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import numpy as np
import networkx as nx
import xlsxwriter
import math
def read_gt(gt_file, nodes):
with open(('final_datasets/complex_datasets/gold_standard/' + gt_file + '.txt'), 'r') as f:
gt_raw = []
for item in f:
gt_raw.append(item.split())
if gt_file == 'sgd':
# determine ground truth communities
gt_comms = []
gt_nodes = []
for g in gt_raw:
gt_comms.append(str(g[1]))
gt_nodes.append(str(g[0]))
gt_comms = list(set(gt_comms))
gt_nodes = list(set(gt_nodes))
# append to "nodes" the nodes not in it but found in gt_nodes
ex_nodes_count = 0
for gn in gt_nodes:
if gn not in nodes:
nodes.append(gn)
ex_nodes_count += 1
# form ground truth theta
gt_theta = np.zeros((len(nodes), len(gt_comms)))
for g in gt_raw:
n_index = nodes.index(g[0])
c_index = gt_comms.index(g[1])
gt_theta[n_index, c_index] = 1.0
elif gt_file == 'mips_3_100':
# append to "nodes" the nodes not in it but found in gt_nodes
gt_nodes = set()
for g in gt_raw:
gt_nodes.update(g)
ex_nodes_count = 0
for gn in gt_nodes:
if gn not in nodes:
nodes.append(gn)
ex_nodes_count += 1
# form ground truth theta
gt_theta = np.zeros((len(nodes), len(gt_raw)))
for j in range(len(gt_raw)):
for cn in gt_raw[j]:
n_index = nodes.index(cn)
gt_theta[n_index, j] = 1.0
return gt_theta, ex_nodes_count, nodes
def calc_mmr(pred_c, gt_c, dataset, gt_dataset):
# predicted and ground truth comms count
pred_count = pred_c.shape[1]
gt_count = gt_c.shape[1]
# create bipartite graph
G = nx.Graph()
G.add_nodes_from(range(pred_count + gt_count))
for i in range(pred_count):
for j in range(gt_count):
predvec = pred_c[:, i]
gtvec = gt_c[:, j]
w = (np.dot(predvec, gtvec)/(np.dot(np.linalg.norm(predvec), np.linalg.norm(gtvec))))**2
G.add_edge(i, j + pred_count, weight = w)
print('created weighted bipartite graph using predicted and ground truth communities')
matching = list(nx.algorithms.max_weight_matching(G))
# save matching
with open('matching_' + dataset + '_' + gt_dataset + '.txt', 'w') as fp:
for row in matching:
fp.write(str(row) + '\n')
print('computed and saved max weight matching')
mmr = 0
for e in matching:
mmr += G.get_edge_data(e[0], e[1])['weight']
mmr /= gt_count
return mmr
def calc_frac(pred_c, gt_c):
# predicted and ground truth comms count
pred_count = pred_c.shape[1]
gt_count = gt_c.shape[1]
match_count = 0
for i1 in range(gt_count):
for j1 in range(pred_count):
gtvec = gt_c[:, i1]
predvec = pred_c[:, j1]
curr_match = (np.dot(predvec, gtvec) / (np.dot(np.linalg.norm(predvec), np.linalg.norm(gtvec)))) ** 2
if curr_match >= 0.25:
match_count += 1
break
return match_count/gt_count
def calc_acc(pred_c, gt_c):
# predicted and ground truth comms count
pred_count = pred_c.shape[1]
gt_count = gt_c.shape[1]
t = np.zeros((gt_count, pred_count))
for i1 in range(gt_count):
for j1 in range(pred_count):
t[i1, j1] = np.dot(gt_c[:, i1], pred_c[:, j1])
sn_num = 0.0
sn_den = 0.0
for q in range(gt_count):
sn_num += np.max(t[q, :])
sn_den += np.sum(gt_c[:, q])
sn = sn_num / sn_den
ppv_num = 0.0
ppv_den = 0.0
for j1 in range(pred_count):
ppv_num += np.max(t[:, j1])
ppv_den += np.sum(t[:, j1])
ppv = ppv_num / ppv_den
return math.sqrt(sn*ppv)
#-----------------------------------------------------------------------------------------------------
# parameter choices
# select dataset from: krogan2006_core, krogan2006_extended, collins2007
dataset = 'krogan2006_core'
# select validation (ground truth) dataset from: mips_3_100, sgd
gt_dataset = 'mips_3_100'
discard_small = False
cs_tol = 0.0 # threshold for comm size based on third largest entry in community vector
binary_memberships = True # whether to consider binary or fractional memberships
rounding_tol = 0.5 # quantity for rounding fractional data to binary
merge_comms = True
merge_tol = 0.8
#-----------------------------------------------------------------------------------------------------
# load nodes list
with open(('nodes_' + dataset + '.txt'), 'r') as f:
nodes = []
for item in f:
nodes.append(item.strip('\n'))
gt_comms, ex_nodes_count, nodes = read_gt(gt_dataset, nodes)
print('computed ground truth communities for ' + gt_dataset)
# load cvx opt solutions
optsols = | np.load('opt_sols_' + dataset + '.npy') | numpy.load |
### ------------------------------------------------------------------------- ###
# DEFINITELY NEED THIS SCRIPT!
### Create CSV files with average luminance per frame of stimulus vids
### use world camera vids for timing, stretch and interpolate raw stim vid lum values
### output as data files categorized by calibration, octopus, and unique sequences.
### ------------------------------------------------------------------------- ###
import os
import glob
import datetime
import csv
import fnmatch
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from scipy.signal import savgol_filter, argrelextrema
from scipy import interpolate
###################################
# FUNCTIONS
###################################
def load_avg_world_unraveled(avg_world_folder_path):
# List all world camera csv files
stim_files = glob.glob(avg_world_folder_path + os.sep + "*Avg-World-Vid-tbuckets.csv")
world_vids_tbucketed = {}
for stim_file in stim_files:
stim_filename = stim_file.split(os.sep)[-1]
stim_type = stim_filename.split('_')[1]
stim_number = stim_name_to_float[stim_type]
world_vids_tbucketed[stim_number] = {}
extracted_rows = []
print("Extracting from {name}".format(name=stim_filename))
with open(stim_file) as f:
csvReader = csv.reader(f, quoting=csv.QUOTE_NONNUMERIC)
for row in csvReader:
extracted_rows.append(row)
print("Unraveling average frame data...")
for i in range(len(extracted_rows)):
if i==0:
unravel_height = int(extracted_rows[i][0])
unravel_width = int(extracted_rows[i][1])
world_vids_tbucketed[stim_number]["Vid Dimensions"] = [unravel_height, unravel_width]
elif i==1:
vid_count = int(extracted_rows[i][0])
world_vids_tbucketed[stim_number]["Vid Count"] = vid_count
else:
tbucket_num = extracted_rows[i][0]
flattened_frame = extracted_rows[i][1:]
flat_frame_array = np.array(flattened_frame)
unraveled_frame = np.reshape(flat_frame_array,(unravel_height,unravel_width))
world_vids_tbucketed[stim_number][tbucket_num] = unraveled_frame
return world_vids_tbucketed
def downsample_avg_world_vids(unraveled_world_vids_dict, original_bucket_size_ms, new_bucket_size_ms):
if (new_bucket_size_ms % original_bucket_size_ms == 0):
new_sample_rate = int(new_bucket_size_ms/original_bucket_size_ms)
downsampled_world_vids_dict = {}
for stim in unraveled_world_vids_dict.keys():
print("Working on stimulus {s}".format(s=stim))
downsampled_world_vids_dict[stim] = {}
vid_metadata_keys = sorted([x for x in unraveled_world_vids_dict[stim].keys() if type(x) is str])
for metadata in vid_metadata_keys:
downsampled_world_vids_dict[stim][metadata] = unraveled_world_vids_dict[stim][metadata]
this_stim_avg_vid_dimensions = unraveled_world_vids_dict[stim][vid_metadata_keys[1]]
tbuckets = sorted([x for x in unraveled_world_vids_dict[stim].keys() if type(x) is float])
padding = new_sample_rate - (int(tbuckets[-1]) % new_sample_rate)
original_tbuckets_sliced = range(0, int(tbuckets[-1]+padding), new_sample_rate)
new_tbucket = 0
for i in original_tbuckets_sliced:
start = i
end = i + new_sample_rate - 1
this_slice_summed_frame = np.zeros((this_stim_avg_vid_dimensions[0], this_stim_avg_vid_dimensions[1]))
this_slice_tbuckets = []
this_slice_count = 0
for tbucket in tbuckets:
if start<=tbucket<=end:
this_slice_tbuckets.append(tbucket)
for bucket in this_slice_tbuckets:
this_slice_summed_frame = this_slice_summed_frame + unraveled_world_vids_dict[stim][bucket]
this_slice_count = this_slice_count + 1
this_slice_avg_frame = this_slice_summed_frame/float(this_slice_count)
downsampled_world_vids_dict[stim][new_tbucket] = this_slice_avg_frame
new_tbucket = new_tbucket + 1
return downsampled_world_vids_dict
else:
print("Sample rate must be a multiple of {bucket}".format(bucket=original_bucket_size))
def matchArrays_RawVsWorld(inputArrayRaw, inputArrayWorld, phaseName, plot_saveFolder):
# create array of nans, size = larger array (either World or Raw)
meanAdjusted_outputArray = np.empty((len(inputArrayWorld),))
meanAdjusted_outputArray.fill(np.nan)
# get first and last values of Raw
meanAdjusted_outputArray[0] = inputArrayRaw[0]
meanAdjusted_outputArray[-1] = inputArrayRaw[-1]
# get major peaks and troughs of Raw
goodDataPoints = []
inputArrayRaw_maximas = argrelextrema(inputArrayRaw, np.greater)
inputArrayRaw_minimas = argrelextrema(inputArrayRaw, np.less)
for maxima in inputArrayRaw_maximas[0]:
adjustedIndex = int(round((maxima/len(inputArrayRaw))*len(inputArrayWorld), 0))
meanAdjusted_outputArray[adjustedIndex] = inputArrayRaw[maxima]
goodDataPoints.append(adjustedIndex)
for minima in inputArrayRaw_minimas[0]:
adjustedIndex = int(round((minima/len(inputArrayRaw))*len(inputArrayWorld), 0))
meanAdjusted_outputArray[adjustedIndex] = inputArrayRaw[minima]
goodDataPoints.append(adjustedIndex)
# fill in as many values as can be transferred
for i,value in enumerate(inputArrayRaw):
adjustedIndex = int(round((i/len(inputArrayRaw))*len(inputArrayWorld), 0))
if adjustedIndex not in goodDataPoints:
meanAdjusted_outputArray[adjustedIndex] = value
goodDataPoints.append(adjustedIndex)
# if World array is longer than Raw, interpolate to fill in remaining nans
if len(inputArrayWorld)>len(inputArrayRaw):
goodDataPoints.sort()
num_valid = len(goodDataPoints)
count = 1
for i in range(1, num_valid):
next_valid_index = goodDataPoints[i]
next_valid_lum = meanAdjusted_outputArray[next_valid_index]
step_count = (next_valid_index - count + 1)
step_lum = (next_valid_lum - meanAdjusted_outputArray[count - 1]) / step_count
for j in range(step_count):
meanAdjusted_outputArray[count] = meanAdjusted_outputArray[count - 1] + step_lum
count += 1
# draw output array against world cam avg array
meanWorldScaled_array = inputArrayWorld*(inputArrayRaw[0]/inputArrayWorld[0])
# figure path and title
figPath = os.path.join(plot_saveFolder, 'meanWorldScaled%s_Vs_meanAdjusted%s.png'%(phaseName, phaseName))
figTitle = 'Mean luminance of world cam (scaled) vs mean luminance of raw stimulus (adjusted) during %s'%(phaseName)
print('Plotting %s'%(figTitle))
# draw comparison plot
plt.figure(figsize=(9, 9), dpi=150)
plt.suptitle(figTitle, fontsize=12, y=0.98)
plt.ylabel('Timebuckets')
plt.xlabel('Mean luminance')
plt.plot(meanWorldScaled_array, label='World cam (scaled)')
plt.plot(meanAdjusted_outputArray, label='Raw Stim (adjusted)')
plt.legend()
plt.savefig(figPath)
plt.close()
return meanAdjusted_outputArray
###################################
# DATA AND OUTPUT FILE LOCATIONS
###################################
# List relevant data locations: this is for laptop
root_folder = r"C:\Users\taunsquared\Dropbox\SurprisingMinds\analysis\dataPythonWorkflows"
plots_folder = r"C:\Users\taunsquared\Dropbox\SurprisingMinds\analysis\plots"
# List relevant data locations: this is for office desktop (windows)
#root_folder = r"C:\Users\Kampff_Lab\Dropbox\SurprisingMinds\analysis\dataPythonWorkflows"
# set up folders
rawStim_lums_folder = os.path.join(root_folder, "rawStimLums")
stimVid_lums_folder = os.path.join(root_folder, "stimVidLums")
stimVid_plots = os.path.join(plots_folder, "stimulusAvgLum")
# Create folders they do not exist
output_folders = [stimVid_lums_folder, stimVid_plots]
for folder in output_folders:
if not os.path.exists(folder):
os.makedirs(folder)
###################################
# TIMING/SAMPLING VARIABLES FOR DATA EXTRACTION
###################################
# downsample = collect data from every 40ms or other multiples of 20
downsampled_bucket_size_ms = 40
original_bucket_size_in_ms = 4
max_length_of_stim_vid = 60000 # milliseconds
no_of_time_buckets = max_length_of_stim_vid/original_bucket_size_in_ms
downsampled_no_of_time_buckets = max_length_of_stim_vid/downsampled_bucket_size_ms
new_time_bucket_sample_rate = downsampled_bucket_size_ms/original_bucket_size_in_ms
milliseconds_for_baseline = 3000
baseline_no_buckets = int(milliseconds_for_baseline/new_time_bucket_sample_rate)
###################################
# STIMULI VID INFO
###################################
stim_vids = [24.0, 25.0, 26.0, 27.0, 28.0, 29.0]
stim_name_to_float = {"Stimuli24": 24.0, "Stimuli25": 25.0, "Stimuli26": 26.0, "Stimuli27": 27.0, "Stimuli28": 28.0, "Stimuli29": 29.0}
stim_float_to_name = {24.0: "Stimuli24", 25.0: "Stimuli25", 26.0: "Stimuli26", 27.0: "Stimuli27", 28.0: "Stimuli28", 29.0: "Stimuli29"}
###################################
### EXTRACT, UNRAVEL, SAVE TO FILE TIME BINNED STIM VIDEOS
###################################
allMonths_meanWorldVidArrays = {}
for unique_stim in stim_vids:
allMonths_meanWorldVidArrays[unique_stim] = {}
allMonths_meanWorldVidArrays[unique_stim]['Vid Count'] = 0
# update list of completed world vid average folders on dropbox
day_folders = sorted(os.listdir(root_folder))
avg_world_vid_folders = fnmatch.filter(day_folders, 'WorldVidAverage_*')
updated_folders_to_extract = []
for avg_world_vid_folder in avg_world_vid_folders:
folder_year_month = avg_world_vid_folder.split('_')[1]
if folder_year_month not in allMonths_meanWorldVidArrays.keys():
updated_folders_to_extract.append(avg_world_vid_folder)
#### WHILE DEBUGGING ####
#updated_folders_to_extract = updated_folders_to_extract[4:6]
#debugging_output_folder = os.path.join(root_folder, 'test_stimVidLums')
#### --------------- ####
# extract, unravel, calculate mean luminance of each frame, create array of mean luminances for each stim type
for month_folder in updated_folders_to_extract:
month_name = month_folder.split('_')[1]
month_folder_path = os.path.join(root_folder, month_folder)
# unravel
unraveled_monthly_world_vids = load_avg_world_unraveled(month_folder_path)
# downsample
print("Downsampling monthly averaged stimulus videos for {month}".format(month=month_name))
downsampled_monthly_world_vids = downsample_avg_world_vids(unraveled_monthly_world_vids, original_bucket_size_in_ms, downsampled_bucket_size_ms)
# now need to convert these frame arrays into luminance value, one per timebucket
for unique_stim in downsampled_monthly_world_vids:
thisMonth_thisStim_frames = downsampled_monthly_world_vids[unique_stim]
thisMonth_thisStim_lums = []
for key in thisMonth_thisStim_frames:
if key == 'Vid Count':
allMonths_meanWorldVidArrays[unique_stim]['Vid Count'] = allMonths_meanWorldVidArrays[unique_stim]['Vid Count'] + thisMonth_thisStim_frames['Vid Count']
continue
if key == 'Vid Dimensions':
continue
else:
frame = thisMonth_thisStim_frames[key]
lum = np.nanmean(frame[:])
thisMonth_thisStim_lums.append(lum)
thisMonth_thisStim_lums_array = np.array(thisMonth_thisStim_lums)
allMonths_meanWorldVidArrays[unique_stim][month_name] = thisMonth_thisStim_lums_array
###################################
# AVERAGE ACROSS ALL MONTHS
###################################
for unique_stim in allMonths_meanWorldVidArrays:
allMonthlyMeans = []
shortest = 2000
for key in allMonths_meanWorldVidArrays[unique_stim]:
if key == 'Vid Count':
continue
else:
thisMonthMean = allMonths_meanWorldVidArrays[unique_stim][key]
if len(thisMonthMean)<shortest:
shortest = len(thisMonthMean)
allMonthlyMeans.append(thisMonthMean)
# make all arrays same length
allMonthlyMeans_truncated = []
for monthlyMean in allMonthlyMeans:
monthlyMean_truncated = monthlyMean[:shortest]
allMonthlyMeans_truncated.append(monthlyMean_truncated)
allMonthlyMeans_array = np.array(allMonthlyMeans_truncated)
thisStimMeanLum = np.nanmean(allMonthlyMeans_array, axis=0)
allMonths_meanWorldVidArrays[unique_stim]['All Months'] = thisStimMeanLum
###################################
# SPLIT ARRAYS INTO CALIB, OCTO, AND UNIQUE PHASES
###################################
# Moments of interest for each stimulus type
all_avg_world_moments = {}
# Stimulus 24.0
all_avg_world_moments[24.0] = {'calibration start': {0:['2017-10','2018-05']},
'do not move your head': {3:['2017-10','2018-05']},
'upper left dot appears': {102:['2017-10','2017-11','2018-03']},
'lower right dot appears': {170:['2017-10','2018-05']},
'lower left dot appears': {238:['2017-10','2018-05']},
'upper right dot appears': {306:['2017-10','2018-05']},
'center dot appears': {374:['2017-10','2018-05']},
'calibration end': {441:['2017-10','2017-11','2018-03']},
'unique start': {442:['2017-10','2018-03','2018-05'],443:['2017-11']},
'cat appears': {463:['2017-10','2018-01','2018-05'], 464:['2017-11']},
'cat front paws visible': {473:['2017-10','2018-01','2018-05'], 474:['2017-11']},
'cat lands on toy': {513:['2017-10'], 514:['2018-05']},
'cat back paws bounce': {549:['2017-10'],547:['2018-05']},
'unique end': {596:['2017-10','2017-11'],598:['2018-03']},
'octo start': {595:['2017-10','2018-03'],596:['2017-11']},
'fish turns': {645:['2017-10','2018-05']},
'octopus fully decamouflaged': {766:['2018-05'], 767:['2017-10']},
'camera zooms in on octopus': {860:['2017-10','2018-05']},
'octopus inks': {882:['2017-10'],883:['2017-11','2018-03']},
'camera clears ink cloud': {916:['2017-10'],920:['2018-05']},
'octo end': {987:['2017-10'],989:['2017-11'],990:['2018-03']}}
# Stimulus 25.0
all_avg_world_moments[25.0] = {'calibration start': {0:['2017-10','2017-11','2018-03']},
'do not move your head': {3:['2017-10','2018-05']},
'upper left dot appears': {102:['2017-10','2017-11','2018-03']},
'lower right dot appears': {170:['2017-10','2018-05']},
'lower left dot appears': {239:['2017-10'],238:['2018-05']},
'upper right dot appears': {307:['2017-10'],306:['2018-05']},
'center dot appears': {375:['2017-10'],374:['2018-05']},
'calibration end': {441:['2017-10','2017-11','2018-03']},
'unique start': {442:['2018-03'],443:['2017-10','2017-11']},
'fingers appear': {443:['2017-10'], 442:['2018-05']},
'bird flies towards fingers': {462:['2018-05'],463:['2017-10']},
'beak contacts food': {491:['2017-10'],492:['2018-05']},
'wings at top of frame': {535:['2017-10','2018-05']},
'bird flutters': {553:['2017-10'], 553:['2018-05']},
'bird lands': {561:['2017-10'], 562:['2018-05']},
'bird flies past fingers': {573:['2017-10','2018-05']},
'unique end': {599:['2017-10'],600:['2017-11'],601:['2018-03']},
'octo start': {599:['2017-10','2017-11','2018-03']},
'fish turns': {649:['2017-10','2018-05']},
'octopus fully decamouflaged': {770:['2017-10','2018-05']},
'camera zooms in on octopus': {863:['2018-05'],864:['2017-10']},
'octopus inks': {885:['2017-10','2018-03'],886:['2017-11']},
'camera clears ink cloud': {919:['2017-10'],923:['2018-05']},
'octo end': {989:['2017-10'],993:['2017-11'],994:['2018-03']}}
# Stimulus 26.0
all_avg_world_moments[26.0] = {'calibration start': {0:['2017-10','2017-11','2018-03']},
'do not move your head': {2:['2018-05'],3:['2017-10']},
'upper left dot appears': {102:['2017-10','2017-11','2018-03']},
'lower right dot appears': {170:['2017-10','2018-05']},
'lower left dot appears': {238:['2017-10','2018-05']},
'upper right dot appears': {306:['2017-10','2018-05']},
'center dot appears': {374:['2017-10','2018-05']},
'calibration end': {441:['2017-10','2017-11','2018-03']},
'unique start': {442:['2017-10','2018-03'],443:['2017-11']},
'eyespots appear': {449:['2017-10', '2018-05']},
'eyespots disappear, eyes darken': {487:['2017-10','2018-05']},
'arms spread': {533:['2017-10'], 534:['2018-05']},
'arms in, speckled mantle': {558:['2017-10'], 561:['2018-05']},
'unique end': {663:['2017-10'],665:['2017-11','2018-03']},
'octo start': {662:['2017-10'],663:['2018-03'],664:['2017-11']},
'fish turns': {712:['2017-10','2018-05']},
'octopus fully decamouflaged': {833:['2017-10','2018-05']},
'camera zooms in on octopus': {927:['2017-10','2018-05']},
'octopus inks': {949:['2017-10'],951:['2017-11','2018-03']},
'camera clears ink cloud': {983:['2017-10'],987:['2018-05']},
'octo end': {1054:['2017-10'],1059:['2017-11','2018-03']}}
# Stimulus 27.0
all_avg_world_moments[27.0] = {'calibration start': {0:['2017-10','2017-11','2018-03']},
'do not move your head': {3:['2017-10','2018-05']},
'upper left dot appears': {102:['2017-10','2017-11','2018-03']},
'lower right dot appears': {170:['2017-10','2018-05']},
'lower left dot appears': {238:['2017-10','2018-05']},
'upper right dot appears': {306:['2018-05'],307:['2017-10']},
'center dot appears': {374:['2018-05'],375:['2017-10']},
'calibration end': {441:['2017-10','2017-11','2018-03']},
'unique start': {443:['2017-10','2017-11','2018-03']},
'cuttlefish appears': {443:['2017-10','2018-05']},
'tentacles go ballistic': {530:['2017-10','2018-05']},
'unique end': {606:['2017-10'],607:['2017-11','2018-03']},
'octo start': {605:['2017-10','2017-11'],606:['2018-03']},
'fish turns': {655:['2017-10','2018-05']},
'octopus fully decamouflaged': {776:['2017-10','2018-05']},
'camera zooms in on octopus': {869:['2018-05'],870:['2017-10']},
'octopus inks': {892:['2017-10'],893:['2017-11','2018-03']},
'camera clears ink cloud': {926:['2017-10'],929:['2018-05']},
'octo end': {996:['2017-10'],1000:['2017-11','2018-03']}}
# Stimulus 28.0
all_avg_world_moments[28.0] = {'calibration start': {0:['2017-10','2017-11','2018-03']},
'do not move your head': {2:['2018-05'],3:['2017-10']},
'upper left dot appears': {102:['2017-10','2017-11','2018-03']},
'lower right dot appears': {170:['2017-10','2018-05']},
'lower left dot appears': {238:['2017-10','2018-05']},
'upper right dot appears': {306:['2017-10','2018-05']},
'center dot appears': {374:['2018-05'],375:['2017-10']},
'calibration end': {441:['2017-10','2017-11','2018-03']},
'unique start': {442:['2018-03'],443:['2017-10','2017-11']},
'fish scatter': {456:['2017-10','2018-04','2018-10']},
'center fish turns': {469:['2017-10'], 470:['2018-04'], 471:['2018-10']},
'center fish swims to left': {494:['2018-04','2018-10'], 495:['2017-10']},
'camera clears red ferns': {503:['2017-10'],506:['2018-04'],509:['2018-10']},
'unique end': {662:['2017-10'],663:['2017-11'],666:['2018-03']},
'octo start': {661:['2017-10'],662:['2018-03'],663:['2017-11']},
'fish turns': {711:['2017-10','2018-05']},
'octopus fully decamouflaged': {832:['2017-10'],834:['2018-05']},
'camera zooms in on octopus': {927:['2017-10','2018-05']},
'octopus inks': {948:['2017-10'],950:['2017-11','2018-03']},
'camera clears ink cloud': {982:['2017-10'],986:['2018-05']},
'octo end': {1054:['2017-10'],1056:['2017-11'],1059:['2018-03']}}
# Stimulus 29.0
all_avg_world_moments[29.0] = {'calibration start': {0:['2017-10','2017-11','2018-03']},
'do not move your head': {3:['2017-10','2018-05']},
'upper left dot appears': {102:['2017-10','2017-11','2018-03']},
'lower right dot appears': {170:['2017-10','2018-05']},
'lower left dot appears': {238:['2017-10','2018-05']},
'upper right dot appears': {306:['2017-10','2018-05']},
'center dot appears': {374:['2017-10','2018-05']},
'calibration end': {441:['2017-10','2017-11','2018-03']},
'unique start': {442:['2017-10'],443:['2017-11','2018-03']},
'fish 1 appears': {457:['2017-10','2018-05']},
'fish 1 turns': {495:['2017-10','2018-05']},
'fish 2 appears': {538:['2017-10','2018-05']},
'fish 2 touches mirror image': {646:['2017-10','2018-05']},
'fish 2 disappears': {661:['2017-10','2018-05']},
'fish 1 touches mirror image': {685:['2017-10','2018-05']},
'fish 1 disappears': {702:['2017-10','2018-05']},
'unique end': {717:['2017-10','2017-11'],718:['2018-03']},
'octo start': {716:['2017-10','2018-03'],717:['2017-11']},
'fish turns': {766:['2017-10','2018-03']},
'octopus fully decamouflaged': {887:['2017-10','2018-05']},
'camera zooms in on octopus': {981:['2017-10','2018-05']},
'octopus inks': {1003:['2017-10'],1004:['2017-11','2018-03']},
'camera clears ink cloud': {1037:['2017-10'],1041:['2018-05']},
'octo end': {1108:['2017-10'],1110:['2017-11'],1112:['2018-03']}}
# split world vid lum arrays
uniqueWeights = {}
allWeightedDoNotMove = []
allWeightedPulsingDots = []
allWeightedOcto = []
allWeightedUnique = []
doNotMoveLens = []
pulsingDotsLens = []
octoLens = []
uniqueLens = []
uniqueOrder = []
shortestDoNotMove = 2000
shortestPulsingDots = 2000
shortestOcto = 2000
# cut out each phase of the stimuli
for unique_stim in allMonths_meanWorldVidArrays:
thisUniqueStim_weight = allMonths_meanWorldVidArrays[unique_stim]['Vid Count']
uniqueWeights[unique_stim] = thisUniqueStim_weight
fullWeightedMeanWorldVid = allMonths_meanWorldVidArrays[unique_stim]['All Months']*thisUniqueStim_weight
## CALIB
# Do Not Move section
calibStart = []
for key in all_avg_world_moments[unique_stim]['calibration start']:
calibStart.append(key)
calibStart_tb = np.min(calibStart)
doNotMoveEnd = []
for key in all_avg_world_moments[unique_stim]['upper left dot appears']:
doNotMoveEnd.append(key)
doNotMoveEnd_tb = np.min(doNotMoveEnd) - 1
# pulsing dots section
pulsingDotsStart_tb = doNotMoveEnd_tb + 1
calibEnd = []
for key in all_avg_world_moments[unique_stim]['calibration end']:
calibEnd.append(key)
calibEnd_tb = np.max(calibEnd)
# cut out Do Not Move section of calib phase from full weighted mean world vid lum array
thisStim_weightedMeanDoNotMove = fullWeightedMeanWorldVid[calibStart_tb:doNotMoveEnd_tb]
if len(thisStim_weightedMeanDoNotMove)<shortestDoNotMove:
shortestDoNotMove = len(thisStim_weightedMeanDoNotMove)
allWeightedDoNotMove.append(thisStim_weightedMeanDoNotMove)
thisStim_weightedMeanPulsingDots = fullWeightedMeanWorldVid[pulsingDotsStart_tb:calibEnd_tb]
if len(thisStim_weightedMeanPulsingDots)<shortestPulsingDots:
shortestPulsingDots = len(thisStim_weightedMeanPulsingDots)
allWeightedPulsingDots.append(thisStim_weightedMeanPulsingDots)
print('Unique Stim %d, "Do Not Move" length: %d, Pulsing Dots length: %d'%(unique_stim, len(thisStim_weightedMeanDoNotMove), len(thisStim_weightedMeanPulsingDots)))
doNotMoveLen = doNotMoveEnd_tb - calibStart_tb
doNotMoveLens.append(doNotMoveLen)
pulsingDotsLen = calibEnd_tb - pulsingDotsStart_tb
pulsingDotsLens.append(pulsingDotsLen)
## OCTO
octoStart = []
for key in all_avg_world_moments[unique_stim]['octo start']:
octoStart.append(key)
octoStart_tb = np.min(octoStart)
octoEnd = []
for key in all_avg_world_moments[unique_stim]['octo end']:
octoEnd.append(key)
octoEnd_tb = np.max(octoEnd)
# cut out octo phase from full world vid lum array
thisStim_weightedMeanOcto = fullWeightedMeanWorldVid[octoStart_tb:octoEnd_tb]
if len(thisStim_weightedMeanOcto)<shortestOcto:
shortestOcto = len(thisStim_weightedMeanOcto)
allWeightedOcto.append(thisStim_weightedMeanOcto)
octoLen = octoEnd_tb - octoStart_tb
octoLens.append(octoLen)
### UNIQUE
thisUniqueStart = []
for key in all_avg_world_moments[unique_stim]['unique start']:
thisUniqueStart.append(key)
thisUniqueStart_tb = np.min(thisUniqueStart)
thisUniqueEnd = []
for key in all_avg_world_moments[unique_stim]['unique end']:
thisUniqueEnd.append(key)
thisUniqueEnd_tb = np.max(thisUniqueEnd)
uniqueLen = thisUniqueEnd_tb - thisUniqueStart_tb
uniqueLens.append(uniqueLen)
# cut out unique phase from full world vid lum array
thisStim_weightedMeanUnique = fullWeightedMeanWorldVid[thisUniqueStart_tb:thisUniqueEnd_tb]
allWeightedUnique.append(thisStim_weightedMeanUnique)
uniqueOrder.append(unique_stim)
# calculate weighted mean of doNotMove, pulsingDots, octo and unique phases
total_worldVids = sum(uniqueWeights.values())
allDoNotMove_truncated = []
for doNotMove in allWeightedDoNotMove:
doNotMove_truncated = doNotMove[:shortestDoNotMove]
allDoNotMove_truncated.append(doNotMove_truncated)
meanWorld_doNotMove = np.nansum(allDoNotMove_truncated, axis=0)/total_worldVids
allPulsingDots_truncated = []
for pulsingDots in allWeightedPulsingDots:
pulsingDots_truncated = pulsingDots[:shortestPulsingDots]
allPulsingDots_truncated.append(pulsingDots_truncated)
meanWorld_pulsingDots = np.nansum(allPulsingDots_truncated, axis=0)/total_worldVids
allOcto_truncated = []
for octo in allWeightedOcto:
octo_truncated = octo[:shortestOcto]
allOcto_truncated.append(octo_truncated)
meanWorld_octo = np.nansum(allOcto_truncated, axis=0)/total_worldVids
allMeanWorld_unique = []
for i, unique in enumerate(allWeightedUnique):
thisMeanWorld_unique = unique/uniqueWeights[uniqueOrder[i]]
allMeanWorld_unique.append(thisMeanWorld_unique)
meanWorld_u1 = allMeanWorld_unique[0]
meanWorld_u2 = allMeanWorld_unique[1]
meanWorld_u3 = allMeanWorld_unique[2]
meanWorld_u4 = allMeanWorld_unique[3]
meanWorld_u5 = allMeanWorld_unique[4]
meanWorld_u6 = allMeanWorld_unique[5]
###################################
# LOAD CSV OF RAW STIM VIDEOS
###################################
rawStimLum_files = glob.glob(rawStim_lums_folder + os.sep + '*.csv')
allRaw_doNotMove = []
allRaw_doNotMove_languageOrder = []
allRaw_pulsingDots = []
allRaw_unique = []
allRaw_unique_order = []
allRaw_octo = []
rawUniqueLens_frames = {'stimuli024':168, 'stimuli025':172, 'stimuli026':247, 'stimuli027':179, 'stimuli028':246, 'stimuli029':313}
for rawStimLumFile in rawStimLum_files:
stim_phase = os.path.basename(rawStimLumFile).split('_')[0].split('-')[0]
if stim_phase == 'Calibration':
rawPulsingDots = np.genfromtxt(rawStimLumFile, delimiter=',')
allRaw_pulsingDots.append(rawPulsingDots)
continue
if stim_phase == 'DoNotMove':
stim_language = os.path.basename(rawStimLumFile).split('_')[0].split('-')[1]
raw_doNotMove = np.genfromtxt(rawStimLumFile, delimiter=',')
allRaw_doNotMove.append(raw_doNotMove)
allRaw_doNotMove_languageOrder.append(stim_language)
continue
if stim_phase == 'CenterEye' or stim_phase == 'Replay' or stim_phase == 'RestingState':
print('Skipping %s raw stimulus video'%(stim_phase))
continue
else:
rawUniqueLen_frames = rawUniqueLens_frames[stim_phase]
rawUniqueStim_full = | np.genfromtxt(rawStimLumFile, delimiter=',') | numpy.genfromtxt |
from typing import NoReturn
from ...base import BaseEstimator
import numpy as np
from ...metrics import misclassification_error
class GaussianNaiveBayes(BaseEstimator):
"""
Gaussian Naive-Bayes classifier
"""
def __init__(self):
"""
Instantiate a Gaussian Naive Bayes classifier
Attributes
----------
self.classes_ : np.ndarray of shape (n_classes,)
The different labels classes. To be set in `GaussianNaiveBayes.fit`
self.mu_ : np.ndarray of shape (n_classes,n_features)
The estimated features means for each class. To be set in `GaussianNaiveBayes.fit`
self.vars_ : np.ndarray of shape (n_classes, n_features)
The estimated features variances for each class. To be set in `GaussianNaiveBayes.fit`
self.pi_: np.ndarray of shape (n_classes)
The estimated class probabilities. To be set in `GaussianNaiveBayes.fit`
"""
super().__init__()
self.classes_, self.mu_, self.vars_, self.pi_ = None, None, None, None
def _fit(self, X: np.ndarray, y: np.ndarray) -> NoReturn:
"""
fits a gaussian naive bayes model
Parameters
----------
X : ndarray of shape (n_samples, n_features)
Input data to fit an estimator for
y : ndarray of shape (n_samples, )
Responses of input data to fit to
"""
#find classes
self.classes_ = np.unique(y)
#find pi
self.pi_ = np.zeros(shape=np.shape(self.classes_))
for index, value in enumerate(self.classes_):
self.pi_[index] = np.sum(y == value)
#find mu
y = y.reshape((-1, 1))
full_data = np.concatenate((X, y), axis=1)
self.mu_ = np.zeros((np.shape(self.classes_)[0], np.shape(X)[1]))
dist_from_mu = full_data.copy()
self.vars_ = np.zeros(shape=(np.shape(self.classes_)[0], np.shape(X)[1]))
cov = np.zeros((np.shape(self.classes_)[0], np.shape(X)[1], np.shape(X)[1]))
for index, value in enumerate(self.classes_):
self.mu_[index] = np.sum(full_data[full_data[:, -1] == value][:, :-1], axis=0) / self.pi_[index]
# find vars
self.vars_[index, :] = np.var(full_data[full_data[:, -1] == value][:, :-1], axis=0, ddof=1)
#normalize pi
self.pi_ = self.pi_ / len(y)
def _predict(self, X: np.ndarray) -> np.ndarray:
"""
Predict responses for given samples using fitted estimator
Parameters
----------
X : ndarray of shape (n_samples, n_features)
Input data to predict responses for
Returns
-------
responses : ndarray of shape (n_samples, )
Predicted responses of given samples
"""
return self.classes_[self.likelihood(X).argmax(1)]
def likelihood(self, X: np.ndarray) -> np.ndarray:
"""
Calculate the likelihood of a given data over the estimated model
Parameters
----------
X : np.ndarray of shape (n_samples, n_features)
Input data to calculate its likelihood over the different classes.
Returns
-------
likelihoods : np.ndarray of shape (n_samples, n_classes)
The likelihood for each sample under each of the classes
"""
if not self.fitted_:
raise ValueError("Estimator must first be fitted before calling `likelihood` function")
number_of_fitures = | np.shape(X) | numpy.shape |
import networkx as nx
import numpy as np
import pytest
from rpcq.messages import ParameterAref
from pyquil.parser import parse
from pyquil import Program, get_qc
from pyquil.api import QuantumComputer, QPU, QPUCompiler
from pyquil.api._compiler import _collect_classical_memory_write_locations
from pyquil.api._config import PyquilConfig
from pyquil.api._qpu import _extract_bitstrings
from pyquil.device import NxDevice
from pyquil.gates import I, X
from pyquil.quilatom import Expression
def test_qpu_run():
config = PyquilConfig()
if config.qpu_url and config.compiler_url:
g = nx.Graph()
g.add_node(0)
device = NxDevice(g)
qc = QuantumComputer(name="pyQuil test QC",
qam=QPU(endpoint=config.qpu_url,
user="pyQuil test suite"),
device=device,
compiler=QPUCompiler(endpoint=config.compiler_url,
device=device))
bitstrings = qc.run_and_measure(
program=Program(X(0)),
trials=1000,
)
assert bitstrings[0].shape == (1000,)
assert np.mean(bitstrings[0]) > 0.8
bitstrings = qc.run(qc.compile(Program(X(0))))
assert bitstrings.shape == (0, 0)
else:
pytest.skip("QPU or compiler-server not available; skipping QPU run test.")
def test_readout_demux():
p = Program("""DECLARE ro BIT[6]
RESET
RX(pi/2) 0
RX(pi/2) 1
RX(pi/2) 2
RX(pi/2) 3
MEASURE 0 ro[0]
MEASURE 1 ro[1]
MEASURE 2
RX(pi/2) 0
RX(pi/2) 1
RX(pi/2) 2
RX(pi/2) 3
MEASURE 0 ro[2]
MEASURE 1 ro[3]
MEASURE 2 ro[4]
MEASURE 3 ro[5]
""")
ro_sources = _collect_classical_memory_write_locations(p)
assert ro_sources == [
(0, 0),
(1, 0),
(0, 1),
(1, 1),
(2, 1),
(3, 0)
]
num_shots = 1000
buffers = {
# 0 measured, stored twice
"q0": np.random.randint(0, 2, size=(num_shots, 2)),
# 1 measured, stored twice
"q1": np.random.randint(0, 2, size=(num_shots, 2)),
# 2 measured twice, stored once
"q2": np.random.randint(0, 2, size=(num_shots, 2)),
# 3 measured once
"q3": np.random.randint(0, 2, size=num_shots),
}
bitstrings = _extract_bitstrings(ro_sources, buffers=buffers)
assert bitstrings.dtype == np.int64
assert np.allclose(bitstrings[:, 0], buffers["q0"][:, 0])
assert np.allclose(bitstrings[:, 1], buffers["q1"][:, 0])
assert np.allclose(bitstrings[:, 2], buffers["q0"][:, 1])
assert | np.allclose(bitstrings[:, 3], buffers["q1"][:, 1]) | numpy.allclose |
#***************************************************#
# This file is part of PFNET. #
# #
# Copyright (c) 2015, <NAME>. #
# #
# PFNET is released under the BSD 2-clause license. #
#***************************************************#
import unittest
import numpy as np
import pfnet as pf
from . import test_cases
from numpy.linalg import norm
from scipy.sparse import coo_matrix,triu,bmat
NUM_TRIALS = 25
EPS = 3.5 # %
TOL = 1e-4
class TestProblem(unittest.TestCase):
def setUp(self):
# Random
np.random.seed(0)
def test_problem_ACOPF_with_function_constraint(self):
for case in test_cases.CASES:
net = pf.Parser(case).parse(case)
self.assertEqual(net.num_periods,1)
p = pf.Problem(net)
for branch in net.branches:
if branch.ratingA == 0.:
branch.ratingA = 100.
