPACK)
#-- get dimensions
ind_first_meas_20hz_01 = fid.variables['ind_first_meas_20hz_01'][:].copy()
ind_meas_1hz_20_ku = fid.variables['ind_meas_1hz_20_ku'][:].copy()
n_records = len(ind_first_meas_20hz_01)
n_SARIN_D_RW = 1024
n_SARIN_RW = 512
n_SAR_D_RW = 256
n_SAR_RW = 128
n_LRM_RW = 128
n_blocks = 20
#-- CryoSat-2 Time and Orbit Group
Location = {}
#-- MDS Time
Location['Time'] = np.ma.zeros((n_records,n_blocks))
Location['Time'].mask = np.zeros((n_records,n_blocks),dtype=np.bool)
time_20_ku = fid.variables['time_20_ku'][:].copy()
#-- Time: day part
Location['Day'] = np.ma.zeros((n_records,n_blocks))
Location['Day'].mask = np.zeros((n_records,n_blocks),dtype=np.bool)
#-- Time: second part
Location['Second'] = | np.ma.zeros((n_records,n_blocks)) | numpy.ma.zeros |
# -*- coding: utf-8 -*-
"""
This module is a work in progress, as such concepts are subject to change.
MAIN IDEA:
`MultiTaskSamples` serves as a structure to contain and manipulate a set of
samples with potentially many different types of labels and features.
"""
import logging
import utool as ut
import ubelt as ub
import numpy as np
from wbia import dtool as dt
import pandas as pd
import sklearn
import sklearn.metrics
import sklearn.ensemble
import sklearn.impute
import sklearn.pipeline
import sklearn.neural_network
from wbia.algo.verif import sklearn_utils
print, rrr, profile = ut.inject2(__name__)
logger = logging.getLogger('wbia')
class XValConfig(dt.Config):
_param_info_list = [
# ut.ParamInfo('type', 'StratifiedKFold'),
ut.ParamInfo('type', 'StratifiedGroupKFold'),
ut.ParamInfo('n_splits', 3),
ut.ParamInfo(
'shuffle', True, hideif=lambda cfg: cfg['type'] == 'StratifiedGroupKFold'
),
ut.ParamInfo(
'random_state',
3953056901,
hideif=lambda cfg: cfg['type'] == 'StratifiedGroupKFold',
),
]
@ut.reloadable_class
class ClfProblem(ut.NiceRepr):
def __init__(pblm):
pblm.deploy_task_clfs = None
pblm.eval_task_clfs = None
pblm.xval_kw = XValConfig()
pblm.eval_task_clfs = None
pblm.task_combo_res = None
pblm.verbose = True
def set_pandas_options(pblm):
# pd.options.display.max_rows = 10
pd.options.display.max_rows = 20
pd.options.display.max_columns = 40
pd.options.display.width = 160
pd.options.display.float_format = lambda x: '%.4f' % (x,)
def set_pandas_options_low(pblm):
# pd.options.display.max_rows = 10
pd.options.display.max_rows = 5
pd.options.display.max_columns = 40
pd.options.display.width = 160
pd.options.display.float_format = lambda x: '%.4f' % (x,)
def set_pandas_options_normal(pblm):
# pd.options.display.max_rows = 10
pd.options.display.max_rows = 20
pd.options.display.max_columns = 40
pd.options.display.width = 160
pd.options.display.float_format = lambda x: '%.4f' % (x,)
def learn_evaluation_classifiers(pblm, task_keys=None, clf_keys=None, data_keys=None):
"""
Evaluates by learning classifiers using cross validation.
Do not use this to learn production classifiers.
python -m wbia.algo.verif.vsone evaluate_classifiers --db PZ_PB_RF_TRAIN --show
Example:
CommandLine:
python -m clf_helpers learn_evaluation_classifiers
Example:
>>> # ENABLE_DOCTEST
>>> from wbia.algo.verif.clf_helpers import * # NOQA
>>> pblm = IrisProblem()
>>> pblm.setup()
>>> pblm.verbose = True
>>> pblm.eval_clf_keys = ['Logit', 'RF']
>>> pblm.eval_task_keys = ['iris']
>>> pblm.eval_data_keys = ['learn(all)']
>>> result = pblm.learn_evaluation_classifiers()
>>> res = pblm.task_combo_res['iris']['Logit']['learn(all)']
>>> res.print_report()
>>> res = pblm.task_combo_res['iris']['RF']['learn(all)']
>>> res.print_report()
>>> print(result)
"""
pblm.eval_task_clfs = ut.AutoVivification()
pblm.task_combo_res = ut.AutoVivification()
if task_keys is None:
task_keys = pblm.eval_task_keys
if data_keys is None:
data_keys = pblm.eval_data_keys
if clf_keys is None:
clf_keys = pblm.eval_clf_keys
if task_keys is None:
task_keys = [pblm.primary_task_key]
if data_keys is None:
data_keys = [pblm.default_data_key]
if clf_keys is None:
clf_keys = [pblm.default_clf_key]
if pblm.verbose:
ut.cprint('[pblm] learn_evaluation_classifiers', color='blue')
ut.cprint('[pblm] task_keys = {}'.format(task_keys))
ut.cprint('[pblm] data_keys = {}'.format(data_keys))
ut.cprint('[pblm] clf_keys = {}'.format(clf_keys))
Prog = ut.ProgPartial(freq=1, adjust=False, prehack='%s')
task_prog = Prog(task_keys, label='Task')
for task_key in task_prog:
dataset_prog = Prog(data_keys, label='Data')
for data_key in dataset_prog:
clf_prog = Prog(clf_keys, label='CLF')
for clf_key in clf_prog:
pblm._ensure_evaluation_clf(task_key, data_key, clf_key)
def _ensure_evaluation_clf(pblm, task_key, data_key, clf_key, use_cache=True):
"""
Learns and caches an evaluation (cross-validated) classifier and tests
and caches the results.
data_key = 'learn(sum,glob)'
clf_key = 'RF'
"""
# TODO: add in params used to construct features into the cfgstr
if hasattr(pblm.samples, 'sample_hashid'):
ibs = pblm.infr.ibs
sample_hashid = pblm.samples.sample_hashid()
feat_dims = pblm.samples.X_dict[data_key].columns.values.tolist()
# cfg_prefix = sample_hashid + pblm.qreq_.get_cfgstr() + feat_cfgstr
est_kw1, est_kw2 = pblm._estimator_params(clf_key)
param_id = ut.get_dict_hashid(est_kw1)
xval_id = pblm.xval_kw.get_cfgstr()
cfgstr = '_'.join(
[
sample_hashid,
param_id,
xval_id,
task_key,
data_key,
clf_key,
ut.hashid_arr(feat_dims, 'feats'),
]
)
fname = 'eval_clfres_' + ibs.dbname
else:
fname = 'foo'
feat_dims = None
cfgstr = 'bar'
use_cache = False
# TODO: ABI class should not be caching
cacher_kw = dict(appname='vsone_rf_train', enabled=use_cache, verbose=1)
cacher_clf = ub.Cacher(fname, cfgstr=cfgstr, meta=[feat_dims], **cacher_kw)
data = cacher_clf.tryload()
if not data:
data = pblm._train_evaluation_clf(task_key, data_key, clf_key)
cacher_clf.save(data)
clf_list, res_list = data
labels = pblm.samples.subtasks[task_key]
combo_res = ClfResult.combine_results(res_list, labels)
pblm.eval_task_clfs[task_key][clf_key][data_key] = clf_list
pblm.task_combo_res[task_key][clf_key][data_key] = combo_res
def _train_evaluation_clf(pblm, task_key, data_key, clf_key, feat_dims=None):
"""
Learns a cross-validated classifier on the dataset
Ignore:
>>> from wbia.algo.verif.vsone import * # NOQA
>>> pblm = OneVsOneProblem()
>>> pblm.load_features()
>>> pblm.load_samples()
>>> data_key = 'learn(all)'
>>> task_key = 'photobomb_state'
>>> clf_key = 'RF-OVR'
>>> task_key = 'match_state'
>>> data_key = pblm.default_data_key
>>> clf_key = pblm.default_clf_key
"""
X_df = pblm.samples.X_dict[data_key]
labels = pblm.samples.subtasks[task_key]
assert np.all(labels.encoded_df.index == X_df.index)
clf_partial = pblm._get_estimator(clf_key)
xval_kw = pblm.xval_kw.asdict()
clf_list = []
res_list = []
skf_list = pblm.samples.stratified_kfold_indices(**xval_kw)
skf_prog = ut.ProgIter(skf_list, label='skf-train-eval')
for train_idx, test_idx in skf_prog:
X_df_train = X_df.iloc[train_idx]
assert X_df_train.index.tolist() == ut.take(pblm.samples.index, train_idx)
# train_uv = X_df.iloc[train_idx].index
# X_train = X_df.loc[train_uv]
# y_train = labels.encoded_df.loc[train_uv]
if feat_dims is not None:
X_df_train = X_df_train[feat_dims]
X_train = X_df_train.values
y_train = labels.encoded_df.iloc[train_idx].values.ravel()
clf = clf_partial()
clf.fit(X_train, y_train)
# Note: There is a corner case where one fold doesn't get any
# labels of a certain class. Because y_train is an encoded integer,
# the clf.classes_ attribute will cause predictions to agree with
# other classifiers trained on the same labels.
# Evaluate results
res = ClfResult.make_single(
clf, X_df, test_idx, labels, data_key, feat_dims=feat_dims
)
clf_list.append(clf)
res_list.append(res)
return clf_list, res_list
def _external_classifier_result(
pblm, clf, task_key, data_key, feat_dims=None, test_idx=None
):
"""
Given an external classifier (ensure its trained on disjoint data)
evaluate all data on it.
Args:
test_idx (list): subset of this classifier to test on
(defaults to all if None)
"""
X_df = pblm.samples.X_dict[data_key]
if test_idx is None:
test_idx = np.arange(len(X_df))
labels = pblm.samples.subtasks[task_key]
res = ClfResult.make_single(
clf, X_df, test_idx, labels, data_key, feat_dims=feat_dims
)
return res
def learn_deploy_classifiers(pblm, task_keys=None, clf_key=None, data_key=None):
"""
Learns on data without any train/validation split
"""
if pblm.verbose > 0:
ut.cprint('[pblm] learn_deploy_classifiers', color='blue')
if clf_key is None:
clf_key = pblm.default_clf_key
if data_key is None:
data_key = pblm.default_data_key
if task_keys is None:
task_keys = list(pblm.samples.supported_tasks())
if pblm.deploy_task_clfs is None:
pblm.deploy_task_clfs = ut.AutoVivification()
Prog = ut.ProgPartial(freq=1, adjust=False, prehack='%s')
task_prog = Prog(task_keys, label='Task')
task_clfs = {}
for task_key in task_prog:
clf = pblm._train_deploy_clf(task_key, data_key, clf_key)
task_clfs[task_key] = clf
pblm.deploy_task_clfs[task_key][clf_key][data_key] = clf
return task_clfs
def _estimator_params(pblm, clf_key):
est_type = clf_key.split('-')[0]
if est_type in {'RF', 'RandomForest'}:
est_kw1 = {
# 'max_depth': 4,
'bootstrap': True,
'class_weight': None,
'criterion': 'entropy',
'max_features': 'sqrt',
# 'max_features': None,
'min_samples_leaf': 5,
'min_samples_split': 2,
# 'n_estimators': 64,
'n_estimators': 256,
}
# Hack to only use missing values if we have the right sklearn
if 'missing_values' in ut.get_func_kwargs(
sklearn.ensemble.RandomForestClassifier.__init__
):
est_kw1['missing_values'] = np.nan
est_kw2 = {
'random_state': 3915904814,
'verbose': 0,
'n_jobs': -1,
}
elif est_type in {'SVC', 'SVM'}:
est_kw1 = dict(kernel='linear')
est_kw2 = {}
elif est_type in {'Logit', 'LogisticRegression'}:
est_kw1 = {}
est_kw2 = {}
elif est_type in {'MLP'}:
est_kw1 = dict(
activation='relu',
alpha=1e-05,
batch_size='auto',
beta_1=0.9,
beta_2=0.999,
early_stopping=False,
epsilon=1e-08,
hidden_layer_sizes=(10, 10),
learning_rate='constant',
learning_rate_init=0.001,
max_iter=200,
momentum=0.9,
nesterovs_momentum=True,
power_t=0.5,
random_state=3915904814,
shuffle=True,
solver='lbfgs',
tol=0.0001,
validation_fraction=0.1,
warm_start=False,
)
est_kw2 = dict(verbose=False)
else:
raise KeyError('Unknown Estimator')
return est_kw1, est_kw2
def _get_estimator(pblm, clf_key):
"""
Returns sklearn classifier
"""
tup = clf_key.split('-')
wrap_type = None if len(tup) == 1 else tup[1]
est_type = tup[0]
multiclass_wrapper = {
None: ut.identity,
'OVR': sklearn.multiclass.OneVsRestClassifier,
'OVO': sklearn.multiclass.OneVsOneClassifier,
}[wrap_type]
est_class = {
'RF': sklearn.ensemble.RandomForestClassifier,
'SVC': sklearn.svm.SVC,
'Logit': sklearn.linear_model.LogisticRegression,
'MLP': sklearn.neural_network.MLPClassifier,
}[est_type]
est_kw1, est_kw2 = pblm._estimator_params(est_type)
est_params = ut.merge_dicts(est_kw1, est_kw2)
# steps = []
# steps.append((est_type, est_class(**est_params)))
# if wrap_type is not None:
# steps.append((wrap_type, multiclass_wrapper))
if est_type == 'MLP':
def clf_partial():
pipe = sklearn.pipeline.Pipeline(
[
('inputer', sklearn.impute.SimpleImputer(strategy='mean')),
# ('scale', sklearn.preprocessing.StandardScaler),
('est', est_class(**est_params)),
]
)
return multiclass_wrapper(pipe)
elif est_type == 'Logit':
def clf_partial():
pipe = sklearn.pipeline.Pipeline(
[
('inputer', sklearn.impute.SimpleImputer(strategy='mean')),
('est', est_class(**est_params)),
]
)
return multiclass_wrapper(pipe)
else:
def clf_partial():
return multiclass_wrapper(est_class(**est_params))
return clf_partial
def _train_deploy_clf(pblm, task_key, data_key, clf_key):
X_df = pblm.samples.X_dict[data_key]
labels = pblm.samples.subtasks[task_key]
assert np.all(labels.encoded_df.index == X_df.index)
clf_partial = pblm._get_estimator(clf_key)
logger.info(
'Training deployment {} classifier on {} for {}'.format(
clf_key, data_key, task_key
)
)
clf = clf_partial()
index = X_df.index
X = X_df.loc[index].values
y = labels.encoded_df.loc[index].values.ravel()
clf.fit(X, y)
return clf
def _optimize_rf_hyperparams(pblm, data_key=None, task_key=None):
"""
helper script I've only run interactively
Example:
>>> # DISABLE_DOCTEST
>>> from wbia.algo.verif.vsone import * # NOQA
>>> pblm = OneVsOneProblem.from_empty('PZ_PB_RF_TRAIN')
#>>> pblm = OneVsOneProblem.from_empty('GZ_Master1')
>>> pblm.load_samples()
>>> pblm.load_features()
>>> pblm.build_feature_subsets()
>>> data_key=None
>>> task_key=None
"""
from sklearn.model_selection import RandomizedSearchCV # NOQA
from sklearn.model_selection import GridSearchCV # NOQA
from sklearn.ensemble import RandomForestClassifier
from wbia.algo.verif import sklearn_utils
if data_key is None:
data_key = pblm.default_data_key
if task_key is None:
task_key = pblm.primary_task_key
# Load data
X = pblm.samples.X_dict[data_key].values
y = pblm.samples.subtasks[task_key].y_enc
groups = pblm.samples.group_ids
# Define estimator and parameter search space
grid = {
'bootstrap': [True, False],
'class_weight': [None, 'balanced'],
'criterion': ['entropy', 'gini'],
# 'max_features': ['sqrt', 'log2'],
'max_features': ['sqrt'],
'min_samples_leaf': list(range(2, 11)),
'min_samples_split': list(range(2, 11)),
'n_estimators': [8, 64, 128, 256, 512, 1024],
}
est = RandomForestClassifier(missing_values=np.nan)
if False:
# debug
params = ut.util_dict.all_dict_combinations(grid)[0]
est.set_params(verbose=10, n_jobs=1, **params)
est.fit(X=X, y=y)
cv = sklearn_utils.StratifiedGroupKFold(n_splits=3)
if True:
n_iter = 25
SearchCV = ut.partial(RandomizedSearchCV, n_iter=n_iter)
else:
n_iter = ut.prod(map(len, grid.values()))
SearchCV = GridSearchCV
search = SearchCV(est, grid, cv=cv, verbose=10)
n_cpus = ut.num_cpus()
thresh = n_cpus * 1.5
n_jobs_est = 1
n_jobs_ser = min(n_cpus, n_iter)
if n_iter < thresh:
n_jobs_est = int(max(1, thresh / n_iter))
est.set_params(n_jobs=n_jobs_est)
search.set_params(n_jobs=n_jobs_ser)
search.fit(X=X, y=y, groups=groups)
res = search.cv_results_.copy()
alias = ut.odict(
[
('rank_test_score', 'rank'),
('mean_test_score', 'μ-test'),
('std_test_score', 'σ-test'),
('mean_train_score', 'μ-train'),
('std_train_score', 'σ-train'),
('mean_fit_time', 'fit_time'),
('params', 'params'),
]
)
res = ut.dict_subset(res, alias.keys())
cvresult_df = pd.DataFrame(res).rename(columns=alias)
cvresult_df = cvresult_df.sort_values('rank').reset_index(drop=True)
params = pd.DataFrame.from_dict(cvresult_df['params'].values.tolist())
logger.info('Varied params:')
logger.info(ut.repr4(ut.map_vals(set, params.to_dict('list'))))
logger.info('Ranked Params')
logger.info(params)
logger.info('Ranked scores on development set:')
logger.info(cvresult_df)
logger.info('Best parameters set found on hyperparam set:')
logger.info('best_params_ = %s' % (ut.repr4(search.best_params_),))
logger.info('Fastest params')
cvresult_df.loc[cvresult_df['fit_time'].idxmin()]['params']
def _dev_calib(pblm):
"""
interactive script only
"""
from sklearn.ensemble import RandomForestClassifier
from sklearn.calibration import CalibratedClassifierCV
from sklearn.calibration import calibration_curve
from sklearn.metrics import log_loss, brier_score_loss
# Load data
data_key = pblm.default_data_key
task_key = pblm.primary_task_key
X = pblm.samples.X_dict[data_key].values
y = pblm.samples.subtasks[task_key].y_enc
groups = pblm.samples.group_ids
# Split into test/train/valid
cv = sklearn_utils.StratifiedGroupKFold(n_splits=2)
test_idx, train_idx = next(cv.split(X, y, groups))
# valid_idx = train_idx[0::2]
# train_idx = train_idx[1::2]
# train_valid_idx = np.hstack([train_idx, valid_idx])
# Train Uncalibrated RF
est_kw = pblm._estimator_params('RF')[0]
uncal_clf = RandomForestClassifier(**est_kw)
uncal_clf.fit(X[train_idx], y[train_idx])
uncal_probs = uncal_clf.predict_proba(X[test_idx]).T[1]
uncal_score = log_loss(y[test_idx] == 1, uncal_probs)
uncal_brier = brier_score_loss(y[test_idx] == 1, uncal_probs)
# Train Calibrated RF
method = 'isotonic' if len(test_idx) > 2000 else 'sigmoid'
precal_clf = RandomForestClassifier(**est_kw)
# cv = sklearn_utils.StratifiedGroupKFold(n_splits=3)
cal_clf = CalibratedClassifierCV(precal_clf, cv=2, method=method)
cal_clf.fit(X[train_idx], y[train_idx])
cal_probs = cal_clf.predict_proba(X[test_idx]).T[1]
cal_score = log_loss(y[test_idx] == 1, cal_probs)
cal_brier = brier_score_loss(y[test_idx] == 1, cal_probs)
logger.info('cal_brier = %r' % (cal_brier,))
logger.info('uncal_brier = %r' % (uncal_brier,))
logger.info('uncal_score = %r' % (uncal_score,))
logger.info('cal_score = %r' % (cal_score,))
import wbia.plottool as pt
ut.qtensure()
pt.figure()
ax = pt.gca()
y_test = y[test_idx] == 1
fraction_of_positives, mean_predicted_value = calibration_curve(
y_test, uncal_probs, n_bins=10
)
ax.plot([0, 1], [0, 1], 'k:', label='Perfectly calibrated')
ax.plot(
mean_predicted_value,
fraction_of_positives,
's-',
label='%s (%1.3f)' % ('uncal-RF', uncal_brier),
)
fraction_of_positives, mean_predicted_value = calibration_curve(
y_test, cal_probs, n_bins=10
)
ax.plot(
mean_predicted_value,
fraction_of_positives,
's-',
label='%s (%1.3f)' % ('cal-RF', cal_brier),
)
pt.legend()
@ut.reloadable_class
class ClfResult(ut.NiceRepr):
r"""
Handles evaluation statistics for a multiclass classifier trained on a
specific dataset with specific labels.
"""
# Attributes that identify the task and data the classifier is evaluated on
_key_attrs = ['task_key', 'data_key', 'class_names']
# Attributes about results and labels of individual samples
_datafame_attrs = ['probs_df', 'probhats_df', 'target_bin_df', 'target_enc_df']
def __init__(res):
pass
def __nice__(res):
return '{}, {}, {}'.format(res.task_key, res.data_key, len(res.index))
@property
def index(res):
return res.probs_df.index
@classmethod
def make_single(ClfResult, clf, X_df, test_idx, labels, data_key, feat_dims=None):
"""
Make a result for a single cross validiation subset
"""
X_df_test = X_df.iloc[test_idx]
if feat_dims is not None:
X_df_test = X_df_test[feat_dims]
index = X_df_test.index
# clf_probs = clf.predict_proba(X_df_test)
# index = pd.Series(test_idx, name='test_idx')
# Ensure shape corresponds with all classes
def align_cols(arr, arr_cols, target_cols):
import utool as ut
alignx = ut.list_alignment(arr_cols, target_cols, missing=True)
aligned_arrT = ut.none_take(arr.T, alignx)
aligned_arrT = ut.replace_nones(aligned_arrT, np.zeros(len(arr)))
aligned_arr = np.vstack(aligned_arrT).T
return aligned_arr
res = ClfResult()
res.task_key = labels.task_name
res.data_key = data_key
res.class_names = ut.lmap(str, labels.class_names)
res.feat_dims = feat_dims
res.probs_df = sklearn_utils.predict_proba_df(clf, X_df_test, res.class_names)
res.target_bin_df = labels.indicator_df.iloc[test_idx]
res.target_enc_df = labels.encoded_df.iloc[test_idx]
if hasattr(clf, 'estimators_') and labels.n_classes > 2:
# The n-th estimator in the OVR classifier predicts the prob of the
# n-th class (as label 1).
probs_hat = np.hstack(
[est.predict_proba(X_df_test)[:, 1:2] for est in clf.estimators_]
)
res.probhats_df = pd.DataFrame(
align_cols(probs_hat, clf.classes_, labels.classes_),
index=index,
columns=res.class_names,
)
# In the OVR-case, ideally things will sum to 1, but when they
# don't normalization happens. An Z-value of more than 1 means
# overconfidence, and under 0 means underconfidence.
res.confidence_ratio = res.probhats_df.sum(axis=1)
else:
res.probhats_df = None
return res
def compress(res, flags):
res2 = ClfResult()
res2.task_key = res.task_key
res2.data_key = res.data_key
res2.class_names = res.class_names
res2.probs_df = res.probs_df[flags]
res2.target_bin_df = res.target_bin_df[flags]
res2.target_enc_df = res.target_enc_df[flags]
if res.probhats_df is None:
res2.probhats_df = None
else:
res2.probhats_df = res.probhats_df[flags]
# res2.confidence_ratio = res.confidence_ratio[flags]
return res2
@classmethod
def combine_results(ClfResult, res_list, labels=None):
"""
Combine results from cross validation runs into a single result
representing the performance of the entire dataset
"""
# Ensure that res_lists are not overlapping
for r1, r2 in ut.combinations(res_list, 2):
assert (
len(r1.index.intersection(r2.index)) == 0
), 'ClfResult dataframes must be disjoint'
# sanity check
for r in res_list:
assert np.all(r.index == r.probs_df.index)
assert np.all(r.index == r.target_bin_df.index)
assert np.all(r.index == r.target_enc_df.index)
# Combine them with pandas
res = ClfResult()
res0 = res_list[0]
# Transfer single attributes (which should all be the same)
for attr in ClfResult._key_attrs:
val = getattr(res0, attr)
setattr(res, attr, val)
assert all(
[getattr(r, attr) == val for r in res_list]
), 'ClfResult with different key attributes are incompatible'
# Combine dataframe properties (which should all have disjoint indices)
for attr in ClfResult._datafame_attrs:
if getattr(res0, attr) is not None:
combo_attr = pd.concat([getattr(r, attr) for r in res_list])
setattr(res, attr, combo_attr)
else:
setattr(res, attr, None)
for attr in ClfResult._datafame_attrs:
val = getattr(res, attr)
if val is not None:
assert np.all(res.index == val.index), 'index got weird'
return res
def hardness_analysis(res, samples, infr=None, method='argmax'):
"""
samples = pblm.samples
# TODO MWE with sklearn data
# ClfResult.make_single(ClfResult, clf, X_df, test_idx, labels,
# data_key, feat_dims=None):
import sklearn.datasets
iris = sklearn.datasets.load_iris()
# TODO: make this setup simpler
pblm = ClfProblem()
task_key, clf_key, data_key = 'iris', 'RF', 'learn(all)'
X_df = pd.DataFrame(iris.data, columns=iris.feature_names)
samples = MultiTaskSamples(X_df.index)
samples.apply_indicators({'iris': {name: iris.target == idx
for idx, name in enumerate(iris.target_names)}})
samples.X_dict = {'learn(all)': X_df}
pblm.samples = samples
pblm.xval_kw['type'] = 'StratifiedKFold'
clf_list, res_list = pblm._train_evaluation_clf(
task_key, data_key, clf_key)
labels = pblm.samples.subtasks[task_key]
res = ClfResult.combine_results(res_list, labels)
res.get_thresholds('mcc', 'maximize')
predict_method = 'argmax'
"""
meta = {}
easiness = ut.ziptake(res.probs_df.values, res.target_enc_df.values)
# pred = sklearn_utils.predict_from_probs(res.probs_df, predict_method)
if method == 'max-mcc':
method = res.get_thresholds('mcc', 'maximize')
pred = sklearn_utils.predict_from_probs(res.probs_df, method, force=True)
meta['easiness'] = np.array(easiness).ravel()
meta['hardness'] = 1 - meta['easiness']
meta['aid1'] = res.probs_df.index.get_level_values(0)
meta['aid2'] = res.probs_df.index.get_level_values(1)
# meta['aid1'] = samples.aid_pairs.T[0].take(res.probs_df.index.values)
# meta['aid2'] = samples.aid_pairs.T[1].take(res.probs_df.index.values)
# meta['pred'] = res.probs_df.values.argmax(axis=1)
meta['pred'] = pred.values
meta['real'] = res.target_enc_df.values.ravel()
meta['failed'] = meta['pred'] != meta['real']
meta = pd.DataFrame(meta)
meta = meta.set_index(['aid1', 'aid2'], drop=False)
if infr is not None:
ibs = infr.ibs
edges = list(meta.index.tolist())
conf_dict = infr.get_edge_attrs(
'confidence',
edges,
on_missing='filter',
default=ibs.const.CONFIDENCE.CODE.UNKNOWN,
)
conf_df = pd.DataFrame.from_dict(conf_dict, orient='index')
conf_df = conf_df[0].map(ibs.const.CONFIDENCE.CODE_TO_INT)
meta = meta.assign(real_conf=conf_df)
meta['real_conf'] = np.nan_to_num(meta['real_conf']).astype(np.int)
meta = meta.sort_values('hardness', ascending=False)
res.meta = meta
return res.meta
def missing_classes(res):
# Find classes that were never predicted
unique_predictions = np.unique(res.probs_df.values.argmax(axis=1))
n_classes = len(res.class_names)
missing_classes = ut.index_complement(unique_predictions, n_classes)
return missing_classes
def augment_if_needed(res):
"""
Adds in dummy values for missing classes
"""
missing_classes = res.missing_classes()
n_classes = len(res.class_names)
y_test_enc_aug = res.target_enc_df.values
y_test_bin_aug = res.target_bin_df.values
clf_probs_aug = res.probs_df.values
sample_weight = np.ones(len(y_test_enc_aug))
n_missing = len(missing_classes)
if res.probhats_df is not None:
clf_probhats_aug = res.probhats_df.values
else:
clf_probhats_aug = None
# Check if augmentation is necessary
if n_missing > 0:
missing_bin = np.zeros((n_missing, n_classes))
missing_bin[(np.arange(n_missing), missing_classes)] = 1.0
missing_enc = np.array(missing_classes)[:, None]
y_test_enc_aug = np.vstack([y_test_enc_aug, missing_enc])
y_test_bin_aug = np.vstack([y_test_bin_aug, missing_bin])
clf_probs_aug = np.vstack([clf_probs_aug, missing_bin])
# make sample weights where dummies have no weight
sample_weight = np.hstack([sample_weight, np.full(n_missing, 0)])
if res.probhats_df is not None:
clf_probhats_aug = np.vstack([clf_probhats_aug, missing_bin])
res.clf_probs = clf_probs_aug
res.clf_probhats = clf_probhats_aug
res.y_test_enc = y_test_enc_aug
res.y_test_bin = y_test_bin_aug
res.sample_weight = sample_weight
def extended_clf_report(res, verbose=True):
res.augment_if_needed()
pred_enc = res.clf_probs.argmax(axis=1)
y_pred = pred_enc
y_true = res.y_test_enc
sample_weight = res.sample_weight
target_names = res.class_names
report = sklearn_utils.classification_report2(
y_true,
y_pred,
target_names=target_names,
sample_weight=sample_weight,
verbose=verbose,
)
return report
def print_report(res):
res.augment_if_needed()
pred_enc = res.clf_probs.argmax(axis=1)
res.extended_clf_report()
report = sklearn.metrics.classification_report(
y_true=res.y_test_enc,
y_pred=pred_enc,
target_names=res.class_names,
sample_weight=res.sample_weight,
)
logger.info('Precision/Recall Report:')
logger.info(report)
def get_thresholds(res, metric='mcc', value='maximize'):
"""
get_metric = 'thresholds'
at_metric = metric = 'mcc'
at_value = value = 'maximize'
a = []
b = []
for x in np.linspace(0, 1, 1000):
a += [cfms.get_metric_at_metric('thresholds', 'fpr', x, subindex=True)]
b += [cfms.get_thresh_at_metric('fpr', x)]
a = np.array(a)
b = np.array(b)
d = (a - b)
logger.info((d.min(), d.max()))
"""
threshes = {}
for class_name in res.class_names:
cfms = res.confusions(class_name)
thresh = cfms.get_metric_at_metric('thresh', metric, value)
threshes[class_name] = thresh
return threshes
@profile
def get_pos_threshes(
res,
metric='fpr',
value=1e-4,
maximize=False,
warmup=200,
priors=None,
min_thresh=0.5,
):
"""
Finds a threshold that achieves the desired `value` for the desired
metric, while maximizing or minimizing the threshold.
For positive classification you want to minimize the threshold.
Priors can be passed in to augment probabilities depending on support.
By default a class prior is 1 for threshold minimization and 0 for
maximization.
"""
pos_threshes = {}
if priors is None:
priors = {name: float(not maximize) for name in res.class_names}
for class_name in res.class_names:
cfms = res.confusions(class_name)
learned_thresh = cfms.get_metric_at_metric('thresh', metric, value)
# learned_thresh = cfms.get_thresh_at_metric(
# metric, value, maximize=maximize)
prior_thresh = priors[class_name]
n_support = cfms.n_pos
if warmup is not None:
"""
python -m wbia.plottool.draw_func2 plot_func --show --range=0,1 \
--func="lambda x: np.maximum(0, (x - .6) / (1 - .6))"
"""
# If n_support < warmup: then interpolate to learned thresh
nmax = warmup if isinstance(warmup, int) else warmup[class_name]
# alpha varies from 0 to 1
alpha = min(nmax, n_support) / nmax
# transform alpha through nonlinear function (similar to ReLU)
p = 0.6 # transition point
alpha = max(0, (alpha - p) / (1 - p))
thresh = prior_thresh * (1 - alpha) + learned_thresh * (alpha)
else:
thresh = learned_thresh
pos_threshes[class_name] = max(min_thresh, thresh)
return pos_threshes
def report_thresholds(res, warmup=200):
# import vtool as vt
ut.cprint('Threshold Report', 'yellow')
y_test_bin = res.target_bin_df.values
# y_test_enc = y_test_bin.argmax(axis=1)
# clf_probs = res.probs_df.values
# The maximum allowed false positive rate
# We expect that we will make 1 error every 1,000 decisions
# thresh_df['foo'] = [1, 2, 3]
# thresh_df['foo'][res.class_names[k]] = 1
# for k in [2, 0, 1]:
choice_mv = ut.odict(
[
('@fpr=.01', ('fpr', 0.01)),
('@fpr=.001', ('fpr', 0.001)),
('@fpr=.0001', ('fpr', 1e-4)),
('@fpr=.0000', ('fpr', 0)),
('@max(mcc)', ('mcc', 'max')),
# (class_name + '@max(acc)', ('acc', 'max')),
# (class_name + '@max(mk)', ('mk', 'max')),
# (class_name + '@max(bm)', ('bm', 'max')),
]
)
for k in range(y_test_bin.shape[1]):
thresh_dict = ut.odict()
class_name = res.class_names[k]
cfms = res.confusions(class_name)
# probs, labels = clf_probs.T[k], y_test_bin.T[k]
# cfms = vt.ConfusionMetrics().fit(probs, labels)
for k, mv in choice_mv.items():
metric, value = mv
idx = cfms.get_index_at_metric(metric, value)
key = class_name + k
thresh_dict[key] = ut.odict()
for metric in ['thresh', 'fpr', 'tpr', 'tpa', 'bm', 'mk', 'mcc']:
thresh_dict[key][metric] = cfms.get_metric_at_index(metric, idx)
thresh_df = pd.DataFrame.from_dict(thresh_dict, orient='index')
thresh_df = thresh_df.loc[list(thresh_dict.keys())]
if cfms.n_pos > 0 and cfms.n_neg > 0:
logger.info('Raw 1vR {} Thresholds'.format(class_name))
logger.info(ut.indent(thresh_df.to_string(float_format='{:.4f}'.format)))
# chosen_type = class_name + '@fpr=0'
# pos_threshes[class_name] = thresh_df.loc[chosen_type]['thresh']
for choice_k, choice_mv in iter(choice_mv.items()):
metric, value = choice_mv
pos_threshes = res.get_pos_threshes(metric, value, warmup=warmup)
logger.info('Choosing threshold based on %s' % (choice_k,))
res.report_auto_thresholds(pos_threshes)
def report_auto_thresholds(res, threshes, verbose=True):
report_lines = []
print_ = report_lines.append
print_(
'Chosen thresholds = %s'
% (ut.repr2(threshes, nl=1, precision=4, align=True),)
)
res.augment_if_needed()
target_names = res.class_names
sample_weight = res.sample_weight
y_true = res.y_test_enc.ravel()
y_pred, can_autodecide = sklearn_utils.predict_from_probs(
res.clf_probs,
threshes,
res.class_names,
force=False,
multi=False,
return_flags=True,
)
can_autodecide[res.sample_weight == 0] = False
auto_pred = y_pred[can_autodecide].astype(np.int)
auto_true = y_true[can_autodecide].ravel()
auto_probs = res.clf_probs[can_autodecide]
total_cases = int(sample_weight.sum())
print_('Will autodecide for %r/%r cases' % (can_autodecide.sum(), (total_cases)))
def frac_str(a, b):
return '{:}/{:} = {:.2f}%'.format(int(a), int(b), a / b)
y_test_bin = res.target_bin_df.values
supported_class_idxs = [k for k, y in enumerate(y_test_bin.T) if y.sum() > 0]
print_(' * Auto-Decide Per-Class Summary')
for k in supported_class_idxs:
# Look at fail/succs in threshold
name = res.class_names[k]
# number of times this class appears overall
n_total_k = (y_test_bin.T[k]).sum()
# get the cases where this class was predicted
auto_true_k = auto_true == k
auto_pred_k = auto_pred == k
# number of cases auto predicted
n_pred_k = auto_pred_k.sum()
# number of times auto was right
n_tp = (auto_true_k & auto_pred_k).sum()
# number of times auto was wrong
n_fp = (~auto_true_k & auto_pred_k).sum()
fail_str = frac_str(n_fp, n_pred_k)
pass_str = frac_str(n_tp, n_total_k)
fmtstr = '\n'.join(
[
'{name}:',
' {n_total_k} samples existed, and did {n_pred_k} auto predictions',
' got {pass_str} right',
' made {fail_str} errors',
]
)
print_(ut.indent(fmtstr.format(**locals())))
report = sklearn_utils.classification_report2(
y_true,
y_pred,
target_names=target_names,
sample_weight=can_autodecide.astype(np.float),
verbose=False,
)
print_(' * Auto-Decide Confusion')
print_(ut.indent(str(report['confusion'])))
print_(' * Auto-Decide Metrics')
print_(ut.indent(str(report['metrics'])))
if 'mcc' in report:
print_(ut.indent(str(report['mcc'])))
try:
auto_truth_bin = res.y_test_bin[can_autodecide]
for k in supported_class_idxs:
auto_truth_k = auto_truth_bin.T[k]
auto_probs_k = auto_probs.T[k]
if auto_probs_k.sum():
auc = sklearn.metrics.roc_auc_score(auto_truth_k, auto_probs_k)
print_(
' * Auto AUC(Macro): {:.4f} for class={}'.format(
auc, res.class_names[k]
)
)
except ValueError:
pass
report = '\n'.join(report_lines)
if verbose:
logger.info(report)
return report
def confusions(res, class_name):
import vtool as vt
y_test_bin = res.target_bin_df.values
clf_probs = res.probs_df.values
k = res.class_names.index(class_name)
probs, labels = clf_probs.T[k], y_test_bin.T[k]
confusions = vt.ConfusionMetrics().fit(probs, labels)
return confusions
def ishow_roc(res):
import vtool as vt
import wbia.plottool as pt
ut.qtensure()
y_test_bin = res.target_bin_df.values
# The maximum allowed false positive rate
# We expect that we will make 1 error every 1,000 decisions
# thresh_df['foo'] = [1, 2, 3]
# thresh_df['foo'][res.class_names[k]] = 1
# for k in [2, 0, 1]:
for k in range(y_test_bin.shape[1]):
if y_test_bin.shape[1] == 2 and k == 0:
# only show one in the binary case
continue
class_name = res.class_names[k]
confusions = res.confusions(class_name)
ROCInteraction = vt.interact_roc_factory(
confusions, show_operating_point=True
)
fnum = pt.ensure_fnum(k)
# ROCInteraction.static_plot(fnum, None, name=class_name)
inter = ROCInteraction(fnum=fnum, pnum=None, name=class_name)
inter.start()
# if False:
# X = probs
# y = labels
# encoder = vt.ScoreNormalizer()
# encoder.fit(probs, labels)
# learn_thresh = encoder.learn_threshold2()
# encoder.inverse_normalize(learn_thresh)
# encoder.visualize(fnum=k)
pass
def show_roc(res, class_name, **kwargs):
import vtool as vt
labels = res.target_bin_df[class_name].values
probs = res.probs_df[class_name].values
confusions = vt.ConfusionMetrics().fit(probs, labels)
confusions.draw_roc_curve(**kwargs)
def roc_scores_ovr_hat(res):
res.augment_if_needed()
for k in range(len(res.class_names)):
class_k_truth = res.y_test_bin.T[k]
class_k_probs = res.probhats_df.values.T[k]
auc = sklearn.metrics.roc_auc_score(class_k_truth, class_k_probs)
yield auc
def roc_scores_ovr(res):
res.augment_if_needed()
for k in range(res.y_test_bin.shape[1]):
class_k_truth = res.y_test_bin.T[k]
class_k_probs = res.clf_probs.T[k]
auc = sklearn.metrics.roc_auc_score(class_k_truth, class_k_probs)
yield auc
def confusions_ovr(res):
# one_vs_rest confusions
import vtool as vt
res.augment_if_needed()
for k in range(res.y_test_bin.shape[1]):
class_k_truth = res.y_test_bin.T[k]
class_k_probs = res.clf_probs.T[k]
cfms = vt.ConfusionMetrics().fit(class_k_probs, class_k_truth)
# auc = sklearn.metrics.roc_auc_score(class_k_truth, class_k_probs)
yield res.class_names[k], cfms
def roc_score(res):
res.augment_if_needed()
auc_learn = sklearn.metrics.roc_auc_score(res.y_test_bin, res.clf_probs)
return auc_learn
@ut.reloadable_class
class MultiTaskSamples(ut.NiceRepr):
"""
Handles samples (i.e. feature-label pairs) with a combination of
non-mutually exclusive subclassification labels
CommandLine:
python -m wbia.algo.verif.clf_helpers MultiTaskSamples
Example:
>>> # ENABLE_DOCTEST
>>> from wbia.algo.verif.clf_helpers import * # NOQA
>>> samples = MultiTaskSamples([0, 1, 2, 3])
>>> tasks_to_indicators = ut.odict([
>>> ('task1', ut.odict([
>>> ('state1', [0, 0, 0, 1]),
>>> ('state2', [0, 0, 1, 0]),
>>> ('state3', [1, 1, 0, 0]),
>>> ])),
>>> ('task2', ut.odict([
>>> ('state4', [0, 0, 0, 1]),
>>> ('state5', [1, 1, 1, 0]),
>>> ]))
>>> ])
>>> samples.apply_indicators(tasks_to_indicators)
"""
def __init__(samples, index):
samples.index = index
samples.subtasks = ut.odict()
# def set_simple_scores(samples, simple_scores):
# if simple_scores is not None:
# edges = ut.emap(tuple, samples.aid_pairs.tolist())
# assert (edges == simple_scores.index.tolist())
# samples.simple_scores = simple_scores
# def set_feats(samples, X_dict):
# if X_dict is not None:
# edges = ut.emap(tuple, samples.aid_pairs.tolist())
# for X in X_dict.values():
# assert np.all(edges == X.index.tolist())
# samples.X_dict = X_dict
def supported_tasks(samples):
for task_key, labels in samples.subtasks.items():
labels = samples.subtasks[task_key]
if labels.has_support():
yield task_key
def apply_indicators(samples, tasks_to_indicators):
"""
Adds labels for a specific task
Args:
tasks_to_indicators (dict): takes the form:
{
`my_task_name1' {
'class1': [list of bools indicating class membership]
...
'classN': [list of bools indicating class membership]
}
...
`my_task_nameN': ...
}
"""
n_samples = None
samples.n_tasks = len(tasks_to_indicators)
for task_name, indicator in tasks_to_indicators.items():
labels = MultiClassLabels.from_indicators(
indicator, task_name=task_name, index=samples.index
)
samples.subtasks[task_name] = labels
if n_samples is None:
n_samples = labels.n_samples
elif n_samples != labels.n_samples:
raise ValueError('numer of samples is different')
samples.n_samples = n_samples
def apply_encoded_labels(samples, y_enc, class_names, task_name):
"""
Adds labels for a specific task. Alternative to `apply_indicators`
Args:
y_enc (list): integer label indicating the class for each sample
class_names (list): list of strings indicating the class-domain
task_name (str): key for denoting this specific task
"""
# convert to indicator structure and use that
tasks_to_indicators = ut.odict(
[
(
task_name,
ut.odict(
[
(name, np.array(y_enc) == i)
for i, name in enumerate(class_names)
]
),
)
]
)
samples.apply_indicators(tasks_to_indicators)
# @ut.memoize
def encoded_2d(samples):
encoded_2d = pd.concat([v.encoded_df for k, v in samples.items()], axis=1)
return encoded_2d
def class_name_basis(samples):
"""corresponds with indexes returned from encoded1d"""
class_name_basis = [
t[::-1]
for t in ut.product(*[v.class_names for k, v in samples.items()][::-1])
]
# class_name_basis = [(b, a) for a, b in ut.product(*[
# v.class_names for k, v in samples.items()][::-1])]
return class_name_basis
def class_idx_basis_2d(samples):
"""2d-index version of class_name_basis"""
class_idx_basis_2d = [
(b, a)
for a, b in ut.product(
*[range(v.n_classes) for k, v in samples.items()][::-1]
)
]
return class_idx_basis_2d
def class_idx_basis_1d(samples):
"""1d-index version of class_name_basis"""
n_states = np.prod([v.n_classes for k, v in samples.items()])
class_idx_basis_1d = np.arange(n_states, dtype=np.int)
return class_idx_basis_1d
# @ut.memoize
def encoded_1d(samples):
"""Returns a unique label for each combination of samples"""
# from sklearn.preprocessing import MultiLabelBinarizer
encoded_2d = samples.encoded_2d()
class_space = [v.n_classes for k, v in samples.items()]
offsets = np.array([1] + np.cumprod(class_space).tolist()[:-1])[None, :]
encoded_1d = (offsets * encoded_2d).sum(axis=1)
# e = MultiLabelBinarizer()
# bin_coeff = e.fit_transform(encoded_2d)
# bin_basis = (2 ** np.arange(bin_coeff.shape[1]))[None, :]
# # encoded_1d = (bin_coeff * bin_basis).sum(axis=1)
# encoded_1d = (bin_coeff * bin_basis[::-1]).sum(axis=1)
# # vt.unique_rows(sklearn.preprocessing.MultiLabelBinarizer().fit_transform(encoded_2d))
# [v.encoded_df.values for k, v in samples.items()]
# encoded_df_1d = pd.concat([v.encoded_df for k, v in samples.items()], axis=1)
return encoded_1d
def __nice__(samples):
return 'nS=%r, nT=%r' % (len(samples), samples.n_tasks)
def __getitem__(samples, task_key):
return samples.subtasks[task_key]
def __len__(samples):
return samples.n_samples
def print_info(samples):
for task_name, labels in samples.items():
labels.print_info()
logger.info('hist(all) = %s' % (ut.repr4(samples.make_histogram())))
logger.info('len(all) = %s' % (len(samples)))
def make_histogram(samples):
"""label histogram"""
class_name_basis = samples.class_name_basis()
class_idx_basis_1d = samples.class_idx_basis_1d()
# logger.info('class_idx_basis_1d = %r' % (class_idx_basis_1d,))
# logger.info(samples.encoded_1d())
multi_task_idx_hist = ut.dict_hist(
samples.encoded_1d().values, labels=class_idx_basis_1d
)
multi_task_hist = ut.map_keys(lambda k: class_name_basis[k], multi_task_idx_hist)
return multi_task_hist
def items(samples):
for task_name, labels in samples.subtasks.items():
yield task_name, labels
# def take(samples, idxs):
# mask = ut.index_to_boolmask(idxs, len(samples))
# return samples.compress(mask)
@property
def group_ids(samples):
return None
def stratified_kfold_indices(samples, **xval_kw):
"""
TODO: check xval label frequency
"""
from sklearn import model_selection
X = np.empty((len(samples), 0))
y = samples.encoded_1d().values
groups = samples.group_ids
type_ = xval_kw.pop('type', 'StratifiedGroupKFold')
if type_ == 'StratifiedGroupKFold':
assert groups is not None
# FIXME: The StratifiedGroupKFold could be implemented better.
splitter = sklearn_utils.StratifiedGroupKFold(**xval_kw)
skf_list = list(splitter.split(X=X, y=y, groups=groups))
elif type_ == 'StratifiedKFold':
splitter = model_selection.StratifiedKFold(**xval_kw)
skf_list = list(splitter.split(X=X, y=y))
return skf_list
def subsplit_indices(samples, subset_idx, **xval_kw):
"""split an existing set"""
from sklearn import model_selection
X = np.empty((len(subset_idx), 0))
y = samples.encoded_1d().values[subset_idx]
groups = samples.group_ids[subset_idx]
xval_kw_ = xval_kw.copy()
if 'n_splits' not in xval_kw_:
xval_kw_['n_splits'] = 3
type_ = xval_kw_.pop('type', 'StratifiedGroupKFold')
if type_ == 'StratifiedGroupKFold':
assert groups is not None
# FIXME: The StratifiedGroupKFold could be implemented better.
splitter = sklearn_utils.StratifiedGroupKFold(**xval_kw_)
rel_skf_list = list(splitter.split(X=X, y=y, groups=groups))
elif type_ == 'StratifiedKFold':
splitter = model_selection.StratifiedKFold(**xval_kw_)
rel_skf_list = list(splitter.split(X=X, y=y))
# map back into original coords
skf_list = [
(subset_idx[rel_idx1], subset_idx[rel_idx2])
for rel_idx1, rel_idx2 in rel_skf_list
]
for idx1, idx2 in skf_list:
assert len(np.intersect1d(subset_idx, idx1)) == len(idx1)
assert len(np.intersect1d(subset_idx, idx2)) == len(idx2)
# assert
return skf_list
@ut.reloadable_class
class MultiClassLabels(ut.NiceRepr):
"""
Used by samples to encode a single set of mutually exclusive labels. These
can either be binary or multiclass.
import pandas as pd
pd.options.display.max_rows = 10
# pd.options.display.max_rows = 20
pd.options.display.max_columns = 40
pd.options.display.width = 160
"""
def __init__(labels):
# Helper Info
labels.task_name = None
labels.n_samples = None
labels.n_classes = None
labels.class_names = None
labels.classes_ = None
# Core data
labels.indicator_df = None
labels.encoded_df = None
labels.default_class = None
def has_support(labels):
return len(labels.make_histogram()) > 1
def lookup_class_idx(labels, class_name):
return ut.dzip(labels.class_names, labels.classes_)[class_name]
@classmethod
def from_indicators(MultiClassLabels, indicator, index=None, task_name=None):
labels = MultiClassLabels()
n_samples = len(next(iter(indicator.values())))
# if index is None:
# index = pd.Series(np.arange(n_samples), name='index')
indicator_df = pd.DataFrame(indicator, index=index)
assert np.all(
indicator_df.sum(axis=1).values
), 'states in the same task must be mutually exclusive'
labels.indicator_df = indicator_df
labels.class_names = indicator_df.columns.values
labels.encoded_df = pd.DataFrame(
indicator_df.values.argmax(axis=1), columns=[task_name], index=index
)
labels.task_name = task_name
labels.n_samples = n_samples
labels.n_classes = len(labels.class_names)
if labels.n_classes == 1:
labels.n_classes = 2 # 1 column means binary case
labels.classes_ = | np.arange(labels.n_classes) | numpy.arange |
#!/usr/bin/env python3
import argparse
import os
from cProfile import label
import matplotlib.pyplot as plt
import numpy as np
import requests
import tensorflow as tf
import tensorflow_probability as tfp
from matplotlib.gridspec import GridSpec
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import precision_recall_fscore_support as prfs
from sklearn.metrics import roc_auc_score
from sklearn.utils import Bunch, check_random_state
from tensorflow import keras
from tensorflow.keras.callbacks import EarlyStopping
from influence.influence.influence_model import InfluenceModel
from negsup.datasets import *
from negsup.fisher import *
from negsup.models import *
from negsup.negotiation import *
from negsup.utils import *
FEW = 100
ecefunc = tfp.stats.expected_calibration_error_quantiles
tf.compat.v1.logging.set_verbosity(tf.compat.v1.logging.ERROR)
def prf(p, phat):
"""Computes precision, recall, F1."""
y, yhat = np.argmax(p, axis=1), np.argmax(phat, axis=1)
pr, rc, f1, _ = prfs(y, yhat, average='weighted')
# expected_calibration_error
log_pred = tf.math.log(np.max(phat, axis=1))
label = tf.cast(y == yhat, dtype=tf.bool)
(ece, _, _, _, _, _,) = ecefunc(label, log_pred, num_buckets=3)
return pr, rc, f1, ece.numpy()
# ===========================================================================
def sample_counterexamples2(args, if_config):
"""Sample counter-examples using kNN, IF, and RIF."""
rng = np.random.RandomState(args.seed)
# Build a subsampled noisy dataset
dataset = DATASETS[args.dataset]()
subsample_train(dataset, args.p_known + args.max_iters, rng=rng)
noisy_dataset, noisy, kn, indices = gen_run_data(dataset, args, rng=rng)[0]
print(f'{len(kn + indices)} examples, {len(noisy)} are noisy')
# Train model (or load model trained) on noisy dataset
model = make_model(args.model,
noisy_dataset,
from_logits=args.from_logits)
model.fit(noisy_dataset.X_tr[kn],
noisy_dataset.y_tr[kn],
epochs=args.n_epochs)
y = np.argmax(dataset.y_tr, axis=1)
y_noisy = np.argmax(noisy_dataset.y_tr, axis=1)
X = tf.convert_to_tensor(dataset.X_tr) # XXX work-around for memory leak
phat = model.predict(X, batch_size=args.batch_size)
yhat = np.argmax(phat, axis=1)
rows = np.arange(len(y))
margins = phat[rows, yhat] - phat[rows, y_noisy]
# Ordina l'indice delle immagini del training set (immagini più incerte prima), ultime 25
temp = 10000
uncertain_mistakes = [
i for i in np.argsort(margins)
if y_noisy[i] != yhat[i] and i not in kn
][:temp]
# Ordina l'indice delle immagini del training set (immagini meno incerte prima)
certain_mistakes = [
i for i in np.argsort(margins)
if y_noisy[i] != yhat[i] and i not in kn
][-temp:]
selected = uncertain_mistakes + certain_mistakes
for t, i in enumerate(selected):
fig, axes = plt.subplots(1, 4, figsize=(3.2 * 4, 2.4))
fig1, axes1 = plt.subplots(1, 4, figsize=(3.2 * 4, 2.4))
labeli, labelhati = dataset.class_names[y[i]], dataset.class_names[yhat[i]]
print(f'EX {i}, "{labeli}" predicted as "{labelhati}" ({margins[i]})')
img_name = f'{labeli}{dataset.class_names[y_noisy[i]]}{labelhati}'
correct = bool(labeli == labelhati)
imgs = []
labels = []
axes[0].imshow(dataset.X_tr[i], cmap=plt.get_cmap('gray'))
axes[0].set_title(f'The machine \nthinks it\'s a "{labelhati}".', fontsize=15, pad=15)
axes[0].axis('off')
axes1[0].imshow(dataset.X_tr[i], cmap=plt.get_cmap('gray'))
#ax1.imshow(dataset.X_tr[i], cmap=plt.get_cmap('gray'))
axes1[0].set_title(f'True label "{labeli}"\n'
f'Annotated as "{dataset.class_names[y_noisy[i]]}"\n'
f'Predicted as "{labelhati}"', fontsize=20, pad=15)
axes1[0].axis('off')
negotiators = ['top_fisher', 'nearest', 'if']
names = ['CINCER', '1-NN', 'IF']
for n, (negotiator, name) in enumerate(zip(negotiators, names)):
print(f'{t}/{len(selected)} : running {negotiator}')
j, _, _ = find_counterexample(model,
noisy_dataset,
kn, i,
negotiator,
if_config,
rng=rng)
assert j in kn and j != i
labelj, labeltildej = dataset.class_names[y[j]], dataset.class_names[
y_noisy[j]]
print(
f'{t}/{len(selected)} : EX {i}, {negotiator} picked {j}, annotatated "{labeltildej}" (actually "{labelj}")')
imgs.append(dataset.X_tr[j])
labels.append(name[0]+labelj+labeltildej)
axes[n + 1].tick_params(axis='both', which='both', bottom=False, left=False,
right=False, top=False, labelleft=False,
labelbottom=False)
axes1[n + 1].imshow(dataset.X_tr[j], cmap=plt.get_cmap('gray'))
axes1[n + 1].set_title(f'True label "{labelj}"\n'
f'Annotated as "{labeltildej}"', fontsize=20, pad=15)
axes1[n + 1].set_xlabel(name, fontsize=20, labelpad=15)
axes1[n + 1].tick_params(axis='both', which='both', bottom=False, left=False,
right=False, top=False, labelleft=False,
labelbottom=False)
axes[2].set_title(f'Supporting examples for machine\'s prediction', fontsize=20, pad=25)
line = plt.Line2D((.31, .31),(.0, 1), color="k", linewidth=3)
fig.add_artist(line)
save_image(fig, axes, fig1, correct, i, t, imgs, labels, img_name)
plt.close(fig)
plt.close(fig1)
def save_image(fig, axes,fig1, corr, i, t, imgs, labels, img_name):
if(corr == True):
path = 'images/correct'
else:
path = 'images/incorrect'
path = path + f'/{i}__{t}'
if(not os.path.exists(path)):
os.makedirs(path)
print("New directory created: "+ path)
axes[1].set_xlabel(f'#1', fontsize=20, labelpad=15)
axes[2].set_xlabel(f'#2', fontsize=20, labelpad=15)
axes[3].set_xlabel(f'#3', fontsize=20, labelpad=15)
fig1.savefig(os.path.join(path, f'{img_name}_main.png'),
bbox_inches='tight',pad_inches=0.3)
for i in range(3) :
for j in range(3) :
if(j!=i):
for k in range(3) :
if(k!=i and k!=j):
axes[1].imshow(imgs[i], cmap=plt.get_cmap('gray'))
axes[2].imshow(imgs[j], cmap=plt.get_cmap('gray'))
axes[3].imshow(imgs[k], cmap=plt.get_cmap('gray'))
fig.savefig(os.path.join(path, f'{img_name}_{labels[i]}_{labels[j]}_{labels[k]}.png'),
bbox_inches='tight',
pad_inches=0.3)
def sample_counterexamples(args, if_config):
"""Sample counter-examples using kNN, IF, and RIF."""
rng = np.random.RandomState(args.seed)
# Build a subsampled noisy dataset
dataset = DATASETS[args.dataset]()
subsample_train(dataset, args.p_known + args.max_iters, rng=rng)
noisy_dataset, noisy, kn, indices = gen_run_data(dataset, args, rng=rng)[0]
# noisy_dataset, clean, noisy = inject_noise(args, dataset, rng=rng)
print(f'{len(kn + indices)} examples, {len(noisy)} are noisy')
# model_path = os.path.join('model-cache', basename)
# model = make_or_load_model(model_path,
# args.model,
# noisy_dataset,
# n_epochs=args.n_epochs,
# from_logits=args.from_logits,
# no_cache=args.no_cache)
model = make_model(args.model,
noisy_dataset,
from_logits=args.from_logits)
model.fit(noisy_dataset.X_tr[kn],
noisy_dataset.y_tr[kn],
epochs=args.n_epochs)
y = np.argmax(dataset.y_tr, axis=1)
y_noisy = np.argmax(noisy_dataset.y_tr, axis=1)
X = tf.convert_to_tensor(dataset.X_tr) # XXX work-around for memory leak
phat = model.predict(X, batch_size=args.batch_size)
yhat = np.argmax(phat, axis=1)
rows = np.arange(len(y))
margins = phat[rows, yhat] - phat[rows, y_noisy]
# Ordina l'indice delle immagini del training set (immagini più incerte prima), ultime 25
temp = 10000
uncertain_mistakes = [
i for i in np.argsort(margins)
if y_noisy[i] != yhat[i] and i not in kn
][:temp]
# Ordina l'indice delle immagini del training set (immagini meno incerte prima)
certain_mistakes = [
i for i in np.argsort(margins)
if y_noisy[i] != yhat[i] and i not in kn
][-temp:]
selected = uncertain_mistakes + certain_mistakes
# Dump the images and their counter-examples using kNN, IF, IF+kNN
for t, i in enumerate(selected):
fig, axes = plt.subplots(1, 4, figsize=(3.2 * 4, 2.4))
labeli, labelhati = dataset.class_names[y[i]], dataset.class_names[yhat[i]]
print(f'EX {i}, "{labeli}" predicted as "{labelhati}" ({margins[i]})')
axes[0].imshow(dataset.X_tr[i], cmap=plt.get_cmap('gray'))
#ax1.imshow(dataset.X_tr[i], cmap=plt.get_cmap('gray'))
axes[0].set_title(f'True label "{labeli}"\n'
f'Annotated as "{dataset.class_names[y_noisy[i]]}"\n'
f'Predicted as "{labelhati}"', fontsize=20, pad=15)
axes[0].axis('off')
#ax1.axis('off')
#negotiators = ['top_fisher', 'nearest', 'if']
#names = ['CINCER', '1-NN', 'IF']
negotiators = ['nearest', 'if']
names = ['1-NN', 'IF']
for n, (negotiator, name) in enumerate(zip(negotiators, names)):
print(f'{t}/{len(selected)} : running {negotiator}')
j, _, _ = find_counterexample(model,
noisy_dataset,
kn, i,
negotiator,
if_config,
rng=rng)
assert j in kn and j != i
labelj, labeltildej = dataset.class_names[y[j]], dataset.class_names[
y_noisy[j]]
print(
f'{t}/{len(selected)} : EX {i}, {negotiator} picked {j}, annotatated "{labeltildej}" (actually "{labelj}")')
axes[n + 1].imshow(dataset.X_tr[j], cmap=plt.get_cmap('gray'))
axes[n + 1].set_title(f'True label "{labelj}"\n'
f'Annotated as "{labeltildej}"', fontsize=20, pad=15)
axes[n + 1].set_xlabel(name, fontsize=20, labelpad=15)
axes[n + 1].tick_params(axis='both', which='both', bottom=False, left=False,
right=False, top=False, labelleft=False,
labelbottom=False)
fig.savefig(os.path.join('images', f'{i}__{t}.png'),
bbox_inches='tight',
pad_inches=0.3)
plt.close(fig)
# ===========================================================================
def _get_suspiciousness_aucs(args, if_config, rng=None):
"""Check whether margin and IFs spot noisy train examples."""
rng = check_random_state(rng)
# Build a subsampled noisy dataset
dataset = DATASETS[args.dataset]()
subsample_train(dataset, args.p_known, rng=rng)
noisy_dataset, clean, noisy = inject_noise(args, dataset, rng=rng)
kn = list(range(len(dataset.y_tr)))
print(f'q1: {len(kn)} examples, {len(noisy)} are noisy')
# Train model (or load model trained) on noisy dataset
basename = _get_basename(args, model_only=True)
model_path = os.path.join('model-cache', basename)
model = make_or_load_model(model_path,
args.model,
noisy_dataset,
n_epochs=args.n_epochs,
from_logits=args.from_logits,
no_cache=args.no_cache)
# Pick a subset of clean + noisy examples, up to $FEW each
n_samples = min(len(clean), len(noisy), FEW)
selected = np.concatenate([
rng.permutation(clean)[:n_samples],
rng.permutation(noisy)[:n_samples],
]).astype(int)
is_mistake = np.concatenate([
0 * np.ones(n_samples), # clean
1 * np.ones(n_samples), # noisy
])
assert len(selected) == len(is_mistake)
assert len(selected) > 0
n_labels = len(dataset.class_names)
# Compute suspiciousness of selected examples & their AUC
print(f'computing margin of {len(selected)} examples')
margins = [
get_margin(model,
noisy_dataset.X_tr,
noisy_dataset.y_tr,
i)
for i in selected
]
# print(f'computing exp. gradient len of {len(selected)} examples')
# expgradlens = [
# get_expected_gradient_len(model,
# noisy_dataset.X_tr,
# noisy_dataset.y_tr,
# i,
# n_labels,
# **if_config)
# for i in selected
# ]
print(f'computing Fisher kernel of {len(selected)} examples')
fishervalues = [
fisher_kernel(i, i,
model,
noisy_dataset.X_tr,
noisy_dataset.y_tr)
for i in selected
]
print(f'computing influence of {len(selected)} examples')
influences = [
get_influence_on_params(model,
noisy_dataset.X_tr,
noisy_dataset.y_tr,
kn, i,
**if_config)
for i in selected
]
m_auc = roc_auc_score(is_mistake, margins)
g_auc = roc_auc_score(is_mistake, fishervalues)
i_auc = None # roc_auc_score(is_mistake, influences)
return m_auc, g_auc, i_auc
def eval_identification(args, if_config):
m_aucs, g_aucs, i_aucs = [], [], []
for repeat in range(args.n_repeats):
rng = np.random.RandomState(args.seed + repeat)
m_auc, g_auc, i_auc = _get_suspiciousness_aucs(args, if_config, rng=rng)
print(f'REP {repeat} AUCs: m={m_auc} g={g_auc} i={i_auc}')
m_aucs.append(m_auc)
g_aucs.append(g_auc)
i_aucs.append(i_auc)
i_aucs = np.array(i_aucs)
g_aucs = np.array(g_aucs)
m_aucs = np.array(m_aucs)
print(f'AVG : ' \
f'margin AUC={m_aucs.mean()}±{m_aucs.std()}, ' \
f'fisher value AUC={g_aucs.mean()}±{g_aucs.std()}, ' \
# f'IF AUC={i_aucs.mean()}±{i_aucs.std()}'
)
# ===========================================================================
def _negotiate(model,
initial_weights,
dataset,
noisy_dataset,
noisy,
kn,
indices,
threshold,
if_config,
args,
return_suspiciousnesses=False,
rng=None):
"""Run the negotiation loop and record various stats."""
rng = check_random_state(rng)
# ===== validate dataset ====
noisy_in_experiment = sum(int(el in noisy) for el in kn + indices)
if args.noise_type != 'random' and noisy_in_experiment == 0:
raise RuntimeError("p_noise = 0.0 (for computing upper bound) for"
"no-random noise is not support,"
"because rng is called a different number of times respect to"
"other baselines.")
expected_n_noisy_ex = args.p_noise * len(kn) if args.ce_precision \
else args.p_noise * len(kn + indices)
print(noisy_in_experiment, expected_n_noisy_ex)
lim = 25 if args.dataset == '20ng' else 10
assert expected_n_noisy_ex - lim < noisy_in_experiment < expected_n_noisy_ex + lim
if args.inspector == 'margin' and not 0 < threshold < 1:
raise RuntimeError('threshold is not between 0 and 1')
if args.inspector == 'fisher' and not threshold > 1:
raise RuntimeError('threshold is not above 1')
# ===========
print(f'NEGOTIATING: {noisy_in_experiment} '
f'noisy, {len(kn)} kn, {len(indices)} iters '
f' -- negotiator "{args.negotiator}" '
f'noise_type "{args.noise_type}" '
f'dataset "{args.dataset}"')
# Evaluate model learned on initial known set
X_ts = tf.convert_to_tensor(dataset.X_ts) # XXX work-around for memory leak
model.set_weights(initial_weights)
baseline = 0.7 if args.model == 'logreg' else 0.9
callback = EarlyStopping(monitor='acc', baseline=baseline, patience=5)
model.fit(noisy_dataset.X_tr[kn],
noisy_dataset.y_tr[kn],
epochs=args.n_epochs,
callbacks=[callback],
verbose=0)
radius = None
if args.negotiator == 'nearest_fisher':
path_dist = 'data/dist_examples_' + args.dataset + '.pickle'
path_max_dist = 'data/max_dist_examples_' + args.dataset + '.pickle'
if os.path.exists(path_max_dist):
print('nearest-fisher: load example max dist')
max_dist = load(path_max_dist)['max_dist']
else:
print('nearest-fisher: computing max dist')
dist = pdist(
noisy_dataset.X_tr.ravel().reshape(noisy_dataset.X_tr.shape[0], -1))
max_dist = np.max(dist)
dump(path_dist, {'dist': dist})
dump(path_max_dist, {'max_dist': max_dist})
assert 0 < args.nfisher_radius < 1
radius = max_dist * args.nfisher_radius
print(f'max distance {max_dist}, radius {radius}')
# phat_ts = model.predict(X_ts, batch_size=args.batch_size)
pr, rc, f1, ece = prf(noisy_dataset.y_ts, model.predict(noisy_dataset.X_ts))
# Negotiate
trace = pd.DataFrame()
stat = Bunch(n_queried=0,
n_mistakes_seen=0,
n_cleaned=0,
n_cleaned_ce=0,
n_cleaned_ex=0,
precision=pr,
recall=rc,
f1=f1,
ece=ece,
zs_value=0,
noisy_ce=0,
suspiciousnesses=0,
case1=0,
case2=0,
case3=0,
case4=0,
case5=0,
case6=0,
case7=0,
case8=0,
case9=0,
case10=0,
case11=0,
case12=0,
case13=0,
case14=0,
ce_pr_at_5=np.nan,
ce_pr_at_10=np.nan,
ce_pr_at_25=np.nan)
trace = trace.append(stat, ignore_index=True)
for t, i in enumerate(indices):
kn.append(i)
if args.inspector == 'random':
suspiciousness = None
suspicious = rng.binomial(1, args.threshold)
else:
suspiciousness = get_suspiciousness(model,
noisy_dataset.X_tr,
noisy_dataset.y_tr,
kn, i,
len(noisy_dataset.class_names),
args.inspector,
**if_config)
suspicious = suspiciousness > threshold
stat.suspiciousnesses = suspiciousness
print(f'{t:3d}/{len(indices):3d} : EX {i} '
f'noisy={i in noisy} '
f'suspicious={suspicious} ({suspiciousness} > {threshold})')
stat.n_mistakes_seen += int(i in noisy)
stat.ce_pr_at_5 = np.nan
stat.ce_pr_at_10 = np.nan
stat.ce_pr_at_25 = np.nan
stat.noisy_ce, stat.zs_value = 0, 0
if suspicious:
in_shape = (1,) + dataset.X_tr.shape[1:]
xi = dataset.X_tr[i].reshape(in_shape)
phati = model.predict(xi)
yhati = np.argmax(phati, axis=1)[0]
candidates = []
# Identify examples to be cleaned
if args.no_ce or return_suspiciousnesses:
if yhati != np.argmax(noisy_dataset.y_tr[i]):
stat.n_queried += int(suspicious)
candidates = [i]
else:
# user and machine don't agree, query the user
if yhati != np.argmax(noisy_dataset.y_tr[i]):
stat.n_queried += int(suspicious)
print('ce start')
j, stat.zs_value, ordered_candidates = find_counterexample(
model,
noisy_dataset,
kn, i,
args.negotiator,
if_config,
radius,
rng=rng)
assert j in kn and j != i
if 'ce_removal' == args.negotiator:
candidates = [i]
if i not in noisy:
kn.remove(j)
else:
candidates = [i, j]
stat = _compute_stat(args, dataset, i, j, noisy,
ordered_candidates, stat, t, yhati)
# if args.dataset == 'synthetic':
# plot_synthetic_dataset(noisy_dataset.X_tr, noisy_dataset.y_tr, kn, i, j, t)
mistakes = [c for c in candidates if c in noisy]
print(f' : EX/CE {candidates}, noisy{mistakes}')
# Clean any mistakes on i and j
for c in mistakes:
assert (dataset.y_tr[c] != noisy_dataset.y_tr[c]).any()
noisy_dataset.y_tr[c] = dataset.y_tr[c]
noisy.remove(c)
stat.n_cleaned += 1
print('cleaned!')
# Update the model
if not args.ce_precision:
if not args.no_reload:
model.set_weights(initial_weights)
model.fit(noisy_dataset.X_tr[kn],
noisy_dataset.y_tr[kn],
epochs=args.n_epochs,
callbacks=[callback],
verbose=0)
phat_ts = model.predict(X_ts, batch_size=args.batch_size)
stat.precision, stat.recall, stat.f1, stat.ece = prf(noisy_dataset.y_ts,
phat_ts)
trace = trace.append(stat, ignore_index=True)
if return_suspiciousnesses:
return trace.suspiciousnesses.to_list()
return trace
def _compute_stat(args, dataset, i, j, noisy, ordered_candidates, stat, t, yhati):
if args.ce_precision:
precisions = []
for lim in [5, 10, 25]:
prec = sum([int(ce in noisy) for ce in ordered_candidates[:lim]]) / lim
precisions.append(prec)
stat.ce_pr_at_5, stat.ce_pr_at_10, stat.ce_pr_at_25 = precisions
stat.n_cleaned_ce += int(j in noisy)
stat.n_cleaned_ex += int(i in noisy)
user_correct = i not in noisy
machine_corret = yhati == np.argmax(dataset.y_tr[i])
ce_corret = j not in noisy
stat.noisy_ce = t if not ce_corret else 0
stat.case1 += int(
not user_correct and not machine_corret and ce_corret)
stat.case2 += int(not user_correct and machine_corret and ce_corret)
stat.case3 += int(user_correct and not machine_corret and ce_corret)
stat.case4 += int(
not user_correct and not machine_corret and not ce_corret)
stat.case5 += int(
not user_correct and machine_corret and not ce_corret)
stat.case6 += int(
user_correct and not machine_corret and not ce_corret)
stat.case7 += int(not machine_corret and not ce_corret)
stat.case8 += int(not user_correct and not ce_corret)
stat.case9 += int(machine_corret and not ce_corret)
stat.case10 += int(user_correct and not ce_corret)
stat.case11 += int(not machine_corret and ce_corret)
stat.case12 += int(not user_correct and ce_corret)
stat.case13 += int(machine_corret and ce_corret)
stat.case14 += int(user_correct and ce_corret)
return stat
def _plot_synthetic_dataset(X_tr, y_tr, kn, i, j, iteration):
plt.figure()
color = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728']
c = np.array([color[x] for x in np.argmax(y_tr, axis=1)])
plt.scatter(X_tr[kn, 0], X_tr[kn, 1], marker='x', c=c[kn])
plt.scatter(X_tr[j, 0], X_tr[j, 1], label='ce', marker='o', c=c[j], s=60,
edgecolors='red')
plt.scatter(X_tr[i, 0], X_tr[i, 1], label='i', marker='s', c=c[i], s=60,
edgecolors='red')
plt.legend()
plt.savefig(f'gif/{iteration}_gif.png')
def gen_run_data(dataset, args, rng=None):
"""Generate several noisy datasets and example sequences."""
n_known = get_n_known(dataset, args.p_known)
n_non_test = len(dataset.y_tr)
run_data = []
for _ in range(args.n_repeats):
noisy_dataset, clean, noisy = inject_noise(args, dataset, rng=rng)
if args.noise_type == 'outlier':
n_non_test = len(noisy_dataset.y_tr)
kn = list(sorted(rng.permutation(n_non_test)[:n_known]))
tr = list(sorted(set(range(n_non_test)) - set(kn)))
n_iters = min(args.max_iters, len(tr))
indices = list(rng.permutation(tr)[:n_iters])
if args.ce_precision:
noisy_dataset.X_tr[indices] = dataset.X_tr[indices]
noisy_dataset.y_tr[indices] = dataset.y_tr[indices]
noisy = list(set(noisy) - set(indices))
run_data.append((noisy_dataset, noisy, kn, indices))
return run_data
def eval_negotiation(args, if_config):
"""Measures the impact of negotiation on learning."""
rng = np.random.RandomState(args.seed)
# Builds noisy datasets and example sequence for all the reruns
print('builds datasets')
dataset = DATASETS[args.dataset]()
if args.noise_type == 'outlier':
# reduce size of dataset to speed up computation
n_ex = int(args.p_known + args.max_iters + 50)
indices = list(rng.permutation(list(set(range(dataset.X_tr.shape[0]))))[:n_ex])
dataset.X_tr, dataset.y_tr = dataset.X_tr[indices], dataset.y_tr[indices]
run_data = gen_run_data(dataset, args, rng=rng)
# Build and save the untrained model
model = make_model(args.model, dataset)
initial_weights = model.get_weights()
# df = pd.DataFrame()
# for iteration, (_, _, _, indices) in enumerate(run_data):
# df[str(iteration)] = indices
# df.to_csv(f'results/indices{_get_basename(args)}.csv')
print('Start runs')
traces = [
_negotiate(model,
initial_weights,
dataset,
noisy_dataset,
noisy,
kn,
indices,
args.threshold,
if_config,
args,
rng=rng)
for noisy_dataset, noisy, kn, indices in run_data
]
dump(os.path.join('results', _get_basename(args) + '.pickle'), {'args': args, 'traces': traces})
def find_threshold(args, if_config):
"""Finds a threshold that makes the inspector."""
rng = np.random.RandomState(args.seed)
# Load clean dataset
dataset = DATASETS[args.dataset]()
run_data = gen_run_data(dataset, args, rng=rng)
# Build and save the untrained model
model = make_model(args.model, dataset)
initial_weights = model.get_weights()
# Compute suspiciousnesses
values = np.concatenate([
_negotiate(model,
initial_weights,
dataset,
noisy_dataset,
noisy,
kn,
indices,
args.threshold,
if_config,
args,
return_suspiciousnesses=True,
rng=rng)
for noisy_dataset, noisy, kn, indices in run_data
])
# Look for a threshold that catches ~half the # of mislabeled examples
n_noisy = int(len(values) * args.p_noise)
ideal_n_of_queries = n_noisy // 2
best_loss, best_value = np.inf, None
for value in sorted(values):
n_suspicious = len([v for v in values if v > value])
loss = np.abs(ideal_n_of_queries - n_suspicious)
if loss < best_loss:
best_loss, best_value = loss, value
print(f'threshold {best_value} ({best_loss})')
# ===========================================================================
def get_logreg_params(dataset, kn):
"""Fits logistic regression to a local optimum, helps with Hessian."""
C = 1 / (len(kn) * 1)
lr = LogisticRegression(penalty='l2',
tol=1e-8,
C=C,
solver='lbfgs',
max_iter=1000,
fit_intercept=False,
multi_class='auto',
# none for binary, multinomial otherwise
warm_start=False,
verbose=1)
lr.fit(dataset.X_tr[kn].reshape(len(kn), -1),
np.argmax(dataset.y_tr[kn], axis=1))
w, b = lr.coef_, lr.intercept_
if w.shape[0] == 1: # binary classification
w = np.concatenate([-w, w], axis=0)
b = np.concatenate([-b, b], axis=0)
return w.T, b
def eval_fisher_and_influence(args, if_config):
"""Measures the correlation between IF and parameter/output changes and between
fisher kernel and output changes."""
rng = np.random.RandomState(args.seed)
# Build a subsampled noisy dataset
dataset = DATASETS[args.dataset]()
subsample_train(dataset, args.p_known, rng=rng)
noisy_dataset, clean, noisy = inject_noise(args, dataset, rng=rng)
kn = list(range(len(dataset.y_tr)))
print(f'{len(kn)} examples, {len(noisy)} are noisy')
# Build and train model
model = make_model(args.model, dataset)
model.fit(noisy_dataset.X_tr[kn],
noisy_dataset.y_tr[kn],
epochs=args.n_epochs,
verbose=0)
if args.model == 'logreg':
w, b = get_logreg_params(noisy_dataset, kn)
model.get_layer('hack').set_weights([w, b])
# Measure difference between removing a point and IF at i_test
y_hat = model.predict(dataset.X_ts)
ee = np.where(np.argmax(y_hat, axis=1) != np.argmax(dataset.y_ts, axis=1))
i_test = ee[0][0]
print(i_test)
# i_test = 0
loss = model.loss(model(noisy_dataset.X_ts[None, i_test]),
noisy_dataset.y_ts[None, i_test])
coords_inf = []
coords_fisher = []
corrds_fisher_mistake = []
try:
e = 0
for i in rng.permutation(kn):
if np.argmax(noisy_dataset.y_tr[i]) != np.argmax(y_hat[i_test]):
continue
if e == FEW:
break
print(e, FEW)
e += 1
# Compute loss at i_test after retraining
kn_minus_i = list(sorted(set(kn) - {i}))
model_minus_i = make_model(args.model, dataset)
model_minus_i.fit(noisy_dataset.X_tr[kn_minus_i],
noisy_dataset.y_tr[kn_minus_i],
epochs=args.n_epochs,
verbose=0)
if args.model == 'logreg':
w, b = get_logreg_params(noisy_dataset, kn_minus_i)
model_minus_i.get_layer('hack').set_weights([w, b])
loss_i = model.loss(model_minus_i(noisy_dataset.X_ts[None, i_test]),
noisy_dataset.y_ts[None, i_test])
# Approximate loss at i_test using IF
if_model = InfluenceModel(model,
noisy_dataset.X_tr,
noisy_dataset.y_tr,
noisy_dataset.X_ts,
noisy_dataset.y_ts,
model.loss,
**if_config)
if_loss = if_model.get_influence_on_loss(i, i_test, known=kn)
coords_inf.append((loss_i - loss, if_loss))
fisher = get_fisher_kernel_on_test_point(model, i, i_test, kn,
noisy_dataset.X_tr,
noisy_dataset.y_tr,
noisy_dataset.X_ts,
noisy_dataset.y_ts,
dataset.n_classes,
args.negotiator,
rng)
if np.argmax(dataset.y_tr[i]) == np.argmax(noisy_dataset.y_tr[i]):
coords_fisher.append((loss_i - loss, fisher))
else:
corrds_fisher_mistake.append((loss_i - loss, fisher))
except KeyboardInterrupt:
print('exit')
pass
coords_inf = | np.array(coords_inf) | numpy.array |
# -*- coding: utf-8 -*-
from abc import ABC, abstractmethod
import numpy as np
import cvxpy as cp
from sklearn_lvq import GlvqModel, GmlvqModel
from tree import get_leafs_from_tree
class HighDensityEllipsoids:
def __init__(self, X, X_densities, cluster_probs, means, covariances, density_threshold=None):
self.X = X
self.X_densities = X_densities
self.density_threshold = density_threshold if density_threshold is not None else float("-inf")
self.cluster_probs = cluster_probs
self.means = means
self.covariances = covariances
self.t = 0.9
self.epsilon = 0
def compute_ellipsoids(self):
return self.build_solve_opt()
def _solve(self, prob):
prob.solve(solver=cp.MOSEK, verbose=False)
def build_solve_opt(self):
n_ellipsoids = self.cluster_probs.shape[1]
n_samples = self.X.shape[0]
# Variables
r = cp.Variable(n_ellipsoids, pos=True)
# Construct constraints
constraints = []
for i in range(n_ellipsoids):
mu_i = self.means[i]
cov_i = np.linalg.inv(self.covariances[i])
for j in range(n_samples):
if self.X_densities[j][i] <= self.density_threshold: # At least as good as a requested NLL
x_j = self.X[j,:]
a = (x_j - mu_i)
b = np.dot(a, np.dot(cov_i, a))
constraints.append(b <= r[i])
# Build the final program
f = cp.Minimize(cp.sum(r))
prob = cp.Problem(f, constraints)
# Solve it!
self._solve(prob)
return r.value
class Ellipsoids:
def __init__(self, means, covariances, r, density_estimator):
self.means = means
self.covariances = [np.linalg.inv(cov) for cov in covariances]
self.r = r
self.n_ellipsoids = self.r.shape[0]
self.density_estimator = density_estimator
def score_samples(self, X):
print(X.shape)
pred = []
pred = self.density_estimator.score_samples(X) >= -10
return np.array(pred).astype(np.int)
class FeasibleCounterfactualSoftmax:
def __init__(self, w, b, X, ellipsoids_r, gmm_weights, gmm_means, gmm_covariances, projection_matrix=None, projection_mean_sub=None, density_threshold=-85):
self.w = w
self.b = b
self.kernel_var = 0.2#0.5 # Kernel density estimator
self.X = X
self.gmm_weights = gmm_weights
self.gmm_means = gmm_means
self.gmm_covariances = gmm_covariances
self.ellipsoids_r = ellipsoids_r
self.projection_matrix = np.eye(self.X.shape[1]) if projection_matrix is None else projection_matrix
self.projection_mean_sub = np.zeros(self.X.shape[1]) if projection_mean_sub is None else projection_mean_sub
self.density_constraint = False
self.gmm_cluster_index = 0
self.min_density = density_threshold
self.epsilon = 1e-1
def _build_constraints(self, var_x, y):
constraints = []
if self.w.shape[0] > 1:
for i in range(self.w.shape[0]):
if i != y:
constraints += [(self.projection_matrix @ (var_x - self.projection_mean_sub)).T @ (self.w[i,:] - self.w[y,:]) + (self.b[i] - self.b[y]) + self.epsilon <= 0]
else:
if y == 0:
return [(self.projection_matrix @ (var_x - self.projection_mean_sub)).T @ self.w.reshape(-1, 1) + self.b + self.epsilon <= 0]
else:
return [(self.projection_matrix @ (var_x - self.projection_mean_sub)).T @ self.w.reshape(-1, 1) + self.b - self.epsilon >= 0]
return constraints
def compute_counterfactual(self, x, y_target, regularizer="l1", use_density_constraints=False):
self.density_constraint = use_density_constraints
mad = None
if regularizer == "l1":
mad = np.ones(x.shape[0])
xcf = None
s = float("inf")
for i in range(self.gmm_weights.shape[0]):
try:
self.gmm_cluster_index = i
xcf_ = self.build_solve_opt(x, y_target, mad)
if xcf_ is None:
continue
s_ = None
if regularizer == "l1":
s_ = np.sum(np.abs(xcf_ - x))
else:
s_ = np.linalg.norm(xcf_ - x, ord=2)
if s_ <= s:
s = s_
xcf = xcf_
except Exception as ex:
print(ex)
return xcf
def _solve(self, prob):
prob.solve(solver=cp.MOSEK, verbose=False)
def build_solve_opt(self, x_orig, y, mad=None):
dim = x_orig.shape[0]
n_samples = self.X.shape[0]
# Variables
x = cp.Variable(dim)
beta = cp.Variable(dim)
t = cp.Variable()
# Constants
c = np.ones(dim)
z = np.zeros(dim)
I = np.eye(dim)
C = 1
C_diag = C * np.eye(dim)
# Construct constraints
constraints = self._build_constraints(x, y)
if self.density_constraint is True:
i = self.gmm_cluster_index
x_i = self.gmm_means[i]
w_i = self.gmm_weights[i]
cov = self.gmm_covariances[i]
cov = np.linalg.inv(cov)
constraints += [cp.quad_form(self.projection_matrix @ (x - self.projection_mean_sub) - x_i, cov) - self.ellipsoids_r[i] + self.epsilon <= 0] # Numerically much more stable than the explicit density omponent constraint
# If necessary, construct the weight matrix for the weighted Manhattan distance
Upsilon = None
if mad is not None:
alpha = 1. / mad
Upsilon = np.diag(alpha)
# Build the final program
f = None
if mad is not None:
f = cp.Minimize(c.T @ beta) # Minimize (weighted) Manhattan distance
constraints += [Upsilon @ (x - x_orig) <= beta, (-1. * Upsilon) @ (x - x_orig) <= beta, I @ beta >= z]
else:
f = cp.Minimize((1/2)*cp.quad_form(x, I) - x_orig.T@x) # Minimize L2 distance
prob = cp.Problem(f, constraints)
# Solve it!
self._solve(prob)
return x.value
class FeasibleCounterfactualOfDecisionTree:
def __init__(self, model, X, ellipsoids_r, gmm_weights, gmm_means, gmm_covariances, projection_matrix=None, projection_mean_sub=None, density_threshold=-85):
self.model = model
self.kernel_var = 0.2 # Kernel density estimator
self.X = X
self.gmm_weights = gmm_weights
self.gmm_means = gmm_means
self.gmm_covariances = gmm_covariances
self.ellipsoids_r = ellipsoids_r
self.projection_matrix = np.eye(self.X.shape[1]) if projection_matrix is None else projection_matrix
self.projection_mean_sub = np.zeros(self.X.shape[1]) if projection_mean_sub is None else projection_mean_sub
self.density_constraint = False
self.gmm_cluster_index = 0
self.min_density = density_threshold
self.epsilon = 0
self.epsilon_plausibility = 1e-5
def _solve(self, prob):
prob.solve(solver=cp.MOSEK, verbose=False)
def _build_constraints(self, var_x, y_target, path_to_leaf):
constraints = []
for j in range(0, len(path_to_leaf) - 1):
feature_id = path_to_leaf[j][1]
threshold = path_to_leaf[j][2]
direction = path_to_leaf[j][3]
if direction == "<":
constraints.append((self.projection_matrix @ var_x)[feature_id] + self.epsilon <= threshold)
elif direction == ">":
constraints.append((self.projection_matrix @ var_x)[feature_id] - self.epsilon >= threshold)
return constraints
def build_solve_opt(self, x_orig, y, path_to_leaf, mad=None):
dim = x_orig.shape[0]
n_samples = self.X.shape[0]
# Variables
x = cp.Variable(dim)
beta = cp.Variable(dim)
t = cp.Variable()
# Constants
c = np.ones(dim)
z = | np.zeros(dim) | numpy.zeros |
#!/usr/bin/env python2.7
import sys
from os.path import dirname
sys.path.append(dirname("/home/hello-robot/stretch_ros/stretch_funmap"))
from tkinter import N
import firebase_admin
from firebase_admin import credentials, db
from math import cos, sin
import rospy
import actionlib
from sensor_msgs.msg import JointState
from geometry_msgs.msg import Transform, TransformStamped, PoseWithCovarianceStamped, PoseStamped, Pose, PointStamped
from nav_msgs.msg import Odometry
from move_base_msgs.msg import MoveBaseAction, MoveBaseResult, MoveBaseFeedback
from nav_msgs.srv import GetPlan
from nav_msgs.msg import Path
from sensor_msgs.msg import PointCloud2
from visualization_msgs.msg import Marker, MarkerArray
from std_srvs.srv import Trigger, TriggerResponse, TriggerRequest
from tf.transformations import euler_from_quaternion
from tf2_geometry_msgs import do_transform_pose
import numpy as np
import scipy.ndimage as nd
import cv2
import math
import time
import threading
import sys
import os
import copy
import tf_conversions
import ros_numpy
import tf2_ros
import argparse as ap
import hello_helpers.hello_misc as hm
import hello_helpers.hello_ros_viz as hr
import stretch_funmap.merge_maps as mm
import stretch_funmap.navigate as nv
import stretch_funmap.mapping as ma
import stretch_funmap.segment_max_height_image as sm
import stretch_funmap.navigation_planning as na
import stretch_funmap.manipulation_planning as mp
import touri_planner
def create_map_to_odom_transform(t_mat):
t = TransformStamped()
t.header.stamp = rospy.Time.now()
t.header.frame_id = 'map'
t.child_frame_id = 'odom'
t.transform = ros_numpy.msgify(Transform, t_mat)
return t
def print_divider():
print("\n#######################################################\n")
def divided_print(input_val):
print("\n#######################################################")
print(input_val)
print("#######################################################\n")
class ManipulationNode(hm.HelloNode):
def __init__(self):
hm.HelloNode.__init__(self)
self.debug_directory = None
def actuate(self, lift, extend, yaw = 0, grip = 0.05, base_linear = 0, base_rotation = 0):
assert lift >= 0.2
pose = {
'joint_lift': lift,
'wrist_extension': extend,
# 'joint_wrist_yaw': yaw,
# 'translate_mobile_base': base_linear,
'rotate_mobile_base': base_rotation,
# 'joint_gripper_finger_left' : grip,
}
self.move_to_pose(pose)
########################################################################################################################
def dance(self):
self.actuate(lift=0.3, extend=0, yaw=0.5, grip=0.05, base_linear=5, base_rotation=3)
self.actuate(lift=0.4, extend=0.3, yaw=0, grip=0.05, base_linear=5, base_rotation=3)
self.actuate(lift=0.45, extend=0, yaw=0.5, grip=0.05, base_linear=5, base_rotation=3)
self.actuate(lift=0.5, extend=0.3, yaw=0, grip=0.05, base_linear=5, base_rotation=3)
self.actuate(lift=0.55, extend=0, yaw=0.5, grip=0.05, base_linear=5, base_rotation=3)
self.actuate(lift=0.6, extend=0.2, yaw=0, grip=0.05, base_linear=5, base_rotation=3)
########################################################################################################################
def correct_robot_pose(self, original_robot_map_pose_xya, corrected_robot_map_pose_xya):
# Compute and broadcast the corrected transformation from
# the map frame to the odom frame.
print('original_robot_map_pose_xya =', original_robot_map_pose_xya)
print('corrected_robot_map_pose_xya =', corrected_robot_map_pose_xya)
x_delta = corrected_robot_map_pose_xya[0] - original_robot_map_pose_xya[0]
y_delta = corrected_robot_map_pose_xya[1] - original_robot_map_pose_xya[1]
ang_rad_correction = hm.angle_diff_rad(corrected_robot_map_pose_xya[2], original_robot_map_pose_xya[2])
c = np.cos(ang_rad_correction)
s = np.sin(ang_rad_correction)
rot_mat = np.array([[c, -s], [s, c]])
x_old, y_old, a_old = original_robot_map_pose_xya
xy_old = np.array([x_old, y_old])
tx, ty = np.matmul(rot_mat, -xy_old) + np.array([x_delta, y_delta]) + xy_old
t = | np.identity(4) | numpy.identity |
# Author: <NAME> <<EMAIL>>
from itertools import cycle
import numpy as np
from sklearn.utils import check_random_state
from .utils.optimization import global_optimization
class BayesianOptimizer(object):
"""Bayesian optimization for global black-box optimization
Bayesian optimization models the landscape of the function to be optimized
internally by a surrogate model (typically a Gaussian process) and
evaluates always those parameters which are considered as global optimum
of an acquisition function defined over this surrogate model. Different
acquisition functions and optimizers can be used internally.
Bayesian optimization aims at reducing the number of evaluations of the
actual function, which is assumed to be costly. To achieve this, a large
computational budget is allocated at modelling the true function and finding
potentially optimal positions based on this model.
.. seealso:: Brochu, Cora, de Freitas
"A tutorial on Bayesian optimization of expensive cost
functions, with application to active user modelling and
hierarchical reinforcement learning"
Parameters
----------
model : surrogate model object
The surrogate model which is used to model the objective function. It
needs to provide a methods fit(X, y) for training the model and
predictive_distribution(X) for determining the predictive distribution
(mean, std-dev) at query point X.
acquisition_function : acquisition function object
When called, this function returns the acquisitability of a query point
i.e., how favourable it is to perform an evaluation at the query point.
For this, internally the trade-off between exploration and exploitation
is handled.
optimizer: string, default: "direct"
The optimizer used to identify the maximum of the acquisition function.
The optimizer is specified by a string which may be any of "direct",
"direct+lbfgs", "random", "random+lbfgs", "cmaes", or "cmaes+lbfgs".
maxf: int, default: 1000
The maximum number of evaluations of the acquisition function by the
optimizer.
initial_random_samples: int, default: 5
The number of initial sample, in which random query points are selected
without using the acquisition function. Setting this to values larger
than 0 might be required if the surrogate model needs to be trained
on datapoints before evaluating it.
random_state : RandomState or int (default: None)
Seed for the random number generator.
"""
def __init__(self, model, acquisition_function, optimizer="direct",
maxf=1000, initial_random_samples=5, random_state=0,
*args, **kwargs):
self.model = model
self.acquisition_function = acquisition_function
self.optimizer = optimizer
self.maxf = maxf
self.initial_random_samples = initial_random_samples
self.rng = check_random_state(random_state)
self.X_ = []
self.y_ = []
def select_query_point(self, boundaries,
incumbent_fct=lambda y: np.max(y)):
""" Select the next query point in boundaries based on acq. function.
Parameters
----------
boundaries : ndarray-like, shape: [n_dims, 2]
Box constraint on allowed query points. First axis corresponds
to dimensions of the search space and second axis to minimum and
maximum allowed value in the respective dimensions.
incumbent_fct: function, default: returns maximum observed value
A function which is used to determine the incumbent for the
acquisition function. Defaults to the maximum observed value.
"""
boundaries = | np.asarray(boundaries) | numpy.asarray |
# -*- coding: utf-8 -*-
# Copyright 2020 The PsiZ Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ============================================================================
"""Module for preprocessing observations.
Functions:
identify_catch_trials: Identify catch trials.
grade_catch_trials: Identify and grade catch trials.
quality_control: Remove observations belonging to agents that do
not meet quality control standards.
remove_catch_trials: Remove catch trials.
"""
from pathlib import Path
import numpy as np
import pandas as pd
def identify_catch_trials(obs):
"""Identify catch trials.
Catch trials are assumed to be any trial where at least one of the
references is the same stimulus as the query.
Arguments:
obs: A psiz.trials.RankObservations object.
Returns:
is_catch: Boolean array indicating catch trial locations.
shape = (n_trial,)
"""
n_trial = obs.n_trial
is_catch = np.zeros([n_trial], dtype=bool)
for i_trial in range(n_trial):
# Determine which references are identical to the query.
is_identical = np.equal(
obs.stimulus_set[i_trial, 0], obs.stimulus_set[i_trial, 1:]
)
if | np.sum(is_identical) | numpy.sum |
import os
import re
from operator import itemgetter
import numpy as np
from deoplete.source.base import Base
class Source(Base):
def __init__(self, vim):
super().__init__(vim)
self.name = 'totolot'
self.filetypes = ['ruby']
self.mark = '[ruby-dictionary3]'
rubymatch = [r'\.[a-zA-Z0-9_?!]*|[a-zA-Z]\w*::\w*']
regexmatch = [r'[<a-zA-Z(?: .+?)?>.*?<\/a-zA-Z>]']
self.input_pattern = '|'.join(rubymatch + regexmatch)
self.rank = 500
def get_complete_position(self, context):
m = re.search('[a-zA-Z0-9_?!]*$', context['input'])
return m.start() if m else -1
def gather_candidates(self, context):
try:
rel_path = "repos/github.com/takkii/ruby-dictionary3/"
paths = [os.path.expanduser(os.path.join(p, rel_path)) for p in [
"~/.cache/dein/",
"~/.local/share/dein/",
"~/.config/nvim/.cache/dein/",
"~/.config/nvim/",
"~/.vim/bundles"
]]
path = next(p for p in paths if os.path.exists(p))
ruby_method = open(os.path.join(path, "autoload/source/ruby_method_deoplete"))
rubymotion_method = open(os.path.join(path, "autoload/source/rubymotion_method"))
rurima_list = open(os.path.join(path, "autoload/source/rurima_list"))
index_ruby = list(ruby_method.readlines()) + list(rubymotion_method.readlines()) + list(
rurima_list.readlines())
sort_ruby = | np.array(index_ruby) | numpy.array |
import typing
import numpy as np
import scipy.special
from fourier_accountant.plds import PrivacyLossDistribution, PrivacyException, DiscretePrivacyLossDistribution
__all__ = ['get_delta_upper_bound', 'get_delta_lower_bound', 'get_epsilon_upper_bound', 'get_epsilon_lower_bound']
def _get_ps_and_Lxs(
pld: PrivacyLossDistribution, omegas: np.ndarray, omega_Lxs: np.ndarray
) -> typing.Tuple[np.ndarray, np.ndarray]:
""" Get the best representation of privacy loss probability mass for computing
error term.
For computation of the delta error term, these are not required to be discretised
to regular intervals, so more efficient representations are possible.
Args:
- pld: Privacy loss distribution instance.
- omegas: Discretized privacy loss probability masses.
- omega_Lxs: Probability loss values corresponding to positions in `omegas`.
Returns:
- ps: Probability mass function for privacy loss values.
- Lxs: The corresponding privacy loss values.
"""
# todo(lumip): This should ideally be bundled in the error computation,
# but that would make that function's interface quite bloated, which indicates
# it should be part of PLD classes. However, that would in turn strongly
# couple those with the accountant computations - tricky...
if isinstance(pld, DiscretePrivacyLossDistribution):
# if pld is a DiscretePrivacyLossDistribution we can get
# privacy loss values and corresponding probabilities directly for
# the error computation and don't need to rely on the discretisation.
# these will typically be smaller arrays and thus faster to compute on.
Lxs = pld.privacy_loss_values
ps = pld.privacy_loss_probabilities
else:
ps = omegas
Lxs = omega_Lxs
return ps, Lxs
def _get_delta_error_term(
Lxs: typing.Sequence[float],
ps: typing.Sequence[float],
num_compositions: int = 500,
L: float = 20.0,
lambd: typing.Optional[float] = None
) -> float:
""" Computes the total error term for δ computed by the Fourier accountant
for repeated application of a privacy mechanism.
The computation follows Theorem 7 in Koskela & Honkela, "Computing Differential Privacy for
Heterogeneous Compositions Using FFT", 2021, arXiv preprint, https://arxiv.org/abs/2102.12412 .
Args:
- Lxs: Sequence of privacy loss values.
- ps: Sequence of privacy loss probability masses.
- num_compositions: The number of compositions (=applications) of the privacy mechanism.
- L: The truncation threshold (in privacy loss space) used by the accountant.
- lambd: The parameter λ for error estimation.
"""
if lambd is None:
lambd = .5 * L
assert np.size(ps) == np.size(Lxs)
nonzero_probability_filter = ~np.isclose(ps, 0)
ps = ps[nonzero_probability_filter]
Lxs = Lxs[nonzero_probability_filter]
assert np.all(ps > 0)
# Compute the lambda-divergence \alpha^+
alpha_plus = scipy.special.logsumexp(np.log(ps) + lambd * Lxs)
# Compute the lambda-divergence \alpha^-
alpha_minus = scipy.special.logsumexp(np.log(ps) - lambd * Lxs)
k = num_compositions
common_factor_log = -(L * lambd + np.log1p(-np.exp(-2 * L * lambd)))
T1_log = k * alpha_plus + common_factor_log
T2_log = k * alpha_minus + common_factor_log
T_max_log = np.maximum(T1_log, T2_log)
error_term = np.exp(T_max_log) * (np.exp(T1_log - T_max_log) + np.exp(T2_log - T_max_log))
return error_term
def _delta_fft_computations(omegas: np.ndarray, num_compositions: int) -> np.ndarray:
""" Core computation of privacy loss distribution convolutions using FFT.