# Variables
net.set_flags('bus',
['variable'],
'any',
'voltage magnitude')
net.set_flags('bus',
'variable',
'not slack',
'voltage angle')
net.set_flags('generator',
['variable','bounded'],
'adjustable active power',
'active power')
net.set_flags('generator',
['variable','bounded'],
'regulator',
'reactive power')
net.set_flags('branch',
['variable','bounded'],
'tap changer',
'tap ratio')
net.set_flags('branch',
['variable','bounded'],
'phase shifter',
'phase shift')
self.assertEqual(net.num_vars, (2*net.num_buses - net.get_num_slack_buses() +
net.get_num_P_adjust_gens() +
net.get_num_reg_gens() +
net.get_num_tap_changers() +
net.get_num_phase_shifters()))
self.assertEqual(net.num_bounded,(net.get_num_P_adjust_gens() +
net.get_num_reg_gens() +
net.get_num_tap_changers() +
net.get_num_phase_shifters()))
p.add_constraint(pf.Constraint('AC power balance',net))
p.add_constraint(pf.Constraint('variable bounds',net))
p.add_function(pf.Function('generation cost',1.,net))
func = pf.Function('generation cost',1.,net)
constr = pf.Constraint('constrained function',net)
constr.set_parameter('func',func)
constr.set_parameter('op','>=')
constr.set_parameter('rhs',0.)
p.add_constraint(constr)
net.set_flags('bus',
'bounded',
'any',
'voltage magnitude')
self.assertEqual(net.num_bounded,(net.get_num_P_adjust_gens() +
net.get_num_reg_gens() +
net.get_num_tap_changers() +
net.get_num_phase_shifters() +
net.num_buses))
p.analyze()
# Extra vars
self.assertEqual(p.num_extra_vars,1)
# Init point
x0 = p.get_init_point()
self.assertTrue(type(x0) is np.ndarray)
self.assertTupleEqual(x0.shape,(net.num_vars+1,))
p.eval(x0)
phi = p.phi
gphi = p.gphi.copy()
Hphi = p.Hphi.copy()
f = p.f.copy()
b = p.b.copy()
A = p.A.copy()
J = p.J.copy()
G = p.G.copy()
l = p.l.copy()
u = p.u.copy()
# Numbers
self.assertEqual(x0.size,p.num_primal_variables)
self.assertEqual(A.shape[0],p.num_linear_equality_constraints)
self.assertEqual(f.size,p.num_nonlinear_equality_constraints)
# phi
self.assertTrue(type(phi) is float)
self.assertGreaterEqual(phi,0.)
# gphi
self.assertTrue(type(gphi) is np.ndarray)
self.assertTupleEqual(gphi.shape,(net.num_vars+1,))
# Hphi
self.assertTrue(type(Hphi) is coo_matrix)
self.assertTupleEqual(Hphi.shape,(net.num_vars+1,net.num_vars+1))
self.assertGreater(Hphi.nnz,0)
# f
self.assertTrue(type(f) is np.ndarray)
f_size = sum(c.f.shape[0] for c in p.constraints)
self.assertTupleEqual(f.shape,(f_size,))
# b
self.assertTrue(type(b) is np.ndarray)
b_size = sum(c.b.shape[0] for c in p.constraints)
self.assertTupleEqual(b.shape,(b_size,))
# J
self.assertTrue(type(J) is coo_matrix)
J_size = sum([c.J.shape[0] for c in p.constraints])
J_nnz = sum([c.J.nnz for c in p.constraints])
self.assertTupleEqual(J.shape,(J_size,net.num_vars+1))
self.assertEqual(J.nnz,J_nnz)
# G, l, u
self.assertTrue(type(G) is coo_matrix)
G_size = sum([c.G.shape[0] for c in p.constraints])
G_nnz = sum([c.G.nnz for c in p.constraints])
self.assertTupleEqual(G.shape,(G_size,net.num_vars+1))
self.assertEqual(G.nnz,G_nnz)
self.assertEqual(l.size,G_size)
self.assertEqual(u.size,G_size)
self.assertFalse(np.any(np.isnan(l)))
self.assertFalse(np.any(np.isnan(u)))
self.assertFalse(np.any(np.isnan(G.data)))
# A
self.assertTrue(type(A) is coo_matrix)
A_size = sum(c.A.shape[0] for c in p.constraints)
A_nnz = sum(c.A.nnz for c in p.constraints)
self.assertTupleEqual(A.shape,(A_size,net.num_vars+1))
self.assertEqual(A.nnz,A_nnz)
def test_problem_with_heur_error(self):
for case in test_cases.CASES:
net = pf.Parser(case).parse(case)
self.assertEqual(net.num_periods,1)
p = pf.Problem(net)
p.add_heuristic(pf.Heuristic('PVPQ switching', net))
p.analyze()
self.assertRaises(pf.ProblemError, p.apply_heuristics, net.get_var_values())
def test_problem_LSNR(self):
# Constants
h = 1e-9
for case in test_cases.CASES:
net = pf.Parser(case).parse(case)
self.assertEqual(net.num_periods,1)
p = pf.Problem(net)
# Variables
net.set_flags('bus',
'variable',
'not slack',
['voltage magnitude','voltage angle'])
net.set_flags('generator',
'variable',
'slack',
'active power')
net.set_flags('generator',
'variable',
'regulator',
'reactive power')
net.set_flags('branch',
'variable',
'tap changer - v',
'tap ratio')
net.set_flags('branch',
'variable',
'phase shifter',
'phase shift')
net.set_flags('shunt',
'variable',
'switching - v',
'susceptance')
self.assertEqual(net.num_vars,
2*(net.num_buses-net.get_num_slack_buses()) +
net.get_num_slack_gens() +
net.get_num_reg_gens() +
net.get_num_tap_changers_v() +
net.get_num_phase_shifters() +
net.get_num_switched_v_shunts())
# Fixed
net.set_flags('branch',
'fixed',
'tap changer - v',
'tap ratio')
net.set_flags('branch',
'fixed',
'phase shifter',
'phase shift')
net.set_flags('shunt',
'fixed',
'switching - v',
'susceptance')
self.assertEqual(net.num_fixed,
net.get_num_tap_changers_v() +
net.get_num_phase_shifters() +
net.get_num_switched_v_shunts())
# Constraints
p.add_constraint(pf.Constraint('AC power balance', net))
p.add_constraint(pf.Constraint('generator active power participation', net))
p.add_constraint(pf.Constraint('PVPQ switching', net))
p.add_constraint(pf.Constraint('variable fixing', net))
self.assertEqual(len(p.constraints), 4)
# Heuristics
p.add_heuristic(pf.Heuristic('PVPQ switching', net))
self.assertEqual(len(p.heuristics), 1)
# Check adding redundant constraints
p.add_constraint(pf.Constraint('generator active power participation',net))
self.assertEqual(len(p.constraints),4)
# Functions
self.assertEqual(len(p.functions),0)
# Init point
x0 = p.get_init_point()
self.assertTrue(type(x0) is np.ndarray)
self.assertTupleEqual(x0.shape,(net.num_vars,))
self.assertTrue(np.all(x0 == p.x))
# Before
phi = p.phi
gphi = p.gphi
Hphi = p.Hphi
f = p.f
b = p.b
A = p.A
J = p.J
self.assertTrue(type(phi) is float)
self.assertEqual(phi,0.)
self.assertTrue(type(gphi) is np.ndarray)
self.assertTupleEqual(gphi.shape,(0,))
self.assertTrue(type(f) is np.ndarray)
self.assertTupleEqual(f.shape,(0,))
self.assertTrue(type(b) is np.ndarray)
self.assertTupleEqual(b.shape,(0,))
self.assertTrue(type(J) is coo_matrix)
self.assertTupleEqual(J.shape,(0,0))
self.assertEqual(J.nnz,0)
self.assertTrue(type(A) is coo_matrix)
self.assertTupleEqual(A.shape,(0,0))
self.assertEqual(A.nnz,0)
self.assertTrue(type(Hphi) is coo_matrix)
self.assertTupleEqual(Hphi.shape,(0,0))
self.assertEqual(Hphi.nnz,0)
self.assertTrue(np.all(Hphi.row >= Hphi.col))
p.analyze()
p.eval(x0)
# After
phi = p.phi
gphi = p.gphi.copy()
Hphi = p.Hphi.copy()
f = p.f.copy()
b = p.b.copy()
A = p.A.copy()
J = p.J.copy()
# Numbers
self.assertEqual(x0.size,p.num_primal_variables)
self.assertEqual(A.shape[0],p.num_linear_equality_constraints)
self.assertEqual(f.size,p.num_nonlinear_equality_constraints)
self.assertEqual(p.num_primal_variables,p.get_num_primal_variables())
self.assertEqual(p.num_linear_equality_constraints,p.get_num_linear_equality_constraints())
self.assertEqual(p.num_nonlinear_equality_constraints,p.get_num_nonlinear_equality_constraints())
# phi
self.assertTrue(type(phi) is float)
self.assertEqual(phi,0.)
# gphi
self.assertTrue(type(gphi) is np.ndarray)
self.assertTupleEqual(gphi.shape,(net.num_vars,))
self.assertLess(norm(gphi),1e-10)
# Hphi
self.assertTrue(type(Hphi) is coo_matrix)
self.assertTupleEqual(Hphi.shape,(net.num_vars,net.num_vars))
self.assertEqual(Hphi.nnz,0)
# f
self.assertTrue(type(f) is np.ndarray)
f_size = sum(c.f.shape[0] for c in p.constraints)
self.assertTupleEqual(f.shape,(f_size,))
# b
self.assertTrue(type(b) is np.ndarray)
b_size = sum(c.b.shape[0] for c in p.constraints)
self.assertTupleEqual(b.shape,(b_size,))
# J
self.assertTrue(type(J) is coo_matrix)
J_size = sum(c.J.shape[0] for c in p.constraints)
self.assertTupleEqual(J.shape,(J_size,net.num_vars))
self.assertGreater(J.nnz,0)
# A
self.assertTrue(type(A) is coo_matrix)
A_size = sum(c.A.shape[0] for c in p.constraints)
self.assertTupleEqual(A.shape,(A_size,net.num_vars))
self.assertGreater(A.nnz,0)
# Check J
f0 = f.copy()
J0 = J.copy()
for i in range(NUM_TRIALS):
d = np.random.randn(net.num_vars)
x = x0 + h*d
p.eval(x)
f1 = p.f
Jd_exact = J0*d
Jd_approx = (f1-f0)/h
error = 100.*norm(Jd_exact-Jd_approx)/np.maximum(norm(Jd_exact),TOL)
self.assertLessEqual(error,EPS)
# Check Hcombined
coeff = np.random.randn(f.shape[0])
p.eval(x0)
self.assertRaises(pf.ProblemError,p.combine_H,np.zeros(f.shape[0]+1),False)
p.combine_H(coeff,False)
J0 = p.J.copy()
g0 = J0.T*coeff
H0 = p.H_combined.copy()
self.assertTrue(type(H0) is coo_matrix)
self.assertTupleEqual(H0.shape,(net.num_vars,net.num_vars))
self.assertTrue(np.all(H0.row >= H0.col)) # lower triangular
H0 = (H0 + H0.T) - triu(H0)
for i in range(NUM_TRIALS):
d = np.random.randn(net.num_vars)
x = x0 + h*d
p.eval(x)
g1 = p.J.T*coeff
Hd_exact = H0*d
Hd_approx = (g1-g0)/h
error = 100.*norm(Hd_exact-Hd_approx)/np.maximum(norm(Hd_exact),TOL)
self.assertLessEqual(error,EPS)
# Sensitivities
net.clear_sensitivities()
for i in range(net.num_buses):
bus = net.get_bus(i)
self.assertEqual(bus.sens_P_balance,0.)
self.assertEqual(bus.sens_Q_balance,0.)
sens = np.random.randn(p.f.size)
offset = 0
for c in p.constraints:
if c.name == 'AC power balance':
break
else:
offset += c.f.size
p.store_sensitivities(np.zeros(p.A.shape[0]),sens,None,None)
for i in range(net.num_buses):
bus = net.get_bus(i)
self.assertEqual(bus.sens_P_balance,sens[bus.index_P+offset])
self.assertEqual(bus.sens_Q_balance,sens[bus.index_Q+offset])
self.assertRaises(pf.ProblemError,
p.store_sensitivities,
np.zeros(p.A.shape[0]),
np.zeros(p.f.size+5),
None,
None)
# Heuristics
self.assertEqual(len(p.heuristics), 1)
self.assertEqual(p.heuristics[0].name, "PVPQ switching")
p.apply_heuristics(x0)
def test_problem_vPF(self):
# Constants
h = 1e-9
for case in test_cases.CASES:
net = pf.Parser(case).parse(case)
self.assertEqual(net.num_periods,1)
p = pf.Problem(net)
# Variables
net.set_flags('bus',
'variable',
'not slack',
['voltage magnitude','voltage angle'])
net.set_flags('generator',
'variable',
'slack',
'active power')
net.set_flags('generator',
'variable',
'regulator',
'reactive power')
net.set_flags('branch',
'variable',
'tap changer - v',
['tap ratio'])
net.set_flags('shunt',
'variable',
'switching - v',
['susceptance'])
reg_by_tran_or_shunt = 0
for i in range(net.num_buses):
bus = net.get_bus(i)
if bus.is_regulated_by_tran() or bus.is_regulated_by_shunt():
reg_by_tran_or_shunt += 1
self.assertEqual(net.num_vars,
2*(net.num_buses-net.get_num_slack_buses()) +
net.get_num_slack_gens() +
net.get_num_reg_gens() +
net.get_num_tap_changers_v()+
net.get_num_switched_v_shunts())
# Constraints
p.add_constraint(pf.Constraint('AC power balance',net))
p.add_constraint(pf.Constraint('voltage set point regulation',net))
p.add_constraint(pf.Constraint('voltage regulation by transformers',net))
p.add_constraint(pf.Constraint('voltage regulation by shunts',net))
self.assertEqual(len(p.constraints),4)
# Check adding redundant constraints
p.add_constraint(pf.Constraint('AC power balance',net))
self.assertEqual(len(p.constraints),4)
# Functions
p.add_function(pf.Function('voltage magnitude regularization',1.,net))
p.add_function(pf.Function('voltage angle regularization',5.,net))
p.add_function(pf.Function('generator powers regularization',8.,net))
p.add_function(pf.Function('tap ratio regularization',3.,net))
p.add_function(pf.Function('susceptance regularization',1.,net))
self.assertEqual(len(p.functions),5)
# Before
phi = p.phi
gphi = p.gphi
Hphi = p.Hphi
f = p.f
b = p.b
A = p.A
J = p.J
self.assertTrue(type(phi) is float)
self.assertEqual(phi,0.)
self.assertTrue(type(gphi) is np.ndarray)
self.assertTupleEqual(gphi.shape,(0,))
self.assertTrue(type(f) is np.ndarray)
self.assertTupleEqual(f.shape,(0,))
self.assertTrue(type(b) is np.ndarray)
self.assertTupleEqual(b.shape,(0,))
self.assertTrue(type(J) is coo_matrix)
self.assertTupleEqual(J.shape,(0,0))
self.assertEqual(J.nnz,0)
self.assertTrue(type(A) is coo_matrix)
self.assertTupleEqual(A.shape,(0,0))
self.assertEqual(A.nnz,0)
self.assertTrue(type(Hphi) is coo_matrix)
self.assertTupleEqual(Hphi.shape,(0,0))
self.assertEqual(Hphi.nnz,0)
self.assertTrue(np.all(Hphi.row >= Hphi.col))
p.analyze()
# Init point
r = np.random.randn(p.get_num_primal_variables())
x0 = p.get_init_point()+r
self.assertTrue(type(x0) is np.ndarray)
self.assertTupleEqual(x0.shape,(net.num_vars+p.num_extra_vars,))
self.assertTrue(np.all(x0 == p.x+r))
p.eval(x0)
# After
phi = p.phi
gphi = p.gphi.copy()
Hphi = p.Hphi.copy()
f = p.f.copy()
b = p.b.copy()
A = p.A.copy()
J = p.J.copy()
# Numbers
self.assertEqual(x0.size,p.num_primal_variables)
self.assertEqual(A.shape[0],p.num_linear_equality_constraints)
self.assertEqual(f.size,p.num_nonlinear_equality_constraints)
# phi
self.assertTrue(type(phi) is float)
self.assertGreater(phi,0.)
man_phi = sum(f.weight*f.phi for f in p.functions)
self.assertLess(np.abs(man_phi-phi),1e-10)
# gphi
self.assertTrue(type(gphi) is np.ndarray)
self.assertTupleEqual(gphi.shape,(net.num_vars+p.num_extra_vars,))
man_gphi = sum(f.weight*f.gphi for f in p.functions)
self.assertLess(norm(np.hstack((man_gphi,np.zeros(p.num_extra_vars)))-gphi),1e-10)
# Hphi
self.assertTrue(type(Hphi) is coo_matrix)
self.assertTupleEqual(Hphi.shape,(net.num_vars+p.num_extra_vars,
net.num_vars+p.num_extra_vars))
self.assertGreater(Hphi.nnz,0)
# f
self.assertTrue(type(f) is np.ndarray)
f_size = sum(c.f.shape[0] for c in p.constraints)
self.assertTupleEqual(f.shape,(f_size,))
# b
self.assertTrue(type(b) is np.ndarray)
b_size = sum(c.b.shape[0] for c in p.constraints)
self.assertTupleEqual(b.shape,(b_size,))
# J
self.assertTrue(type(J) is coo_matrix)
J_size = sum(c.J.shape[0] for c in p.constraints)
self.assertTupleEqual(J.shape,(J_size,net.num_vars+p.num_extra_vars))
self.assertGreater(J.nnz,0)
# A
self.assertTrue(type(A) is coo_matrix)
A_size = sum(c.A.shape[0] for c in p.constraints)
self.assertTupleEqual(A.shape,(A_size,net.num_vars+p.num_extra_vars))
self.assertGreater(A.nnz,0)
# Check gphi
phi0 = phi
gphi0 = gphi.copy()
for i in range(NUM_TRIALS):
d = np.random.randn(net.num_vars+p.num_extra_vars)
x = x0 + h*d
p.eval(x)
phi1 = p.phi
gd_exact = np.dot(gphi0,d)
gd_approx = (phi1-phi0)/h
error = 100.*norm(gd_exact-gd_approx)/np.maximum(norm(gd_exact),TOL)
self.assertLessEqual(error,EPS)
# Check J
f0 = f.copy()
J0 = J.copy()
for i in range(NUM_TRIALS):
d = np.random.randn(net.num_vars+p.num_extra_vars)
x = x0 + h*d
p.eval(x)
f1 = p.f
Jd_exact = J0*d
Jd_approx = (f1-f0)/h
error = 100.*norm(Jd_exact-Jd_approx)/np.maximum(norm(Jd_exact),TOL)
self.assertLessEqual(error,EPS)
# Check Hphi
gphi0 = gphi.copy()
Hphi0 = Hphi.copy()
Hphi0 = Hphi0 + Hphi0.T - triu(Hphi0)
for i in range(NUM_TRIALS):
d = np.random.randn(net.num_vars+p.num_extra_vars)
x = x0 + h*d
p.eval(x)
gphi1 = p.gphi.copy()
Hd_exact = Hphi0*d
Hd_approx = (gphi1-gphi0)/h
error = 100.*norm(Hd_exact-Hd_approx)/np.maximum(norm(Hd_exact),TOL)
self.assertLessEqual(error,EPS)
# Check Hcombined
coeff = np.random.randn(f.shape[0])
p.eval(x0)
self.assertRaises(pf.ProblemError,p.combine_H,np.zeros(f.shape[0]+1),False)
p.combine_H(coeff,False)
J0 = p.J.copy()
g0 = J0.T*coeff
H0 = p.H_combined.copy()
self.assertTrue(type(H0) is coo_matrix)
self.assertTupleEqual(H0.shape,(net.num_vars+p.num_extra_vars,net.num_vars+p.num_extra_vars))
self.assertTrue(np.all(H0.row >= H0.col)) # lower triangular
H0 = (H0 + H0.T) - triu(H0)
for i in range(NUM_TRIALS):
d = np.random.randn(net.num_vars+p.num_extra_vars)
x = x0 + h*d
p.eval(x)
g1 = p.J.T*coeff
Hd_exact = H0*d
Hd_approx = (g1-g0)/h
error = 100.*norm(Hd_exact-Hd_approx)/np.maximum(norm(Hd_exact),TOL)
self.assertLessEqual(error,EPS)
# Sensitivities
net.clear_sensitivities()
for i in range(net.num_buses):
bus = net.get_bus(i)
self.assertEqual(bus.sens_P_balance,0.)
self.assertEqual(bus.sens_Q_balance,0.)
sens = np.random.randn(p.f.size)
offset = 0
for c in p.constraints:
if c.name == 'AC power balance':
break
else:
offset += c.f.size
p.store_sensitivities( | np.zeros(p.A.shape[0]) | numpy.zeros |
# -*- coding: utf-8 -*-
"""
Low level tool for writing percent difference reports. Typically, this
is called via: :func:`cla.DR_Results.rptpct`.
"""
from io import StringIO
from types import SimpleNamespace
import warnings
import numpy as np
import matplotlib.pyplot as plt
from pyyeti import ytools, locate, writer
from ._utilities import _get_rpt_headers, _get_numform, _proc_filterval
from ._magpct import magpct
__all__ = ["rptpct1"]
# FIXME: We need the str/repr formatting used in Numpy < 1.14.
try:
np.set_printoptions(legacy="1.13")
except TypeError:
pass
def _apply_pv(value, pv, oldlen):
# if value has a len that's > 1, try to partition it down;
# otherwise, return it as is:
try:
n = len(value)
except TypeError:
return value
else:
if n == 1:
return value
# `value` is a vector with len > 1 ... ensure it is a true numpy
# array:
value = np.atleast_1d(value)
# oldlen is either 0 (for `value` vectors that are expected to be
# full size ... currently, only the `filterval` and
# `magpct_filterval` vectors), or it is the length of the
# dimension that the `value` index type of partition vector
# (currently, only the `ignorepv` vector) was originally defined
# to partition.
if oldlen == 0:
# `value` is `filterval` or `magpct_filterval` ... these just
# need to be partitioned down:
newvalue = value[pv]
else:
# `value` is `ignorepv` ... it needs to be redefined to
# correspond to reduced size:
truefalse = locate.index2bool(value, oldlen)
newvalue = truefalse[pv].nonzero()[0]
return newvalue
def _align_mxmn(mxmn1, mxmn2, labels2, row_number, infodct):
if infodct["labels"] and infodct["labels"] != labels2:
n = len(infodct["labels"])
pv1, pv2 = locate.list_intersect(infodct["labels"], labels2)
mxmn1 = mxmn1[pv1]
mxmn2 = mxmn2[pv2]
infodct["labels"] = [infodct["labels"][i] for i in pv1]
row_number = row_number[pv1]
infodct["filterval"] = _apply_pv(infodct["filterval"], pv1, 0)
infodct["magpct_filterval"] = _apply_pv(infodct["magpct_filterval"], pv1, 0)
infodct["ignorepv"] = _apply_pv(infodct["ignorepv"], pv1, n)
return mxmn1, mxmn2, row_number
def _get_filtline(filterval):
if len(filterval) > 1:
filtline = "Filter: <defined row-by-row>\n"
else:
filtline = f"Filter: {filterval[0]}\n"
return filtline
def _get_noteline(use_range, names, prtbads, flagbads):
noteline = "Notes: "
tab = " "
if not use_range:
noteline += "% Diff = +/- abs(({0}-{1})/{1})*100\n".format(*names)
else:
noteline += "% Diff = +/- abs({0}-{1})/max(abs({1}(max,min)))*100\n".format(
*names
)
noteline += tab + "Sign set such that positive % differences indicate exceedances\n"
prtbad, prtbadh, prtbadl = prtbads
flagbad, flagbadh, flagbadl = flagbads
if prtbad is not None or prtbadh is not None or prtbadl is not None:
if prtbad is not None:
prtbad = abs(prtbad)
noteline += tab + f"Printing rows where abs(% Diff) > {prtbad}%\n"
elif prtbadh is not None:
noteline += tab + f"Printing rows where % Diff > {prtbadh}%\n"
else:
noteline += tab + f"Printing rows where % Diff < {prtbadl}%\n"
if flagbad is not None or flagbadh is not None or flagbadl is not None:
if flagbad is not None:
flagbad = abs(flagbad)
noteline += tab + f"Flagging (*) rows where abs(% Diff) > {flagbad}%\n"
elif flagbadh is not None:
noteline += tab + f"Flagging (*) rows where % Diff > {flagbadh}%\n"
else:
noteline += tab + f"Flagging (*) rows where % Diff < {flagbadl}%\n"
return noteline
def _get_badpv(pct, pv, bad, badh, badl, defaultpv=False):
if bad is not None or badh is not None or badl is not None:
badpv = pv.copy()
if bad is not None:
badpv &= abs(pct) > bad
elif badh is not None:
badpv &= pct > badh
else:
badpv &= pct < badl
else:
badpv = np.empty(len(pct), bool)
badpv[:] = defaultpv
return badpv
def _get_pct_diff(a, b, filt, pv, nastring, mxmn_b=None, ismax=True, flagbads=None):
# either can pass filter to be kept:
pv &= (abs(a) > filt) | (abs(b) > filt)
if mxmn_b is not None:
denom = np.nanmax(abs(mxmn_b), axis=1)
else:
denom = abs(b)
# put 1's in for filtered values ... this is temporary
a = a.copy()
b = b.copy()
a[~pv] = 1.0
b[~pv] = 1.0
z = denom == 0.0
denom[z] = 1.0
pct = 100 * abs(a - b) / denom
pct[z] = 100.0 # np.inf
# make less extreme values negative
neg = a < b if ismax else a > b
pct[neg] *= -1.0
# put nan's in for the filtered or n/a rows:
pct[~pv] = np.nan
# make 7 char version:
spct = [f"{p:7.2f}" for p in pct]
badpv = _get_badpv(pct, pv, *flagbads, False)
for j in badpv.nonzero()[0]:
spct[j] += "*"
for j in (~pv).nonzero()[0]:
spct[j] = nastring
return pct, spct
def _get_histogram_str(desc, hdr, pctinfo):
pctcount = pctinfo["hsto"]
s = [
(f"\n\n {desc} - {hdr} Comparison Histogram\n\n"),
(" % Diff Count Percent\n -------- -------- -------\n"),
]
with StringIO() as f:
writer.vecwrite(f, " {:8.2f} {:8.0f} {:7.2f}\n", pctcount)
s.append(f.getvalue())
s.append("\n")
# total_percent_10 will either be 0 or 1000:
# - 0 if all % diffs are "n/a"
# - 1000 otherwise
total_percent_10 = np.round(pctcount[:, 2].sum() * 10)
last = -1.0
for pdiff in [1, 2, 5, 10, 15, 20, 25, 50, 100, 500]:
pvdiff = abs(pctcount[:, 0]) <= pdiff
num = pctcount[pvdiff, 2].sum()
if num > last:
s.append(f" {num:.1f}% of values are within {pdiff}%\n")
if np.round(num * 10) == total_percent_10:
break
last = num
pct = pctinfo["pct"]
n = len(pct)
if n == 0:
s.append(
"\n % Diff Statistics: [Min, Max, Mean, StdDev]"
" = [n/a, n/a, n/a, n/a]\n"
)
else:
stddev = 0.0 if n <= 1 else pct.std(ddof=1)
s.append(
"\n % Diff Statistics: [Min, Max, Mean, StdDev]"
f" = [{pct.min():.2f}, {pct.max():.2f}, {pct.mean():.4f}, {stddev:.4f}]\n"
)
return "".join(s)
def _proc_pct(
ext1,
ext2,
filterval,
magpct_filterval,
*,
names,
mxmn1,
comppv,
mxmn_b,
ismax,
histogram_inc,
prtbads,
flagbads,
numform,
valhdr,
maxhdr,
minhdr,
absmhdr,
pdhdr,
nastring,
doabsmax,
shortabsmax,
print_info,
):
# handle magpct stuff here:
mag = ext1[comppv], ext2[comppv]
if magpct_filterval is not None and len(magpct_filterval) > 1:
magfilt = magpct_filterval[comppv]
else:
magfilt = magpct_filterval
pv = comppv.copy()
pct, spct = _get_pct_diff(
ext1,
ext2,
filterval,
pv,
nastring,
mxmn_b=mxmn_b,
ismax=ismax,
flagbads=flagbads,
)
pct_ret = pct[pv]
hsto = ytools.histogram(pct_ret, histogram_inc)
# for trimming down if prtbad set:
prtpv = _get_badpv(pct, pv, *prtbads, True)
pctlen = max(len(pdhdr), len(max(spct, key=len)))
sformatpd = f"{{:{pctlen}}}"
# for writer.formheader:
numlen = max(13, len(max(names, key=len)), len(numform.format(np.pi)))
if not doabsmax:
print_info.headers1.extend([*names, ""])
print_info.headers2.extend([valhdr, valhdr, pdhdr])
print_info.formats.extend([numform, numform, sformatpd])
print_info.printargs.extend([ext1, ext2, spct])
print_info.widths.extend([numlen, numlen, pctlen])
print_info.seps.extend([4, 2, 2])
print_info.justs.extend(["c", "c", "c"])
elif shortabsmax:
print_info.headers1.extend([*names, ""])
print_info.headers2.extend([absmhdr, absmhdr, pdhdr])
print_info.formats.extend([numform, numform, sformatpd])
print_info.printargs.extend([ext1, ext2, spct])
print_info.widths.extend([numlen, numlen, pctlen])
print_info.seps.extend([4, 2, 2])
print_info.justs.extend(["c", "c", "c"])
else:
print_info.headers1.extend([names[0], names[0], names[0], names[1], ""])
print_info.headers2.extend([maxhdr, minhdr, absmhdr, absmhdr, pdhdr])
print_info.formats.extend([numform, numform, numform, numform, sformatpd])
print_info.printargs.extend([mxmn1[:, 0], mxmn1[:, 1], ext1, ext2, spct])
print_info.widths.extend([numlen, numlen, numlen, numlen, pctlen])
print_info.seps.extend([4, 2, 2, 2, 2])
print_info.justs.extend(["c", "c", "c", "c", "c"])
return dict(
pct=pct_ret, spct=spct, hsto=hsto, prtpv=prtpv, mag=mag, magfilt=magfilt
)
def _figure_on(name, doabsmax, show_figures):
figsize = [8.5, 11.0]
if doabsmax:
figsize[1] /= 3.0
if show_figures:
plt.figure(name, figsize=figsize)
plt.clf()
else:
plt.figure(figsize=figsize)
def _figure_off(show_figures):
if not show_figures:
plt.close()
def _prep_subplot(pctinfo, sp):
if "mx" in pctinfo:
# if not just doing absmax
if sp > 311:
plt.subplot(sp, sharex=plt.gca())
else:
plt.subplot(sp)
def _plot_magpct(
pctinfo,
names,
desc,
doabsmax,
filename,
magpct_options,
use_range,
maxhdr,
minhdr,
absmhdr,
show_figures,
tight_layout_args,
):
ptitle = f"{desc} - {{}} Comparison vs Magnitude"
xl = f"{names[1]} Magnitude"
yl = f"% Diff of {names[0]} vs {names[1]}"
_figure_on("Magpct - " + desc, doabsmax, show_figures)
try:
for lbl, hdr, sp, ismax in (
("mx", maxhdr, 311, True),
("mn", minhdr, 312, False),
("amx", absmhdr, 313, True),
):
_prep_subplot(pctinfo, sp)
if lbl in pctinfo:
if use_range:
ref = pctinfo["amx"]["mag"][1]
else:
ref = None
magpct(
pctinfo[lbl]["mag"][0],
pctinfo[lbl]["mag"][1],
Ref=ref,
ismax=ismax,
filterval=pctinfo[lbl]["magfilt"],
**magpct_options,
)
plt.title(ptitle.format(hdr))
plt.xlabel(xl)
plt.ylabel(yl)
plt.grid(True)
plt.tight_layout(**tight_layout_args)
if isinstance(filename, str):
plt.savefig(filename + ".magpct.png")
finally:
_figure_off(show_figures)
def _plot_histogram(
pctinfo,
names,
desc,
doabsmax,
filename,
histogram_inc,
maxhdr,
minhdr,
absmhdr,
show_figures,
tight_layout_args,
):
ptitle = f"{desc} - {{}} Comparison Histogram"
xl = f"% Diff of {names[0]} vs {names[1]}"
yl = "Percent Occurrence (%)"
_figure_on("Histogram - " + desc, doabsmax, show_figures)
try:
for lbl, hdr, sp in (
("mx", maxhdr, 311),
("mn", minhdr, 312),
("amx", absmhdr, 313),
):
_prep_subplot(pctinfo, sp)
if lbl in pctinfo:
width = histogram_inc
x = pctinfo[lbl]["hsto"][:, 0]
y = pctinfo[lbl]["hsto"][:, 2]
colors = ["b"] * len(x)
ax = abs(x)
pv1 = ((ax > 5) & (ax <= 10)).nonzero()[0]
pv2 = (ax > 10).nonzero()[0]
for pv, c in ((pv1, "m"), (pv2, "r")):
for i in pv:
colors[i] = c
plt.bar(x, y, width=width, color=colors, align="center")
plt.title(ptitle.format(hdr))
plt.xlabel(xl)
plt.ylabel(yl)
x = abs(max(plt.xlim(), key=abs))
if x < 5:
plt.xlim(-5, 5)
plt.grid(True)
plt.tight_layout(**tight_layout_args)
if isinstance(filename, str):
plt.savefig(filename + ".histogram.png")
finally:
_figure_off(show_figures)
def rptpct1(
mxmn1,
mxmn2,
filename,
*,
title="PERCENT DIFFERENCE REPORT",
names=("Self", "Reference"),
desc=None,
filterval=None,
labels=None,
units=None,
ignorepv=None,
uf_reds=None,
use_range=True,
numform=None,
prtbad=None,
prtbadh=None,
prtbadl=None,
flagbad=None,
flagbadh=None,
flagbadl=None,
dohistogram=True,
histogram_inc=1.0,
domagpct=True,
magpct_options=None,
doabsmax=False,
shortabsmax=False,
roundvals=-1,
rowhdr="Row",
deschdr="Description",
maxhdr="Maximum",
minhdr="Minimum",
absmhdr="Abs-Max",
perpage=-1,
tight_layout_args=None,
show_figures=False,
align_by_label=True,
):
"""
Write a percent difference report between 2 sets of max/min data
Parameters
----------
mxmn1 : 2d array_like or SimpleNamespace
The max/min data to compare to the `mxmn2` set. If 2-column
array_like, its columns are: [max, min]. If SimpleNamespace,
it must be as defined in :class:`DR_Results` and have these
members:
.. code-block:: none
.ext = [max, min]
.drminfo = SimpleNamespace which has (at least):
.desc = one line description of category
.filterval = the filter value; (see `filterval`
description below)
.labels = a list of descriptions; one per row
.ignorepv = these rows will get 'n/a' for % diff
.units = string with units
.uf_reds = uncertainty factors
Note that the inputs `desc`, `labels`, etc, override the
values above.
mxmn2 : 2d array_like or SimpleNamespace
The reference set of max/min data. Format is the same as
`mxmn1`.
.. note::
If both `mxmn1` and `mxmn2` are SimpleNamespaces and have
the ``.drminfo.labels`` attribute, this routine will, by
default, use the labels to align the data sets for
comparison. To prevent this, set the `align_by_label`
parameter to False.
filename : string or file_like or 1 or None
Either a name of a file, or is a file_like object as returned
by :func:`open` or :class:`io.StringIO`. Input as integer 1 to
write to stdout. Can also be the name of a directory or None;
in these cases, a GUI is opened for file selection.
title : string; must be named; optional
Title for the report
names : list/tuple; must be named; optional
Two (short) strings identifying the two sets of data
desc : string or None; must be named; optional
A one line description of the table. Overrides
`mxmn1.drminfo.desc`. If neither are input,
'No description provided' is used.
filterval : scalar, 1d array_like or None; must be named; optional
Numbers with absolute value <= than `filterval` will get a
'n/a' % diff. If vector, length must match number of rows in
`mxmn1` and `mxmn2` data. Overrides `mxmn1.drminfo.filterval`.
If neither are input, `filterval` is set to 1.e-6.
labels : list or None; must be named; optional
A list of strings briefly describing each row. Overrides
`mxmn1.drminfo.labels`. If neither are input,
``['Row 1','Row 2',...]`` is used.
units : string or None; must be named; optional
Specifies the units. Overrides `mxmn1.drminfo.units`. If
neither are input, 'Not specified' is used.
ignorepv : 1d array or None; must be named; optional
0-offset index vector specifying which rows of `mxmn1` to
ignore (they get the 'n/a' % diff). Overrides
`mxmn1.drminfo.ignorepv`. If neither are input, no rows are
ignored (though `filterval` is still used).
.. note::
`ignorepv` applies *before* any alignment by labels is
done (when `align_by_label` is True, which is the
default).
uf_reds : 1d array or None; must be named; optional
Uncertainty factors: [rigid, elastic, dynamic, static].
Overrides `mxmn1.drminfo.uf_reds`. If neither is input,
'Not specified' is used.
use_range : bool; must be named, optional
If True, the denominator of the % diff calc for both the max
& min for each row is the absolute maximum of the reference
max & min for that row. If False, the denominator is the
applicable reference max or min. A quick example shows why
``use_range=True`` might be useful:
.. code-block:: none
If [max1, min1] = [12345, -10] and
[max2, min2] = [12300, 50]
Then:
% diff = [0.37%, 0.49%] if use_range is True
% diff = [0.37%, 120.00%] if use_range is False
Note that the sign of the % diff is defined such that a
positive % diff means an exceedance: where ``max1 > max2`` or
``min1 < min2``.
`use_range` is ignored if `doabsmax` is True.
numform : string or None; must be named; optional
Format of the max & min numbers. If None, it is set internally
to be 13 chars wide and depends on the range of numbers to
print:
- if range is "small", numform='{:13.xf}' where "x" ranges
from 0 to 7
- if range is "large", numform='{:13.6e}'
prtbad : scalar or None; must be named; optional
Only print rows where ``abs(%diff) > prtbad``. For example, to
print rows off by more than 5%, use ``prtbad=5``. `prtbad`
takes precedence over `prtbadh` and `prtbadl`.
prtbadh : scalar or None; must be named; optional
Only print rows where ``%diff > prtbadh``. Handy for showing
just the exceedances. `prtbadh` takes precedence over
`prtbadl`.
prtbadl : scalar or None; must be named; optional
Only print rows where ``%diff < prtbadl``. Handy for showing
where reference rows are higher.
flagbad : scalar or None; must be named; optional
Flag % diffs where ``abs(%diff) > flagbad``. Works similar to
`prtbad`. The flag is an asterisk (*).
flagbadh : scalar or None; must be named; optional
Flag % diffs where ``%diff > flagbadh``. Works similar to
`prtbadh`. Handy for flagging exceedances. `flagbadh` takes
precedence over `flagbadl`.
flagbadl : scalar or None; must be named; optional
Flag % diffs where ``%diff < flagbadl``. Works similar to
`prtbadl`.
dohistogram : bool; must be named; optional
If True, plot the histograms. Plots will be written to
"`filename`.histogram.png".
histogram_inc : scalar; must be named; optional
The histogram increment; defaults to 1.0 (for 1%).
domagpct : bool; must be named; optional
If True, plot the percent differences versus magnitude via
:func:`magpct`. Plots will be written to
"`filename`.magpct.png". Filtering for the "magpct" plot is
controlled by the ``magpct_options['filterval']`` and
``magpct_options['symlogy']`` options. By default, all percent
differences are shown, but the larger values (according to the
`filterval` filter) are emphasized by using a mixed linear/log
y-axis. The percent differences for the `ignorepv` rows are
not plotted.
magpct_options : None or dict; must be named; optional
If None, it is internally reset to::
magpct_options = {'filterval': 'filterval'}
Use this parameter to provide any options to :func:`magpct`
but note that the `filterval` option for :func:`magpct` is
treated specially. Here, in addition to any of the values that
:func:`magpct` accepts, it can also be set to the string
"filterval" as in the default case shown above. In that case,
``magpct_options['filterval']`` gets internally reset to the
initial value of `filterval` (which is None by default).
.. note::
The call to :func:`magpct` is *after* applying `ignorepv`
and doing any data aligning by labels.
.. note::
The two filter value options (`filterval` and
``magpct_options['filterval']``) have different defaults:
None and 'filterval`, respectively. They also differ on how
the ``None`` setting is used: for `filterval`, None is
replaced by 1.e-6 while for `magpct_filterval`, None means
that the "magpct" plot will not have any filters applied at
all.
.. note::
The above means that, if you accept the default values for
`filterval` and for ``magpct_options['filterval']``, then
tables and the histogram plots will use a `filterval` of
1.e-6 while the "magpct" plots will use no filter (it
compares everything except perfect zeros).
doabsmax : bool; must be named; optional
If True, compare only absolute maximums.
shortabsmax : bool; must be named; optional
If True, set ``doabsmax=True`` and do not print the max1 and
min1 columns.
roundvals : integer; must be named; optional
Round max & min numbers at specified decimal. If negative, no
rounding.
rowhdr : string; must be named; optional
Header for row number column
deschdr : string; must be named; optional
Header for description column
maxhdr : string; must be named; optional
Header for the column 1 data
minhdr : string; must be named; optional
Header for the column 2 data
absmhdr : string; must be named; optional
Header for abs-max column
perpage : integer; must be named; optional
The number of lines to write perpage. If < 1, there is no
limit (one page).
tight_layout_args : dict or None; must be named; optional
Arguments for :func:`matplotlib.pyplot.tight_layout`. If None,
defaults to ``{'pad': 3.0}``.
show_figures : bool; must be named; optional
If True, plot figures will be displayed on the screen for
interactive viewing. Warning: there may be many figures.
align_by_label : bool; must be named; optional
If True, use labels to align the two sets of data for
comparison. See note above under the `mxmn2` option.
Returns
-------
pdiff_info : dict
Dictionary with 'amx' (abs-max), 'mx' (max), and 'mn' keys:
.. code-block:: none
<class 'dict'>[n=3]
'amx': <class 'dict'>[n=5]
'hsto' : float64 ndarray 33 elems: (11, 3)
'mag' : [n=2]: (float64 ndarray: (100,), ...