Args:
- omegas: Numpy array of probability masses omega for discrete bins of privacy loss values
for a single invocation of a privacy mechanism.
- num_compositions: The number of sequential invocations of the privacy mechanism.
Returns:
- Numpy array of probability masses for the discrete bins of privacy loss values
after `num_compositions` sequential invocations of the privacy mechanisms
characterized by `omegas`.
"""
# Flip omegas, i.e. fx <- D(omega_y), the matrix D = [0 I;I 0]
nx = len(omegas)
assert nx % 2 == 0
half = nx // 2
fx = np.concatenate((omegas[half:], omegas[:half]))
assert np.size(fx) == np.size(omegas)
# Compute the DFT
FF1 = np.fft.rfft(fx)
# Take elementwise powers and compute the inverse DFT
cfx = np.real(np.fft.irfft((FF1 ** num_compositions)))
# Flip again, i.e. cfx <- D(cfx), D = [0 I;I 0]
cfx = np.concatenate((cfx[half:], cfx[:half]))
return cfx # todo(lumip): there are sometimes values < 0, all quite small, probably should be 0 but numerical precision strikes... problem?
def _compute_delta(
convolved_omegas: np.ndarray, target_eps: float, L: float, compute_derivative: bool=False
) -> typing.Union[float, typing.Tuple[float, float]]:
""" Compute delta from privacy loss probability masses.
Args:
- convolved_omegas: Numpy array of probability masses after convolving all
privacy mechanism invocations.
- target_eps: The targeted epsilon to compute delta for.
- L: The bound for the discretisation interval.
- compute_derivative: If True, additionally return the derivative of delta with
respect to epsilon.
Returns:
- delta: The computed delta.
- ddelta (Optional, if `compute_derivative = True`): The derivative of delta wrt epsilon.
"""
nx = len(convolved_omegas)
# Evaluate \delta(target_eps)
x = np.linspace(-L, L, nx, endpoint=False) # grid for the numerical integration
integral_mask = x > target_eps
x = x[integral_mask]
convolved_omegas = convolved_omegas[integral_mask]
dexp_e = -np.exp(target_eps - x)
exp_e = 1 + dexp_e
assert np.all(exp_e > 0)
integrand = exp_e * convolved_omegas
assert np.all(~(integrand < 0 ) | np.isclose(integrand, 0)), "encountered negative values in pld after composition"
delta = np.sum(integrand)
if not compute_derivative:
return delta
dintegrand = dexp_e * convolved_omegas
ddelta = np.sum(dintegrand)
return delta, ddelta
def get_delta_upper_bound(
pld: PrivacyLossDistribution,
target_eps: float,
num_compositions: int,
num_discretisation_bins_half: int = int(1E6),
L: float = 20.0
):
""" Computes the upper bound for privacy parameter δ for repeated application
of a privacy mechanism.
The computation follows the Fourier accountant method described in Koskela et al.,
"Tight Differential Privacy for Discrete-Valued Mechanisms and for the Subsampled
Gaussian Mechanism Using FFT", Proceedings of The 24th International Conference
on Artificial Intelligence and Statistics, PMLR 130:3358-3366, 2021.
Args:
- pld: The privacy loss distribution of a single application of the privacy mechanism.
- target_eps: The privacy parameter ε for which to compute δ.
- num_compositions: The number of compositions (=applications) of the privacy mechanism.
- num_discretisation_bins_half: The number of discretisation bins used by the accountant, divided by 2.
- L: The truncation threshold (in privacy loss space) used by the accountant.
"""
# obtain discretized privacy loss densities
_, omega_y, Lxs = pld.discretize_privacy_loss_distribution(-L, L, num_discretisation_bins_half)
# compute delta
convolved_omegas = _delta_fft_computations(omega_y, num_compositions)
delta = _compute_delta(convolved_omegas, target_eps, L)
ps, Lxs = _get_ps_and_Lxs(pld, omega_y, Lxs)
error_term = _get_delta_error_term(Lxs, ps, num_compositions, L)
delta += error_term
return | np.clip(delta, 0., 1.) | numpy.clip |
import numpy as np
import random
import keras
import matplotlib.pyplot as plt
from keras.datasets import mnist
from keras.models import Sequential, Model
from keras.layers.core import Dense, Dropout, Activation
from keras.optimizers import RMSprop
from keras.utils import np_utils
(X_train, y_train), (X_test, y_test) = mnist.load_data()
print(X_train.shape, y_train.shape)
print(X_test.shape, y_test.shape)
X_train = X_train.reshape(X_train.shape[0], -1) # 等价于X_train = X_train.reshape(60000,784)
X_test = X_test.reshape(X_test.shape[0], -1) # 等价于X_test = X_test.reshape(10000,784)
X_train = X_train.astype("float32")
X_test = X_test.astype("float32")
X_train /= 255
X_test /= 255
y_train = np_utils.to_categorical(y_train, num_classes=10)
y_test = np_utils.to_categorical(y_test, num_classes=10)
model = Sequential()
model.add(Dense(512, input_shape=(784,)))
model.add(Activation('relu'))
model.add(Dropout(0.2))
model.add(Dense(512))
model.add(Activation('relu'))
model.add(Dropout(0.2))
model.add(Dense(10))
model.add(Activation('softmax'))
model.summary()
model.compile(loss = 'categorical_crossentropy',
optimizer = 'rmsprop', #RMSprop()
metrics=['accuracy'])
rmsprop = RMSprop(lr=0.001, rho=0.9, epsilon=1e-08, decay=0.0)
# metrics means you want to get more results during the training process
model.compile(optimizer=rmsprop,
loss='categorical_crossentropy',
metrics=['accuracy'])
history = model.fit(X_train, y_train, epochs=10, batch_size=128,
verbose = 1, validation_data=[X_test, y_test])
history.params
score = model.evaluate(X_test, y_test, verbose = 0)
print('Test score:', score[0])
print('Test accuracy:', score[1])
X_test_0 = X_test[0,:].reshape(1,784)
y_test_0 = y_test[0,:]
plt.imshow(X_test_0.reshape([28,28]))
pred = model.predict(X_test_0[:])
print('Label of testing sample', np.argmax(y_test_0))
print('Output of the softmax layer', pred[0])
print('Network prediction:', | np.argmax([pred[0]]) | numpy.argmax |
import numpy as np
import tensorflow as tf
from tensorflow import keras
import nltk
nltk.download('wordnet')
import json
from nltk.stem import WordNetLemmatizer
import random
import pickle
lemm=WordNetLemmatizer()
def load_chatbot(path):
model = keras.models.load_model(path)
return model
def input_bag(sen,words):
bag=[0]*len(words)
wrds=nltk.word_tokenize(sen)
wrds=[lemm.lemmatize(w.lower()) for w in wrds]
for s in wrds:
for i,j in enumerate(words):
if j==s:
bag[i]=1
return ( | np.array(bag) | numpy.array |
# -*- coding: utf-8 -*-
"""
Created on Fri May 30 16:22:29 2014
Author: <NAME>
License: BSD-3
"""
from io import StringIO
import numpy as np
from numpy.testing import assert_allclose, assert_equal, assert_
import pandas as pd
import patsy
import pytest
from statsmodels.discrete.discrete_model import Poisson
from statsmodels.genmod.generalized_linear_model import GLM
from statsmodels.genmod import families
from statsmodels.base._constraints import fit_constrained
from statsmodels.tools.tools import add_constant
from statsmodels import datasets
from .results import results_poisson_constrained as results
from .results import results_glm_logit_constrained as reslogit
spector_data = datasets.spector.load(as_pandas=False)
spector_data.exog = add_constant(spector_data.exog, prepend=False)
DEBUG = False
ss = '''\
agecat smokes deaths pyears
1 1 32 52407
2 1 104 43248
3 1 206 28612
4 1 186 12663
5 1 102 5317
1 0 2 18790
2 0 12 10673
3 0 28 5710
4 0 28 2585
5 0 31 1462'''
data = pd.read_csv(StringIO(ss), delimiter='\t')
data = data.astype(int)
data['logpyears'] = np.log(data['pyears'])
class CheckPoissonConstrainedMixin(object):
def test_basic(self):
res1 = self.res1
res2 = self.res2
assert_allclose(res1[0], res2.params[self.idx], rtol=1e-6)
# see below Stata has nan, we have zero
bse1 = np.sqrt(np.diag(res1[1]))
mask = (bse1 == 0) & np.isnan(res2.bse[self.idx])
assert_allclose(bse1[~mask], res2.bse[self.idx][~mask], rtol=1e-6)
def test_basic_method(self):
if hasattr(self, 'res1m'):
res1 = (self.res1m if not hasattr(self.res1m, '_results')
else self.res1m._results)
res2 = self.res2
assert_allclose(res1.params, res2.params[self.idx], rtol=1e-6)
# when a parameter is fixed, the Stata has bse=nan, we have bse=0
mask = (res1.bse == 0) & np.isnan(res2.bse[self.idx])
assert_allclose(res1.bse[~mask], res2.bse[self.idx][~mask],
rtol=1e-6)
tvalues = res2.params_table[self.idx, 2]
# when a parameter is fixed, the Stata has tvalue=nan,
# we have tvalue=inf
mask = np.isinf(res1.tvalues) & np.isnan(tvalues)
assert_allclose(res1.tvalues[~mask], tvalues[~mask], rtol=1e-6)
pvalues = res2.params_table[self.idx, 3]
# note most pvalues are very small
# examples so far agree at 8 or more decimal, but rtol is stricter
# see above
mask = (res1.pvalues == 0) & np.isnan(pvalues)
assert_allclose(res1.pvalues[~mask], pvalues[~mask], rtol=5e-5)
ci_low = res2.params_table[self.idx, 4]
ci_upp = res2.params_table[self.idx, 5]
ci = np.column_stack((ci_low, ci_upp))
# note most pvalues are very small
# examples so far agree at 8 or more decimal, but rtol is stricter
# see above: nan versus value
assert_allclose(res1.conf_int()[~np.isnan(ci)], ci[~np.isnan(ci)],
rtol=5e-5)
# other
assert_allclose(res1.llf, res2.ll, rtol=1e-6)
assert_equal(res1.df_model, res2.df_m)
# Stata does not have df_resid
df_r = res2.N - res2.df_m - 1
assert_equal(res1.df_resid, df_r)
else:
pytest.skip("not available yet")
def test_other(self):
# some results may not be valid or available for all models
if hasattr(self, 'res1m'):
res1 = self.res1m
res2 = self.res2
if hasattr(res2, 'll_0'):
assert_allclose(res1.llnull, res2.ll_0, rtol=1e-6)
else:
if DEBUG:
import warnings
message = ('test: ll_0 not available, llnull=%6.4F'
% res1.llnull)
warnings.warn(message)
else:
pytest.skip("not available yet")
class TestPoissonConstrained1a(CheckPoissonConstrainedMixin):
@classmethod
def setup_class(cls):
cls.res2 = results.results_noexposure_constraint
# 2 is dropped baseline for categorical
cls.idx = [7, 3, 4, 5, 6, 0, 1]
# example without offset
formula = 'deaths ~ logpyears + smokes + C(agecat)'
mod = Poisson.from_formula(formula, data=data)
# get start_params, example fails to converge on one py TravisCI
k_vars = len(mod.exog_names)
start_params = np.zeros(k_vars)
start_params[0] = np.log(mod.endog.mean())
# if we need it, this is desired params
# p = np.array([-3.93478643, 1.37276214, 2.33077032, 2.71338891,
# 2.71338891, 0.57966535, 0.97254074])
constr = 'C(agecat)[T.4] = C(agecat)[T.5]'
lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr)
cls.res1 = fit_constrained(mod, lc.coefs, lc.constants,
start_params=start_params,
fit_kwds={'method': 'bfgs', 'disp': 0})
# TODO: Newton fails
# test method of Poisson, not monkey patched
cls.res1m = mod.fit_constrained(constr, start_params=start_params,
method='bfgs', disp=0)
@pytest.mark.smoke
def test_summary(self):
# trailing text in summary, assumes it's the first extra string
# NOTE: see comment about convergence in llnull for self.res1m
summ = self.res1m.summary()
assert_('linear equality constraints' in summ.extra_txt)
@pytest.mark.smoke
def test_summary2(self):
# trailing text in summary, assumes it's the first extra string
# NOTE: see comment about convergence in llnull for self.res1m
summ = self.res1m.summary2()
assert_('linear equality constraints' in summ.extra_txt[0])
class TestPoissonConstrained1b(CheckPoissonConstrainedMixin):
@classmethod
def setup_class(cls):
cls.res2 = results.results_exposure_constraint
cls.idx = [6, 2, 3, 4, 5, 0] # 2 is dropped baseline for categorical
# example without offset
formula = 'deaths ~ smokes + C(agecat)'
mod = Poisson.from_formula(formula, data=data,
exposure=data['pyears'].values)
constr = 'C(agecat)[T.4] = C(agecat)[T.5]'
lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr)
cls.res1 = fit_constrained(mod, lc.coefs, lc.constants,
fit_kwds={'method': 'newton',
'disp': 0})
cls.constraints = lc
# TODO: bfgs fails
# test method of Poisson, not monkey patched
cls.res1m = mod.fit_constrained(constr, method='newton',
disp=0)
class TestPoissonConstrained1c(CheckPoissonConstrainedMixin):
@classmethod
def setup_class(cls):
cls.res2 = results.results_exposure_constraint
cls.idx = [6, 2, 3, 4, 5, 0] # 2 is dropped baseline for categorical
# example without offset
formula = 'deaths ~ smokes + C(agecat)'
mod = Poisson.from_formula(formula, data=data,
offset=np.log(data['pyears'].values))
constr = 'C(agecat)[T.4] = C(agecat)[T.5]'
lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr)
cls.res1 = fit_constrained(mod, lc.coefs, lc.constants,
fit_kwds={'method': 'newton',
'disp': 0})
cls.constraints = lc
# TODO: bfgs fails
# test method of Poisson, not monkey patched
cls.res1m = mod.fit_constrained(constr, method='newton', disp=0)
class TestPoissonNoConstrained(CheckPoissonConstrainedMixin):
@classmethod
def setup_class(cls):
cls.res2 = results.results_exposure_noconstraint
cls.idx = [6, 2, 3, 4, 5, 0] # 1 is dropped baseline for categorical
# example without offset
formula = 'deaths ~ smokes + C(agecat)'
mod = Poisson.from_formula(formula, data=data,
offset=np.log(data['pyears'].values))
res1 = mod.fit(disp=0)._results
# res1 is duplicate check, so we can follow the same pattern
cls.res1 = (res1.params, res1.cov_params())
cls.res1m = res1
class TestPoissonConstrained2a(CheckPoissonConstrainedMixin):
@classmethod
def setup_class(cls):
cls.res2 = results.results_noexposure_constraint2
# 2 is dropped baseline for categorical
cls.idx = [7, 3, 4, 5, 6, 0, 1]
# example without offset
formula = 'deaths ~ logpyears + smokes + C(agecat)'
mod = Poisson.from_formula(formula, data=data)
# get start_params, example fails to converge on one py TravisCI
k_vars = len(mod.exog_names)
start_params = np.zeros(k_vars)
start_params[0] = np.log(mod.endog.mean())
# if we need it, this is desired params
# p = np.array([-9.43762015, 1.52762442, 2.74155711, 3.58730007,
# 4.08730007, 1.15987869, 0.12111539])
constr = 'C(agecat)[T.5] - C(agecat)[T.4] = 0.5'
lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr)
cls.res1 = fit_constrained(mod, lc.coefs, lc.constants,
start_params=start_params,
fit_kwds={'method': 'bfgs', 'disp': 0})
# TODO: Newton fails
# test method of Poisson, not monkey patched
cls.res1m = mod.fit_constrained(constr, start_params=start_params,
method='bfgs', disp=0)
class TestPoissonConstrained2b(CheckPoissonConstrainedMixin):
@classmethod
def setup_class(cls):
cls.res2 = results.results_exposure_constraint2
cls.idx = [6, 2, 3, 4, 5, 0] # 2 is dropped baseline for categorical
# example without offset
formula = 'deaths ~ smokes + C(agecat)'
mod = Poisson.from_formula(formula, data=data,
exposure=data['pyears'].values)
constr = 'C(agecat)[T.5] - C(agecat)[T.4] = 0.5'
lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr)
cls.res1 = fit_constrained(mod, lc.coefs, lc.constants,
fit_kwds={'method': 'newton',
'disp': 0})
cls.constraints = lc
# TODO: bfgs fails to converge. overflow somewhere?
# test method of Poisson, not monkey patched
cls.res1m = mod.fit_constrained(constr, method='bfgs', disp=0,
start_params=cls.res1[0])
class TestPoissonConstrained2c(CheckPoissonConstrainedMixin):
@classmethod
def setup_class(cls):
cls.res2 = results.results_exposure_constraint2
cls.idx = [6, 2, 3, 4, 5, 0] # 2 is dropped baseline for categorical
# example without offset
formula = 'deaths ~ smokes + C(agecat)'
mod = Poisson.from_formula(formula, data=data,
offset=np.log(data['pyears'].values))
constr = 'C(agecat)[T.5] - C(agecat)[T.4] = 0.5'
lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr)
cls.res1 = fit_constrained(mod, lc.coefs, lc.constants,
fit_kwds={'method': 'newton', 'disp': 0})
cls.constraints = lc
# TODO: bfgs fails
# test method of Poisson, not monkey patched
cls.res1m = mod.fit_constrained(constr,
method='bfgs', disp=0,
start_params=cls.res1[0])
class TestGLMPoissonConstrained1a(CheckPoissonConstrainedMixin):
@classmethod
def setup_class(cls):
from statsmodels.base._constraints import fit_constrained
cls.res2 = results.results_noexposure_constraint
# 2 is dropped baseline for categorical
cls.idx = [7, 3, 4, 5, 6, 0, 1]
# example without offset
formula = 'deaths ~ logpyears + smokes + C(agecat)'
mod = GLM.from_formula(formula, data=data,
family=families.Poisson())
constr = 'C(agecat)[T.4] = C(agecat)[T.5]'
lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr)
cls.res1 = fit_constrained(mod, lc.coefs, lc.constants,
fit_kwds={'atol': 1e-10})
cls.constraints = lc
cls.res1m = mod.fit_constrained(constr, atol=1e-10)
class TestGLMPoissonConstrained1b(CheckPoissonConstrainedMixin):
@classmethod
def setup_class(cls):
from statsmodels.genmod.generalized_linear_model import GLM
from statsmodels.genmod import families
from statsmodels.base._constraints import fit_constrained
cls.res2 = results.results_exposure_constraint
cls.idx = [6, 2, 3, 4, 5, 0] # 2 is dropped baseline for categorical
# example with offset
formula = 'deaths ~ smokes + C(agecat)'
mod = GLM.from_formula(formula, data=data,
family=families.Poisson(),
offset=np.log(data['pyears'].values))
constr = 'C(agecat)[T.4] = C(agecat)[T.5]'
lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr)
cls.res1 = fit_constrained(mod, lc.coefs, lc.constants,
fit_kwds={'atol': 1e-10})
cls.constraints = lc
cls.res1m = mod.fit_constrained(constr, atol=1e-10)._results
def test_compare_glm_poisson(self):
res1 = self.res1m
res2 = self.res2
formula = 'deaths ~ smokes + C(agecat)'
mod = Poisson.from_formula(formula, data=data,
exposure=data['pyears'].values)
constr = 'C(agecat)[T.4] = C(agecat)[T.5]'
res2 = mod.fit_constrained(constr, start_params=self.res1m.params,
method='newton', warn_convergence=False,
disp=0)
# we get high precision because we use the params as start_params
# basic, just as check that we have the same model
assert_allclose(res1.params, res2.params, rtol=1e-12)
assert_allclose(res1.bse, res2.bse, rtol=1e-11)
# check predict, fitted, ...
predicted = res1.predict()
assert_allclose(predicted, res2.predict(), rtol=1e-10)
assert_allclose(res1.mu, predicted, rtol=1e-10)
assert_allclose(res1.fittedvalues, predicted, rtol=1e-10)
assert_allclose(res2.predict(linear=True), res2.predict(linear=True),
rtol=1e-10)
class CheckGLMConstrainedMixin(CheckPoissonConstrainedMixin):
# add tests for some GLM specific attributes
def test_glm(self):
res2 = self.res2 # reference results
res1 = self.res1m
# FIXME: dont leave commented-out
# assert_allclose(res1.aic, res2.aic, rtol=1e-10) # far away
# Stata aic in ereturn and in estat ic are very different
# we have the same as estat ic
# see issue GH#1733
assert_allclose(res1.aic, res2.infocrit[4], rtol=1e-10)
assert_allclose(res1.bic, res2.bic, rtol=1e-10)
# bic is deviance based
# FIXME: dont leave commented-out
# assert_allclose(res1.bic, res2.infocrit[5], rtol=1e-10)
assert_allclose(res1.deviance, res2.deviance, rtol=1e-10)
# FIXME: dont leave commented-out
# TODO: which chi2 are these
# assert_allclose(res1.pearson_chi2, res2.chi2, rtol=1e-10)
class TestGLMLogitConstrained1(CheckGLMConstrainedMixin):
@classmethod
def setup_class(cls):
cls.idx = slice(None)
# params sequence same as Stata, but Stata reports param = nan
# and we have param = value = 0
cls.res2 = reslogit.results_constraint1
mod1 = GLM(spector_data.endog, spector_data.exog,
family=families.Binomial())
constr = 'x1 = 2.8'
cls.res1m = mod1.fit_constrained(constr)
R, q = cls.res1m.constraints.coefs, cls.res1m.constraints.constants
cls.res1 = fit_constrained(mod1, R, q)
class TestGLMLogitConstrained2(CheckGLMConstrainedMixin):
@classmethod
def setup_class(cls):
cls.idx = slice(None) # params sequence same as Stata
cls.res2 = reslogit.results_constraint2
mod1 = GLM(spector_data.endog, spector_data.exog,
family=families.Binomial())
constr = 'x1 - x3 = 0'
cls.res1m = mod1.fit_constrained(constr, atol=1e-10)
R, q = cls.res1m.constraints.coefs, cls.res1m.constraints.constants
cls.res1 = fit_constrained(mod1, R, q, fit_kwds={'atol': 1e-10})
cls.constraints_rq = (R, q)
def test_predict(self):
# results only available for this case
res2 = self.res2 # reference results
res1 = self.res1m
predicted = res1.predict()
assert_allclose(predicted, res2.predict_mu, atol=1e-7)
assert_allclose(res1.mu, predicted, rtol=1e-10)
assert_allclose(res1.fittedvalues, predicted, rtol=1e-10)
@pytest.mark.smoke
def test_summary(self):
# trailing text in summary, assumes it's the first extra string
summ = self.res1m.summary()
| assert_('linear equality constraints' in summ.extra_txt) | numpy.testing.assert_ |
# Copyright (c) 2019 - The Procedural Generation for Gazebo authors
# For information on the respective copyright owner see the NOTICE file
#
# 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 ...parsers.sdf import create_sdf_element
import os
import collections
import itertools
import re
import rospkg
import numpy as np
from visualization_msgs.msg import Marker
from .mesh import Mesh
from .footprint import Footprint
from ...log import PCG_ROOT_LOGGER
class Geometry(object):
_GEO_TYPES = ['box', 'cylinder', 'sphere', 'plane', 'mesh']
def __init__(self, geo_type=None, **kwargs):
self._sdf = None
self._mesh = None
self._mesh_pkg_name = None
self._mesh_resource = None
self._geo_type = geo_type
if geo_type is not None:
assert geo_type in self._GEO_TYPES, \
'Invalid geometry type, options={}'.format(self._GEO_TYPES)
if geo_type == 'mesh':
self.set_mesh(**kwargs)
else:
self._sdf = create_sdf_element(geo_type)
if len(kwargs):
for tag in kwargs:
self.set_param(tag, kwargs[tag])
if geo_type == 'box':
self._mesh = Mesh.create_box(
size=self.get_param('size'))
elif geo_type == 'cylinder':
self._mesh = Mesh.create_cylinder(
radius=self.get_param('radius'),
height=self.get_param('length'))
elif geo_type == 'sphere':
self._mesh = Mesh.create_sphere(
radius=self.get_param('radius'))
elif geo_type == 'plane':
self._mesh = Mesh.create_box(
size=self.get_param('size') + [0.001])
def get_samples(self):
pnts = None
if self.get_type() == 'sphere':
n = 10
radius = self.get_param('radius')
for theta in np.linspace(0, 2 * np.pi, n / 2):
for psi in np.linspace(0, 2 * np.pi, n / 2):
pnt = np.array([
radius * np.sin(theta) * np.cos(psi),
radius * np.sin(theta) * np.sin(psi),
radius * np.cos(theta)])
if pnts is None:
pnts = pnt
else:
pnts = np.vstack((pnts, pnt))
elif self.get_type() == 'plane':
size = self.get_param('size')
for i in [-size[0] / 2, size[0] / 2]:
for j in [-size[1] / 2, size[1] / 2]:
if pnts is None:
pnts = | np.array([i, j]) | numpy.array |
from __future__ import division
import glob
import numpy as NP
from functools import reduce
import numpy.ma as MA
import progressbar as PGB
import h5py
import healpy as HP
import warnings
import copy
import astropy.cosmology as CP
from astropy.time import Time, TimeDelta
from astropy.io import fits
from astropy import units as U
from astropy import constants as FCNST
from scipy import interpolate
from astroutils import DSP_modules as DSP
from astroutils import constants as CNST
from astroutils import nonmathops as NMO
from astroutils import mathops as OPS
from astroutils import lookup_operations as LKP
import prisim
from prisim import interferometry as RI
from prisim import primary_beams as PB
from prisim import delay_spectrum as DS
try:
from pyuvdata import UVBeam
except ImportError:
uvbeam_module_found = False
else:
uvbeam_module_found = True
prisim_path = prisim.__path__[0]+'/'
cosmoPlanck15 = CP.Planck15 # Planck 2015 cosmology
cosmo100 = cosmoPlanck15.clone(name='Modified Planck 2015 cosmology with h=1.0', H0=100.0) # Modified Planck 2015 cosmology with h=1.0, H= 100 km/s/Mpc
################################################################################
def write_PRISim_bispectrum_phase_to_npz(infile_prefix, outfile_prefix,
triads=None, bltriplet=None,
hdf5file_prefix=None, infmt='npz',
datakey='noisy', blltol=0.1):
"""
----------------------------------------------------------------------------
Write closure phases computed in a PRISim simulation to a NPZ file with
appropriate format for further analysis.
Inputs:
infile_prefix
[string] HDF5 file or NPZ file created by a PRISim simulation or
its replication respectively. If infmt is specified as 'hdf5',
then hdf5file_prefix will be ignored and all the observing
info will be read from here. If infmt is specified as 'npz',
then hdf5file_prefix needs to be specified in order to read the
observing parameters.
triads [list or numpy array or None] Antenna triads given as a list of
3-element lists or a ntriads x 3 array. Each element in the
inner list is an antenna label. They will be converted to
strings internally. If set to None, then all triads determined
by bltriplet will be used. If specified, then inputs in blltol
and bltriplet will be ignored.
bltriplet [numpy array or None] 3x3 numpy array containing the 3 baseline
vectors. The first axis denotes the three baselines, the second
axis denotes the East, North, Up coordinates of the baseline
vector. Units are in m. Will be used only if triads is set to
None.
outfile_prefix
[string] Prefix of the NPZ file. It will be appended by
'_noiseless', '_noisy', and '_noise' and further by extension
'.npz'
infmt [string] Format of the input file containing visibilities.
Accepted values are 'npz' (default), and 'hdf5'. If infmt is
specified as 'npz', then hdf5file_prefix also needs to be
specified for reading the observing parameters
datakey [string] Specifies which -- 'noiseless', 'noisy' (default), or
'noise' -- visibilities are to be written to the output. If set
to None, and infmt is 'hdf5', then all three sets of
visibilities are written. The datakey string will also be added
as a suffix in the output file.
blltol [scalar] Baseline length tolerance (in m) for matching baseline
vectors in triads. It must be a scalar. Default = 0.1 m. Will
be used only if triads is set to None and bltriplet is to be
used.
----------------------------------------------------------------------------
"""
if not isinstance(infile_prefix, str):
raise TypeError('Input infile_prefix must be a string')
if not isinstance(outfile_prefix, str):
raise TypeError('Input outfile_prefix must be a string')
if (triads is None) and (bltriplet is None):
raise ValueError('One of triads or bltriplet must be set')
if triads is None:
if not isinstance(bltriplet, NP.ndarray):
raise TypeError('Input bltriplet must be a numpy array')
if not isinstance(blltol, (int,float)):
raise TypeError('Input blltol must be a scalar')
if bltriplet.ndim != 2:
raise ValueError('Input bltriplet must be a 2D numpy array')
if bltriplet.shape[0] != 3:
raise ValueError('Input bltriplet must contain three baseline vectors')
if bltriplet.shape[1] != 3:
raise ValueError('Input bltriplet must contain baseline vectors along three corrdinates in the ENU frame')
else:
if not isinstance(triads, (list, NP.ndarray)):
raise TypeError('Input triads must be a list or numpy array')
triads = NP.asarray(triads).astype(str)
if not isinstance(infmt, str):
raise TypeError('Input infmt must be a string')
if infmt.lower() not in ['npz', 'hdf5']:
raise ValueError('Input file format must be npz or hdf5')
if infmt.lower() == 'npz':
if not isinstance(hdf5file_prefix, str):
raise TypeError('If infmt is npz, then hdf5file_prefix needs to be specified for observing parameters information')
if datakey is None:
datakey = ['noisy']
if isinstance(datakey, str):
datakey = [datakey]
elif not isinstance(datakey, list):
raise TypeError('Input datakey must be a list')
for dkey in datakey:
if dkey.lower() not in ['noiseless', 'noisy', 'noise']:
raise ValueError('Invalid input found in datakey')
if infmt.lower() == 'hdf5':
fullfnames_with_extension = glob.glob(infile_prefix + '*' + infmt.lower())
fullfnames_without_extension = [fname.split('.hdf5')[0] for fname in fullfnames_with_extension]
else:
fullfnames_without_extension = [infile_prefix]
if len(fullfnames_without_extension) == 0:
raise IOError('No input files found with pattern {0}'.format(infile_prefix))
try:
if infmt.lower() == 'hdf5':
simvis = RI.InterferometerArray(None, None, None, init_file=fullfnames_without_extension[0])
else:
simvis = RI.InterferometerArray(None, None, None, init_file=hdf5file_prefix)
except:
raise IOError('Input PRISim file does not contain a valid PRISim output')
latitude = simvis.latitude
longitude = simvis.longitude
location = ('{0:.5f}d'.format(longitude), '{0:.5f}d'.format(latitude))
last = simvis.lst / 15.0 / 24.0 # from degrees to fraction of day
last = last.reshape(-1,1)
daydata = NP.asarray(simvis.timestamp[0]).ravel()
if infmt.lower() == 'npz':
simvisinfo = NP.load(fullfnames_without_extension[0]+'.'+infmt.lower())
skyvis = simvisinfo['noiseless'][0,...]
vis = simvisinfo['noisy']
noise = simvisinfo['noise']
n_realize = vis.shape[0]
else:
n_realize = len(fullfnames_without_extension)
cpdata = {}
outfile = {}
for fileind in range(n_realize):
if infmt.lower() == 'npz':
simvis.vis_freq = vis[fileind,...]
simvis.vis_noise_freq = noise[fileind,...]
else:
simvis = RI.InterferometerArray(None, None, None, init_file=fullfnames_without_extension[fileind])
if fileind == 0:
if triads is None:
triads, bltriplets = simvis.getThreePointCombinations(unique=False)
# triads = NP.asarray(prisim_BSP_info['antenna_triplets']).reshape(-1,3)
# bltriplets = NP.asarray(prisim_BSP_info['baseline_triplets'])
triads = NP.asarray(triads).reshape(-1,3)
bltriplets = NP.asarray(bltriplets)
blinds = []
matchinfo = LKP.find_NN(bltriplet, bltriplets.reshape(-1,3), distance_ULIM=blltol)
revind = []
for blnum in NP.arange(bltriplet.shape[0]):
if len(matchinfo[0][blnum]) == 0:
revind += [blnum]
if len(revind) > 0:
flip_factor = NP.ones(3, dtype=NP.float)
flip_factor[NP.array(revind)] = -1
rev_bltriplet = bltriplet * flip_factor.reshape(-1,1)
matchinfo = LKP.find_NN(rev_bltriplet, bltriplets.reshape(-1,3), distance_ULIM=blltol)
for blnum in NP.arange(bltriplet.shape[0]):
if len(matchinfo[0][blnum]) == 0:
raise ValueError('Some baselines in the triplet are not found in the model triads')
triadinds = []
for blnum in NP.arange(bltriplet.shape[0]):
triadind, blind = NP.unravel_index(NP.asarray(matchinfo[0][blnum]), (bltriplets.shape[0], bltriplets.shape[1]))
triadinds += [triadind]
triadind_intersection = NP.intersect1d(triadinds[0], NP.intersect1d(triadinds[1], triadinds[2]))
if triadind_intersection.size == 0:
raise ValueError('Specified triad not found in the PRISim model. Try other permutations of the baseline vectors and/or reverse individual baseline vectors in the triad before giving up.')
triads = triads[triadind_intersection,:]
selected_bltriplets = bltriplets[triadind_intersection,:,:].reshape(-1,3,3)
prisim_BSP_info = simvis.getClosurePhase(antenna_triplets=triads.tolist(),
delay_filter_info=None,
specsmooth_info=None,
spectral_window_info=None,
unique=False)
if fileind == 0:
triads = NP.asarray(prisim_BSP_info['antenna_triplets']).reshape(-1,3) # Re-establish the triads returned after the first iteration (to accunt for any order flips)
for outkey in datakey:
if fileind == 0:
outfile[outkey] = outfile_prefix + '_{0}.npz'.format(outkey)
if outkey == 'noiseless':
if fileind == 0:
# cpdata = prisim_BSP_info['closure_phase_skyvis'][triadind_intersection,:,:][NP.newaxis,...]
cpdata[outkey] = prisim_BSP_info['closure_phase_skyvis'][NP.newaxis,...]
else:
# cpdata = NP.concatenate((cpdata, prisim_BSP_info['closure_phase_skyvis'][triadind_intersection,:,:][NP.newaxis,...]), axis=0)
cpdata[outkey] = NP.concatenate((cpdata[outkey], prisim_BSP_info['closure_phase_skyvis'][NP.newaxis,...]), axis=0)
if outkey == 'noisy':
if fileind == 0:
# cpdata = prisim_BSP_info['closure_phase_vis'][triadind_intersection,:,:][NP.newaxis,...]
cpdata[outkey] = prisim_BSP_info['closure_phase_vis'][NP.newaxis,...]
else:
# cpdata = NP.concatenate((cpdata, prisim_BSP_info['closure_phase_vis'][triadind_intersection,:,:][NP.newaxis,...]), axis=0)
cpdata[outkey] = NP.concatenate((cpdata[outkey], prisim_BSP_info['closure_phase_vis'][NP.newaxis,...]), axis=0)
if outkey == 'noise':
if fileind == 0:
# cpdata = prisim_BSP_info['closure_phase_noise'][triadind_intersection,:,:]
cpdata[outkey] = prisim_BSP_info['closure_phase_noise'][NP.newaxis,:,:]
else:
# cpdata = NP.concatenate((cpdata, prisim_BSP_info['closure_phase_noise'][triadind_intersection,:,:][NP.newaxis,...]), axis=0)
cpdata[outkey] = NP.concatenate((cpdata[outkey], prisim_BSP_info['closure_phase_noise'][NP.newaxis,...]), axis=0)
for outkey in datakey:
cpdata[outkey] = NP.rollaxis(cpdata[outkey], 3, start=0)
flagsdata = NP.zeros(cpdata[outkey].shape, dtype=NP.bool)
NP.savez_compressed(outfile[outkey], closures=cpdata[outkey],
flags=flagsdata, triads=triads,
last=last+NP.zeros((1,n_realize)),
days=daydata+NP.arange(n_realize))
################################################################################
def loadnpz(npzfile, longitude=0.0, latitude=0.0, lst_format='fracday'):
"""
----------------------------------------------------------------------------
Read an input NPZ file containing closure phase data output from CASA and
return a dictionary
Inputs:
npzfile [string] Input NPZ file including full path containing closure
phase data. It must have the following files/keys inside:
'closures' [numpy array] Closure phase (radians). It is of
shape (nlst,ndays,ntriads,nchan)
'triads' [numpy array] Array of triad tuples, of shape
(ntriads,3)
'flags' [numpy array] Array of flags (boolean), of shape
(nlst,ndays,ntriads,nchan)
'last' [numpy array] Array of LST for each day (CASA units
which is MJD+6713). Shape is (nlst,ndays)
'days' [numpy array] Array of days, shape is (ndays,)
'averaged_closures'
[numpy array] optional array of closure phases
averaged across days. Shape is (nlst,ntriads,nchan)
'std_dev_lst'
[numpy array] optional array of standard deviation
of closure phases across days. Shape is
(nlst,ntriads,nchan)
'std_dev_triads'
[numpy array] optional array of standard deviation
of closure phases across triads. Shape is
(nlst,ndays,nchan)
latitude [scalar int or float] Latitude of site (in degrees).
Default=0.0 deg.
longitude [scalar int or float] Longitude of site (in degrees).
Default=0.0 deg.
lst_format [string] Specifies the format/units in which the 'last' key
is to be interpreted. If set to 'hourangle', the LST is in
units of hour angle. If set to 'fracday', the fractional
portion of the 'last' value is the LST in units of days.
Output:
cpinfo [dictionary] Contains one top level keys, namely, 'raw'
Under key 'raw' which holds a dictionary, the subkeys
include 'cphase' (nlst,ndays,ntriads,nchan),
'triads' (ntriads,3), 'lst' (nlst,ndays), and 'flags'
(nlst,ndays,ntriads,nchan), and some other optional keys
----------------------------------------------------------------------------
"""
npzdata = NP.load(npzfile)
cpdata = npzdata['closures']
triadsdata = npzdata['triads']
flagsdata = npzdata['flags']
location = ('{0:.5f}d'.format(longitude), '{0:.5f}d'.format(latitude))
daydata = Time(npzdata['days'].astype(NP.float64), scale='utc', format='jd', location=location)
# lstdata = Time(npzdata['last'].astype(NP.float64) - 6713.0, scale='utc', format='mjd', location=('+21.4278d', '-30.7224d')).sidereal_time('apparent') # Subtract 6713 based on CASA convention to obtain MJD
if lst_format.lower() == 'hourangle':
lstHA = npzdata['last']
lstday = daydata.reshape(1,-1) + TimeDelta(NP.zeros(lstHA.shape[0]).reshape(-1,1)*U.s)
elif lst_format.lower() == 'fracday':
lstfrac, lstint = NP.modf(npzdata['last'])
lstday = Time(lstint.astype(NP.float64) - 6713.0, scale='utc', format='mjd', location=location) # Subtract 6713 based on CASA convention to obtain MJD
lstHA = lstfrac * 24.0 # in hours
else:
raise ValueError('Input lst_format invalid')
cp = cpdata.astype(NP.float64)
flags = flagsdata.astype(NP.bool)
cpinfo = {}
datapool = ['raw']
for dpool in datapool:
cpinfo[dpool] = {}
if dpool == 'raw':
qtys = ['cphase', 'triads', 'flags', 'lst', 'lst-day', 'days', 'dayavg', 'std_triads', 'std_lst']
for qty in qtys:
if qty == 'cphase':
cpinfo[dpool][qty] = NP.copy(cp)
elif qty == 'triads':
cpinfo[dpool][qty] = NP.copy(triadsdata)
elif qty == 'flags':
cpinfo[dpool][qty] = NP.copy(flags)
elif qty == 'lst':
cpinfo[dpool][qty] = NP.copy(lstHA)
elif qty == 'lst-day':
cpinfo[dpool][qty] = NP.copy(lstday.jd)
elif qty == 'days':
cpinfo[dpool][qty] = NP.copy(daydata.jd)
elif qty == 'dayavg':
if 'averaged_closures' in npzdata:
cpinfo[dpool][qty] = NP.copy(cp_dayavg)
elif qty == 'std_triads':
if 'std_dev_triad' in npzdata:
cpinfo[dpool][qty] = NP.copy(cp_std_triads)
elif qty == 'std_lst':
if 'std_dev_lst' in npzdata:
cpinfo[dpool][qty] = NP.copy(cp_std_lst)
return cpinfo
################################################################################
def npz2hdf5(npzfile, hdf5file, longitude=0.0, latitude=0.0,
lst_format='fracday'):
"""
----------------------------------------------------------------------------
Read an input NPZ file containing closure phase data output from CASA and
save it to HDF5 format
Inputs:
npzfile [string] Input NPZ file including full path containing closure
phase data. It must have the following files/keys inside:
'closures' [numpy array] Closure phase (radians). It is of
shape (nlst,ndays,ntriads,nchan)
'triads' [numpy array] Array of triad tuples, of shape
(ntriads,3)
'flags' [numpy array] Array of flags (boolean), of shape
(nlst,ndays,ntriads,nchan)
'last' [numpy array] Array of LST for each day (CASA units
ehich is MJD+6713). Shape is (nlst,ndays)
'days' [numpy array] Array of days, shape is (ndays,)
'averaged_closures'
[numpy array] optional array of closure phases
averaged across days. Shape is (nlst,ntriads,nchan)
'std_dev_lst'
[numpy array] optional array of standard deviation
of closure phases across days. Shape is
(nlst,ntriads,nchan)
'std_dev_triads'
[numpy array] optional array of standard deviation
of closure phases across triads. Shape is
(nlst,ndays,nchan)
hdf5file [string] Output HDF5 file including full path.
latitude [scalar int or float] Latitude of site (in degrees).
Default=0.0 deg.
longitude [scalar int or float] Longitude of site (in degrees).
Default=0.0 deg.
lst_format [string] Specifies the format/units in which the 'last' key
is to be interpreted. If set to 'hourangle', the LST is in
units of hour angle. If set to 'fracday', the fractional
portion of the 'last' value is the LST in units of days.
----------------------------------------------------------------------------
"""
npzdata = NP.load(npzfile)
cpdata = npzdata['closures']
triadsdata = npzdata['triads']
flagsdata = npzdata['flags']
location = ('{0:.5f}d'.format(longitude), '{0:.5f}d'.format(latitude))
daydata = Time(npzdata['days'].astype(NP.float64), scale='utc', format='jd', location=location)
# lstdata = Time(npzdata['last'].astype(NP.float64) - 6713.0, scale='utc', format='mjd', location=('+21.4278d', '-30.7224d')).sidereal_time('apparent') # Subtract 6713 based on CASA convention to obtain MJD
if lst_format.lower() == 'hourangle':
lstHA = npzdata['last']
lstday = daydata.reshape(1,-1) + TimeDelta(NP.zeros(lstHA.shape[0]).reshape(-1,1)*U.s)
elif lst_format.lower() == 'fracday':
lstfrac, lstint = NP.modf(npzdata['last'])
lstday = Time(lstint.astype(NP.float64) - 6713.0, scale='utc', format='mjd', location=location) # Subtract 6713 based on CASA convention to obtain MJD
lstHA = lstfrac * 24.0 # in hours
else:
raise ValueError('Input lst_format invalid')
cp = cpdata.astype(NP.float64)
flags = flagsdata.astype(NP.bool)
if 'averaged_closures' in npzdata:
day_avg_cpdata = npzdata['averaged_closures']
cp_dayavg = day_avg_cpdata.astype(NP.float64)
if 'std_dev_triad' in npzdata:
std_triads_cpdata = npzdata['std_dev_triad']
cp_std_triads = std_triads_cpdata.astype(NP.float64)
if 'std_dev_lst' in npzdata:
std_lst_cpdata = npzdata['std_dev_lst']
cp_std_lst = std_lst_cpdata.astype(NP.float64)
with h5py.File(hdf5file, 'w') as fobj:
datapool = ['raw']
for dpool in datapool:
if dpool == 'raw':
qtys = ['cphase', 'triads', 'flags', 'lst', 'lst-day', 'days', 'dayavg', 'std_triads', 'std_lst']
for qty in qtys:
data = None
if qty == 'cphase':
data = NP.copy(cp)
elif qty == 'triads':
data = NP.copy(triadsdata)
elif qty == 'flags':
data = NP.copy(flags)
elif qty == 'lst':
data = NP.copy(lstHA)
elif qty == 'lst-day':
data = NP.copy(lstday.jd)
elif qty == 'days':
data = NP.copy(daydata.jd)
elif qty == 'dayavg':
if 'averaged_closures' in npzdata:
data = NP.copy(cp_dayavg)
elif qty == 'std_triads':
if 'std_dev_triad' in npzdata:
data = NP.copy(cp_std_triads)
elif qty == 'std_lst':
if 'std_dev_lst' in npzdata:
data = NP.copy(cp_std_lst)
if data is not None:
dset = fobj.create_dataset('{0}/{1}'.format(dpool, qty), data=data, compression='gzip', compression_opts=9)
################################################################################
def save_CPhase_cross_power_spectrum(xcpdps, outfile):
"""
----------------------------------------------------------------------------
Save cross-power spectrum information in a dictionary to a HDF5 file
Inputs:
xcpdps [dictionary] This dictionary is essentially an output of the
member function compute_power_spectrum() of class
ClosurePhaseDelaySpectrum. It has the following key-value
structure:
'triads' ((ntriads,3) array), 'triads_ind',
((ntriads,) array), 'lstXoffsets' ((ndlst_range,) array), 'lst'
((nlst,) array), 'dlst' ((nlst,) array), 'lst_ind' ((nlst,)
array), 'days' ((ndays,) array), 'day_ind' ((ndays,) array),
'dday' ((ndays,) array), 'oversampled' and 'resampled'
corresponding to whether resample was set to False or True in
call to member function FT(). Values under keys 'triads_ind'
and 'lst_ind' are numpy array corresponding to triad and time
indices used in selecting the data. Values under keys
'oversampled' and 'resampled' each contain a dictionary with
the following keys and values:
'z' [numpy array] Redshifts corresponding to the band
centers in 'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,)
'kprll' [numpy array] k_parallel modes (in h/Mpc) corresponding
to 'lags'. It has shape=(nspw,nlags)
'freq_center'
[numpy array] contains the center frequencies (in Hz)
of the frequency subbands of the subband delay spectra.
It is of size n_win. It is roughly equivalent to
redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on
each frequency sub-band during the subband delay
transform. It is of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz)
of the subbands being delay transformed. It is of size
n_win. It is roughly equivalent to width in redshift or
along line-of-sight
'shape' [string] shape of the frequency window function applied.
Usual values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was
raised. The value is be a positive scalar with
default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in
pixels) of the subband delay spectra. It is proportional
to inverse of effective bandwidth. It is of size n_win.
The unit size of a pixel is determined by the difference
between adjacent pixels in lags under key 'lags' which
in turn is effectively inverse of the effective
bandwidth of the subband specified in bw_eff
It further contains one or more of the following keys named
'whole', 'submodel', 'residual', and 'errinfo' each of which is
a dictionary. 'whole' contains power spectrum info about the
input closure phases. 'submodel' contains power spectrum info
about the model that will have been subtracted (as closure
phase) from the 'whole' model. 'residual' contains power
spectrum info about the closure phases obtained as a difference
between 'whole' and 'submodel'. It contains the following keys
and values:
'mean' [numpy array] Delay power spectrum incoherently
estimated over the axes specified in xinfo['axes']
using the 'mean' key in input cpds or attribute
cPhaseDS['processed']['dspec']. It has shape that
depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are
not set, those axes will be replaced with square
covariance matrices. If collapse_axes is provided but
avgcov is False, those axes will be of shape 2*Naxis-1.
'median'
[numpy array] Delay power spectrum incoherently averaged
over the axes specified in incohax using the 'median'
key in input cpds or attribute
cPhaseDS['processed']['dspec']. It has shape that
depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are not
set, those axes will be replaced with square covariance
matrices. If collapse_axes is provided bu avgcov is
False, those axes will be of shape 2*Naxis-1.
'diagoffsets'
[dictionary] Same keys corresponding to keys under
'collapse_axes' in input containing the diagonal
offsets for those axes. If 'avgcov' was set, those
entries will be removed from 'diagoffsets' since all the
leading diagonal elements have been collapsed (averaged)
further. Value under each key is a numpy array where
each element in the array corresponds to the index of
that leading diagonal. This should match the size of the
output along that axis in 'mean' or 'median' above.
'diagweights'
[dictionary] Each key is an axis specified in
collapse_axes and the value is a numpy array of weights
corresponding to the diagonal offsets in that axis.
'axesmap'
[dictionary] If covariance in cross-power is calculated
but is not collapsed, the number of dimensions in the
output will have changed. This parameter tracks where
the original axis is now placed. The keys are the
original axes that are involved in incoherent
cross-power, and the values are the new locations of
those original axes in the output.