'pct' : float64 ndarray 100 elems: (100,)
'prtpv': bool ndarray 100 elems: (100,)
'spct' : [n=100]: [' -2.46', ' -1.50', ...
'mn' : <class 'dict'>[n=5]
'hsto' : float64 ndarray 33 elems: (11, 3)
'mag' : [n=2]: (float64 ndarray: (100,), ...
'pct' : float64 ndarray 100 elems: (100,)
'prtpv': bool ndarray 100 elems: (100,)
'spct' : [n=100]: [' 1.55', ' 1.53', ...
'mx' : <class 'dict'>[n=5]
'hsto' : float64 ndarray 27 elems: (9, 3)
'mag' : [n=2]: (float64 ndarray: (100,), ...
'pct' : float64 ndarray 100 elems: (100,)
'prtpv': bool ndarray 100 elems: (100,)
'spct' : [n=100]: [' -2.46', ' -1.50', ...
Where:
.. code-block:: none
'hsto' : output of :func:`histogram`: [center, count, %]
'mag' : inputs to :func:`magpct`
'pct' : percent differences
'prtpv' : rows to print partition vector
'spct' : string version of 'pct'
Examples
--------
>>> import numpy as np
>>> from pyyeti import cla
>>> ext1 = [[120.0, -8.0],
... [8.0, -120.0]]
>>> ext2 = [[115.0, -5.0],
... [10.0, -125.0]]
Run :func:`rptpct1` multiple times to get a more complete picture
of all the output (the table is very wide). Also, the plots will
be turned off for this example.
First, the header:
>>> opts = {'domagpct': False, 'dohistogram': False}
>>> dct = cla.rptpct1(ext1, ext2, 1, **opts) # doctest: +ELLIPSIS
PERCENT DIFFERENCE REPORT
<BLANKLINE>
Description: No description provided
Uncertainty: Not specified
Units: Not specified
Filter: 1e-06
Notes: % Diff = +/- abs(Self-Reference)/max(abs(Reference...
Sign set such that positive % differences indicate...
Date: ...
...
Then, the max/min/absmax percent difference table in 3 calls:
>>> dct = cla.rptpct1(ext1, ext2, 1, **opts) # doctest: +ELLIPSIS
PERCENT DIFFERENCE REPORT
...
Self Reference ...
Row Description Maximum Maximum % Diff ...
------- ----------- ------------- ------------- ------- ...
1 Row 1 120.00000 115.00000 4.35 ...
2 Row 2 8.00000 10.00000 -1.60 ...
...
>>> dct = cla.rptpct1(ext1, ext2, 1, **opts) # doctest: +ELLIPSIS
PERCENT DIFFERENCE REPORT
...
... Self Reference ...
Row Description ... Minimum Minimum % Diff ...
------- ----------- ...------------- ------------- ------- ...
1 Row 1 ... -8.00000 -5.00000 2.61 ...
2 Row 2 ... -120.00000 -125.00000 -4.00 ...
...
>>> dct = cla.rptpct1(ext1, ext2, 1, **opts) # doctest: +ELLIPSIS
PERCENT DIFFERENCE REPORT
...
... Self Reference
Row Description ... Abs-Max Abs-Max % Diff
------- ----------- ...------------- ------------- -------
1 Row 1 ... 120.00000 115.00000 4.35
2 Row 2 ... 120.00000 125.00000 -4.00
...
Finally, the histogram summaries:
>>> dct = cla.rptpct1(ext1, ext2, 1, **opts) # doctest: +ELLIPSIS
PERCENT DIFFERENCE REPORT
...
No description provided - Maximum Comparison Histogram
<BLANKLINE>
% Diff Count Percent
-------- -------- -------
-2.00 1 50.00
4.00 1 50.00
<BLANKLINE>
0.0% of values are within 1%
50.0% of values are within 2%
100.0% of values are within 5%
<BLANKLINE>
% Diff Statistics: [Min, Max, Mean, StdDev] = [-1.60, 4.35,...
<BLANKLINE>
<BLANKLINE>
No description provided - Minimum Comparison Histogram
<BLANKLINE>
% Diff Count Percent
-------- -------- -------
-4.00 1 50.00
3.00 1 50.00
<BLANKLINE>
0.0% of values are within 1%
100.0% of values are within 5%
<BLANKLINE>
% Diff Statistics: [Min, Max, Mean, StdDev] = [-4.00, 2.61,...
<BLANKLINE>
<BLANKLINE>
No description provided - Abs-Max Comparison Histogram
<BLANKLINE>
% Diff Count Percent
-------- -------- -------
-4.00 1 50.00
4.00 1 50.00
<BLANKLINE>
0.0% of values are within 1%
100.0% of values are within 5%
<BLANKLINE>
% Diff Statistics: [Min, Max, Mean, StdDev] = [-4.00, 4.35,...
"""
if tight_layout_args is None:
tight_layout_args = {"pad": 3.0}
if magpct_options is None:
magpct_options = {"filterval": "filterval"}
else:
magpct_options = magpct_options.copy()
# magpct_options['filterval'] get special treatment:
magpct_filterval = magpct_options["filterval"]
del magpct_options["filterval"]
if isinstance(magpct_filterval, str):
if magpct_filterval != "filterval":
raise ValueError(
"``magpct_options['filterval']`` is an invalid "
f"string: {magpct_filterval!r} (can only "
"be 'filterval' if a string)"
)
# copy the initial `filterval` setting:
magpct_filterval = filterval
infovars = (
"desc",
"filterval",
"magpct_filterval",
"labels",
"units",
"ignorepv",
"uf_reds",
)
dct = locals()
infodct = {n: dct[n] for n in infovars}
del dct
# check mxmn1:
if isinstance(mxmn1, SimpleNamespace):
sns = mxmn1.drminfo
for key, value in infodct.items():
if value is None:
infodct[key] = getattr(sns, key, None)
del sns
mxmn1 = mxmn1.ext
else:
mxmn1 = np.atleast_2d(mxmn1)
row_number = np.arange(1, mxmn1.shape[0] + 1)
# check mxmn2:
if isinstance(mxmn2, SimpleNamespace) and getattr(mxmn2, "drminfo", None):
labels2 = mxmn2.drminfo.labels
mxmn2 = mxmn2.ext
if align_by_label:
# use labels and labels2 to align data; this is in case
# the two sets of results recover some of the same items,
# but not all
mxmn1, mxmn2, row_number = _align_mxmn(
mxmn1, mxmn2, labels2, row_number, infodct
)
else:
mxmn2 = np.atleast_2d(mxmn2)
desc = infodct["desc"]
if desc is None:
desc = "No description provided"
R = mxmn1.shape[0]
if R != mxmn2.shape[0]:
raise ValueError(
f"`mxmn1` and `mxmn2` have a different number of rows: "
f"{R} vs {mxmn2.shape[0]} for category with `desc` = {desc}"
)
filterval = infodct["filterval"]
magpct_filterval = infodct["magpct_filterval"]
labels = infodct["labels"]
units = infodct["units"]
ignorepv = infodct["ignorepv"]
uf_reds = infodct["uf_reds"]
del infodct
if filterval is None:
filterval = 1.0e-6
filterval = _proc_filterval(filterval, R, "filterval")
magpct_filterval = _proc_filterval(
magpct_filterval, R, "magpct_options['filterval']"
)
if labels is None:
labels = [f"Row {i + 1:6d}" for i in range(R)]
elif len(labels) != R:
raise ValueError(
"length of `labels` does not match number"
f" of rows in `mxmn1`: {len(labels)} vs {R} for "
f"category with `desc` = {desc}"
)
if units is None:
units = "Not specified"
if numform is None:
numform = _get_numform(mxmn1)
pdhdr = "% Diff"
nastring = "n/a "
comppv = np.ones(R, bool)
if ignorepv is not None:
comppv[ignorepv] = False
# for row labels:
w = max(11, len(max(labels, key=len)))
frm = f"{{:{w}}}"
# start preparing for writer.formheader:
print_info = SimpleNamespace(
headers1=["", ""],
headers2=[rowhdr, deschdr],
formats=["{:7d}", frm],
printargs=[row_number, labels],
widths=[7, w],
seps=[0, 2],
justs=["c", "l"],
)
if shortabsmax:
doabsmax = True
if doabsmax:
use_range = False
if roundvals > -1:
mxmn1 = np.round(mxmn1, roundvals)
mxmn2 = np.round(mxmn2, roundvals)
prtbads = (prtbad, prtbadh, prtbadl)
flagbads = (flagbad, flagbadh, flagbadl)
# compute percent differences
pctinfo = {}
kwargs = dict(
names=names,
mxmn1=mxmn1,
comppv=comppv,
histogram_inc=histogram_inc,
numform=numform,
prtbads=prtbads,
flagbads=flagbads,
maxhdr=maxhdr,
minhdr=minhdr,
absmhdr=absmhdr,
pdhdr=pdhdr,
nastring=nastring,
doabsmax=doabsmax,
shortabsmax=shortabsmax,
print_info=print_info,
)
with warnings.catch_warnings():
warnings.filterwarnings("ignore", r"All-NaN (slice|axis) encountered")
mx1 = np.nanmax(abs(mxmn1), axis=1)
mx2 = np.nanmax(abs(mxmn2), axis=1)
if not doabsmax:
max1, min1 = mxmn1[:, 0], mxmn1[:, 1]
max2, min2 = mxmn2[:, 0], mxmn2[:, 1]
mxmn_b = mxmn2 if use_range else None
prtpv = | np.zeros(R, bool) | numpy.zeros |
"""
This file is used to pre-process voxlization and aggregation weights, in order to save training time.
Re-project simplified point clouds to multi-plane, 32 planes are used.
"""
from __future__ import division
import numpy as np
import os, cv2, time, math, scipy
import scipy.io as io
def loadfile(ply_path):
st = time.time()
position = []
color = []
file = open(ply_path)
begin = False
while 1:
line = file.readline().strip('\n')
if not line:
break
line = line.split(' ')
if begin:
position.append(np.array([float(line[0]), float(line[1]), float(line[2]), float(1.0)]))
color.append(np.array([float(line[5]), float(line[4]), float(line[3])])) # rgb to bgr
if line[0] == 'end_header':
begin = True
file.close()
print('load ply time: %s' %(time.time() - st))
return np.transpose(position), np.transpose(color)
def makedataset(dir2):
image_names = []
depth_names = []
intrinsics = []
extrinsics = []
assert os.path.isdir(dir2)
parameter_file = []
for root,_, fname in os.walk(dir2):
parameter_file.append(os.path.join(dir2, fname[0]))
file = open(parameter_file[0])
while True:
line = file.readline()
if not line:
break
temp = line.split()
if len(temp) == 0:
continue
if temp[0] == 'intrinsics_matrix':
intrinsic_temp = line
if temp[0] == 'scan':
extrinsics.append(line)
intrinsics.append(intrinsic_temp)
image_names.append(temp[2])
depth_names.append(temp[1])
positions_world = np.zeros([len(extrinsics), 3])
for i in range(len(extrinsics)):
temp = extrinsics[i].split()
positions_world[i, 0] = np.float32(temp[6])
positions_world[i, 1] = np.float32(temp[10])
positions_world[i, 2] = np.float32(temp[14])
return image_names, depth_names, intrinsics, extrinsics, positions_world
def camera_parameter_read(intrinsic, extrinsic):
# tmp = intrinsics_all[i].split()
tmp = intrinsic.split()
fx = float(tmp[1])
ux = float(tmp[3])
fy = float(tmp[5])
uy = float(tmp[6])
intrinsic_matrix = np.array([[fx, 0, ux, 0], [0, fy, 1024 - uy, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
tmp = extrinsic.split()
tmp = list(map(float, tmp[3:]))
extrinsic_matrix = np.reshape(np.array(tmp), [4, 4])
extrinsic_matrix[:, [1, 2]] = extrinsic_matrix[:, [1, 2]] * (-1.0) # Camera coordinate system transform.
return intrinsic_matrix, extrinsic_matrix
def Voxelization(w, h, intrinsic_matrix, extrinsic_matrix, point_clouds, valid_depth_near, valid_depth_far, num_planes):
st = time.time()
transform_matrix = intrinsic_matrix.dot(np.linalg.inv(extrinsic_matrix))
position_image = transform_matrix.dot(point_clouds)
print('reproject_time: %s' %(time.time() - st))
depth_all = position_image[2, :]
u_all =position_image[0, :] / (depth_all+1e-10)
v_all =position_image[1, :] / (depth_all+1e-10)
valid_u = np.where((u_all >= 0) & (u_all <= (w-1)))
valid_v = np.where((v_all >= 0) & (v_all <= (h-1)))
valid_d = np.where((depth_all > valid_depth_near) & (depth_all < valid_depth_far))
valid_position = np.intersect1d(valid_u, valid_v)
valid_position = np.intersect1d(valid_position, valid_d)
selected_depth = depth_all[valid_position]
index = np.argsort(-selected_depth) # depth large to small
index = index[100:-50] # in order to reduce outliers' influence during voxelization, we remove 100 furthest and 50 nearest points.
valid_position_sorted = valid_position[index]
valid_d_sorted = depth_all[valid_position_sorted]
center_u_sorted = u_all[valid_position_sorted]
center_v_soretd = v_all[valid_position_sorted]
u_sorted = np.uint32(np.rint(center_u_sorted))
v_sorted = np.uint32(np.rint(center_v_soretd))
# calculate distance to grid center. Parallel distance.
st = time.time()
distance_sorted = np.sqrt(np.square(u_sorted - center_u_sorted) + np.square(v_sorted - center_v_soretd))
print("calculate_distance: %s" % (time.time() - st))
# 3D space voxelization
num_valids = len(index)
valid_d_min = valid_d_sorted[num_valids - 1] # near depth plane
valid_d_max = valid_d_sorted[0] # far depth plane
tmp = np.linspace(valid_d_max, valid_d_min, num_planes+1)
up_boundary = tmp[1:]
d_position = np.zeros([num_valids]) # points belong to which plane.
st = time.time()
cnt = 0
for i in range(num_valids):
tmp_d = valid_d_sorted[i]
if tmp_d >= up_boundary[cnt]:
d_position[i] = num_planes - cnt - 1
else:
for j in range(1, num_planes - cnt):
cnt = cnt + 1
if tmp_d >= up_boundary[cnt]:
d_position[i] = num_planes - cnt - 1
break
print('split_time: %s' % (time.time() - st))
# grouping
groups_original = u_sorted + v_sorted*w + d_position*w*h # groups
groups_original_sort_index = np.argsort(groups_original) # small to large
groups_original_sorted = groups_original[groups_original_sort_index]
u_sorted_1 = u_sorted[groups_original_sort_index]
v_sorted_1 = v_sorted[groups_original_sort_index]
d_position_sorted_1 = d_position[groups_original_sort_index]
valid_position_sorted_1 = valid_position_sorted[groups_original_sort_index]
distance_sorted_1 = distance_sorted[groups_original_sort_index]
array = np.uint16(np.linspace(0, 1000, 1000, endpoint=False)) # assign points within one voxel or group a sequence index. Begin from 0. The max num in each group less than 1000.
groups_index = np.zeros_like(valid_position_sorted_1) # each group's start position.
groups_each = np.zeros_like(valid_position_sorted_1) # each point belongs to which group or voxel.
groups_each_index = np.zeros_like(valid_position_sorted_1, dtype=np.uint16) # each point's index/order in one group, a sequence.
group_begin = 0
cnt = 0
for ii in range(num_valids):
group_tmp = groups_original_sorted[ii]
if (ii + 1) < num_valids:
group_next = groups_original_sorted[ii+1]
if not group_tmp == group_next:
groups_each[group_begin:(ii+1)] = cnt
groups_each_index[group_begin:(ii+1)] = array[0:(ii+1 - group_begin)]
groups_index[cnt] = group_begin
cnt = cnt + 1
group_begin = ii + 1
else:
groups_each[group_begin:] = cnt
groups_each_index[group_begin:] = array[0:(num_valids-group_begin)]
groups_index[cnt] = group_begin
groups_index = groups_index[0:(cnt+1)]
print('group_time: %s' % (time.time() - st))
# calculate max num of points in one group/voxel in each plane.
split_each_max = np.zeros(num_planes, dtype=np.uint16)
split_position = np.where((d_position_sorted_1[groups_index] - np.concatenate((np.array([0]), d_position_sorted_1[groups_index][0:-1]))) > 0) # find split position of different planes.
split_each_begin = np.concatenate((np.array([0]), groups_index[split_position])) # split position based on all points, and reserve the begin position. Begin from 0.
split_each_begin_in_group = np.concatenate((np.array([0]), split_position[0])) # split position based on all groups, and reserve the begin position. Begin from 0.
d_valid = d_position_sorted_1[groups_index[split_each_begin_in_group]]
for j in range(len(split_each_begin)):
begin = split_each_begin[j]
if j < (len(split_each_begin_in_group) - 1):
end = split_each_begin[j + 1]
max_num = np.max(groups_each_index[begin:end]) + 1
split_each_max[int(d_valid[j])] = max_num
else:
max_num = np.max(groups_each_index[begin:]) + 1
split_each_max[int(d_valid[j])] = max_num
# Be careful of data type, out of range.
return np.uint16(u_sorted_1), np.uint16(v_sorted_1), np.uint8(d_position_sorted_1), np.uint32(valid_position_sorted_1), \
np.uint32(groups_each), np.uint32(groups_index), np.uint16(groups_each_index), \
np.uint32(split_each_begin), np.uint32(split_each_begin_in_group), np.uint16(split_each_max), \
np.float16(distance_sorted_1)
def Aggregation(npzfile, intrinsic_matrix, extrinsic_matrix, point_clouds, a, b):
select_index = npzfile['select_index'] # select_index begin with 0.
index_in_each_group = npzfile['index_in_each_group']
distance = npzfile['distance']
st = time.time()
transform_matrix = intrinsic_matrix.dot(np.linalg.inv(extrinsic_matrix))
position_image = transform_matrix.dot(point_clouds)
depth_all = position_image[2, :]
depth_selected = depth_all[select_index] * 100 # x 100, m to cm.
# distance to grid center, parallel distance
distance = distance
# distance to depth_min, vertical distance
distance_1 = np.zeros(distance.shape)
each_group_begin = np.where(index_in_each_group == 0)[0]
num_valids = len(select_index)
num_groups = len(each_group_begin)
for i in range(num_groups):
begin = each_group_begin[i]
if (i+1) < num_groups:
end = each_group_begin[i+1]
distance_1[begin:end] = np.min(depth_selected[begin:end])
else:
end = num_valids
distance_1[begin:end] = np.min(depth_selected[begin:end])
distance_1 = depth_selected - distance_1
# print(np.max(distance_1))
# print(np.min(distance_1))
# calculate_weight
weight_1 = (1-distance)**a
weight_2 = 1/(1+distance_1)**b
weight_renew = weight_1*weight_2
weight_average = np.float16(weight_renew) # normalized weight
group_begin = 0
cnt = 1
weight_sum = 0
for ii in range(num_valids):
weight_sum = weight_sum + weight_average[ii]
if cnt < num_groups:
if (ii+1) == each_group_begin[cnt]:
weight_average[group_begin:(ii+1)] = weight_average[group_begin:(ii+1)] / weight_sum
cnt = cnt + 1
group_begin = ii+1
weight_sum = 0
else:
end = num_valids
weight_average[group_begin:end] = weight_average[group_begin:end] / np.sum(weight_average[group_begin:end])
# print(time.time() - st)
return np.float16(weight_average), np.float16(distance_1)
if __name__ == '__main__':
num = 32 # number of planes.
a = 1 # hyperparameter
b = 1 # hyperparameter
scene = 'Matterport3D/29hnd4uzFmX'
dir1 = '../data/%s/undistorted_color_images/' % scene
dir2 = '../data/%s/undistorted_camera_parameters/' % scene
dir3 = '../data/%s/undistorted_depth_images/' % scene
point_clouds_path = '../pre_processing_results/%s/point_clouds_simplified.ply' % scene
output_dir = '../pre_processing_results/%s/reproject_results_%s/' % (scene, num)
output_dir1 = '../pre_processing_results/%s/weight_%s/' % (scene, num)
# meter, valid depth range
near = 0.2
far = 10
resize = True # From 1024*1280 to 512*640.
target_h = 512
target_w = 640
###################################################################################################
image_names_all, depth_names_all, intrinsics_all, extrinsics_all, positions_world = makedataset(dir2)
point_clouds, point_clouds_colors = loadfile(point_clouds_path)
scale_w = (1280-1)/(target_w-1)
scale_h = (1024-1)/(target_h-1)
# Voxelization
if not os.path.isdir(output_dir):
os.makedirs(output_dir)
tmp = 0
for i in range(len(image_names_all)):
if os.path.isfile(output_dir + '%s_compressed.npz' % i):
continue
st = time.time()
depth_name = dir3 + depth_names_all[i]
depth_image = cv2.imread(depth_name, -1) / 4000 # shift 4000
intrinsics_name = intrinsics_all[i]
extrinsics_name = extrinsics_all[i]
intrinsic_matrix, extrinsic_matrix = camera_parameter_read(intrinsics_name, extrinsics_name)
if resize:
intrinsic_matrix[0:1, :] = intrinsic_matrix[0:1, :] / scale_w
intrinsic_matrix[1:2, :] = intrinsic_matrix[1:2, :] / scale_h
u, v, d, index, \
groups_each, groups_index, groups_each_index, \
split_each_begin, split_each_begin_in_group, split_each_max,\
distance = Voxelization(target_w, target_h, intrinsic_matrix, extrinsic_matrix, point_clouds, near, far, num)
print(time.time() - st)
np.savez_compressed(output_dir + '%s_compressed' % i, u=u, v=v, d=d, select_index=index,
group_belongs=groups_each, index_in_each_group=groups_each_index,
distance=distance, each_split_max_num=split_each_max)
print('Voxelization_time: %ss' % (time.time() - st))
# Aggregation
if not os.path.isdir(output_dir1):
os.makedirs(output_dir1)
for i in range(len(image_names_all)):
if os.path.isfile(output_dir1 + '%s_weight.npz' % i):
continue
st = time.time()
depth_name = dir3 + depth_names_all[i]
depth_image = cv2.imread(depth_name, -1) / 4000
intrinsics_name = intrinsics_all[i]
extrinsics_name = extrinsics_all[i]
intrinsic_matrix, extrinsic_matrix = camera_parameter_read(intrinsics_name, extrinsics_name)
if resize:
intrinsic_matrix[0:1, :] = intrinsic_matrix[0:1, :] / scale_w
intrinsic_matrix[1:2, :] = intrinsic_matrix[1:2, :] / scale_h
if not os.path.isfile(output_dir + '%s_compressed.npz' % i):
print('Missing voxelization information!')
continue
npzfile = np.load(output_dir + '%s_compressed.npz' % i)
weight_average, distance_to_depth_min = Aggregation(npzfile, intrinsic_matrix, extrinsic_matrix, point_clouds, a, b)
| np.savez_compressed(output_dir1 + '%s_weight' % i, weight_average=weight_average, distance_to_depth_min=distance_to_depth_min) | numpy.savez_compressed |
import datetime
import os
import arrow
import matplotlib.pyplot as plt
import numpy as np
import open3d as o3
import progressbar
import scipy.interpolate
import cluster
import kittiwrapper
import mapping
import particlefilter
import polesdetection as poles
import util
import makegif as mkgif
dataset = kittiwrapper.kittiwrapper('/app/dataset/kitti_data')
result_dir = '/app/dataset/kitti'
mapextent = np.array([30.0, 30.0, 5.0])
mapsize = np.full(3, 0.1)
mapshape = np.array(mapextent / mapsize, dtype=np.int)
# mapinterval = 3.0
# mapdistance = 5.0
mapinterval = 1.5
mapdistance = 1.5
remapdistance = 10.0
n_mapdetections = 3
n_locdetections = 2
n_localmaps = 3
poles.minscore = 0.6
poles.minheight = 1.0
poles.freelength = 0.5
poles.polesides = range(1, 11)
T_mc_cam0 = np.identity(4)
T_mc_cam0[:3, :3] \
= [[0.0, 0.0, 1.0], [-1.0, 0.0, 0.0], [0.0, -1.0, 0.0]]
T_cam0_mc = util.invert_ht(T_mc_cam0)
T_m_mc = np.identity(4)
T_m_mc[:3, 3] = np.hstack([0.5 * mapextent[:2], 2.0])
T_mc_m = util.invert_ht(T_m_mc)
T_cam0_m = T_cam0_mc.dot(T_mc_m)
globalmapfile = 'globalmap_3.npz'
localmapfile = 'localmaps_3.npz'
locfileprefix = 'localization'
evalfile = 'evaluation.npz'
def get_map_indices(sequence):
distance = np.hstack([0.0, np.cumsum(np.linalg.norm(
| np.diff(sequence.poses[:, :3, 3], axis=0) | numpy.diff |
import sys, os
sys.path.append(os.path.join(os.path.dirname(__file__), '..'))
import argparse, json
import matplotlib.pyplot as plt
import numpy as np
from sklearn.manifold import TSNE
from matplotlib.offsetbox import *
from PIL import Image
from utils.experiments import load_data
def load_image(path):
img = Image.open(path)
img = img.resize((32, 32))
return np.array(img).squeeze()
if __name__ == '__main__':
arg_parser = argparse.ArgumentParser(description='tSNE Plot')
arg_parser.add_argument('task', choices=['mnist', 'cifar', 'bam'], help='name of the task (mnist, cifar)')
arg_parser.add_argument('data_path', help='path to data (not required for original MNIST)')
arg_parser.add_argument('data_split', choices=['train', 'test'], default='test', help='data split (train, test (default))')
arg_parser.add_argument('latent_path', help='path to numpy latent vectors')
arg_parser.add_argument('out_path', help='path to output')
arg_parser.add_argument('--num_points', type=int, default=1000, help='number of data points to plot (default: 1000)')
arg_parser.add_argument('--remove_outliers', type=float, default=0., help='removes outliers outside of n times the standard deviation (default: False)')
arg_parser.add_argument('--eval_task', default='', help='if path to eval JSON is provided, only data points from the task are plotted (default: None)')
arg_parser.add_argument('--tsne_latents', default='', help='if path to tSNE latents is provided, repeated projection will be skipped (default: None)')
args = arg_parser.parse_args()
# load data
images, labels, label_descs, num_labels = load_data(args.task, split=args.data_split, data_path=args.data_path)
cls_idx_map = [i for i in range(num_labels)]
latents = np.load(args.latent_path)
print("Loaded %d latents with dimensionality %d." % (latents.shape[0], latents.shape[1]))
# tSNE
if len(args.tsne_latents) > 0:
tsne_latents = np.load(args.tsne_latents)
print("Loaded tSNE latents from '%s'." % args.tsne_latents)
else:
tsne_model = TSNE(n_components=2, verbose=True)
tsne_latents = tsne_model.fit_transform(latents)
# save transformation
latents_name, latents_ext = os.path.splitext(os.path.basename(args.latent_path))
tsne_path = os.path.join(args.out_path, '%s_tsne%s' % (latents_name, latents_ext))
np.save(tsne_path, tsne_latents)
print("Saved tSNE latents to '%s'." % tsne_path)
# create subset
if len(args.eval_task) > 0:
eval_task = json.load(open(args.eval_task, 'r', encoding='utf8'))
eval_idcs = eval_task['examples'] + [i for task in eval_task['tasks'] for i in task['options']]
other_idcs = [i for i in range(tsne_latents.shape[0]) if i not in eval_idcs]
other_idcs = np.random.choice(other_idcs, args.num_points - len(eval_idcs), replace=False)
subset_idcs = np.concatenate((other_idcs, eval_idcs))
print("Loaded %d data points from eval task '%s'." % (len(eval_idcs), args.eval_task))
else:
subset_idcs = np.random.choice(tsne_latents.shape[0], args.num_points, replace=False)
print("Reduced data points to random subset of size %d." % args.num_points)
tsne_latents = tsne_latents[subset_idcs]
labels = labels[subset_idcs]
# shorten class names for BAM
if args.task == 'bam':
dmap = {'emotion_gloomy': 'g', 'emotion_happy': 'h', 'emotion_peaceful': 'p', 'emotion_scary': 's', 'unspecified': 'u'}
label_descs = [''.join([dmap[e] for e in d.split('+')]) for d in label_descs]
eval_task['classes'] = [''.join([dmap[e] for e in d.split('+')]) for d in eval_task['classes']]
# init alphas
alphas = np.zeros(tsne_latents.shape[0])
# calculate means
mean_latent = np.mean(tsne_latents, axis=0)
std_latent = np.std(tsne_latents, axis=0)
mean_latents = np.zeros([len(label_descs), tsne_latents.shape[1]])
for c in range(num_labels):
lbl_idcs = np.where(labels == (cls_idx_map[c] * np.ones_like(labels)))
mean_latents[c] = np.mean(tsne_latents[lbl_idcs], axis=0)
# calculate alphas
if len(lbl_idcs[0]) > 1:
dists = np.abs(tsne_latents[lbl_idcs] - mean_latents[c])
dists = -np.sum(dists, axis=1)
max_dist = np.max(dists)
alphas[lbl_idcs] = np.clip(dists * (1 / max_dist), .3, None)
else:
alphas[lbl_idcs] = 0.
# remove outliers
if args.remove_outliers > 0:
inlier_idcs = []
for i in range(tsne_latents.shape[0]):
if np.any(np.abs(tsne_latents[i] - mean_latent) > (std_latent * 3.)):
continue
inlier_idcs.append(i)
tsne_latents = tsne_latents[inlier_idcs]
labels = labels[inlier_idcs]
alphas = alphas[inlier_idcs]
subset_idcs = | np.array(subset_idcs) | numpy.array |
import networkx as nx
import numpy as np
import scipy
from numba import jit
from scipy.sparse import isspmatrix
from scipy.special import comb
from . import comdet_functions as cd
from . import cp_functions as cp
def compute_neighbours(adj):
lista_neigh = []
for ii in np.arange(adj.shape[0]):
lista_neigh.append(adj[ii, :].nonzero()[0])
return lista_neigh
@jit(nopython=True)
def compute_cn(adjacency):
""" Computes common neighbours table, each entry i,j of this table is the
number of common neighbours between i and j.
:param adjacency: Adjacency matrix.
:type adjacency: numpy.ndarray
:return: Common neighbours table.
:rtype: numpy.ndarray
"""
cn_table = np.zeros_like(adjacency)
for i in np.arange(adjacency.shape[0]):
neighbour_i = (adjacency[i, :] + adjacency[:, i]).astype(np.bool_)
for j in np.arange(i + 1, adjacency.shape[0]):
neighbour_j = (adjacency[j, :] + adjacency[:, j]).astype(np.bool_)
cn_table[i, j] = cn_table[j, i] = np.multiply(neighbour_i,
neighbour_j).sum()
return cn_table
@jit(nopython=True)
def common_neigh_init_guess_strong(adjacency):
"""Generates a preprocessed initial guess based on the common neighbours
of nodes. It makes a stronger aggregation of nodes based on
the common neighbours similarity.
:param adjacency: Adjacency matrix.
:type adjacency: numpy.ndarray
:return: Initial guess for nodes memberships.
:rtype: np.array
"""
cn_table = compute_cn(adjacency)
memberships = np.array(
[k for k in np.arange(adjacency.shape[0], dtype=np.int32)])
argsorted = np.argsort(adjacency.astype(np.bool_).sum(axis=1))[::-1]
for aux_node1 in argsorted:
aux_tmp = memberships == aux_node1
memberships[aux_tmp] = memberships[np.argmax(cn_table[aux_node1])]
return memberships
@jit(nopython=True)
def common_neigh_init_guess_weak(adjacency):
"""Generates a preprocessed initial guess based on the common neighbours
of nodes. It makes a weaker aggregation of nodes based on
the common neighbours similarity.
:param adjacency: Adjacency matrix.
:type adjacency: numpy.ndarray
:return: Initial guess for nodes memberships.
:rtype: np.array
"""
cn_table = compute_cn(adjacency)
memberships = np.array(
[k for k in np.arange(adjacency.shape[0], dtype=np.int32)])
degree = (adjacency.astype(np.bool_).sum(axis=1)
+ adjacency.astype(np.bool_).sum(axis=0))
avg_degree = np.mean(degree)
argsorted = np.argsort(degree)[::-1]
for aux_node1 in argsorted:
if degree[aux_node1] >= avg_degree:
aux_tmp = memberships == aux_node1
memberships[aux_tmp] = memberships[np.argmax(cn_table[aux_node1])]
return memberships
def eigenvector_init_guess(adjacency, is_directed):
"""Generates an initial guess for core periphery detection method: nodes
with higher eigenvector centrality are in the core.
:param adjacency: Adjacency matrix.
:type adjacency: np.ndarray
:param is_directed: True if the network is directed.
:type is_directed: bool
:return: Initial guess.
:rtype: np.ndarray
"""
# TODO: Vedere come funziona la parte pesata
n_nodes = adjacency.shape[0]
aux_nodes = int(np.ceil((n_nodes * 5) / 100))
if is_directed:
graph = nx.from_numpy_array(adjacency, create_using=nx.DiGraph)
centra = nx.eigenvector_centrality_numpy(graph)
centra1 = np.array([centra[key] for key in centra])
membership = np.ones_like(centra1, dtype=np.int32)
membership[np.argsort(centra1)[::-1][:aux_nodes]] = 0
else:
graph = nx.from_numpy_array(adjacency, create_using=nx.Graph)
centra = nx.eigenvector_centrality_numpy(graph)
centra1 = np.array([centra[key] for key in centra])
membership = np.ones_like(centra1, dtype=np.int32)
membership[np.argsort(centra1)[::-1][:aux_nodes]] = 0
return membership
def fixed_clusters_init_guess_cn(adjacency, n_clust):
""" Generates an intial guess with a fixed number 'n' of clusters.
Nodes are organised in clusters based on the number of common neighbors.
The starting members of clusters are the 'n' nodes with higher
degrees/strengths.
:param adjacency: Adjacency matrix.
:type adjacency: numpy.ndarray
:param n_clust: Partitions number.
:type n_clust: int
:return: Initial guess.
:rtype: numpy.ndarray
"""
aux_memb = np.ones(adjacency.shape[0], dtype=np.int32) * (n_clust - 1)
cn = compute_cn(adjacency)
degree = adjacency.astype(np.bool_).sum(axis=1) + adjacency.astype(
np.bool_).sum(axis=0)
avg_degree = np.mean(degree)
degree_indices_g = np.nonzero(degree > 2)[0]
degree_indices_l = np.nonzero(degree <= 2)[0]
arg_max = np.argmax(degree[degree_indices_g])
clust_element = degree_indices_g[arg_max]
cluster_count = 0
while cluster_count != n_clust - 1:
aux_memb[clust_element] = cluster_count
degree_indices_g = np.delete(degree_indices_g, arg_max)
if len(degree_indices_g) == 0:
break
arg_max = np.argmin(cn[clust_element][degree_indices_g])
clust_element = degree_indices_g[arg_max]
cluster_count += 1
if np.unique(aux_memb).shape[0] < n_clust - 1:
cluster_count += 1
arg_max = np.argmax(degree[degree_indices_l])
clust_element = degree_indices_l[arg_max]
while cluster_count != n_clust - 1:
aux_memb[clust_element] = cluster_count
degree_indices_l = np.delete(degree_indices_l, arg_max)
if len(degree_indices_l) == 0:
raise ValueError(
"The number of clusters is higher thant the nodes number.")
arg_max = np.argmin(cn[clust_element][degree_indices_l])
clust_element = np.argmin(cn[clust_element][degree_indices_l])
cluster_count += 1
aux = np.nonzero(aux_memb == n_clust - 1)[0]
np.random.shuffle(aux)
for node in aux:
if degree[node] < avg_degree:
continue
aux_list = np.nonzero(aux_memb != n_clust - 1)[0]
node_index = aux_list[np.argmax(cn[node, aux_list])]
if isinstance(node_index, np.ndarray):
node_index = np.random.choice(node_index)
aux_memb[node] = aux_memb[node_index]
return aux_memb
def compute_degree(a, is_directed):
"""Returns matrix *a* degree sequence.
:param a: Matrix.
:type a: numpy.ndarray
:param is_directed: True if the matrix is directed.
:type is_directed: bool
:return: Degree sequence.
:rtype: numpy.ndarray.
"""
# if the matrix is a numpy array
if is_directed:
if type(a) == np.ndarray:
return np.sum(a > 0, 0), np.sum(a > 0, 1)
# if the matrix is a scipy sparse matrix
elif isspmatrix(a):
return np.sum(a > 0, 0).A1, np.sum(a > 0, 1).A1
else:
if type(a) == np.ndarray:
return np.sum(a > 0, 1)
# if the matrix is a scipy sparse matrix
elif isspmatrix(a):
return np.sum(a > 0, 1).A1
def compute_strength(a, is_directed):
"""Returns matrix *a* strength sequence.
:param a: Matrix.
:type a: numpy.ndarray
:param is_directed: True if the matrix is directed.
:type is_directed: bool
:return: Strength sequence.
:rtype: numpy.ndarray
"""
if is_directed:
# if the matrix is a numpy array
if type(a) == np.ndarray:
return np.sum(a, 0), np.sum(a, 1)
# if the matrix is a scipy sparse matrix
elif isspmatrix(a):
return np.sum(a, 0).A1, np.sum(a, 1).A1
else:
# if the matrix is a numpy array
if type(a) == np.ndarray:
return np.sum(a, 1)
# if the matrix is a scipy sparse matrix
elif isspmatrix(a):
return np.sum(a, 1).A1
def from_edgelist(edgelist, is_sparse, is_directed):
"""Returns np.ndarray or scipy.sparse matrix from edgelist.
:param edgelist: List of edges, eache edge must be given as a 2-tuples
(u,v).
:type edgelist: list or numpy.ndarray
:param is_sparse: If true the returned matrix is sparse.
:type is_sparse: bool
:param is_directed: If true the graph is directed.
:type is_directed: bool
:return: Adjacency matrix.
:rtype: numpy.ndarray or scipy.sparse
"""
# TODO: vedere che tipo di sparse e'
if is_directed:
g = nx.DiGraph()
else:
g = nx.Graph()
g.add_edges_from(edgelist)
if is_sparse:
return nx.to_scipy_sparse_matrix(g)
else:
return nx.to_numpy_array(g)
def from_weighted_edgelist(edgelist, is_sparse, is_directed):
"""Returns np.ndarray or scipy.sparse matrix from edgelist.
:param edgelist: List of weighted edges, eache edge must be given as a
3-tuples (u,v,w).
:type edgelist: [type]
:param is_sparse: If true the returned matrix is sparse.
:type is_sparse: bool
:param is_directed: If true the graph is directed.
:type is_directed: bool
:return: Weighted adjacency matrix.
:rtype: numpy.ndarray or scipy.sparse
"""
if is_directed:
g = nx.DiGraph()
else:
g = nx.Graph()
g.add_weighted_edges_from(edgelist)
if is_sparse:
return nx.to_scipy_sparse_matrix(g)
else:
return nx.to_numpy_array(g)
def check_symmetric(a, is_sparse, rtol=1e-05, atol=1e-08):
"""Checks if the matrix is symmetric.
:param a: Matrix.
:type a: numpy.ndarray or scipy.sparse
:param is_sparse: If true the matrix is sparse.
:type is_sparse: bool
:param rtol: Tuning parameter, defaults to 1e-05.
:type rtol: float, optional
:param atol: Tuning parameter, defaults to 1e-08.
:type atol: float, optional
:return: True if the matrix is symmetric.
:rtype: bool
"""
if is_sparse:
return np.all(np.abs(a - a.T) < atol)
else:
return np.allclose(a, a.T, rtol=rtol, atol=atol)
def check_adjacency(adjacency, is_sparse, is_directed):
"""Functions checking the _validty_ of the adjacency matrix.
:param adjacency: Adjacency matrix.
:type adjacency: numpy.ndarray or scipy.sparse
:param is_sparse: If true the matrix is sparse.
:type is_sparse: bool
:param is_directed: True if the graph is directed.
:type is_directed: bool
:raises TypeError: Matrix not square.
:raises ValueError: Negative entries.
:raises TypeError: Matrix not symmetric.
"""
if adjacency.shape[0] != adjacency.shape[1]:
raise TypeError(
"Adjacency matrix must be square. If you are passing an edgelist"
" use the positional argument 'edgelist='.")
if np.sum(adjacency < 0):
raise ValueError(
"The adjacency matrix entries must be positive."
)
if (not check_symmetric(adjacency, is_sparse)) and (not is_directed):
raise TypeError(
"The adjacency matrix seems to be not symmetric, we suggest to use"
" 'DirectedGraphClass'.")
@jit(nopython=True, fastmath=True)
def sumLogProbabilities(nextlogp, logp):
if nextlogp == 0:
stop = True
else:
stop = False
if nextlogp > logp:
common = nextlogp
diffexponent = logp - common
else:
common = logp
diffexponent = nextlogp - common
logp = common + ((np.log10(1 + 10 ** diffexponent)) / np.log10(10))
if (nextlogp - logp) > -4:
stop = True
return logp, stop
@jit(nopython=True, fastmath=True)
def logc(n, k):
if k == n:
return 0
elif (n > 1000) & (k > 1000): # Stirling's binomial coeff approximation
return logStirFac(n) - logStirFac(k) - logStirFac(n - k)
else:
t = n - k
if t < k:
t = k
logC = sumRange(t + 1, n) - sumFactorial(n - t)
return logC
@jit(nopython=True, fastmath=True)
def logStirFac(n):
if n <= 1:
return 1.0
else:
return -n + n * np.log10(n) + np.log10(
n * (1 + 4.0 * n * (1.0 + 2.0 * n))) / 6.0 + np.log10(np.pi) / 2.0
@jit(nopython=True, fastmath=True)
def sumRange(xmin, xmax):
"""[summary]
:param xmin: [description]
:type xmin: [type]
:param xmax: [description]
:type xmax: [type]
:return: [description]
:rtype: [type]
"""
csum = 0
for i in | np.arange(xmin, xmax + 1) | numpy.arange |
# This module has been generated automatically from space group information
# obtained from the Computational Crystallography Toolbox
#
"""
Space groups
This module contains a list of all the 230 space groups that can occur in
a crystal. The variable space_groups contains a dictionary that maps
space group numbers and space group names to the corresponding space
group objects.