'nsamples_incoh'
[integer] Number of incoherent samples in producing the
power spectrum
'nsamples_coh'
[integer] Number of coherent samples in producing the
power spectrum
outfile [string] Full path to the external HDF5 file where the cross-
power spectrum information provided in xcpdps will be saved
----------------------------------------------------------------------------
"""
if not isinstance(xcpdps, dict):
raise TypeError('Input xcpdps must be a dictionary')
with h5py.File(outfile, 'w') as fileobj:
hdrgrp = fileobj.create_group('header')
hdrkeys = ['triads', 'triads_ind', 'lst', 'lst_ind', 'dlst', 'days', 'day_ind', 'dday']
for key in hdrkeys:
dset = hdrgrp.create_dataset(key, data=xcpdps[key])
sampling = ['oversampled', 'resampled']
sampling_keys = ['z', 'kprll', 'lags', 'freq_center', 'bw_eff', 'shape', 'freq_wts', 'lag_corr_length']
dpool_keys = ['whole', 'submodel', 'residual', 'errinfo']
for smplng in sampling:
if smplng in xcpdps:
smplgrp = fileobj.create_group(smplng)
for key in sampling_keys:
dset = smplgrp.create_dataset(key, data=xcpdps[smplng][key])
for dpool in dpool_keys:
if dpool in xcpdps[smplng]:
dpoolgrp = smplgrp.create_group(dpool)
keys = ['diagoffsets', 'diagweights', 'axesmap', 'nsamples_incoh', 'nsamples_coh']
for key in keys:
if key in xcpdps[smplng][dpool]:
if isinstance(xcpdps[smplng][dpool][key], dict):
subgrp = dpoolgrp.create_group(key)
for subkey in xcpdps[smplng][dpool][key]:
dset = subgrp.create_dataset(str(subkey), data=xcpdps[smplng][dpool][key][subkey])
else:
dset = dpoolgrp.create_dataset(key, data=xcpdps[smplng][dpool][key])
for stat in ['mean', 'median']:
if stat in xcpdps[smplng][dpool]:
if isinstance(xcpdps[smplng][dpool][stat], list):
for ii in range(len(xcpdps[smplng][dpool][stat])):
dset = dpoolgrp.create_dataset(stat+'/diagcomb_{0}'.format(ii), data=xcpdps[smplng][dpool][stat][ii].si.value)
dset.attrs['units'] = str(xcpdps[smplng][dpool][stat][ii].si.unit)
else:
dset = dpoolgrp.create_dataset(stat, data=xcpdps[smplng][dpool][stat].si.value)
dset.attrs['units'] = str(xcpdps[smplng][dpool][stat].si.unit)
################################################################################
def read_CPhase_cross_power_spectrum(infile):
"""
----------------------------------------------------------------------------
Read information about cross power spectrum from an external HDF5 file into
a dictionary. This is the counterpart to save_CPhase_corss_power_spectrum()
Input:
infile [string] Full path to the external HDF5 file that contains info
about cross-power spectrum.
Output:
xcpdps [dictionary] This dictionary has structure the same as output
of the member function compute_power_spectrum() of class
ClosurePhaseDelaySpectrum. It has the following key-value
structure:
'triads' ((ntriads,3) array), 'triads_ind',
((ntriads,) array), 'lstXoffsets' ((ndlst_range,) array), 'lst'
((nlst,) array), 'dlst' ((nlst,) array), 'lst_ind' ((nlst,)
array), 'days' ((ndays,) array), 'day_ind' ((ndays,) array),
'dday' ((ndays,) array), 'oversampled' and 'resampled'
corresponding to whether resample was set to False or True in
call to member function FT(). Values under keys 'triads_ind'
and 'lst_ind' are numpy array corresponding to triad and time
indices used in selecting the data. Values under keys
'oversampled' and 'resampled' each contain a dictionary with
the following keys and values:
'z' [numpy array] Redshifts corresponding to the band
centers in 'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,)
'kprll' [numpy array] k_parallel modes (in h/Mpc) corresponding
to 'lags'. It has shape=(nspw,nlags)
'freq_center'
[numpy array] contains the center frequencies (in Hz)
of the frequency subbands of the subband delay spectra.
It is of size n_win. It is roughly equivalent to
redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on
each frequency sub-band during the subband delay
transform. It is of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz)
of the subbands being delay transformed. It is of size
n_win. It is roughly equivalent to width in redshift or
along line-of-sight
'shape' [string] shape of the frequency window function applied.
Usual values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was
raised. The value is be a positive scalar with
default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in
pixels) of the subband delay spectra. It is proportional
to inverse of effective bandwidth. It is of size n_win.
The unit size of a pixel is determined by the difference
between adjacent pixels in lags under key 'lags' which
in turn is effectively inverse of the effective
bandwidth of the subband specified in bw_eff
It further contains one or more of the following keys named
'whole', 'submodel', 'residual', and 'errinfo' each of which is
a dictionary. 'whole' contains power spectrum info about the
input closure phases. 'submodel' contains power spectrum info
about the model that will have been subtracted (as closure
phase) from the 'whole' model. 'residual' contains power
spectrum info about the closure phases obtained as a difference
between 'whole' and 'submodel'. It contains the following keys
and values:
'mean' [numpy array] Delay power spectrum incoherently
estimated over the axes specified in xinfo['axes']
using the 'mean' key in input cpds or attribute
cPhaseDS['processed']['dspec']. It has shape that
depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are
not set, those axes will be replaced with square
covariance matrices. If collapse_axes is provided but
avgcov is False, those axes will be of shape 2*Naxis-1.
'median'
[numpy array] Delay power spectrum incoherently averaged
over the axes specified in incohax using the 'median'
key in input cpds or attribute
cPhaseDS['processed']['dspec']. It has shape that
depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are not
set, those axes will be replaced with square covariance
matrices. If collapse_axes is provided bu avgcov is
False, those axes will be of shape 2*Naxis-1.
'diagoffsets'
[dictionary] Same keys corresponding to keys under
'collapse_axes' in input containing the diagonal
offsets for those axes. If 'avgcov' was set, those
entries will be removed from 'diagoffsets' since all the
leading diagonal elements have been collapsed (averaged)
further. Value under each key is a numpy array where
each element in the array corresponds to the index of
that leading diagonal. This should match the size of the
output along that axis in 'mean' or 'median' above.
'diagweights'
[dictionary] Each key is an axis specified in
collapse_axes and the value is a numpy array of weights
corresponding to the diagonal offsets in that axis.
'axesmap'
[dictionary] If covariance in cross-power is calculated
but is not collapsed, the number of dimensions in the
output will have changed. This parameter tracks where
the original axis is now placed. The keys are the
original axes that are involved in incoherent
cross-power, and the values are the new locations of
those original axes in the output.
'nsamples_incoh'
[integer] Number of incoherent samples in producing the
power spectrum
'nsamples_coh'
[integer] Number of coherent samples in producing the
power spectrum
outfile [string] Full path to the external HDF5 file where the cross-
power spectrum information provided in xcpdps will be saved
----------------------------------------------------------------------------
"""
if not isinstance(infile, str):
raise TypeError('Input infile must be a string')
xcpdps = {}
with h5py.File(infile, 'r') as fileobj:
hdrgrp = fileobj['header']
hdrkeys = ['triads', 'triads_ind', 'lst', 'lst_ind', 'dlst', 'days', 'day_ind', 'dday']
for key in hdrkeys:
xcpdps[key] = hdrgrp[key].value
sampling = ['oversampled', 'resampled']
sampling_keys = ['z', 'kprll', 'lags', 'freq_center', 'bw_eff', 'shape', 'freq_wts', 'lag_corr_length']
dpool_keys = ['whole', 'submodel', 'residual', 'errinfo']
for smplng in sampling:
if smplng in fileobj:
smplgrp = fileobj[smplng]
xcpdps[smplng] = {}
for key in sampling_keys:
xcpdps[smplng][key] = smplgrp[key].value
for dpool in dpool_keys:
if dpool in smplgrp:
xcpdps[smplng][dpool] = {}
dpoolgrp = smplgrp[dpool]
keys = ['diagoffsets', 'diagweights', 'axesmap', 'nsamples_incoh', 'nsamples_coh']
for key in keys:
if key in dpoolgrp:
if isinstance(dpoolgrp[key], h5py.Group):
xcpdps[smplng][dpool][key] = {}
for subkey in dpoolgrp[key]:
xcpdps[smplng][dpool][key][int(subkey)] = dpoolgrp[key][subkey].value
elif isinstance(dpoolgrp[key], h5py.Dataset):
xcpdps[smplng][dpool][key] = dpoolgrp[key].value
else:
raise TypeError('Invalid h5py data type encountered')
for stat in ['mean', 'median']:
if stat in dpoolgrp:
if isinstance(dpoolgrp[stat], h5py.Dataset):
valunits = dpoolgrp[stat].attrs['units']
xcpdps[smplng][dpool][stat] = dpoolgrp[stat].value * U.Unit(valunits)
elif isinstance(dpoolgrp[stat], h5py.Group):
xcpdps[smplng][dpool][stat] = []
for diagcomb_ind in range(len(dpoolgrp[stat].keys())):
if 'diagcomb_{0}'.format(diagcomb_ind) in dpoolgrp[stat]:
valunits = dpoolgrp[stat]['diagcomb_{0}'.format(diagcomb_ind)].attrs['units']
xcpdps[smplng][dpool][stat] += [dpoolgrp[stat]['diagcomb_{0}'.format(diagcomb_ind)].value * U.Unit(valunits)]
return xcpdps
################################################################################
def incoherent_cross_power_spectrum_average(xcpdps, excpdps=None, diagoffsets=None):
"""
----------------------------------------------------------------------------
Perform incoherent averaging of cross power spectrum along specified axes
Inputs:
xcpdps [dictionary or list of dictionaries] If provided as a list of
dictionaries, each dictionary consists of cross power spectral
information coming possible from different sources, and they
will be averaged be averaged incoherently. If a single
dictionary is provided instead of a list of dictionaries, the
said averaging does not take place. Each dictionary is
essentially an output of the member function
compute_power_spectrum() of class ClosurePhaseDelaySpectrum. It
has the following key-value structure:
'triads' ((ntriads,3) array), 'triads_ind',
((ntriads,) array), 'lstXoffsets' ((ndlst_range,) array), 'lst'
((nlst,) array), 'dlst' ((nlst,) array), 'lst_ind' ((nlst,)
array), 'days' ((ndays,) array), 'day_ind' ((ndays,) array),
'dday' ((ndays,) array), 'oversampled' and 'resampled'
corresponding to whether resample was set to False or True in
call to member function FT(). Values under keys 'triads_ind'
and 'lst_ind' are numpy array corresponding to triad and time
indices used in selecting the data. Values under keys
'oversampled' and 'resampled' each contain a dictionary with
the following keys and values:
'z' [numpy array] Redshifts corresponding to the band
centers in 'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,)
'kprll' [numpy array] k_parallel modes (in h/Mpc) corresponding
to 'lags'. It has shape=(nspw,nlags)
'freq_center'
[numpy array] contains the center frequencies (in Hz)
of the frequency subbands of the subband delay spectra.
It is of size n_win. It is roughly equivalent to
redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on
each frequency sub-band during the subband delay
transform. It is of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz)
of the subbands being delay transformed. It is of size
n_win. It is roughly equivalent to width in redshift or
along line-of-sight
'shape' [string] shape of the frequency window function applied.
Usual values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was
raised. The value is be a positive scalar with
default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in
pixels) of the subband delay spectra. It is proportional
to inverse of effective bandwidth. It is of size n_win.
The unit size of a pixel is determined by the difference
between adjacent pixels in lags under key 'lags' which
in turn is effectively inverse of the effective
bandwidth of the subband specified in bw_eff
It further contains 3 keys named 'whole', 'submodel', and
'residual' each of which is a dictionary. 'whole' contains power
spectrum info about the input closure phases. 'submodel'
contains power spectrum info about the model that will have been
subtracted (as closure phase) from the 'whole' model. 'residual'
contains power spectrum info about the closure phases obtained
as a difference between 'whole' and 'submodel'. It contains the
following keys and values:
'mean' [numpy array] Delay power spectrum incoherently
estimated over the axes specified in xinfo['axes']
using the 'mean' key in input cpds or attribute
cPhaseDS['processed']['dspec']. It has shape that
depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are
not set, those axes will be replaced with square
covariance matrices. If collapse_axes is provided but
avgcov is False, those axes will be of shape 2*Naxis-1.
'median'
[numpy array] Delay power spectrum incoherently averaged
over the axes specified in incohax using the 'median'
key in input cpds or attribute
cPhaseDS['processed']['dspec']. It has shape that
depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are not
set, those axes will be replaced with square covariance
matrices. If collapse_axes is provided bu avgcov is
False, those axes will be of shape 2*Naxis-1.
'diagoffsets'
[dictionary] Same keys corresponding to keys under
'collapse_axes' in input containing the diagonal
offsets for those axes. If 'avgcov' was set, those
entries will be removed from 'diagoffsets' since all the
leading diagonal elements have been collapsed (averaged)
further. Value under each key is a numpy array where
each element in the array corresponds to the index of
that leading diagonal. This should match the size of the
output along that axis in 'mean' or 'median' above.
'diagweights'
[dictionary] Each key is an axis specified in
collapse_axes and the value is a numpy array of weights
corresponding to the diagonal offsets in that axis.
'axesmap'
[dictionary] If covariance in cross-power is calculated
but is not collapsed, the number of dimensions in the
output will have changed. This parameter tracks where
the original axis is now placed. The keys are the
original axes that are involved in incoherent
cross-power, and the values are the new locations of
those original axes in the output.
'nsamples_incoh'
[integer] Number of incoherent samples in producing the
power spectrum
'nsamples_coh'
[integer] Number of coherent samples in producing the
power spectrum
excpdps [dictionary or list of dictionaries] If provided as a list of
dictionaries, each dictionary consists of cross power spectral
information of subsample differences coming possible from
different sources, and they will be averaged be averaged
incoherently. This is optional. If not set (default=None), no
incoherent averaging happens. If a single dictionary is provided
instead of a list of dictionaries, the said averaging does not
take place. Each dictionary is essentially an output of the
member function compute_power_spectrum_uncertainty() of class
ClosurePhaseDelaySpectrum. It has the following key-value
structure:
'triads' ((ntriads,3) array), 'triads_ind',
((ntriads,) array), 'lstXoffsets' ((ndlst_range,) array), 'lst'
((nlst,) array), 'dlst' ((nlst,) array), 'lst_ind' ((nlst,)
array), 'days' ((ndaycomb,) array), 'day_ind' ((ndaycomb,)
array), 'dday' ((ndaycomb,) array), 'oversampled' and
'resampled' corresponding to whether resample was set to False
or True in call to member function FT(). Values under keys
'triads_ind' and 'lst_ind' are numpy array corresponding to
triad and time indices used in selecting the data. Values under
keys 'oversampled' and 'resampled' each contain a dictionary
with the following keys and values:
'z' [numpy array] Redshifts corresponding to the band
centers in 'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,)
'kprll' [numpy array] k_parallel modes (in h/Mpc) corresponding
to 'lags'. It has shape=(nspw,nlags)
'freq_center'
[numpy array] contains the center frequencies (in Hz) of
the frequency subbands of the subband delay spectra. It
is of size n_win. It is roughly equivalent to
redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on each
frequency sub-band during the subband delay transform.
It is of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz)
of the subbands being delay transformed. It is of size
n_win. It is roughly equivalent to width in redshift or
along line-of-sight
'shape' [string] shape of the frequency window function applied.
Usual values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was
raised. The value is be a positive scalar with
default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in
pixels) of the subband delay spectra. It is proportional
to inverse of effective bandwidth. It is of size n_win.
The unit size of a pixel is determined by the difference
between adjacent pixels in lags under key 'lags' which
in turn is effectively inverse of the effective
bandwidth of the subband specified in bw_eff
It further contains a key named 'errinfo' which is a dictionary.
It contains information about power spectrum uncertainties
obtained from subsample differences. It contains the following
keys and values:
'mean' [numpy array] Delay power spectrum uncertainties
incoherently estimated over the axes specified in
xinfo['axes'] using the 'mean' key in input cpds or
attribute cPhaseDS['errinfo']['dspec']. It has shape
that depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are not
set, those axes will be replaced with square covariance
matrices. If collapse_axes is provided but avgcov is
False, those axes will be of shape 2*Naxis-1.
'median'
[numpy array] Delay power spectrum uncertainties
incoherently averaged over the axes specified in incohax
using the 'median' key in input cpds or attribute
cPhaseDS['errinfo']['dspec']. It has shape that depends
on the combination of input parameters. See examples
below. If both collapse_axes and avgcov are not set,
those axes will be replaced with square covariance
matrices. If collapse_axes is provided but avgcov is
False, those axes will be of shape 2*Naxis-1.
'diagoffsets'
[dictionary] Same keys corresponding to keys under
'collapse_axes' in input containing the diagonal offsets
for those axes. If 'avgcov' was set, those entries will
be removed from 'diagoffsets' since all the leading
diagonal elements have been collapsed (averaged) further.
Value under each key is a numpy array where each element
in the array corresponds to the index of that leading
diagonal. This should match the size of the output along
that axis in 'mean' or 'median' above.
'diagweights'
[dictionary] Each key is an axis specified in
collapse_axes and the value is a numpy array of weights
corresponding to the diagonal offsets in that axis.
'axesmap'
[dictionary] If covariance in cross-power is calculated
but is not collapsed, the number of dimensions in the
output will have changed. This parameter tracks where
the original axis is now placed. The keys are the
original axes that are involved in incoherent
cross-power, and the values are the new locations of
those original axes in the output.
'nsamples_incoh'
[integer] Number of incoherent samples in producing the
power spectrum
'nsamples_coh'
[integer] Number of coherent samples in producing the
power spectrum
diagoffsets [NoneType or dictionary or list of dictionaries] This info is
used for incoherent averaging along specified diagonals along
specified axes. This incoherent averaging is performed after
incoherently averaging multiple cross-power spectra (if any).
If set to None, this incoherent averaging is not performed.
Many combinations of axes and diagonals can be specified as
individual dictionaries in a list. If only one dictionary is
specified, then it assumed that only one combination of axes
and diagonals is requested. If a list of dictionaries is given,
each dictionary in the list specifies a different combination
for incoherent averaging. Each dictionary should have the
following key-value pairs. The key is the axis number (allowed
values are 1, 2, 3) that denote the axis type (1=LST, 2=Days,
3=Triads to be averaged), and the value under they keys is a
list or numpy array of diagonals to be averaged incoherently.
These axes-diagonal combinations apply to both the inputs
xcpdps and excpdps, except axis=2 does not apply to excpdps
(since it is made of subsample differences already) and will be
skipped.
Outputs:
A tuple consisting of two dictionaries. The first dictionary contains the
incoherent averaging of xcpdps as specified by the inputs, while the second
consists of incoherent of excpdps as specified by the inputs. The structure
of these dictionaries are practically the same as the dictionary inputs
xcpdps and excpdps respectively. The only differences in dictionary
structure are:
* Under key ['oversampled'/'resampled']['whole'/'submodel'/'residual'
/'effinfo']['mean'/'median'] is a list of numpy arrays, where each
array in the list corresponds to the dictionary in the list in input
diagoffsets that defines the axes-diagonal combination.
----------------------------------------------------------------------------
"""
if isinstance(xcpdps, dict):
xcpdps = [xcpdps]
if not isinstance(xcpdps, list):
raise TypeError('Invalid data type provided for input xcpdps')
if excpdps is not None:
if isinstance(excpdps, dict):
excpdps = [excpdps]
if not isinstance(excpdps, list):
raise TypeError('Invalid data type provided for input excpdps')
if len(xcpdps) != len(excpdps):
raise ValueError('Inputs xcpdps and excpdps found to have unequal number of values')
out_xcpdps = {'triads': xcpdps[0]['triads'], 'triads_ind': xcpdps[0]['triads_ind'], 'lst': xcpdps[0]['lst'], 'lst_ind': xcpdps[0]['lst_ind'], 'dlst': xcpdps[0]['dlst'], 'days': xcpdps[0]['days'], 'day_ind': xcpdps[0]['day_ind'], 'dday': xcpdps[0]['dday']}
out_excpdps = None
if excpdps is not None:
out_excpdps = {'triads': excpdps[0]['triads'], 'triads_ind': excpdps[0]['triads_ind'], 'lst': excpdps[0]['lst'], 'lst_ind': excpdps[0]['lst_ind'], 'dlst': excpdps[0]['dlst'], 'days': excpdps[0]['days'], 'day_ind': excpdps[0]['day_ind'], 'dday': excpdps[0]['dday']}
for smplng in ['oversampled', 'resampled']:
if smplng in xcpdps[0]:
out_xcpdps[smplng] = {'z': xcpdps[0][smplng]['z'], 'kprll': xcpdps[0][smplng]['kprll'], 'lags': xcpdps[0][smplng]['lags'], 'freq_center': xcpdps[0][smplng]['freq_center'], 'bw_eff': xcpdps[0][smplng]['bw_eff'], 'shape': xcpdps[0][smplng]['shape'], 'freq_wts': xcpdps[0][smplng]['freq_wts'], 'lag_corr_length': xcpdps[0][smplng]['lag_corr_length']}
if excpdps is not None:
out_excpdps[smplng] = {'z': excpdps[0][smplng]['z'], 'kprll': excpdps[0][smplng]['kprll'], 'lags': excpdps[0][smplng]['lags'], 'freq_center': excpdps[0][smplng]['freq_center'], 'bw_eff': excpdps[0][smplng]['bw_eff'], 'shape': excpdps[0][smplng]['shape'], 'freq_wts': excpdps[0][smplng]['freq_wts'], 'lag_corr_length': excpdps[0][smplng]['lag_corr_length']}
for dpool in ['whole', 'submodel', 'residual']:
if dpool in xcpdps[0][smplng]:
out_xcpdps[smplng][dpool] = {'diagoffsets': xcpdps[0][smplng][dpool]['diagoffsets'], 'axesmap': xcpdps[0][smplng][dpool]['axesmap']}
for stat in ['mean', 'median']:
if stat in xcpdps[0][smplng][dpool]:
out_xcpdps[smplng][dpool][stat] = {}
arr = []
diagweights = []
for i in range(len(xcpdps)):
arr += [xcpdps[i][smplng][dpool][stat].si.value]
arr_units = xcpdps[i][smplng][dpool][stat].si.unit
if isinstance(xcpdps[i][smplng][dpool]['diagweights'], dict):
diagwts = 1.0
diagwts_shape = NP.ones(xcpdps[i][smplng][dpool][stat].ndim, dtype=NP.int)
for ax in xcpdps[i][smplng][dpool]['diagweights']:
tmp_shape = NP.copy(diagwts_shape)
tmp_shape[xcpdps[i][smplng][dpool]['axesmap'][ax]] = xcpdps[i][smplng][dpool]['diagweights'][ax].size
diagwts = diagwts * xcpdps[i][smplng][dpool]['diagweights'][ax].reshape(tuple(tmp_shape))
elif isinstance(xcpdps[i][smplng][dpool]['diagweights'], NP.ndarray):
diagwts = NP.copy(xcpdps[i][smplng][dpool]['diagweights'])
else:
raise TypeError('Diagonal weights in input must be a dictionary or a numpy array')
diagweights += [diagwts]
diagweights = NP.asarray(diagweights)
arr = NP.asarray(arr)
arr = NP.nansum(arr * diagweights, axis=0) / NP.nansum(diagweights, axis=0) * arr_units
diagweights = NP.nansum(diagweights, axis=0)
out_xcpdps[smplng][dpool][stat] = arr
out_xcpdps[smplng][dpool]['diagweights'] = diagweights
for dpool in ['errinfo']:
if dpool in excpdps[0][smplng]:
out_excpdps[smplng][dpool] = {'diagoffsets': excpdps[0][smplng][dpool]['diagoffsets'], 'axesmap': excpdps[0][smplng][dpool]['axesmap']}
for stat in ['mean', 'median']:
if stat in excpdps[0][smplng][dpool]:
out_excpdps[smplng][dpool][stat] = {}
arr = []
diagweights = []
for i in range(len(excpdps)):
arr += [excpdps[i][smplng][dpool][stat].si.value]
arr_units = excpdps[i][smplng][dpool][stat].si.unit
if isinstance(excpdps[i][smplng][dpool]['diagweights'], dict):
diagwts = 1.0
diagwts_shape = NP.ones(excpdps[i][smplng][dpool][stat].ndim, dtype=NP.int)
for ax in excpdps[i][smplng][dpool]['diagweights']:
tmp_shape = NP.copy(diagwts_shape)
tmp_shape[excpdps[i][smplng][dpool]['axesmap'][ax]] = excpdps[i][smplng][dpool]['diagweights'][ax].size
diagwts = diagwts * excpdps[i][smplng][dpool]['diagweights'][ax].reshape(tuple(tmp_shape))
elif isinstance(excpdps[i][smplng][dpool]['diagweights'], NP.ndarray):
diagwts = NP.copy(excpdps[i][smplng][dpool]['diagweights'])
else:
raise TypeError('Diagonal weights in input must be a dictionary or a numpy array')
diagweights += [diagwts]
diagweights = NP.asarray(diagweights)
arr = NP.asarray(arr)
arr = NP.nansum(arr * diagweights, axis=0) / NP.nansum(diagweights, axis=0) * arr_units
diagweights = NP.nansum(diagweights, axis=0)
out_excpdps[smplng][dpool][stat] = arr
out_excpdps[smplng][dpool]['diagweights'] = diagweights
if diagoffsets is not None:
if isinstance(diagoffsets, dict):
diagoffsets = [diagoffsets]
if not isinstance(diagoffsets, list):
raise TypeError('Input diagoffsets must be a list of dictionaries')
for ind in range(len(diagoffsets)):
for ax in diagoffsets[ind]:
if not isinstance(diagoffsets[ind][ax], (list, NP.ndarray)):
raise TypeError('Values in input dictionary diagoffsets must be a list or numpy array')
diagoffsets[ind][ax] = NP.asarray(diagoffsets[ind][ax])
for smplng in ['oversampled', 'resampled']:
if smplng in out_xcpdps:
for dpool in ['whole', 'submodel', 'residual']:
if dpool in out_xcpdps[smplng]:
masks = []
for ind in range(len(diagoffsets)):
mask_ones = NP.ones(out_xcpdps[smplng][dpool]['diagweights'].shape, dtype=NP.bool)
mask_agg = None
for ax in diagoffsets[ind]:
mltdim_slice = [slice(None)] * mask_ones.ndim
mltdim_slice[out_xcpdps[smplng][dpool]['axesmap'][ax].squeeze()] = NP.where(NP.isin(out_xcpdps[smplng][dpool]['diagoffsets'][ax], diagoffsets[ind][ax]))[0]
mask_tmp = NP.copy(mask_ones)
mask_tmp[tuple(mltdim_slice)] = False
if mask_agg is None:
mask_agg = NP.copy(mask_tmp)
else:
mask_agg = NP.logical_or(mask_agg, mask_tmp)
masks += [NP.copy(mask_agg)]
diagwts = NP.copy(out_xcpdps[smplng][dpool]['diagweights'])
out_xcpdps[smplng][dpool]['diagweights'] = []
for stat in ['mean', 'median']:
if stat in out_xcpdps[smplng][dpool]:
arr = NP.copy(out_xcpdps[smplng][dpool][stat].si.value)
arr_units = out_xcpdps[smplng][dpool][stat].si.unit
out_xcpdps[smplng][dpool][stat] = []
for ind in range(len(diagoffsets)):
masked_diagwts = MA.array(diagwts, mask=masks[ind])
axes_to_avg = tuple([out_xcpdps[smplng][dpool]['axesmap'][ax][0] for ax in diagoffsets[ind]])
out_xcpdps[smplng][dpool][stat] += [MA.sum(arr * masked_diagwts, axis=axes_to_avg, keepdims=True) / MA.sum(masked_diagwts, axis=axes_to_avg, keepdims=True) * arr_units]
if len(out_xcpdps[smplng][dpool]['diagweights']) < len(diagoffsets):
out_xcpdps[smplng][dpool]['diagweights'] += [MA.sum(masked_diagwts, axis=axes_to_avg, keepdims=True)]
if excpdps is not None:
for smplng in ['oversampled', 'resampled']:
if smplng in out_excpdps:
for dpool in ['errinfo']:
if dpool in out_excpdps[smplng]:
masks = []
for ind in range(len(diagoffsets)):
mask_ones = NP.ones(out_excpdps[smplng][dpool]['diagweights'].shape, dtype=NP.bool)
mask_agg = None
for ax in diagoffsets[ind]:
if ax != 2:
mltdim_slice = [slice(None)] * mask_ones.ndim
mltdim_slice[out_excpdps[smplng][dpool]['axesmap'][ax].squeeze()] = NP.where(NP.isin(out_excpdps[smplng][dpool]['diagoffsets'][ax], diagoffsets[ind][ax]))[0]
mask_tmp = NP.copy(mask_ones)
mask_tmp[tuple(mltdim_slice)] = False
if mask_agg is None:
mask_agg = NP.copy(mask_tmp)
else:
mask_agg = NP.logical_or(mask_agg, mask_tmp)
masks += [NP.copy(mask_agg)]
diagwts = NP.copy(out_excpdps[smplng][dpool]['diagweights'])
out_excpdps[smplng][dpool]['diagweights'] = []
for stat in ['mean', 'median']:
if stat in out_excpdps[smplng][dpool]:
arr = NP.copy(out_excpdps[smplng][dpool][stat].si.value)
arr_units = out_excpdps[smplng][dpool][stat].si.unit
out_excpdps[smplng][dpool][stat] = []
for ind in range(len(diagoffsets)):
masked_diagwts = MA.array(diagwts, mask=masks[ind])
axes_to_avg = tuple([out_excpdps[smplng][dpool]['axesmap'][ax][0] for ax in diagoffsets[ind] if ax!=2])
out_excpdps[smplng][dpool][stat] += [MA.sum(arr * masked_diagwts, axis=axes_to_avg, keepdims=True) / MA.sum(masked_diagwts, axis=axes_to_avg, keepdims=True) * arr_units]
if len(out_excpdps[smplng][dpool]['diagweights']) < len(diagoffsets):
out_excpdps[smplng][dpool]['diagweights'] += [MA.sum(masked_diagwts, axis=axes_to_avg, keepdims=True)]
return (out_xcpdps, out_excpdps)
################################################################################
def incoherent_kbin_averaging(xcpdps, kbins=None, num_kbins=None, kbintype='log'):
"""
----------------------------------------------------------------------------
Averages the power spectrum incoherently by binning in bins of k. Returns
the power spectrum in units of both standard power spectrum and \Delta^2
Inputs:
xcpdps [dictionary] A dictionary that contains the incoherent averaged
power spectrum along LST and/or triads axes. This dictionary is
essentially the one(s) returned as the output of the function
incoherent_cross_power_spectrum_average()
kbins [NoneType, list or numpy array] Bins in k. If set to None
(default), it will be determined automatically based on the
inputs in num_kbins, and kbintype. If num_kbins is None and
kbintype='linear', the negative and positive values of k are
folded into a one-sided power spectrum. In this case, the
bins will approximately have the same resolution as the k-values
in the input power spectrum for all the spectral windows.
num_kbins [NoneType or integer] Number of k-bins. Used only if kbins is
set to None. If kbintype is set to 'linear', the negative and
positive values of k are folded into a one-sided power spectrum.
In this case, the bins will approximately have the same
resolution as the k-values in the input power spectrum for all
the spectral windows.
kbintype [string] Specifies the type of binning, used only if kbins is
set to None. Accepted values are 'linear' and 'log' for linear
and logarithmic bins respectively.
Outputs:
Dictionary containing the power spectrum information. At the top level, it
contains keys specifying the sampling to be 'oversampled' or 'resampled'.
Under each of these keys is another dictionary containing the following
keys:
'z' [numpy array] Redshifts corresponding to the band centers in
'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,).
'freq_center'
[numpy array] contains the center frequencies (in Hz) of the
frequency subbands of the subband delay spectra. It is of size
n_win. It is roughly equivalent to redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on each
frequency sub-band during the subband delay transform. It is
of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz) of the
subbands being delay transformed. It is of size n_win. It is
roughly equivalent to width in redshift or along line-of-sight
'shape' [string] shape of the frequency window function applied. Usual
values are 'rect' (rectangular), 'bhw' (Blackman-Harris),
'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was raised.
The value is be a positive scalar with default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in pixels) of
the subband delay spectra. It is proportional to inverse of
effective bandwidth. It is of size n_win. The unit size of a
pixel is determined by the difference between adjacent pixels
in lags under key 'lags' which in turn is effectively inverse
of the effective bandwidth of the subband specified in bw_eff
It further contains 3 keys named 'whole', 'submodel', and 'residual'
or one key named 'errinfo' each of which is a dictionary. 'whole'
contains power spectrum info about the input closure phases. 'submodel'
contains power spectrum info about the model that will have been
subtracted (as closure phase) from the 'whole' model. 'residual'
contains power spectrum info about the closure phases obtained as a
difference between 'whole' and 'submodel'. 'errinfo' contains power
spectrum information about the subsample differences. There is also
another dictionary under key 'kbininfo' that contains information about
k-bins. These dictionaries contain the following keys and values:
'whole'/'submodel'/'residual'/'errinfo'
[dictionary] It contains the following keys and values:
'mean' [dictionary] Delay power spectrum information under the
'mean' statistic incoherently obtained by averaging the
input power spectrum in bins of k. It contains output power
spectrum expressed as two quantities each of which is a
dictionary with the following key-value pairs:
'PS' [list of numpy arrays] Standard power spectrum in
units of 'K2 Mpc3'. Each numpy array in the list
maps to a specific combination of axes and axis
diagonals chosen for incoherent averaging in
earlier processing such as in the function
incoherent_cross_power_spectrum_average(). The
numpy array has a shape similar to the input power
spectrum, but that last axis (k-axis) will have a
different size that depends on the k-bins that
were used in the incoherent averaging along that
axis.
'Del2' [list of numpy arrays] power spectrum in Delta^2
units of 'K2'. Each numpy array in the list
maps to a specific combination of axes and axis
diagonals chosen for incoherent averaging in
earlier processing such as in the function
incoherent_cross_power_spectrum_average(). The
numpy array has a shape similar to the input power
spectrum, but that last axis (k-axis) will have a
different size that depends on the k-bins that
were used in the incoherent averaging along that
axis.
'median'
[dictionary] Delay power spectrum information under the
'median' statistic incoherently obtained by averaging the
input power spectrum in bins of k. It contains output power
spectrum expressed as two quantities each of which is a
dictionary with the following key-value pairs:
'PS' [list of numpy arrays] Standard power spectrum in
units of 'K2 Mpc3'. Each numpy array in the list
maps to a specific combination of axes and axis
diagonals chosen for incoherent averaging in
earlier processing such as in the function
incoherent_cross_power_spectrum_average(). The
numpy array has a shape similar to the input power
spectrum, but that last axis (k-axis) will have a
different size that depends on the k-bins that
were used in the incoherent averaging along that
axis.
'Del2' [list of numpy arrays] power spectrum in Delta^2
units of 'K2'. Each numpy array in the list
maps to a specific combination of axes and axis
diagonals chosen for incoherent averaging in
earlier processing such as in the function
incoherent_cross_power_spectrum_average(). The
numpy array has a shape similar to the input power
spectrum, but that last axis (k-axis) will have a
different size that depends on the k-bins that
were used in the incoherent averaging along that
axis.
'kbininfo'
[dictionary] Contains the k-bin information. It contains the
following key-value pairs:
'counts'
[list] List of numpy arrays where each numpy array in the stores
the counts in the determined k-bins. Each numpy array in the
list corresponds to a spectral window (redshift subband). The
shape of each numpy array is (nkbins,)
'kbin_edges'
[list] List of numpy arrays where each numpy array contains the
k-bin edges. Each array in the list corresponds to a spectral
window (redshift subband). The shape of each array is
(nkbins+1,).
'kbinnum'
[list] List of numpy arrays containing the bin number under
which the k value falls. Each array in the list corresponds to
a spectral window (redshift subband). The shape of each array
is (nlags,).
'ri'
[list] List of numpy arrays containing the reverse indices for
each k-bin. Each array in the list corresponds to a spectral
window (redshift subband). The shape of each array is
(nlags+nkbins+1,).
'whole'/'submodel'/'residual' or 'errinfo' [dictionary] k-bin info
estimated for the different datapools under different stats
and PS definitions. It has the keys 'mean' and 'median' for the
mean and median statistic respectively. Each of them contain a
dictionary with the following key-value pairs:
'PS' [list] List of numpy arrays where each numpy array
contains a standard power spectrum typically in units of
'K2 Mpc3'. Its shape is the same as input power spectrum
except the k-axis which now has nkbins number of
elements.
'Del2' [list] List of numpy arrays where each numpy array
contains a Delta^2 power spectrum typically in units of
'K2'. Its shape is the same as input power spectrum
except the k-axis which now has nkbins number of
elements.
----------------------------------------------------------------------------
"""
if not isinstance(xcpdps, dict):
raise TypeError('Input xcpdps must be a dictionary')
if kbins is not None:
if not isinstance(kbins, (list,NP.ndarray)):
raise TypeError('Input kbins must be a list or numpy array')
else:
if not isinstance(kbintype, str):
raise TypeError('Input kbintype must be a string')
if kbintype.lower() not in ['linear', 'log']:
raise ValueError('Input kbintype must be set to "linear" or "log"')
if kbintype.lower() == 'log':
if num_kbins is None:
num_kbins = 10
psinfo = {}
keys = ['triads', 'triads_ind', 'lst', 'lst_ind', 'dlst', 'days', 'day_ind', 'dday']
for key in keys:
psinfo[key] = xcpdps[key]
sampling = ['oversampled', 'resampled']
sampling_keys = ['z', 'freq_center', 'bw_eff', 'shape', 'freq_wts', 'lag_corr_length']
dpool_keys = ['whole', 'submodel', 'residual', 'errinfo']
for smplng in sampling:
if smplng in xcpdps:
psinfo[smplng] = {}
for key in sampling_keys:
psinfo[smplng][key] = xcpdps[smplng][key]
kprll = xcpdps[smplng]['kprll']
lags = xcpdps[smplng]['lags']
eps = 1e-10
if kbins is None:
dkprll = NP.max(NP.mean(NP.diff(kprll, axis=-1), axis=-1))
if kbintype.lower() == 'linear':
bins_kprll = NP.linspace(eps, NP.abs(kprll).max()+eps, num=kprll.shape[1]/2+1, endpoint=True)
else:
bins_kprll = NP.geomspace(eps, NP.abs(kprll).max()+eps, num=num_kbins+1, endpoint=True)
bins_kprll = NP.insert(bins_kprll, 0, -eps)
else:
bins_kprll = NP.asarray(kbins)
num_kbins = bins_kprll.size - 1
psinfo[smplng]['kbininfo'] = {'counts': [], 'kbin_edges': [], 'kbinnum': [], 'ri': []}
for spw in range(kprll.shape[0]):
counts, kbin_edges, kbinnum, ri = OPS.binned_statistic(NP.abs(kprll[spw,:]), statistic='count', bins=bins_kprll)
counts = counts.astype(NP.int)
psinfo[smplng]['kbininfo']['counts'] += [NP.copy(counts)]
psinfo[smplng]['kbininfo']['kbin_edges'] += [kbin_edges / U.Mpc]
psinfo[smplng]['kbininfo']['kbinnum'] += [NP.copy(kbinnum)]
psinfo[smplng]['kbininfo']['ri'] += [NP.copy(ri)]
for dpool in dpool_keys:
if dpool in xcpdps[smplng]:
psinfo[smplng][dpool] = {}
psinfo[smplng]['kbininfo'][dpool] = {}
keys = ['diagoffsets', 'diagweights', 'axesmap']
for key in keys:
psinfo[smplng][dpool][key] = xcpdps[smplng][dpool][key]
for stat in ['mean', 'median']:
if stat in xcpdps[smplng][dpool]:
psinfo[smplng][dpool][stat] = {'PS': [], 'Del2': []}
psinfo[smplng]['kbininfo'][dpool][stat] = []
for combi in range(len(xcpdps[smplng][dpool][stat])):
outshape = NP.asarray(xcpdps[smplng][dpool][stat][combi].shape)
outshape[-1] = num_kbins
tmp_dps = NP.full(tuple(outshape), NP.nan, dtype=NP.complex) * U.Unit(xcpdps[smplng][dpool][stat][combi].unit)
tmp_Del2 = NP.full(tuple(outshape), NP.nan, dtype=NP.complex) * U.Unit(xcpdps[smplng][dpool][stat][combi].unit / U.Mpc**3)
tmp_kprll = NP.full(tuple(outshape), NP.nan, dtype=NP.float) / U.Mpc
for spw in range(kprll.shape[0]):
counts = NP.copy(psinfo[smplng]['kbininfo']['counts'][spw])
ri = NP.copy(psinfo[smplng]['kbininfo']['ri'][spw])
print('Processing datapool={0}, stat={1}, LST-Day-Triad combination={2:0d}, spw={3:0d}...'.format(dpool, stat, combi, spw))
progress = PGB.ProgressBar(widgets=[PGB.Percentage(), PGB.Bar(marker='-', left=' |', right='| '), PGB.Counter(), '/{0:0d} k-bins '.format(num_kbins), PGB.ETA()], maxval=num_kbins).start()
for binnum in range(num_kbins):
if counts[binnum] > 0:
ind_kbin = ri[ri[binnum]:ri[binnum+1]]
tmp_dps[spw,...,binnum] = NP.nanmean(NP.take(xcpdps[smplng][dpool][stat][combi][spw], ind_kbin, axis=-1), axis=-1)
k_shape = NP.ones(NP.take(xcpdps[smplng][dpool][stat][combi][spw], ind_kbin, axis=-1).ndim, dtype=NP.int)
k_shape[-1] = -1
tmp_Del2[spw,...,binnum] = NP.nanmean(NP.abs(kprll[spw,ind_kbin].reshape(tuple(k_shape))/U.Mpc)**3 * NP.take(xcpdps[smplng][dpool][stat][combi][spw], ind_kbin, axis=-1), axis=-1) / (2*NP.pi**2)
tmp_kprll[spw,...,binnum] = NP.nansum(NP.abs(kprll[spw,ind_kbin].reshape(tuple(k_shape))/U.Mpc) * NP.abs(NP.take(xcpdps[smplng][dpool][stat][combi][spw], ind_kbin, axis=-1)), axis=-1) / NP.nansum(NP.abs(NP.take(xcpdps[smplng][dpool][stat][combi][spw], ind_kbin, axis=-1)), axis=-1)
progress.update(binnum+1)
progress.finish()
psinfo[smplng][dpool][stat]['PS'] += [copy.deepcopy(tmp_dps)]
psinfo[smplng][dpool][stat]['Del2'] += [copy.deepcopy(tmp_Del2)]
psinfo[smplng]['kbininfo'][dpool][stat] += [copy.deepcopy(tmp_kprll)]
return psinfo
################################################################################
class ClosurePhase(object):
"""
----------------------------------------------------------------------------
Class to hold and operate on Closure Phase information.
It has the following attributes and member functions.
Attributes:
extfile [string] Full path to external file containing information
of ClosurePhase instance. The file is in HDF5 format
cpinfo [dictionary] Contains the following top level keys,
namely, 'raw', 'processed', and 'errinfo'
Under key 'raw' which holds a dictionary, the subkeys
include 'cphase' (nlst,ndays,ntriads,nchan),
'triads' (ntriads,3), 'lst' (nlst,ndays), and 'flags'
(nlst,ndays,ntriads,nchan).
Under the 'processed' key are more subkeys, namely,
'native', 'prelim', and optionally 'submodel' and 'residual'
each holding a dictionary.
Under 'native' dictionary, the subsubkeys for further
dictionaries are 'cphase' (masked array:
(nlst,ndays,ntriads,nchan)), 'eicp' (complex masked
array: (nlst,ndays,ntriads,nchan)), and 'wts' (masked
array: (nlst,ndays,ntriads,nchan)).
Under 'prelim' dictionary, the subsubkeys for further
dictionaries are 'tbins' (numpy array of tbin centers
after smoothing), 'dtbins' (numpy array of tbin
intervals), 'wts' (masked array:
(ntbins,ndays,ntriads,nchan)), 'eicp' and 'cphase'.
The dictionaries under 'eicp' are indexed by keys
'mean' (complex masked array:
(ntbins,ndays,ntriads,nchan)), and 'median' (complex
masked array: (ntbins,ndays,ntriads,nchan)).
The dictionaries under 'cphase' are indexed by keys
'mean' (masked array: (ntbins,ndays,ntriads,nchan)),
'median' (masked array: (ntbins,ndays,ntriads,nchan)),
'rms' (masked array: (ntbins,ndays,ntriads,nchan)), and
'mad' (masked array: (ntbins,ndays,ntriads,nchan)). The
last one denotes Median Absolute Deviation.
Under 'submodel' dictionary, the subsubkeys for further
dictionaries are 'cphase' (masked array:
(nlst,ndays,ntriads,nchan)), and 'eicp' (complex masked
array: (nlst,ndays,ntriads,nchan)).
Under 'residual' dictionary, the subsubkeys for further
dictionaries are 'cphase' and 'eicp'. These are
dictionaries too. The dictionaries under 'eicp' are
indexed by keys 'mean' (complex masked array:
(ntbins,ndays,ntriads,nchan)), and 'median' (complex
masked array: (ntbins,ndays,ntriads,nchan)).
The dictionaries under 'cphase' are indexed by keys
'mean' (masked array: (ntbins,ndays,ntriads,nchan)),
and 'median' (masked array:
(ntbins,ndays,ntriads,nchan)).
Under key 'errinfo', it contains the following keys and
values:
'list_of_pair_of_pairs'
List of pair of pairs for which differences of
complex exponentials have been computed, where the
elements are bins of days. The number of elements
in the list is ncomb. And each element is a smaller
(4-element) list of pair of pairs
'eicp_diff'
Difference of complex exponentials between pairs
of day bins. This will be used in evaluating noise
properties in power spectrum. It is a dictionary
with two keys '0' and '1' where each contains the
difference from a pair of subsamples. Each of these
keys contains a numpy array of shape
(nlstbins,ncomb,2,ntriads,nchan)
'wts' Weights in difference of complex exponentials
obtained by sum of squares of weights that are
associated with the pair that was used in the
differencing. It is a dictionary with two keys '0'
and '1' where each contains the weights associated
It is of shape (nlstbins,ncomb,2,ntriads,nchan)
Member functions:
__init__() Initialize an instance of class ClosurePhase
expicp() Compute and return complex exponential of the closure phase
as a masked array
smooth_in_tbins()
Smooth the complex exponentials of closure phases in LST
bins. Both mean and median smoothing is produced.
subtract() Subtract complex exponential of the bispectrum phase
from the current instance and updates the cpinfo attribute
subsample_differencing()
Create subsamples and differences between subsamples to
evaluate noise properties from the data set.
save() Save contents of attribute cpinfo in external HDF5 file
----------------------------------------------------------------------------
"""
def __init__(self, infile, freqs, infmt='npz'):
"""
------------------------------------------------------------------------
Initialize an instance of class ClosurePhase
Inputs:
infile [string] Input file including full path. It could be a NPZ
with raw data, or a HDF5 file that could contain raw or
processed data. The input file format is specified in the
input infmt. If it is a NPZ file, it must contain the
following keys/files:
'closures' [numpy array] Closure phase (radians). It is of
shape (nlst,ndays,ntriads,nchan)
'triads' [numpy array] Array of triad tuples, of shape
(ntriads,3)
'flags' [numpy array] Array of flags (boolean), of shape
(nlst,ndays,ntriads,nchan)
'last' [numpy array] Array of LST for each day (CASA
units which is MJD+6713). Shape is (nlst,ndays)
'days' [numpy array] Array of days, shape is (ndays,)
'averaged_closures'
[numpy array] optional array of closure phases
averaged across days. Shape is
(nlst,ntriads,nchan)
'std_dev_lst'
[numpy array] optional array of standard
deviation of closure phases across days. Shape
is (nlst,ntriads,nchan)
'std_dev_triads'
[numpy array] optional array of standard
deviation of closure phases across triads.
Shape is (nlst,ndays,nchan)
freqs [numpy array] Frequencies (in Hz) in the input. Size is
nchan.
infmt [string] Input file format. Accepted values are 'npz'
(default) and 'hdf5'.
------------------------------------------------------------------------
"""
if not isinstance(infile, str):
raise TypeError('Input infile must be a string')
if not isinstance(freqs, NP.ndarray):
raise TypeError('Input freqs must be a numpy array')
freqs = freqs.ravel()
if not isinstance(infmt, str):
raise TypeError('Input infmt must be a string')
if infmt.lower() not in ['npz', 'hdf5']:
raise ValueError('Input infmt must be "npz" or "hdf5"')
if infmt.lower() == 'npz':
infilesplit = infile.split('.npz')
infile_noext = infilesplit[0]
self.cpinfo = loadnpz(infile)
# npz2hdf5(infile, infile_noext+'.hdf5')
self.extfile = infile_noext + '.hdf5'
else:
# if not isinstance(infile, h5py.File):
# raise TypeError('Input infile is not a valid HDF5 file')
self.extfile = infile
self.cpinfo = NMO.load_dict_from_hdf5(self.extfile)
if freqs.size != self.cpinfo['raw']['cphase'].shape[-1]:
raise ValueError('Input frequencies do not match with dimensions of the closure phase data')
self.f = freqs
self.df = freqs[1] - freqs[0]
force_expicp = False
if 'processed' not in self.cpinfo:
force_expicp = True
else:
if 'native' not in self.cpinfo['processed']:
force_expicp = True
self.expicp(force_action=force_expicp)
if 'prelim' not in self.cpinfo['processed']:
self.cpinfo['processed']['prelim'] = {}
self.cpinfo['errinfo'] = {}
############################################################################
def expicp(self, force_action=False):
"""
------------------------------------------------------------------------
Compute the complex exponential of the closure phase as a masked array
Inputs:
force_action [boolean] If set to False (default), the complex
exponential is computed only if it has not been done so
already. Otherwise the computation is forced.
------------------------------------------------------------------------
"""
if 'processed' not in self.cpinfo:
self.cpinfo['processed'] = {}
force_action = True
if 'native' not in self.cpinfo['processed']:
self.cpinfo['processed']['native'] = {}
force_action = True
if 'cphase' not in self.cpinfo['processed']['native']:
self.cpinfo['processed']['native']['cphase'] = MA.array(self.cpinfo['raw']['cphase'].astype(NP.float64), mask=self.cpinfo['raw']['flags'])
force_action = True
if not force_action:
if 'eicp' not in self.cpinfo['processed']['native']:
self.cpinfo['processed']['native']['eicp'] = NP.exp(1j * self.cpinfo['processed']['native']['cphase'])
self.cpinfo['processed']['native']['wts'] = MA.array(NP.logical_not(self.cpinfo['raw']['flags']).astype(NP.float), mask=self.cpinfo['raw']['flags'])
else:
self.cpinfo['processed']['native']['eicp'] = NP.exp(1j * self.cpinfo['processed']['native']['cphase'])
self.cpinfo['processed']['native']['wts'] = MA.array(NP.logical_not(self.cpinfo['raw']['flags']).astype(NP.float), mask=self.cpinfo['raw']['flags'])
############################################################################
def smooth_in_tbins(self, daybinsize=None, ndaybins=None, lstbinsize=None):
"""
------------------------------------------------------------------------
Smooth the complex exponentials of closure phases in time bins. Both
mean and median smoothing is produced.
Inputs:
daybinsize [Nonetype or scalar] Day bin size (in days) over which mean
and median are estimated across different days for a fixed
LST bin. If set to None, it will look for value in input
ndaybins. If both are None, no smoothing is performed. Only
one of daybinsize or ndaybins must be set to non-None value.
ndaybins [NoneType or integer] Number of bins along day axis. Only
if daybinsize is set to None. It produces bins that roughly
consist of equal number of days in each bin regardless of
how much the days in each bin are separated from each other.
If both are None, no smoothing is performed. Only one of
daybinsize or ndaybins must be set to non-None value.
lstbinsize [NoneType or scalar] LST bin size (in seconds) over which
mean and median are estimated across the LST. If set to
None, no smoothing is performed
------------------------------------------------------------------------
"""
if (ndaybins is not None) and (daybinsize is not None):
raise ValueError('Only one of daybinsize or ndaybins should be set')
if (daybinsize is not None) or (ndaybins is not None):
if daybinsize is not None:
if not isinstance(daybinsize, (int,float)):
raise TypeError('Input daybinsize must be a scalar')
dres = NP.diff(self.cpinfo['raw']['days']).min() # in days
dextent = self.cpinfo['raw']['days'].max() - self.cpinfo['raw']['days'].min() + dres # in days
if daybinsize > dres:
daybinsize = NP.clip(daybinsize, dres, dextent)
eps = 1e-10
daybins = NP.arange(self.cpinfo['raw']['days'].min(), self.cpinfo['raw']['days'].max() + dres + eps, daybinsize)
ndaybins = daybins.size
daybins = NP.concatenate((daybins, [daybins[-1]+daybinsize+eps]))
if ndaybins > 1:
daybinintervals = daybins[1:] - daybins[:-1]
daybincenters = daybins[:-1] + 0.5 * daybinintervals
else:
daybinintervals = NP.asarray(daybinsize).reshape(-1)
daybincenters = daybins[0] + 0.5 * daybinintervals
counts, daybin_edges, daybinnum, ri = OPS.binned_statistic(self.cpinfo['raw']['days'], statistic='count', bins=daybins)
counts = counts.astype(NP.int)
# if 'prelim' not in self.cpinfo['processed']:
# self.cpinfo['processed']['prelim'] = {}
# self.cpinfo['processed']['prelim']['eicp'] = {}
# self.cpinfo['processed']['prelim']['cphase'] = {}
# self.cpinfo['processed']['prelim']['daybins'] = daybincenters
# self.cpinfo['processed']['prelim']['diff_dbins'] = daybinintervals
wts_daybins = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]))
eicp_dmean = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]), dtype=NP.complex128)
eicp_dmedian = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]), dtype=NP.complex128)
cp_drms = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]))
cp_dmad = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]))
for binnum in xrange(counts.size):
ind_daybin = ri[ri[binnum]:ri[binnum+1]]
wts_daybins[:,binnum,:,:] = NP.sum(self.cpinfo['processed']['native']['wts'][:,ind_daybin,:,:].data, axis=1)
eicp_dmean[:,binnum,:,:] = NP.exp(1j*NP.angle(MA.mean(self.cpinfo['processed']['native']['eicp'][:,ind_daybin,:,:], axis=1)))
eicp_dmedian[:,binnum,:,:] = NP.exp(1j*NP.angle(MA.median(self.cpinfo['processed']['native']['eicp'][:,ind_daybin,:,:].real, axis=1) + 1j * MA.median(self.cpinfo['processed']['native']['eicp'][:,ind_daybin,:,:].imag, axis=1)))
cp_drms[:,binnum,:,:] = MA.std(self.cpinfo['processed']['native']['cphase'][:,ind_daybin,:,:], axis=1).data
cp_dmad[:,binnum,:,:] = MA.median(NP.abs(self.cpinfo['processed']['native']['cphase'][:,ind_daybin,:,:] - NP.angle(eicp_dmedian[:,binnum,:,:][:,NP.newaxis,:,:])), axis=1).data
# mask = wts_daybins <= 0.0
# self.cpinfo['processed']['prelim']['wts'] = MA.array(wts_daybins, mask=mask)
# self.cpinfo['processed']['prelim']['eicp']['mean'] = MA.array(eicp_dmean, mask=mask)
# self.cpinfo['processed']['prelim']['eicp']['median'] = MA.array(eicp_dmedian, mask=mask)
# self.cpinfo['processed']['prelim']['cphase']['mean'] = MA.array(NP.angle(eicp_dmean), mask=mask)
# self.cpinfo['processed']['prelim']['cphase']['median'] = MA.array(NP.angle(eicp_dmedian), mask=mask)
# self.cpinfo['processed']['prelim']['cphase']['rms'] = MA.array(cp_drms, mask=mask)
# self.cpinfo['processed']['prelim']['cphase']['mad'] = MA.array(cp_dmad, mask=mask)
else:
if not isinstance(ndaybins, int):
raise TypeError('Input ndaybins must be an integer')
if ndaybins <= 0:
raise ValueError('Input ndaybins must be positive')
days_split = NP.array_split(self.cpinfo['raw']['days'], ndaybins)
daybincenters = NP.asarray([NP.mean(days) for days in days_split])
daybinintervals = NP.asarray([days.max()-days.min() for days in days_split])
counts = NP.asarray([days.size for days in days_split])
wts_split = NP.array_split(self.cpinfo['processed']['native']['wts'].data, ndaybins, axis=1)
# mask_split = NP.array_split(self.cpinfo['processed']['native']['wts'].mask, ndaybins, axis=1)
wts_daybins = NP.asarray([NP.sum(wtsitem, axis=1) for wtsitem in wts_split]) # ndaybins x nlst x ntriads x nchan
wts_daybins = NP.moveaxis(wts_daybins, 0, 1) # nlst x ndaybins x ntriads x nchan
mask_split = NP.array_split(self.cpinfo['processed']['native']['eicp'].mask, ndaybins, axis=1)
eicp_split = NP.array_split(self.cpinfo['processed']['native']['eicp'].data, ndaybins, axis=1)
eicp_dmean = MA.array([MA.mean(MA.array(eicp_split[i], mask=mask_split[i]), axis=1) for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
eicp_dmean = NP.exp(1j * NP.angle(eicp_dmean))
eicp_dmean = NP.moveaxis(eicp_dmean, 0, 1) # nlst x ndaybins x ntriads x nchan
eicp_dmedian = MA.array([MA.median(MA.array(eicp_split[i].real, mask=mask_split[i]), axis=1) + 1j * MA.median(MA.array(eicp_split[i].imag, mask=mask_split[i]), axis=1) for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
eicp_dmedian = NP.exp(1j * NP.angle(eicp_dmedian))
eicp_dmedian = NP.moveaxis(eicp_dmedian, 0, 1) # nlst x ndaybins x ntriads x nchan
cp_split = NP.array_split(self.cpinfo['processed']['native']['cphase'].data, ndaybins, axis=1)
cp_drms = NP.array([MA.std(MA.array(cp_split[i], mask=mask_split[i]), axis=1).data for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
cp_drms = NP.moveaxis(cp_drms, 0, 1) # nlst x ndaybins x ntriads x nchan
cp_dmad = NP.array([MA.median(NP.abs(cp_split[i] - NP.angle(eicp_dmedian[:,[i],:,:])), axis=1).data for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
cp_dmad = NP.moveaxis(cp_dmad, 0, 1) # nlst x ndaybins x ntriads x nchan
if 'prelim' not in self.cpinfo['processed']:
self.cpinfo['processed']['prelim'] = {}
self.cpinfo['processed']['prelim']['eicp'] = {}
self.cpinfo['processed']['prelim']['cphase'] = {}
self.cpinfo['processed']['prelim']['daybins'] = daybincenters
self.cpinfo['processed']['prelim']['diff_dbins'] = daybinintervals
mask = wts_daybins <= 0.0
self.cpinfo['processed']['prelim']['wts'] = MA.array(wts_daybins, mask=mask)
self.cpinfo['processed']['prelim']['eicp']['mean'] = MA.array(eicp_dmean, mask=mask)
self.cpinfo['processed']['prelim']['eicp']['median'] = MA.array(eicp_dmedian, mask=mask)
self.cpinfo['processed']['prelim']['cphase']['mean'] = MA.array(NP.angle(eicp_dmean), mask=mask)
self.cpinfo['processed']['prelim']['cphase']['median'] = MA.array(NP.angle(eicp_dmedian), mask=mask)
self.cpinfo['processed']['prelim']['cphase']['rms'] = MA.array(cp_drms, mask=mask)
self.cpinfo['processed']['prelim']['cphase']['mad'] = MA.array(cp_dmad, mask=mask)
rawlst = NP.degrees(NP.unwrap(NP.radians(self.cpinfo['raw']['lst'] * 15.0), discont=NP.pi, axis=0)) / 15.0 # in hours but unwrapped to have no discontinuities
if NP.any(rawlst > 24.0):
rawlst -= 24.0
if rawlst.shape[0] > 1: # LST bin only if there are multiple LST
if lstbinsize is not None:
if not isinstance(lstbinsize, (int,float)):
raise TypeError('Input lstbinsize must be a scalar')
lstbinsize = lstbinsize / 3.6e3 # in hours
tres = NP.diff(rawlst[:,0]).min() # in hours
textent = rawlst[:,0].max() - rawlst[:,0].min() + tres # in hours
eps = 1e-10
if 'prelim' not in self.cpinfo['processed']:
self.cpinfo['processed']['prelim'] = {}
no_change_in_lstbins = False
if lstbinsize > tres:
lstbinsize = NP.clip(lstbinsize, tres, textent)
lstbins = NP.arange(rawlst[:,0].min(), rawlst[:,0].max() + tres + eps, lstbinsize)
nlstbins = lstbins.size
lstbins = NP.concatenate((lstbins, [lstbins[-1]+lstbinsize+eps]))
if nlstbins > 1:
lstbinintervals = lstbins[1:] - lstbins[:-1]
lstbincenters = lstbins[:-1] + 0.5 * lstbinintervals
else:
lstbinintervals = NP.asarray(lstbinsize).reshape(-1)
lstbincenters = lstbins[0] + 0.5 * lstbinintervals
self.cpinfo['processed']['prelim']['lstbins'] = lstbincenters
self.cpinfo['processed']['prelim']['dlstbins'] = lstbinintervals
no_change_in_lstbins = False
else:
# Perform no binning and keep the current LST resolution, data and weights
warnings.warn('LST bin size found to be smaller than the LST resolution in the data. No LST binning/averaging will be performed.')
lstbinsize = tres
lstbins = NP.arange(rawlst[:,0].min(), rawlst[:,0].max() + lstbinsize + eps, lstbinsize)
nlstbins = lstbins.size - 1
if nlstbins > 1:
lstbinintervals = lstbins[1:] - lstbins[:-1]
else:
lstbinintervals = NP.asarray(lstbinsize).reshape(-1)
self.cpinfo['processed']['prelim']['dlstbins'] = lstbinintervals
self.cpinfo['processed']['prelim']['lstbins'] = lstbins[:-1]
# Ensure that the LST bins are inside the min/max envelope to
# error-free interpolation later
self.cpinfo['processed']['prelim']['lstbins'][0] += eps
self.cpinfo['processed']['prelim']['lstbins'][-1] -= eps
no_change_in_lstbins = True
counts, lstbin_edges, lstbinnum, ri = OPS.binned_statistic(rawlst[:,0], statistic='count', bins=lstbins)
counts = counts.astype(NP.int)
if 'wts' not in self.cpinfo['processed']['prelim']:
outshape = (counts.size, self.cpinfo['processed']['native']['eicp'].shape[1], self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3])
else:
outshape = (counts.size, self.cpinfo['processed']['prelim']['wts'].shape[1], self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3])
wts_lstbins = NP.zeros(outshape)
eicp_tmean = NP.zeros(outshape, dtype=NP.complex128)
eicp_tmedian = NP.zeros(outshape, dtype=NP.complex128)
cp_trms = NP.zeros(outshape)
cp_tmad = NP.zeros(outshape)
for binnum in xrange(counts.size):
if no_change_in_lstbins:
ind_lstbin = [binnum]
else:
ind_lstbin = ri[ri[binnum]:ri[binnum+1]]
if 'wts' not in self.cpinfo['processed']['prelim']:
indict = self.cpinfo['processed']['native']
else:
indict = self.cpinfo['processed']['prelim']
wts_lstbins[binnum,:,:,:] = NP.sum(indict['wts'][ind_lstbin,:,:,:].data, axis=0)
if 'wts' not in self.cpinfo['processed']['prelim']:
eicp_tmean[binnum,:,:,:] = NP.exp(1j*NP.angle(MA.mean(indict['eicp'][ind_lstbin,:,:,:], axis=0)))
eicp_tmedian[binnum,:,:,:] = NP.exp(1j*NP.angle(MA.median(indict['eicp'][ind_lstbin,:,:,:].real, axis=0) + 1j * MA.median(self.cpinfo['processed']['native']['eicp'][ind_lstbin,:,:,:].imag, axis=0)))
cp_trms[binnum,:,:,:] = MA.std(indict['cphase'][ind_lstbin,:,:,:], axis=0).data
cp_tmad[binnum,:,:,:] = MA.median(NP.abs(indict['cphase'][ind_lstbin,:,:,:] - NP.angle(eicp_tmedian[binnum,:,:,:][NP.newaxis,:,:,:])), axis=0).data
else:
eicp_tmean[binnum,:,:,:] = NP.exp(1j*NP.angle(MA.mean(NP.exp(1j*indict['cphase']['mean'][ind_lstbin,:,:,:]), axis=0)))
eicp_tmedian[binnum,:,:,:] = NP.exp(1j*NP.angle(MA.median(NP.cos(indict['cphase']['median'][ind_lstbin,:,:,:]), axis=0) + 1j * MA.median(NP.sin(indict['cphase']['median'][ind_lstbin,:,:,:]), axis=0)))
cp_trms[binnum,:,:,:] = MA.std(indict['cphase']['mean'][ind_lstbin,:,:,:], axis=0).data
cp_tmad[binnum,:,:,:] = MA.median(NP.abs(indict['cphase']['median'][ind_lstbin,:,:,:] - NP.angle(eicp_tmedian[binnum,:,:,:][NP.newaxis,:,:,:])), axis=0).data
mask = wts_lstbins <= 0.0
self.cpinfo['processed']['prelim']['wts'] = MA.array(wts_lstbins, mask=mask)
if 'eicp' not in self.cpinfo['processed']['prelim']:
self.cpinfo['processed']['prelim']['eicp'] = {}
if 'cphase' not in self.cpinfo['processed']['prelim']:
self.cpinfo['processed']['prelim']['cphase'] = {}
self.cpinfo['processed']['prelim']['eicp']['mean'] = MA.array(eicp_tmean, mask=mask)
self.cpinfo['processed']['prelim']['eicp']['median'] = MA.array(eicp_tmedian, mask=mask)
self.cpinfo['processed']['prelim']['cphase']['mean'] = MA.array(NP.angle(eicp_tmean), mask=mask)
self.cpinfo['processed']['prelim']['cphase']['median'] = MA.array(NP.angle(eicp_tmedian), mask=mask)
self.cpinfo['processed']['prelim']['cphase']['rms'] = MA.array(cp_trms, mask=mask)
self.cpinfo['processed']['prelim']['cphase']['mad'] = MA.array(cp_tmad, mask=mask)
# else:
# # Perform no binning and keep the current LST resolution, data and weights
# warnings.warn('LST bin size found to be smaller than the LST resolution in the data. No LST binning/averaging will be performed.')
# lstbinsize = tres
# lstbins = NP.arange(rawlst[:,0].min(), rawlst[:,0].max() + lstbinsize + eps, lstbinsize)
# nlstbins = lstbins.size - 1
# if nlstbins > 1:
# lstbinintervals = lstbins[1:] - lstbins[:-1]
# lstbincenters = lstbins[:-1] + 0.5 * lstbinintervals
# else:
# lstbinintervals = NP.asarray(lstbinsize).reshape(-1)
# lstbincenters = lstbins[0] + 0.5 * lstbinintervals
# if 'prelim' not in self.cpinfo['processed']:
# self.cpinfo['processed']['prelim'] = {}
# self.cpinfo['processed']['prelim']['lstbins'] = lstbincenters
# self.cpinfo['processed']['prelim']['dlstbins'] = lstbinintervals
if (rawlst.shape[0] <= 1) or (lstbinsize is None):
nlstbins = rawlst.shape[0]
lstbins = NP.mean(rawlst, axis=1)
if 'prelim' not in self.cpinfo['processed']:
self.cpinfo['processed']['prelim'] = {}
self.cpinfo['processed']['prelim']['lstbins'] = lstbins
if lstbinsize is not None:
self.cpinfo['processed']['prelim']['dlstbins'] = NP.asarray(lstbinsize).reshape(-1)
else:
self.cpinfo['processed']['prelim']['dlstbins'] = NP.zeros(1)
############################################################################
def subtract(self, cphase):
"""
------------------------------------------------------------------------
Subtract complex exponential of the bispectrum phase from the current
instance and updates the cpinfo attribute
Inputs:
cphase [masked array] Bispectrum phase array as a maked array. It
must be of same size as freqs along the axis specified in
input axis.
Action: Updates 'submodel' and 'residual' keys under attribute
cpinfo under key 'processed'
------------------------------------------------------------------------
"""
if not isinstance(cphase, NP.ndarray):
raise TypeError('Input cphase must be a numpy array')
if not isinstance(cphase, MA.MaskedArray):
cphase = MA.array(cphase, mask=NP.isnan(cphase))
if not OPS.is_broadcastable(cphase.shape, self.cpinfo['processed']['prelim']['cphase']['median'].shape):
raise ValueError('Input cphase has shape incompatible with that in instance attribute')
else:
minshape = tuple(NP.ones(self.cpinfo['processed']['prelim']['cphase']['median'].ndim - cphase.ndim, dtype=NP.int)) + cphase.shape
cphase = cphase.reshape(minshape)
# cphase = NP.broadcast_to(cphase, minshape)
eicp = NP.exp(1j*cphase)
self.cpinfo['processed']['submodel'] = {}
self.cpinfo['processed']['submodel']['cphase'] = cphase
self.cpinfo['processed']['submodel']['eicp'] = eicp
self.cpinfo['processed']['residual'] = {'eicp': {}, 'cphase': {}}
for key in ['mean', 'median']:
eicpdiff = self.cpinfo['processed']['prelim']['eicp'][key] - eicp
eicpratio = self.cpinfo['processed']['prelim']['eicp'][key] / eicp
self.cpinfo['processed']['residual']['eicp'][key] = eicpdiff
self.cpinfo['processed']['residual']['cphase'][key] = MA.array(NP.angle(eicpratio.data), mask=self.cpinfo['processed']['residual']['eicp'][key].mask)
############################################################################
def subsample_differencing(self, daybinsize=None, ndaybins=4, lstbinsize=None):
"""
------------------------------------------------------------------------
Create subsamples and differences between subsamples to evaluate noise
properties from the data set.
Inputs:
daybinsize [Nonetype or scalar] Day bin size (in days) over which mean
and median are estimated across different days for a fixed
LST bin. If set to None, it will look for value in input
ndaybins. If both are None, no smoothing is performed. Only
one of daybinsize or ndaybins must be set to non-None value.
Must yield greater than or equal to 4 bins
ndaybins [NoneType or integer] Number of bins along day axis. Only
if daybinsize is set to None. It produces bins that roughly
consist of equal number of days in each bin regardless of
how much the days in each bin are separated from each other.
If both are None, no smoothing is performed. Only one of
daybinsize or ndaybins must be set to non-None value. If set,
it must be set to greater than or equal to 4
lstbinsize [NoneType or scalar] LST bin size (in seconds) over which
mean and median are estimated across the LST. If set to
None, no smoothing is performed
------------------------------------------------------------------------
"""
if (ndaybins is not None) and (daybinsize is not None):
raise ValueError('Only one of daybinsize or ndaybins should be set')
if (daybinsize is not None) or (ndaybins is not None):
if daybinsize is not None:
if not isinstance(daybinsize, (int,float)):
raise TypeError('Input daybinsize must be a scalar')
dres = NP.diff(self.cpinfo['raw']['days']).min() # in days
dextent = self.cpinfo['raw']['days'].max() - self.cpinfo['raw']['days'].min() + dres # in days
if daybinsize > dres:
daybinsize = NP.clip(daybinsize, dres, dextent)
eps = 1e-10
daybins = NP.arange(self.cpinfo['raw']['days'].min(), self.cpinfo['raw']['days'].max() + dres + eps, daybinsize)
ndaybins = daybins.size
daybins = NP.concatenate((daybins, [daybins[-1]+daybinsize+eps]))
if ndaybins >= 4:
daybinintervals = daybins[1:] - daybins[:-1]
daybincenters = daybins[:-1] + 0.5 * daybinintervals
else:
raise ValueError('Could not find at least 4 bins along repeating days. Adjust binning interval.')
counts, daybin_edges, daybinnum, ri = OPS.binned_statistic(self.cpinfo['raw']['days'], statistic='count', bins=daybins)
counts = counts.astype(NP.int)
wts_daybins = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]))
eicp_dmean = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]), dtype=NP.complex128)
eicp_dmedian = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]), dtype=NP.complex128)
cp_drms = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]))
cp_dmad = NP.zeros((self.cpinfo['processed']['native']['eicp'].shape[0], counts.size, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3]))
for binnum in xrange(counts.size):
ind_daybin = ri[ri[binnum]:ri[binnum+1]]
wts_daybins[:,binnum,:,:] = NP.sum(self.cpinfo['processed']['native']['wts'][:,ind_daybin,:,:].data, axis=1)
eicp_dmean[:,binnum,:,:] = NP.exp(1j*NP.angle(MA.mean(self.cpinfo['processed']['native']['eicp'][:,ind_daybin,:,:], axis=1)))
eicp_dmedian[:,binnum,:,:] = NP.exp(1j*NP.angle(MA.median(self.cpinfo['processed']['native']['eicp'][:,ind_daybin,:,:].real, axis=1) + 1j * MA.median(self.cpinfo['processed']['native']['eicp'][:,ind_daybin,:,:].imag, axis=1)))
cp_drms[:,binnum,:,:] = MA.std(self.cpinfo['processed']['native']['cphase'][:,ind_daybin,:,:], axis=1).data
cp_dmad[:,binnum,:,:] = MA.median(NP.abs(self.cpinfo['processed']['native']['cphase'][:,ind_daybin,:,:] - NP.angle(eicp_dmedian[:,binnum,:,:][:,NP.newaxis,:,:])), axis=1).data
else:
if not isinstance(ndaybins, int):
raise TypeError('Input ndaybins must be an integer')
if ndaybins < 4:
raise ValueError('Input ndaybins must be greater than or equal to 4')
days_split = NP.array_split(self.cpinfo['raw']['days'], ndaybins)
daybincenters = NP.asarray([NP.mean(days) for days in days_split])
daybinintervals = NP.asarray([days.max()-days.min() for days in days_split])
counts = NP.asarray([days.size for days in days_split])
wts_split = NP.array_split(self.cpinfo['processed']['native']['wts'].data, ndaybins, axis=1)
# mask_split = NP.array_split(self.cpinfo['processed']['native']['wts'].mask, ndaybins, axis=1)
wts_daybins = NP.asarray([NP.sum(wtsitem, axis=1) for wtsitem in wts_split]) # ndaybins x nlst x ntriads x nchan
wts_daybins = NP.moveaxis(wts_daybins, 0, 1) # nlst x ndaybins x ntriads x nchan
mask_split = NP.array_split(self.cpinfo['processed']['native']['eicp'].mask, ndaybins, axis=1)
eicp_split = NP.array_split(self.cpinfo['processed']['native']['eicp'].data, ndaybins, axis=1)
eicp_dmean = MA.array([MA.mean(MA.array(eicp_split[i], mask=mask_split[i]), axis=1) for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
eicp_dmean = NP.exp(1j * NP.angle(eicp_dmean))
eicp_dmean = NP.moveaxis(eicp_dmean, 0, 1) # nlst x ndaybins x ntriads x nchan
eicp_dmedian = MA.array([MA.median(MA.array(eicp_split[i].real, mask=mask_split[i]), axis=1) + 1j * MA.median(MA.array(eicp_split[i].imag, mask=mask_split[i]), axis=1) for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
eicp_dmedian = NP.exp(1j * NP.angle(eicp_dmedian))
eicp_dmedian = NP.moveaxis(eicp_dmedian, 0, 1) # nlst x ndaybins x ntriads x nchan
cp_split = NP.array_split(self.cpinfo['processed']['native']['cphase'].data, ndaybins, axis=1)
cp_drms = NP.array([MA.std(MA.array(cp_split[i], mask=mask_split[i]), axis=1).data for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
cp_drms = NP.moveaxis(cp_drms, 0, 1) # nlst x ndaybins x ntriads x nchan
cp_dmad = NP.array([MA.median(NP.abs(cp_split[i] - NP.angle(eicp_dmedian[:,[i],:,:])), axis=1).data for i in range(daybincenters.size)]) # ndaybins x nlst x ntriads x nchan
cp_dmad = NP.moveaxis(cp_dmad, 0, 1) # nlst x ndaybins x ntriads x nchan
mask = wts_daybins <= 0.0
wts_daybins = MA.array(wts_daybins, mask=mask)
cp_dmean = MA.array(NP.angle(eicp_dmean), mask=mask)
cp_dmedian = MA.array(NP.angle(eicp_dmedian), mask=mask)
self.cpinfo['errinfo']['daybins'] = daybincenters
self.cpinfo['errinfo']['diff_dbins'] = daybinintervals
self.cpinfo['errinfo']['wts'] = {'{0}'.format(ind): None for ind in range(2)}
self.cpinfo['errinfo']['eicp_diff'] = {'{0}'.format(ind): {} for ind in range(2)}
rawlst = NP.degrees(NP.unwrap(NP.radians(self.cpinfo['raw']['lst'] * 15.0), discont=NP.pi, axis=0)) / 15.0 # in hours but unwrapped to have no discontinuities
if NP.any(rawlst > 24.0):
rawlst -= 24.0
if rawlst.shape[0] > 1: # LST bin only if there are multiple LST
if lstbinsize is not None:
if not isinstance(lstbinsize, (int,float)):
raise TypeError('Input lstbinsize must be a scalar')
lstbinsize = lstbinsize / 3.6e3 # in hours
tres = NP.diff(rawlst[:,0]).min() # in hours
textent = rawlst[:,0].max() - rawlst[:,0].min() + tres # in hours
eps = 1e-10
no_change_in_lstbins = False
if lstbinsize > tres:
lstbinsize = NP.clip(lstbinsize, tres, textent)
lstbins = NP.arange(rawlst[:,0].min(), rawlst[:,0].max() + tres + eps, lstbinsize)
nlstbins = lstbins.size
lstbins = NP.concatenate((lstbins, [lstbins[-1]+lstbinsize+eps]))
if nlstbins > 1:
lstbinintervals = lstbins[1:] - lstbins[:-1]
lstbincenters = lstbins[:-1] + 0.5 * lstbinintervals
else:
lstbinintervals = NP.asarray(lstbinsize).reshape(-1)
lstbincenters = lstbins[0] + 0.5 * lstbinintervals
self.cpinfo['errinfo']['lstbins'] = lstbincenters
self.cpinfo['errinfo']['dlstbins'] = lstbinintervals
no_change_in_lstbins = False
else:
# Perform no binning and keep the current LST resolution
warnings.warn('LST bin size found to be smaller than the LST resolution in the data. No LST binning/averaging will be performed.')
lstbinsize = tres
lstbins = NP.arange(rawlst[:,0].min(), rawlst[:,0].max() + lstbinsize + eps, lstbinsize)
nlstbins = lstbins.size - 1
if nlstbins > 1:
lstbinintervals = lstbins[1:] - lstbins[:-1]
else:
lstbinintervals = NP.asarray(lstbinsize).reshape(-1)
self.cpinfo['errinfo']['dlstbins'] = lstbinintervals
self.cpinfo['errinfo']['lstbins'] = lstbins[:-1]
# Ensure that the LST bins are inside the min/max envelope to
# error-free interpolation later
self.cpinfo['errinfo']['lstbins'][0] += eps
self.cpinfo['errinfo']['lstbins'][-1] -= eps
no_change_in_lstbins = True
counts, lstbin_edges, lstbinnum, ri = OPS.binned_statistic(rawlst[:,0], statistic='count', bins=lstbins)
counts = counts.astype(NP.int)
outshape = (counts.size, wts_daybins.shape[1], self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3])
wts_lstbins = NP.zeros(outshape)
eicp_tmean = NP.zeros(outshape, dtype=NP.complex128)
eicp_tmedian = NP.zeros(outshape, dtype=NP.complex128)
cp_trms = NP.zeros(outshape)
cp_tmad = NP.zeros(outshape)
for binnum in xrange(counts.size):
if no_change_in_lstbins:
ind_lstbin = [binnum]
else:
ind_lstbin = ri[ri[binnum]:ri[binnum+1]]
wts_lstbins[binnum,:,:,:] = NP.sum(wts_daybins[ind_lstbin,:,:,:].data, axis=0)
eicp_tmean[binnum,:,:,:] = NP.exp(1j*NP.angle(MA.mean(NP.exp(1j*cp_dmean[ind_lstbin,:,:,:]), axis=0)))
eicp_tmedian[binnum,:,:,:] = NP.exp(1j*NP.angle(MA.median(NP.cos(cp_dmedian[ind_lstbin,:,:,:]), axis=0) + 1j * MA.median(NP.sin(cp_dmedian[ind_lstbin,:,:,:]), axis=0)))
mask = wts_lstbins <= 0.0
wts_lstbins = MA.array(wts_lstbins, mask=mask)
eicp_tmean = MA.array(eicp_tmean, mask=mask)
eicp_tmedian = MA.array(eicp_tmedian, mask=mask)
else:
wts_lstbins = MA.copy(wts_daybins)
mask = wts_lstbins.mask
eicp_tmean = MA.array(NP.exp(1j*NP.angle(NP.exp(1j*cp_dmean))), mask=mask)
eicp_tmedian = MA.array(NP.exp(1j*NP.angle(NP.cos(cp_dmedian) + 1j * NP.sin(cp_dmedian))), mask=mask)
if (rawlst.shape[0] <= 1) or (lstbinsize is None):
nlstbins = rawlst.shape[0]
lstbins = NP.mean(rawlst, axis=1)
self.cpinfo['errinfo']['lstbins'] = lstbins
if lstbinsize is not None:
self.cpinfo['errinfo']['dlstbins'] = NP.asarray(lstbinsize).reshape(-1)
else:
self.cpinfo['errinfo']['dlstbins'] = NP.zeros(1)
ncomb = NP.sum(NP.asarray([(ndaybins-i-1)*(ndaybins-i-2)*(ndaybins-i-3)/2 for i in range(ndaybins-3)])).astype(int)
diff_outshape = (nlstbins, ncomb, self.cpinfo['processed']['native']['eicp'].shape[2], self.cpinfo['processed']['native']['eicp'].shape[3])
for diffind in range(2):
self.cpinfo['errinfo']['eicp_diff']['{0}'.format(diffind)]['mean'] = MA.empty(diff_outshape, dtype=NP.complex)
self.cpinfo['errinfo']['eicp_diff']['{0}'.format(diffind)]['median'] = MA.empty(diff_outshape, dtype=NP.complex)
self.cpinfo['errinfo']['wts']['{0}'.format(diffind)] = MA.empty(diff_outshape, dtype=NP.float)
ind = -1
self.cpinfo['errinfo']['list_of_pair_of_pairs'] = []
list_of_pair_of_pairs = []
for i in range(ndaybins-1):
for j in range(i+1,ndaybins):
for k in range(ndaybins-1):
if (k != i) and (k != j):
for m in range(k+1,ndaybins):
if (m != i) and (m != j):
pair_of_pairs = [set([i,j]), set([k,m])]
if (pair_of_pairs not in list_of_pair_of_pairs) and (pair_of_pairs[::-1] not in list_of_pair_of_pairs):
ind += 1
list_of_pair_of_pairs += [copy.deepcopy(pair_of_pairs)]
self.cpinfo['errinfo']['list_of_pair_of_pairs'] += [[i,j,k,m]]
for stat in ['mean', 'median']:
if stat == 'mean':
self.cpinfo['errinfo']['eicp_diff']['0'][stat][:,ind,:,:] = MA.array(0.5 * (eicp_tmean[:,j,:,:].data - eicp_tmean[:,i,:,:].data), mask=NP.logical_or(eicp_tmean[:,j,:,:].mask, eicp_tmean[:,i,:,:].mask))
self.cpinfo['errinfo']['eicp_diff']['1'][stat][:,ind,:,:] = MA.array(0.5 * (eicp_tmean[:,m,:,:].data - eicp_tmean[:,k,:,:].data), mask=NP.logical_or(eicp_tmean[:,m,:,:].mask, eicp_tmean[:,k,:,:].mask))
self.cpinfo['errinfo']['wts']['0'][:,ind,:,:] = MA.array(NP.sqrt(wts_lstbins[:,j,:,:].data**2 + wts_lstbins[:,i,:,:].data**2), mask=NP.logical_or(wts_lstbins[:,j,:,:].mask, wts_lstbins[:,i,:,:].mask))
self.cpinfo['errinfo']['wts']['1'][:,ind,:,:] = MA.array(NP.sqrt(wts_lstbins[:,m,:,:].data**2 + wts_lstbins[:,k,:,:].data**2), mask=NP.logical_or(wts_lstbins[:,m,:,:].mask, wts_lstbins[:,k,:,:].mask))
# self.cpinfo['errinfo']['eicp_diff']['0'][stat][:,ind,:,:] = 0.5 * (eicp_tmean[:,j,:,:] - eicp_tmean[:,i,:,:])
# self.cpinfo['errinfo']['eicp_diff']['1'][stat][:,ind,:,:] = 0.5 * (eicp_tmean[:,m,:,:] - eicp_tmean[:,k,:,:])
# self.cpinfo['errinfo']['wts']['0'][:,ind,:,:] = NP.sqrt(wts_lstbins[:,j,:,:]**2 + wts_lstbins[:,i,:,:]**2)
# self.cpinfo['errinfo']['wts']['1'][:,ind,:,:] = NP.sqrt(wts_lstbins[:,m,:,:]**2 + wts_lstbins[:,k,:,:]**2)
else:
self.cpinfo['errinfo']['eicp_diff']['0'][stat][:,ind,:,:] = MA.array(0.5 * (eicp_tmedian[:,j,:,:].data - eicp_tmedian[:,i,:,:].data), mask=NP.logical_or(eicp_tmedian[:,j,:,:].mask, eicp_tmedian[:,i,:,:].mask))
self.cpinfo['errinfo']['eicp_diff']['1'][stat][:,ind,:,:] = MA.array(0.5 * (eicp_tmedian[:,m,:,:].data - eicp_tmedian[:,k,:,:].data), mask=NP.logical_or(eicp_tmedian[:,m,:,:].mask, eicp_tmedian[:,k,:,:].mask))
# self.cpinfo['errinfo']['eicp_diff']['0'][stat][:,ind,:,:] = 0.5 * (eicp_tmedian[:,j,:,:] - eicp_tmedian[:,i,:,:])
# self.cpinfo['errinfo']['eicp_diff']['1'][stat][:,ind,:,:] = 0.5 * (eicp_tmedian[:,m,:,:] - eicp_tmedian[:,k,:,:])
mask0 = self.cpinfo['errinfo']['wts']['0'] <= 0.0
mask1 = self.cpinfo['errinfo']['wts']['1'] <= 0.0
self.cpinfo['errinfo']['eicp_diff']['0'][stat] = MA.array(self.cpinfo['errinfo']['eicp_diff']['0'][stat], mask=mask0)
self.cpinfo['errinfo']['eicp_diff']['1'][stat] = MA.array(self.cpinfo['errinfo']['eicp_diff']['1'][stat], mask=mask1)
self.cpinfo['errinfo']['wts']['0'] = MA.array(self.cpinfo['errinfo']['wts']['0'], mask=mask0)
self.cpinfo['errinfo']['wts']['1'] = MA.array(self.cpinfo['errinfo']['wts']['1'], mask=mask1)
############################################################################
def save(self, outfile=None):
"""
------------------------------------------------------------------------
Save contents of attribute cpinfo in external HDF5 file
Inputs:
outfile [NoneType or string] Output file (HDF5) to save contents to.
If set to None (default), it will be saved in the file
pointed to by the extfile attribute of class ClosurePhase
------------------------------------------------------------------------
"""
if outfile is None:
outfile = self.extfile
NMO.save_dict_to_hdf5(self.cpinfo, outfile, compressinfo={'compress_fmt': 'gzip', 'compress_opts': 9})
################################################################################
class ClosurePhaseDelaySpectrum(object):
"""
----------------------------------------------------------------------------
Class to hold and operate on Closure Phase information.
It has the following attributes and member functions.
Attributes:
cPhase [instance of class ClosurePhase] Instance of class
ClosurePhase
f [numpy array] Frequencies (in Hz) in closure phase spectra
df [float] Frequency resolution (in Hz) in closure phase
spectra
cPhaseDS [dictionary] Possibly oversampled Closure Phase Delay
Spectrum information.
cPhaseDS_resampled
[dictionary] Resampled Closure Phase Delay Spectrum
information.
Member functions:
__init__() Initialize instance of class ClosurePhaseDelaySpectrum
FT() Fourier transform of complex closure phase spectra mapping
from frequency axis to delay axis.
subset() Return triad and time indices to select a subset of
processed data
compute_power_spectrum()
Compute power spectrum of closure phase data. It is in units
of Mpc/h.
rescale_power_spectrum()
Rescale power spectrum to dimensional quantity by converting
the ratio given visibility amplitude information
average_rescaled_power_spectrum()
Average the rescaled power spectrum with physical units
along certain axes with inverse variance or regular
averaging
beam3Dvol() Compute three-dimensional volume of the antenna power
pattern along two transverse axes and one LOS axis.
----------------------------------------------------------------------------
"""
def __init__(self, cPhase):
"""
------------------------------------------------------------------------
Initialize instance of class ClosurePhaseDelaySpectrum
Inputs:
cPhase [class ClosurePhase] Instance of class ClosurePhase
------------------------------------------------------------------------
"""
if not isinstance(cPhase, ClosurePhase):
raise TypeError('Input cPhase must be an instance of class ClosurePhase')
self.cPhase = cPhase
self.f = self.cPhase.f
self.df = self.cPhase.df
self.cPhaseDS = None
self.cPhaseDS_resampled = None
############################################################################
def FT(self, bw_eff, freq_center=None, shape=None, fftpow=None, pad=None,
datapool='prelim', visscaleinfo=None, method='fft', resample=True,
apply_flags=True):
"""
------------------------------------------------------------------------
Fourier transform of complex closure phase spectra mapping from
frequency axis to delay axis.
Inputs:
bw_eff [scalar or numpy array] effective bandwidths (in Hz) on the
selected frequency windows for subband delay transform of
closure phases. If a scalar value is provided, the same
will be applied to all frequency windows
freq_center [scalar, list or numpy array] frequency centers (in Hz) of
the selected frequency windows for subband delay transform
of closure phases. The value can be a scalar, list or numpy
array. If a scalar is provided, the same will be applied to
all frequency windows. Default=None uses the center
frequency from the class attribute named channels
shape [string] frequency window shape for subband delay transform
of closure phases. Accepted values for the string are
'rect' or 'RECT' (for rectangular), 'bnw' and 'BNW' (for
Blackman-Nuttall), and 'bhw' or 'BHW' (for
Blackman-Harris). Default=None sets it to 'rect'
(rectangular window)
fftpow [scalar] the power to which the FFT of the window will be
raised. The value must be a positive scalar. Default = 1.0
pad [scalar] padding fraction relative to the number of
frequency channels for closure phases. Value must be a
non-negative scalar. For e.g., a pad of 1.0 pads the
frequency axis with zeros of the same width as the number
of channels. After the delay transform, the transformed
closure phases are downsampled by a factor of 1+pad. If a
negative value is specified, delay transform will be
performed with no padding. Default=None sets to padding
factor to 1.0
datapool [string] Specifies which data set is to be Fourier
transformed
visscaleinfo
[dictionary] Dictionary containing reference visibilities
based on which the closure phases will be scaled to units
of visibilities. It contains the following keys and values:
'vis' [numpy array or instance of class
InterferometerArray] Reference visibilities from the
baselines that form the triad. It can be an instance
of class RI.InterferometerArray or a numpy array.
If an instance of class InterferometerArray, the
baseline triplet must be set in key 'bltriplet'
and value in key 'lst' will be ignored. If the
value under this key 'vis' is set to a numpy array,
it must be of shape (nbl=3, nlst_vis, nchan). In
this case the value under key 'bltriplet' will be
ignored. The nearest LST will be looked up and
applied after smoothing along LST based on the
smoothing parameter 'smooth'
'bltriplet'
[Numpy array] Will be used in searching for matches
to these three baseline vectors if the value under
key 'vis' is set to an instance of class
InterferometerArray. However, if value under key
'vis' is a numpy array, this key 'bltriplet' will
be ignored.
'lst' [numpy array] Reference LST (in hours). It is of
shape (nlst_vis,). It will be used only if value
under key 'vis' is a numpy array, otherwise it will
be ignored and read from the instance of class
InterferometerArray passed under key 'vis'. If the
specified LST range does not cover the data LST
range, those LST will contain NaN in the delay
spectrum
'smoothinfo'
[dictionary] Dictionary specifying smoothing and/or
interpolation parameters. It has the following keys
and values:
'op_type' [string] Specifies the interpolating
operation. Must be specified (no
default). Accepted values are
'interp1d' (scipy.interpolate),
'median' (skimage.filters), 'tophat'
(astropy.convolution) and 'gaussian'
(astropy.convolution)
'interp_kind' [string (optional)] Specifies the
interpolation kind (if 'op_type' is
set to 'interp1d'). For accepted
values, see
scipy.interpolate.interp1d()
'window_size' [integer (optional)] Specifies the
size of the interpolating/smoothing
kernel. Only applies when 'op_type'
is set to 'median', 'tophat' or
'gaussian' The kernel is a tophat
function when 'op_type' is set to
'median' or 'tophat'. If refers to
FWHM when 'op_type' is set to
'gaussian'
resample [boolean] If set to True (default), resample the delay
spectrum axis to independent samples along delay axis. If
set to False, return the results as is even if they may be
be oversampled and not all samples may be independent
method [string] Specifies the Fourier transform method to be used.
Accepted values are 'fft' (default) for FFT and 'nufft' for
non-uniform FFT
apply_flags [boolean] If set to True (default), weights determined from
flags will be applied. If False, no weights from flagging
will be applied, and thus even flagged data will be included
Outputs:
A dictionary that contains the oversampled (if resample=False) or
resampled (if resample=True) delay spectrum information. It has the
following keys and values:
'freq_center' [numpy array] contains the center frequencies
(in Hz) of the frequency subbands of the subband
delay spectra. It is of size n_win. It is roughly
equivalent to redshift(s)
'freq_wts' [numpy array] Contains frequency weights applied
on each frequency sub-band during the subband delay
transform. It is of size n_win x nchan.
'bw_eff' [numpy array] contains the effective bandwidths
(in Hz) of the subbands being delay transformed. It
is of size n_win. It is roughly equivalent to width
in redshift or along line-of-sight
'shape' [string] shape of the window function applied.
Accepted values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow' [scalar] the power to which the FFT of the window was
raised. The value is be a positive scalar with
default = 1.0
'npad' [scalar] Numbber of zero-padded channels before
performing the subband delay transform.
'lags' [numpy array] lags of the subband delay spectra
after padding in frequency during the transform. It
is of size nlags=nchan+npad if resample=True, where
npad is the number of frequency channels padded
specified under the key 'npad'. If resample=False,
nlags = number of delays after resampling only
independent delays. The lags roughly correspond to
k_parallel.
'lag_kernel' [numpy array] delay transform of the frequency
weights under the key 'freq_wts'. It is of size
n_win x nlst x ndays x ntriads x nlags.
nlags=nchan+npad if resample=True, where npad is the
number of frequency channels padded specified under
the key 'npad'. If resample=False, nlags = number of
delays after resampling only independent delays.
'lag_corr_length'
[numpy array] It is the correlation timescale (in
pixels) of the subband delay spectra. It is
proportional to inverse of effective bandwidth. It
is of size n_win. The unit size of a pixel is
determined by the difference between adjacent pixels
in lags under key 'lags' which in turn is
effectively inverse of the effective bandwidth of
the subband specified in bw_eff
'whole' [dictionary] Delay spectrum results corresponding to
bispectrum phase in 'prelim' key of attribute cpinfo.
Contains the following keys and values:
'dspec' [dictionary] Contains the following keys and
values:
'twts' [numpy array] Weights from time-based
flags that went into time-averaging.
Shape=(nlst,ndays,ntriads,nchan)
'mean' [numpy array] Delay spectrum of closure
phases based on their mean across time
intervals.
Shape=(nspw,nlst,ndays,ntriads,nlags)
'median'
[numpy array] Delay spectrum of closure
phases based on their median across time
intervals.
Shape=(nspw,nlst,ndays,ntriads,nlags)
'submodel' [dictionary] Delay spectrum results corresponding to
bispectrum phase in 'submodel' key of attribute cpinfo.
Contains the following keys and values:
'dspec' [numpy array] Delay spectrum of closure phases
Shape=(nspw,nlst,ndays,ntriads,nlags)
'residual' [dictionary] Delay spectrum results corresponding to
bispectrum phase in 'residual' key of attribute cpinfo
after subtracting 'submodel' bispectrum phase from that
of 'prelim'. It contains the following keys and values:
'dspec' [dictionary] Contains the following keys and
values:
'twts' [numpy array] Weights from time-based
flags that went into time-averaging.
Shape=(nlst,ndays,ntriads,nchan)
'mean' [numpy array] Delay spectrum of closure
phases based on their mean across time
intervals.
Shape=(nspw,nlst,ndays,ntriads,nlags)
'median'
[numpy array] Delay spectrum of closure
phases based on their median across time
intervals.