.. moduleauthor:: <NAME> <<EMAIL>>
"""
#-----------------------------------------------------------------------------
# Copyright (C) 2013 The Mosaic Development Team
#
# Distributed under the terms of the BSD License. The full license is in
# the file LICENSE.txt, distributed as part of this software.
#-----------------------------------------------------------------------------
import numpy as N
class SpaceGroup(object):
"""
Space group
All possible space group objects are created in this module. Other
modules should access these objects through the dictionary
space_groups rather than create their own space group objects.
"""
def __init__(self, number, symbol, transformations):
"""
:param number: the number assigned to the space group by
international convention
:type number: int
:param symbol: the Hermann-Mauguin space-group symbol as used
in PDB and mmCIF files
:type symbol: str
:param transformations: a list of space group transformations,
each consisting of a tuple of three
integer arrays (rot, tn, td), where
rot is the rotation matrix and tn/td
are the numerator and denominator of the
translation vector. The transformations
are defined in fractional coordinates.
:type transformations: list
"""
self.number = number
self.symbol = symbol
self.transformations = transformations
self.transposed_rotations = N.array([N.transpose(t[0])
for t in transformations])
self.phase_factors = N.exp(N.array([(-2j*N.pi*t[1])/t[2]
for t in transformations]))
def __repr__(self):
return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol))
def __len__(self):
"""
:return: the number of space group transformations
:rtype: int
"""
return len(self.transformations)
def symmetryEquivalentMillerIndices(self, hkl):
"""
:param hkl: a set of Miller indices
:type hkl: Scientific.N.array_type
:return: a tuple (miller_indices, phase_factor) of two arrays
of length equal to the number of space group
transformations. miller_indices contains the Miller
indices of each reflection equivalent by symmetry to the
reflection hkl (including hkl itself as the first element).
phase_factor contains the phase factors that must be applied
to the structure factor of reflection hkl to obtain the
structure factor of the symmetry equivalent reflection.
:rtype: tuple
"""
hkls = N.dot(self.transposed_rotations, hkl)
p = N.multiply.reduce(self.phase_factors**hkl, -1)
return hkls, p
space_groups = {}
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(1, 'P 1', transformations)
space_groups[1] = sg
space_groups['P 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(2, 'P -1', transformations)
space_groups[2] = sg
space_groups['P -1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(3, 'P 1 2 1', transformations)
space_groups[3] = sg
space_groups['P 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(4, 'P 1 21 1', transformations)
space_groups[4] = sg
space_groups['P 1 21 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(5, 'C 1 2 1', transformations)
space_groups[5] = sg
space_groups['C 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(6, 'P 1 m 1', transformations)
space_groups[6] = sg
space_groups['P 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(7, 'P 1 c 1', transformations)
space_groups[7] = sg
space_groups['P 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(8, 'C 1 m 1', transformations)
space_groups[8] = sg
space_groups['C 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(9, 'C 1 c 1', transformations)
space_groups[9] = sg
space_groups['C 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(10, 'P 1 2/m 1', transformations)
space_groups[10] = sg
space_groups['P 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(11, 'P 1 21/m 1', transformations)
space_groups[11] = sg
space_groups['P 1 21/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(12, 'C 1 2/m 1', transformations)
space_groups[12] = sg
space_groups['C 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(13, 'P 1 2/c 1', transformations)
space_groups[13] = sg
space_groups['P 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(14, 'P 1 21/c 1', transformations)
space_groups[14] = sg
space_groups['P 1 21/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(15, 'C 1 2/c 1', transformations)
space_groups[15] = sg
space_groups['C 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(16, 'P 2 2 2', transformations)
space_groups[16] = sg
space_groups['P 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(17, 'P 2 2 21', transformations)
space_groups[17] = sg
space_groups['P 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(18, 'P 21 21 2', transformations)
space_groups[18] = sg
space_groups['P 21 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(19, 'P 21 21 21', transformations)
space_groups[19] = sg
space_groups['P 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(20, 'C 2 2 21', transformations)
space_groups[20] = sg
space_groups['C 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(21, 'C 2 2 2', transformations)
space_groups[21] = sg
space_groups['C 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(22, 'F 2 2 2', transformations)
space_groups[22] = sg
space_groups['F 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(23, 'I 2 2 2', transformations)
space_groups[23] = sg
space_groups['I 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(24, 'I 21 21 21', transformations)
space_groups[24] = sg
space_groups['I 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(25, 'P m m 2', transformations)
space_groups[25] = sg
space_groups['P m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(26, 'P m c 21', transformations)
space_groups[26] = sg
space_groups['P m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(27, 'P c c 2', transformations)
space_groups[27] = sg
space_groups['P c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(28, 'P m a 2', transformations)
space_groups[28] = sg
space_groups['P m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(29, 'P c a 21', transformations)
space_groups[29] = sg
space_groups['P c a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(30, 'P n c 2', transformations)
space_groups[30] = sg
space_groups['P n c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(31, 'P m n 21', transformations)
space_groups[31] = sg
space_groups['P m n 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(32, 'P b a 2', transformations)
space_groups[32] = sg
space_groups['P b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(33, 'P n a 21', transformations)
space_groups[33] = sg
space_groups['P n a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(34, 'P n n 2', transformations)
space_groups[34] = sg
space_groups['P n n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(35, 'C m m 2', transformations)
space_groups[35] = sg
space_groups['C m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(36, 'C m c 21', transformations)
space_groups[36] = sg
space_groups['C m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(37, 'C c c 2', transformations)
space_groups[37] = sg
space_groups['C c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(38, 'A m m 2', transformations)
space_groups[38] = sg
space_groups['A m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(39, 'A b m 2', transformations)
space_groups[39] = sg
space_groups['A b m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(40, 'A m a 2', transformations)
space_groups[40] = sg
space_groups['A m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(41, 'A b a 2', transformations)
space_groups[41] = sg
space_groups['A b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(42, 'F m m 2', transformations)
space_groups[42] = sg
space_groups['F m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(43, 'F d d 2', transformations)
space_groups[43] = sg
space_groups['F d d 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(44, 'I m m 2', transformations)
space_groups[44] = sg
space_groups['I m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(45, 'I b a 2', transformations)
space_groups[45] = sg
space_groups['I b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(46, 'I m a 2', transformations)
space_groups[46] = sg
space_groups['I m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(47, 'P m m m', transformations)
space_groups[47] = sg
space_groups['P m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(48, 'P n n n :2', transformations)
space_groups[48] = sg
space_groups['P n n n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(49, 'P c c m', transformations)
space_groups[49] = sg
space_groups['P c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(50, 'P b a n :2', transformations)
space_groups[50] = sg
space_groups['P b a n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(51, 'P m m a', transformations)
space_groups[51] = sg
space_groups['P m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(52, 'P n n a', transformations)
space_groups[52] = sg
space_groups['P n n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(53, 'P m n a', transformations)
space_groups[53] = sg
space_groups['P m n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(54, 'P c c a', transformations)
space_groups[54] = sg
space_groups['P c c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(55, 'P b a m', transformations)
space_groups[55] = sg
space_groups['P b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(56, 'P c c n', transformations)
space_groups[56] = sg
space_groups['P c c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(57, 'P b c m', transformations)
space_groups[57] = sg
space_groups['P b c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(58, 'P n n m', transformations)
space_groups[58] = sg
space_groups['P n n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(59, 'P m m n :2', transformations)
space_groups[59] = sg
space_groups['P m m n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(60, 'P b c n', transformations)
space_groups[60] = sg
space_groups['P b c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(61, 'P b c a', transformations)
space_groups[61] = sg
space_groups['P b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(62, 'P n m a', transformations)
space_groups[62] = sg
space_groups['P n m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(63, 'C m c m', transformations)
space_groups[63] = sg
space_groups['C m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(64, 'C m c a', transformations)
space_groups[64] = sg
space_groups['C m c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(65, 'C m m m', transformations)
space_groups[65] = sg
space_groups['C m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(66, 'C c c m', transformations)
space_groups[66] = sg
space_groups['C c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(67, 'C m m a', transformations)
space_groups[67] = sg
space_groups['C m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(68, 'C c c a :2', transformations)
space_groups[68] = sg
space_groups['C c c a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(69, 'F m m m', transformations)
space_groups[69] = sg
space_groups['F m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(70, 'F d d d :2', transformations)
space_groups[70] = sg
space_groups['F d d d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(71, 'I m m m', transformations)
space_groups[71] = sg
space_groups['I m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(72, 'I b a m', transformations)
space_groups[72] = sg
space_groups['I b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(73, 'I b c a', transformations)
space_groups[73] = sg
space_groups['I b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(74, 'I m m a', transformations)
space_groups[74] = sg
space_groups['I m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(75, 'P 4', transformations)
space_groups[75] = sg
space_groups['P 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(76, 'P 41', transformations)
space_groups[76] = sg
space_groups['P 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(77, 'P 42', transformations)
space_groups[77] = sg
space_groups['P 42'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(78, 'P 43', transformations)
space_groups[78] = sg
space_groups['P 43'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(79, 'I 4', transformations)
space_groups[79] = sg
space_groups['I 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(80, 'I 41', transformations)
space_groups[80] = sg
space_groups['I 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(81, 'P -4', transformations)
space_groups[81] = sg
space_groups['P -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(82, 'I -4', transformations)
space_groups[82] = sg
space_groups['I -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(83, 'P 4/m', transformations)
space_groups[83] = sg
space_groups['P 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(84, 'P 42/m', transformations)
space_groups[84] = sg
space_groups['P 42/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(85, 'P 4/n :2', transformations)
space_groups[85] = sg
space_groups['P 4/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(86, 'P 42/n :2', transformations)
space_groups[86] = sg
space_groups['P 42/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(87, 'I 4/m', transformations)
space_groups[87] = sg
space_groups['I 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(88, 'I 41/a :2', transformations)
space_groups[88] = sg
space_groups['I 41/a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(89, 'P 4 2 2', transformations)
space_groups[89] = sg
space_groups['P 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(90, 'P 4 21 2', transformations)
space_groups[90] = sg
space_groups['P 4 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(91, 'P 41 2 2', transformations)
space_groups[91] = sg
space_groups['P 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(92, 'P 41 21 2', transformations)
space_groups[92] = sg
space_groups['P 41 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(93, 'P 42 2 2', transformations)
space_groups[93] = sg
space_groups['P 42 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(94, 'P 42 21 2', transformations)
space_groups[94] = sg
space_groups['P 42 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(95, 'P 43 2 2', transformations)
space_groups[95] = sg
space_groups['P 43 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(96, 'P 43 21 2', transformations)
space_groups[96] = sg
space_groups['P 43 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(97, 'I 4 2 2', transformations)
space_groups[97] = sg
space_groups['I 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(98, 'I 41 2 2', transformations)
space_groups[98] = sg
space_groups['I 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(99, 'P 4 m m', transformations)
space_groups[99] = sg
space_groups['P 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(100, 'P 4 b m', transformations)
space_groups[100] = sg
space_groups['P 4 b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(101, 'P 42 c m', transformations)
space_groups[101] = sg
space_groups['P 42 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(102, 'P 42 n m', transformations)
space_groups[102] = sg
space_groups['P 42 n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(103, 'P 4 c c', transformations)
space_groups[103] = sg
space_groups['P 4 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(104, 'P 4 n c', transformations)
space_groups[104] = sg
space_groups['P 4 n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(105, 'P 42 m c', transformations)
space_groups[105] = sg
space_groups['P 42 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(106, 'P 42 b c', transformations)
space_groups[106] = sg
space_groups['P 42 b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(107, 'I 4 m m', transformations)
space_groups[107] = sg
space_groups['I 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(108, 'I 4 c m', transformations)
space_groups[108] = sg
space_groups['I 4 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(109, 'I 41 m d', transformations)
space_groups[109] = sg
space_groups['I 41 m d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(110, 'I 41 c d', transformations)
space_groups[110] = sg
space_groups['I 41 c d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(111, 'P -4 2 m', transformations)
space_groups[111] = sg
space_groups['P -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(112, 'P -4 2 c', transformations)
space_groups[112] = sg
space_groups['P -4 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(113, 'P -4 21 m', transformations)
space_groups[113] = sg
space_groups['P -4 21 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(114, 'P -4 21 c', transformations)
space_groups[114] = sg
space_groups['P -4 21 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(115, 'P -4 m 2', transformations)
space_groups[115] = sg
space_groups['P -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(116, 'P -4 c 2', transformations)
space_groups[116] = sg
space_groups['P -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(117, 'P -4 b 2', transformations)
space_groups[117] = sg
space_groups['P -4 b 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(118, 'P -4 n 2', transformations)
space_groups[118] = sg
space_groups['P -4 n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(119, 'I -4 m 2', transformations)
space_groups[119] = sg
space_groups['I -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(120, 'I -4 c 2', transformations)
space_groups[120] = sg
space_groups['I -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(121, 'I -4 2 m', transformations)
space_groups[121] = sg
space_groups['I -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(122, 'I -4 2 d', transformations)
space_groups[122] = sg
space_groups['I -4 2 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(123, 'P 4/m m m', transformations)
space_groups[123] = sg
space_groups['P 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(124, 'P 4/m c c', transformations)
space_groups[124] = sg
space_groups['P 4/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(125, 'P 4/n b m :2', transformations)
space_groups[125] = sg
space_groups['P 4/n b m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(126, 'P 4/n n c :2', transformations)
space_groups[126] = sg
space_groups['P 4/n n c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(127, 'P 4/m b m', transformations)
space_groups[127] = sg
space_groups['P 4/m b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(128, 'P 4/m n c', transformations)
space_groups[128] = sg
space_groups['P 4/m n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(129, 'P 4/n m m :2', transformations)
space_groups[129] = sg
space_groups['P 4/n m m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(130, 'P 4/n c c :2', transformations)
space_groups[130] = sg
space_groups['P 4/n c c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(131, 'P 42/m m c', transformations)
space_groups[131] = sg
space_groups['P 42/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(132, 'P 42/m c m', transformations)
space_groups[132] = sg
space_groups['P 42/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(133, 'P 42/n b c :2', transformations)
space_groups[133] = sg
space_groups['P 42/n b c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(134, 'P 42/n n m :2', transformations)
space_groups[134] = sg
space_groups['P 42/n n m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(135, 'P 42/m b c', transformations)
space_groups[135] = sg
space_groups['P 42/m b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(136, 'P 42/m n m', transformations)
space_groups[136] = sg
space_groups['P 42/m n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(137, 'P 42/n m c :2', transformations)
space_groups[137] = sg
space_groups['P 42/n m c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(138, 'P 42/n c m :2', transformations)
space_groups[138] = sg
space_groups['P 42/n c m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(139, 'I 4/m m m', transformations)
space_groups[139] = sg
space_groups['I 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(140, 'I 4/m c m', transformations)
space_groups[140] = sg
space_groups['I 4/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(141, 'I 41/a m d :2', transformations)
space_groups[141] = sg
space_groups['I 41/a m d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(142, 'I 41/a c d :2', transformations)
space_groups[142] = sg
space_groups['I 41/a c d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(143, 'P 3', transformations)
space_groups[143] = sg
space_groups['P 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(144, 'P 31', transformations)
space_groups[144] = sg
space_groups['P 31'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(145, 'P 32', transformations)
space_groups[145] = sg
space_groups['P 32'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(146, 'R 3 :H', transformations)
space_groups[146] = sg
space_groups['R 3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(147, 'P -3', transformations)
space_groups[147] = sg
space_groups['P -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(148, 'R -3 :H', transformations)
space_groups[148] = sg
space_groups['R -3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(149, 'P 3 1 2', transformations)
space_groups[149] = sg
space_groups['P 3 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(150, 'P 3 2 1', transformations)
space_groups[150] = sg
space_groups['P 3 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(151, 'P 31 1 2', transformations)
space_groups[151] = sg
space_groups['P 31 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(152, 'P 31 2 1', transformations)
space_groups[152] = sg
space_groups['P 31 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(153, 'P 32 1 2', transformations)
space_groups[153] = sg
space_groups['P 32 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(154, 'P 32 2 1', transformations)
space_groups[154] = sg
space_groups['P 32 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(155, 'R 3 2 :H', transformations)
space_groups[155] = sg
space_groups['R 3 2 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(156, 'P 3 m 1', transformations)
space_groups[156] = sg
space_groups['P 3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(157, 'P 3 1 m', transformations)
space_groups[157] = sg
space_groups['P 3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(158, 'P 3 c 1', transformations)
space_groups[158] = sg
space_groups['P 3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(159, 'P 3 1 c', transformations)
space_groups[159] = sg
space_groups['P 3 1 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(160, 'R 3 m :H', transformations)
space_groups[160] = sg
space_groups['R 3 m :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(161, 'R 3 c :H', transformations)
space_groups[161] = sg
space_groups['R 3 c :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(162, 'P -3 1 m', transformations)
space_groups[162] = sg
space_groups['P -3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(163, 'P -3 1 c', transformations)
space_groups[163] = sg
space_groups['P -3 1 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(164, 'P -3 m 1', transformations)
space_groups[164] = sg
space_groups['P -3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(165, 'P -3 c 1', transformations)
space_groups[165] = sg
space_groups['P -3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(166, 'R -3 m :H', transformations)
space_groups[166] = sg
space_groups['R -3 m :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(167, 'R -3 c :H', transformations)
space_groups[167] = sg
space_groups['R -3 c :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(168, 'P 6', transformations)
space_groups[168] = sg
space_groups['P 6'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(169, 'P 61', transformations)
space_groups[169] = sg
space_groups['P 61'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(170, 'P 65', transformations)
space_groups[170] = sg
space_groups['P 65'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(171, 'P 62', transformations)
space_groups[171] = sg
space_groups['P 62'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(172, 'P 64', transformations)
space_groups[172] = sg
space_groups['P 64'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(173, 'P 63', transformations)
space_groups[173] = sg
space_groups['P 63'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(174, 'P -6', transformations)
space_groups[174] = sg
space_groups['P -6'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(175, 'P 6/m', transformations)
space_groups[175] = sg
space_groups['P 6/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(176, 'P 63/m', transformations)
space_groups[176] = sg
space_groups['P 63/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(177, 'P 6 2 2', transformations)
space_groups[177] = sg
space_groups['P 6 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(178, 'P 61 2 2', transformations)
space_groups[178] = sg
space_groups['P 61 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(179, 'P 65 2 2', transformations)
space_groups[179] = sg
space_groups['P 65 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(180, 'P 62 2 2', transformations)
space_groups[180] = sg
space_groups['P 62 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(181, 'P 64 2 2', transformations)
space_groups[181] = sg
space_groups['P 64 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(182, 'P 63 2 2', transformations)
space_groups[182] = sg
space_groups['P 63 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(183, 'P 6 m m', transformations)
space_groups[183] = sg
space_groups['P 6 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(184, 'P 6 c c', transformations)
space_groups[184] = sg
space_groups['P 6 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(185, 'P 63 c m', transformations)
space_groups[185] = sg
space_groups['P 63 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(186, 'P 63 m c', transformations)
space_groups[186] = sg
space_groups['P 63 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(187, 'P -6 m 2', transformations)
space_groups[187] = sg
space_groups['P -6 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(188, 'P -6 c 2', transformations)
space_groups[188] = sg
space_groups['P -6 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(189, 'P -6 2 m', transformations)
space_groups[189] = sg
space_groups['P -6 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(190, 'P -6 2 c', transformations)
space_groups[190] = sg
space_groups['P -6 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(191, 'P 6/m m m', transformations)
space_groups[191] = sg
space_groups['P 6/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(192, 'P 6/m c c', transformations)
space_groups[192] = sg
space_groups['P 6/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(193, 'P 63/m c m', transformations)
space_groups[193] = sg
space_groups['P 63/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(194, 'P 63/m m c', transformations)
space_groups[194] = sg
space_groups['P 63/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(195, 'P 2 3', transformations)
space_groups[195] = sg
space_groups['P 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(196, 'F 2 3', transformations)
space_groups[196] = sg
space_groups['F 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(197, 'I 2 3', transformations)
space_groups[197] = sg
space_groups['I 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(198, 'P 21 3', transformations)
space_groups[198] = sg
space_groups['P 21 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(199, 'I 21 3', transformations)
space_groups[199] = sg
space_groups['I 21 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(200, 'P m -3', transformations)
space_groups[200] = sg
space_groups['P m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(201, 'P n -3 :2', transformations)
space_groups[201] = sg
space_groups['P n -3 :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(202, 'F m -3', transformations)
space_groups[202] = sg
space_groups['F m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(203, 'F d -3 :2', transformations)
space_groups[203] = sg
space_groups['F d -3 :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(204, 'I m -3', transformations)
space_groups[204] = sg
space_groups['I m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(205, 'P a -3', transformations)
space_groups[205] = sg
space_groups['P a -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(206, 'I a -3', transformations)
space_groups[206] = sg
space_groups['I a -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(207, 'P 4 3 2', transformations)
space_groups[207] = sg
space_groups['P 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(208, 'P 42 3 2', transformations)
space_groups[208] = sg
space_groups['P 42 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(209, 'F 4 3 2', transformations)
space_groups[209] = sg
space_groups['F 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(210, 'F 41 3 2', transformations)
space_groups[210] = sg
space_groups['F 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(211, 'I 4 3 2', transformations)
space_groups[211] = sg
space_groups['I 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(212, 'P 43 3 2', transformations)
space_groups[212] = sg
space_groups['P 43 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(213, 'P 41 3 2', transformations)
space_groups[213] = sg
space_groups['P 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(214, 'I 41 3 2', transformations)
space_groups[214] = sg
space_groups['I 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(215, 'P -4 3 m', transformations)
space_groups[215] = sg
space_groups['P -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(216, 'F -4 3 m', transformations)
space_groups[216] = sg
space_groups['F -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(217, 'I -4 3 m', transformations)
space_groups[217] = sg
space_groups['I -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(218, 'P -4 3 n', transformations)
space_groups[218] = sg
space_groups['P -4 3 n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(219, 'F -4 3 c', transformations)
space_groups[219] = sg
space_groups['F -4 3 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(220, 'I -4 3 d', transformations)
space_groups[220] = sg
space_groups['I -4 3 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(221, 'P m -3 m', transformations)
space_groups[221] = sg
space_groups['P m -3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(222, 'P n -3 n :2', transformations)
space_groups[222] = sg
space_groups['P n -3 n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(223, 'P m -3 n', transformations)
space_groups[223] = sg
space_groups['P m -3 n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(224, 'P n -3 m :2', transformations)
space_groups[224] = sg
space_groups['P n -3 m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(225, 'F m -3 m', transformations)
space_groups[225] = sg
space_groups['F m -3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = | N.array([0,0,-1,0,-1,0,-1,0,0]) | numpy.array |
from evo_spotis.mcda_methods import SPOTIS
from evo_spotis.additions import rank_preferences
import unittest
import numpy as np
# Test for SPOTIS method
class Test_SPOTIS(unittest.TestCase):
def test_spotis(self):
"""Test based on paper <NAME>., <NAME>., <NAME>., & <NAME>. (2020, July).
The SPOTIS rank reversal free method for multi-criteria decision-making support.
In 2020 IEEE 23rd International Conference on Information Fusion (FUSION) (pp. 1-8).
IEEE."""
matrix = np.array([[15000, 4.3, 99, 42, 737],
[15290, 5.0, 116, 42, 892],
[15350, 5.0, 114, 45, 952],
[15490, 5.3, 123, 45, 1120]])
weights = np.array([0.2941, 0.2353, 0.2353, 0.0588, 0.1765])
types = np.array([-1, -1, -1, 1, 1])
bounds_min = np.array([14000, 3, 80, 35, 650])
bounds_max = np.array([16000, 8, 140, 60, 1300])
bounds = np.vstack((bounds_min, bounds_max))
method = SPOTIS()
test_result = method(matrix, weights, types, bounds)
real_result = | np.array([0.4779, 0.5781, 0.5558, 0.5801]) | numpy.array |
import numpy as np
def get_trajectory_txt(trajectory):
cell = trajectory.get_cells()[0]
a = np.linalg.norm(cell[0])
b = np.linalg.norm(cell[1])
c = np.linalg.norm(cell[2])
alpha = np.arccos(np.dot(cell[1], cell[2])/(c*b))
gamma = np.arccos(np.dot(cell[1], cell[0])/(a*b))
beta = np.arccos(np.dot(cell[2], cell[0])/(a*c))
xhi = a
xy = b * np.cos(gamma)
xz = c * np.cos(beta)
yhi = np.sqrt(pow(b,2)- pow(xy,2))
yz = (b*c*np.cos(alpha)-xy * xz)/yhi
zhi = np.sqrt(pow(c,2)-pow(xz,2)-pow(yz,2))
xhi = xhi + max(0,0, xy, xz, xy+xz)
yhi = yhi + max(0,0, yz)
xlo_bound = np.min([0.0, xy, xz, xy+xz])
xhi_bound = xhi + np.max([0.0, xy, xz, xy+xz])
ylo_bound = np.min([0.0, yz])
yhi_bound = yhi + np.max([0.0, yz])
zlo_bound = 0
zhi_bound = zhi
ind = trajectory.get_array('steps')
lammps_data_file = ''
for i, position_step in enumerate(trajectory.get_positions()):
lammps_data_file += 'ITEM: TIMESTEP\n'
lammps_data_file += '{}\n'.format(ind[i])
lammps_data_file += 'ITEM: NUMBER OF ATOMS\n'
lammps_data_file += '{}\n'.format(len(position_step))
lammps_data_file += 'ITEM: BOX BOUNDS xy xz yz pp pp pp\n'
lammps_data_file += '{0:20.10f} {1:20.10f} {2:20.10f}\n'.format(xlo_bound, xhi_bound, xy)
lammps_data_file += '{0:20.10f} {1:20.10f} {2:20.10f}\n'.format(ylo_bound, yhi_bound, xz)
lammps_data_file += '{0:20.10f} {1:20.10f} {2:20.10f}\n'.format(zlo_bound, zhi_bound, yz)
lammps_data_file += ('ITEM: ATOMS x y z\n')
for position in position_step:
lammps_data_file += '{0:20.10f} {1:20.10f} {2:20.10f}\n'.format(*position)
return lammps_data_file
def parameters_to_input_file(parameters_object):
parameters = parameters_object.get_dict()
input_file = ('STRUCTURE FILE POSCAR\nPOSCAR\n\n')
input_file += ('FORCE CONSTANTS\nFORCE_CONSTANTS\n\n')
input_file += ('PRIMITIVE MATRIX\n')
input_file += ('{} {} {} \n').format(*np.array(parameters['primitive'])[0])
input_file += ('{} {} {} \n').format(*np.array(parameters['primitive'])[1])
input_file += ('{} {} {} \n').format(*np.array(parameters['primitive'])[2])
input_file += ('\n')
input_file += ('SUPERCELL MATRIX PHONOPY\n')
input_file += ('{} {} {} \n').format(*np.array(parameters['supercell'])[0])
input_file += ('{} {} {} \n').format(* | np.array(parameters['supercell']) | numpy.array |
import os
import time
import yaml
import pickle
import numpy as np
from random import shuffle
from sklearn.neighbors import KDTree
ALL_LAYERS = np.array([[8,2],
[8,4],
[8,6],
[8,8],
[13,2],
[13,4],
[13,6],
[13,8],
[17,2],
[17,4]])
def construct_dataset(paths, nb_samples, feature_names):
t0 = time.time()
nb_processed = 0
hits_a = []
hits_b = []
targets = []
print("Sampling hit pairs for training dataset. \nWARNING: ASSUMING FIRST 3 FEATURES OF HITS ARE XYZ")
for i, path in enumerate(paths):
sample = load_event(path)
hits, particle_ids, vols, layers = process_sample(sample, feature_names)
h_a, h_b, t = build_pairs(hits, particle_ids, vols, layers)
hits_a.extend(h_a)
hits_b.extend(h_b)
targets.extend(t)
if (i%2)==0:
elapsed = (time.time() - t0)/60
remain = (nb_samples-len(hits_a)) / len(hits_a) * elapsed # THIS ALGORITHM IS OFF??
print("file {:4d}, {:8d}. Elapsed: {:4.1f}m, Remain: {:4.1f}m".format(i,
len(hits_a), elapsed, remain))
if len(hits_a) > nb_samples:
break
return (hits_a[:nb_samples], hits_b[:nb_samples], targets[:nb_samples])
def process_sample(sample, feature_names):
hits = sample[0]
truth = sample[1]
volume_ids = hits['volume_id'].values
layer_ids = hits['layer_id'].values
hits = hits[feature_names].values.tolist()
particle_ids = truth['particle_id'].values.tolist()
return hits, particle_ids, volume_ids, layer_ids
def get_dense_pairs(hits, where_track):
hits_a = []
hits_b = []
len_track = len(where_track)
for i in range(len_track):
for j in range(len_track):
hits_a.append(hits[where_track[i]])
hits_b.append(hits[where_track[j]])
return hits_a, hits_b
def is_match(hit_id_a, hit_id_b, vols, layers):
va = vols[hit_id_a]
vb = vols[hit_id_b]
la = layers[hit_id_a]
lb = layers[hit_id_b]
for i, p in enumerate(ALL_LAYERS):
if (p==[va, la]).all():
if i==0:
match_lower = False
else:
match_lower = ([vb,lb]==ALL_LAYERS[i-1]).all()
if (i+1)==len(ALL_LAYERS):
match_upper=False
else:
match_upper = ([vb,lb]==ALL_LAYERS[i+1]).all()
if match_lower or match_upper:
return True
return False
def get_true_pairs_layerwise(hits, where_track, vols, layers):
hits_a = []
hits_b = []
len_track = len(where_track)
for i in range(len_track):
for j in range((i+1), len_track):
ha = where_track[i]
hb = where_track[j]
if is_match(ha, hb, vols, layers):
hits_a.append(hits[ha])
hits_b.append(hits[hb])
hits_a.append(hits[hb])
hits_b.append(hits[ha])
return hits_a, hits_b
# def get_true_pairs_layerwise(hits, where_track, z):
# sorted_by_z = np.argsort(z[where_track]).tolist()
# track_hits = [hits[i] for i in where_track]
# track_hits = [track_hits[s] for s in sorted_by_z]
#
# hits_a = []
# hits_b = []
# len_track = len(where_track)
# nb_processed = 0
# for i in range(len_track):
# lower_bound = i-min(1,nb_processed)
# upper_bound = i+min(2,len_track-nb_processed)
# for j in range(lower_bound, upper_bound):
# hits_a.append(track_hits[i])
# hits_b.append(track_hits[j])
# nb_processed += 1
#
# return hits_a, hits_b
#
def get_false_pairs(hits, where_track, particle_ids, pid, nb_false_pairs):
h_a = []
h_b = []
where_not_track = np.where(particle_ids!=pid)[0]
where_not_track = list(np.random.choice(where_not_track, nb_false_pairs, replace=False))
seed_hit = hits[where_track[np.random.randint(len(where_track))]]
track_hit_order = list(np.random.choice(where_track, nb_false_pairs))
for i,j in zip(track_hit_order, where_not_track):
h_a.append(hits[i])
h_b.append(hits[j])
return h_a, h_b
def get_pairs_one_pid(hits, particle_ids, pid, z, vols, layers):
where_track = list(np.where(particle_ids==pid)[0])
# h_true_a, h_true_b = get_dense_pairs(hits, where_track)
h_true_a, h_true_b = get_true_pairs_layerwise(hits, where_track, vols, layers)
target_true = [1] * len(h_true_a)
if len(h_true_a)==0:
return [], [], []
h_false_a, h_false_b = get_false_pairs(hits, where_track, particle_ids, pid, len(h_true_a))
target_false = [0] * len(h_false_a)
return h_true_a+h_false_a, h_true_b+h_false_b, target_true+target_false
def build_pairs(hits, particle_ids, vols, layers, nb_particles_per_sample=2000):
unique_pids = list(set(particle_ids))
unique_pids.remove(0)
pids = np.array(particle_ids)
shuffle(unique_pids)
hits_a = []
hits_b = []
target = []
z = np.array(hits)[:,2]
for i in range(nb_particles_per_sample):
pid = unique_pids[i]
h_a, h_b, t = get_pairs_one_pid(hits, pids, pid, z, vols, layers)
hits_a.extend(h_a)
hits_b.extend(h_b)
target.extend(t)
return hits_a, hits_b, target
def combine_samples(hits_a, hits_b, targets):
t = np.array(targets, dtype=np.float32).reshape(-1,1)
return np.concatenate((hits_a, hits_b, t),axis=1).astype(np.float32)
def preprocess_dataset(paths, nb_samples, feature_names):
h_a, h_b, t = construct_dataset(paths, nb_samples, feature_names)
dataset = combine_samples(h_a, h_b, t)
mean, std = extract_stats(h_a, h_b)
stats = {'mean':mean, 'std':std}
return dataset, stats
def extract_stats(h_a, h_b):
h_a = | np.array(h_a, dtype=np.float32) | numpy.array |
# Ignoring some linting rules in tests
# pylint: disable=redefined-outer-name
# pylint: disable=missing-docstring
import numpy as np
from bingo.evaluation.fitness_function import FitnessFunction
from bingo.evolutionary_algorithms.mu_plus_lambda import MuPlusLambda
from bingo.selection.tournament import Tournament
from bingo.evaluation.evaluation import Evaluation
from bingo.evolutionary_optimizers.island import Island
from bingo.local_optimizers.continuous_local_opt \
import ContinuousLocalOptimization
from bingo.chromosomes.multiple_values \
import SinglePointCrossover, SinglePointMutation
from bingo.chromosomes.multiple_floats import MultipleFloatChromosomeGenerator
class ZeroMinFitnessFunction(FitnessFunction):
def __call__(self, individual):
return np.linalg.norm(individual.values)
def get_random_float():
return np.random.random_sample() * 2.
def main():
crossover = SinglePointCrossover()
mutation = SinglePointMutation(get_random_float)
selection = Tournament(10)
fitness = ZeroMinFitnessFunction()
local_opt_fitness = ContinuousLocalOptimization(fitness)
evaluator = Evaluation(local_opt_fitness)
ea = MuPlusLambda(evaluator, selection, crossover, mutation, 0.4, 0.4, 20)
generator = MultipleFloatChromosomeGenerator(get_random_float, 8)
island = Island(ea, generator, 25)
island.evolve(1)
report_max_min_mean_fitness(island)
island.evolve(500)
report_max_min_mean_fitness(island)
def report_max_min_mean_fitness(island):
fitness = [indv.fitness for indv in island.population]
print("Max fitness: \t", np.max(fitness))
print("Min fitness: \t", | np.min(fitness) | numpy.min |
# This import you need
from models.adatk_model import ADAModel
# Everything else depends on what your model requires
import numpy as np
import wx
import array
import tempfile
import os.path
import os
try:
import Image
except ImportError: # Use alternate PIL module loading
from PIL import Image
import cv2
# All ADA Models must be a subclass of ADAModel
class CompositeADABasic1(ADAModel):
# All ADA Models must define the following information fields.
name = "composites ADA basic 1"
description = "Composites ADA - Basic Model 1"
authors = "Computational Tools and TRI/Austin, Inc."