Shape=(nspw,nlst,ndays,ntriads,nlags)
'errinfo' [dictionary] It has two keys 'dspec0' and 'dspec1' each
of which are dictionaries with the following keys and
values:
'twts' [numpy array] Weights for the subsample
difference. It is of shape (nlst, ndays,
ntriads, nchan)
'mean' [numpy array] Delay spectrum of the
subsample difference obtained by using the
mean statistic. It is of shape (nspw, nlst,
ndays, ntriads, nlags)
'median'
[numpy array] Delay spectrum of the subsample
difference obtained by using the median
statistic. It is of shape (nspw, nlst, ndays,
ntriads, nlags)
------------------------------------------------------------------------
"""
try:
bw_eff
except NameError:
raise NameError('Effective bandwidth must be specified')
else:
if not isinstance(bw_eff, (int, float, list, NP.ndarray)):
raise TypeError('Value of effective bandwidth must be a scalar, list or numpy array')
bw_eff = NP.asarray(bw_eff).reshape(-1)
if NP.any(bw_eff <= 0.0):
raise ValueError('All values in effective bandwidth must be strictly positive')
if freq_center is None:
freq_center = NP.asarray(self.f[self.f.size/2]).reshape(-1)
elif isinstance(freq_center, (int, float, list, NP.ndarray)):
freq_center = NP.asarray(freq_center).reshape(-1)
if NP.any((freq_center <= self.f.min()) | (freq_center >= self.f.max())):
raise ValueError('Value(s) of frequency center(s) must lie strictly inside the observing band')
else:
raise TypeError('Values(s) of frequency center must be scalar, list or numpy array')
if (bw_eff.size == 1) and (freq_center.size > 1):
bw_eff = NP.repeat(bw_eff, freq_center.size)
elif (bw_eff.size > 1) and (freq_center.size == 1):
freq_center = NP.repeat(freq_center, bw_eff.size)
elif bw_eff.size != freq_center.size:
raise ValueError('Effective bandwidth(s) and frequency center(s) must have same number of elements')
if shape is not None:
if not isinstance(shape, str):
raise TypeError('Window shape must be a string')
if shape not in ['rect', 'bhw', 'bnw', 'RECT', 'BHW', 'BNW']:
raise ValueError('Invalid value for window shape specified.')
else:
shape = 'rect'
if fftpow is None:
fftpow = 1.0
else:
if not isinstance(fftpow, (int, float)):
raise TypeError('Power to raise window FFT by must be a scalar value.')
if fftpow < 0.0:
raise ValueError('Power for raising FFT of window by must be positive.')
if pad is None:
pad = 1.0
else:
if not isinstance(pad, (int, float)):
raise TypeError('pad fraction must be a scalar value.')
if pad < 0.0:
pad = 0.0
if verbose:
print('\tPad fraction found to be negative. Resetting to 0.0 (no padding will be applied).')
if not isinstance(datapool, str):
raise TypeError('Input datapool must be a string')
if datapool.lower() not in ['prelim']:
raise ValueError('Specified datapool not supported')
if visscaleinfo is not None:
if not isinstance(visscaleinfo, dict):
raise TypeError('Input visscaleinfo must be a dictionary')
if 'vis' not in visscaleinfo:
raise KeyError('Input visscaleinfo does not contain key "vis"')
if not isinstance(visscaleinfo['vis'], RI.InterferometerArray):
if 'lst' not in visscaleinfo:
raise KeyError('Input visscaleinfo does not contain key "lst"')
lst_vis = visscaleinfo['lst'] * 15.0
if not isinstance(visscaleinfo['vis'], (NP.ndarray,MA.MaskedArray)):
raise TypeError('Input visibilities must be a numpy or a masked array')
if not isinstance(visscaleinfo['vis'], MA.MaskedArray):
visscaleinfo['vis'] = MA.array(visscaleinfo['vis'], mask=NP.isnan(visscaleinfo['vis']))
vistriad = MA.copy(visscaleinfo['vis'])
else:
if 'bltriplet' not in visscaleinfo:
raise KeyError('Input dictionary visscaleinfo does not contain key "bltriplet"')
blind, blrefind, dbl = LKP.find_1NN(visscaleinfo['vis'].baselines, visscaleinfo['bltriplet'], distance_ULIM=0.2, remove_oob=True)
if blrefind.size != 3:
blind_missing = NP.setdiff1d(NP.arange(3), blind, assume_unique=True)
blind_next, blrefind_next, dbl_next = LKP.find_1NN(visscaleinfo['vis'].baselines, -1*visscaleinfo['bltriplet'][blind_missing,:], distance_ULIM=0.2, remove_oob=True)
if blind_next.size + blind.size != 3:
raise ValueError('Exactly three baselines were not found in the reference baselines')
else:
blind = NP.append(blind, blind_missing[blind_next])
blrefind = NP.append(blrefind, blrefind_next)
else:
blind_missing = []
vistriad = NP.transpose(visscaleinfo['vis'].skyvis_freq[blrefind,:,:], (0,2,1))
if len(blind_missing) > 0:
vistriad[-blrefind_next.size:,:,:] = vistriad[-blrefind_next.size:,:,:].conj()
vistriad = MA.array(vistriad, mask=NP.isnan(vistriad))
lst_vis = visscaleinfo['vis'].lst
viswts = MA.array(NP.ones_like(vistriad.data), mask=vistriad.mask, dtype=NP.float)
lst_out = self.cPhase.cpinfo['processed']['prelim']['lstbins'] * 15.0
if lst_vis.size == 1: # Apply the visibility scaling from one reference LST to all LST
vis_ref = vistriad * NP.ones(lst_out.size).reshape(1,-1,1)
wts_ref = viswts * NP.ones(lst_out.size).reshape(1,-1,1)
else:
vis_ref, wts_ref = OPS.interpolate_masked_array_1D(vistriad, viswts, 1, visscaleinfo['smoothinfo'], inploc=lst_vis, outloc=lst_out)
if not isinstance(method, str):
raise TypeError('Input method must be a string')
if method.lower() not in ['fft', 'nufft']:
raise ValueError('Specified FFT method not supported')
if not isinstance(apply_flags, bool):
raise TypeError('Input apply_flags must be boolean')
flagwts = 1.0
visscale = 1.0
if datapool.lower() == 'prelim':
if method.lower() == 'fft':
freq_wts = NP.empty((bw_eff.size, self.f.size), dtype=NP.float_) # nspw x nchan
frac_width = DSP.window_N2width(n_window=None, shape=shape, fftpow=fftpow, area_normalize=False, power_normalize=True)
window_loss_factor = 1 / frac_width
n_window = NP.round(window_loss_factor * bw_eff / self.df).astype(NP.int)
ind_freq_center, ind_channels, dfrequency = LKP.find_1NN(self.f.reshape(-1,1), freq_center.reshape(-1,1), distance_ULIM=0.51*self.df, remove_oob=True)
sortind = NP.argsort(ind_channels)
ind_freq_center = ind_freq_center[sortind]
ind_channels = ind_channels[sortind]
dfrequency = dfrequency[sortind]
n_window = n_window[sortind]
for i,ind_chan in enumerate(ind_channels):
window = NP.sqrt(frac_width * n_window[i]) * DSP.window_fftpow(n_window[i], shape=shape, fftpow=fftpow, centering=True, peak=None, area_normalize=False, power_normalize=True)
window_chans = self.f[ind_chan] + self.df * (NP.arange(n_window[i]) - int(n_window[i]/2))
ind_window_chans, ind_chans, dfreq = LKP.find_1NN(self.f.reshape(-1,1), window_chans.reshape(-1,1), distance_ULIM=0.51*self.df, remove_oob=True)
sind = NP.argsort(ind_window_chans)
ind_window_chans = ind_window_chans[sind]
ind_chans = ind_chans[sind]
dfreq = dfreq[sind]
window = window[ind_window_chans]
window = NP.pad(window, ((ind_chans.min(), self.f.size-1-ind_chans.max())), mode='constant', constant_values=((0.0,0.0)))
freq_wts[i,:] = window
npad = int(self.f.size * pad)
lags = DSP.spectral_axis(self.f.size + npad, delx=self.df, use_real=False, shift=True)
result = {'freq_center': freq_center, 'shape': shape, 'freq_wts': freq_wts, 'bw_eff': bw_eff, 'fftpow': fftpow, 'npad': npad, 'lags': lags, 'lag_corr_length': self.f.size / NP.sum(freq_wts, axis=-1), 'whole': {'dspec': {'twts': self.cPhase.cpinfo['processed'][datapool]['wts']}}, 'residual': {'dspec': {'twts': self.cPhase.cpinfo['processed'][datapool]['wts']}}, 'errinfo': {'dspec0': {'twts': self.cPhase.cpinfo['errinfo']['wts']['0']}, 'dspec1': {'twts': self.cPhase.cpinfo['errinfo']['wts']['1']}}, 'submodel': {}}
if visscaleinfo is not None:
visscale = NP.nansum(NP.transpose(vis_ref[NP.newaxis,NP.newaxis,:,:,:], axes=(0,3,1,2,4)) * freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:], axis=-1, keepdims=True) / NP.nansum(freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:], axis=-1, keepdims=True) # nspw x nlst x (ndays=1) x (nbl=3) x (nchan=1)
visscale = NP.sqrt(1.0/NP.nansum(1/NP.abs(visscale)**2, axis=-2, keepdims=True)) # nspw x nlst x (ndays=1) x (ntriads=1) x (nchan=1)
for dpool in ['errinfo', 'prelim', 'submodel', 'residual']:
if dpool.lower() == 'errinfo':
for diffind in range(2):
if apply_flags:
flagwts = NP.copy(self.cPhase.cpinfo['errinfo']['wts']['{0}'.format(diffind)].data)
flagwts = flagwts[NP.newaxis,...] # nlst x ndays x ntriads x nchan --> (nspw=1) x nlst x ndays x ntriads x nchan
flagwts = 1.0 * flagwts / NP.mean(flagwts, axis=-1, keepdims=True) # (nspw=1) x nlst x ndays x ntriads x nchan
for stat in self.cPhase.cpinfo[dpool]['eicp_diff']['{0}'.format(diffind)]:
eicp = NP.copy(self.cPhase.cpinfo[dpool]['eicp_diff']['{0}'.format(diffind)][stat].data) # Minimum shape as stored
# eicp = NP.copy(self.cPhase.cpinfo[dpool]['eicp_diff']['{0}'.format(diffind)][stat].filled(0.0)) # Minimum shape as stored
eicp = NP.broadcast_to(eicp, self.cPhase.cpinfo[dpool]['eicp_diff']['{0}'.format(diffind)][stat].shape) # Broadcast to final shape
eicp = eicp[NP.newaxis,...] # nlst x ndayscomb x ntriads x nchan --> (nspw=1) x nlst x ndayscomb x ntriads x nchan
ndim_padtuple = [(0,0)]*(eicp.ndim-1) + [(0,npad)] # [(0,0), (0,0), (0,0), (0,0), (0,npad)]
result[dpool]['dspec{0}'.format(diffind)][stat] = DSP.FT1D(NP.pad(eicp*flagwts*freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:]*visscale.filled(NP.nan), ndim_padtuple, mode='constant'), ax=-1, inverse=True, use_real=False, shift=True) * (npad + self.f.size) * self.df
else:
if dpool in self.cPhase.cpinfo['processed']:
if apply_flags:
flagwts = NP.copy(self.cPhase.cpinfo['processed'][datapool]['wts'].data)
flagwts = flagwts[NP.newaxis,...] # nlst x ndays x ntriads x nchan --> (nspw=1) x nlst x ndays x ntriads x nchan
flagwts = 1.0 * flagwts / NP.mean(flagwts, axis=-1, keepdims=True) # (nspw=1) x nlst x ndays x ntriads x nchan
if dpool == 'submodel':
eicp = NP.copy(self.cPhase.cpinfo['processed'][dpool]['eicp'].data) # Minimum shape as stored
# eicp = NP.copy(self.cPhase.cpinfo['processed'][dpool]['eicp'].filled(1.0)) # Minimum shape as stored
eicp = NP.broadcast_to(eicp, self.cPhase.cpinfo['processed'][datapool]['eicp']['mean'].shape) # Broadcast to final shape
eicp = eicp[NP.newaxis,...] # nlst x ndays x ntriads x nchan --> (nspw=1) x nlst x ndays x ntriads x nchan
ndim_padtuple = [(0,0)]*(eicp.ndim-1) + [(0,npad)] # [(0,0), (0,0), (0,0), (0,0), (0,npad)]
result[dpool]['dspec'] = DSP.FT1D(NP.pad(eicp*flagwts*freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:]*visscale.filled(NP.nan), ndim_padtuple, mode='constant'), ax=-1, inverse=True, use_real=False, shift=True) * (npad + self.f.size) * self.df
else:
for key in self.cPhase.cpinfo['processed'][dpool]['eicp']:
eicp = NP.copy(self.cPhase.cpinfo['processed'][dpool]['eicp'][key].data)
# eicp = NP.copy(self.cPhase.cpinfo['processed'][dpool]['eicp'][key].filled(1.0))
eicp = eicp[NP.newaxis,...] # nlst x ndays x ntriads x nchan --> (nspw=1) x nlst x ndays x ntriads x nchan
ndim_padtuple = [(0,0)]*(eicp.ndim-1) + [(0,npad)] # [(0,0), (0,0), (0,0), (0,0), (0,npad)]
if dpool == 'prelim':
result['whole']['dspec'][key] = DSP.FT1D(NP.pad(eicp*flagwts*freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:]*visscale.filled(NP.nan), ndim_padtuple, mode='constant'), ax=-1, inverse=True, use_real=False, shift=True) * (npad + self.f.size) * self.df
else:
result[dpool]['dspec'][key] = DSP.FT1D(NP.pad(eicp*flagwts*freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:]*visscale.filled(NP.nan), ndim_padtuple, mode='constant'), ax=-1, inverse=True, use_real=False, shift=True) * (npad + self.f.size) * self.df
result['lag_kernel'] = DSP.FT1D(NP.pad(flagwts*freq_wts[:,NP.newaxis,NP.newaxis,NP.newaxis,:], ndim_padtuple, mode='constant'), ax=-1, inverse=True, use_real=False, shift=True) * (npad + self.f.size) * self.df
self.cPhaseDS = result
if resample:
result_resampled = copy.deepcopy(result)
downsample_factor = NP.min((self.f.size + npad) * self.df / bw_eff)
result_resampled['lags'] = DSP.downsampler(result_resampled['lags'], downsample_factor, axis=-1, method='interp', kind='linear')
result_resampled['lag_kernel'] = DSP.downsampler(result_resampled['lag_kernel'], downsample_factor, axis=-1, method='interp', kind='linear')
for dpool in ['errinfo', 'prelim', 'submodel', 'residual']:
if dpool.lower() == 'errinfo':
for diffind in self.cPhase.cpinfo[dpool]['eicp_diff']:
for key in self.cPhase.cpinfo[dpool]['eicp_diff'][diffind]:
result_resampled[dpool]['dspec'+diffind][key] = DSP.downsampler(result_resampled[dpool]['dspec'+diffind][key], downsample_factor, axis=-1, method='FFT')
if dpool in self.cPhase.cpinfo['processed']:
if dpool == 'submodel':
result_resampled[dpool]['dspec'] = DSP.downsampler(result_resampled[dpool]['dspec'], downsample_factor, axis=-1, method='FFT')
else:
for key in self.cPhase.cpinfo['processed'][datapool]['eicp']:
if dpool == 'prelim':
result_resampled['whole']['dspec'][key] = DSP.downsampler(result_resampled['whole']['dspec'][key], downsample_factor, axis=-1, method='FFT')
else:
result_resampled[dpool]['dspec'][key] = DSP.downsampler(result_resampled[dpool]['dspec'][key], downsample_factor, axis=-1, method='FFT')
self.cPhaseDS_resampled = result_resampled
return result_resampled
else:
return result
############################################################################
def subset(self, selection=None):
"""
------------------------------------------------------------------------
Return triad and time indices to select a subset of processed data
Inputs:
selection [NoneType or dictionary] Selection parameters based on which
triad, LST, and day indices will be returned. If set to None
(default), all triad, LST, and day indices will be returned.
Otherwise it must be a dictionary with the following keys
and values:
'triads' [NoneType or list of 3-element tuples] If set
to None (default), indices of all triads are
returned. Otherwise, the specific triads must
be specified such as [(1,2,3), (1,2,4), ...]
and their indices will be returned
'lst' [NoneType, list or numpy array] If set to None
(default), indices of all LST are returned.
Otherwise must be a list or numpy array
containing indices to LST.
'days' [NoneType, list or numpy array] If set to None
(default), indices of all days are returned.
Otherwise must be a list or numpy array
containing indices to days.
Outputs:
Tuple (triad_ind, lst_ind, day_ind, day_ind_eicpdiff) containing the
triad, LST, day, and day-pair (for subsample differences) indices,
each as a numpy array
------------------------------------------------------------------------
"""
if selection is None:
selsection = {}
else:
if not isinstance(selection, dict):
raise TypeError('Input selection must be a dictionary')
triads = map(tuple, self.cPhase.cpinfo['raw']['triads'])
if 'triads' not in selection:
selection['triads'] = triads
if selection['triads'] is None:
selection['triads'] = triads
triad_ind = [triads.index(triad) for triad in selection['triads']]
triad_ind = NP.asarray(triad_ind)
lst_ind = None
if 'lst' not in selection:
if 'prelim' in self.cPhase.cpinfo['processed']:
lst_ind = NP.arange(self.cPhase.cpinfo['processed']['prelim']['wts'].shape[0])
else:
if selection['lst'] is None:
if 'prelim' in self.cPhase.cpinfo['processed']:
lst_ind = NP.arange(self.cPhase.cpinfo['processed']['prelim']['wts'].shape[0])
elif isinstance(selection['lst'], (list,NP.ndarray)):
if 'prelim' in self.cPhase.cpinfo['processed']:
lst_ind = selection['lst']
if NP.any(NP.logical_or(lst_ind < 0, lst_ind >= self.cPhase.cpinfo['processed']['prelim']['wts'].shape[0])):
raise ValueError('Input processed lst indices out of bounds')
else:
raise TypeError('Wrong type for processed lst indices')
if lst_ind is None:
raise ValueError('LST index selection could not be performed')
day_ind = None
day_ind_eicpdiff = None
if 'days' not in selection:
if 'prelim' in self.cPhase.cpinfo['processed']:
day_ind = NP.arange(self.cPhase.cpinfo['processed']['prelim']['wts'].shape[1])
if 'errinfo' in self.cPhase.cpinfo:
day_ind_eicpdiff = NP.arange(len(self.cPhase.cpinfo['errinfo']['list_of_pair_of_pairs']))
else:
if selection['days'] is None:
if 'prelim' in self.cPhase.cpinfo['processed']:
day_ind = NP.arange(self.cPhase.cpinfo['processed']['prelim']['wts'].shape[1])
if 'errinfo' in self.cPhase.cpinfo:
day_ind_eicpdiff = NP.arange(len(self.cPhase.cpinfo['errinfo']['list_of_pair_of_pairs']))
elif isinstance(selection['days'], (list,NP.ndarray)):
if 'prelim' in self.cPhase.cpinfo['processed']:
day_ind = selection['days']
if NP.any(NP.logical_or(day_ind < 0, day_ind >= self.cPhase.cpinfo['processed']['prelim']['wts'].shape[1])):
raise ValueError('Input processed day indices out of bounds')
if 'errinfo' in self.cPhase.cpinfo:
day_ind_eicpdiff = [i for i,item in enumerate(self.cPhase.cpinfo['errinfo']['list_of_pair_of_pairs']) if len(set(item)-set(selection['days']))==0]
else:
raise TypeError('Wrong type for processed day indices')
if day_ind is None:
raise ValueError('Day index selection could not be performed')
return (triad_ind, lst_ind, day_ind, day_ind_eicpdiff)
############################################################################
def compute_power_spectrum(self, cpds=None, selection=None, autoinfo=None,
xinfo=None, cosmo=cosmo100, units='K', beamparms=None):
"""
------------------------------------------------------------------------
Compute power spectrum of closure phase data. It is in units of Mpc/h
Inputs:
cpds [dictionary] A dictionary that contains the 'oversampled' (if
resample=False) and/or 'resampled' (if resample=True) delay
spectrum information. If it is not specified the attributes
cPhaseDS['processed'] and cPhaseDS_resampled['processed'] are
used. Under each of these keys, it holds a dictionary that has
the following keys and values:
'freq_center' [numpy array] contains the center frequencies
(in Hz) of the frequency subbands of the subband
delay spectra. It is of size n_win. It is
roughly equivalent to redshift(s)
'freq_wts' [numpy array] Contains frequency weights applied
on each frequency sub-band during the subband
delay transform. It is of size n_win x nchan.
'bw_eff' [numpy array] contains the effective bandwidths
(in Hz) of the subbands being delay transformed.
It is of size n_win. It is roughly equivalent to
width in redshift or along line-of-sight
'shape' [string] shape of the window function applied.
Accepted values are 'rect' (rectangular), 'bhw'
(Blackman-Harris), 'bnw' (Blackman-Nuttall).
'fftpow' [scalar] the power to which the FFT of the window
was raised. The value is be a positive scalar
with default = 1.0
'npad' [scalar] Numbber of zero-padded channels before
performing the subband delay transform.
'lags' [numpy array] lags of the subband delay spectra
after padding in frequency during the transform.
It is of size nlags. The lags roughly correspond
to k_parallel.
'lag_kernel' [numpy array] delay transform of the frequency
weights under the key 'freq_wts'. It is of size
n_bl x n_win x nlags x n_t.
'lag_corr_length'
[numpy array] It is the correlation timescale
(in pixels) of the subband delay spectra. It is
proportional to inverse of effective bandwidth.
It is of size n_win. The unit size of a pixel is
determined by the difference between adjacent
pixels in lags under key 'lags' which in turn is
effectively inverse of the effective bandwidth
of the subband specified in bw_eff
'processed' [dictionary] Contains the following keys and
values:
'dspec' [dictionary] Contains the following keys
and values:
'twts' [numpy array] Weights from
time-based flags that went into
time-averaging.
Shape=(ntriads,npol,nchan,nt)
'mean' [numpy array] Delay spectrum of
closure phases based on their
mean across time intervals.
Shape=(nspw,npol,nt,ntriads,nlags)
'median'
[numpy array] Delay spectrum of
closure phases based on their
median across time intervals.
Shape=(nspw,npol,nt,ntriads,nlags)
selection [NoneType or dictionary] Selection parameters based on which
triad, LST, and day indices will be returned. If set to None
(default), all triad, LST, and day indices will be returned.
Otherwise it must be a dictionary with the following keys
and values:
'triads' [NoneType or list of 3-element tuples] If set
to None (default), indices of all triads are
returned. Otherwise, the specific triads must
be specified such as [(1,2,3), (1,2,4), ...]
and their indices will be returned
'lst' [NoneType, list or numpy array] If set to None
(default), indices of all LST are returned.
Otherwise must be a list or numpy array
containing indices to LST.
'days' [NoneType, list or numpy array] If set to None
(default), indices of all days are returned.
Otherwise must be a list or numpy array
containing indices to days.
autoinfo
[NoneType or dictionary] Specifies parameters for processing
before power spectrum in auto or cross modes. If set to None,
a dictionary will be created with the default values as
described below. The dictionary must have the following keys
and values:
'axes' [NoneType/int/list/tuple/numpy array] Axes that will
be averaged coherently before squaring (for auto) or
cross-multiplying (for cross) power spectrum. If set
to None (default), no axes are averaged coherently.
If set to int, list, tuple or numpy array, those axes
will be averaged coherently after applying the weights
specified under key 'wts' along those axes. 1=lst,
2=days, 3=triads.
'wts' [NoneType/list/numpy array] If not provided (equivalent
to setting it to None) or set to None (default), it is
set to a one element list which is a one element numpy
array of unity. Otherwise, it must be a list of same
number of elements as in key 'axes' and each of these
must be a numpy broadcast compatible array corresponding
to each of the axis specified in 'axes'
xinfo [NoneType or dictionary] Specifies parameters for processing
cross power spectrum. If set to None, a dictionary will be
created with the default values as described below. The
dictionary must have the following keys and values:
'axes' [NoneType/int/list/tuple/numpy array] Axes over which
power spectrum will be computed incoherently by cross-
multiplication. If set to None (default), no cross-
power spectrum is computed. If set to int, list, tuple
or numpy array, cross-power over those axes will be
computed incoherently by cross-multiplication. The
cross-spectrum over these axes will be computed after
applying the pre- and post- cross-multiplication
weights specified in key 'wts'. 1=lst, 2=days,
3=triads.
'collapse_axes'
[list] The axes that will be collpased after the
cross-power matrix is produced by cross-multiplication.
If this key is not set, it will be initialized to an
empty list (default), in which case none of the axes
is collapsed and the full cross-power matrix will be
output. it must be a subset of values under key 'axes'.
This will reduce it from a square matrix along that axis
to collapsed values along each of the leading diagonals.
1=lst, 2=days, 3=triads.
'dlst' [scalar] LST interval (in mins) or difference between LST
pairs which will be determined and used for
cross-power spectrum. Will only apply if values under
'axes' contains the LST axis(=1).
'dlst_range'
[scalar, numpy array, or NoneType] Specifies the LST
difference(s) in minutes that are to be used in the
computation of cross-power spectra. If a scalar, only
the diagonal consisting of pairs with that LST
difference will be computed. If a numpy array, those
diagonals consisting of pairs with that LST difference
will be computed. If set to None (default), the main
diagonal (LST difference of 0) and the first off-main
diagonal (LST difference of 1 unit) corresponding to
pairs with 0 and 1 unit LST difference are computed.
Applies only if key 'axes' contains LST axis (=1).
'avgcov'
[boolean] It specifies if the collapse of square
covariance matrix is to be collapsed further to a single
number after applying 'postX' weights. If not set or
set to False (default), this late stage collapse will
not be performed. Otherwise, it will be averaged in a
weighted average sense where the 'postX' weights would
have already been applied during the collapsing
operation
'wts' [NoneType or Dictionary] If not set, a default
dictionary (see default values below) will be created.
It must have the follwoing keys and values:
'preX' [list of numpy arrays] It contains pre-cross-
multiplication weights. It is a list where
each element in the list is a numpy array, and
the number of elements in the list must match
the number of entries in key 'axes'. If 'axes'
is set None, 'preX' may be set to a list
with one element which is a numpy array of ones.
The number of elements in each of the numpy
arrays must be numpy broadcastable into the
number of elements along that axis in the
delay spectrum.
'preXnorm'
[boolean] If False (default), no normalization
is done after the application of weights. If
set to True, the delay spectrum will be
normalized by the sum of the weights.
'postX' [list of numpy arrays] It contains post-cross-
multiplication weights. It is a list where
each element in the list is a numpy array, and
the number of elements in the list must match
the number of entries in key 'axes'. If 'axes'
is set None, 'preX' may be set to a list
with one element which is a numpy array of ones.
The number of elements in each of the numpy
arrays must be numpy broadcastable into the
number of elements along that axis in the
delay spectrum.
'preXnorm'
[boolean] If False (default), no normalization
is done after the application of 'preX' weights.
If set to True, the delay spectrum will be
normalized by the sum of the weights.
'postXnorm'
[boolean] If False (default), no normalization
is done after the application of postX weights.
If set to True, the delay cross power spectrum
will be normalized by the sum of the weights.
cosmo [instance of cosmology class from astropy] An instance of class
FLRW or default_cosmology of astropy cosmology module. Default
uses Planck 2015 cosmology, with H0=100 h km/s/Mpc
units [string] Specifies the units of output power spectum. Accepted
values are 'Jy' and 'K' (default)) and the power spectrum will
be in corresponding squared units.
Output:
Dictionary with the keys 'triads' ((ntriads,3) array), 'triads_ind',
((ntriads,) array), 'lstXoffsets' ((ndlst_range,) array), 'lst'
((nlst,) array), 'dlst' ((nlst,) array), 'lst_ind' ((nlst,) array),
'days' ((ndays,) array), 'day_ind' ((ndays,) array), 'dday'
((ndays,) array), 'oversampled' and 'resampled' corresponding to whether
resample was set to False or True in call to member function FT().
Values under keys 'triads_ind' and 'lst_ind' are numpy array
corresponding to triad and time indices used in selecting the data.
Values under keys 'oversampled' and 'resampled' each contain a
dictionary with the following keys and values:
'z' [numpy array] Redshifts corresponding to the band centers in
'freq_center'. It has shape=(nspw,)
'lags' [numpy array] Delays (in seconds). It has shape=(nlags,).
'kprll' [numpy array] k_parallel modes (in h/Mpc) corresponding to
'lags'. It has shape=(nspw,nlags)
'freq_center'
[numpy array] contains the center frequencies (in Hz) of the
frequency subbands of the subband delay spectra. It is of size
n_win. It is roughly equivalent to redshift(s)
'freq_wts'
[numpy array] Contains frequency weights applied on each
frequency sub-band during the subband delay transform. It is
of size n_win x nchan.
'bw_eff'
[numpy array] contains the effective bandwidths (in Hz) of the
subbands being delay transformed. It is of size n_win. It is
roughly equivalent to width in redshift or along line-of-sight
'shape' [string] shape of the frequency window function applied. Usual
values are 'rect' (rectangular), 'bhw' (Blackman-Harris),
'bnw' (Blackman-Nuttall).
'fftpow'
[scalar] the power to which the FFT of the window was raised.
The value is be a positive scalar with default = 1.0
'lag_corr_length'
[numpy array] It is the correlation timescale (in pixels) of
the subband delay spectra. It is proportional to inverse of
effective bandwidth. It is of size n_win. The unit size of a
pixel is determined by the difference between adjacent pixels
in lags under key 'lags' which in turn is effectively inverse
of the effective bandwidth of the subband specified in bw_eff
It further contains 3 keys named 'whole', 'submodel', and 'residual'
each of which is a dictionary. 'whole' contains power spectrum info
about the input closure phases. 'submodel' contains power spectrum info
about the model that will have been subtracted (as closure phase) from
the 'whole' model. 'residual' contains power spectrum info about the
closure phases obtained as a difference between 'whole' and 'submodel'.
It contains the following keys and values:
'mean' [numpy array] Delay power spectrum incoherently estiamted over
the axes specified in xinfo['axes'] using the 'mean' key in input
cpds or attribute cPhaseDS['processed']['dspec']. It has shape
that depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are not set,
those axes will be replaced with square covariance matrices. If
collapse_axes is provided but avgcov is False, those axes will be
of shape 2*Naxis-1.
'median'
[numpy array] Delay power spectrum incoherently averaged over
the axes specified in incohax using the 'median' key in input
cpds or attribute cPhaseDS['processed']['dspec']. It has shape
that depends on the combination of input parameters. See
examples below. If both collapse_axes and avgcov are not set,
those axes will be replaced with square covariance matrices. If
collapse_axes is provided bu avgcov is False, those axes will be
of shape 2*Naxis-1.
'diagoffsets'
[dictionary] Same keys corresponding to keys under
'collapse_axes' in input containing the diagonal offsets for
those axes. If 'avgcov' was set, those entries will be removed
from 'diagoffsets' since all the leading diagonal elements have
been collapsed (averaged) further. Value under each key is a
numpy array where each element in the array corresponds to the
index of that leading diagonal. This should match the size of
the output along that axis in 'mean' or 'median' above.
'diagweights'
[dictionary] Each key is an axis specified in collapse_axes and
the value is a numpy array of weights corresponding to the
diagonal offsets in that axis.
'axesmap'
[dictionary] If covariance in cross-power is calculated but is
not collapsed, the number of dimensions in the output will have
changed. This parameter tracks where the original axis is now
placed. The keys are the original axes that are involved in
incoherent cross-power, and the values are the new locations of
those original axes in the output.
'nsamples_incoh'
[integer] Number of incoherent samples in producing the power
spectrum
'nsamples_coh'
[integer] Number of coherent samples in producing the power
spectrum
Examples:
(1)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': 2, 'wts': None}
xinfo = {'axes': None, 'avgcov': False, 'collapse_axes': [],
'wts':{'preX': None, 'preXnorm': False,
'postX': None, 'postXnorm': False}}
Output delay power spectrum has shape (Nspw, Nlst, 1, Ntriads, Nlags)
(2)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': 2, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': False, 'collapse_axes': [],
'wts':{'preX': None, 'preXnorm': False,
'postX': None, 'postXnorm': False},
'dlst_range': None}
Output delay power spectrum has shape
(Nspw, 2, Nlst, 1, Ntriads, Ntriads, Nlags)
diagoffsets = {1: NP.arange(n_dlst_range)},
axesmap = {1: [1,2], 3: [4,5]}
(3)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': 2, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': False, 'collapse_axes': [3],
'dlst_range': [0.0, 1.0, 2.0]}
Output delay power spectrum has shape
(Nspw, 3, Nlst, 1, 2*Ntriads-1, Nlags)
diagoffsets = {1: NP.arange(n_dlst_range),
3: NP.arange(-Ntriads,Ntriads)},
axesmap = {1: [1,2], 3: [4]}
(4)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': None, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': False, 'collapse_axes': [1,3],
'dlst_range': [1.0, 2.0, 3.0, 4.0]}
Output delay power spectrum has shape
(Nspw, 4, Ndays, 2*Ntriads-1, Nlags)
diagoffsets = {1: NP.arange(n_dlst_range),
3: NP.arange(-Ntriads,Ntriads)},
axesmap = {1: [1], 3: [3]}
(5)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': None, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': True, 'collapse_axes': [3],
'dlst_range': None}
Output delay power spectrum has shape
(Nspw, 2, Nlst, Ndays, 1, Nlags)
diagoffsets = {1: NP.arange(n_dlst_range)}, axesmap = {1: [1,2], 3: [4]}
(6)
Input delay spectrum of shape (Nspw, Nlst, Ndays, Ntriads, Nlags)
autoinfo = {'axes': None, 'wts': None}
xinfo = {'axes': [1,3], 'avgcov': True, 'collapse_axes': []}
Output delay power spectrum has shape
(Nspw, 1, Ndays, 1, Nlags)
diagoffsets = {}, axesmap = {1: [1], 3: [3]}
------------------------------------------------------------------------
"""
if not isinstance(units,str):
raise TypeError('Input parameter units must be a string')
if units.lower() == 'k':
if not isinstance(beamparms, dict):
raise TypeError('Input beamparms must be a dictionary')
if 'freqs' not in beamparms:
beamparms['freqs'] = self.f
beamparms_orig = copy.deepcopy(beamparms)
if autoinfo is None:
autoinfo = {'axes': None, 'wts': [NP.ones(1, dtpye=NP.float)]}
elif not isinstance(autoinfo, dict):
raise TypeError('Input autoinfo must be a dictionary')
if 'axes' not in autoinfo:
autoinfo['axes'] = None
else:
if autoinfo['axes'] is not None:
if not isinstance(autoinfo['axes'], (list,tuple,NP.ndarray,int)):
raise TypeError('Value under key axes in input autoinfo must be an integer, list, tuple or numpy array')
else:
autoinfo['axes'] = NP.asarray(autoinfo['axes']).reshape(-1)
if 'wts' not in autoinfo:
if autoinfo['axes'] is not None:
autoinfo['wts'] = [NP.ones(1, dtype=NP.float)] * len(autoinfo['axes'])
else:
autoinfo['wts'] = [NP.ones(1, dtype=NP.float)]
else:
if autoinfo['axes'] is not None:
if not isinstance(autoinfo['wts'], list):
raise TypeError('wts in input autoinfo must be a list of numpy arrays')
else:
if len(autoinfo['wts']) != len(autoinfo['axes']):
raise ValueError('Input list of wts must be same as length of autoinfo axes')
else:
autoinfo['wts'] = [NP.ones(1, dtype=NP.float)]
if xinfo is None:
xinfo = {'axes': None, 'wts': {'preX': [NP.ones(1, dtpye=NP.float)], 'postX': [NP.ones(1, dtpye=NP.float)], 'preXnorm': False, 'postXnorm': False}}
elif not isinstance(xinfo, dict):
raise TypeError('Input xinfo must be a dictionary')
if 'axes' not in xinfo:
xinfo['axes'] = None
else:
if not isinstance(xinfo['axes'], (list,tuple,NP.ndarray,int)):
raise TypeError('Value under key axes in input xinfo must be an integer, list, tuple or numpy array')
else:
xinfo['axes'] = NP.asarray(xinfo['axes']).reshape(-1)
if 'wts' not in xinfo:
xinfo['wts'] = {}
for xkey in ['preX', 'postX']:
if xinfo['axes'] is not None:
xinfo['wts'][xkey] = [NP.ones(1, dtype=NP.float)] * len(xinfo['axes'])
else:
xinfo['wts'][xkey] = [NP.ones(1, dtype=NP.float)]
xinfo['wts']['preXnorm'] = False
xinfo['wts']['postXnorm'] = False
else:
if xinfo['axes'] is not None:
if not isinstance(xinfo['wts'], dict):
raise TypeError('wts in input xinfo must be a dictionary')
for xkey in ['preX', 'postX']:
if not isinstance(xinfo['wts'][xkey], list):
raise TypeError('{0} wts in input xinfo must be a list of numpy arrays'.format(xkey))
else:
if len(xinfo['wts'][xkey]) != len(xinfo['axes']):
raise ValueError('Input list of {0} wts must be same as length of xinfo axes'.format(xkey))
else:
for xkey in ['preX', 'postX']:
xinfo['wts'][xkey] = [NP.ones(1, dtype=NP.float)]
if 'preXnorm' not in xinfo['wts']:
xinfo['wts']['preXnorm'] = False
if 'postXnorm' not in xinfo['wts']:
xinfo['wts']['postXnorm'] = False
if not isinstance(xinfo['wts']['preXnorm'], NP.bool):
raise TypeError('preXnorm in input xinfo must be a boolean')
if not isinstance(xinfo['wts']['postXnorm'], NP.bool):
raise TypeError('postXnorm in input xinfo must be a boolean')
if 'avgcov' not in xinfo:
xinfo['avgcov'] = False
if not isinstance(xinfo['avgcov'], NP.bool):
raise TypeError('avgcov under input xinfo must be boolean')
if 'collapse_axes' not in xinfo:
xinfo['collapse_axes'] = []
if not isinstance(xinfo['collapse_axes'], (int,list,tuple,NP.ndarray)):
raise TypeError('collapse_axes under input xinfo must be an integer, tuple, list or numpy array')
else:
xinfo['collapse_axes'] = NP.asarray(xinfo['collapse_axes']).reshape(-1)
if (autoinfo['axes'] is not None) and (xinfo['axes'] is not None):
if NP.intersect1d(autoinfo['axes'], xinfo['axes']).size > 0:
raise ValueError("Inputs autoinfo['axes'] and xinfo['axes'] must have no intersection")
cohax = autoinfo['axes']
if cohax is None:
cohax = []
incohax = xinfo['axes']
if incohax is None:
incohax = []
if selection is None:
selection = {'triads': None, 'lst': None, 'days': None}
else:
if not isinstance(selection, dict):
raise TypeError('Input selection must be a dictionary')
if cpds is None:
cpds = {}
sampling = ['oversampled', 'resampled']
for smplng in sampling:
if smplng == 'oversampled':
cpds[smplng] = copy.deepcopy(self.cPhaseDS)
else:
cpds[smplng] = copy.deepcopy(self.cPhaseDS_resampled)
triad_ind, lst_ind, day_ind, day_ind_eicpdiff = self.subset(selection=selection)
result = {'triads': self.cPhase.cpinfo['raw']['triads'][triad_ind], 'triads_ind': triad_ind, 'lst': self.cPhase.cpinfo['processed']['prelim']['lstbins'][lst_ind], 'lst_ind': lst_ind, 'dlst': self.cPhase.cpinfo['processed']['prelim']['dlstbins'][lst_ind], 'days': self.cPhase.cpinfo['processed']['prelim']['daybins'][day_ind], 'day_ind': day_ind, 'dday': self.cPhase.cpinfo['processed']['prelim']['diff_dbins'][day_ind]}
dlstbin = NP.mean(self.cPhase.cpinfo['processed']['prelim']['dlstbins'])
if 'dlst_range' in xinfo:
if xinfo['dlst_range'] is None:
dlst_range = None
lstshifts = NP.arange(2) # LST index offsets of 0 and 1 are only estimated
else:
dlst_range = | NP.asarray(xinfo['dlst_range']) | numpy.asarray |
from pathlib import Path
import cv2
import numpy as np
import torch
import torchvision
from PIL import Image
from torch.utils.data import Dataset
from scipy.spatial.transform import Rotation
from utils import map_fn
class TUMMonoVOMultiDataset(Dataset):
def __init__(self, dataset_dirs, **kwargs):
if isinstance(dataset_dirs, list):
self.datasets = [TUMMonoVODataset(dataset_dir, **kwargs) for dataset_dir in dataset_dirs]
else:
self.datasets = [TUMMonoVODataset(dataset_dirs, **kwargs)]
def __getitem__(self, index):
for dataset in self.datasets:
l = len(dataset)
if index >= l:
index -= l
else:
return dataset.__getitem__(index)
return None
def __len__(self):
sum = 0
for dataset in self.datasets:
sum += len(dataset)
return sum
class TUMMonoVODataset(Dataset):
def __init__(self, dataset_dir, frame_count=2, target_image_size=(480, 640), max_length=None, dilation=1, only_keyframes=False, color_augmentation=True, scale_factor=1):
"""
Dataset implementation for TUMMonoVO. Requires the images to be rectified first. Support for depth maps is WIP.
:param dataset_dir: Folder of a single sequence (e.g. .../tummonovo/sequence_50). This folder should contain images/.
:param frame_count: Number of frames used per sample (excluding the keyframe). (Default=2)
:param target_image_size: Desired image size. (Default=(480, 640))
:param max_length: Crop dataset to given length. (Default=None)
:param dilation: Spacing between the different frames. (Default=1)
:param only_keyframes: Only use frames that were used as keyframes in DSO. Relies on depth maps -> WIP. (Default=False)
:param color_augmentation: Use color jitter augmentation. (Default=False)
:param scale_factor: Scale poses for the sequence. Useful for DSO, which does not necessarily detect the correct world-scale. (Default=1)
"""
self.dataset_dir = Path(dataset_dir)
self.frame_count = frame_count
self.only_keyframes = only_keyframes
self.dilation = dilation
self.target_image_size = target_image_size
self.color_augmentation = color_augmentation
self.scale_factor = scale_factor
self._result = np.loadtxt(self.dataset_dir / "result.txt")
self._times = np.loadtxt(self.dataset_dir / "times.txt")
self._pcalib = self.invert_pcalib(np.loadtxt(self.dataset_dir / "pcalib.txt"))
self._image_index = self.build_image_index()
if self.only_keyframes:
self._keyframe_index = self.build_keyframe_index()
self.length = self._keyframe_index.shape[0]
else:
self.length = self._result.shape[0] - frame_count * dilation
if max_length is not None:
self.length = min(self.length, max_length)
self._offset = (frame_count // 2) * self.dilation
self._intrinsics, self._crop_box = self.compute_target_intrinsics()
self._intrinsics = format_intrinsics(self._intrinsics, self.target_image_size)
self._poses = self.build_poses()
self._depth = torch.zeros((1, target_image_size[0], target_image_size[1]), dtype=torch.float32)
if self.color_augmentation:
self.color_augmentation_transform = ColorJitterMulti(brightness=.2, contrast=.2, saturation=.2, hue=.1)
def preprocess_image(self, img: Image.Image, crop_box=None):
img = img.convert('RGB')
if crop_box:
img = img.crop(crop_box)
if self.target_image_size:
img = img.resize((self.target_image_size[1], self.target_image_size[0]), resample=Image.BILINEAR)
if self.color_augmentation:
img = self.color_augmentation_transform(img)
image_tensor = torch.tensor(np.array(img)).to(dtype=torch.float32)
image_tensor = self._pcalib[image_tensor.to(dtype=torch.long)]
image_tensor = image_tensor / 255 - .5
if len(image_tensor.shape) == 2:
image_tensor = torch.stack((image_tensor, image_tensor, image_tensor))
else:
image_tensor = image_tensor.permute(2, 0, 1)
del img
return image_tensor
def preprocess_depth(self, depth: Image.Image, crop_box=None):
if crop_box:
depth = depth.crop(crop_box)
if self.target_image_size:
if self.target_image_size[0] * 2 == depth.size[1]:
depth_tensor = torch.tensor(np.array(depth).astype(np.float32))
depth_tensor = torch.nn.functional.max_pool2d(depth_tensor.unsqueeze(0), kernel_size=2)
else:
depth = depth.resize((self.target_image_size[1], self.target_image_size[0]), resample=Image.BILINEAR)
depth_tensor = torch.tensor(np.array(depth).astype(np.float32)).unsqueeze(0)
depth_tensor[depth_tensor < 0] = 0
return depth_tensor
def __getitem__(self, index: int):
frame_count = self.frame_count
offset = self._offset
if self.color_augmentation:
self.color_augmentation_transform.fix_transform()
if self.only_keyframes:
index = self._keyframe_index[index] - offset
keyframe_intrinsics = self._intrinsics
keyframe = self.preprocess_image(self.open_image(index + offset), self._crop_box)
keyframe_pose = self._poses[index + offset]
keyframe_depth = self.open_depth(index + offset)
if keyframe_depth is None:
keyframe_depth = self._depth
else:
keyframe_depth = self.preprocess_depth(keyframe_depth, self._crop_box)
frames = [self.preprocess_image(self.open_image(index + i), self._crop_box) for i in range(0, (frame_count + 1) * self.dilation, self.dilation) if i != offset]
intrinsics = [self._intrinsics for _ in range(frame_count)]
poses = [self._poses[index + i] for i in range(0, (frame_count + 1) * self.dilation, self.dilation) if i != offset]
data = {
"keyframe": keyframe,
"keyframe_pose": keyframe_pose,
"keyframe_intrinsics": keyframe_intrinsics,
"frames": frames,
"poses": poses,
"intrinsics": intrinsics,
"sequence": torch.tensor([0]),
"image_id": torch.tensor([index + offset])
}
return data, keyframe_depth
def __len__(self) -> int:
return self.length
def build_image_index(self):
eps = 1e-5
current_index = 0
image_index = np.zeros((self._result.shape[0]), dtype=np.int)
for i in range(self._result.shape[0]):
timestamp = self._result[i, 0]
while not timestamp <= self._times[current_index, 1] + eps:
current_index += 1
image_index[i] = current_index
return image_index
def build_keyframe_index(self):
keyframe_index = []
image_index_pos = 0
for p in sorted((self.dataset_dir / "images_depth").glob("*.exr")):
index = int(p.stem[:5])
while self._image_index[image_index_pos] < index:
image_index_pos += 1
index = image_index_pos
if not (index >= len(self._image_index) - (self.frame_count // 2 + 1) * self.dilation or index < (self.frame_count // 2) * self.dilation):
keyframe_index.append(index)
return np.array(keyframe_index)
def load_orig_intrinsics(self):
camera_file = self.dataset_dir / "camera.txt"
with open(camera_file) as f:
intrinsics_use_first_col = ord("0") <= ord(f.readline()[0]) <= ord("9")
if intrinsics_use_first_col:
intrinsics_v = np.loadtxt(camera_file, usecols=list(range(4)), max_rows=1)
else:
intrinsics_v = | np.loadtxt(camera_file, usecols=[1, 2, 3, 4], max_rows=1) | numpy.loadtxt |
import os
os.environ['DGLBACKEND']='pytorch'
from multiprocessing import Process
import argparse, time, math
import numpy as np
from functools import wraps
import tqdm
import sklearn.linear_model as lm
import sklearn.metrics as skm
import dgl
from dgl import DGLGraph
from dgl.data import register_data_args, load_data
from dgl.data.utils import load_graphs
import dgl.function as fn
import dgl.nn.pytorch as dglnn
import torch as th
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
import torch.multiprocessing as mp
from dgl.distributed import DistDataLoader
from train_dist_unsupervised import SAGE, NeighborSampler, PosNeighborSampler, CrossEntropyLoss, compute_acc
from train_dist_transductive import DistEmb, load_embs
def generate_emb(standalone, model, emb_layer, g, batch_size, device):
"""
Generate embeddings for each node
emb_layer : Embedding layer
g : The entire graph.
inputs : The features of all the nodes.
batch_size : Number of nodes to compute at the same time.
device : The GPU device to evaluate on.
"""
model.eval()
emb_layer.eval()
with th.no_grad():
inputs = load_embs(standalone, emb_layer, g)
pred = model.inference(g, inputs, batch_size, device)
g.barrier()
return pred
def run(args, device, data):
# Unpack data
train_eids, train_nids, g, global_train_nid, global_valid_nid, global_test_nid, labels = data
# Create sampler
sampler = NeighborSampler(g, [int(fanout) for fanout in args.fan_out.split(',')], train_nids,
dgl.distributed.sample_neighbors, args.num_negs, args.remove_edge)
# Create PyTorch DataLoader for constructing blocks
dataloader = dgl.distributed.DistDataLoader(
dataset=train_eids.numpy(),
batch_size=args.batch_size,
collate_fn=sampler.sample_blocks,
shuffle=True,
drop_last=False)
# Define model and optimizer
emb_layer = DistEmb(g.num_nodes(), args.num_hidden, dgl_sparse_emb=args.dgl_sparse, dev_id=device)
model = SAGE(args.num_hidden, args.num_hidden, args.num_hidden, args.num_layers, F.relu, args.dropout)
model = model.to(device)
if not args.standalone:
if args.num_gpus == -1:
model = th.nn.parallel.DistributedDataParallel(model)
else:
dev_id = g.rank() % args.num_gpus
model = th.nn.parallel.DistributedDataParallel(model, device_ids=[dev_id], output_device=dev_id)
if not args.dgl_sparse:
emb_layer = th.nn.parallel.DistributedDataParallel(emb_layer)
loss_fcn = CrossEntropyLoss()
loss_fcn = loss_fcn.to(device)
optimizer = optim.Adam(model.parameters(), lr=args.lr)
if args.dgl_sparse:
emb_optimizer = dgl.distributed.optim.SparseAdam([emb_layer.sparse_emb], lr=args.sparse_lr)
print('optimize DGL sparse embedding:', emb_layer.sparse_emb)
elif args.standalone:
emb_optimizer = th.optim.SparseAdam(list(emb_layer.sparse_emb.parameters()), lr=args.sparse_lr)
print('optimize Pytorch sparse embedding:', emb_layer.sparse_emb)
else:
emb_optimizer = th.optim.SparseAdam(list(emb_layer.module.sparse_emb.parameters()), lr=args.sparse_lr)
print('optimize Pytorch sparse embedding:', emb_layer.module.sparse_emb)
# Training loop
epoch = 0
for epoch in range(args.num_epochs):
sample_time = 0
copy_time = 0
forward_time = 0
backward_time = 0
update_time = 0
num_seeds = 0
num_inputs = 0
step_time = []
iter_t = []
sample_t = []
feat_copy_t = []
forward_t = []
backward_t = []
update_t = []
iter_tput = []
start = time.time()
# Loop over the dataloader to sample the computation dependency graph as a list of
# blocks.
for step, (pos_graph, neg_graph, blocks) in enumerate(dataloader):
tic_step = time.time()
sample_t.append(tic_step - start)
pos_graph = pos_graph.to(device)
neg_graph = neg_graph.to(device)
blocks = [block.to(device) for block in blocks]
# The nodes for input lies at the LHS side of the first block.
# The nodes for output lies at the RHS side of the last block.
# Load the input features as well as output labels
batch_inputs = blocks[0].srcdata[dgl.NID]
copy_time = time.time()
feat_copy_t.append(copy_time - tic_step)
# Compute loss and prediction
batch_inputs = emb_layer(batch_inputs)
batch_pred = model(blocks, batch_inputs)
loss = loss_fcn(batch_pred, pos_graph, neg_graph)
forward_end = time.time()
emb_optimizer.zero_grad()
optimizer.zero_grad()
loss.backward()
compute_end = time.time()
forward_t.append(forward_end - copy_time)
backward_t.append(compute_end - forward_end)
# Aggregate gradients in multiple nodes.
emb_optimizer.step()
optimizer.step()
update_t.append(time.time() - compute_end)
pos_edges = pos_graph.number_of_edges()
neg_edges = neg_graph.number_of_edges()
step_t = time.time() - start
step_time.append(step_t)
iter_tput.append(pos_edges / step_t)
num_seeds += pos_edges
if step % args.log_every == 0:
print('[{}] Epoch {:05d} | Step {:05d} | Loss {:.4f} | Speed (samples/sec) {:.4f} | time {:.3f} s' \
'| sample {:.3f} | copy {:.3f} | forward {:.3f} | backward {:.3f} | update {:.3f}'.format(
g.rank(), epoch, step, loss.item(), np.mean(iter_tput[3:]), np.sum(step_time[-args.log_every:]),
np.sum(sample_t[-args.log_every:]), np.sum(feat_copy_t[-args.log_every:]), np.sum(forward_t[-args.log_every:]),
| np.sum(backward_t[-args.log_every:]) | numpy.sum |
import numpy as np
from warnings import warn
from typing import List, Callable
from desdeo_emo.selection.SelectionBase import SelectionBase
from desdeo_emo.population.Population import Population
from desdeo_emo.utilities.ReferenceVectors import ReferenceVectors
class APD_Select(SelectionBase):
"""The selection operator for the RVEA algorithm. Read the following paper for more
details.
<NAME>, <NAME>, <NAME> and <NAME>, A Reference Vector Guided
Evolutionary Algorithm for Many-objective Optimization, IEEE Transactions on
Evolutionary Computation, 2016
Parameters
----------
pop : Population
The population instance
time_penalty_function : Callable
A function that returns the time component in the penalty function.
alpha : float, optional
The RVEA alpha parameter, by default 2
"""
def __init__(
self, pop: Population, time_penalty_function: Callable, alpha: float = 2
):
self.time_penalty_function = time_penalty_function
self.alpha = alpha
self.n_of_objectives = pop.problem.n_of_objectives
def do(self, pop: Population, vectors: ReferenceVectors) -> List[int]:
"""Select individuals for mating on basis of Angle penalized distance.
Parameters
----------
pop : Population
The current population.
vectors : ReferenceVectors
Class instance containing reference vectors.
Returns
-------
List[int]
List of indices of the selected individuals
"""
partial_penalty_factor = self._partial_penalty_factor()
refV = vectors.neighbouring_angles_current
# Normalization - There may be problems here
if pop.ideal_fitness_val is not None:
fmin = pop.ideal_fitness_val
else:
fmin = np.amin(pop.fitness, axis=0)
translated_fitness = pop.fitness - fmin
fitness_norm = np.linalg.norm(translated_fitness, axis=1)
# TODO check if you need the next line
fitness_norm = np.repeat(fitness_norm, len(translated_fitness[0, :])).reshape(
len(pop.fitness), len(pop.fitness[0, :])
)
# Convert zeros to eps to avoid divide by zero.
# Has to be checked!
fitness_norm[fitness_norm == 0] = np.finfo(float).eps
normalized_fitness = np.divide(
translated_fitness, fitness_norm
) # Checked, works.
cosine = np.dot(normalized_fitness, np.transpose(vectors.values))
if cosine[np.where(cosine > 1)].size:
warn("RVEA.py line 60 cosine larger than 1 decreased to 1")
cosine[np.where(cosine > 1)] = 1
if cosine[np.where(cosine < 0)].size:
warn("RVEA.py line 64 cosine smaller than 0 increased to 0")
cosine[ | np.where(cosine < 0) | numpy.where |
# -*- coding: utf-8 -*-
"""
### NOI_DFT.py ############################################################
Darstellung von Signal und Quantisierungsrauschen mit DFT
Korrekte Skalierung von Signal und Breitbandrauschen
# <NAME>, 27-5-2015
###########################################################################
"""
from __future__ import division, print_function, unicode_literals
import numpy as np
from numpy import sin, cos, pi, array, arange, log10, zeros, tan, sqrt
import matplotlib.pyplot as plt
import sys
sys.path.append('..')
import dsp_fpga_fix_lib as fx
print(plt.style.available)
plt.style.use('seaborn-poster') # sucht in stylelib Directories
#plt.style.use('../presentation.mplstyle') # sucht im Pfad
# Definiere Anzahl Samples, FFT - Länge, Samplingfrequenz etc.
N_FFT = 2048 # Anzahl Datenpunkte für FFT
TWIN_AX = False # Drucke zweite Achse für Rauschleistung
PRINT_AVG = True
PRINT_SNR = False # Drucke SNR und ENOB
PRINT_NOISE = False # Drucke Rauschleistung
DITHER = True
f_S = 2048 # Abtastfrequenz (eigentlich beliebig, ergibt Skalierungsfaktor)
f_S_Print = 50 # Abtastfrequenz für Plot
unit = ""
Ts = 1 / f_S # Abtastperiode
t = arange(N_FFT) * Ts # Zeitvektor 0 ... (Nx-1) Ts
#f = [0:1:L-1] / N_FFT * f_S # Frequenzvektor 0 ... f_S in N_FFT Schritten
#f = f_S/2*np.linspace(0,1,N_FFT/2) # Frequenzvektor 0 ... f_S/2 in N_FFT/2 Schritten
Hmin = -150 # Min. y-Wert (dB) für Anzeige und Ersetzen von -infinity Werten
Hmax = 2 # Max. y-Wert (dB) für Anzeige
#########################################################################
# Vorbelegen der Vektoren mit Nullen zur Initialisierung und Beschleunigung
x = zeros(N_FFT) # Eingangssignal
xq = zeros(N_FFT) # " (quantisiert durch ADC)
#########################################################################
# Definiere Testsignal für eine kohärente DFT ohne Leckeffekt
N_per = 53 # Anzahl der Perioden des Signals im DFT-Rechteckfenster
# N_per muss kleiner als N_FFT / 2 sein (sonst gibt's Aliasing!)
# und am besten eine Primzahl, z.B. 63, 131, 251, 509, 1021, ...
# N_per entspricht außerdem der Signalfrequenz!
a_sig = 1 # Signalamplitude
fsig = f_S * N_per / N_FFT
x = a_sig * sin(2*pi*t*fsig+1)# + 2^-18 #Testsignal mit Startphase
#x = a_sig * sin(2*pi*t*fsig+1) + 0.001*sin(2*pi*t*251) #Two-Tone Testsignal
#########################################################################
# Definiere Quantizer-Objekte:
#
q_adc = {'QI':1, 'QF':15, 'quant':'round', 'ovfl': 'sat'}
fx_adc = fx.Fixed(q_adc) # instanstiiere Quantizer
##################################################################
### Input Quantization (ADC, q_adc)
if DITHER:
### add uniform dithering noise, -1/4 LSB < eps_N < 1/4 LSB
x += 2**(-q_adc['QF']-2)*np.random.rand(len(x))
xq = fx_adc.fix(x) # quantisiere
if fx_adc.N_over: print('Anzahl der Überläufe = ', fx_adc.N_over)
#################################################################
#
# FFT über N_FFT Datenpunkte skaliert mit 1/N_FFT über Freq. von 0 ... f_S
#
# Um korrekte Amplituden bei einseitiger Darstellung (0 ... f_S/2 anstatt
# -f_S/2 ... f_S/2) zu erhalten, werden die Spektralwerte verdoppelt:
Yq = 2 * abs(np.fft.fft(xq[0:N_FFT], N_FFT))/ N_FFT # Amplituden
Yq_eff = Yq / sqrt(2) # Effektivwerte
f = np.fft.fftfreq(N_FFT, d = 1./f_S)[0:N_FFT//2] # DFT Frequenzen 0 ... f_S/2
k = np.arange(N_FFT/2) # DFT Index
#------------------------------------------------------------------
#
Yq_sig = Yq_eff[N_per] # Eff.Wert des quantisierten Testsignals
PSigQ = Yq_sig ** 2 # Leistung des quantisierten Testsignals
Yq_sig_dB = 10 * log10(PSigQ) # " in dB
PSig = a_sig ** 2 / 2 # Leistung des Testsignals
PSig_dB = 10*log10(PSig)
#
Yq_dc = Yq[0]/2. # DC-Wert des Ausgangssignals (für Debugging)
Yq_dc_dB = 20 * log10(Yq_dc) # " in dB
# Überspringe Signalamplitude bei Berechnung der mittleren Rauschleistung / bin
Pq_avg = (np.sum(Yq_eff[0:N_per] ** 2) + np.sum(Yq_eff[N_per+1:N_FFT//2] ** 2)) / (N_FFT//2-1)
Pq_avg_dB = 10 * log10(Pq_avg)
Yq_eff[N_per] = | np.sqrt(Pq_avg) | numpy.sqrt |
import numpy as np
from numba import jit, int32, float32, double, cfunc
from numba.experimental import jitclass
spec = [
('x', double[:]), ('dq', double[:]), ('u', double[:]),
('m', double), ('Iz', double),
('lf', double), ('lr', double),
('Bf', double), ('Cf', double), ('Df', double),
('Br', double), ('Cr', double), ('Dr', double),
('Cr0', double), ('Cr2', double),
('Cm1', double), ('Cm2', double),
('iterNum', int32), ('sim_dt', double), ('control_dt', double),
('car_shape', double[:,:]),
]
@jitclass(spec)
class VehicleSimModel(object):
def __init__(self, m=0.041, Iz=27.8E-6,
lf=0.029, lr=0.033,
Bf=2.579, Cf=1.2, Df=0.192,
Br=3.3852, Cr=1.2691, Dr=0.1737,
Cm1=0.287, Cm2=0.0545,
Cr0= 0.0518,
Cr2=0.00035, scale=1.0, control_dt = 10.0, sim_dt=1.0):
self.x = np.asfortranarray(np.zeros(3, dtype=np.float64))
self.dq = np.zeros(3, dtype=np.float64)
self.u = np.zeros(2, dtype=np.float64)
self.m = m
self.Iz= Iz
self.lf = lf
self.lr = lr
self.Bf = Bf
self.Cf = Cf
self.Df = Df
self.Br = Br
self.Cr = Cr
self.Dr = Dr
self.Cr0 = Cr0
self.Cr2 = Cr2
self.Cm1 = Cm1
self.Cm2 = Cm2
car_l = (lf + lr)/2 * scale
car_w = car_l/2
self.car_shape = np.asfortranarray(np.array([ [ car_l, car_w, 1.],
[ car_l,-car_w, 1.],
[-car_l,-car_w, 1.],
[-car_l, car_w, 1.],
[ car_l, car_w, 1.]], dtype=np.float64))
self.sim_dt = sim_dt
self.control_dt = control_dt
self.iterNum = int(self.control_dt/self.sim_dt)
@property
def shape(self):
shape = np.dot(self.car_shape,
np.asfortranarray(np.array([
[ np.cos(self.x[2]), np.sin(self.x[2]), 0.],
[-np.sin(self.x[2]), | np.cos(self.x[2]) | numpy.cos |
from __future__ import print_function, absolute_import, division
import contextlib
import sys
import numpy as np
import random
import threading
import gc
from numba import unittest_support as unittest
from numba.errors import TypingError
from numba import config
from numba import njit
from numba import types
from numba import utils
from numba.numpy_support import version as numpy_version
from .support import MemoryLeakMixin, TestCase, tag
nrtjit = njit(_nrt=True, nogil=True)
def np_concatenate1(a, b, c):
return np.concatenate((a, b, c))
def np_concatenate2(a, b, c, axis):
return np.concatenate((a, b, c), axis=axis)
def np_stack1(a, b, c):
return np.stack((a, b, c))
def np_stack2(a, b, c, axis):
return np.stack((a, b, c), axis=axis)
def np_hstack(a, b, c):
return np.hstack((a, b, c))
def np_vstack(a, b, c):
return np.vstack((a, b, c))
def np_dstack(a, b, c):
return np.dstack((a, b, c))
def np_column_stack(a, b, c):
return np.column_stack((a, b, c))
class BaseTest(TestCase):
def check_outputs(self, pyfunc, argslist, exact=True):
cfunc = nrtjit(pyfunc)
for args in argslist:
expected = pyfunc(*args)
ret = cfunc(*args)
self.assertEqual(ret.size, expected.size)
self.assertEqual(ret.dtype, expected.dtype)
self.assertStridesEqual(ret, expected)
if exact:
np.testing.assert_equal(expected, ret)
else:
np.testing.assert_allclose(expected, ret)
class NrtRefCtTest(MemoryLeakMixin):
def assert_array_nrt_refct(self, arr, expect):
self.assertEqual(arr.base.refcount, expect)
class TestDynArray(NrtRefCtTest, TestCase):
def test_empty_0d(self):
@nrtjit
def foo():
arr = np.empty(())
arr[()] = 42
return arr
arr = foo()
self.assert_array_nrt_refct(arr, 1)
np.testing.assert_equal(42, arr)
self.assertEqual(arr.size, 1)
self.assertEqual(arr.shape, ())
self.assertEqual(arr.dtype, np.dtype(np.float64))
self.assertEqual(arr.strides, ())
arr.fill(123) # test writability
np.testing.assert_equal(123, arr)
del arr
def test_empty_1d(self):
@nrtjit
def foo(n):
arr = np.empty(n)
for i in range(n):
arr[i] = i
return arr
n = 3
arr = foo(n)
self.assert_array_nrt_refct(arr, 1)
np.testing.assert_equal(np.arange(n), arr)
self.assertEqual(arr.size, n)
self.assertEqual(arr.shape, (n,))
self.assertEqual(arr.dtype, np.dtype(np.float64))
self.assertEqual(arr.strides, (np.dtype(np.float64).itemsize,))
arr.fill(123) # test writability
np.testing.assert_equal(123, arr)
del arr
def test_empty_2d(self):
def pyfunc(m, n):
arr = np.empty((m, n), np.int32)
for i in range(m):
for j in range(n):
arr[i, j] = i + j
return arr
cfunc = nrtjit(pyfunc)
m = 4
n = 3
expected_arr = pyfunc(m, n)
got_arr = cfunc(m, n)
self.assert_array_nrt_refct(got_arr, 1)
np.testing.assert_equal(expected_arr, got_arr)
self.assertEqual(expected_arr.size, got_arr.size)
self.assertEqual(expected_arr.shape, got_arr.shape)
self.assertEqual(expected_arr.strides, got_arr.strides)
del got_arr
@tag('important')
def test_empty_3d(self):
def pyfunc(m, n, p):
arr = np.empty((m, n, p), np.int32)
for i in range(m):
for j in range(n):
for k in range(p):
arr[i, j, k] = i + j + k
return arr
cfunc = nrtjit(pyfunc)
m = 4
n = 3
p = 2
expected_arr = pyfunc(m, n, p)
got_arr = cfunc(m, n, p)
self.assert_array_nrt_refct(got_arr, 1)
np.testing.assert_equal(expected_arr, got_arr)
self.assertEqual(expected_arr.size, got_arr.size)
self.assertEqual(expected_arr.shape, got_arr.shape)
self.assertEqual(expected_arr.strides, got_arr.strides)
del got_arr
@tag('important')
def test_empty_2d_sliced(self):
def pyfunc(m, n, p):
arr = np.empty((m, n), np.int32)
for i in range(m):
for j in range(n):
arr[i, j] = i + j
return arr[p]
cfunc = nrtjit(pyfunc)
m = 4
n = 3
p = 2
expected_arr = pyfunc(m, n, p)
got_arr = cfunc(m, n, p)
self.assert_array_nrt_refct(got_arr, 1)
np.testing.assert_equal(expected_arr, got_arr)
self.assertEqual(expected_arr.size, got_arr.size)
self.assertEqual(expected_arr.shape, got_arr.shape)
self.assertEqual(expected_arr.strides, got_arr.strides)
del got_arr
@tag('important')
def test_return_global_array(self):
y = np.ones(4, dtype=np.float32)
initrefct = sys.getrefcount(y)
def return_external_array():
return y
cfunc = nrtjit(return_external_array)
out = cfunc()
# out reference by cfunc
self.assertEqual(initrefct + 1, sys.getrefcount(y))
np.testing.assert_equal(y, out)
np.testing.assert_equal(y, np.ones(4, dtype=np.float32))
np.testing.assert_equal(out, np.ones(4, dtype=np.float32))
del out
gc.collect()
# out is only referenced by cfunc
self.assertEqual(initrefct + 1, sys.getrefcount(y))
del cfunc
gc.collect()
# y is no longer referenced by cfunc
self.assertEqual(initrefct, sys.getrefcount(y))
@tag('important')
def test_return_global_array_sliced(self):
y = np.ones(4, dtype=np.float32)
def return_external_array():
return y[2:]
cfunc = nrtjit(return_external_array)
out = cfunc()
self.assertIsNone(out.base)
yy = y[2:]
np.testing.assert_equal(yy, out)
np.testing.assert_equal(yy, np.ones(2, dtype=np.float32))
np.testing.assert_equal(out, np.ones(2, dtype=np.float32))
def test_array_pass_through(self):
def pyfunc(y):
return y
arr = np.ones(4, dtype=np.float32)
cfunc = nrtjit(pyfunc)
expected = cfunc(arr)
got = pyfunc(arr)
np.testing.assert_equal(expected, arr)
np.testing.assert_equal(expected, got)
self.assertIs(expected, arr)
self.assertIs(expected, got)
@tag('important')
def test_array_pass_through_sliced(self):
def pyfunc(y):
return y[y.size // 2:]
arr = np.ones(4, dtype=np.float32)
initrefct = sys.getrefcount(arr)
cfunc = nrtjit(pyfunc)
got = cfunc(arr)
self.assertEqual(initrefct + 1, sys.getrefcount(arr))
expected = pyfunc(arr)
self.assertEqual(initrefct + 2, sys.getrefcount(arr))
np.testing.assert_equal(expected, arr[arr.size // 2])
np.testing.assert_equal(expected, got)
del expected
self.assertEqual(initrefct + 1, sys.getrefcount(arr))
del got
self.assertEqual(initrefct, sys.getrefcount(arr))
def test_ufunc_with_allocated_output(self):
def pyfunc(a, b):
out = np.empty(a.shape)
np.add(a, b, out)
return out
cfunc = nrtjit(pyfunc)
# 1D case
arr_a = np.random.random(10)
arr_b = np.random.random(10)
np.testing.assert_equal(pyfunc(arr_a, arr_b),
cfunc(arr_a, arr_b))
self.assert_array_nrt_refct(cfunc(arr_a, arr_b), 1)
# 2D case
arr_a = np.random.random(10).reshape(2, 5)
arr_b = np.random.random(10).reshape(2, 5)
np.testing.assert_equal(pyfunc(arr_a, arr_b),
cfunc(arr_a, arr_b))
self.assert_array_nrt_refct(cfunc(arr_a, arr_b), 1)
# 3D case
arr_a = np.random.random(70).reshape(2, 5, 7)
arr_b = np.random.random(70).reshape(2, 5, 7)
np.testing.assert_equal(pyfunc(arr_a, arr_b),
cfunc(arr_a, arr_b))
self.assert_array_nrt_refct(cfunc(arr_a, arr_b), 1)
def test_allocation_mt(self):
"""
This test exercises the array allocation in multithreaded usecase.
This stress the freelist inside NRT.
"""
def pyfunc(inp):
out = np.empty(inp.size)
# Zero fill
for i in range(out.size):
out[i] = 0
for i in range(inp[0]):
# Allocate inside a loop
tmp = np.empty(inp.size)
# Write to tmp
for j in range(tmp.size):
tmp[j] = inp[j]
# out = tmp + i
for j in range(tmp.size):
out[j] += tmp[j] + i
return out
cfunc = nrtjit(pyfunc)
size = 10 # small array size so that the computation is short
arr = np.random.randint(1, 10, size)
frozen_arr = arr.copy()
np.testing.assert_equal(pyfunc(arr), cfunc(arr))
# Ensure we did not modify the input
np.testing.assert_equal(frozen_arr, arr)
workers = []
inputs = []
outputs = []
# Make wrapper to store the output
def wrapped(inp, out):
out[:] = cfunc(inp)
# Create a lot of worker threads to create contention
for i in range(100):
arr = np.random.randint(1, 10, size)
out = np.empty_like(arr)
thread = threading.Thread(target=wrapped,
args=(arr, out),
name="worker{0}".format(i))
workers.append(thread)
inputs.append(arr)
outputs.append(out)
# Launch worker threads
for thread in workers:
thread.start()
# Join worker threads
for thread in workers:
thread.join()
# Check result
for inp, out in zip(inputs, outputs):
np.testing.assert_equal(pyfunc(inp), out)
def test_refct_mt(self):
"""
This test exercises the refct in multithreaded code
"""
def pyfunc(n, inp):
out = np.empty(inp.size)
for i in range(out.size):
out[i] = inp[i] + 1
# Use swap to trigger many refct ops
for i in range(n):
out, inp = inp, out
return out
cfunc = nrtjit(pyfunc)
size = 10
input = np.arange(size, dtype=np.float)
expected_refct = sys.getrefcount(input)
swapct = random.randrange(1000)
expected = pyfunc(swapct, input)
np.testing.assert_equal(expected, cfunc(swapct, input))
# The following checks can discover a reference count error
del expected
self.assertEqual(expected_refct, sys.getrefcount(input))
workers = []
outputs = []
swapcts = []
# Make wrapper to store the output
def wrapped(n, input, out):
out[:] = cfunc(n, input)
# Create worker threads
for i in range(100):
out = np.empty(size)
# All thread shares the same input
swapct = random.randrange(1000)
thread = threading.Thread(target=wrapped,
args=(swapct, input, out),
name="worker{0}".format(i))
workers.append(thread)
outputs.append(out)
swapcts.append(swapct)
# Launch worker threads
for thread in workers:
thread.start()
# Join worker threads
for thread in workers:
thread.join()
# Check result
for swapct, out in zip(swapcts, outputs):
np.testing.assert_equal(pyfunc(swapct, input), out)
del outputs, workers
# The following checks can discover a reference count error
self.assertEqual(expected_refct, sys.getrefcount(input))
def test_swap(self):
def pyfunc(x, y, t):
"""Swap array x and y for t number of times
"""
for i in range(t):
x, y = y, x
return x, y
cfunc = nrtjit(pyfunc)
x = np.random.random(100)
y = np.random.random(100)
t = 100
initrefct = sys.getrefcount(x), sys.getrefcount(y)
expect, got = pyfunc(x, y, t), cfunc(x, y, t)
self.assertIsNone(got[0].base)
self.assertIsNone(got[1].base)
np.testing.assert_equal(expect, got)
del expect, got
self.assertEqual(initrefct, (sys.getrefcount(x), sys.getrefcount(y)))
def test_return_tuple_of_array(self):
def pyfunc(x):
y = np.empty(x.size)
for i in range(y.size):
y[i] = x[i] + 1
return x, y
cfunc = nrtjit(pyfunc)
x = np.random.random(5)
initrefct = sys.getrefcount(x)
expected_x, expected_y = pyfunc(x)
got_x, got_y = cfunc(x)
self.assertIs(x, expected_x)
self.assertIs(x, got_x)
np.testing.assert_equal(expected_x, got_x)
np.testing.assert_equal(expected_y, got_y)
del expected_x, got_x
self.assertEqual(initrefct, sys.getrefcount(x))
self.assertEqual(sys.getrefcount(expected_y), sys.getrefcount(got_y))
def test_return_tuple_of_array_created(self):
def pyfunc(x):
y = np.empty(x.size)
for i in range(y.size):
y[i] = x[i] + 1
out = y, y
return out
cfunc = nrtjit(pyfunc)
x = np.random.random(5)
expected_x, expected_y = pyfunc(x)
got_x, got_y = cfunc(x)
np.testing.assert_equal(expected_x, got_x)
np.testing.assert_equal(expected_y, got_y)
# getrefcount owns 1, got_y owns 1
self.assertEqual(2, sys.getrefcount(got_y))
# getrefcount owns 1, got_y owns 1
self.assertEqual(2, sys.getrefcount(got_y))
def test_issue_with_return_leak(self):
"""
Dispatcher returns a new reference.
It need to workaround it for now.
"""
@nrtjit
def inner(out):
return out
def pyfunc(x):
return inner(x)
cfunc = nrtjit(pyfunc)
arr = np.arange(10)
old_refct = sys.getrefcount(arr)
self.assertEqual(old_refct, sys.getrefcount(pyfunc(arr)))
self.assertEqual(old_refct, sys.getrefcount(cfunc(arr)))
self.assertEqual(old_refct, sys.getrefcount(arr))
class ConstructorBaseTest(NrtRefCtTest):
def check_0d(self, pyfunc):
cfunc = nrtjit(pyfunc)
expected = pyfunc()
ret = cfunc()
self.assert_array_nrt_refct(ret, 1)
self.assertEqual(ret.size, expected.size)
self.assertEqual(ret.shape, expected.shape)
self.assertEqual(ret.dtype, expected.dtype)
self.assertEqual(ret.strides, expected.strides)
self.check_result_value(ret, expected)
# test writability
expected = np.empty_like(ret) # np.full_like was not added until Numpy 1.8
expected.fill(123)
ret.fill(123)
np.testing.assert_equal(ret, expected)
def check_1d(self, pyfunc):
cfunc = nrtjit(pyfunc)
n = 3
expected = pyfunc(n)
ret = cfunc(n)
self.assert_array_nrt_refct(ret, 1)
self.assertEqual(ret.size, expected.size)
self.assertEqual(ret.shape, expected.shape)
self.assertEqual(ret.dtype, expected.dtype)
self.assertEqual(ret.strides, expected.strides)
self.check_result_value(ret, expected)
# test writability
expected = np.empty_like(ret) # np.full_like was not added until Numpy 1.8
expected.fill(123)
ret.fill(123)
np.testing.assert_equal(ret, expected)
# errors
with self.assertRaises(ValueError) as cm:
cfunc(-1)
self.assertEqual(str(cm.exception), "negative dimensions not allowed")
def check_2d(self, pyfunc):
cfunc = nrtjit(pyfunc)
m, n = 2, 3
expected = pyfunc(m, n)
ret = cfunc(m, n)
self.assert_array_nrt_refct(ret, 1)
self.assertEqual(ret.size, expected.size)
self.assertEqual(ret.shape, expected.shape)
self.assertEqual(ret.dtype, expected.dtype)
self.assertEqual(ret.strides, expected.strides)
self.check_result_value(ret, expected)
# test writability
expected = np.empty_like(ret) # np.full_like was not added until Numpy 1.8
expected.fill(123)
ret.fill(123)
np.testing.assert_equal(ret, expected)
# errors
with self.assertRaises(ValueError) as cm:
cfunc(2, -1)
self.assertEqual(str(cm.exception), "negative dimensions not allowed")
def check_alloc_size(self, pyfunc):
"""Checks that pyfunc will error, not segfaulting due to array size."""
cfunc = nrtjit(pyfunc)
with self.assertRaises(ValueError) as e:
cfunc()
self.assertIn(
"array is too big",
str(e.exception)
)
class TestNdZeros(ConstructorBaseTest, TestCase):
def setUp(self):
super(TestNdZeros, self).setUp()
self.pyfunc = np.zeros
def check_result_value(self, ret, expected):
np.testing.assert_equal(ret, expected)
def test_0d(self):
pyfunc = self.pyfunc
def func():
return pyfunc(())
self.check_0d(func)
def test_1d(self):
pyfunc = self.pyfunc
def func(n):
return pyfunc(n)
self.check_1d(func)
def test_1d_dtype(self):
pyfunc = self.pyfunc
def func(n):
return pyfunc(n, np.int32)
self.check_1d(func)
def test_1d_dtype_instance(self):
# dtype as numpy dtype, not as scalar class
pyfunc = self.pyfunc
_dtype = np.dtype('int32')
def func(n):
return pyfunc(n, _dtype)
self.check_1d(func)
def test_2d(self):
pyfunc = self.pyfunc
def func(m, n):
return pyfunc((m, n))
self.check_2d(func)
def test_2d_shape_dtypes(self):
# Test for issue #4575
pyfunc = self.pyfunc
def func1(m, n):
return pyfunc((np.int16(m), np.int32(n)))
self.check_2d(func1)
# Using a 64-bit value checks that 32 bit systems will downcast to intp
def func2(m, n):
return pyfunc((np.int64(m), np.int8(n)))
self.check_2d(func2)
# Make sure an error is thrown if we can't downcast safely
if config.IS_32BITS:
cfunc = nrtjit(lambda m, n: pyfunc((m, n)))
with self.assertRaises(ValueError):
cfunc(np.int64(1 << (32 - 1)), 1)
@tag('important')
def test_2d_dtype_kwarg(self):
pyfunc = self.pyfunc
def func(m, n):
return pyfunc((m, n), dtype=np.complex64)
self.check_2d(func)
def test_alloc_size(self):
pyfunc = self.pyfunc
width = types.intp.bitwidth
def gen_func(shape, dtype):
return lambda : pyfunc(shape, dtype)
# Under these values numba will segfault, but thats another issue
self.check_alloc_size(gen_func(1 << width - 2, np.intp))
self.check_alloc_size(gen_func((1 << width - 8, 64), np.intp))
class TestNdOnes(TestNdZeros):
def setUp(self):
super(TestNdOnes, self).setUp()
self.pyfunc = np.ones
@unittest.skipIf(numpy_version < (1, 8), "test requires Numpy 1.8 or later")
class TestNdFull(ConstructorBaseTest, TestCase):
def check_result_value(self, ret, expected):
np.testing.assert_equal(ret, expected)
def test_0d(self):
def func():
return np.full((), 4.5)
self.check_0d(func)
def test_1d(self):
def func(n):
return np.full(n, 4.5)
self.check_1d(func)
def test_1d_dtype(self):
def func(n):
return np.full(n, 4.5, np.bool_)
self.check_1d(func)
def test_1d_dtype_instance(self):
dtype = np.dtype('bool')
def func(n):
return np.full(n, 4.5, dtype)
self.check_1d(func)
def test_2d(self):
def func(m, n):
return np.full((m, n), 4.5)
self.check_2d(func)
def test_2d_dtype_kwarg(self):
def func(m, n):
return np.full((m, n), 1 + 4.5j, dtype=np.complex64)
self.check_2d(func)
def test_2d_dtype_from_type(self):
# tests issue #2862
def func(m, n):
return np.full((m, n), np.int32(1))
self.check_2d(func)
# tests meta issues from #2862, that np < 1.12 always
# returns float64. Complex uses `.real`, imaginary part dropped
def func(m, n):
return np.full((m, n), np.complex128(1))
self.check_2d(func)
# and that if a dtype is specified, this influences the return type
def func(m, n):
return np.full((m, n), 1, dtype=np.int8)
self.check_2d(func)
def test_2d_shape_dtypes(self):
# Test for issue #4575
def func1(m, n):
return np.full(( | np.int16(m) | numpy.int16 |
# Lint as: python3
# Copyright 2019 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Tests for bond_curve."""
import math
from absl.testing import parameterized
import numpy as np
import tensorflow.compat.v2 as tf
from tensorflow.python.framework import test_util # pylint: disable=g-direct-tensorflow-import
from tf_quant_finance.rates.hagan_west import bond_curve
from tf_quant_finance.rates.hagan_west import monotone_convex
@test_util.run_all_in_graph_and_eager_modes
class BondCurveTest(tf.test.TestCase, parameterized.TestCase):
@parameterized.named_parameters(
('single_precision', np.float32),
('double_precision', np.float64),
)
def test_cashflow_times_cashflow_before_settelment_error(self, dtype):
with self.assertRaises(tf.errors.InvalidArgumentError):
self.evaluate(
bond_curve.bond_curve(
bond_cashflows=[
np.array([12.5, 12.5, 12.5, 1012.5], dtype=dtype),
np.array([30.0, 30.0, 30.0, 1030.0], dtype=dtype)
],
bond_cashflow_times=[
np.array([0.25, 0.5, 0.75, 1.0], dtype=dtype),
np.array([0.5, 1.0, 1.5, 2.0], dtype=dtype)
],
present_values=np.array([999.0, 1022.0], dtype=dtype),
present_values_settlement_times=np.array([0.25, 0.25],
dtype=dtype),
validate_args=True,
dtype=dtype))
@parameterized.named_parameters(
('single_precision', np.float32),
('double_precision', np.float64),
)
def test_cashflow_times_are_strongly_ordered_error(self, dtype):
with self.assertRaises(tf.errors.InvalidArgumentError):
self.evaluate(
bond_curve.bond_curve(
bond_cashflows=[
np.array([12.5, 12.5, 12.5, 1012.5], dtype=dtype),
np.array([30.0, 30.0, 30.0, 1030.0], dtype=dtype)
],
bond_cashflow_times=[
| np.array([0.25, 0.5, 0.75, 1.0], dtype=dtype) | numpy.array |
# author : <NAME>
# <EMAIL>
#
# date : March 19, 2018
"""
Plotting functions for the BSM flavor ratio analysis
"""
from __future__ import absolute_import, division, print_function
import os
import sys
import socket
from copy import deepcopy
import warnings
warnings.filterwarnings("ignore")
import numpy as np
import numpy.ma as ma
from scipy.interpolate import splev, splprep
from scipy.ndimage.filters import gaussian_filter
import matplotlib
import matplotlib as mpl
import matplotlib.patches as patches
import matplotlib.gridspec as gridspec
if 'submitter' in socket.gethostname() or 'cobalt' in socket.gethostname():
mpl.use('Agg', warn=False)
from matplotlib import rc
from matplotlib import pyplot as plt
from matplotlib.offsetbox import AnchoredText
from matplotlib.lines import Line2D
from matplotlib.patches import Patch
from matplotlib.patches import Arrow
tRed = list(np.array([226,101,95]) / 255.)
tBlue = list(np.array([96,149,201]) / 255.)
tGreen = list(np.array([170,196,109]) / 255.)
import getdist
from getdist import plots, mcsamples
import logging
logging.getLogger().setLevel(logging.CRITICAL)
import ternary
from ternary.heatmapping import polygon_generator
import shapely.geometry as geometry
from shapely.ops import cascaded_union, polygonize
from scipy.spatial import Delaunay
from golemflavor.enums import DataType, str_enum
from golemflavor.enums import Likelihood, ParamTag, StatCateg, Texture
from golemflavor.misc import get_units, make_dir, solve_ratio, interval
from golemflavor.fr import angles_to_u, flat_angles_to_u, angles_to_fr
from golemflavor.fr import SCALE_BOUNDARIES
if os.path.isfile('./plot_llh/paper.mplstyle'):
plt.style.use('./plot_llh/paper.mplstyle')
elif os.path.isfile('./paper.mplstyle'):
plt.style.use('./paper.mplstyle')
elif os.environ.get('GOLEMSOURCEPATH') is not None:
plt.style.use(os.environ['GOLEMSOURCEPATH']+'/GolemFit/scripts/paper/paper.mplstyle')
if 'submitter' in socket.gethostname():
rc('text', usetex=False)
else:
rc('text', usetex=True)
mpl.rcParams['text.latex.preamble'] = [
r'\usepackage{xcolor}',
r'\usepackage{amsmath}',
r'\usepackage{amssymb}']
if sys.version_info < (3, 0):
mpl.rcParams['text.latex.unicode'] = True
BAYES_K = 1. # Strong degree of belief.
# BAYES_K = 3/2. # Very strong degree of belief.
# BAYES_K = 2. # Decisive degree of belief
LV_ATMO_90PC_LIMITS = {
3: (2E-24, 1E-1),
4: (2.7E-28, 3.16E-25),
5: (1.5E-32, 1.12E-27),
6: (9.1E-37, 2.82E-30),
7: (3.6E-41, 1.77E-32),
8: (1.4E-45, 1.00E-34)
}
PS = 8.203E-20 # GeV^{-1}
PLANCK_SCALE = {
5: PS,
6: PS**2,
7: PS**3,
8: PS**4
}
def gen_figtext(args):
"""Generate the figure text."""
t = r'$'
if args.data is DataType.REAL:
t += r'\textbf{IceCube\:Preliminary}' + '$\n$'
elif args.data in [DataType.ASIMOV, DataType.REALISATION]:
t += r'{\rm\bf IceCube\:Simulation}' + '$\n$'
t += r'\rm{Injected\:composition}'+r'\:=\:({0})_\oplus'.format(
solve_ratio(args.injected_ratio).replace('_', ':')
) + '$\n$'
t += r'{\rm Source\:composition}'+r'\:=\:({0})'.format(
solve_ratio(args.source_ratio).replace('_', ':')
) + r'_\text{S}'
t += '$\n$' + r'{\rm Dimension}'+r' = {0}$'.format(args.dimension)
return t
def texture_label(x, dim):
cpt = r'c' if dim % 2 == 0 else r'a'
if x == Texture.OEU:
# return r'$\mathcal{O}_{e\mu}$'
return r'$\mathring{'+cpt+r'}_{e\mu}^{('+str(int(dim))+r')}$'
elif x == Texture.OET:
# return r'$\mathcal{O}_{e\tau}$'
return r'$\mathring{'+cpt+r'}_{\tau e}^{('+str(int(dim))+r')}$'
elif x == Texture.OUT:
# return r'$\mathcal{O}_{\mu\tau}$'
return r'$\mathring{'+cpt+r'}_{\mu\tau}^{('+str(int(dim))+r')}$'
else:
raise AssertionError
def cmap_discretize(cmap, N):
colors_i = np.concatenate((np.linspace(0, 1., N), (0.,0.,0.,0.)))
colors_rgba = cmap(colors_i)
indices = np.linspace(0, 1., N+1)
cdict = {}
for ki,key in enumerate(('red','green','blue')):
cdict[key] = [ (indices[i], colors_rgba[i-1,ki], colors_rgba[i,ki]) for i in range(N+1) ]
# Return colormap object.
return mpl.colors.LinearSegmentedColormap(cmap.name + "_%d"%N, cdict, 1024)
def get_limit(scales, statistic, args, mask_initial=False, return_interp=False):
max_st = np.max(statistic)
print('scales, stat', zip(scales, statistic))
if args.stat_method is StatCateg.BAYESIAN:
if (statistic[0] - max_st) > np.log(10**(BAYES_K)):
raise AssertionError('Discovered LV!')
else:
raise NotImplementedError
try:
tck, u = splprep([scales, statistic], s=0)
except:
print('Failed to spline')
# return None
raise
sc, st = splev(np.linspace(0, 1, 1000), tck)
if mask_initial:
scales_rm = sc[sc >= scales[1]]
statistic_rm = st[sc >= scales[1]]
else:
scales_rm = sc
statistic_rm = st
min_idx = np.argmin(scales)
null = statistic[min_idx]
# if np.abs(statistic_rm[0] - null) > 0.8:
# print('Warning, null incompatible with smallest scanned scale! For ' \
# 'DIM {0} [{1}, {2}, {3}]!'.format(
# args.dimension, *args.source_ratio
# ))
# null = statistic_rm[0]
if args.stat_method is StatCateg.BAYESIAN:
reduced_ev = -(statistic_rm - null)
print('[reduced_ev > np.log(10**(BAYES_K))]', np.sum([reduced_ev > np.log(10**(BAYES_K))]))
al = scales_rm[reduced_ev > np.log(10**(BAYES_K))]
else:
assert 0
if len(al) == 0:
print('No points for DIM {0} [{1}, {2}, {3}]!'.format(
args.dimension, *args.source_ratio
))
return None
re = -(statistic-null)[scales > al[0]]
if np.sum(re < | np.log(10**(BAYES_K)) | numpy.log |
# UTIL.MATH: small math functions
__author__ = 'vlad'
import numpy as np
from numpy import dot
from scipy.stats import entropy
from scipy.linalg import norm
class dist:
@staticmethod
def cosine(x_, y_):
return dot(x_, y_) / (norm(x_)*norm(y_))
@staticmethod
def euclid(x_, y_):
return norm(x_, y_)
@staticmethod
def kl(x_, y_):
# Kullback-Leibler
return 0.5*(entropy(x_, y_) + entropy(y_, x_))
@staticmethod
def js(x_, y_):
# Jensen-Shannon
return 0.5*(entropy(x_, 0.5*(x_+y_))+entropy(y_,0.5*(x_+y_)))
@staticmethod
def bhattacharyya(x_, y_):
# Bhattacharyya distance between histograms
return -np.log(np.sum(np.sqrt(x_*y_)))
@staticmethod
def matusita(x_, y_):
# Matusita distance between histograms
return np.sqrt(np.sum((np.sqrt(x_)- | np.sqrt(y_) | numpy.sqrt |
import numpy as np
from cvxpy import *
from cvxopt import matrix, solvers
from mosek import iparam
solvers.options['mosek'] = {iparam.log: 0}
import time
class SolverFailedException(Exception):
def __init__(self, message):
self.message = message
class CuttingPlaneModel:
def __init__(self, dim, bounds, x0, memory=None, LP_solver="mosek", QP_solver="mosek"):
self.dim = dim
self.bounds = bounds
self.coefficients = np.empty((0,dim+1))
self.x0 = x0
self.LP_solver = LP_solver
self.QP_solver = QP_solver
self.memory = memory
self.memory_index = 0
self.times = {
"LP": [],
"QP": []
}
if memory is not None and memory < dim:
print(f"Warning: Memory is smaller than input dimension dim={dim}, memory={memory}")
assert dim == len(x0)
def __call__(self, x):#REMOVE
y = [np.sum(np.multiply(coefficients_i, np.hstack((1,x)))) for coefficients_i in self.coefficients]
return np.max(y), 0
def add_plane(self, f, g, x):
c = f - np.sum(np.multiply(g,x))
new_plane = np.append(c,g)
# Implements cutting plane memory
if self.memory is not None and self.coefficients.shape[0] >= self.memory:
self.coefficients[self.memory_index] = new_plane
self.memory_index = (self.memory_index + 1) % self.memory
else:
self.coefficients = np.append(self.coefficients, [new_plane], axis=0)
def get_LP_constraints(self):
A = np.asarray([[c[i] for i in range(1, len(c))] + [-1] for c in self.coefficients])
A_ub = np.hstack((np.eye(self.dim),np.zeros((self.dim,1))))
A_lb = -np.hstack((np.eye(self.dim),np.zeros((self.dim,1))))
A = np.vstack((A, A_ub, A_lb))
b = np.asarray([-c[0] for c in self.coefficients])
b_ub = self.x0 + self.bounds
b_lb = -self.x0 + self.bounds
b = np.concatenate((b, b_ub, b_lb))
return A, b
def get_QP_constraints(self, level):
A = np.asarray([[c[i] for i in range(1, len(c))] for c in self.coefficients])
A_ub = np.eye(self.dim)
A_lb = -np.eye(self.dim)
A = np.vstack((A, A_ub, A_lb))
b = np.asarray([-c[0] + level for c in self.coefficients])
b_ub = self.x0 + self.bounds
b_lb = -self.x0 + self.bounds
b = np.concatenate((b, b_ub, b_lb))
return A, b
def solve(self):
# Builds the LP
A, b = self.get_LP_constraints()
c = np.zeros(self.dim + 1)
c[-1] = 1
c = matrix(c)
A = matrix(A)
b = matrix(b)
try:
t0 = time.time()
sol = solvers.lp(c, A, b, solver=self.LP_solver)
self.times["LP"].append(time.time() - t0)
except Exception as e:
print(e)
raise SolverFailedException("LP failed")
return | np.array(sol['x'][:-1]) | numpy.array |
#!/usr/bin/python
from __future__ import division
import numpy as np
import math
from scipy.special import *
from numpy.matlib import repmat
from scipy.signal import lfilter
from scikits.audiolab import Sndfile, Format
import argparse
import sys
np.seterr('ignore')
def MMSESTSA(signal, fs, IS=0.25, W=1024, NoiseMargin=3, saved_params=None):
SP = 0.4
wnd = np.hamming(W)
y = segment(signal, W, SP, wnd)
Y = np.fft.fft(y, axis=0)
YPhase = np.angle(Y[0:int(np.fix(len(Y)/2))+1,:])
Y = np.abs(Y[0:int(np.fix(len(Y)/2))+1,:])
numberOfFrames = Y.shape[1]
NoiseLength = 9
NoiseCounter = 0
alpha = 0.99
NIS = int(np.fix(((IS * fs - W) / (SP * W) + 1)))
N = np.mean(Y[:,0:NIS].T).T
LambdaD = np.mean((Y[:,0:NIS].T) ** 2).T
if saved_params != None:
NIS = 0
N = saved_params['N']
LambdaD = saved_params['LambdaD']
NoiseCounter = saved_params['NoiseCounter']
G = np.ones(N.shape)
Gamma = G
Gamma1p5 = math.gamma(1.5)
X = | np.zeros(Y.shape) | numpy.zeros |
from skimage import transform
import cv2
import numpy as np
import sys
import warnings
warnings.filterwarnings('ignore') #忽略掉一堆警告
sys.path.append(r'./') #添加模块路径为后面引入本路径下的模块做准备
#print(sys.path)
import back_project #加入自编反投影模块
image = cv2.imread(r"data\shepp_logan.jpg", cv2.IMREAD_GRAYSCALE)
cv2.imshow("test", image) #显示shepp logan原图
tmp = transform.radon(image).astype('float64')
img_radon = np.rint(tmp / np.max(tmp) * 254).astype('uint8') #标准化radon变换
cv2.imshow("radon", img_radon) #显示雷登变换后的图片
#cv2.imwrite(r"result\radon.png", img_radon)
#print(img_radon)
result = back_project.bp_star(img_radon)
bp_img = np.rint(result / | np.max(result) | numpy.max |
# Cite from https://github.com/metrofun/E3D-LSTM
from functools import reduce
import copy
import operator
import torch
import torch.nn as nn
import torch.nn.functional as F
from .rnn_cell import E3DLSTMCell, ConvDeconv3d
from .utils import window
from tqdm import tqdm
import numpy as np
class E3DLSTM_Module(nn.Module):
def __init__(self, input_shape, hidden_size, num_layers, kernel_size, tau):
super().__init__()
self._tau = tau
self._cells = []
input_shape = list(input_shape)
for i in range(num_layers):
cell = E3DLSTMCell(input_shape, hidden_size, kernel_size)
# NOTE hidden state becomes input to the next cell
input_shape[0] = hidden_size
self._cells.append(cell)
# Hook to register submodule
setattr(self, "cell{}".format(i), cell)
def forward(self, input):
# NOTE (seq_len, batch, input_shape)
batch_size = input.size(1)
c_history_states = []
h_states = []
outputs = []
for step, x in enumerate(input):
for cell_idx, cell in enumerate(self._cells):
if step == 0:
c_history, m, h = self._cells[cell_idx].init_hidden(
batch_size, self._tau, input.device
)
c_history_states.append(c_history)
h_states.append(h)
# NOTE c_history and h are coming from the previous time stamp, but we iterate over cells
c_history, m, h = cell(
x, c_history_states[cell_idx], m, h_states[cell_idx]
)
c_history_states[cell_idx] = c_history
h_states[cell_idx] = h
# NOTE hidden state of previous LSTM is passed as input to the next one
x = h
outputs.append(h)
# NOTE Concat along the channels
return torch.cat(outputs, dim=1)
class E3DLSTM_Model(nn.Module):
def __init__(self, params):
super().__init__()
self.encoder = E3DLSTM_Module(params.input_shape, params.hidden_size, params.lstm_layers, params.kernel, params.tau)
# self.decoder = nn.Conv3d(params.hidden_size * params.time_steps, params.output_shape[0], params.kernel, padding=(0, 2, 2))
self.decoder = nn.Conv3d(64, 1, kernel_size=(1, 5, 5), stride=(1, 1, 1), padding=(0, 2, 2))
def forward(self, x):
return self.decoder(self.encoder(x))
from .basic_algo import Basic_algo
class E3DLSTM(Basic_algo):
def __init__(self, params):
config = params.__dict__
config.update({
'input_shape': (3, 4, 128, 128),
'output_shape': (3, 4, 128, 128),
'hidden_size': 64,
'lstm_layers': 4,
'kernel': (2, 5, 5),
'tau': 2,
'temporal_frames': 4,
'temporal_stride': 1,
'input_time_window': 4,
'output_time_horizon': 1,
'time_steps': 1,
'lr': 0.001,
'device': torch.device('cuda:0')
})
model = E3DLSTM_Model(params).to(params.device)
Basic_algo.__init__(self, model)
self.device = params.device
self.params = params
self.optimizer = torch.optim.Adam(self.model.parameters(), lr=params.lr)
self.criterion = torch.nn.MSELoss()
def _iter_batch(self, x, y):
pred = self.model(x)
loss = self.criterion(pred, y)
return pred, loss
def train(self, train_loader, epoch):
'''
Train the model with train_loader.
Input params:
train_loader: dataloader of train.
Output params:
mse_loss: mean square loss between predictions and ground truth.
'''
self.model.train()
train_pbar = tqdm(train_loader)
mse_loss = []
for i, (batch_x, batch_y, _) in enumerate(train_pbar):
batch_x, batch_y = batch_x.to(self.device), batch_y.to(self.device)
batch_x = batch_x.permute(0, 2, 1, 3, 4)
batch_y = batch_y.permute(0, 2, 1, 3, 4)
# train model
self.optimizer.zero_grad()
frames_seq = []
for indices in window(range(self.params.input_time_window), \
self.params.temporal_frames, self.params.temporal_stride):
frames_seq.append(batch_x[:, :, indices[0] : indices[-1] + 1])
batch_x = torch.stack(frames_seq, dim=0)
pred, loss = self._iter_batch(batch_x, batch_y)
loss.backward()
self.optimizer.step()
# trian model
train_pbar.set_description('train loss: {:.4f}'.format(loss.item()))
mse_loss.append(loss.item())
mse_loss = np.average(mse_loss)
return mse_loss
def evaluate(self, val_loader):
'''
Evaluate the model with val_loader.
Input params:
val_loader: dataloader of validation.
Output params:
(mse, mae, ssim): mse, mas, ssim between predictions and ground truth.
'''
self.model.eval()
val_pbar = tqdm(val_loader)
mse_loss, preds, trues = [], [], []
for i, (batch_x, batch_y, _) in enumerate(val_pbar):
batch_x, batch_y = batch_x.to(self.device), batch_y.to(self.device)
# eval model
batch_x = batch_x.permute(0, 2, 1, 3, 4)
batch_y = batch_y.permute(0, 2, 1, 3, 4)
frames_seq = []
for indices in window(range(self.params.input_time_window), \
self.params.temporal_frames, self.params.temporal_stride):
frames_seq.append(batch_x[:, :, indices[0] : indices[-1] + 1])
batch_x = torch.stack(frames_seq, dim=0)
pred_y, loss = self._iter_batch(batch_x, batch_y)
# eval model
true, pred_y = batch_y.detach().cpu(), pred_y.detach().cpu()
val_pbar.set_description('vali loss: {:.4f}'.format(loss.item()))
mse_loss.append(loss.item())
preds.append(pred_y.numpy())
trues.append(true.numpy())
mse_loss = | np.average(mse_loss) | numpy.average |
import numpy
from sklearn.covariance import oas, ledoit_wolf, fast_mcd, empirical_covariance
from matplotlib import mlab
# Mapping different estimator on the sklearn toolbox
def _lwf(X):
"""Wrapper for sklearn ledoit wolf covariance estimator"""
C, _ = ledoit_wolf(X.T)
return C
def _oas(X):
"""Wrapper for sklearn oas covariance estimator"""
C, _ = oas(X.T)
return C
def _scm(X):
"""Wrapper for sklearn sample covariance estimator"""
return empirical_covariance(X.T)
def _mcd(X):
"""Wrapper for sklearn mcd covariance estimator"""
_, C, _, _ = fast_mcd(X.T)
return C
def _check_est(est):
"""Check if a given estimator is valid"""
# Check estimator exist and return the correct function
estimators = {
'cov': numpy.cov,
'scm': _scm,
'lwf': _lwf,
'oas': _oas,
'mcd': _mcd,
'corr': numpy.corrcoef
}
if callable(est):
# All good (cross your fingers)
pass
elif est in estimators.keys():
# Map the corresponding estimator
est = estimators[est]
else:
# raise an error
raise ValueError(
"""%s is not an valid estimator ! Valid estimators are : %s or a
callable function""" % (est, (' , ').join(estimators.keys())))
return est
def covariances(X, estimator='cov'):
"""Estimation of covariance matrix."""
est = _check_est(estimator)
Nt, Ne, Ns = X.shape
covmats = numpy.zeros((Nt, Ne, Ne))
for i in range(Nt):
covmats[i, :, :] = est(X[i, :, :])
return covmats
def covariances_EP(X, P, estimator='cov'):
"""Special form covariance matrix."""
est = _check_est(estimator)
Nt, Ne, Ns = X.shape
Np, Ns = P.shape
covmats = numpy.zeros((Nt, Ne + Np, Ne + Np))
for i in range(Nt):
covmats[i, :, :] = est(numpy.concatenate((P, X[i, :, :]), axis=0))
return covmats
def eegtocov(sig, window=128, overlapp=0.5, padding=True, estimator='cov'):
"""Convert EEG signal to covariance using sliding window"""
est = _check_est(estimator)
X = []
if padding:
padd = numpy.zeros((int(window / 2), sig.shape[1]))
sig = numpy.concatenate((padd, sig, padd), axis=0)
Ns, Ne = sig.shape
jump = int(window * overlapp)
ix = 0
while (ix + window < Ns):
X.append(est(sig[ix:ix + window, :].T))
ix = ix + jump
return numpy.array(X)
def coherence(X, window=128, overlap=0.75, fmin=None, fmax=None, fs=None):
"""Compute coherence."""
n_chan = X.shape[0]
overlap = int(overlap * window)
ij = []
if fs is None:
fs = window
for i in range(n_chan):
for j in range(i+1, n_chan):
ij.append((i, j))
Cxy, Phase, freqs = mlab.cohere_pairs(X.T, ij, NFFT=window, Fs=fs,
noverlap=overlap)
if fmin is None:
fmin = freqs[0]
if fmax is None:
fmax = freqs[-1]
index_f = (freqs >= fmin) & (freqs <= fmax)
freqs = freqs[index_f]
# reshape coherence
coh = numpy.zeros((n_chan, n_chan, len(freqs)))
for i in range(n_chan):
coh[i, i] = 1
for j in range(i + 1, n_chan):
coh[i, j] = coh[j, i] = Cxy[(i, j)][index_f]
return coh
def cospectrum(X, window=128, overlap=0.75, fmin=None, fmax=None, fs=None):
"""Compute Cospectrum."""