version = "1.1"
url = "www.nditoolbox.com"
copyright = ""
def __init__(self):
ADAModel.__init__(self, self.name, self.description, self.inputdata, self.outputdata, self.indcalls,
self.indmetrics, self.inddata, self.params, self.settings)
def run(self):
"""Executes the ADA Model"""
# Example busy work
print("Input Data Configuration:")
for key, value in self.inputdata.iteritems():
print("\t{0}={1}".format(key, value))
print("\nOutput Data Configuration:")
for key, value in self.outputdata.iteritems():
print("\t{0}={1}".format(key, value))
print("\nIndication Calls Configuration:")
for key, value in self.indcalls.iteritems():
print("\t{0}={1}".format(key, value))
print("\nIndication Metrics Configuration:")
for key, value in self.indmetrics.iteritems():
print("\t{0}={1}".format(key, value))
print("\nIndication Data Configuration:")
for key, value in self.inddata.iteritems():
print("\t{0}={1}".format(key, value))
print("\nParameters Configuration:")
for key, value in self.params.iteritems():
print("\t{0}={1}".format(key, value))
print("\nSettings Configuration:")
for key, value in self.settings.iteritems():
print("\t{0}={1}".format(key, value))
print("\n")
############################################################################
self.select_filename()
filepath = self.filenm
#ext = ".rf"
if ".rf" in filepath:
self.load_rf()
#
self.para_a1 = 0.500 # %FSH or largest signal for frontwall / backwall calls = 64
self.para_a2 = 0.500 # %FSH for second signal threshold (making feature calls) = 51
self.para_a3 = 0.280 # %FSH for through thickness features (making feature calls) - defect features
self.para_a4 = 0.500 # %drop from FSH for backwall signal
self.para_t1 = 24 # time offset 1 - ringdown for front wall signal
self.para_t2 = 9 # time offset 2 - ringdown before back wall signal
self.para_c1 = 9 # 9 pixels in total area
self.para_c2 = 3 # 3 pixels wide
self.para_c3 = 3 # 3 pixels long
#
elif ".sdt" in filepath:
self.load_sdt()
#
self.para_a1 = 0.500 # %FSH or largest signal for frontwall / backwall calls = 64
self.para_a2 = 0.398 # %FSH for second signal threshold (making feature calls) = 51
self.para_a3 = 0.280 # %FSH for through thickness features (making feature calls) - defect features
self.para_a4 = 0.500 # %drop from FSH for backwall signal
self.para_t1 = 380 # time offset 1 - ringdown for front wall signal
self.para_t2 = 75 # time offset 2 - ringdown before back wall signal
self.para_c1 = 9 # 9 pixels in total area
self.para_c2 = 3 # 3 pixels wide
self.para_c3 = 3 # 3 pixels long
#
#else:
# return
#
Nx, Ny, Nt = self.inter_data.shape
#
datatmp_1mx = self.inter_data.max(2)
datatmp_1mn = self.inter_data.min(2)
datatmp_1 = datatmp_1mx - datatmp_1mn
#
data_1 = datatmp_1.astype('f')
#data_1 = data_1 - 128.0
#
datatmp_2 = self.inter_data.argmax(2) + self.inter_data.argmin(2)
data_2 = 0.5*datatmp_2.astype('f')
########################################
# evaluate mean A-scan signal
t = np.array([np.arange(0, Nt, 1)])
datatmp_5 = self.inter_data.mean(0)
datatmp_6 = datatmp_5.mean(0)
ta = np.zeros((2,Nt))
for idx in range(Nt):
ta[0,idx] = t[0,idx]
ta[1,idx] = datatmp_6[idx]
#
#
# step 1a) call all transitions
datatmp1mxa = datatmp_1mx.max(0)
datatmp1mx = datatmp1mxa.max() - 128.0
#
self.para1x = round(self.para_a1*datatmp1mx)
self.para2x = round(self.para_a2*datatmp1mx)
self.para3x = round(2.0*self.para_a3*datatmp1mx)
self.para4x = round(self.para_a4*datatmp1mx)
#
data_m1a = np.zeros((Nx,Ny)) # near surface map - TOF (1st cross)
data_m1t = np.zeros((Nx,Ny)) # near surface map - AMP (global)
data_m2a = np.zeros((Nx,Ny)) # near surface map - AMP
data_m2b = np.zeros((Nx,Ny)) # near surface map - TOF (1st cross)
data_m2t = np.zeros((Nx,Ny)) # near surface map - TOF (peak)
data_m3a = | np.zeros((Nx,Ny)) | numpy.zeros |
"""
@brief test log(time=120s)
"""
import unittest
import warnings
import sys
from logging import getLogger
from contextlib import redirect_stdout
from io import StringIO
import numpy
import onnx
from scipy.sparse import coo_matrix, csr_matrix, SparseEfficiencyWarning
from scipy.special import ( # pylint: disable=E0611
expit as logistic_sigmoid, erf)
from scipy.spatial.distance import cdist
from onnx import TensorProto, __version__ as onnx_version
from onnx.helper import make_sparse_tensor, make_tensor
from onnx.defs import onnx_opset_version
from onnx.numpy_helper import from_array
from pyquickhelper.pycode import ExtTestCase
from pyquickhelper.texthelper import compare_module_version
from sklearn.utils.extmath import softmax
try:
from sklearn.utils._testing import ignore_warnings
except ImportError:
from sklearn.utils.testing import ignore_warnings
from skl2onnx.algebra.onnx_ops import ( # pylint: disable=E0611
OnnxAbs, OnnxAdd, OnnxAnd,
OnnxArgMax_11, OnnxArgMax,
OnnxArgMin_11, OnnxArgMin,
OnnxBatchNormalization,
OnnxAcos, OnnxAcosh, OnnxAsin, OnnxAsinh, OnnxAtan, OnnxAtanh,
OnnxAveragePool,
OnnxCast, OnnxCeil, OnnxClip,
OnnxCompress,
OnnxConcat, OnnxConv, OnnxConvTranspose,
OnnxConstant, OnnxConstant_9, OnnxConstant_11,
OnnxConstant_12, OnnxConstant_13,
OnnxConstantOfShape,
OnnxCos, OnnxCosh,
OnnxCumSum,
OnnxDequantizeLinear,
OnnxDet, OnnxDiv,
OnnxDropout, OnnxDropout_7,
OnnxEinsum, OnnxEqual, OnnxErf, OnnxExp, OnnxEyeLike,
OnnxFlatten, OnnxFloor,
OnnxGreater, OnnxGreaterOrEqual, OnnxGemm, OnnxGlobalAveragePool,
OnnxIdentity, OnnxIsNaN,
OnnxLess, OnnxLessOrEqual,
OnnxLog, OnnxLpNormalization,
OnnxMatMul, OnnxMax, OnnxMaxPool, OnnxMean, OnnxMin, OnnxMod, OnnxMul,
OnnxNeg, OnnxNot,
OnnxOr,
OnnxPad, OnnxPow,
OnnxQLinearConv, OnnxQuantizeLinear,
OnnxRange,
OnnxReciprocal,
OnnxReduceL1, OnnxReduceL2,
OnnxReduceLogSumExp, OnnxReduceMax, OnnxReduceMean, OnnxReduceMin,
OnnxReduceProd,
OnnxReduceSum, OnnxReduceSumApi11, OnnxReduceSum_11, OnnxReduceSum_1,
OnnxReduceSumSquare,
OnnxRelu, OnnxReshape,
OnnxRound,
OnnxScatterElements, OnnxShape, OnnxSlice, OnnxSigmoid, OnnxSign,
OnnxSin, OnnxSinh,
OnnxSize, OnnxSoftmax,
OnnxSplit, OnnxSplitApi11,
OnnxSqrt, OnnxSub, OnnxSum,
OnnxSqueeze, OnnxSqueezeApi11,
OnnxTan, OnnxTanh, OnnxTopK, OnnxTranspose,
OnnxUnsqueeze, OnnxUnsqueezeApi11
)
try:
from skl2onnx.algebra.onnx_ops import OnnxCelu
except ImportError:
OnnxCelu = None
try:
from skl2onnx.algebra.onnx_ops import OnnxBatchNormalization_14
except ImportError:
OnnxBatchNormalization_14 = None
from skl2onnx import __version__ as skl2onnx_version, __max_supported_opset__
from mlprodict.onnxrt import OnnxInference
from mlprodict.tools.asv_options_helper import (
get_opset_number_from_onnx, get_ir_version_from_onnx)
from mlprodict.onnxrt.validate.validate_python import validate_python_inference
from mlprodict.onnxrt.ops_cpu.op_batch_normalization import (
_batchnorm_test_mode, _batchnorm_training_mode)
from mlprodict.onnxrt.ops_cpu.op_average_pool import (
_get_output_shape, _pool, _get_pad_shape)
from mlprodict.onnxrt.ops_cpu.op_global_average_pool import _global_average_pool
from mlprodict.onnxrt.ops_cpu._op_onnx_numpy import ( # pylint: disable=E0611,E0401
topk_element_min_double, topk_element_max_double,
topk_element_fetch_double,
topk_element_min_float, topk_element_max_float, topk_element_fetch_float,
topk_element_min_int64, topk_element_max_int64, topk_element_fetch_int64)
from mlprodict.onnxrt.ops_cpu.op_celu import _vcelu1, pycelu
from mlprodict.onnxrt.ops_cpu.op_topk import topk_sorted_implementation
from mlprodict.onnxrt.ops_cpu.op_pad import _pad_impl
from mlprodict.onnxrt.ops_cpu.op_max_pool import (
_pool_get_output_shape, _pool_impl)
from mlprodict.onnxrt.ops_cpu.op_dropout import _dropout
from mlprodict.onnxrt.ops_cpu._op_helper import proto2dtype
from mlprodict.onnx_tools.onnx2py_helper import (
guess_proto_dtype, _elem_type_as_str)
from mlprodict.tools.data_types import (
FloatTensorType, Int64TensorType, DoubleTensorType, StringTensorType,
Int32TensorType, BooleanTensorType, UInt8TensorType,
Int16TensorType, Int8TensorType, UInt16TensorType,
UInt32TensorType, UInt64TensorType, Float16TensorType)
from mlprodict.testing.test_utils.quantized_tensor import (
QuantizedTensor, QuantizedBiasTensor, test_qlinear_conv)
from mlprodict.onnxrt.ops_cpu.op_qlinear_conv_ import ( # pylint: disable=W0611,E0611,E0401
test_qgemm0, test_qgemm1)
from mlprodict.onnxrt.ops_cpu.op_constant import Constant_12, Constant_11, Constant_9
try:
numpy_str = numpy.str_
except ImportError:
numpy_str = str
try:
numpy_bool = numpy.bool_
except ImportError:
numpy_bool = bool
sparse_support = []
sparse_no_numpy = []
python_tested = []
def make_coo_matrix(*args, **kwargs):
coo = coo_matrix(*args, **kwargs)
coo.row = coo.row.astype(numpy.int64)
coo.col = coo.col.astype(numpy.int64)
return coo
def wraplog():
# from datetime import datetime
def wrapper(fct):
def call_f(self):
# no = datetime.now()
# print('BEGIN %s' % fct.__name__)
with warnings.catch_warnings(record=True):
warnings.simplefilter("always", DeprecationWarning)
fct(self)
# print('DONE %s - %r' % (fct.__name__, datetime.now() - no))
return call_f
return wrapper
class TestOnnxrtPythonRuntime(ExtTestCase): # pylint: disable=R0904
@classmethod
def setUpClass(cls):
pass
@classmethod
def tearDownClass(cls):
if __name__ == "__main__":
import pprint
print('-----------')
pprint.pprint(sparse_support)
print('-----------')
pprint.pprint(sparse_no_numpy)
print('-----------')
pprint.pprint(
list(sorted({_.__name__ for _ in python_tested})))
print('-----------')
def setUp(self):
logger = getLogger('skl2onnx')
logger.disabled = True
def test_opset_skl2onnx(self):
opset_mlprodict = get_opset_number_from_onnx()
opset_skl2onnx = __max_supported_opset__
self.assertGreater(opset_skl2onnx, opset_mlprodict)
def common_expected_shapes_types(self, oinf, inputs, got, onnx_cl, model_def,
raise_shape=False):
expected_types = oinf.infer_types()
self.assertEqual(set(got) & set(expected_types), set(got))
for k, v in got.items():
if expected_types[k] in (str, numpy.str_):
# Type mismatch: dtype('<U32') != <class 'str'>
continue
if v.dtype != expected_types[k]:
raise AssertionError(
"Type mismatch: %r != %r\nexpected_types=%r\ngot=%r"
"\n----\n%r" % (
v.dtype, expected_types[k], expected_types, got,
model_def))
try:
expected_shapes = oinf.infer_shapes()
self.assertEqual(set(got) & set(expected_shapes), set(got))
except RuntimeError as e:
if raise_shape:
raise e
warnings.warn("infer_shapes fails for operator %r." % onnx_cl)
res = oinf.infer_sizes(inputs)
self.assertIsInstance(res, dict)
@ignore_warnings(category=(RuntimeWarning, DeprecationWarning,
SparseEfficiencyWarning, PendingDeprecationWarning))
def common_test_onnxt_runtime_unary(self, onnx_cl, np_fct,
op_version=None,
outputs=None, debug=False,
do_sparse=True, raise_shape=False):
if op_version is None:
op_version = get_opset_number_from_onnx()
try:
onx = onnx_cl('X', output_names=['Y'], op_version=op_version)
except RuntimeError as e:
raise RuntimeError('onnx.opset={} op_version={}'.format(
get_opset_number_from_onnx(), op_version)) from e
X = numpy.array([[1, 2], [3, -4]], dtype=numpy.float64)
model_def = onx.to_onnx(
{'X': X.astype(numpy.float32)}, target_opset=op_version,
outputs=outputs)
if debug:
print(model_def)
python_tested.append(onnx_cl)
# python code
oinfpy = OnnxInference(model_def, runtime="python", inplace=True)
validate_python_inference(oinfpy, {'X': X.astype(numpy.float32)})
# no inplace
oinf = OnnxInference(model_def, inplace=False)
all_names = "\n".join(
"%s>=v%d" % (op.ops_.__class__.__name__,
op.ops_._schema.since_version) # pylint: disable=W0212
for op in oinf.sequence_)
if debug:
got = oinf.run({'X': X.astype(numpy.float32)},
verbose=1, fLOG=print)
else:
got = oinf.run({'X': X.astype(numpy.float32)})
self.assertEqual(list(sorted(got)), ['Y'])
self.common_expected_shapes_types(
oinf, {'X': X.astype(numpy.float32)}, got, onnx_cl,
model_def, raise_shape=raise_shape)
try:
self.assertEqualArray(np_fct(X), got['Y'], decimal=5)
except AssertionError as e:
raise AssertionError(
'onnx.opset={} op_version={}\n--ONNX--\n{}\n--NAMES--\n{}'.format(
get_opset_number_from_onnx(), op_version, model_def,
all_names)) from e
# inplace
oinf = OnnxInference(model_def, input_inplace=False, inplace=True)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(np_fct(X), got['Y'], decimal=5)
# inplace2
onx2 = OnnxIdentity(
onnx_cl('X', op_version=op_version),
output_names=['Y'], op_version=op_version)
model_def2 = onx2.to_onnx(
{'X': X.astype(numpy.float32)}, target_opset=op_version,
outputs=outputs)
oinf = OnnxInference(model_def2, input_inplace=False, inplace=True)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(np_fct(X), got['Y'], decimal=5)
# input inplace
expe = np_fct(X)
oinf = OnnxInference(model_def, input_inplace=True, inplace=True)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(expe, got['Y'], decimal=5)
# sparse
if do_sparse:
row = numpy.array([0, 0, 1, 3, 1])
col = numpy.array([0, 2, 1, 3, 1])
data = numpy.array([1, 1, 1, 1, 1])
X = make_coo_matrix((data, (row.astype(numpy.int64),
col.astype(numpy.int64))),
shape=(4, 4), dtype=numpy.float32)
try:
exp = np_fct(X)
except (TypeError, NotImplementedError, ValueError) as e:
# Function np_fct does not work on sparse data.
sparse_no_numpy.append((onnx_cl.__name__, op_version, e))
return
model_def_sparse = onx.to_onnx(
{'X': X.astype(numpy.float32)}, target_opset=op_version)
oinf = OnnxInference(
model_def_sparse, input_inplace=False, inplace=True)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualSparseArray(exp, got['Y'], decimal=5)
sparse_support.append(('UnOp', op_version, onnx_cl.__name__))
@ignore_warnings(category=(RuntimeWarning, DeprecationWarning,
SparseEfficiencyWarning, PendingDeprecationWarning))
def common_test_onnxt_runtime_binary(self, onnx_cl, np_fct,
dtype=numpy.float32,
op_version=None, debug=False,
raise_shape=False):
if op_version is None:
op_version = get_opset_number_from_onnx()
idi = numpy.identity(2, dtype=dtype)
onx = onnx_cl('X', idi, output_names=['Y'], op_version=op_version)
X = numpy.array([[1, 2], [3, -4]], dtype=numpy.float64)
model_def = onx.to_onnx({'X': X.astype(dtype)},
target_opset=op_version)
oinf = OnnxInference(model_def)
if debug:
got = oinf.run({'X': X.astype(dtype)}, verbose=1, fLOG=print)
else:
got = oinf.run({'X': X.astype(dtype)})
self.assertEqual(list(sorted(got)), ['Y'])
self.common_expected_shapes_types(
oinf, {'X': X.astype(dtype)}, got, onnx_cl, model_def,
raise_shape=raise_shape)
exp = np_fct(X, idi)
self.assertEqualArray(exp, got['Y'], decimal=5)
# python code
python_tested.append(onnx_cl)
oinfpy = OnnxInference(model_def, runtime="python", inplace=True)
validate_python_inference(oinfpy, {'X': X.astype(dtype)})
# sparse
idi = make_coo_matrix(numpy.identity(2)).astype(numpy.float32)
X = make_coo_matrix(numpy.array(
[[0, 2], [3, -4]], dtype=numpy.float32))
try:
exp = np_fct(X, idi)
except (TypeError, NotImplementedError, ValueError) as e:
# Function np_fct does not work on sparse data.
sparse_no_numpy.append((onnx_cl.__name__, op_version, e))
return
onx = onnx_cl('X', idi, output_names=['Y'], op_version=op_version)
model_def_sparse = onx.to_onnx({'X': X}, target_opset=op_version)
try:
oinf = OnnxInference(
model_def_sparse, input_inplace=False, inplace=True)
except RuntimeError as e:
raise RuntimeError(
"Unable to load sparse model\n{}".format(
model_def_sparse)) from e
if debug:
got = oinf.run({'X': X}, verbose=1, fLOG=print)
else:
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
if isinstance(exp, (coo_matrix, csr_matrix)):
self.assertEqualSparseArray(exp, got['Y'], decimal=5)
elif isinstance(exp, numpy.ndarray):
self.assertEqualArray(exp, got['Y'], decimal=5)
else:
self.assertEqual(exp, got['Y'])
sparse_support.append(('BinOp', op_version, onnx_cl.__name__))
@wraplog()
def test_onnxt_runtime_abs(self):
self.common_test_onnxt_runtime_unary(OnnxAbs, numpy.abs)
@wraplog()
def test_onnxt_runtime_abs_debug(self):
f = StringIO()
with redirect_stdout(f):
self.common_test_onnxt_runtime_unary(
OnnxAbs, numpy.abs, debug=True)
@wraplog()
def test_onnxt_runtime_acos(self):
self.common_test_onnxt_runtime_unary(OnnxAcos, numpy.arccos)
@wraplog()
def test_onnxt_runtime_acosh(self):
self.common_test_onnxt_runtime_unary(OnnxAcosh, numpy.arccosh)
@wraplog()
def test_onnxt_runtime_add(self):
self.common_test_onnxt_runtime_binary(OnnxAdd, numpy.add)
@wraplog()
def test_onnxt_runtime_and(self):
self.common_test_onnxt_runtime_binary(
OnnxAnd, numpy.logical_and, dtype=numpy.bool_)
@wraplog()
def test_onnxt_runtime_argmax(self):
opsets = list(range(11, get_opset_number_from_onnx() + 1))
opsets = ['11only'] + opsets
for opset in opsets:
with self.subTest(opset=opset):
X = numpy.array([[2, 1], [0, 1]], dtype=float)
if opset == '11only':
clarg = OnnxArgMax_11
opset = 11
br = True
else:
clarg = OnnxArgMax
br = False
onx = clarg('X', output_names=['Y'], keepdims=0,
op_version=opset)
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
target_opset=opset)
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(numpy.argmax(
X, axis=0), got['Y'], decimal=5)
self.common_expected_shapes_types(
oinf, {'X': X}, got, clarg, model_def)
if br:
continue
oinfpy = OnnxInference(
model_def, runtime="python", inplace=True)
validate_python_inference(
oinfpy, {'X': X.astype(numpy.float32)})
onx = OnnxArgMax('X', output_names=['Y'], axis=1, keepdims=0,
op_version=opset)
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
target_opset=opset)
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(numpy.argmax(X, axis=1).ravel(),
got['Y'].ravel())
onx = OnnxArgMax('X', output_names=['Y'], axis=1, keepdims=1,
op_version=opset)
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
target_opset=opset)
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(numpy.argmax(X, axis=1).ravel(),
got['Y'].ravel())
# sparse
X = make_coo_matrix(X, dtype=numpy.float32)
try:
exp = numpy.argmax(X, axis=1)
except (TypeError, NotImplementedError, ValueError) as e:
# Function np_fct does not work on sparse data.
sparse_no_numpy.append((OnnxArgMax.__name__, None, e))
return
model_def_sparse = onx.to_onnx({'X': X},
target_opset=opset)
oinf = OnnxInference(model_def_sparse, input_inplace=False)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(exp, got['Y'], decimal=5)
X = numpy.array([[2, 1], [0, 1]], dtype=float)
sparse_support.append(('UnOp', None, OnnxArgMax.__name__))
python_tested.append(OnnxArgMax)
@unittest.skipIf(onnx_opset_version() < 12, reason="needs onnx 1.7.0")
@wraplog()
def test_onnxt_runtime_argmax_12(self):
self.assertGreater(onnx_opset_version(), 12)
from skl2onnx.algebra.onnx_ops import OnnxArgMax_12 # pylint: disable=E0611
X = numpy.array([[2, 2, 1], [0, 1, 1]], dtype=float)
onx = OnnxArgMax_12('X', output_names=['Y'], keepdims=0, axis=1,
select_last_index=1, op_version=12)
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(numpy.array([1, 2], dtype=numpy.int64),
got['Y'], decimal=5)
self.common_expected_shapes_types(
oinf, {'X': X}, got, OnnxArgMax_12, model_def)
@wraplog()
def test_onnxt_runtime_argmin(self):
opsets = list(range(11, get_opset_number_from_onnx() + 1))
opsets = ['11only'] + opsets
for opset in opsets:
with self.subTest(opset=opset):
if opset == '11only':
clarg = OnnxArgMin_11
opset = 11
br = True
else:
clarg = OnnxArgMin
br = False
X = numpy.array([[2, 1], [0, 1]], dtype=float)
onx = clarg('X', output_names=['Y'], keepdims=0,
op_version=opset)
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
target_opset=opset)
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(numpy.argmin(
X, axis=0), got['Y'], decimal=5)
if br:
continue
oinfpy = OnnxInference(
model_def, runtime="python", inplace=True)
validate_python_inference(
oinfpy, {'X': X.astype(numpy.float32)})
self.common_expected_shapes_types(
oinfpy, {'X': X.astype(numpy.float32)},
got, clarg, model_def)
onx = OnnxArgMin('X', output_names=['Y'], axis=1, keepdims=0,
op_version=opset)
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
target_opset=opset)
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(numpy.argmin(X, axis=1).ravel(),
got['Y'].ravel())
onx = OnnxArgMin('X', output_names=['Y'], axis=1, keepdims=1,
op_version=opset)
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
target_opset=opset)
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(numpy.argmin(X, axis=1).ravel(),
got['Y'].ravel())
# sparse
X = make_coo_matrix(X, dtype=numpy.float32)
try:
exp = numpy.argmin(X, axis=1)
except (TypeError, NotImplementedError, ValueError) as e:
# Function np_fct does not work on sparse data.
sparse_no_numpy.append((OnnxArgMin.__name__, None, e))
return
model_def_sparse = onx.to_onnx({'X': X}, target_opset=opset)
oinf = OnnxInference(model_def_sparse, input_inplace=False)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(exp, got['Y'], decimal=5)
sparse_support.append(('UnOp', None, OnnxArgMin.__name__))
python_tested.append(OnnxArgMin)
@unittest.skipIf(onnx_opset_version() < 12, reason="needs onnx 1.7.0")
@wraplog()
def test_onnxt_runtime_argmin_12(self):
self.assertGreater(onnx_opset_version(), 12)
from skl2onnx.algebra.onnx_ops import OnnxArgMin_12 # pylint: disable=E0611
X = numpy.array([[2, 1, 1], [0, 0, 1]], dtype=float)
onx = OnnxArgMin_12('X', output_names=['Y'], keepdims=0, axis=1,
select_last_index=1, op_version=12)
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(numpy.array([2, 1], dtype=numpy.int64),
got['Y'], decimal=5)
self.common_expected_shapes_types(
oinf, {'X': X}, got, OnnxArgMin_12, model_def)
@wraplog()
def test_onnxt_runtime_asin(self):
self.common_test_onnxt_runtime_unary(OnnxAsin, numpy.arcsin)
@wraplog()
def test_onnxt_runtime_asinh(self):
self.common_test_onnxt_runtime_unary(OnnxAsinh, numpy.arcsinh)
@wraplog()
def test_onnxt_runtime_atan(self):
self.common_test_onnxt_runtime_unary(OnnxAtan, numpy.arctan)
@wraplog()
def test_onnxt_runtime_atanh(self):
self.common_test_onnxt_runtime_unary(OnnxAtanh, numpy.arctanh)
@wraplog()
def test_onnxt_runtime_atan2(self):
test_pairs = [[y, x]
for x in [3., -4., 0., -1., 1.]
for y in [5., -6., 0., -1., 1.]]
y_val = numpy.array([y for y, x in test_pairs], dtype=numpy.float32)
x_val = numpy.array([x for y, x in test_pairs], dtype=numpy.float32)
def atan2(y, x):
# size: 100000
# timeit arctan: 0.00205
# timeit arctan2: 0.00361
# timeit atan2: 0.00599
sx = numpy.sign(x)
sy = numpy.sign(y)
pi_part = (sy + sx * (sy ** 2 - 1)) * (sx - 1) * (-numpy.pi / 2)
atan_part = numpy.arctan(y / (x + (1 - sx ** 2))) * sx ** 2
return atan_part + pi_part
self.assertEqualArray(
numpy.arctan2(y_val, x_val), atan2(y_val, x_val), decimal=5)
def _expect_average_pool(self, node, inputs, outputs, opset=None):
if opset is None:
opset = get_opset_number_from_onnx()
ginputs = [
onnx.helper.make_tensor_value_info(
node.input[0], TensorProto.FLOAT, []), # pylint: disable=E1101,
]
goutputs = [
onnx.helper.make_tensor_value_info(
node.output[0], TensorProto.FLOAT, []), # pylint: disable=E1101,
]
model_def = onnx.helper.make_model(
opset_imports=[onnx.helper.make_operatorsetid('', opset)],
graph=onnx.helper.make_graph(
name='test_average_pool', inputs=ginputs, outputs=goutputs,
nodes=[node]))
oinf = OnnxInference(model_def)
got = oinf.run({n: v for n, v in zip(node.input, inputs)})
self.assertEqual(len(got), 1)
self.assertEqualArray(outputs[0], got['y'])
@wraplog()
def test_onnxt_runtime_average_pool(self):
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[2, 2], auto_pad='SAME_UPPER')
x = numpy.random.randn(1, 3, 32, 32).astype(numpy.float32)
x_shape = numpy.shape(x)
kernel_shape = (2, 2)
strides = (1, 1)
out_shape = _get_output_shape(
'SAME_UPPER', x_shape[2:], kernel_shape, strides)
pad_shape = _get_pad_shape(
'SAME_UPPER', x_shape[2:], kernel_shape, strides, out_shape)
pad_top = pad_shape[0] // 2
pad_bottom = pad_shape[0] - pad_top
pad_left = pad_shape[1] // 2
pad_right = pad_shape[1] - pad_left
padded = numpy.pad(
x, ((0, 0), (0, 0), (pad_top, pad_bottom), (pad_left, pad_right)),
mode='constant', constant_values=numpy.nan)
y = _pool(
padded, x_shape, kernel_shape, strides, out_shape, pad_shape, 'AVG')
self._expect_average_pool(node, inputs=[x], outputs=[y])
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[3, 3], pads=[2, 2, 2, 2],
count_include_pad=1)
x = numpy.random.randn(1, 3, 28, 28).astype(numpy.float32)
x_shape = numpy.shape(x)
kernel_shape = (3, 3)
strides = (1, 1)
pad_bottom = 2
pad_top = 2
pad_right = 2
pad_left = 2
pad_shape = [pad_top + pad_bottom, pad_left + pad_right]
out_shape = _get_output_shape(
'VALID', numpy.add(x_shape[2:], pad_shape), kernel_shape, strides)
padded = numpy.pad(
x, ((0, 0), (0, 0), (pad_top, pad_bottom), (pad_left, pad_right)),
mode='constant', constant_values=0)
y = _pool(
padded, x_shape, kernel_shape, strides, out_shape,
pad_shape, 'AVG', count_include_pad=1)
self._expect_average_pool(node, inputs=[x], outputs=[y])
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[2, 2], auto_pad='SAME_LOWER')
x = numpy.random.randn(1, 3, 32, 32).astype(numpy.float32)
x_shape = numpy.shape(x)
kernel_shape = (2, 2)
strides = (1, 1)
out_shape = _get_output_shape(
'SAME_LOWER', x_shape[2:], kernel_shape, strides)
pad_shape = _get_pad_shape(
'SAME_LOWER', x_shape[2:], kernel_shape, strides, out_shape)
pad_bottom = pad_shape[0] // 2
pad_top = pad_shape[0] - pad_bottom
pad_right = pad_shape[1] // 2
pad_left = pad_shape[1] - pad_right
padded = numpy.pad(
x, ((0, 0), (0, 0), (pad_top, pad_bottom), (pad_left, pad_right)),
mode='constant', constant_values=numpy.nan)
y = _pool(
padded, x_shape, kernel_shape, strides, out_shape, pad_shape, 'AVG')
self._expect_average_pool(node, inputs=[x], outputs=[y])
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[3, 3], pads=[2, 2, 2, 2])
x = numpy.random.randn(1, 3, 28, 28).astype(numpy.float32)
x_shape = numpy.shape(x)
kernel_shape = (3, 3)
strides = (1, 1)
pad_bottom = 2
pad_top = 2
pad_right = 2
pad_left = 2
pad_shape = [pad_top + pad_bottom, pad_left + pad_right]
out_shape = _get_output_shape(
'VALID', numpy.add(x_shape[2:], pad_shape), kernel_shape, strides)
padded = numpy.pad(
x, ((0, 0), (0, 0), (pad_top, pad_bottom), (pad_left, pad_right)),
mode='constant', constant_values=numpy.nan)
y = _pool(
padded, x_shape, kernel_shape, strides, out_shape, pad_shape, 'AVG')
self._expect_average_pool(node, inputs=[x], outputs=[y])
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[2])
x = numpy.random.randn(1, 3, 32).astype(numpy.float32)
x_shape = numpy.shape(x)
kernel_shape = [2]
strides = [1]
out_shape = _get_output_shape(
'VALID', x_shape[2:], kernel_shape, strides)
padded = x
y = _pool(padded, x_shape, kernel_shape,
strides, out_shape, [0], 'AVG')
self._expect_average_pool(node, inputs=[x], outputs=[y])
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[2, 2])
x = numpy.random.randn(1, 3, 32, 32).astype(numpy.float32)
x_shape = numpy.shape(x)
kernel_shape = (2, 2)
strides = (1, 1)
out_shape = _get_output_shape(
'VALID', x_shape[2:], kernel_shape, strides)
padded = x
y = _pool(
padded, x_shape, kernel_shape, strides, out_shape, (0, 0), 'AVG')
self._expect_average_pool(node, inputs=[x], outputs=[y])
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[5, 5], strides=[3, 3])
x = numpy.random.randn(1, 3, 32, 32).astype(numpy.float32)
x_shape = numpy.shape(x)
kernel_shape = (5, 5)
strides = (3, 3)
out_shape = _get_output_shape(
'VALID', x_shape[2:], kernel_shape, strides)
padded = x
y = _pool(
padded, x_shape, kernel_shape, strides, out_shape, (0, 0), 'AVG')
self._expect_average_pool(node, inputs=[x], outputs=[y])
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[2, 2, 2])
x = numpy.random.randn(1, 3, 32, 32, 32).astype(numpy.float32)
x_shape = numpy.shape(x)
kernel_shape = [2, 2, 2]
strides = [1, 1, 1]
out_shape = _get_output_shape(
'VALID', x_shape[2:], kernel_shape, strides)
padded = x
y = _pool(
padded, x_shape, kernel_shape, strides, out_shape, [0, 0, 0], 'AVG')
self._expect_average_pool(node, inputs=[x], outputs=[y])
python_tested.append(OnnxAveragePool)
@wraplog()
@unittest.skipIf(True, "not implemented yet")
def test_onnxt_runtime_average_pool_ceil(self):
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[3, 3], strides=[2, 2], ceil_mode=True)
x = numpy.array([[[
[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16]]]]).astype(numpy.float32)
y = numpy.array([[[
[6, 7.5], [12, 13.5]]]]).astype(numpy.float32)
self._expect_average_pool(node, inputs=[x], outputs=[y])
@wraplog()
def test_onnxt_runtime_average_pool_big(self):
with self.subTest(name='test_averagepool_2d_precomputed_pads'):
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[5, 5], pads=[2, 2, 2, 2])
x = numpy.array([[[
[1, 2, 3, 4, 5],
[6, 7, 8, 9, 10],
[11, 12, 13, 14, 15],
[16, 17, 18, 19, 20],
[21, 22, 23, 24, 25]]]]).astype(numpy.float32)
y = numpy.array([[[[7, 7.5, 8, 8.5, 9],
[9.5, 10, 10.5, 11, 11.5],
[12, 12.5, 13, 13.5, 14],
[14.5, 15, 15.5, 16, 16.5],
[17, 17.5, 18, 18.5, 19]]]]).astype(numpy.float32)
self._expect_average_pool(node, inputs=[x], outputs=[y])
with self.subTest(name='test_averagepool_2d_precomputed_pads_count_include_pad'):
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[5, 5], pads=[2, 2, 2, 2], count_include_pad=1)
x = numpy.array([[[
[1, 2, 3, 4, 5],
[6, 7, 8, 9, 10],
[11, 12, 13, 14, 15],
[16, 17, 18, 19, 20],
[21, 22, 23, 24, 25]]]]).astype(numpy.float32)
y = numpy.array([[[[2.5200, 3.6000, 4.8000, 4.0800, 3.2400],
[4.5600, 6.4000, 8.4000, 7.0400, 5.5200],
[7.2000, 10.0000, 13.0000, 10.8000, 8.4000],
[6.9600, 9.6000, 12.4000, 10.2400, 7.9200],
[6.1200, 8.4000, 10.8000, 8.8800, 6.8400]]]]).astype(numpy.float32)
self._expect_average_pool(node, inputs=[x], outputs=[y])
with self.subTest(name='test_averagepool_2d_precomputed_same_upper'):
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[3, 3], strides=[2, 2], auto_pad='SAME_UPPER')
x = numpy.array([[[
[1, 2, 3, 4, 5],
[6, 7, 8, 9, 10],
[11, 12, 13, 14, 15],
[16, 17, 18, 19, 20],
[21, 22, 23, 24, 25]]]]).astype(numpy.float32)
y = numpy.array([[[[4, 5.5, 7],
[11.5, 13, 14.5],
[19, 20.5, 22]]]]).astype(numpy.float32)
self._expect_average_pool(node, inputs=[x], outputs=[y])
with self.subTest(name='test_averagepool_2d_precomputed_strides'):
node = onnx.helper.make_node(
'AveragePool', inputs=['x'], outputs=['y'],
kernel_shape=[2, 2], strides=[2, 2])
x = numpy.array([[[
[1, 2, 3, 4, 5],
[6, 7, 8, 9, 10],
[11, 12, 13, 14, 15],
[16, 17, 18, 19, 20],
[21, 22, 23, 24, 25]]]]).astype(numpy.float32)
y = numpy.array([[[[4, 6],
[14, 16]]]]).astype(numpy.float32)
self._expect_average_pool(node, inputs=[x], outputs=[y])
@wraplog()
def test_onnxt_runtime_batch_normalization(self):
# input size: (1, 2, 1, 3)
x = numpy.array([[[[-1, 0, 1]], [[2, 3, 4]]]]).astype(numpy.float32)
s = numpy.array([1.0, 1.5]).astype(numpy.float32)
bias = numpy.array([0, 1]).astype(numpy.float32)
mean = numpy.array([0, 3]).astype(numpy.float32)
var = numpy.array([1, 1.5]).astype(numpy.float32)
y = _batchnorm_test_mode(x, s, bias, mean, var).astype(numpy.float32)
onx = OnnxBatchNormalization(
'X', s, bias, mean, var, output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y, got['Y'])
self.common_expected_shapes_types(
oinf, {'X': x}, got, OnnxBatchNormalization, model_def)
# input size: (2, 3, 4, 5)
x = numpy.random.randn(2, 3, 4, 5).astype(numpy.float32)
s = numpy.random.randn(3).astype(numpy.float32)
bias = numpy.random.randn(3).astype(numpy.float32)
mean = numpy.random.randn(3).astype(numpy.float32)
var = numpy.random.rand(3).astype(numpy.float32)
epsilon = 1e-2
y = _batchnorm_test_mode(
x, s, bias, mean, var, epsilon).astype(numpy.float32)
onx = OnnxBatchNormalization(
'X', s, bias, mean, var,
output_names=['Y'], epsilon=epsilon,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y, got['Y'])
python_tested.append(OnnxBatchNormalization)
@wraplog()
def test_onnxt_runtime_batch_normalization_training_fct(self):
x = numpy.array([[[[-1, 0, 1]], [[2, 3, 4]]]]).astype(numpy.float32)
s = numpy.array([1.0, 1.5]).astype(numpy.float32)
bias = numpy.array([0, 1]).astype(numpy.float32)
mean = numpy.array([0, 3]).astype(numpy.float32)
var = numpy.array([1, 1.5]).astype(numpy.float32)
y, scale, bias, mean, var = (
_batchnorm_training_mode(x, s, bias, mean, var))
self.assertEqualArray(
numpy.array([[[[-1.2247356, 0., 1.2247356]],
[[-0.8371035, 1., 2.8371034]]]],
dtype=numpy.float32), y)
self.assertEqualArray(
numpy.array([0., 3.], dtype=numpy.float32), scale)
self.assertEqualArray(
numpy.array([0.6666667, 0.6666667], dtype=numpy.float32), bias)
self.assertEqualArray(
numpy.array([0., 2.9999998], dtype=numpy.float32), mean)
self.assertEqualArray(
numpy.array([0.96666664, 1.4166666], dtype=numpy.float32), var)
@wraplog()
@unittest.skipIf(OnnxBatchNormalization_14 is None,
reason="onnx too old")
def test_onnxt_runtime_batch_normalization_training(self):
# input size: (1, 2, 1, 3)
x = numpy.array([[[[-1, 0, 1]], [[2, 3, 4]]]]).astype(numpy.float32)
s = numpy.array([1.0, 1.5]).astype(numpy.float32)
bias = numpy.array([0, 1]).astype(numpy.float32)
mean = numpy.array([0, 3]).astype(numpy.float32)
var = numpy.array([1, 1.5]).astype(numpy.float32)
y, scale, bias, mean, var = (
_batchnorm_training_mode(x, s, bias, mean, var))
onx = OnnxBatchNormalization_14(
'X', s, bias, mean, var,
output_names=['Y', 'scale', 'bias', 'mean', 'var'],
training_mode=1, op_version=14)
try:
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=14)
except RuntimeError as e:
if "Shape inference fails" in str(e):
warnings.warn(str(e))
return
raise e
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
self.assertEqual(
list(sorted(got)), ['Y', 'bias', 'mean', 'scale', 'var'])
self.assertEqualArray(scale, got['scale'])
self.assertEqualArray(bias, got['bias'])
self.assertEqualArray(mean, got['mean'])
# self.assertEqualArray(var, got['var'])
# self.assertEqualArray(y, got['Y'])
self.assertNotEmpty(y)
self.assertNotEmpty(var)
@wraplog()
def test_onnxt_runtime_cast_out(self):
x = numpy.array([1., 2., 3., 4., 5., 6.]).astype(
numpy.float32) # pylint: disable=E1101
dest = [(TensorProto.FLOAT, numpy.float32, FloatTensorType), # pylint: disable=E1101
(TensorProto.DOUBLE, numpy.float64, # pylint: disable=E1101
DoubleTensorType), # pylint: disable=E1101
(TensorProto.INT32, numpy.int32, # pylint: disable=E1101
Int32TensorType), # pylint: disable=E1101
(TensorProto.INT64, numpy.int64, # pylint: disable=E1101
Int64TensorType), # pylint: disable=E1101
(TensorProto.INT8, numpy.int8, # pylint: disable=E1101
Int8TensorType), # pylint: disable=E1101
(TensorProto.INT16, numpy.int16, # pylint: disable=E1101
Int16TensorType), # pylint: disable=E1101
(TensorProto.UINT8, numpy.uint8, # pylint: disable=E1101
UInt8TensorType), # pylint: disable=E1101
(TensorProto.UINT32, numpy.uint32, # pylint: disable=E1101
UInt32TensorType), # pylint: disable=E1101
(TensorProto.UINT16, numpy.uint16, # pylint: disable=E1101
UInt16TensorType), # pylint: disable=E1101
(TensorProto.UINT64, numpy.uint64, # pylint: disable=E1101
UInt64TensorType), # pylint: disable=E1101
(TensorProto.FLOAT16, numpy.float16, # pylint: disable=E1101
Float16TensorType), # pylint: disable=E1101
(TensorProto.BOOL, numpy.bool_, # pylint: disable=E1101
BooleanTensorType), # pylint: disable=E1101
(TensorProto.STRING, numpy.str_, StringTensorType), ] # pylint: disable=E1101
for opset in range(9, get_opset_number_from_onnx() + 1):
for to, nptp, outp in dest:
if nptp == numpy.bool_:
self.assertIn(proto2dtype(to), (nptp, bool))
elif nptp == numpy.str_:
self.assertIn(proto2dtype(to), (nptp, str))
else:
self.assertEqual(proto2dtype(to), nptp)
self.assertEqual(to, guess_proto_dtype(nptp))
self.assertNotEmpty(_elem_type_as_str(to))
with self.subTest(opset=opset, to=to):
onx = OnnxCast('X', to=to, output_names=['Y'],
op_version=opset)
model_def = onx.to_onnx(
{'X': x}, outputs=[('Y', outp())],
target_opset=opset)
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
if nptp == numpy.str_:
self.assertEqual(
x.astype(nptp).tolist(), got['Y'].tolist())
else:
self.assertEqualArray(x.astype(nptp), got['Y'])
self.common_expected_shapes_types(
oinf, {'X': x}, got, OnnxCast, model_def)
python_tested.append(OnnxCast)
@wraplog()
def test_onnxt_runtime_cast_in(self):
x = numpy.array([1., 2., 3., 4., 5., 6.]).astype(
numpy.float32) # pylint: disable=E1101
dest = [(TensorProto.FLOAT, numpy.float32, FloatTensorType), # pylint: disable=E1101
(TensorProto.DOUBLE, numpy.float64, # pylint: disable=E1101
DoubleTensorType), # pylint: disable=E1101
(TensorProto.INT32, numpy.int32, # pylint: disable=E1101
Int32TensorType), # pylint: disable=E1101
(TensorProto.INT64, numpy.int64, # pylint: disable=E1101
Int64TensorType), # pylint: disable=E1101
(TensorProto.INT8, numpy.int8, # pylint: disable=E1101
Int8TensorType), # pylint: disable=E1101
(TensorProto.INT16, numpy.int16, # pylint: disable=E1101
Int16TensorType), # pylint: disable=E1101
(TensorProto.UINT8, numpy.uint8, # pylint: disable=E1101
UInt8TensorType), # pylint: disable=E1101
(TensorProto.UINT32, numpy.uint32, # pylint: disable=E1101
UInt32TensorType), # pylint: disable=E1101
(TensorProto.UINT16, numpy.uint16, # pylint: disable=E1101
UInt16TensorType), # pylint: disable=E1101
(TensorProto.UINT64, numpy.uint64, # pylint: disable=E1101
UInt64TensorType), # pylint: disable=E1101
(TensorProto.FLOAT16, numpy.float16, # pylint: disable=E1101
Float16TensorType), # pylint: disable=E1101
(TensorProto.BOOL, numpy.bool_, # pylint: disable=E1101
BooleanTensorType), # pylint: disable=E1101
(TensorProto.STRING, numpy.str_, StringTensorType), ] # pylint: disable=E1101
for opset in range(9, get_opset_number_from_onnx() + 1):
for to, nptp, _ in dest:
if nptp == numpy.bool_:
self.assertIn(proto2dtype(to), (nptp, bool))
elif nptp == numpy.str_:
self.assertIn(proto2dtype(to), (nptp, str))
else:
self.assertEqual(proto2dtype(to), nptp)
self.assertEqual(to, guess_proto_dtype(nptp))
self.assertNotEmpty(_elem_type_as_str(to))
with self.subTest(opset=opset, to=to):
xi = x.astype(nptp)
onx = OnnxCast('X', to=TensorProto.STRING, # pylint: disable=E1101
output_names=['Y'],
op_version=opset)
model_def = onx.to_onnx(
{'X': xi}, outputs=[('Y', StringTensorType())],
target_opset=opset)
got = OnnxInference(model_def).run({'X': xi})
self.assertEqual(
xi.astype(str).tolist(), got['Y'].tolist())
python_tested.append(OnnxCast)
@wraplog()
def test_onnxt_runtime_ceil(self):
self.common_test_onnxt_runtime_unary(OnnxCeil, numpy.ceil)
@unittest.skipIf(OnnxCelu is None, reason="onnx too recent")
@wraplog()
def test_onnxt_runtime_celu1(self):
self.common_test_onnxt_runtime_unary(
OnnxCelu, _vcelu1, op_version=12,
outputs=[('Y', FloatTensorType([None, 2]))])
@unittest.skipIf(OnnxCelu is None, reason="onnx too recent")
@wraplog()
def test_onnxt_runtime_celu2(self):
_vcelu2 = numpy.vectorize(
lambda x: pycelu(x, 1.), otypes=[numpy.float])
self.common_test_onnxt_runtime_unary(
OnnxCelu, _vcelu2, op_version=12,
outputs=[('Y', FloatTensorType([None, 2]))])
@unittest.skipIf(onnx_opset_version() < 11,
reason="Explicitely tests Clip >= 11")
@wraplog()
def test_onnxt_runtime_clip(self):
self.common_test_onnxt_runtime_unary(
lambda x, output_names=None, op_version=None: OnnxClip(
x, numpy.array([0], dtype=numpy.float32),
output_names=output_names, op_version=op_version),
lambda x: numpy.clip(x, 0, 1e5))
self.common_test_onnxt_runtime_unary(
lambda x, output_names=None, op_version=None: OnnxClip(
x, numpy.array([-1000], dtype=numpy.float32),
numpy.array([0], dtype=numpy.float32),
op_version=op_version,
output_names=output_names),
lambda x: numpy.clip(x, -1e5, 0))
self.common_test_onnxt_runtime_unary(
lambda x, output_names=None, op_version=None: OnnxClip(
x,
numpy.array([0.1], dtype=numpy.float32),
numpy.array([2.1], dtype=numpy.float32),
output_names=output_names,
op_version=op_version),
lambda x: numpy.clip(x, 0.1, 2.1))
python_tested.append(OnnxClip)
@wraplog()
def test_onnxt_runtime_compress(self):
# axis is None
x = numpy.array([1., 2., 3., 4., 5., 6.]).astype(numpy.float32)
x = x.reshape((-1, 2))
cond = numpy.array([False, True, False])
onx = OnnxCompress('X', 'cond', output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x, 'cond': cond},
outputs=[('Y', FloatTensorType())],
target_opset=get_opset_number_from_onnx())
exp = numpy.compress(cond, x)
oinf = OnnxInference(model_def)
got = oinf.run({'X': x, 'cond': cond})
self.assertEqualArray(exp, got['Y'])
self.common_expected_shapes_types(
oinf, {'X': x, 'cond': cond}, got, OnnxCompress, model_def)
python_tested.append(OnnxCompress)
@wraplog()
def test_onnxt_runtime_clip_10(self):
from skl2onnx.algebra.onnx_ops import OnnxClip_6 # pylint: disable=E0611
self.common_test_onnxt_runtime_unary(
lambda x, output_names=None, op_version=10: OnnxClip_6(
x, min=1e-5, max=1e5, output_names=output_names,
op_version=10),
lambda x: numpy.clip(x, 1e-5, 1e5),
op_version=10)
self.common_test_onnxt_runtime_unary(
lambda x, output_names=None, op_version=10: OnnxClip(
x, min=1e-5, max=1e5, output_names=output_names,
op_version=10),
lambda x: numpy.clip(x, 1e-5, 1e5),
op_version=10)
self.common_test_onnxt_runtime_unary(
lambda x, output_names=None, op_version=10: OnnxClip(
x, max=1e-5, output_names=output_names,
op_version=10),
lambda x: numpy.clip(x, -1e5, 1e-5),
op_version=10)
self.common_test_onnxt_runtime_unary(
lambda x, output_names=None, op_version=10: OnnxClip(
x, min=0.1, max=2.1,
output_names=output_names,
op_version=10),
lambda x: numpy.clip(x, 0.1, 2.1),
op_version=10)
@wraplog()
def test_onnxt_runtime_concat(self):
cst = numpy.array([[1, 2]], dtype=numpy.float32)
onx = OnnxConcat('X', 'Y', cst, output_names=['Z'],
op_version=get_opset_number_from_onnx())
X = numpy.array([[1, 2], [3, 4]], dtype=numpy.float64)
Y = numpy.array([[8, 9], [10, 11], [12, 13]], dtype=numpy.float64)
model_def = onx.to_onnx({'X': X.astype(numpy.float32),
'Y': Y.astype(numpy.float32)},
outputs=[('Z', FloatTensorType([2]))],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': X.astype(numpy.float32),
'Y': Y.astype(numpy.float32)})
self.assertEqual(list(sorted(got)), ['Z'])
self.assertEqual(got['Z'].shape, (6, 2))
exp = numpy.vstack([X, Y, cst])
self.assertEqualArray(exp, got['Z'])
self.common_expected_shapes_types(
oinf, {'X': X.astype(numpy.float32),
'Y': Y.astype(numpy.float32)},
got, OnnxConcat, model_def)
python_tested.append(OnnxConstantOfShape)
oinfpy = OnnxInference(model_def, runtime="python", inplace=True)
validate_python_inference(
oinfpy, {'X': X.astype(numpy.float32),
'Y': Y.astype(numpy.float32)})
python_tested.append(OnnxConcat)
@wraplog()
def test_onnxt_runtime_constant_of_shape(self):
x = numpy.array([2, 2], dtype=numpy.int64)
y = numpy.zeros((2, 2), dtype=numpy.float32)
onx = OnnxConstantOfShape('X', output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.int64)},
outputs=[('Y', FloatTensorType())],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': x.astype(numpy.int64)})
self.assertEqualArray(y, got['Y'])
self.common_expected_shapes_types(
oinf, {'X': x.astype(numpy.int64)}, got,
OnnxConstantOfShape, model_def)
python_tested.append(OnnxConstantOfShape)
oinfpy = OnnxInference(model_def, runtime="python", inplace=True)
validate_python_inference(oinfpy, {'X': x})
@wraplog()
def test_onnxt_runtime_conv0(self):
x = numpy.array([[[[0., 1., 2., 3., 4.], # (1, 1, 5, 5) input tensor
[5., 6., 7., 8., 9.],
[10., 11., 12., 13., 14.],
[15., 16., 17., 18., 19.],
[20., 21., 22., 23., 24.]]]]).astype(numpy.float32)
W = numpy.array([[[[1., 1., 1.], # (1, 1, 3, 3) tensor for convolution weights
[1., 1., 1.],
[1., 1., 1.]]]]).astype(numpy.float32)
# test 1
y_with_padding = numpy.array([[[[12., 21., 27., 33., 24.], # (1, 1, 5, 5) output tensor
[33., 54., 63., 72., 51.],
[63., 99., 108., 117., 81.],
[93., 144., 153., 162., 111.],
[72., 111., 117., 123., 84.]]]]).astype(numpy.float32)
onx = OnnxConv(
'X', W, output_names=['Y'],
kernel_shape=[3, 3], pads=[1, 1, 1, 1],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
for rt in ['python', 'onnxruntime1']:
with self.subTest(runtime=rt):
oinf = OnnxInference(model_def, runtime=rt)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_padding, got['Y'])
# test 2
y_without_padding = numpy.array([[[[54., 63., 72.], # (1, 1, 3, 3) output tensor
[99., 108., 117.],
[144., 153., 162.]]]]).astype(numpy.float32)
onx = OnnxConv(
'X', W, output_names=['Y'],
kernel_shape=[3, 3], pads=[0, 0, 0, 0],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
for rt in ['python', 'onnxruntime1']:
with self.subTest(runtime=rt):
oinf = OnnxInference(model_def, runtime=rt)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_without_padding, got['Y'])
if rt == 'python':
self.common_expected_shapes_types(
oinf, {'X': x}, got, OnnxConv, model_def)
else:
self.assertRaise(
lambda: self.common_expected_shapes_types(
oinf, {'X': x}, got, OnnxConv, model_def),
RuntimeError)
# test 3
y = numpy.array([[[[12., 27., 24.],
[63., 108., 81.],
[72., 117., 84.]]]]).astype(numpy.float32)
onx = OnnxConv(
'X', W, output_names=['Y'],
kernel_shape=[3, 3],
auto_pad='SAME_LOWER', strides=[2, 2],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
for rt in ['python', 'onnxruntime1']:
with self.subTest(runtime=rt):
oinf = OnnxInference(model_def, runtime=rt)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y, got['Y'])
python_tested.append(OnnxConv)
@wraplog()
def test_onnxt_runtime_conv1(self):
x = numpy.array([[[[0., 1., 2., 3., 4.],
[5., 6., 7., 8., 9.],
[10., 11., 12., 13., 14.],
[15., 16., 17., 18., 19.],
[20., 21., 22., 23., 24.],
[25., 26., 27., 28., 29.],
[30., 31., 32., 33., 34.]]]]).astype(numpy.float32)
W = numpy.array([[[[1., 1., 1.], # (1, 1, 3, 3) tensor for convolution weights
[1., 1., 1.],
[1., 1., 1.]]]]).astype(numpy.float32)
# test 1
y_with_padding = numpy.array([[[[12., 27., 24.], # (1, 1, 4, 3) output tensor
[63., 108., 81.],
[123., 198., 141.],
[112., 177., 124.]]]]).astype(numpy.float32)
onx = OnnxConv(
'X', W, output_names=['Y'],
kernel_shape=[3, 3], pads=[1, 1, 1, 1], strides=[2, 2],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
for rt in ['python', 'onnxruntime1']:
with self.subTest(runtime=rt):
oinf = OnnxInference(model_def, runtime=rt)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_padding, got['Y'])
# test 2
y_without_padding = numpy.array([[[[54., 72.], # (1, 1, 3, 2) output tensor
[144., 162.],
[234., 252.]]]]).astype(numpy.float32)
onx = OnnxConv(
'X', W, output_names=['Y'],
kernel_shape=[3, 3], pads=[0, 0, 0, 0], strides=[2, 2],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
for rt in ['python', 'onnxruntime1']:
with self.subTest(runtime=rt):
oinf = OnnxInference(model_def, runtime=rt)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_without_padding, got['Y'])
# test 3
y_with_asymmetric_padding = numpy.array([[[[21., 33.], # (1, 1, 4, 2) output tensor
[99., 117.],
[189., 207.],
[171., 183.]]]]).astype(numpy.float32)
onx = OnnxConv(
'X', W, output_names=['Y'],
kernel_shape=[3, 3], pads=[1, 0, 1, 0], strides=[2, 2],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
for rt in ['python', 'onnxruntime1']:
with self.subTest(runtime=rt):
oinf = OnnxInference(model_def, runtime=rt)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_asymmetric_padding, got['Y'])
@wraplog()
def test_onnxt_runtime_conv2_B(self):
x = numpy.random.rand(1, 3, 5, 4).astype(numpy.float32)
W = numpy.random.rand(4, 3, 3, 3).astype(numpy.float32)
B = numpy.array([100, 700, 1000, 7000], dtype=numpy.float32)
onx = OnnxConv(
'X', 'W', 'B', output_names=['Y'],
kernel_shape=[3, 3], pads=[1, 1, 1, 1], strides=[2, 2],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x, 'W': W, 'B': B},
target_opset=get_opset_number_from_onnx())
ys = []
for rt in ['python', 'onnxruntime1']:
oinf = OnnxInference(model_def, runtime=rt)
got = oinf.run({'X': x, 'W': W, 'B': B})
ys.append(got['Y'])
self.assertEqualArray(ys[0], ys[1], decimal=4)
@wraplog()
def test_onnxt_runtime_conv_transpose(self):
x = numpy.array([[[[0., 1., 2.], # (1, 1, 3, 3)
[3., 4., 5.],
[6., 7., 8.]]]]).astype(numpy.float32)
W = numpy.array([[[[1., 1., 1.], # (1, 2, 3, 3)
[1., 1., 1.],
[1., 1., 1.]],
[[1., 1., 1.],
[1., 1., 1.],
[1., 1., 1.]]]]).astype(numpy.float32)
y_with_padding = numpy.array([[[[0., 1., 3., 3., 2.], # (1, 2, 5, 5)
[3., 8., 15., 12., 7.],
[9., 21., 36., 27., 15.],
[9., 20., 33., 24., 13.],
[6., 13., 21., 15., 8.]],
[[0., 1., 3., 3., 2.],
[3., 8., 15., 12., 7.],
[9., 21., 36., 27., 15.],
[9., 20., 33., 24., 13.],
[6., 13., 21., 15., 8.]]]]).astype(numpy.float32)
onx = OnnxConvTranspose(
'X', W, output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_padding, got['Y'])
python_tested.append(OnnxConv)
@wraplog()
def test_onnxt_runtime_conv_transpose_B(self):
x = numpy.random.rand(1, 3, 5, 4).astype(numpy.float32)
W = numpy.random.rand(3, 4, 3, 3).astype(numpy.float32)
B = numpy.array([100, 700, 1000, 7000], dtype=numpy.float32)
onx = OnnxConvTranspose(
'X', 'W', 'B', output_names=['Y'],
kernel_shape=[3, 3], pads=[1, 1, 1, 1], strides=[2, 2],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x, 'W': W, 'B': B},
target_opset=get_opset_number_from_onnx())
ys = []
for rt in ['python', 'onnxruntime1']:
oinf = OnnxInference(model_def, runtime=rt)
got = oinf.run({'X': x, 'W': W, 'B': B})
ys.append(got['Y'])
self.assertEqual(len(ys), 2)
# self.assertEqualArray(ys[0], ys[1])
@wraplog()
def test_onnxt_runtime_conv_transpose_1d(self):
x = numpy.array([[[0., 1., 2.]]]).astype(numpy.float32)
W = numpy.array([[[1., 1., 1.], # (1, 2, 3)
[1., 1., 1.]]]).astype(numpy.float32)
y_with_padding = numpy.array(
[[[0., 1., 3., 3., 2.], # (1, 2, 5)
[0., 1., 3., 3., 2.]]]).astype(numpy.float32)
onx = OnnxConvTranspose(
'X', W, output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def, runtime="onnxruntime1")
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_padding, got['Y'])
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_padding, got['Y'])
python_tested.append(OnnxConvTranspose)
@wraplog()
def test_onnxt_runtime_conv_transpose_3d(self):
x = numpy.arange(60).reshape((1, 1, 3, 4, 5)).astype(numpy.float32)
W = numpy.ones((1, 2, 3, 3, 3)).astype(numpy.float32)
y_with_padding = numpy.array(
[[[[[0., 1., 3., 6., 9., 7., 4.], # (1, 2, 5, 6, 7)
[5., 12., 21., 27., 33., 24., 13.],
[15., 33., 54., 63., 72., 51., 27.],
[30., 63., 99., 108., 117., 81., 42.],
[25., 52., 81., 87., 93., 64., 33.],
[15., 31., 48., 51., 54., 37., 19.]],
[[20., 42., 66., 72., 78., 54., 28.],
[50., 104., 162., 174., 186., 128., 66.],
[90., 186., 288., 306., 324., 222., 114.],
[120., 246., 378., 396., 414., 282., 144.],
[90., 184., 282., 294., 306., 208., 106.],
[50., 102., 156., 162., 168., 114., 58.]],
[[60., 123., 189., 198., 207., 141., 72.],
[135., 276., 423., 441., 459., 312., 159.],
[225., 459., 702., 729., 756., 513., 261.],
[270., 549., 837., 864., 891., 603., 306.],
[195., 396., 603., 621., 639., 432., 219.],
[105., 213., 324., 333., 342., 231., 117.]],
[[60., 122., 186., 192., 198., 134., 68.],
[130., 264., 402., 414., 426., 288., 146.],
[210., 426., 648., 666., 684., 462., 234.],
[240., 486., 738., 756., 774., 522., 264.],
[170., 344., 522., 534., 546., 368., 186.],
[90., 182., 276., 282., 288., 194., 98.]],
[[40., 81., 123., 126., 129., 87., 44.],
[85., 172., 261., 267., 273., 184., 93.],
[135., 273., 414., 423., 432., 291., 147.],
[150., 303., 459., 468., 477., 321., 162.],
[105., 212., 321., 327., 333., 224., 113.],
[55., 111., 168., 171., 174., 117., 59.]]],
[[[0., 1., 3., 6., 9., 7., 4.],
[5., 12., 21., 27., 33., 24., 13.],
[15., 33., 54., 63., 72., 51., 27.],
[30., 63., 99., 108., 117., 81., 42.],
[25., 52., 81., 87., 93., 64., 33.],
[15., 31., 48., 51., 54., 37., 19.]],
[[20., 42., 66., 72., 78., 54., 28.],
[50., 104., 162., 174., 186., 128., 66.],
[90., 186., 288., 306., 324., 222., 114.],
[120., 246., 378., 396., 414., 282., 144.],
[90., 184., 282., 294., 306., 208., 106.],
[50., 102., 156., 162., 168., 114., 58.]],
[[60., 123., 189., 198., 207., 141., 72.],
[135., 276., 423., 441., 459., 312., 159.],
[225., 459., 702., 729., 756., 513., 261.],
[270., 549., 837., 864., 891., 603., 306.],
[195., 396., 603., 621., 639., 432., 219.],
[105., 213., 324., 333., 342., 231., 117.]],
[[60., 122., 186., 192., 198., 134., 68.],
[130., 264., 402., 414., 426., 288., 146.],
[210., 426., 648., 666., 684., 462., 234.],
[240., 486., 738., 756., 774., 522., 264.],
[170., 344., 522., 534., 546., 368., 186.],
[90., 182., 276., 282., 288., 194., 98.]],
[[40., 81., 123., 126., 129., 87., 44.],
[85., 172., 261., 267., 273., 184., 93.],
[135., 273., 414., 423., 432., 291., 147.],
[150., 303., 459., 468., 477., 321., 162.],
[105., 212., 321., 327., 333., 224., 113.],
[55., 111., 168., 171., 174., 117., 59.]]]]]).astype(numpy.float32)
onx = OnnxConvTranspose(
'X', W, output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_padding, got['Y'])
@unittest.skipIf(True, reason="fails with output_shape")
@wraplog()
def test_onnxt_runtime_conv_transpose_output_shape(self):
x = numpy.arange(9).reshape((1, 1, 3, 3)).astype(numpy.float32)
W = numpy.ones((1, 2, 3, 3)).astype(numpy.float32)
y_with_padding = numpy.array(
[[[[0., 0., 1., 1., 3., 2., 2., 0.], # (1, 2, 10, 8)
[0., 0., 1., 1., 3., 2., 2., 0.],
[0., 0., 1., 1., 3., 2., 2., 0.],
[3., 3., 7., 4., 9., 5., 5., 0.],
[3., 3., 7., 4., 9., 5., 5., 0.],
[3., 3., 7., 4., 9., 5., 5., 0.],
[6., 6., 13., 7., 15., 8., 8., 0.],
[6., 6., 13., 7., 15., 8., 8., 0.],
[6., 6., 13., 7., 15., 8., 8., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.]],
[[0., 0., 1., 1., 3., 2., 2., 0.],
[0., 0., 1., 1., 3., 2., 2., 0.],
[0., 0., 1., 1., 3., 2., 2., 0.],
[3., 3., 7., 4., 9., 5., 5., 0.],
[3., 3., 7., 4., 9., 5., 5., 0.],
[3., 3., 7., 4., 9., 5., 5., 0.],
[6., 6., 13., 7., 15., 8., 8., 0.],
[6., 6., 13., 7., 15., 8., 8., 0.],
[6., 6., 13., 7., 15., 8., 8., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.]]]]).astype(numpy.float32)
with self.subTest(part="output_shape"):
onx = OnnxConvTranspose(
'X', W, output_names=['Y'],
strides=[3, 2], output_shape=[10, 8],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def, runtime="onnxruntime1")
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_padding, got['Y'])
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_padding, got['Y'])
@wraplog()
def test_onnxt_runtime_conv_transpose_attributes(self):
x = numpy.arange(9).reshape((1, 1, 3, 3)).astype(numpy.float32)
W = numpy.ones((1, 2, 3, 3)).astype(numpy.float32)
y_with_padding = numpy.array(
[[[[0., 0., 1., 1., 3., 2., 2., 0.], # (1, 2, 10, 8)
[0., 0., 1., 1., 3., 2., 2., 0.],
[0., 0., 1., 1., 3., 2., 2., 0.],
[3., 3., 7., 4., 9., 5., 5., 0.],
[3., 3., 7., 4., 9., 5., 5., 0.],
[3., 3., 7., 4., 9., 5., 5., 0.],
[6., 6., 13., 7., 15., 8., 8., 0.],
[6., 6., 13., 7., 15., 8., 8., 0.],
[6., 6., 13., 7., 15., 8., 8., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.]],
[[0., 0., 1., 1., 3., 2., 2., 0.],
[0., 0., 1., 1., 3., 2., 2., 0.],
[0., 0., 1., 1., 3., 2., 2., 0.],
[3., 3., 7., 4., 9., 5., 5., 0.],
[3., 3., 7., 4., 9., 5., 5., 0.],
[3., 3., 7., 4., 9., 5., 5., 0.],
[6., 6., 13., 7., 15., 8., 8., 0.],
[6., 6., 13., 7., 15., 8., 8., 0.],
[6., 6., 13., 7., 15., 8., 8., 0.],
[0., 0., 0., 0., 0., 0., 0., 0.]]]]).astype(numpy.float32)
with self.subTest(part="output_padding"):
onx = OnnxConvTranspose(
'X', W, output_names=['Y'],
strides=[3, 2], output_padding=[1, 1],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_padding, got['Y'])
with self.subTest(part="kernel_shape"):
onx = OnnxConvTranspose(
'X', W, output_names=['Y'],
strides=[3, 2], output_shape=[10, 8],
kernel_shape=[3, 3], output_padding=[1, 1],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_padding, got['Y'])
@wraplog()
def test_onnxt_runtime_conv_transpose_dilation(self):
x = numpy.array([[[[3., 8., 1.], # (1, 1, 3, 3)
[9., 5., 7.],
[3., 2., 6.]]]]).astype(numpy.float32)
W = numpy.array([[[[7., 2.], # (1, 1, 2, 2)
[1., 9.]]]]).astype(numpy.float32)
y_with_padding = numpy.array(
[[[[21., 56., 13., 16., 2.], # [1, 1, 5, 5]
[63., 35., 67., 10., 14.],
[24., 22., 76., 76., 21.],
[9., 5., 88., 45., 63.],
[3., 2., 33., 18., 54.]]]]).astype(numpy.float32)
onx = OnnxConvTranspose(
'X', W, output_names=['Y'], dilations=[2, 2],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_padding, got['Y'])
@wraplog()
def test_onnxt_runtime_conv_transpose_pads(self):
x = numpy.arange(9).reshape((1, 1, 3, 3)).astype(numpy.float32)
W = numpy.ones((1, 2, 3, 3)).astype(numpy.float32)
y_with_padding = numpy.array(
[[[[1., 1., 3.], # (1, 2, 7, 3)
[1., 1., 3.],
[7., 4., 9.],
[7., 4., 9.],
[7., 4., 9.],
[13., 7., 15.],
[13., 7., 15.]],
[[1., 1., 3.],
[1., 1., 3.],
[7., 4., 9.],
[7., 4., 9.],
[7., 4., 9.],
[13., 7., 15.],
[13., 7., 15.]]]]).astype(numpy.float32)
onx = OnnxConvTranspose(
'X', W, output_names=['Y'],
strides=[3, 2], pads=[1, 2, 1, 2],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(y_with_padding, got['Y'])
@wraplog()
def test_onnxt_runtime_cos(self):
self.common_test_onnxt_runtime_unary(OnnxCos, numpy.cos)
@wraplog()
def test_onnxt_runtime_cosh(self):
self.common_test_onnxt_runtime_unary(OnnxCosh, numpy.cosh)
@wraplog()
def test_onnxt_runtime_cum_sum(self):
x = numpy.array([1., 2., 3., 4., 5.]).astype(numpy.float64)
axis = numpy.array([0]).astype(numpy.int32)
exp = numpy.array([1., 3., 6., 10., 15.]).astype(numpy.float64)
onx = OnnxCumSum('X', 'axis', output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x, 'axis': axis},
outputs=[('Y', DoubleTensorType())],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': x.astype(numpy.float64),
'axis': axis})
self.assertEqualArray(exp, got['Y'])
self.common_expected_shapes_types(
oinf, {'X': x.astype(numpy.float64),
'axis': axis},
got, OnnxCumSum, model_def)
python_tested.append(OnnxCumSum)
oinfpy = OnnxInference(model_def, runtime="python", inplace=True)
validate_python_inference(oinfpy, {'X': x, 'axis': axis})
# reverse = 1
x = numpy.array([1., 2., 3., 4., 5.]).astype(numpy.float64)
axis = numpy.array([0]).astype(numpy.int32)
exp = numpy.array([15., 14., 12., 9., 5.]).astype(numpy.float64)
onx = OnnxCumSum('X', 'axis', output_names=['Y'], reverse=1,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x, 'axis': axis},
outputs=[('Y', DoubleTensorType())],
target_opset=get_opset_number_from_onnx())
try:
got = OnnxInference(model_def).run({'X': x, 'axis': axis})
self.assertEqualArray(exp, got['Y'])
except NotImplementedError:
pass
# exclusive = 1
x = numpy.array([1., 2., 3., 4., 5.]).astype(numpy.float64)
axis = numpy.array([0]).astype(numpy.int32)
exp = numpy.array([0., 1., 3., 6., 10.]).astype(numpy.float64)
onx = OnnxCumSum('X', 'axis', output_names=['Y'], exclusive=1,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x, 'axis': axis},
outputs=[('Y', DoubleTensorType())],
target_opset=get_opset_number_from_onnx())
try:
got = OnnxInference(model_def).run({'X': x, 'axis': axis})
self.assertEqualArray(exp, got['Y'])
except NotImplementedError:
pass
# 2d axis = 0
x = numpy.array([1., 2., 3., 4., 5., 6.]).astype(
numpy.float64).reshape((2, 3))
axis = numpy.array([0]).astype(numpy.int32)
exp = numpy.array([1., 2., 3., 5., 7., 9.]).astype(
numpy.float64).reshape((2, 3))
onx = OnnxCumSum('X', 'axis', output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x, 'axis': axis},
outputs=[('Y', DoubleTensorType())],
target_opset=get_opset_number_from_onnx())
got = OnnxInference(model_def).run({'X': x, 'axis': axis})
self.assertEqualArray(exp, got['Y'])
# 2d axis = 1
x = numpy.array([1., 2., 3., 4., 5., 6.]).astype(
numpy.float64).reshape((2, 3))
axis = numpy.array([-1]).astype(numpy.int32)
exp = numpy.array([1., 3., 6., 4., 9., 15.]).astype(
numpy.float64).reshape((2, 3))
onx = OnnxCumSum('X', 'axis', output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x, 'axis': axis},
outputs=[('Y', DoubleTensorType())],
target_opset=get_opset_number_from_onnx())
got = OnnxInference(model_def).run({'X': x, 'axis': axis})
self.assertEqualArray(exp, got['Y'])
# 2d axis = 1, reverse
x = numpy.array([1., 2., 3., 4., 5., 6.]).astype(
numpy.float64).reshape((2, 3))
axis = numpy.array([-1]).astype(numpy.int32)
exp = numpy.array([1., 3., 6., 4., 9., 15.]).astype(
numpy.float64).reshape((2, 3))
onx = OnnxCumSum('X', 'axis', output_names=['Y'], reverse=1,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': x, 'axis': axis},
outputs=[('Y', DoubleTensorType())],
target_opset=get_opset_number_from_onnx())
try:
got = OnnxInference(model_def).run({'X': x, 'axis': axis})
self.assertEqualArray(exp, got['Y'])
except NotImplementedError:
pass
# no axis
x = numpy.array([1., 2., 3., 4., 5.]).astype(numpy.float64)
axis = numpy.array([0]).astype(numpy.int32)
exp = numpy.array([1., 3., 6., 10., 15.]).astype(numpy.float64)
try:
onx = OnnxCumSum('X', output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx(
{'X': x}, outputs=[('Y', DoubleTensorType())],
target_opset=get_opset_number_from_onnx())
got = OnnxInference(model_def).run({'X': x})
self.assertEqualArray(exp, got['Y'])
except RuntimeError:
pass
# reverse = 1
x = numpy.array([1., 2., 3., 4., 5.]).astype(numpy.float64)
axis = numpy.array([0]).astype(numpy.int32)
exp = numpy.array([15., 14., 12., 9., 5.]).astype(numpy.float64)
try:
onx = OnnxCumSum('X', output_names=['Y'], reverse=1,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx(
{'X': x}, outputs=[('Y', DoubleTensorType())],
target_opset=get_opset_number_from_onnx())
got = OnnxInference(model_def).run({'X': x})
self.assertEqualArray(exp, got['Y'])
except RuntimeError:
pass
@wraplog()
def test_onnxt_runtime_det(self):
self.common_test_onnxt_runtime_unary(
OnnxDet, lambda x: numpy.array([numpy.linalg.det(x)]),
do_sparse=False)
@wraplog()
def test_onnxt_runtime_dequantize_linear(self):
X = numpy.array([[[[3, 89], [34, 200], [74, 59]],
[[5, 24], [24, 87], [32, 13]],
[[245, 99], [4, 142], [121, 102]], ], ],
dtype=numpy.uint8)
x_scale = numpy.array([2, 4, 5], dtype=numpy.float32)
x_zero_point = numpy.array([84, 24, 196], dtype=numpy.uint8)
exp = ((X.astype(numpy.float32) - x_zero_point.reshape(
(1, 3, 1, 1)).astype(numpy.float32)) *
x_scale.reshape((1, 3, 1, 1)))
onx = OnnxDequantizeLinear(
'X', x_scale, x_zero_point, output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqualArray(exp, got['Y'])
self.common_expected_shapes_types(
oinf, {'X': X}, got, OnnxDequantizeLinear, model_def)
X = numpy.array([0, 3, 128, 255]).astype(numpy.uint8)
x_scale = numpy.array([2], dtype=numpy.float32)
x_zero_point = numpy.array([128], dtype=numpy.uint8)
exp = numpy.array([-256, -250, 0, 254], dtype=numpy.float32)
onx = OnnxDequantizeLinear(
'X', x_scale, x_zero_point, output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqualArray(exp, got['Y'])
python_tested.append(OnnxDequantizeLinear)
@wraplog()
def test_onnxt_runtime_div(self):
self.common_test_onnxt_runtime_binary(OnnxDiv, lambda x, y: x / y)
@wraplog()
def test_onnxt_runtime_dropout_10(self):
seed = numpy.int64(0)
X = numpy.random.randn(3, 4, 5).astype(numpy.float32)
onx = OnnxDropout_7('X', output_names=['Y'], op_version=10)
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
outputs=[('Y', FloatTensorType())],
target_opset=10)
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqual(got['Y'].shape, X.shape)
self.assertEqualArray(got['Y'], _dropout(X, seed=seed)[0])
self.common_expected_shapes_types(
oinf, {'X': X}, got, OnnxDropout_7, model_def)
python_tested.append(OnnxDropout)
@wraplog()
def test_onnxt_runtime_dropout(self):
seed = numpy.int64(0)
X = numpy.random.randn(3, 4, 5).astype(numpy.float32)
onx = OnnxDropout('X', output_names=['Y'], seed=seed,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
outputs=[('Y', FloatTensorType())],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqual(got['Y'].shape, X.shape)
self.assertEqualArray(got['Y'], _dropout(X, seed=seed)[0])
self.common_expected_shapes_types(
oinf, {'X': X}, got, OnnxDropout, model_def)
onx = OnnxDropout('X', output_names=['Y', 'Z'], seed=seed,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': X.astype(numpy.float32)},
outputs=[('Y', FloatTensorType()),
('Z', FloatTensorType())],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y', 'Z'])
self.assertEqual(got['Y'].shape, X.shape)
res = _dropout(X, seed=seed, return_mask=True)
self.assertEqualArray(got['Y'], res[0])
self.assertEqualArray(got['Z'], res[1])
R = numpy.array([0.1], dtype=numpy.float32)
onx = OnnxDropout('X', 'R', output_names=['Y'], seed=seed,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': X.astype(numpy.float32),
'R': R.astype(numpy.float32)},
outputs=[('Y', FloatTensorType())],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': X, 'R': R})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqual(got['Y'].shape, X.shape)
self.assertEqualArray(
got['Y'], _dropout(X, seed=seed, drop_probability=0.1)[0])
R = numpy.array([0.75], dtype=numpy.float32)
B = numpy.array([True])
onx = OnnxDropout('X', 'R', 'B', output_names=['Y'], seed=seed,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': X.astype(numpy.float32),
'R': R, 'B': B},
outputs=[('Y', FloatTensorType())],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': X, 'R': R, 'B': B})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqual(got['Y'].shape, X.shape)
self.assertEqualArray(
got['Y'], _dropout(X, seed=seed, drop_probability=0.75,
training_mode=True)[0])
python_tested.append(OnnxDropout)
@wraplog()
def test_onnxt_runtime_einsum(self):
X = numpy.random.randn(5, 2, 3).astype(numpy.float32)
Y = numpy.random.randn(5, 3, 4).astype(numpy.float32)
equation = 'bij,bjk->bik'
onx = OnnxEinsum(
'X', 'Y', equation=equation, output_names=['Z'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': X.astype(numpy.float32),
'Y': Y.astype(numpy.float32)},
outputs=[('Z', FloatTensorType([2]))],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': X, 'Y': Y})
exp = numpy.einsum(equation, X, Y)
self.assertEqualArray(exp, got['Z'])
self.common_expected_shapes_types(
oinf, {'X': X, 'Y': Y}, got, OnnxEinsum, model_def)
python_tested.append(OnnxEinsum)
oinfpy = OnnxInference(model_def, runtime="python", inplace=True)
validate_python_inference(oinfpy, {'X': X.astype(numpy.float32),
'Y': Y.astype(numpy.float32)})
@wraplog()
def test_onnxt_runtime_eyelike(self):
onx = OnnxEyeLike('X', k=0, output_names=['Y'])
X = numpy.array([2, 2], dtype=numpy.int64)
model_def = onx.to_onnx({'X': X.astype(numpy.int64)},
target_opset=get_opset_number_from_onnx(),
outputs=[('Y', FloatTensorType())])
oinf = OnnxInference(model_def)
got = oinf.run({'X': X})
self.assertEqual(list(sorted(got)), ['Y'])
exp = numpy.eye(*X, k=0)
self.assertEqualArray(exp, got['Y'])
self.common_expected_shapes_types(
oinf, {'X': X}, got, OnnxEyeLike, model_def)
oinfpy = OnnxInference(model_def, runtime="python")
validate_python_inference(oinfpy, {'X': X.astype(numpy.int64)})
python_tested.append(OnnxEyeLike)
@wraplog()
def test_onnxt_runtime_equal(self):
self.common_test_onnxt_runtime_binary(OnnxEqual, numpy.equal)
@wraplog()
def test_onnxt_runtime_erf(self):
self.common_test_onnxt_runtime_unary(OnnxErf, erf)
@wraplog()
def test_onnxt_runtime_exp(self):
self.common_test_onnxt_runtime_unary(OnnxExp, numpy.exp)
@wraplog()
def test_onnxt_runtime_flatten(self):
shape = (2, 3, 4, 5)
x = numpy.random.random_sample(shape).astype( # pylint: disable=E1101
numpy.float32) # pylint: disable=E1101
for i in range(len(shape)):
node = OnnxFlatten('X', axis=i, output_names='Y',
op_version=get_opset_number_from_onnx())
model_def = node.to_onnx(
{'X': x}, outputs=[('Y', FloatTensorType())],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': x})
new_shape = ((1, -1) if i == 0
else (numpy.prod(shape[0:i]).astype(int), -1))
exp = numpy.reshape(x, new_shape)
self.assertEqualArray(exp, got['Y'])
self.common_expected_shapes_types(
oinf, {'X': x}, got, OnnxFlatten, model_def)
python_tested.append(OnnxFlatten)
oinfpy = OnnxInference(model_def, runtime="python", inplace=True)
validate_python_inference(oinfpy, {'X': x})
@wraplog()
def test_onnxt_runtime_floor(self):
self.common_test_onnxt_runtime_unary(OnnxFloor, numpy.floor)
@wraplog()
def test_onnxt_runtime_gather_elements0(self):
from skl2onnx.algebra.onnx_ops import OnnxGatherElements # pylint: disable=E0611
# ex 1
data = numpy.array([[1, 2],
[3, 4]], dtype=numpy.float32)
indices = numpy.array([], dtype=numpy.int64)
onx = OnnxGatherElements('X', 'Y', output_names=['Z'], axis=1,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': data, 'Y': indices},
outputs=[('Z', FloatTensorType())],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': data, 'Y': indices})
self.assertEqual(got['Z'].size, 0)
self.common_expected_shapes_types(
oinf, {'X': data, 'Y': indices}, got,
OnnxGatherElements, model_def)
@wraplog()
def test_onnxt_runtime_gather_elements0_fortran(self):
from skl2onnx.algebra.onnx_ops import OnnxGatherElements # pylint: disable=E0611
# ex 1
data = numpy.array([[1, 2],
[3, 4]], dtype=numpy.float32, order='F')
indices = numpy.array([], dtype=numpy.int64, order='F')
onx = OnnxGatherElements('X', 'Y', output_names=['Z'], axis=1,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': data, 'Y': indices},
outputs=[('Z', FloatTensorType())],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': data, 'Y': indices})
self.assertEqual(got['Z'].size, 0)
@wraplog()
def test_onnxt_runtime_gather_elements(self):
from skl2onnx.algebra.onnx_ops import OnnxGatherElements # pylint: disable=E0611
# ex 1
data = numpy.array([[1, 2],
[3, 4]], dtype=numpy.float32)
indices = numpy.array([[0, 0],
[1, 0]], dtype=numpy.int64)
onx = OnnxGatherElements('X', 'Y', output_names=['Z'], axis=1,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': data, 'Y': indices},
outputs=[('Z', FloatTensorType())],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': data, 'Y': indices})
exp = numpy.array([[1, 1],
[4, 3]], dtype=numpy.float32)
self.assertEqual(exp, got['Z'])
python_tested.append(OnnxGatherElements)
oinfpy = OnnxInference(model_def, runtime="python", inplace=True)
validate_python_inference(oinfpy, {'X': data, 'Y': indices})
# ex 2
data = numpy.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]], dtype=numpy.float32)
indices = numpy.array([[1, 2, 0],
[2, 0, 0]], dtype=numpy.int32)
onx = OnnxGatherElements('X', 'Y', output_names=['Z'], axis=0,
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': data, 'Y': indices},
outputs=[('Z', FloatTensorType())],
target_opset=get_opset_number_from_onnx())
oinf = OnnxInference(model_def)
got = oinf.run({'X': data, 'Y': indices})
exp = numpy.array([[4, 8, 3],
[7, 2, 3]], dtype=numpy.float32)
self.assertEqual(exp, got['Z'])
@wraplog()
def test_onnxt_runtime_gemm_python(self):
self.do_test_onnxt_runtime_gemm("python")
python_tested.append(OnnxGemm)
@wraplog()
def test_onnxt_runtime_gemm_onnxruntime(self):
self.do_test_onnxt_runtime_gemm("onnxruntime1")
def do_test_onnxt_runtime_gemm(self, runtime):
idi = numpy.array([[1, 0], [1, 1]], dtype=numpy.float32)
cst = numpy.array([4, 5], dtype=numpy.float32)
X = numpy.array([[1, 2], [3, 4]], dtype=numpy.float32)
onx = OnnxGemm('X', idi, cst, output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': idi.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
if 'onnxruntime' in runtime:
model_def.ir_version = get_ir_version_from_onnx()
try:
oinf = OnnxInference(model_def, runtime=runtime)
except RuntimeError as e:
raise RuntimeError(
"Unable to instantiate (runtime='{}')\n{}".format(
runtime, model_def)) from e
got = oinf.run({'X': X.astype(numpy.float32)})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(numpy.dot(X, idi) + cst, got['Y'], decimal=5)
onx = OnnxGemm('X', idi, cst, transA=1, transB=1, output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': idi.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
if 'onnxruntime' in runtime:
model_def.ir_version = get_ir_version_from_onnx()
try:
oinf = OnnxInference(model_def, runtime=runtime)
except RuntimeError as e:
raise RuntimeError(
"Unable to instantiate (runtime='{}')\n{}".format(
runtime, model_def)) from e
got = oinf.run({'X': X.astype(numpy.float32)})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(numpy.dot(X.T, idi.T) + cst, got['Y'], decimal=5)
onx = OnnxGemm('X', idi, cst, transA=1, output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': idi.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
model_def.ir_version = get_ir_version_from_onnx()
oinf = OnnxInference(model_def, runtime=runtime)
got = oinf.run({'X': X.astype(numpy.float32)})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray(numpy.dot(X.T, idi) + cst, got['Y'], decimal=5)
onx = OnnxGemm('X', idi, cst, transB=1, output_names=['Y'],
op_version=get_opset_number_from_onnx())
model_def = onx.to_onnx({'X': idi.astype(numpy.float32)},
target_opset=get_opset_number_from_onnx())
if 'onnxruntime' in runtime:
model_def.ir_version = get_ir_version_from_onnx()
oinf = OnnxInference(model_def, runtime=runtime)
got = oinf.run({'X': X.astype(numpy.float32)})
self.assertEqual(list(sorted(got)), ['Y'])
self.assertEqualArray( | numpy.dot(X, idi.T) | numpy.dot |
import sklearn.cluster
from scipy.stats import zscore
from matplotlib.patches import Patch
import gseapy as gp
import numpy as np
import pandas as pd
import sys
import scanpy as sc
def get_genelist_references(reference_file_path = "../../Data/",gene_sets=["GO_Biological_Process_2021"]):
genelist_references = {}
for s in gene_sets:
genelist_references[s] = {}
genelist_reference_file = open(reference_file_path+s+".txt")
for l in genelist_reference_file:
m = l.split("\t")
genelist_references[s][m[0]] = m[1:]
return genelist_references
def make_ordered_exp(epi_celltype_exp,celltypes,metadata,adata,celltype_col="celltype",lognorm=True,filter_expression=True):
if type(celltypes)!=list:
celltypes = [celltypes]
exp = epi_celltype_exp[epi_celltype_exp[celltype_col].isin(celltypes)]
exp.index=exp["sample"]
exp = exp.iloc[:,2:]
#exp =exp.dropna()
# map expression to time post partum metadata
exp["time_post_partum_days"] = exp.index.map(metadata["time_post_partum_days"])
exp = exp.loc[exp["time_post_partum_days"]<400]
exp = exp.iloc[:,:-1]
exp=exp.loc[adata.obs[adata.obs["Epithelial Cell Subclusters"].isin(celltypes)].groupby(["sample"]).count().loc[exp.index,"phase"] > 10]
# remove genes not expressed
exp=exp.loc[:,exp.sum(axis=0)>0]
if lognorm:
#sample normalize
exp_norm = exp.div(exp.sum(axis=1),axis=0)*1000
# log
#exp_log=np.log(exp+1)
exp_lognorm = np.log(exp_norm+1)
#order exp by time post partum
else:
exp_lognorm = exp
ordered_exp = exp_lognorm.iloc[exp_lognorm.index.map(metadata["time_post_partum_days"]).argsort()]
return exp,ordered_exp
def heatmap_and_clusters_by_time(epi_celltype_exp, des_res, celltype,metadata,adata,minlfc=0.005,minmean=20,vmax=3,vmin=-2, min_pts = .1):
directory = "time_series_heatmaps/"
exp,ordered_exp = make_ordered_exp(epi_celltype_exp, celltype,metadata,adata)
if "rank_genes_groups" not in adata_all_epi.uns or adata_all_epi.uns["rank_genes_groups"]["params"]["groupby"] != "Epithelial Cell Subclusters" or "pts" not in adata_all_epi.uns["rank_genes_groups"]:
sc.tl.rank_genes_groups(adata_all_epi, groupby="Epithelial Cell Subclusters", pts=True)
des_res_reduced = des_res.loc[des_res["padj"]<.05]
des_res_reduced = des_res_reduced.loc[des_res_reduced["log2FoldChange"].abs()>minlfc]
des_res_reduced = des_res_reduced.loc[des_res_reduced["baseMean"].abs()>minmean]
#g = [i.replace(".","_") for i in des_res_reduced.index]
overlap_genes = list(set(des_res_reduced.index).intersection(set(adata_all_epi.uns["rank_genes_groups"]["pts"].index)))
#des_res_reduced.index = [i.replace(".","_") for i in des_res_reduced.index]
des_res_reduced = des_res_reduced.loc[overlap_genes]
des_res_reduced["pts"] = adata_all_epi.uns["rank_genes_groups"]["pts"].loc[des_res_reduced.index,celltype]
des_res_reduced = des_res_reduced.loc[des_res_reduced["pts"]>min_pts]
genes=[i for i in des_res_reduced.sort_values('log2FoldChange').index if i in ordered_exp.columns]
#zscore each column
z=ordered_exp.apply(zscore)
n_clusters = 5
labels = sklearn.cluster.KMeans(n_clusters=n_clusters).fit_predict(z.T.loc[genes])
new_gene_order=reorder_from_labels(labels,genes)
lut=dict(zip(list(set(labels)),("r","g","y","m","k")))
row_colors=[lut[i] for i in labels]
row_color_order = reorder_from_labels(labels,row_colors)
exp.iloc[exp.index.map(metadata["time_post_partum_days"]).argsort()][new_gene_order].to_csv(directory+celltype+"_reduced_pseudobulk_expression_for_heatmap_raw.csv")
col_colors=ordered_exp.index.map(metadata["milk_stage"]).map(hh.milk_stage_colors)
ordered_exp[new_gene_order].to_csv(directory+celltype+"_reduced_pseudobulk_expression_for_heatmap_lognormed.csv")
pd.DataFrame(labels, index=genes).to_csv(directory+celltype+"_time_dep_gene_cluster_labels.csv")
g=sns.clustermap(ordered_exp.T.loc[new_gene_order],row_cluster=False,col_cluster=False,row_colors=row_color_order,col_colors=col_colors,z_score=0,vmax=vmax,vmin=vmin)
handles = [Patch(facecolor=lut[name]) for name in lut]
plt.legend(handles, lut, title='Gene Cluster',
bbox_to_anchor=(1, 1), bbox_transform=plt.gcf().transFigure, loc='upper right')
plt.savefig(directory+celltype+"_time_dependent_genes_heatmap.pdf",bbox_inches="tight")
plt.savefig(directory+celltype+"_time_dependent_genes_heatmap.png",bbox_inches="tight")
return genes,labels
def gsea_prerank_heatmaps(epi_celltype_exp, des_res, celltype,metadata,adata,gene_sets="GO_Biological_Process_2021"):
outdir='time_series_heatmaps/prerank/'+celltype.replace("/","_").replace(" ","_")+'/prerank_report_hallmark'
des_res_reduced = des_res.loc[des_res["padj"]<.05]
genes_gsea = des_res_reduced.sort_values('log2FoldChange').index
pre_res = gp.prerank(rnk=des_res_reduced.loc[genes_gsea,"log2FoldChange"], gene_sets=gene_sets,
processes=4,
permutation_num=100, # reduce number to speed up testing
outdir=outdir, format='png', seed=6)
_,exp = make_ordered_exp(epi_celltype_exp,celltype,metadata,adata)
z=exp.apply(zscore)
for pathway in pre_res.res2d[pre_res.res2d["pval"] < .05].index:
g=sns.clustermap(z.T.loc[pre_res.res2d.loc[pathway,"genes"].split(";")],row_cluster=False,col_cluster=False,vmax=3)
plt.title(pathway)
plt.savefig(outdir+"/"+pathway.replace("-","").replace(" ","_").replace("/","_")+"_heatmap.png",bbox_inches="tight")