Ne, Ns = X.shape
number_freqs = int(window / 2)
step = int((1.0 - overlap) * window)
step = max(1, step)
number_windows = int((Ns - window) / step + 1)
# pre-allocation of memory
fdata = numpy.zeros((number_windows, Ne, number_freqs), dtype=complex)
win = numpy.hanning(window)
# Loop on all frequencies
for window_ix in range(int(number_windows)):
# time markers to select the data
# marker of the beginning of the time window
t1 = int(window_ix * step)
# marker of the end of the time window
t2 = int(t1 + window)
# select current window and apodize it
cdata = X[:, t1:t2] * win
# FFT calculation
fdata[window_ix, :, :] = numpy.fft.fft(
cdata, n=window, axis=1)[:, 0:number_freqs]
# Adjust Frequency range to specified range (in case it is a parameter)
if fmin is not None:
f = | numpy.arange(0, 1, 1.0 / number_freqs) | numpy.arange |
from __future__ import division
import mxnet as mx
import numpy as np
import mxnet.ndarray as nd
import cv2
__all__ = ['FaceDetector',
'retinaface_r50_v1',
'retinaface_mnet025_v1',
'retinaface_mnet025_v2',
'get_retinaface']
def _whctrs(anchor):
"""
Return width, height, x center, and y center for an anchor (window).
"""
w = anchor[2] - anchor[0] + 1
h = anchor[3] - anchor[1] + 1
x_ctr = anchor[0] + 0.5 * (w - 1)
y_ctr = anchor[1] + 0.5 * (h - 1)
return w, h, x_ctr, y_ctr
def _mkanchors(ws, hs, x_ctr, y_ctr):
"""
Given a vector of widths (ws) and heights (hs) around a center
(x_ctr, y_ctr), output a set of anchors (windows).
"""
ws = ws[:, np.newaxis]
hs = hs[:, np.newaxis]
anchors = np.hstack((x_ctr - 0.5 * (ws - 1),
y_ctr - 0.5 * (hs - 1),
x_ctr + 0.5 * (ws - 1),
y_ctr + 0.5 * (hs - 1)))
return anchors
def _ratio_enum(anchor, ratios):
"""
Enumerate a set of anchors for each aspect ratio wrt an anchor.
"""
w, h, x_ctr, y_ctr = _whctrs(anchor)
size = w * h
size_ratios = size / ratios
ws = np.round(np.sqrt(size_ratios))
hs = | np.round(ws * ratios) | numpy.round |
# coding: utf-8
# Copyright (c) Max-Planck-Institut für Eisenforschung GmbH - Computational Materials Design (CM) Department
# Distributed under the terms of "New BSD License", see the LICENSE file.
from __future__ import division, print_function
import ast
from copy import copy
from collections import OrderedDict
from math import cos, sin
import numpy as np
from six import string_types
import warnings
from ase.geometry import cellpar_to_cell, complete_cell, get_distances
from matplotlib.colors import rgb2hex
from scipy.interpolate import interp1d
from pyiron.atomistics.structure.atom import Atom
from pyiron.atomistics.structure.sparse_list import SparseArray, SparseList
from pyiron.atomistics.structure.periodic_table import PeriodicTable, ChemicalElement, ElementColorDictionary
from pyiron.base.settings.generic import Settings
from scipy.spatial import cKDTree, Voronoi
try:
import spglib
except ImportError:
try:
import pyspglib as spglib
except ImportError:
raise ImportError("The spglib package needs to be installed")
__author__ = "<NAME>, <NAME>"
__copyright__ = "Copyright 2019, Max-Planck-Institut für Eisenforschung GmbH - " \
"Computational Materials Design (CM) Department"
__version__ = "1.0"
__maintainer__ = "<NAME>"
__email__ = "<EMAIL>"
__status__ = "production"
__date__ = "Sep 1, 2017"
s = Settings()
class Atoms(object):
"""
The Atoms class represents all the information required to describe a structure at the atomic scale. This class is
written in such a way that is compatible with the `ASE atoms class`_. Some of the functions in this module is based
on the corresponding implementation in the ASE package
Args:
elements (list/numpy.ndarray): List of strings containing the elements or a list of
atomistics.structure.periodic_table.ChemicalElement instances
numbers (list/numpy.ndarray): List of atomic numbers of elements
symbols (list/numpy.ndarray): List of chemical symbols
positions (list/numpy.ndarray): List of positions
scaled_positions (list/numpy.ndarray): List of scaled positions (relative coordinates)
pbc (list/numpy.ndarray/boolean): Tells if periodic boundary conditions should be applied on the three axes
cell (list/numpy.ndarray instance): A 3x3 array representing the lattice vectors of the structure
Note: Only one of elements/symbols or numbers should be assigned during initialization
Attributes:
indices (numpy.ndarray): A list of size N which gives the species index of the structure which has N atoms
.. _ASE atoms class: https://wiki.fysik.dtu.dk/ase/ase/atoms.html
"""
def __init__(self, symbols=None, positions=None, numbers=None, tags=None, momenta=None, masses=None,
magmoms=None, charges=None, scaled_positions=None, cell=None, pbc=None, celldisp=None, constraint=None,
calculator=None, info=None, indices=None, elements=None, dimension=None, species=None,
**qwargs):
if symbols is not None:
if elements is None:
elements = symbols
else:
raise ValueError("Only elements OR symbols should be given.")
if tags is not None or momenta is not None or masses is not None or charges is not None \
or celldisp is not None or constraint is not None or calculator is not None or info is not None:
s.logger.debug('Not supported parameter used!')
self._store_elements = dict()
self._species_to_index_dict = None
self.colorLut = ElementColorDictionary().to_lut()
self._is_scaled = False
if cell is not None:
# make it ASE compatible
if np.linalg.matrix_rank(cell) == 1:
cell = np.eye(len(cell)) * cell
else:
cell = np.array(cell)
self._cell = cell
self._species = list()
self.positions= None
self._pse = PeriodicTable()
self._tag_list = SparseArray()
self.indices = np.array([])
self._info = dict()
self.arrays = dict()
self.adsorbate_info = {}
self.bonds = None
self._pbc = False
self.dimension = 3 # Default
self.units = {"length": "A", "mass": "u"}
el_index_lst = list()
element_list = None
if (elements is None) and (numbers is None) and (indices is None):
return
if numbers is not None: # for ASE compatibility
if not (elements is None):
raise AssertionError()
elements = self.numbers_to_elements(numbers)
if elements is not None:
el_object_list = None
if isinstance(elements, str):
element_list = self.convert_formula(elements)
elif isinstance(elements, (list, tuple, np.ndarray)):
if not all([isinstance(el, elements[0].__class__) for el in elements]):
object_list = list()
for el in elements:
if isinstance(el, (str, np.str, np.str_)):
object_list.append(self.convert_element(el))
if isinstance(el, ChemicalElement):
object_list.append(el)
if isinstance(el, Atom):
object_list.append(el.element)
if isinstance(el, (int, np.integer)):
# pse = PeriodicTable()
object_list.append(self._pse.element(el))
el_object_list = object_list
if len(elements) == 0:
element_list = elements
else:
if isinstance(elements[0], (list, tuple, np.ndarray)):
elements = np.array(elements).flatten()
if isinstance(elements[0], string_types):
element_list = elements
elif isinstance(elements[0], ChemicalElement):
el_object_list = elements
elif isinstance(elements[0], Atom):
el_object_list = [el.element for el in elements]
positions = [el.position for el in elements]
elif elements.dtype in [int, np.integer]:
el_object_list = self.numbers_to_elements(elements)
else:
raise ValueError('Unknown static type for element in list: ' + str(type(elements[0])))
if el_object_list is None:
el_object_list = [self.convert_element(el) for el in element_list]
self.set_species(list(set(el_object_list)))
# species_to_index_dict = {el: i for i, el in enumerate(self.species)}
el_index_lst = [self._species_to_index_dict[el] for el in el_object_list]
elif indices is not None:
el_index_lst = indices
self.set_species(species)
if scaled_positions is not None:
if positions is not None:
raise ValueError("either position or scaled_positions can be given")
if cell is None:
raise ValueError('scaled_positions can only be used with a given cell')
positions = np.dot(np.array(cell).T, np.array(scaled_positions).T).T
if positions is None:
self.dimension = 3
if cell is not None:
positions = np.zeros((len(el_index_lst), self.dimension))
self.indices = np.array(el_index_lst)
self.positions = np.array(positions).astype(np.float)
self._tag_list._length = len(positions)
for key, val in qwargs.items():
print('set qwargs (ASE): ', key, val)
setattr(self, key, val)
if len(positions) > 0:
self.dimension = len(positions[0])
else:
self.dimension = 3
if dimension is not None:
self.dimension = dimension
if cell is not None:
if pbc is None:
self.pbc = True # default setting
else:
self.pbc = pbc
self.set_initial_magnetic_moments(magmoms)
@property
def cell(self):
"""
numpy.ndarray: A size 3x3 array which gives the lattice vectors of the cell as [a1, a2, a3]
"""
return self._cell
@cell.setter
def cell(self, value):
if value is None:
self._cell = None
else:
if self._is_scaled:
self.set_cell(value, scale_atoms=True)
else:
self.set_cell(value)
@property
def species(self):
"""
list: A list of atomistics.structure.periodic_table.ChemicalElement instances
"""
return self._species
# @species.setter
def set_species(self, value):
"""
Setting the species list
Args:
value (list): A list atomistics.structure.periodic_table.ChemicalElement instances
"""
if value is None:
return
value = list(value)
self._species_to_index_dict = {el: i for i, el in enumerate(value)}
self._species = value[:]
self._store_elements = {el.Abbreviation: el for el in value}
@property
def info(self):
"""
dict: This dictionary is merely used to be compatible with the ASE Atoms class.
"""
return self._info
@info.setter
def info(self, val):
self._info = val
@property
def pbc(self):
"""
list: A list of boolean values which gives the periodic boundary consitions along the three axes.
The default value is [True, True, True]
"""
if not isinstance(self._pbc, np.ndarray):
self.set_pbc(self._pbc)
return self._pbc
@pbc.setter
def pbc(self, val):
self._pbc = val
@property
def elements(self):
"""
numpy.ndarray: A size N list of atomistics.structure.periodic_table.ChemicalElement instances according
to the ordering of the atoms in the instance
"""
return np.array([self.species[el] for el in self.indices])
def new_array(self, name, a, dtype=None, shape=None):
"""
Adding a new array to the instance. This function is for the purpose of compatibility with the ASE package
Args:
name (str): Name of the array
a (list/numpy.ndarray): The array to be added
dtype (type): Data type of the array
shape (list/turple): Shape of the array
"""
if dtype is not None:
a = np.array(a, dtype, order='C')
if len(a) == 0 and shape is not None:
a.shape = (-1,) + shape
else:
if not a.flags['C_CONTIGUOUS']:
a = np.ascontiguousarray(a)
else:
a = a.copy()
if name in self.arrays:
raise RuntimeError
for b in self.arrays.values():
if len(a) != len(b):
raise ValueError('Array has wrong length: %d != %d.' %
(len(a), len(b)))
break
if shape is not None and a.shape[1:] != shape:
raise ValueError('Array has wrong shape %s != %s.' %
(a.shape, (a.shape[0:1] + shape)))
self.arrays[name] = a
def get_array(self, name, copy=True):
"""
Get an array. This function is for the purpose of compatibility with the ASE package
Args:
name (str): Name of the required array
copy (bool): True if a copy of the array is to be returned
Returns:
An array of a copy of the array
"""
if copy:
return self.arrays[name].copy()
else:
return self.arrays[name]
def set_array(self, name, a, dtype=None, shape=None):
"""
Update array. This function is for the purpose of compatibility with the ASE package
Args:
name (str): Name of the array
a (list/numpy.ndarray): The array to be added
dtype (type): Data type of the array
shape (list/turple): Shape of the array
"""
b = self.arrays.get(name)
if b is None:
if a is not None:
self.new_array(name, a, dtype, shape)
else:
if a is None:
del self.arrays[name]
else:
a = np.asarray(a)
if a.shape != b.shape:
raise ValueError('Array has wrong shape %s != %s.' %
(a.shape, b.shape))
b[:] = a
def add_tag(self, *args, **qwargs):
"""
Add tags to the atoms object.
Examples:
For selective dynamics::
>>> self.add_tag(selective_dynamics=[False, False, False])
"""
self._tag_list.add_tag(*args, **qwargs)
# @staticmethod
def numbers_to_elements(self, numbers):
"""
Convert atomic numbers in element objects (needed for compatibility with ASE)
Args:
numbers (list): List of Element Numbers (as Integers; default in ASE)
Returns:
list: A list of elements as needed for pyiron
"""
# pse = PeriodicTable() # TODO; extend to internal PSE which can contain additional elements and tags
atom_number_to_element = {}
for i_el in set(numbers):
i_el = int(i_el)
atom_number_to_element[i_el] = self._pse.element(i_el)
return [atom_number_to_element[i_el] for i_el in numbers]
def copy(self):
"""
Returns a copy of the instance
Returns:
pyiron.atomistics.structure.atoms.Atoms: A copy of the instance
"""
return self.__copy__()
def to_hdf(self, hdf, group_name="structure"):
"""
Save the object in a HDF5 file
Args:
hdf (pyiron.base.generic.hdfio.FileHDFio): HDF path to which the object is to be saved
group_name (str):
Group name with which the object should be stored. This same name should be used to retrieve the object
"""
# import time
with hdf.open(group_name) as hdf_structure:
# time_start = time.time()
hdf_structure["TYPE"] = str(type(self))
for el in self.species:
if isinstance(el.tags, dict):
with hdf_structure.open("new_species") as hdf_species:
el.to_hdf(hdf_species)
hdf_structure['species'] = [el.Abbreviation for el in self.species]
hdf_structure["indices"] = self.indices
with hdf_structure.open("tags") as hdf_tags:
for tag in self._tag_list.keys():
tag_value = self._tag_list[tag]
if isinstance(tag_value, SparseList):
tag_value.to_hdf(hdf_tags, tag)
hdf_structure["units"] = self.units
hdf_structure["dimension"] = self.dimension
if self.cell is not None:
with hdf_structure.open("cell") as hdf_cell:
hdf_cell["cell"] = self.cell
hdf_cell["pbc"] = self.pbc
# hdf_structure["coordinates"] = self.positions # "Atomic coordinates"
hdf_structure["positions"] = self.positions # "Atomic coordinates"
# potentials with explicit bonds (TIP3P, harmonic, etc.)
if self.bonds is not None:
hdf_structure["explicit_bonds"] = self.bonds
# print ('time in atoms.to_hdf: ', time.time() - time_start)
def from_hdf(self, hdf, group_name="structure"):
"""
Retrieve the object from a HDF5 file
Args:
hdf (pyiron.base.generic.hdfio.FileHDFio): HDF path to which the object is to be saved
group_name (str): Group name from which the Atoms object is retreived.
Returns:
pyiron_atomistic.structure.atoms.Atoms: The retrieved atoms class
"""
if "indices" in hdf[group_name].list_nodes():
with hdf.open(group_name) as hdf_atoms:
if "new_species" in hdf_atoms.list_groups():
with hdf_atoms.open("new_species") as hdf_species:
self._pse.from_hdf(hdf_species)
el_object_list = [self.convert_element(el, self._pse) for el in hdf_atoms["species"]]
self.indices = hdf_atoms["indices"]
self._tag_list._length = len(self)
self.set_species(el_object_list)
self.bonds = None
if "explicit_bonds" in hdf_atoms.list_nodes():
# print "bonds: "
self.bonds = hdf_atoms["explicit_bonds"]
if "tags" in hdf_atoms.list_groups():
with hdf_atoms.open("tags") as hdf_tags:
tags = hdf_tags.list_nodes()
for tag in tags:
# tr_dict = {'0': False, '1': True}
if isinstance(hdf_tags[tag], (list, np.ndarray)):
my_list = hdf_tags[tag]
self._tag_list[tag] = SparseList(my_list, length=len(self))
else:
my_dict = hdf_tags.get_pandas(tag).to_dict()
my_dict = {i: val for i, val in zip(my_dict["index"], my_dict["values"])}
self._tag_list[tag] = SparseList(my_dict, length=len(self))
tr_dict = {1: True, 0: False}
self.dimension = hdf_atoms["dimension"]
self.units = hdf_atoms["units"]
self.cell = None
if "cell" in hdf_atoms.list_groups():
with hdf_atoms.open("cell") as hdf_cell:
self.cell = hdf_cell["cell"]
self.pbc = hdf_cell["pbc"]
# Backward compatibility
position_tag = "positions"
if position_tag not in hdf_atoms.list_nodes():
position_tag = "coordinates"
if "is_absolute" in hdf_atoms.list_nodes():
if not tr_dict[hdf_atoms["is_absolute"]]:
self.set_scaled_positions(hdf_atoms[position_tag])
else:
self.positions = hdf_atoms[position_tag]
else:
self.positions = hdf_atoms[position_tag]
if "bonds" in hdf_atoms.list_nodes():
self.bonds = hdf_atoms["explicit_bonds"]
return self
else:
return self._from_hdf_old(hdf, group_name)
def _from_hdf_old(self, hdf, group_name="structure"):
"""
This function exits merely for the purpose of backward compatibility
"""
with hdf.open(group_name) as hdf_atoms:
self._pse = PeriodicTable()
if "species" in hdf_atoms.list_groups():
with hdf_atoms.open("species") as hdf_species:
self._pse.from_hdf(hdf_species)
chemical_symbols = np.array(hdf_atoms["elements"], dtype=str)
el_object_list = [self.convert_element(el, self._pse) for el in chemical_symbols]
self.set_species(list(set(el_object_list)))
self.indices = [self._species_to_index_dict[el] for el in el_object_list]
self._tag_list._length = len(self)
self.bonds = None
if "explicit_bonds" in hdf_atoms.list_nodes():
# print "bonds: "
self.bonds = hdf_atoms["explicit_bonds"]
if "tags" in hdf_atoms.list_groups():
with hdf_atoms.open("tags") as hdf_tags:
tags = hdf_tags.list_nodes()
for tag in tags:
# tr_dict = {'0': False, '1': True}
if isinstance(hdf_tags[tag], (list, np.ndarray)):
my_list = hdf_tags[tag]
self._tag_list[tag] = SparseList(my_list, length=len(self))
else:
my_dict = hdf_tags.get_pandas(tag).to_dict()
my_dict = {i: val for i, val in zip(my_dict["index"], my_dict["values"])}
self._tag_list[tag] = SparseList(my_dict, length=len(self))
self.cell = None
if "cell" in hdf_atoms.list_groups():
with hdf_atoms.open("cell") as hdf_cell:
self.cell = hdf_cell["cell"]
self.pbc = hdf_cell["pbc"]
tr_dict = {1: True, 0: False}
self.dimension = hdf_atoms["dimension"]
if "is_absolute" in hdf_atoms and not tr_dict[hdf_atoms["is_absolute"]]:
self.positions = hdf_atoms["coordinates"]
else:
self.set_scaled_positions(hdf_atoms["coordinates"])
self.units = hdf_atoms["units"]
if "bonds" in hdf_atoms.list_nodes():
self.bonds = hdf_atoms["explicit_bonds"]
return self
def center(self, vacuum=None, axis=(0, 1, 2)):
"""
Center atoms in unit cell.
Adopted from ASE code (https://wiki.fysik.dtu.dk/ase/_modules/ase/atoms.html#Atoms.center)
Args:
vacuum (float): If specified adjust the amount of vacuum when centering. If vacuum=10.0 there will thus be
10 Angstrom of vacuum on each side.
axis (tuple/list): List or turple of integers specifying the axis along which the atoms should be centered
"""
# Find the orientations of the faces of the unit cell
c = self.cell
if c is None:
c = np.identity(self.dimension)
self.cell = c
dirs = np.zeros_like(c)
for i in range(3):
dirs[i] = np.cross(c[i - 1], c[i - 2])
dirs[i] /= np.linalg.norm(dirs[i]) # normalize
if np.dot(dirs[i], c[i]) < 0.0:
dirs[i] *= -1
# Now, decide how much each basis vector should be made longer
if isinstance(axis, int):
axes = (axis,)
else:
axes = axis
p = self.positions
longer = np.zeros(3)
shift = np.zeros(3)
for i in axes:
p0 = | np.dot(p, dirs[i]) | numpy.dot |
# 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]) | numpy.array |
# This module has been generated automatically from space group information
# obtained from the Computational Crystallography Toolbox
#
"""
Space groups
This module contains a list of all the 230 space groups that can occur in
a crystal. The variable space_groups contains a dictionary that maps
space group numbers and space group names to the corresponding space
group objects.
.. moduleauthor:: <NAME> <<EMAIL>>
"""
#-----------------------------------------------------------------------------
# Copyright (C) 2013 The Mosaic Development Team
#
# Distributed under the terms of the BSD License. The full license is in
# the file LICENSE.txt, distributed as part of this software.
#-----------------------------------------------------------------------------
import numpy as N
class SpaceGroup(object):
"""
Space group
All possible space group objects are created in this module. Other
modules should access these objects through the dictionary
space_groups rather than create their own space group objects.
"""
def __init__(self, number, symbol, transformations):
"""
:param number: the number assigned to the space group by
international convention
:type number: int
:param symbol: the Hermann-Mauguin space-group symbol as used
in PDB and mmCIF files
:type symbol: str
:param transformations: a list of space group transformations,
each consisting of a tuple of three
integer arrays (rot, tn, td), where
rot is the rotation matrix and tn/td
are the numerator and denominator of the
translation vector. The transformations
are defined in fractional coordinates.
:type transformations: list
"""
self.number = number
self.symbol = symbol
self.transformations = transformations
self.transposed_rotations = N.array([N.transpose(t[0])
for t in transformations])
self.phase_factors = N.exp(N.array([(-2j*N.pi*t[1])/t[2]
for t in transformations]))
def __repr__(self):
return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol))
def __len__(self):
"""
:return: the number of space group transformations
:rtype: int
"""
return len(self.transformations)
def symmetryEquivalentMillerIndices(self, hkl):
"""
:param hkl: a set of Miller indices
:type hkl: Scientific.N.array_type
:return: a tuple (miller_indices, phase_factor) of two arrays
of length equal to the number of space group
transformations. miller_indices contains the Miller
indices of each reflection equivalent by symmetry to the
reflection hkl (including hkl itself as the first element).
phase_factor contains the phase factors that must be applied
to the structure factor of reflection hkl to obtain the
structure factor of the symmetry equivalent reflection.
:rtype: tuple
"""
hkls = N.dot(self.transposed_rotations, hkl)
p = N.multiply.reduce(self.phase_factors**hkl, -1)
return hkls, p
space_groups = {}
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(1, 'P 1', transformations)
space_groups[1] = sg
space_groups['P 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(2, 'P -1', transformations)
space_groups[2] = sg
space_groups['P -1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(3, 'P 1 2 1', transformations)
space_groups[3] = sg
space_groups['P 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(4, 'P 1 21 1', transformations)
space_groups[4] = sg
space_groups['P 1 21 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(5, 'C 1 2 1', transformations)
space_groups[5] = sg
space_groups['C 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(6, 'P 1 m 1', transformations)
space_groups[6] = sg
space_groups['P 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(7, 'P 1 c 1', transformations)
space_groups[7] = sg
space_groups['P 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(8, 'C 1 m 1', transformations)
space_groups[8] = sg
space_groups['C 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(9, 'C 1 c 1', transformations)
space_groups[9] = sg
space_groups['C 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(10, 'P 1 2/m 1', transformations)
space_groups[10] = sg
space_groups['P 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(11, 'P 1 21/m 1', transformations)
space_groups[11] = sg
space_groups['P 1 21/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(12, 'C 1 2/m 1', transformations)
space_groups[12] = sg
space_groups['C 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(13, 'P 1 2/c 1', transformations)
space_groups[13] = sg
space_groups['P 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(14, 'P 1 21/c 1', transformations)
space_groups[14] = sg
space_groups['P 1 21/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(15, 'C 1 2/c 1', transformations)
space_groups[15] = sg
space_groups['C 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(16, 'P 2 2 2', transformations)
space_groups[16] = sg
space_groups['P 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(17, 'P 2 2 21', transformations)
space_groups[17] = sg
space_groups['P 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(18, 'P 21 21 2', transformations)
space_groups[18] = sg
space_groups['P 21 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(19, 'P 21 21 21', transformations)
space_groups[19] = sg
space_groups['P 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(20, 'C 2 2 21', transformations)
space_groups[20] = sg
space_groups['C 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(21, 'C 2 2 2', transformations)
space_groups[21] = sg
space_groups['C 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(22, 'F 2 2 2', transformations)
space_groups[22] = sg
space_groups['F 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(23, 'I 2 2 2', transformations)
space_groups[23] = sg
space_groups['I 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(24, 'I 21 21 21', transformations)
space_groups[24] = sg
space_groups['I 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(25, 'P m m 2', transformations)
space_groups[25] = sg
space_groups['P m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(26, 'P m c 21', transformations)
space_groups[26] = sg
space_groups['P m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(27, 'P c c 2', transformations)
space_groups[27] = sg
space_groups['P c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(28, 'P m a 2', transformations)
space_groups[28] = sg
space_groups['P m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(29, 'P c a 21', transformations)
space_groups[29] = sg
space_groups['P c a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(30, 'P n c 2', transformations)
space_groups[30] = sg
space_groups['P n c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(31, 'P m n 21', transformations)
space_groups[31] = sg
space_groups['P m n 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(32, 'P b a 2', transformations)
space_groups[32] = sg
space_groups['P b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(33, 'P n a 21', transformations)
space_groups[33] = sg
space_groups['P n a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(34, 'P n n 2', transformations)
space_groups[34] = sg
space_groups['P n n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(35, 'C m m 2', transformations)
space_groups[35] = sg
space_groups['C m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(36, 'C m c 21', transformations)
space_groups[36] = sg
space_groups['C m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(37, 'C c c 2', transformations)
space_groups[37] = sg
space_groups['C c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(38, 'A m m 2', transformations)
space_groups[38] = sg
space_groups['A m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(39, 'A b m 2', transformations)
space_groups[39] = sg
space_groups['A b m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(40, 'A m a 2', transformations)
space_groups[40] = sg
space_groups['A m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(41, 'A b a 2', transformations)
space_groups[41] = sg
space_groups['A b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(42, 'F m m 2', transformations)
space_groups[42] = sg
space_groups['F m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(43, 'F d d 2', transformations)
space_groups[43] = sg
space_groups['F d d 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(44, 'I m m 2', transformations)
space_groups[44] = sg
space_groups['I m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(45, 'I b a 2', transformations)
space_groups[45] = sg
space_groups['I b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(46, 'I m a 2', transformations)
space_groups[46] = sg
space_groups['I m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(47, 'P m m m', transformations)
space_groups[47] = sg
space_groups['P m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(48, 'P n n n :2', transformations)
space_groups[48] = sg
space_groups['P n n n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(49, 'P c c m', transformations)
space_groups[49] = sg
space_groups['P c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(50, 'P b a n :2', transformations)
space_groups[50] = sg
space_groups['P b a n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(51, 'P m m a', transformations)
space_groups[51] = sg
space_groups['P m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(52, 'P n n a', transformations)
space_groups[52] = sg
space_groups['P n n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(53, 'P m n a', transformations)
space_groups[53] = sg
space_groups['P m n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(54, 'P c c a', transformations)
space_groups[54] = sg
space_groups['P c c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(55, 'P b a m', transformations)
space_groups[55] = sg
space_groups['P b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(56, 'P c c n', transformations)
space_groups[56] = sg
space_groups['P c c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(57, 'P b c m', transformations)
space_groups[57] = sg
space_groups['P b c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(58, 'P n n m', transformations)
space_groups[58] = sg
space_groups['P n n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(59, 'P m m n :2', transformations)
space_groups[59] = sg
space_groups['P m m n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(60, 'P b c n', transformations)
space_groups[60] = sg
space_groups['P b c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(61, 'P b c a', transformations)
space_groups[61] = sg
space_groups['P b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(62, 'P n m a', transformations)
space_groups[62] = sg
space_groups['P n m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(63, 'C m c m', transformations)
space_groups[63] = sg
space_groups['C m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(64, 'C m c a', transformations)
space_groups[64] = sg
space_groups['C m c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(65, 'C m m m', transformations)
space_groups[65] = sg
space_groups['C m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(66, 'C c c m', transformations)
space_groups[66] = sg
space_groups['C c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(67, 'C m m a', transformations)
space_groups[67] = sg
space_groups['C m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(68, 'C c c a :2', transformations)
space_groups[68] = sg
space_groups['C c c a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(69, 'F m m m', transformations)
space_groups[69] = sg
space_groups['F m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(70, 'F d d d :2', transformations)
space_groups[70] = sg
space_groups['F d d d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(71, 'I m m m', transformations)
space_groups[71] = sg
space_groups['I m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(72, 'I b a m', transformations)
space_groups[72] = sg
space_groups['I b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(73, 'I b c a', transformations)
space_groups[73] = sg
space_groups['I b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(74, 'I m m a', transformations)
space_groups[74] = sg
space_groups['I m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(75, 'P 4', transformations)
space_groups[75] = sg
space_groups['P 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(76, 'P 41', transformations)
space_groups[76] = sg
space_groups['P 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(77, 'P 42', transformations)
space_groups[77] = sg
space_groups['P 42'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(78, 'P 43', transformations)
space_groups[78] = sg
space_groups['P 43'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(79, 'I 4', transformations)
space_groups[79] = sg
space_groups['I 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(80, 'I 41', transformations)
space_groups[80] = sg
space_groups['I 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(81, 'P -4', transformations)
space_groups[81] = sg
space_groups['P -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(82, 'I -4', transformations)
space_groups[82] = sg
space_groups['I -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(83, 'P 4/m', transformations)
space_groups[83] = sg
space_groups['P 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(84, 'P 42/m', transformations)
space_groups[84] = sg
space_groups['P 42/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(85, 'P 4/n :2', transformations)
space_groups[85] = sg
space_groups['P 4/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(86, 'P 42/n :2', transformations)
space_groups[86] = sg
space_groups['P 42/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(87, 'I 4/m', transformations)
space_groups[87] = sg
space_groups['I 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(88, 'I 41/a :2', transformations)
space_groups[88] = sg
space_groups['I 41/a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(89, 'P 4 2 2', transformations)
space_groups[89] = sg
space_groups['P 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(90, 'P 4 21 2', transformations)
space_groups[90] = sg
space_groups['P 4 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(91, 'P 41 2 2', transformations)
space_groups[91] = sg
space_groups['P 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(92, 'P 41 21 2', transformations)
space_groups[92] = sg
space_groups['P 41 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(93, 'P 42 2 2', transformations)
space_groups[93] = sg
space_groups['P 42 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(94, 'P 42 21 2', transformations)
space_groups[94] = sg
space_groups['P 42 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(95, 'P 43 2 2', transformations)
space_groups[95] = sg
space_groups['P 43 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(96, 'P 43 21 2', transformations)
space_groups[96] = sg
space_groups['P 43 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(97, 'I 4 2 2', transformations)
space_groups[97] = sg
space_groups['I 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(98, 'I 41 2 2', transformations)
space_groups[98] = sg
space_groups['I 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(99, 'P 4 m m', transformations)
space_groups[99] = sg
space_groups['P 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(100, 'P 4 b m', transformations)
space_groups[100] = sg
space_groups['P 4 b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(101, 'P 42 c m', transformations)
space_groups[101] = sg
space_groups['P 42 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(102, 'P 42 n m', transformations)
space_groups[102] = sg
space_groups['P 42 n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(103, 'P 4 c c', transformations)
space_groups[103] = sg
space_groups['P 4 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(104, 'P 4 n c', transformations)
space_groups[104] = sg
space_groups['P 4 n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(105, 'P 42 m c', transformations)
space_groups[105] = sg
space_groups['P 42 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(106, 'P 42 b c', transformations)
space_groups[106] = sg
space_groups['P 42 b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(107, 'I 4 m m', transformations)
space_groups[107] = sg
space_groups['I 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(108, 'I 4 c m', transformations)
space_groups[108] = sg
space_groups['I 4 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(109, 'I 41 m d', transformations)
space_groups[109] = sg
space_groups['I 41 m d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(110, 'I 41 c d', transformations)
space_groups[110] = sg
space_groups['I 41 c d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(111, 'P -4 2 m', transformations)
space_groups[111] = sg
space_groups['P -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(112, 'P -4 2 c', transformations)
space_groups[112] = sg
space_groups['P -4 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(113, 'P -4 21 m', transformations)
space_groups[113] = sg
space_groups['P -4 21 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(114, 'P -4 21 c', transformations)
space_groups[114] = sg
space_groups['P -4 21 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(115, 'P -4 m 2', transformations)
space_groups[115] = sg
space_groups['P -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(116, 'P -4 c 2', transformations)
space_groups[116] = sg
space_groups['P -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(117, 'P -4 b 2', transformations)
space_groups[117] = sg
space_groups['P -4 b 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(118, 'P -4 n 2', transformations)
space_groups[118] = sg
space_groups['P -4 n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(119, 'I -4 m 2', transformations)
space_groups[119] = sg
space_groups['I -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(120, 'I -4 c 2', transformations)
space_groups[120] = sg
space_groups['I -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(121, 'I -4 2 m', transformations)
space_groups[121] = sg
space_groups['I -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(122, 'I -4 2 d', transformations)
space_groups[122] = sg
space_groups['I -4 2 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(123, 'P 4/m m m', transformations)
space_groups[123] = sg
space_groups['P 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(124, 'P 4/m c c', transformations)
space_groups[124] = sg
space_groups['P 4/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(125, 'P 4/n b m :2', transformations)
space_groups[125] = sg
space_groups['P 4/n b m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(126, 'P 4/n n c :2', transformations)
space_groups[126] = sg
space_groups['P 4/n n c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(127, 'P 4/m b m', transformations)
space_groups[127] = sg
space_groups['P 4/m b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(128, 'P 4/m n c', transformations)
space_groups[128] = sg
space_groups['P 4/m n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(129, 'P 4/n m m :2', transformations)
space_groups[129] = sg
space_groups['P 4/n m m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(130, 'P 4/n c c :2', transformations)
space_groups[130] = sg
space_groups['P 4/n c c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(131, 'P 42/m m c', transformations)
space_groups[131] = sg
space_groups['P 42/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(132, 'P 42/m c m', transformations)
space_groups[132] = sg
space_groups['P 42/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(133, 'P 42/n b c :2', transformations)
space_groups[133] = sg
space_groups['P 42/n b c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(134, 'P 42/n n m :2', transformations)
space_groups[134] = sg
space_groups['P 42/n n m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(135, 'P 42/m b c', transformations)
space_groups[135] = sg
space_groups['P 42/m b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(136, 'P 42/m n m', transformations)
space_groups[136] = sg
space_groups['P 42/m n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(137, 'P 42/n m c :2', transformations)
space_groups[137] = sg
space_groups['P 42/n m c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(138, 'P 42/n c m :2', transformations)
space_groups[138] = sg
space_groups['P 42/n c m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(139, 'I 4/m m m', transformations)
space_groups[139] = sg
space_groups['I 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(140, 'I 4/m c m', transformations)
space_groups[140] = sg
space_groups['I 4/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(141, 'I 41/a m d :2', transformations)
space_groups[141] = sg
space_groups['I 41/a m d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(142, 'I 41/a c d :2', transformations)
space_groups[142] = sg
space_groups['I 41/a c d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(143, 'P 3', transformations)
space_groups[143] = sg
space_groups['P 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(144, 'P 31', transformations)
space_groups[144] = sg
space_groups['P 31'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(145, 'P 32', transformations)
space_groups[145] = sg
space_groups['P 32'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(146, 'R 3 :H', transformations)
space_groups[146] = sg
space_groups['R 3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(147, 'P -3', transformations)
space_groups[147] = sg
space_groups['P -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(148, 'R -3 :H', transformations)
space_groups[148] = sg
space_groups['R -3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(149, 'P 3 1 2', transformations)
space_groups[149] = sg
space_groups['P 3 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(150, 'P 3 2 1', transformations)
space_groups[150] = sg
space_groups['P 3 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(151, 'P 31 1 2', transformations)
space_groups[151] = sg
space_groups['P 31 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(152, 'P 31 2 1', transformations)
space_groups[152] = sg
space_groups['P 31 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(153, 'P 32 1 2', transformations)
space_groups[153] = sg
space_groups['P 32 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(154, 'P 32 2 1', transformations)
space_groups[154] = sg
space_groups['P 32 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(155, 'R 3 2 :H', transformations)
space_groups[155] = sg
space_groups['R 3 2 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(156, 'P 3 m 1', transformations)
space_groups[156] = sg
space_groups['P 3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(157, 'P 3 1 m', transformations)
space_groups[157] = sg
space_groups['P 3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(158, 'P 3 c 1', transformations)
space_groups[158] = sg
space_groups['P 3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_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]) | numpy.array |
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 pytest
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.neural_network import flexible_shape_utils
from coremltools.models.utils import macos_version, is_macos
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:
# check if shape has 0 valued dimension
if np.prod(np_preds.shape) == 0 and np.prod(coreml_preds.shape) == 0:
return True
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)
try:
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]))
finally:
# Remove the temporary directory if we created one
if model_dir and os.path.exists(model_dir):
shutil.rmtree(model_dir)
@unittest.skipIf(not is_macos() or 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)
self.assertEquals(len(input_dim), builder._get_rank('output'))
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)
self.assertEqual(len(input_dim), builder._get_rank('output'))
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)
for output_ in output_names:
self.assertEqual(len(input_dim), builder._get_rank(output_))
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)
self.assertEqual(len(input_dim), builder._get_rank('output'))
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)
self.assertEqual(len(input_dim), builder._get_rank('output'))
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)
self.assertEqual(len(input_dim), builder._get_rank('output'))
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)
target_dim = (10, 1, 1)
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=target_dim,
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)
self.assertEqual(len(target_dim), builder._get_rank('output'))
def test_reshape_target_shape_4(self):
input_dim = (1, 2, 5) # (C,H,W)
target_dim = (1, 10, 1, 1)
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=target_dim,
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)
self.assertEqual(len(target_dim), builder._get_rank('output'))
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(not is_macos() or 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)
def test_shape_flexibility_enumeration(self, rank=4):
default_shape = tuple(np.random.randint(1, 15, size=rank))
input_features = [('data', datatypes.Array(*default_shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features=input_features,
output_features=[('output', None)],
disable_rank5_shape_mapping=True)
builder.add_sin(name='sin', input_name='data', output_name='output')
spec = builder.spec
shapes = [tuple(np.random.randint(1, 15, size=rank)),
tuple(np.random.randint(1, 15, size=rank))]
flexible_shape_utils.add_multiarray_ndshape_enumeration(
spec, feature_name='data', enumerated_shapes=shapes)
shapes.append(default_shape)
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_shape_flexibility_enumeration_rank3(self):
self.test_shape_flexibility_enumeration(rank=3)
def test_shape_flexibility_enumeration_rank2(self):
self.test_shape_flexibility_enumeration(rank=2)
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_dynamic_weight_conv(self):
input_dim = (1, 3, 16, 16)
# weight layout: (output_channels, kernel_channels, height, width)
weight_dim = (4, 3, 3, 3)
output_dim = (1, 4, 14, 14)
kernel_channels = input_dim[0]
output_channels, kernel_channels, height, width = weight_dim
input_features = [
('input', datatypes.Array(*input_dim)),
('weight', datatypes.Array(*weight_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features,
output_features,
disable_rank5_shape_mapping=True)
builder.add_convolution(
name='two_input_conv_layer',
kernel_channels=kernel_channels,
output_channels=output_channels,
height=height,
width=width,
stride_height=1,
stride_width=1,
border_mode='valid',
groups=1,
W=None,
b=None,
has_bias=False,
input_name=['input', 'weight'],
output_name='output')
# Assigning everything to ones should cover the execution path
# and engine failures, but is not a complete check on numerics.
input_val = np.ones(input_dim)
weight_val = np.ones(weight_dim)
expected = np.ones(output_dim) * 27
feed_dict = {'input': input_val, 'weight': weight_val}
expected = {'output': expected}
self._test_model(builder.spec, feed_dict, expected, useCPUOnly=True)
self._test_model(builder.spec, feed_dict, expected, useCPUOnly=False)
@pytest.mark.xfail
def test_dynamic_weight_deconv(self):
# Expect to fail in Core ML 3
input_dim = (1, 1, 16, 16)
# weight layout: (output_channels, kernel_channels, height, width)
weight_dim = (1, 1, 3, 3)
output_dim = (1, 1, 18, 18)
output_channels, kernel_channels, height, width = weight_dim
input_features = [
('data', datatypes.Array(*input_dim)),
('weight', datatypes.Array(*weight_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features,
output_features,
disable_rank5_shape_mapping=True)
builder.add_convolution(
name='deconv',
kernel_channels=kernel_channels,
output_channels=output_channels,
height=height,
width=width,
stride_height=1,
stride_width=1,
border_mode='valid',
groups=1,
W=None,
b=None,
has_bias=False,
is_deconv=True,
input_name=['data', 'weight'],
output_name='output')
input_val = np.ones(input_dim)
weight_val = np.ones(weight_dim)
expected = np.ones(output_dim) * 27
feed_dict = {'data': input_val, 'weight': weight_val}
expected = {'output': expected}
self._test_model(builder.spec, feed_dict, expected)
def test_batched_mat_mul_cpu(self, cpu_only=True):
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=cpu_only,
output_name_shape_dict=shape_dict)
self.assertEqual(len(outShape), builder._get_rank('output'))
def test_batched_mat_mul_gpu(self):
self.test_batched_mat_mul_cpu(cpu_only=False)
def test_batched_mat_mul_with_transposes_cpu(self, cpu_only=True):
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=cpu_only)
def test_batched_mat_mul_with_transposes_gpu(self):
self.test_batched_mat_mul_with_transposes_cpu(cpu_only=False)
def test_batched_mat_mul_single_input_cpu(self,
model_precision=_MLMODEL_FULL_PRECISION,
cpu_only=True):
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=cpu_only)
def test_batched_mat_mul_single_input_half_precision_cpu(self):
self.test_batched_mat_mul_single_input_cpu(
model_precision=_MLMODEL_HALF_PRECISION,
cpu_only=True)
def test_batched_mat_mul_single_input_gpu(self):
self.test_batched_mat_mul_single_input_cpu(model_precision=_MLMODEL_FULL_PRECISION, cpu_only=False)
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_nan_bug_cpu(self):
input_shape = [2,2]
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
for axis in [0,1]:
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.array([[0.5, 0.5],[1e8, 1e8]])
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_softmax_nd_cpu(self, cpu_only=True):
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=cpu_only)
def test_softmax_nd_gpu(self):
self.test_softmax_nd_cpu(cpu_only=False)
def test_concat_nd_cpu(self, cpu_only=True):
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=cpu_only)
def test_concat_nd_gpu(self):
self.test_concat_nd_cpu(cpu_only=False)
def test_fill_like_cpu(self, cpu_only=True):
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=cpu_only)
def test_fill_like_gpu(self):
self.test_fill_like_cpu(cpu_only=False)
def test_fill_static_cpu(self, cpu_only=True):
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=cpu_only)
self.assertEqual(len(shape), builder._get_rank('output'))
def test_fill_static_gpu(self):
self.test_fill_static_cpu(cpu_only=False)
def test_fill_dynamic_cpu(self, cpu_only=True):
for rank in range(1, 6):
input_shape = | np.random.randint(low=2, high=8, size=rank) | numpy.random.randint |
import sys
import argparse
import os
from os import listdir
from os.path import isfile, isdir, join
import numpy as np
import pandas as pd
import multiprocessing
import sys
sys.path.insert(0, "./")
import deepAccNet
import torch.optim as optim
import os
import matplotlib.pyplot as plt
import seaborn as sns
from torch.utils.data import Dataset, DataLoader
import torch
def main():
parser = argparse.ArgumentParser(description="Error predictor network trainer",
epilog="v0.0.1")
parser.add_argument("folder",
action="store",
help="Location of folder to save checkpoints to.")
parser.add_argument("--epoch",
"-e", action="store",
type=int,
default=200,
help="# of epochs (path over all proteins) to train for (Default: 200)")
parser.add_argument("--bert",
"-bert",
action="store_true",
default=False,
help="Run with bert features (Default: False)")
parser.add_argument("--multi_dir",
"-multi_dir",
action="store_true",
default=False,
help="Run with multiple direcotory sources (Default: False)")
parser.add_argument("--num_blocks",
"-numb", action="store",
type=int,
default=5,
help="# of reidual blocks (Default: 8)")
parser.add_argument("--num_filters",
"-numf", action="store",
type=int,
default=128,
help="# of base filter size in residual blocks (Default: 256)")
parser.add_argument("--size_limit",
"-size_limit", action="store",
type=int,
default=280,
help="protein size limit (Default: 300)")
parser.add_argument("--decay",
"-d", action="store",
type=float,
default=0.99,
help="Decay rate for learning rate (Default: 0.99)")
parser.add_argument("--base",
"-b", action="store",
type=float,
default=0.0005,
help="Base learning rate (Default: 0.0005)")
parser.add_argument("--debug",
"-debug",
action="store_true",
default=False,
help="Debug mode (Default: False)")
parser.add_argument("--silent",
"-s",
action="store_true",
default=False,
help="Run in silent mode (Default: False)")
args = parser.parse_args()
script_dir = os.path.dirname(__file__)
base = join(script_dir, "data/")
epochs = args.epoch
base_learning_rate = args.base
decay = args.decay
loss_weight = [1, 0.25, 10] #change if you need different loss
validation = True #validation is always up
name = args.folder
lengthmax = args.size_limit
if not args.silent: print("Loading samples")
proteins = np.load(join(base, "train_proteins.npy"))
if args.debug: proteins = proteins[:100]
train_decoys = deepAccNet.DecoyDataset(targets = proteins,
lengthmax = lengthmax,
bert = args.bert,
multi_dir = args.multi_dir)
train_dataloader = DataLoader(train_decoys, batch_size=1, shuffle=True, num_workers=4)
proteins = np.load(join(base, "valid_proteins.npy"))
if args.debug: proteins = proteins[:100]
valid_decoys = deepAccNet.DecoyDataset(targets = proteins,
lengthmax = lengthmax,
bert = args.bert,
multi_dir = args.multi_dir)
valid_dataloader = DataLoader(valid_decoys, batch_size=1, shuffle=True, num_workers=4)
# Load the model if needed
if not args.silent: print("Instantitating a model")
net = deepAccNet.DeepAccNet(num_chunks = args.num_blocks,
num_channel = args.num_filters,
twobody_size = 49 if args.bert else 33)
restoreModel = False
if isdir(args.folder):
if not args.silent: print("Loading a checkpoint")
checkpoint = torch.load(join(name, "model.pkl"))
net.load_state_dict(checkpoint["model_state_dict"])
#optimizer.load_state_dict(checkpoint['optimizer_state_dict'])
epoch = checkpoint["epoch"]+1
train_loss = checkpoint["train_loss"]
valid_loss = checkpoint["valid_loss"]
best_models = checkpoint["best_models"]
if not args.silent: print("Restarting at epoch", epoch)
assert(len(train_loss["total"]) == epoch)
assert(len(valid_loss["total"]) == epoch)
restoreModel = True
else:
if not args.silent: print("Training a new model")
epoch = 0
train_loss = {"total":[], "esto":[], "mask":[], "lddt":[]}
valid_loss = {"total":[], "esto":[], "mask":[], "lddt":[]}
best_models = []
if not isdir(name):
if not args.silent: print("Creating a new dir at", name)
os.mkdir(name)
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
net.to(device)
optimizer = optim.Adam(net.parameters(), lr=0.0005)
if restoreModel:
checkpoint = torch.load(join(name, "model.pkl"))
optimizer.load_state_dict(checkpoint['optimizer_state_dict'])
# Loop over the dataset multiple times
start_epoch = epoch
for epoch in range(start_epoch, epochs):
# Update the learning rate
lr = base_learning_rate*np.power(decay, epoch)
for param_group in optimizer.param_groups:
param_group['lr'] = lr
# Loop over batches
net.train(True)
temp_loss = {"total":[], "esto":[], "mask":[], "lddt":[]}
for i, data in enumerate(train_dataloader):
# Get the data, Hardcoded transformation for whatever reasons.
idx, val, f1d, f2d, esto, esto_1hot, mask = data["idx"], data["val"], data["1d"], data["2d"],\
data["estogram"], data["estogram_1hot"], data["mask"]
idx = idx[0].long().to(device)
val = val[0].to(device)
f1d = f1d[0].to(device)
f2d = f2d[0].to(device)
esto_true = esto[0].to(device)
esto_1hot_true = esto_1hot[0].to(device)
mask_true = mask[0].to(device)
# Zero the parameter gradients
optimizer.zero_grad()
# forward + backward + optimize
esto_pred, mask_pred, lddt_pred, (esto_logits, mask_logits) = net(idx, val, f1d, f2d)
lddt_true = deepAccNet.calculate_LDDT(esto_1hot_true[0], mask_true[0])
Esto_Loss = torch.nn.CrossEntropyLoss()
Mask_Loss = torch.nn.BCEWithLogitsLoss()
Lddt_Loss = torch.nn.MSELoss()
esto_loss = Esto_Loss(esto_logits, esto_true.long())
mask_loss = Mask_Loss(mask_logits, mask_true)
lddt_loss = Lddt_Loss(lddt_pred, lddt_true.float())
loss = loss_weight[0]*esto_loss + loss_weight[1]*mask_loss + loss_weight[2]*lddt_loss
loss.backward()
optimizer.step()
# Get training loss
temp_loss["total"].append(loss.cpu().detach().numpy())
temp_loss["esto"].append(esto_loss.cpu().detach().numpy())
temp_loss["mask"].append(mask_loss.cpu().detach().numpy())
temp_loss["lddt"].append(lddt_loss.cpu().detach().numpy())
# Display training results
sys.stdout.write("\rEpoch: [%2d/%2d], Batch: [%2d/%2d], loss: %.2f, esto-loss: %.2f, lddt-loss: %.2f, mask: %.2f"
%(epoch, epochs, i, len(train_decoys),
temp_loss["total"][-1], temp_loss["esto"][-1], temp_loss["lddt"][-1], temp_loss["mask"][-1]))
train_loss["total"].append(np.array(temp_loss["total"]))
train_loss["esto"].append(np.array(temp_loss["esto"]))
train_loss["mask"].append(np.array(temp_loss["mask"]))
train_loss["lddt"].append( | np.array(temp_loss["lddt"]) | numpy.array |
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