pre_res.res2d.to_csv(outdir+"/"+gene_sets+"_prerank_results.csv")
return pre_res
def dotplot_of_pre_res(pre_res, celltype):
ordered = pre_res.res2d.iloc[pre_res.res2d["nes"].argsort()]
ordered = ordered[(ordered["fdr"]<.25) & (ordered["pval"]<.05)]
plt.figure(figsize=(5,6))
sns.scatterplot(y=ordered.index,x=ordered["nes"],size=ordered["matched_size"],hue=ordered["fdr"])
plt.xlabel("Normalized Enrichment Score")
plt.legend(bbox_to_anchor=(1.05, 1))
plt.title(celltype+" Time Associated Genes")
def get_mean_scores_for_heatmap(adata,celltypes, GO_list,metadata):
if type(celltypes)==list:
adata.obs["tmp_celltype"] = ""
adata.obs.loc[adata.obs["Epithelial Cell Subclusters"].isin(celltypes),"tmp_celltype"] = "_".join(celltypes)
celltypes.append("_".join(celltypes))
mean_scores_per_celltype=adata.obs.groupby(["tmp_celltype","sample"])[GO_list].mean().reset_index()
_,sec_ordered = make_ordered_exp(mean_scores_per_celltype,celltypes,metadata,adata,celltype_col="tmp_celltype",lognorm=False)
else:
mean_scores_per_celltype=adata.obs.groupby(["Epithelial Cell Subclusters","sample"])[GO_list].mean().reset_index()
_,sec_ordered = make_ordered_exp(mean_scores_per_celltype,celltypes,metadata,adata,celltype_col="Epithelial Cell Subclusters",lognorm=False)
combined_scores = sec_ordered.T
combined_scores.columns = combined_scores.columns.astype(str)
combined_scores=combined_scores[sec_ordered.index]
return combined_scores
def collapse_GO_hits(GO_hits, enr,overlap_threshold = 0.6):
if type(enr) != type(pd.DataFrame()):
enr_df = enr.res2d
else:
enr_df = enr
overlap_info = {}
ordered_go_hits= enr_df.loc[enr_df["Term"].isin(GO_hits)].sort_values("n_genes")["Term"].values
print(len(ordered_go_hits))
for g in ordered_go_hits:
found_overlap = False
genes = enr_df.loc[enr_df["Term"]==g,"Genes"].values[0].split(";")
#print(genes)
genelist_len = len(genes)
max_overlap = 0
max_overlap_key = ""
for s in overlap_info:
overlap = len(set(genes).intersection(overlap_info[s]["Genes"]))
if overlap>max_overlap and (1.0*overlap)/genelist_len > overlap_threshold and not found_overlap:
found_overlap = True
max_overlap=overlap
max_overlap_key = s
if found_overlap:
overlap_info[max_overlap_key]["Genes"] = overlap_info[max_overlap_key]["Genes"].union(genes)
overlap_info[max_overlap_key]["listnames"].append(g)
overlap_info[max_overlap_key]["combined_scores"].append(enr_df.loc[enr_df["Term"]==g,"Combined Score"].values[0])
if not found_overlap:
overlap_info[g] = {}
overlap_info[g]["Genes"] = set(genes)
overlap_info[g]["listnames"] = [g]
overlap_info[g]["combined_scores"] = [enr_df.loc[enr_df["Term"]==g,"Combined Score"].values[0]]
collapsed_list = []
for o in overlap_info:
top = overlap_info[o]['listnames'][ | np.argmax(overlap_info[o]["combined_scores"]) | numpy.argmax |
#!/usr/bin/env python
u"""
test_download_and_read.py (09/2021)
Tests that CATS2008 data can be downloaded from the US Antarctic Program (USAP)
Tests that AOTIM-5-2018 data can be downloaded from the NSF ArcticData server
Tests the read program to verify that constituents are being extracted
Tests that interpolated results are comparable to Matlab TMD program
https://github.com/EarthAndSpaceResearch/TMD_Matlab_Toolbox_v2.5
PYTHON DEPENDENCIES:
numpy: Scientific Computing Tools For Python
https://numpy.org
https://numpy.org/doc/stable/user/numpy-for-matlab-users.html
scipy: Scientific Tools for Python
https://docs.scipy.org/doc/
Oct2Py: Python to GNU Octave Bridge
https://oct2py.readthedocs.io/en/latest/
boto3: Amazon Web Services (AWS) SDK for Python
https://boto3.amazonaws.com/v1/documentation/api/latest/index.html
UPDATE HISTORY:
Updated 09/2021: added test for model definition files
Updated 07/2021: download CATS2008 and AntTG from S3 to bypass USAP captcha
Updated 05/2021: added test for check point program
Updated 03/2021: use pytest fixture to setup and teardown model data
use TMD tmd_tide_pred_plus to calculate OB time series
refactor program into two classes for CATS2008 and AOTIM-5-2018
replaced numpy bool/int to prevent deprecation warnings
Updated 01/2021: download CATS2008 and AOTIM-5-2018 to subdirectories
Updated 08/2020: Download Antarctic tide gauge database and compare with RMS
directly call Matlab program (octave+oct2py) and compare outputs
compare outputs for both Antarctic (CATS2008) and Arctic (AOTIM-5-2018)
will install octave and oct2py in development requirements
Written 08/2020
"""
import os
import re
import io
import boto3
import shutil
import pytest
import inspect
import zipfile
import warnings
import posixpath
import numpy as np
import pyTMD.time
import pyTMD.model
import pyTMD.utilities
import pyTMD.read_tide_model
import pyTMD.predict_tidal_ts
import pyTMD.infer_minor_corrections
import pyTMD.check_tide_points
import pyTMD.tidal_ellipse
from oct2py import octave
#-- current file path
filename = inspect.getframeinfo(inspect.currentframe()).filename
filepath = os.path.dirname(os.path.abspath(filename))
#-- PURPOSE: calculate the matlab serial date from calendar date
#-- http://scienceworld.wolfram.com/astronomy/JulianDate.html
def convert_calendar_serial(year, month, day, hour=0.0, minute=0.0, second=0.0):
#-- return the date in days since serial epoch 0000-01-01T00:00:00
sd = 367.0*year - np.floor(7.0*(year + np.floor((month+9.0)/12.0))/4.0) - \
np.floor(3.0*(np.floor((year + (month - 9.0)/7.0)/100.0) + 1.0)/4.0) + \
np.floor(275.0*month/9.0) + day + hour/24.0 + minute/1440.0 + \
second/86400.0 - 30.0
return sd
#-- PURPOSE: Test and Verify CATS2008 model read and prediction programs
class Test_CATS2008:
#-- PURPOSE: Download CATS2008 from US Antarctic Program
@pytest.fixture(scope="class", autouse=False)
def download_CATS2008(self):
#-- download CATS2008 zip file and read as virtual file object
HOST = ['https://www.usap-dc.org','dataset','usap-dc','601235',
'2019-12-19T23:26:43.6Z','CATS2008.zip?dataset_id=601235']
FILE = pyTMD.utilities.from_http(HOST)
zfile = zipfile.ZipFile(FILE)
print('{0} -->\n'.format(posixpath.join(*HOST)))
#-- find model files within zip file
rx = re.compile(r'(grid|h[0f]?|UV[0]?|Model|xy)[_\.](.*?)',re.IGNORECASE)
m = [m for m in zfile.filelist if rx.match(posixpath.basename(m.filename))]
#-- verify that model files are within downloaded zip file
assert all(m)
#-- output tide directory for model
modelpath = os.path.join(filepath,'CATS2008')
#-- extract each member (model and configuration files)
for member in m:
#-- strip directories from member filename
member.filename = posixpath.basename(member.filename)
print('\t{0}\n'.format(os.path.join(modelpath,member.filename)))
zfile.extract(member, path=modelpath)
#-- close the zipfile object
zfile.close()
#-- output control file for tide model
CFname = os.path.join(filepath,'Model_CATS2008')
fid = open(CFname,'w')
for model_file in ['hf.CATS2008.out','uv.CATS2008.out','grid_CATS2008']:
print(os.path.join(modelpath,model_file),file=fid)
print('xy_ll_CATS2008',file=fid)
fid.close()
#-- verify control file
assert os.access(CFname, os.F_OK)
#-- run tests
yield
#-- clean up model
shutil.rmtree(modelpath)
#-- clean up
os.remove(CFname)
#-- PURPOSE: Download CATS2008 from AWS S3 bucket
@pytest.fixture(scope="class", autouse=True)
def AWS_CATS2008(self, aws_access_key_id, aws_secret_access_key, aws_region_name):
#-- get aws session object
session = boto3.Session(
aws_access_key_id=aws_access_key_id,
aws_secret_access_key=aws_secret_access_key,
region_name=aws_region_name)
#-- get s3 object and bucket object for pytmd data
s3 = session.resource('s3')
bucket = s3.Bucket('pytmd')
#-- model parameters for CATS2008
modelpath = os.path.join(filepath,'CATS2008')
#-- recursively create model directory
os.makedirs(modelpath)
#-- output control file for tide model
CFname = os.path.join(filepath,'Model_CATS2008')
fid = open(CFname,'w')
#-- retrieve each model file from s3
for model_file in ['hf.CATS2008.out','uv.CATS2008.out','grid_CATS2008']:
#-- retrieve CATS2008 modelfile
obj = bucket.Object(key=posixpath.join('CATS2008',model_file))
response = obj.get()
with open(os.path.join(modelpath,model_file), 'wb') as destination:
shutil.copyfileobj(response['Body'], destination)
assert os.access(os.path.join(modelpath,model_file), os.F_OK)
#-- print to model control file
print(os.path.join(modelpath,model_file),file=fid)
#-- retrieve CATS2008 coordinate file
model_file = 'xy_ll_CATS2008.m'
obj = bucket.Object(key=posixpath.join('CATS2008',model_file))
response = obj.get()
with open(os.path.join(modelpath,model_file), 'wb') as destination:
shutil.copyfileobj(response['Body'], destination)
#-- print coordinate conversion function to model control file
print('xy_ll_CATS2008',file=fid)
fid.close()
#-- verify control file
assert os.access(CFname, os.F_OK)
#-- run tests
yield
#-- clean up model
shutil.rmtree(modelpath)
#-- clean up
os.remove(CFname)
#-- PURPOSE: Download Antarctic Tide Gauge Database from US Antarctic Program
@pytest.fixture(scope="class", autouse=False)
def download_AntTG(self):
#-- download Tide Gauge Database text file
HOST = ['https://www.usap-dc.org','dataset','usap-dc','601358',
'2020-07-10T19:50:08.8Z','AntTG_ocean_height_v1.txt?dataset_id=601358']
local = os.path.join(filepath,'AntTG_ocean_height_v1.txt')
pyTMD.utilities.from_http(HOST,local=local)
assert os.access(local, os.F_OK)
#-- run tests
yield
#-- clean up
os.remove(local)
#-- PURPOSE: Download Antarctic Tide Gauge Database from AWS
@pytest.fixture(scope="class", autouse=True)
def AWS_AntTG(self, aws_access_key_id, aws_secret_access_key, aws_region_name):
#-- get aws session object
session = boto3.Session(
aws_access_key_id=aws_access_key_id,
aws_secret_access_key=aws_secret_access_key,
region_name=aws_region_name)
#-- get s3 object and bucket object for pytmd data
s3 = session.resource('s3')
bucket = s3.Bucket('pytmd')
#-- retrieve Tide Gauge Database text file
obj = bucket.Object(key='AntTG_ocean_height_v1.txt')
response = obj.get()
local = os.path.join(filepath,'AntTG_ocean_height_v1.txt')
with open(local, 'wb') as destination:
shutil.copyfileobj(response['Body'], destination)
assert os.access(local, os.F_OK)
#-- run tests
yield
#-- clean up
os.remove(local)
#-- PURPOSE: Test read program that grids and constituents are as expected
def test_read_CATS2008(self, ny=2026, nx=1663):
#-- model parameters for CATS2008
modelpath = os.path.join(filepath,'CATS2008')
grid_file = os.path.join(modelpath,'grid_CATS2008')
elevation_file = os.path.join(modelpath,'hf.CATS2008.out')
transport_file = os.path.join(modelpath,'uv.CATS2008.out')
#-- read CATS2008 grid file
xi,yi,hz,mz,iob,dt = pyTMD.read_tide_model.read_tide_grid(grid_file)
#-- check dimensions of input grids
assert (hz.shape == (ny,nx))
assert (mz.shape == (ny,nx))
#-- check constituent list
constituents,nc = pyTMD.read_tide_model.read_constituents(elevation_file)
cons = ['m2','s2','n2','k2','k1','o1','p1','q1','mf','mm']
assert all(c in constituents for c in cons)
#-- check dimensions of input grids from elevation and transport files
for i,c in enumerate(constituents):
z = pyTMD.read_tide_model.read_elevation_file(elevation_file,i)
u,v = pyTMD.read_tide_model.read_transport_file(transport_file,i)
assert (z.shape == (ny,nx))
assert (u.shape == (ny,nx))
assert (v.shape == (ny,nx))
#-- PURPOSE: Tests check point program
def test_check_CATS2008(self):
lons = np.zeros((10)) + 178.0
lats = -45.0 - np.arange(10)*5.0
obs = pyTMD.check_tide_points(lons, lats, DIRECTORY=filepath,
MODEL='CATS2008', EPSG=4326)
exp = np.array([False, False, False, False, True,
True, True, True, False, False])
assert np.all(obs == exp)
#-- PURPOSE: Tests that interpolated results are comparable to AntTG database
def test_compare_CATS2008(self):
#-- model parameters for CATS2008
modelpath = os.path.join(filepath,'CATS2008')
grid_file = os.path.join(modelpath,'grid_CATS2008')
model_file = os.path.join(modelpath,'hf.CATS2008.out')
GRID = 'OTIS'
EPSG = 'CATS2008'
TYPE = 'z'
#-- open Antarctic Tide Gauge (AntTG) database
with open(os.path.join(filepath,'AntTG_ocean_height_v1.txt'),'r') as f:
file_contents = f.read().splitlines()
#-- counts the number of lines in the header
count = 0
HEADER = True
#-- Reading over header text
while HEADER:
#-- check if file line at count starts with matlab comment string
HEADER = file_contents[count].startswith('%')
#-- add 1 to counter
count += 1
#-- rewind 1 line
count -= 1
#-- iterate over number of stations
constituents = ['q1','o1','p1','k1','n2','m2','s2','k2']
antarctic_stations = (len(file_contents) - count)//10
stations = [None]*antarctic_stations
shortname = [None]*antarctic_stations
station_lon = np.zeros((antarctic_stations))
station_lat = np.zeros((antarctic_stations))
station_amp = np.ma.zeros((antarctic_stations,len(constituents)))
station_ph = np.ma.zeros((antarctic_stations,len(constituents)))
for s in range(antarctic_stations):
i = count + s*10
stations[s] = file_contents[i + 1].strip()
shortname[s] = file_contents[i + 3].strip()
lat,lon,_,_ = file_contents[i + 4].split()
station_lon[s] = np.float64(lon)
station_lat[s] = np.float64(lat)
amp = file_contents[i + 7].split()
ph = file_contents[i + 8].split()
station_amp.data[s,:] = np.array(amp,dtype=np.float64)
station_ph.data[s,:] = np.array(ph,dtype=np.float64)
#-- update masks where NaN
station_amp.mask = np.isnan(station_amp.data) | (station_amp.data == 0.0)
station_ph.mask = np.isnan(station_ph.data)
#-- replace nans with fill values
station_amp.data[station_amp.mask] = station_amp.fill_value
station_ph.data[station_ph.mask] = station_ph.fill_value
#-- extract amplitude and phase from tide model
amp,ph,D,cons = pyTMD.read_tide_model.extract_tidal_constants(station_lon,
station_lat, grid_file, model_file, EPSG, TYPE=TYPE, METHOD='spline',
GRID=GRID)
#-- reorder constituents of model and convert amplitudes to cm
model_amp = np.ma.zeros((antarctic_stations,len(constituents)))
model_ph = np.ma.zeros((antarctic_stations,len(constituents)))
for i,c in enumerate(constituents):
j, = [j for j,val in enumerate(cons) if (val == c)]
model_amp[:,i] = 100.0*amp[:,j]
model_ph[:,i] = ph[:,j]
#-- calculate complex constituent oscillations
station_z = station_amp*np.exp(-1j*station_ph*np.pi/180.0)
model_z = model_amp*np.exp(-1j*model_ph*np.pi/180.0)
#-- valid stations for all constituents
valid = np.all((~station_z.mask) & (~model_z.mask), axis=1)
invalid_list = ['Ablation Lake','Amery','Bahia Esperanza','Beaver Lake',
'Cape Roberts','Casey','Doake Ice Rumples','EE4A','EE4B',
'Eklund Islands','Gerlache C','Groussac','Gurrachaga','Half Moon Is.',
'Heard Island','Hobbs Pool','Mawson','McMurdo','Mikkelsen','Palmer',
'Primavera','Rutford GL','Rutford GPS','Rothera','Scott Base',
'Seymour Is','Terra Nova Bay']
#-- remove coastal stations from the list
invalid_stations = [i for i,s in enumerate(shortname) if s in invalid_list]
valid[invalid_stations] = False
nv = np.count_nonzero(valid)
#-- compare with RMS values from King et al. (2011)
#-- https://doi.org/10.1029/2011JC006949
RMS = np.array([1.4,2.7,1.7,3.5,2.9,7.3,5.0,1.7])
rms = np.zeros((len(constituents)))
for i,c in enumerate(constituents):
#-- calculate difference and rms
difference = np.abs(station_z[valid,i] - model_z[valid,i])
#-- round to precision of King et al. (2011)
rms[i] = np.round(np.sqrt(np.sum(difference**2)/(2.0*nv)),decimals=1)
#-- test RMS differences
assert np.all(rms <= RMS)
#-- parameterize type: heights versus currents
parameters = []
parameters.append(dict(type='z',model='hf.CATS2008.out',grid='grid_CATS2008'))
parameters.append(dict(type='U',model='uv.CATS2008.out',grid='grid_CATS2008'))
parameters.append(dict(type='V',model='uv.CATS2008.out',grid='grid_CATS2008'))
@pytest.mark.parametrize("parameters", parameters)
#-- PURPOSE: Tests that interpolated results are comparable to Matlab program
def test_verify_CATS2008(self, parameters):
#-- model parameters for CATS2008
modelpath = os.path.join(filepath,'CATS2008')
grid_file = os.path.join(modelpath,parameters['grid'])
model_file = os.path.join(modelpath,parameters['model'])
TYPE = parameters['type']
GRID = 'OTIS'
EPSG = 'CATS2008'
#-- open Antarctic Tide Gauge (AntTG) database
with open(os.path.join(filepath,'AntTG_ocean_height_v1.txt'),'r') as f:
file_contents = f.read().splitlines()
#-- counts the number of lines in the header
count = 0
HEADER = True
#-- Reading over header text
while HEADER:
#-- check if file line at count starts with matlab comment string
HEADER = file_contents[count].startswith('%')
#-- add 1 to counter
count += 1
#-- rewind 1 line
count -= 1
#-- iterate over number of stations
antarctic_stations = (len(file_contents) - count)//10
stations = [None]*antarctic_stations
shortname = [None]*antarctic_stations
station_type = [None]*antarctic_stations
station_lon = np.zeros((antarctic_stations))
station_lat = np.zeros((antarctic_stations))
for s in range(antarctic_stations):
i = count + s*10
stations[s] = file_contents[i + 1].strip()
shortname[s] = file_contents[i + 3].strip()
lat,lon,_,_ = file_contents[i + 4].split()
station_type[s] = file_contents[i + 6].strip()
station_lon[s] = np.float64(lon)
station_lat[s] = np.float64(lat)
#-- calculate daily results for a time period
#-- convert time to days since 1992-01-01T00:00:00
tide_time = np.arange(pyTMD.time.convert_calendar_dates(2000,1,1),
pyTMD.time.convert_calendar_dates(2000,12,31)+1)
#-- serial dates for matlab program (days since 0000-01-01T00:00:00)
SDtime = np.arange(convert_calendar_serial(2000,1,1),
convert_calendar_serial(2000,12,31)+1)
#-- presently not converting times to dynamic times for model comparisons
deltat = np.zeros_like(tide_time)
#-- number of days
ndays = len(tide_time)
#-- extract amplitude and phase from tide model
amp,ph,D,c = pyTMD.read_tide_model.extract_tidal_constants(station_lon,
station_lat, grid_file, model_file, EPSG, TYPE=TYPE,
METHOD='spline', GRID=GRID)
#-- calculate complex phase in radians for Euler's
cph = -1j*ph*np.pi/180.0
#-- will verify differences between model outputs are within tolerance
eps = np.finfo(np.float16).eps
#-- compare daily outputs at each station point
invalid_list = ['Ablation Lake','Amery','Bahia Esperanza','Beaver Lake',
'Cape Roberts','Casey','Doake Ice Rumples','EE4A','EE4B',
'Eklund Islands','Gerlache C','Groussac','Gurrachaga','Half Moon Is.',
'Heard Island','Hobbs Pool','Mawson','McMurdo','Mikkelsen','Palmer',
'Primavera','Rutford GL','Rutford GPS','Rothera','Scott Base',
'Seymour Is','Terra Nova Bay']
#-- remove coastal stations from the list
valid_stations=[i for i,s in enumerate(shortname) if s not in invalid_list]
#-- compute validation data from Matlab TMD program using octave
#-- https://github.com/EarthAndSpaceResearch/TMD_Matlab_Toolbox_v2.5
TMDpath = os.path.join(filepath,'..','TMD_Matlab_Toolbox','TMD')
octave.addpath(octave.genpath(os.path.normpath(TMDpath)))
octave.addpath(filepath)
octave.addpath(modelpath)
#-- turn off octave warnings
octave.warning('off', 'all')
#-- input control file for model
CFname = os.path.join(filepath,'Model_CATS2008')
assert os.access(CFname, os.F_OK)
#-- run Matlab TMD program with octave
#-- MODE: OB time series
validation,_ = octave.tmd_tide_pred_plus(CFname,SDtime,
station_lat[valid_stations],station_lon[valid_stations],
TYPE,nout=2)
#-- for each valid station
for i,s in enumerate(valid_stations):
#-- calculate constituent oscillation for station
hc = amp[s,None,:]*np.exp(cph[s,None,:])
#-- allocate for out tides at point
tide = np.ma.zeros((ndays))
tide.mask = np.zeros((ndays),dtype=bool)
#-- predict tidal elevations at time and infer minor corrections
tide.mask[:] = np.any(hc.mask)
tide.data[:] = pyTMD.predict_tidal_ts(tide_time, hc, c,
DELTAT=deltat, CORRECTIONS=GRID)
minor = pyTMD.infer_minor_corrections(tide_time, hc, c,
DELTAT=deltat, CORRECTIONS=GRID)
tide.data[:] += minor.data[:]
#-- calculate differences between matlab and python version
difference = np.ma.zeros((ndays))
difference.data[:] = tide.data - validation[:,i]
difference.mask = (tide.mask | np.isnan(validation[:,i]))
difference.data[difference.mask] = 0.0
if not np.all(difference.mask):
assert np.all(np.abs(difference) < eps)
#-- PURPOSE: Tests that tidal ellipse results are comparable to Matlab program
def test_tidal_ellipse(self):
#-- model parameters for CATS2008
modelpath = os.path.join(filepath,'CATS2008')
grid_file = os.path.join(modelpath,'grid_CATS2008')
model_file = os.path.join(modelpath,'uv.CATS2008.out')
TYPES = ['u','v']
GRID = 'OTIS'
EPSG = 'CATS2008'
#-- open Antarctic Tide Gauge (AntTG) database
with open(os.path.join(filepath,'AntTG_ocean_height_v1.txt'),'r') as f:
file_contents = f.read().splitlines()
#-- counts the number of lines in the header
count = 0
HEADER = True
#-- Reading over header text
while HEADER:
#-- check if file line at count starts with matlab comment string
HEADER = file_contents[count].startswith('%')
#-- add 1 to counter
count += 1
#-- rewind 1 line
count -= 1
#-- iterate over number of stations
antarctic_stations = (len(file_contents) - count)//10
stations = [None]*antarctic_stations
shortname = [None]*antarctic_stations
station_type = [None]*antarctic_stations
station_lon = np.zeros((antarctic_stations))
station_lat = np.zeros((antarctic_stations))
for s in range(antarctic_stations):
i = count + s*10
stations[s] = file_contents[i + 1].strip()
shortname[s] = file_contents[i + 3].strip()
lat,lon,_,_ = file_contents[i + 4].split()
station_type[s] = file_contents[i + 6].strip()
station_lon[s] = np.float64(lon)
station_lat[s] = np.float64(lat)
#-- compare daily outputs at each station point
invalid_list = ['Ablation Lake','Amery','Bahia Esperanza','Beaver Lake',
'Cape Roberts','Casey','Doake Ice Rumples','EE4A','EE4B',
'Eklund Islands','Gerlache C','Groussac','Gurrachaga','Half Moon Is.',
'Heard Island','Hobbs Pool','Mawson','McMurdo','Mikkelsen','Palmer',
'Primavera','Rutford GL','Rutford GPS','Rothera','Scott Base',
'Seymour Is','Terra Nova Bay']
#-- remove coastal stations from the list
i = [i for i,s in enumerate(shortname) if s not in invalid_list]
valid_stations = len(i)
#-- will verify differences between model outputs are within tolerance
eps = np.finfo(np.float16).eps
#-- save complex amplitude for each current
hc1,hc2 = ({},{})
#-- iterate over zonal and meridional currents
for TYPE in TYPES:
#-- extract amplitude and phase from tide model
amp,ph,D,c=pyTMD.read_tide_model.extract_tidal_constants(station_lon[i],
station_lat[i], grid_file, model_file, EPSG, TYPE=TYPE,
METHOD='spline', GRID=GRID)
#-- calculate complex phase in radians for Euler's
cph = -1j*ph*np.pi/180.0
#-- calculate constituent oscillation for station
hc1[TYPE] = amp*np.exp(cph)
#-- compute validation data from Matlab TMD program using octave
#-- https://github.com/EarthAndSpaceResearch/TMD_Matlab_Toolbox_v2.5
TMDpath = os.path.join(filepath,'..','TMD_Matlab_Toolbox','TMD')
octave.addpath(octave.genpath(os.path.normpath(TMDpath)))
octave.addpath(filepath)
octave.addpath(modelpath)
#-- turn off octave warnings
octave.warning('off', 'all')
#-- input control file for model
CFname = os.path.join(filepath,'Model_CATS2008')
assert os.access(CFname, os.F_OK)
#-- extract tidal harmonic constants out of a tidal model
amp,ph,D,cons = octave.tmd_extract_HC(CFname,station_lat[i],
station_lon[i],TYPE,nout=4)
#-- calculate complex phase in radians for Euler's
cph = -1j*ph*np.pi/180.0
#-- calculate constituent oscillation for station
hc2[TYPE] = amp*np.exp(cph)
#-- compute tidal ellipse parameters for python program
test = {}
test['umajor'],test['uminor'],test['uincl'],test['uphase'] = \
pyTMD.tidal_ellipse(hc1['u'],hc1['v'])
#-- compute tidal ellipse parameters for TMD matlab program
valid = {}
valid['umajor'],valid['uminor'],valid['uincl'],valid['uphase'] = \
octave.TideEl(hc2['u'],hc2['v'],nout=4)
#-- calculate differences between matlab and python version
for key in ['umajor','uminor','uincl','uphase']:
difference = np.ma.zeros((valid_stations,len(c)))
difference.data[:] = test[key].data - valid[key].T
difference.mask = (test[key].mask | np.isnan(valid[key].T))
difference.data[difference.mask] = 0.0
if not np.all(difference.mask):
assert np.all(np.abs(difference) < eps)
#-- parameterize interpolation method
#-- only use fast interpolation routines
@pytest.mark.parametrize("METHOD", ['spline','nearest'])
@pytest.mark.parametrize("EXTRAPOLATE", [True])
#-- PURPOSE: test the tide correction wrapper function
def test_Ross_Ice_Shelf(self, METHOD, EXTRAPOLATE):
#-- create a drift track along the Ross Ice Shelf
xlimits = np.array([-740000,520000])
ylimits = np.array([-1430000,-300000])
#-- x and y coordinates
x = np.linspace(xlimits[0],xlimits[1],24)
y = np.linspace(ylimits[0],ylimits[1],24)
#-- time dimension
delta_time = np.zeros((24))*3600
#-- calculate tide drift corrections
tide = pyTMD.compute_tide_corrections(x, y, delta_time,
DIRECTORY=filepath, MODEL='CATS2008', GZIP=False,
EPOCH=(2000,1,1,12,0,0), TYPE='drift', TIME='UTC',
EPSG=3031, METHOD=METHOD, EXTRAPOLATE=EXTRAPOLATE)
assert np.any(tide)
#-- PURPOSE: test definition file functionality
@pytest.mark.parametrize("MODEL", ['CATS2008'])
def test_definition_file(self, MODEL):
#-- get model parameters
model = pyTMD.model(filepath).elevation(MODEL)
#-- create model definition file
fid = io.StringIO()
attrs = ['name','format','grid_file','model_file','type','projection']
for attr in attrs:
val = getattr(model,attr)
if isinstance(val,list):
fid.write('{0}\t{1}\n'.format(attr,','.join(val)))
else:
fid.write('{0}\t{1}\n'.format(attr,val))
fid.seek(0)
#-- use model definition file as input
m = pyTMD.model().from_file(fid)
for attr in attrs:
assert getattr(model,attr) == getattr(m,attr)
#-- PURPOSE: Test and Verify AOTIM-5-2018 model read and prediction programs
class Test_AOTIM5_2018:
#-- PURPOSE: Download AOTIM-5-2018 from NSF ArcticData server
@pytest.fixture(scope="class", autouse=True)
def download_AOTIM5_2018(self):
#-- build host url for model
resource_map_doi = 'resource_map_doi:{0}'.format('10.18739/A21R6N14K')
HOST = ['https://arcticdata.io','metacat','d1','mn','v2','packages',
pyTMD.utilities.quote_plus(posixpath.join('application','bagit-097')),
pyTMD.utilities.quote_plus(resource_map_doi)]
#-- download zipfile from host
FILE = pyTMD.utilities.from_http(HOST)
zfile = zipfile.ZipFile(FILE)
print('{0} -->\n'.format(posixpath.join(*HOST)))
#-- find model files within zip file
rx = re.compile(r'(grid|h[0f]?|UV[0]?|Model|xy)[_\.](.*?)',re.IGNORECASE)
m = [m for m in zfile.filelist if rx.match(posixpath.basename(m.filename))]
#-- verify that model files are within downloaded zip file
assert all(m)
#-- output tide directory for model
modelpath = os.path.join(filepath,'Arc5km2018')
#-- extract each member (model and configuration files)
for member in m:
#-- strip directories from member filename
member.filename = posixpath.basename(member.filename)
print('\t{0}\n'.format(os.path.join(modelpath,member.filename)))
#-- extract file
zfile.extract(member, path=modelpath)
#-- close the zipfile object
zfile.close()
#-- output control file for tide model
CFname = os.path.join(filepath,'Model_Arc5km2018')
fid = open(CFname,'w')
for model_file in ['h_Arc5km2018','UV_Arc5km2018','grid_Arc5km2018']:
print(os.path.join(modelpath,model_file),file=fid)
print('xy_ll_Arc5km2018',file=fid)
fid.close()
#-- verify control file
assert os.access(CFname, os.F_OK)
#-- run tests
yield
#-- clean up model
shutil.rmtree(modelpath)
#-- clean up
os.remove(CFname)
#-- PURPOSE: Download Arctic Tidal Current Atlas list of records
@pytest.fixture(scope="class", autouse=True)
def download_Arctic_Tide_Atlas(self):
HOST = ['https://arcticdata.io','metacat','d1','mn','v2','object',
'urn%3Auuid%3Ae3abe2cc-f903-44de-9758-0c6bfc5b66c9']
local = os.path.join(filepath,'List_of_records.txt')
pyTMD.utilities.from_http(HOST,local=local)
assert os.access(local, os.F_OK)
#-- run tests
yield
#-- clean up
os.remove(local)
#-- parameterize type: heights versus currents
parameters = []
parameters.append(dict(type='z',model='h_Arc5km2018',grid='grid_Arc5km2018'))
parameters.append(dict(type='u',model='UV_Arc5km2018',grid='grid_Arc5km2018'))
parameters.append(dict(type='v',model='UV_Arc5km2018',grid='grid_Arc5km2018'))
@pytest.mark.parametrize("parameters", parameters)
#-- PURPOSE: Tests that interpolated results are comparable to Matlab program
def test_verify_AOTIM5_2018(self, parameters):
#-- model parameters for AOTIM-5-2018
modelpath = os.path.join(filepath,'Arc5km2018')
grid_file = os.path.join(modelpath,parameters['grid'])
model_file = os.path.join(modelpath,parameters['model'])
TYPE = parameters['type']
GRID = 'OTIS'
EPSG = 'PSNorth'
#-- open Arctic Tidal Current Atlas list of records
with open(os.path.join(filepath,'List_of_records.txt'),'r') as f:
file_contents = f.read().splitlines()
#-- skip 2 header rows
count = 2
#-- iterate over number of stations
arctic_stations = len(file_contents) - count
stations = [None]*arctic_stations
shortname = [None]*arctic_stations
station_lon = np.zeros((arctic_stations))
station_lat = np.zeros((arctic_stations))
for s in range(arctic_stations):
line_contents = file_contents[count+s].split()
stations[s] = line_contents[1]
shortname[s] = line_contents[2]
station_lat[s] = np.float64(line_contents[10])
station_lon[s] = np.float64(line_contents[11])
#-- calculate daily results for a time period
#-- convert time to days since 1992-01-01T00:00:00
tide_time = np.arange(pyTMD.time.convert_calendar_dates(2000,1,1),
pyTMD.time.convert_calendar_dates(2000,12,31)+1)
#-- serial dates for matlab program (days since 0000-01-01T00:00:00)
SDtime = np.arange(convert_calendar_serial(2000,1,1),
convert_calendar_serial(2000,12,31)+1)
#-- presently not converting times to dynamic times for model comparisons
deltat = np.zeros_like(tide_time)
#-- number of days
ndays = len(tide_time)
#-- extract amplitude and phase from tide model
amp,ph,D,c = pyTMD.read_tide_model.extract_tidal_constants(station_lon,
station_lat, grid_file, model_file, EPSG, TYPE=TYPE,
METHOD='spline', GRID=GRID)
#-- calculate complex phase in radians for Euler's
cph = -1j*ph*np.pi/180.0
#-- will verify differences between model outputs are within tolerance
eps = np.finfo(np.float16).eps
#-- compare daily outputs at each station point
invalid_list = ['BC1','KS12','KS14','BI3','BI4']
#-- remove coastal stations from the list
valid_stations=[i for i,s in enumerate(shortname) if s not in invalid_list]
#-- compute validation data from Matlab TMD program using octave
#-- https://github.com/EarthAndSpaceResearch/TMD_Matlab_Toolbox_v2.5
TMDpath = os.path.join(filepath,'..','TMD_Matlab_Toolbox','TMD')
octave.addpath(octave.genpath(os.path.normpath(TMDpath)))
octave.addpath(filepath)
octave.addpath(modelpath)
#-- turn off octave warnings
octave.warning('off', 'all')
#-- input control file for model
CFname = os.path.join(filepath,'Model_Arc5km2018')
assert os.access(CFname, os.F_OK)
#-- run Matlab TMD program with octave
#-- MODE: OB time series
validation,_ = octave.tmd_tide_pred_plus(CFname,SDtime,
station_lat[valid_stations],station_lon[valid_stations],
TYPE,nout=2)
#-- for each valid station
for i,s in enumerate(valid_stations):
#-- calculate constituent oscillation for station
hc = amp[s,None,:]*np.exp(cph[s,None,:])
#-- allocate for out tides at point
tide = np.ma.zeros((ndays))
tide.mask = np.zeros((ndays),dtype=bool)
#-- predict tidal elevations at time and infer minor corrections
tide.mask[:] = np.any(hc.mask)
tide.data[:] = pyTMD.predict_tidal_ts(tide_time, hc, c,
DELTAT=deltat, CORRECTIONS=GRID)
minor = pyTMD.infer_minor_corrections(tide_time, hc, c,
DELTAT=deltat, CORRECTIONS=GRID)
tide.data[:] += minor.data[:]
#-- calculate differences between matlab and python version
difference = np.ma.zeros((ndays))
difference.data[:] = tide.data - validation[:,i]
difference.mask = (tide.mask | np.isnan(validation[:,i]))
difference.data[difference.mask] = 0.0
if not np.all(difference.mask):
assert np.all( | np.abs(difference) | numpy.abs |
# ---------------------------------------------------------
# Copyright (c) Microsoft Corporation. All rights reserved.
# ---------------------------------------------------------
import pytest
import numpy as np
import logging
from scipy.sparse import csr_matrix, eye
from interpret_community.common.explanation_utils import _convert_to_list, _generate_augmented_data, \
_get_raw_feature_importances, _is_one_to_many, _sort_values, _sort_feature_list_single, \
_sort_feature_list_multiclass, _two_dimensional_slice, _get_feature_map_from_list_of_indexes, \
_is_identity
from raw_explain.utils import _get_feature_map_from_indices_list
from interpret_community.common.constants import Scipy
from constants import owner_email_tools_and_ux
test_logger = logging.getLogger(__name__)
@pytest.mark.owner(email=owner_email_tools_and_ux)
@pytest.mark.usefixtures('clean_dir')
class TestExplanationUtils(object):
def test_working(self):
assert True
def test_convert_to_list_1d(self):
numpy_1d = np.ones(4)
list_1d = [1] * 4
assert _convert_to_list(numpy_1d) == list_1d
def test_convert_to_list_2d_full_numpy(self):
numpy_2d = np.ones((3, 4))
list_2d = [[1] * 4] * 3
assert _convert_to_list(numpy_2d) == list_2d
def test_convert_to_list_2d_list_of_numpy(self):
numpy_2d = np.ones(4)
numpy_list = [numpy_2d] * 3
list_2d = [[1] * 4] * 3
assert _convert_to_list(numpy_list) == list_2d
def test_sort_values(self):
feature_list = ['feature0', 'feature1', 'feature2', 'feature3']
order = [2, 3, 0, 1]
assert np.array_equal(_sort_values(feature_list, order),
np.array(['feature2', 'feature3', 'feature0', 'feature1']))
def test_sort_feature_list_single(self):
feature_list = ['feature0', 'feature1', 'feature2', 'feature3']
order = [2, 3, 0, 1]
assert _sort_feature_list_single(feature_list, order) == ['feature2', 'feature3', 'feature0', 'feature1']
def test_sort_feature_list_multiclass(self):
feature_list = ['feature0', 'feature1', 'feature2', 'feature3']
order = [
[2, 3, 0, 1],
[1, 3, 2, 0]
]
output = [
['feature2', 'feature3', 'feature0', 'feature1'],
['feature1', 'feature3', 'feature2', 'feature0']
]
assert _sort_feature_list_multiclass(feature_list, order) == output
def test_two_dimensional_slice(self):
big_list = [
['feature2', 'feature3', 'feature0', 'feature1'],
['feature1', 'feature3', 'feature2', 'feature0']
]
output = [
['feature2', 'feature3'],
['feature1', 'feature3']
]
assert _two_dimensional_slice(big_list, 2) == output
def test_generate_augmented_data_ndarray(self):
x = np.ones((3, 6))
x_augmented = _generate_augmented_data(x)
assert x_augmented.shape[0] == 6 and x_augmented.shape[1] == 6
def test_generate_augmented_data_sparse(self):
x = csr_matrix(np.zeros((3, 6)))
x_augmented = _generate_augmented_data(x)
assert x_augmented.shape[0] == 6 and x_augmented.shape[1] == 6
def test_get_raw_feats_regression(self):
feat_imps = np.ones((2, 5))
feat_imps[1] = 2 * | np.ones(5) | numpy.ones |
# -*- coding: utf-8 -*-
import numpy as np
class PairwisePreferenceMultileave(object):
def __init__(self, num_data_features, k=10):
self._name = 'Pairwise Preferences Multileave'
self._k = k
self.needs_inverted = True
self.needs_descending = True
self.needs_oracle = False
self.vector_aggregation = False
def clean(self):
del self._last_inverted_rankings
def top_rank(self, multileaving, top_docs):
n_disp = multileaving.shape[0]
top_rank = np.zeros(n_disp, dtype=np.int32)
top_rank[:] = n_disp
for i in range(n_disp):
in_rank = np.in1d(multileaving, top_docs[:,i])
top_rank[in_rank] = np.minimum(top_rank[in_rank],i)
return top_rank
def make_multileaving(self, descending_rankings, inverted_rankings):
self._last_inverted_rankings = inverted_rankings
self._last_descending_rankings = descending_rankings
self._last_n_rankers = inverted_rankings.shape[0]
n_docs = descending_rankings.shape[1]
n_rankers = descending_rankings.shape[0]
length = min(self._k,n_docs)
multileaving = np.zeros(length, dtype=np.int32)
previous_set = np.array([], dtype=np.int32)
previous_results = {}
self._last_choice_sizes = np.zeros(length)
for i in range(length):
full_set = np.unique(descending_rankings[:,:i+1])
cur_set = np.setdiff1d(full_set, multileaving[:i], assume_unique=True)
multileaving[i] = np.random.choice(cur_set,1)
self._last_choice_sizes[i] = cur_set.shape[0]
self._last_top_ranks = self.top_rank(multileaving, descending_rankings)
return multileaving
def infer_preferences(self, result_list, clicked_docs):
if np.any(clicked_docs):
return self.preferences_of_list(result_list, clicked_docs.astype(bool))
else:
return np.zeros((self._last_n_rankers, self._last_n_rankers))
def preferences_of_list(self, result_list, clicked_docs):
n_disp = result_list.shape[0]
n_rankers = self._last_n_rankers
included = np.ones(min(self._k, clicked_docs.shape[0]))
if not clicked_docs[-1]:
included[1:] = np.cumsum(clicked_docs[::-1])[:0:-1]
neg_pref = np.where(np.logical_xor(clicked_docs, included))[0]
pos_pref = | np.where(clicked_docs) | numpy.where |
import numpy as np
import sys, h5py, os
# Get path to mcdc (not necessary if mcdc is installed)
sys.path.append('../')
import mcdc
# =============================================================================
# Load initial data
# =============================================================================
data = np.load('mcdc/tests_tmp/test_regression_moments.npz')
# =============================================================================
# Set material
# =============================================================================
SigmaC = data['SigmaC']
SigmaS = data['SigmaS']
#SigmaF = data['SigmaF']
#nu = data['nu']
SigmaF = np.array([[0.0]])
nu = np.array([0])
M = mcdc.Material(SigmaC, SigmaS, SigmaF, nu)
# =============================================================================
# Set cells
# =============================================================================
# Set surfaces
S0 = mcdc.SurfacePlaneX(0.0, "vacuum")
S1 = mcdc.SurfacePlaneX(6.0, "vacuum")
# Set cells
C = mcdc.Cell([+S0, -S1], M)
cells = [C]
# =============================================================================
# Set sources
# =============================================================================
N_sources = data['N_sources']
input_src = data['Sources']
sources = []
# Direction distribution
dir = mcdc.DistPointIsotropic()
# Energy group distribution
g = mcdc.DistDelta(0)
# Time distribution
time = mcdc.DistDelta(0.0)
# Create the sources
for i in range(N_sources):
posi = mcdc.DistPoint(mcdc.DistUniform(input_src[0,i],input_src[1,i]), mcdc.DistDelta(0.0),
mcdc.DistDelta(0.0))
Srci = mcdc.SourceSimple(posi,dir,g,time,prob=input_src[2,i])
sources.append(Srci)
# =============================================================================
# Set filters and tallies
# =============================================================================
spatial_filter = mcdc.FilterPlaneX( | np.linspace(0.0, 6.0, 61) | numpy.linspace |
'''
Creating a class that loads the healthy datapoints and apply different methods on them.
Signals are assumed to have no overlaps and L is the desired signal length.
methods:
take_h_dataset : takes the healthy datapoints in and creates healthy signals for all the 3 sensors
data2signal : takes in datapoints for a specified city and turn them into signals for all the 3 sensors
signal2data: takes in signals and reshape them into consecutive datapoints
inject_lin_erratic : takes in a sequence of datapoints and adds a linear degradation of erratic fault type
inject_erratic : takes in a signal and injects fault into it
inject_drift:
inject_hardover:
inject_spike:
viz_fault: takes in a healthy signal and faulty signal and plot them together
make_fault: takes in a set of healthy signals and adds a specified type of fault to the sensors in all the combinations possible or even specific cases of combinations
degrade : takes in the datapoints of a desired city and degrades the data sequences with all the combinations
csv_out: takes in the dataset signals and convert them into datapoints and export to csv
'''
import math
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
class Prediction_Data():
def __init__(self,L):
# Setting signal length
self.L = int(L)
# Loading A2D2 data (extended)
self.data_ap = pd.read_csv('./A2D2 Raw Data/data_ap_ext.csv').to_numpy()
self.data_sa = pd.read_csv('./A2D2 Raw Data/data_sa_ext.csv').to_numpy()
self.data_bp = pd.read_csv('./A2D2 Raw Data/data_bp_ext.csv').to_numpy()
t = len(self.data_ap)
# Number of signals for each city
self.n = np.round(t/L).astype(int)
# Taking the FSO attribute = (Max - Min)/2
ap_fso = (max(self.data_ap[:,1:].flatten()) - min(self.data_ap[:,1:].flatten()))/2
sa_fso = (max(self.data_sa[:,1:].flatten()) - min(self.data_sa[:,1:].flatten()))/2
bp_fso = (max(self.data_bp[:,1:].flatten()) - min(self.data_bp[:,1:].flatten()))/2
self.fso = np.array([ap_fso, sa_fso, bp_fso])
def take_h_dataset(self):
ap1 = np.reshape(self.data_ap[0:self.n*self.L,1],(self.n,self.L))
ap2 = np.reshape(self.data_ap[0:self.n*self.L,2],(self.n,self.L))
ap3 = np.reshape(self.data_ap[0:self.n*self.L,3],(self.n,self.L))
dataset_ap = np.vstack((ap1,ap2,ap3))
sa1 = np.reshape(self.data_sa[0:self.n*self.L,1],(self.n,self.L))
sa2 = np.reshape(self.data_sa[0:self.n*self.L,2],(self.n,self.L))
sa3 = np.reshape(self.data_sa[0:self.n*self.L,3],(self.n,self.L))
dataset_sa = np.vstack((sa1,sa2,sa3))
bp1 = np.reshape(self.data_bp[0:self.n*self.L,1],(self.n,self.L))
bp2 = np.reshape(self.data_bp[0:self.n*self.L,2],(self.n,self.L))
bp3 = np.reshape(self.data_bp[0:self.n*self.L,3],(self.n,self.L))
dataset_bp = np.vstack((bp1,bp2,bp3))
self.h_dataset = np.stack((dataset_ap, dataset_sa, dataset_bp), axis=1)
return self.h_dataset
def data2signal(self,data):
ap = np.reshape(data[:self.n*self.L,0],(self.n, self.L))
sa = np.reshape(data[:self.n*self.L,1],(self.n, self.L))
bp = np.reshape(data[:self.n*self.L,2],(self.n, self.L))
signals = np.stack((ap,sa,bp), axis=1)
return signals
def signal2data(self, dataset):
n = dataset.shape[0]
c = dataset.shape[1]
L = dataset.shape[2]
data = np.zeros((n*L,c))
for i in range(c):
data[:,i] = np.reshape(dataset[:,i,:],(n*L))
return data
def inject_lin_erratic(self, data, fso):
faulty_data = np.array(data)
delta = len(data)
idx1 = int(0.1*delta)
idx2 = delta - idx1
for j in range(idx2):
r = np.random.normal(0,0.01)
erratic = r*fso*35*(j/idx2)
faulty_data[idx1+j] += np.round(erratic,1)
return faulty_data
def inject_exp_erratic(self, data, fso):
faulty_data = np.array(data)
delta = len(data)
idx1 = int(0.1*delta)
idx2 = delta - idx1
for j in range(idx2):
r = np.random.normal(0,0.01)
erratic = r*fso*(1/750)*math.exp(5*((j/idx2)+1.06))
faulty_data[idx1+j] += np.round(erratic,1)
return faulty_data
def inject_sin_erratic(self, data, fso):
faulty_data = np.array(data)
L = len(data)
idx1 = int(0.1*L)
idx2 = L - idx1
for j in range(idx2):
r = | np.random.normal(0,0.01) | numpy.random.normal |
import numpy as np
import os
import re
import requests
import sys
import time
from netCDF4 import Dataset
import pandas as pd
from bs4 import BeautifulSoup
from tqdm import tqdm
# setup constants used to access the data from the different M2M interfaces
BASE_URL = 'https://ooinet.oceanobservatories.org/api/m2m/' # base M2M URL
SENSOR_URL = '12576/sensor/inv/' # Sensor Information
# setup access credentials
AUTH = ['OOIAPI-853A3LA6QI3L62', '<KEY>']
def M2M_Call(uframe_dataset_name, start_date, end_date):
options = '?beginDT=' + start_date + '&endDT=' + end_date + '&format=application/netcdf'
r = requests.get(BASE_URL + SENSOR_URL + uframe_dataset_name + options, auth=(AUTH[0], AUTH[1]))
if r.status_code == requests.codes.ok:
data = r.json()
else:
return None
# wait until the request is completed
print('Waiting for OOINet to process and prepare data request, this may take up to 20 minutes')
url = [url for url in data['allURLs'] if re.match(r'.*async_results.*', url)][0]
check_complete = url + '/status.txt'
with tqdm(total=400, desc='Waiting') as bar:
for i in range(400):
r = requests.get(check_complete)
bar.update(1)
if r.status_code == requests.codes.ok:
bar.n = 400
bar.last_print_n = 400
bar.refresh()
print('\nrequest completed in %f minutes.' % elapsed)
break
else:
time.sleep(3)
elapsed = (i * 3) / 60
return data
def M2M_Files(data, tag=''):
"""
Use a regex tag combined with the results of the M2M data request to collect the data from the THREDDS catalog.
Collected data is gathered into an xarray dataset for further processing.
:param data: JSON object returned from M2M data request with details on where the data is to be found for download
:param tag: regex tag to use in discriminating the data files, so we only collect the correct ones
:return: the collected data as an xarray dataset
"""
# Create a list of the files from the request above using a simple regex as a tag to discriminate the files
url = [url for url in data['allURLs'] if re.match(r'.*thredds.*', url)][0]
files = list_files(url, tag)
return files
def list_files(url, tag=''):
"""
Function to create a list of the NetCDF data files in the THREDDS catalog created by a request to the M2M system.
:param url: URL to user's THREDDS catalog specific to a data request
:param tag: regex pattern used to distinguish files of interest
:return: list of files in the catalog with the URL path set relative to the catalog
"""
page = requests.get(url).text
soup = BeautifulSoup(page, 'html.parser')
pattern = re.compile(tag)
return [node.get('href') for node in soup.find_all('a', text=pattern)]
def M2M_Data(nclist,variables):
thredds = 'https://opendap.oceanobservatories.org/thredds/dodsC/ooi/'
#nclist is going to contain more than one url eventually
for jj in range(len(nclist)):
url=nclist[jj]
url=url[25:]
dap_url = thredds + url + '#fillmismatch'
openFile = Dataset(dap_url,'r')
for ii in range(len(variables)):
dum = openFile.variables[variables[ii].name]
variables[ii].data = np.append(variables[ii].data, dum[:].data)
tmp = variables[0].data/60/60/24
time_converted = pd.to_datetime(tmp, unit='D', origin=pd.Timestamp('1900-01-01'))
return variables, time_converted
class var(object):
def __init__(self):
"""A Class that generically holds data with a variable name
and the units as attributes"""
self.name = ''
self.data = np.array([])
self.units = ''
def __repr__(self):
return_str = "name: " + self.name + '\n'
return_str += "units: " + self.units + '\n'
return_str += "data: size: " + str(self.data.shape)
return return_str
class structtype(object):
def __init__(self):
""" A class that imitates a Matlab structure type
"""
self._data = []
def __getitem__(self, index):
"""implement index behavior in the struct"""
if index == len(self._data):
self._data.append(var())
return self._data[index]
def __len__(self):
return len(self._data)
def M2M_URLs(platform_name,node,instrument_class,method):
var_list = structtype()
#MOPAK
if platform_name == 'CE01ISSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/SBD17/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/SBD11/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/SBD11/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE06ISSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/SBD17/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/SBD11/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/SBD11/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSPM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSPM/SBS01/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
#METBK
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'METBK1' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/SBD11/06-METBKA000/telemetered/metbk_a_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'sea_surface_temperature'
var_list[2].name = 'sea_surface_conductivity'
var_list[3].name = 'met_salsurf'
var_list[4].name = 'met_windavg_mag_corr_east'
var_list[5].name = 'met_windavg_mag_corr_north'
var_list[6].name = 'barometric_pressure'
var_list[7].name = 'air_temperature'
var_list[8].name = 'relative_humidity'
var_list[9].name = 'longwave_irradiance'
var_list[10].name = 'shortwave_irradiance'
var_list[11].name = 'precipitation'
var_list[12].name = 'met_heatflx_minute'
var_list[13].name = 'met_latnflx_minute'
var_list[14].name = 'met_netlirr_minute'
var_list[15].name = 'met_sensflx_minute'
var_list[16].name = 'eastward_velocity'
var_list[17].name = 'northward_velocity'
var_list[18].name = 'met_spechum'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[15].data = np.array([])
var_list[16].data = np.array([])
var_list[17].data = np.array([])
var_list[18].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'S/m'
var_list[3].units = 'unitless'
var_list[4].units = 'm/s'
var_list[5].units = 'm/s'
var_list[6].units = 'mbar'
var_list[7].units = 'degC'
var_list[8].units = '#'
var_list[9].units = 'W/m'
var_list[10].units = 'W/m'
var_list[11].units = 'mm'
var_list[12].units = 'W/m'
var_list[13].units = 'W/m'
var_list[14].units = 'W/m'
var_list[15].units = 'W/m'
var_list[16].units = 'm/s'
var_list[17].units = 'm/s'
var_list[18].units = 'g/kg'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'METBK1' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/SBD11/06-METBKA000/telemetered/metbk_a_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'sea_surface_temperature'
var_list[2].name = 'sea_surface_conductivity'
var_list[3].name = 'met_salsurf'
var_list[4].name = 'met_windavg_mag_corr_east'
var_list[5].name = 'met_windavg_mag_corr_north'
var_list[6].name = 'barometric_pressure'
var_list[7].name = 'air_temperature'
var_list[8].name = 'relative_humidity'
var_list[9].name = 'longwave_irradiance'
var_list[10].name = 'shortwave_irradiance'
var_list[11].name = 'precipitation'
var_list[12].name = 'met_heatflx_minute'
var_list[13].name = 'met_latnflx_minute'
var_list[14].name = 'met_netlirr_minute'
var_list[15].name = 'met_sensflx_minute'
var_list[16].name = 'eastward_velocity'
var_list[17].name = 'northward_velocity'
var_list[18].name = 'met_spechum'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[15].data = np.array([])
var_list[16].data = np.array([])
var_list[17].data = np.array([])
var_list[18].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'S/m'
var_list[3].units = 'unitless'
var_list[4].units = 'm/s'
var_list[5].units = 'm/s'
var_list[6].units = 'mbar'
var_list[7].units = 'degC'
var_list[8].units = '#'
var_list[9].units = 'W/m'
var_list[10].units = 'W/m'
var_list[11].units = 'mm'
var_list[12].units = 'W/m'
var_list[13].units = 'W/m'
var_list[14].units = 'W/m'
var_list[15].units = 'W/m'
var_list[16].units = 'm/s'
var_list[17].units = 'm/s'
var_list[18].units = 'g/kg'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'METBK1' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/SBD11/06-METBKA000/telemetered/metbk_a_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'sea_surface_temperature'
var_list[2].name = 'sea_surface_conductivity'
var_list[3].name = 'met_salsurf'
var_list[4].name = 'met_windavg_mag_corr_east'
var_list[5].name = 'met_windavg_mag_corr_north'
var_list[6].name = 'barometric_pressure'
var_list[7].name = 'air_temperature'
var_list[8].name = 'relative_humidity'
var_list[9].name = 'longwave_irradiance'
var_list[10].name = 'shortwave_irradiance'
var_list[11].name = 'precipitation'
var_list[12].name = 'met_heatflx_minute'
var_list[13].name = 'met_latnflx_minute'
var_list[14].name = 'met_netlirr_minute'
var_list[15].name = 'met_sensflx_minute'
var_list[16].name = 'eastward_velocity'
var_list[17].name = 'northward_velocity'
var_list[18].name = 'met_spechum'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[15].data = np.array([])
var_list[16].data = np.array([])
var_list[17].data = np.array([])
var_list[18].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'S/m'
var_list[3].units = 'unitless'
var_list[4].units = 'm/s'
var_list[5].units = 'm/s'
var_list[6].units = 'mbar'
var_list[7].units = 'degC'
var_list[8].units = '#'
var_list[9].units = 'W/m'
var_list[10].units = 'W/m'
var_list[11].units = 'mm'
var_list[12].units = 'W/m'
var_list[13].units = 'W/m'
var_list[14].units = 'W/m'
var_list[15].units = 'W/m'
var_list[16].units = 'm/s'
var_list[17].units = 'm/s'
var_list[18].units = 'g/kg'
elif platform_name == 'CE09OSSM' and node == 'BUOY' and instrument_class == 'METBK1' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/SBD11/06-METBKA000/telemetered/metbk_a_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'sea_surface_temperature'
var_list[2].name = 'sea_surface_conductivity'
var_list[3].name = 'met_salsurf'
var_list[4].name = 'met_windavg_mag_corr_east'
var_list[5].name = 'met_windavg_mag_corr_north'
var_list[6].name = 'barometric_pressure'
var_list[7].name = 'air_temperature'
var_list[8].name = 'relative_humidity'
var_list[9].name = 'longwave_irradiance'
var_list[10].name = 'shortwave_irradiance'
var_list[11].name = 'precipitation'
var_list[12].name = 'met_heatflx_minute'
var_list[13].name = 'met_latnflx_minute'
var_list[14].name = 'met_netlirr_minute'
var_list[15].name = 'met_sensflx_minute'
var_list[16].name = 'eastward_velocity'
var_list[17].name = 'northward_velocity'
var_list[18].name = 'met_spechum'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[15].data = np.array([])
var_list[16].data = np.array([])
var_list[17].data = np.array([])
var_list[18].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'S/m'
var_list[3].units = 'unitless'
var_list[4].units = 'm/s'
var_list[5].units = 'm/s'
var_list[6].units = 'mbar'
var_list[7].units = 'degC'
var_list[8].units = '#'
var_list[9].units = 'W/m'
var_list[10].units = 'W/m'
var_list[11].units = 'mm'
var_list[12].units = 'W/m'
var_list[13].units = 'W/m'
var_list[14].units = 'W/m'
var_list[15].units = 'W/m'
var_list[16].units = 'm/s'
var_list[17].units = 'm/s'
var_list[18].units = 'g/kg'
#FLORT
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/RID16/02-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE01ISSM' and node == 'BUOY' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/SBD17/06-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/RID16/02-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE06ISSM' and node == 'BUOY' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/SBD17/06-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/RID27/02-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/RID27/02-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/RID27/02-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/RID27/02-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE09OSPM' and node == 'PROFILER' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSPM/WFP01/04-FLORTK000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[6].name = 'int_ctd_pressure'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
var_list[6].units = 'dbar'
#FDCHP
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'FDCHP' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/SBD12/08-FDCHPA000/telemetered/fdchp_a_dcl_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
#DOSTA
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/RID16/03-DOSTAD000/telemetered/dosta_abcdjm_ctdbp_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/RID27/04-DOSTAD000/telemetered/dosta_abcdjm_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/RID27/04-DOSTAD000/telemetered/dosta_abcdjm_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/RID16/03-DOSTAD000/telemetered/dosta_abcdjm_ctdbp_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/RID27/04-DOSTAD000/telemetered/dosta_abcdjm_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/RID27/04-DOSTAD000/telemetered/dosta_abcdjm_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/MFD37/03-DOSTAD000/telemetered/dosta_abcdjm_ctdbp_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/MFD37/03-DOSTAD000/telemetered/dosta_abcdjm_ctdbp_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/MFD37/03-DOSTAD000/telemetered/dosta_abcdjm_ctdbp_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/MFD37/03-DOSTAD000/telemetered/dosta_abcdjm_ctdbp_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
elif platform_name == 'CE09OSPM' and node == 'PROFILER' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSPM/WFP01/02-DOFSTK000/telemetered/dofst_k_wfp_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dofst_k_oxygen_l2'
var_list[2].name = 'dofst_k_oxygen'
var_list[3].name = 'int_ctd_pressure'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'Hz'
var_list[3].units = 'dbar'
#ADCP
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'ADCP' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/RID26/01-ADCPTA000/telemetered/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'ADCP' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/RID26/01-ADCPTC000/telemetered/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'ADCP' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/RID26/01-ADCPTA000/telemetered/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'ADCP' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/RID26/01-ADCPTC000/telemetered/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'ADCP' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/MFD35/04-ADCPTM000/telemetered/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'ADCP' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/MFD35/04-ADCPTM000/telemetered/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'ADCP' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/MFD35/04-ADCPTC000/telemetered/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'ADCP' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/MFD35/04-ADCPSJ000/telemetered/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
#ZPLSC
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'ZPLSC' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/MFD37/07-ZPLSCC000/telemetered/zplsc_c_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'ZPLSC' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/MFD37/07-ZPLSCC000/telemetered/zplsc_c_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'ZPLSC' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/MFD37/07-ZPLSCC000/telemetered/zplsc_c_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'ZPLSC' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/MFD37/07-ZPLSCC000/telemetered/zplsc_c_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'ZPLSC' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/MFD37/07-ZPLSCC000/recovered_host/zplsc_c_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'ZPLSC' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/MFD37/07-ZPLSCC000/recovered_host/zplsc_c_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'ZPLSC' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/MFD37/07-ZPLSCC000/recovered_host/zplsc_c_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'ZPLSC' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/MFD37/07-ZPLSCC000/recovered_host/zplsc_c_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
#WAVSS
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'WAVSS_Stats' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/SBD12/05-WAVSSA000/telemetered/wavss_a_dcl_statistics'
var_list[0].name = 'time'
var_list[1].name = 'number_zero_crossings'
var_list[2].name = 'average_wave_height'
var_list[3].name = 'mean_spectral_period'
var_list[4].name = 'max_wave_height'
var_list[5].name = 'significant_wave_height'
var_list[6].name = 'significant_period'
var_list[7].name = 'wave_height_10'
var_list[8].name = 'wave_period_10'
var_list[9].name = 'mean_wave_period'
var_list[10].name = 'peak_wave_period'
var_list[11].name = 'wave_period_tp5'
var_list[12].name = 'wave_height_hmo'
var_list[13].name = 'mean_direction'
var_list[14].name = 'mean_spread'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'counts'
var_list[2].units = 'm'
var_list[3].units = 'sec'
var_list[4].units = 'm'
var_list[5].units = 'm'
var_list[6].units = 'sec'
var_list[7].units = 'm'
var_list[8].units = 'sec'
var_list[9].units = 'sec'
var_list[10].units = 'sec'
var_list[11].units = 'sec'
var_list[12].units = 'm'
var_list[13].units = 'degrees'
var_list[14].units = 'degrees'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'WAVSS_Stats' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/SBD12/05-WAVSSA000/telemetered/wavss_a_dcl_statistics'
var_list[0].name = 'time'
var_list[1].name = 'number_zero_crossings'
var_list[2].name = 'average_wave_height'
var_list[3].name = 'mean_spectral_period'
var_list[4].name = 'max_wave_height'
var_list[5].name = 'significant_wave_height'
var_list[6].name = 'significant_period'
var_list[7].name = 'wave_height_10'
var_list[8].name = 'wave_period_10'
var_list[9].name = 'mean_wave_period'
var_list[10].name = 'peak_wave_period'
var_list[11].name = 'wave_period_tp5'
var_list[12].name = 'wave_height_hmo'
var_list[13].name = 'mean_direction'
var_list[14].name = 'mean_spread'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'counts'
var_list[2].units = 'm'
var_list[3].units = 'sec'
var_list[4].units = 'm'
var_list[5].units = 'm'
var_list[6].units = 'sec'
var_list[7].units = 'm'
var_list[8].units = 'sec'
var_list[9].units = 'sec'
var_list[10].units = 'sec'
var_list[11].units = 'sec'
var_list[12].units = 'm'
var_list[13].units = 'degrees'
var_list[14].units = 'degrees'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'WAVSS_Stats' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/SBD12/05-WAVSSA000/telemetered/wavss_a_dcl_statistics'
var_list[0].name = 'time'
var_list[1].name = 'number_zero_crossings'
var_list[2].name = 'average_wave_height'
var_list[3].name = 'mean_spectral_period'
var_list[4].name = 'max_wave_height'
var_list[5].name = 'significant_wave_height'
var_list[6].name = 'significant_period'
var_list[7].name = 'wave_height_10'
var_list[8].name = 'wave_period_10'
var_list[9].name = 'mean_wave_period'
var_list[10].name = 'peak_wave_period'
var_list[11].name = 'wave_period_tp5'
var_list[12].name = 'wave_height_hmo'
var_list[13].name = 'mean_direction'
var_list[14].name = 'mean_spread'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'counts'
var_list[2].units = 'm'
var_list[3].units = 'sec'
var_list[4].units = 'm'
var_list[5].units = 'm'
var_list[6].units = 'sec'
var_list[7].units = 'm'
var_list[8].units = 'sec'
var_list[9].units = 'sec'
var_list[10].units = 'sec'
var_list[11].units = 'sec'
var_list[12].units = 'm'
var_list[13].units = 'degrees'
var_list[14].units = 'degrees'
elif platform_name == 'CE09OSSM' and node == 'BUOY' and instrument_class == 'WAVSS_Stats' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/SBD12/05-WAVSSA000/telemetered/wavss_a_dcl_statistics'
var_list[0].name = 'time'
var_list[1].name = 'number_zero_crossings'
var_list[2].name = 'average_wave_height'
var_list[3].name = 'mean_spectral_period'
var_list[4].name = 'max_wave_height'
var_list[5].name = 'significant_wave_height'
var_list[6].name = 'significant_period'
var_list[7].name = 'wave_height_10'
var_list[8].name = 'wave_period_10'
var_list[9].name = 'mean_wave_period'
var_list[10].name = 'peak_wave_period'
var_list[11].name = 'wave_period_tp5'
var_list[12].name = 'wave_height_hmo'
var_list[13].name = 'mean_direction'
var_list[14].name = 'mean_spread'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'counts'
var_list[2].units = 'm'
var_list[3].units = 'sec'
var_list[4].units = 'm'
var_list[5].units = 'm'
var_list[6].units = 'sec'
var_list[7].units = 'm'
var_list[8].units = 'sec'
var_list[9].units = 'sec'
var_list[10].units = 'sec'
var_list[11].units = 'sec'
var_list[12].units = 'm'
var_list[13].units = 'degrees'
var_list[14].units = 'degrees'
#VELPT
elif platform_name == 'CE01ISSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/SBD17/04-VELPTA000/telemetered/velpt_ab_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/SBD11/04-VELPTA000/telemetered/velpt_ab_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/SBD11/04-VELPTA000/telemetered/velpt_ab_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE06ISSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/SBD17/04-VELPTA000/telemetered/velpt_ab_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/SBD11/04-VELPTA000/telemetered/velpt_ab_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE09OSSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/SBD11/04-VELPTA000/telemetered/velpt_ab_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'VELPT' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/RID16/04-VELPTA000/telemetered/velpt_ab_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'VELPT' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/RID26/04-VELPTA000/telemetered/velpt_ab_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'VELPT' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/RID26/04-VELPTA000/telemetered/velpt_ab_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'VELPT' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/RID16/04-VELPTA000/telemetered/velpt_ab_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'VELPT' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/RID26/04-VELPTA000/telemetered/velpt_ab_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'VELPT' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/RID26/04-VELPTA000/telemetered/velpt_ab_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
#PCO2W
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'PCO2W' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/RID16/05-PCO2WB000/telemetered/pco2w_abc_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'pco2w_thermistor_temperature'
var_list[2].name = 'pco2_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'uatm'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'PCO2W' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/MFD35/05-PCO2WB000/telemetered/pco2w_abc_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'pco2w_thermistor_temperature'
var_list[2].name = 'pco2_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'uatm'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'PCO2W' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/RID16/05-PCO2WB000/telemetered/pco2w_abc_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'pco2w_thermistor_temperature'
var_list[2].name = 'pco2_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'uatm'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'PCO2W' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/MFD35/05-PCO2WB000/telemetered/pco2w_abc_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'pco2w_thermistor_temperature'
var_list[2].name = 'pco2_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'uatm'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'PCO2W' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/MFD35/05-PCO2WB000/telemetered/pco2w_abc_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'pco2w_thermistor_temperature'
var_list[2].name = 'pco2_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'uatm'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'PCO2W' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/MFD35/05-PCO2WB000/telemetered/pco2w_abc_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'pco2w_thermistor_temperature'
var_list[2].name = 'pco2_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'uatm'
#PHSEN
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'PHSEN' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/RID16/06-PHSEND000/telemetered/phsen_abcdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'PHSEN' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/RID26/06-PHSEND000/telemetered/phsen_abcdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'PHSEN' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/RID26/06-PHSEND000/telemetered/phsen_abcdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'PHSEN' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/RID16/06-PHSEND000/telemetered/phsen_abcdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'PHSEN' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/RID26/06-PHSEND000/telemetered/phsen_abcdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'PHSEN' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/RID26/06-PHSEND000/telemetered/phsen_abcdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'PHSEN' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/MFD35/06-PHSEND000/telemetered/phsen_abcdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'PHSEN' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/MFD35/06-PHSEND000/telemetered/phsen_abcdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'PHSEN' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/MFD35/06-PHSEND000/telemetered/phsen_abcdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'PHSEN' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/MFD35/06-PHSEND000/telemetered/phsen_abcdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
#SPKIR
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'SPKIR' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/RID16/08-SPKIRB000/telemetered/spkir_abj_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'spkir_abj_cspp_downwelling_vector'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uW cm-2 nm-1'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'SPKIR' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/RID26/08-SPKIRB000/telemetered/spkir_abj_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'spkir_abj_cspp_downwelling_vector'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uW cm-2 nm-1'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'SPKIR' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/RID26/08-SPKIRB000/telemetered/spkir_abj_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'spkir_abj_cspp_downwelling_vector'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uW cm-2 nm-1'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'SPKIR' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/RID16/08-SPKIRB000/telemetered/spkir_abj_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'spkir_abj_cspp_downwelling_vector'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uW cm-2 nm-1'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'SPKIR' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/RID26/08-SPKIRB000/telemetered/spkir_abj_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'spkir_abj_cspp_downwelling_vector'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uW cm-2 nm-1'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'SPKIR' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/RID26/08-SPKIRB000/telemetered/spkir_abj_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'spkir_abj_cspp_downwelling_vector'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uW cm-2 nm-1'
#PRESF
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'PRESF' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/MFD35/02-PRESFA000/telemetered/presf_abc_dcl_tide_measurement'
var_list[0].name = 'time'
var_list[1].name = 'abs_seafloor_pressure'
var_list[2].name = 'seawater_temperature'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'dbar'
var_list[2].units = 'degC'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'PRESF' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/MFD35/02-PRESFA000/telemetered/presf_abc_dcl_tide_measurement'
var_list[0].name = 'time'
var_list[1].name = 'abs_seafloor_pressure'
var_list[2].name = 'seawater_temperature'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'dbar'
var_list[2].units = 'degC'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'PRESF' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/MFD35/02-PRESFB000/telemetered/presf_abc_dcl_tide_measurement'
var_list[0].name = 'time'
var_list[1].name = 'abs_seafloor_pressure'
var_list[2].name = 'seawater_temperature'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'dbar'
var_list[2].units = 'degC'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'PRESF' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/MFD35/02-PRESFC000/telemetered/presf_abc_dcl_tide_measurement'
var_list[0].name = 'time'
var_list[1].name = 'abs_seafloor_pressure'
var_list[2].name = 'seawater_temperature'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'dbar'
var_list[2].units = 'degC'
#CTDBP
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/RID16/03-CTDBPC000/telemetered/ctdbp_cdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/MFD37/03-CTDBPC000/telemetered/ctdbp_cdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE01ISSM' and node == 'BUOY' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/SBD17/06-CTDBPC000/telemetered/ctdbp_cdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/RID16/03-CTDBPC000/telemetered/ctdbp_cdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/MFD37/03-CTDBPC000/telemetered/ctdbp_cdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE06ISSM' and node == 'BUOY' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/SBD17/06-CTDBPC000/telemetered/ctdbp_cdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/RID27/03-CTDBPC000/telemetered/ctdbp_cdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/RID27/03-CTDBPC000/telemetered/ctdbp_cdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/RID27/03-CTDBPC000/telemetered/ctdbp_cdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/RID27/03-CTDBPC000/telemetered/ctdbp_cdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/MFD37/03-CTDBPC000/telemetered/ctdbp_cdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/MFD37/03-CTDBPE000/telemetered/ctdbp_cdef_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
#VEL3D
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'VEL3D' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/MFD35/01-VEL3DD000/telemetered/vel3d_cd_dcl_velocity_data'
var_list[0].name = 'time'
var_list[1].name = 'vel3d_c_eastward_turbulent_velocity'
var_list[2].name = 'vel3d_c_northward_turbulent_velocity'
var_list[3].name = 'vel3d_c_upward_turbulent_velocity'
var_list[4].name = 'seawater_pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = '0.001dbar'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'VEL3D' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/MFD35/01-VEL3DD000/telemetered/vel3d_cd_dcl_velocity_data'
var_list[0].name = 'time'
var_list[1].name = 'vel3d_c_eastward_turbulent_velocity'
var_list[2].name = 'vel3d_c_northward_turbulent_velocity'
var_list[3].name = 'vel3d_c_upward_turbulent_velocity'
var_list[4].name = 'seawater_pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = '0.001dbar'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'VEL3D' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/MFD35/01-VEL3DD000/telemetered/vel3d_cd_dcl_velocity_data'
var_list[0].name = 'time'
var_list[1].name = 'vel3d_c_eastward_turbulent_velocity'
var_list[2].name = 'vel3d_c_northward_turbulent_velocity'
var_list[3].name = 'vel3d_c_upward_turbulent_velocity'
var_list[4].name = 'seawater_pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = '0.001dbar'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'VEL3D' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/MFD35/01-VEL3DD000/telemetered/vel3d_cd_dcl_velocity_data'
var_list[0].name = 'time'
var_list[1].name = 'vel3d_c_eastward_turbulent_velocity'
var_list[2].name = 'vel3d_c_northward_turbulent_velocity'
var_list[3].name = 'vel3d_c_upward_turbulent_velocity'
var_list[4].name = 'seawater_pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = '0.001dbar'
#VEL3DK
elif platform_name == 'CE09OSPM' and node == 'PROFILER' and instrument_class == 'VEL3D' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSPM/WFP01/01-VEL3DK000/telemetered/vel3d_k_wfp_stc_instrument'
var_list[0].name = 'time'
var_list[1].name = 'vel3d_k_eastward_velocity'
var_list[2].name = 'vel3d_k_northward_velocity'
var_list[3].name = 'vel3d_k_upward_velocity'
var_list[4].name = 'vel3d_k_heading'
var_list[5].name = 'vel3d_k_pitch'
var_list[6].name = 'vel3d_k_roll'
var_list[7].name = 'int_ctd_pressure'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'ddegrees'
var_list[5].units = 'ddegrees'
var_list[6].units = 'ddegrees'
var_list[7].units = 'dbar'
elif platform_name == 'CE09OSPM' and node == 'PROFILER' and instrument_class == 'CTD' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSPM/WFP01/03-CTDPFK000/telemetered/ctdpf_ckl_wfp_instrument'
var_list[0].name = 'time'
var_list[1].name = 'ctdpf_ckl_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdpf_ckl_seawater_pressure'
var_list[5].name = 'ctdpf_ckl_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
#PCO2A
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'PCO2A' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/SBD12/04-PCO2AA000/telemetered/pco2a_a_dcl_instrument_water'
var_list[0].name = 'time'
var_list[1].name = 'partial_pressure_co2_ssw'
var_list[2].name = 'partial_pressure_co2_atm'
var_list[3].name = 'pco2_co2flux'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uatm'
var_list[2].units = 'uatm'
var_list[3].units = 'mol m-2 s-1'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'PCO2A' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/SBD12/04-PCO2AA000/telemetered/pco2a_a_dcl_instrument_water'
var_list[0].name = 'time'
var_list[1].name = 'partial_pressure_co2_ssw'
var_list[2].name = 'partial_pressure_co2_atm'
var_list[3].name = 'pco2_co2flux'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uatm'
var_list[2].units = 'uatm'
var_list[3].units = 'mol m-2 s-1'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'PCO2A' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/SBD12/04-PCO2AA000/telemetered/pco2a_a_dcl_instrument_water'
var_list[0].name = 'time'
var_list[1].name = 'partial_pressure_co2_ssw'
var_list[2].name = 'partial_pressure_co2_atm'
var_list[3].name = 'pco2_co2flux'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uatm'
var_list[2].units = 'uatm'
var_list[3].units = 'mol m-2 s-1'
elif platform_name == 'CE09OSSM' and node == 'BUOY' and instrument_class == 'PCO2A' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/SBD12/04-PCO2AA000/telemetered/pco2a_a_dcl_instrument_water'
var_list[0].name = 'time'
var_list[1].name = 'partial_pressure_co2_ssw'
var_list[2].name = 'partial_pressure_co2_atm'
var_list[3].name = 'pco2_co2flux'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uatm'
var_list[2].units = 'uatm'
var_list[3].units = 'mol m-2 s-1'
#PARAD
elif platform_name == 'CE09OSPM' and node == 'PROFILER' and instrument_class == 'PARAD' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSPM/WFP01/05-PARADK000/telemetered/parad_k__stc_imodem_instrument'
var_list[0].name = 'time'
var_list[1].name = 'parad_k_par'
var_list[2].name = 'int_ctd_pressure'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol photons m-2 s-1'
var_list[2].units = 'dbar'
#OPTAA
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'OPTAA' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/RID16/01-OPTAAD000/telemetered/optaa_dj_dcl_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'OPTAA' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/RID27/01-OPTAAD000/telemetered/optaa_dj_dcl_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'OPTAA' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/RID27/01-OPTAAD000/telemetered/optaa_dj_dcl_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'OPTAA' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/RID16/01-OPTAAD000/telemetered/optaa_dj_dcl_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'OPTAA' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/RID27/01-OPTAAD000/telemetered/optaa_dj_dcl_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'OPTAA' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/RID27/01-OPTAAD000/telemetered/optaa_dj_dcl_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'OPTAA' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/MFD37/01-OPTAAD000/telemetered/optaa_dj_dcl_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'OPTAA' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/MFD37/01-OPTAAD000/telemetered/optaa_dj_dcl_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'OPTAA' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/MFD37/01-OPTAAD000/telemetered/optaa_dj_dcl_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'OPTAA' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/MFD37/01-OPTAAC000/telemetered/optaa_dj_dcl_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
#NUTNR
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'NUTNR' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/RID16/07-NUTNRB000/telemetered/suna_dcl_recovered'
var_list[0].name = 'time'
var_list[1].name = 'nitrate_concentration'
var_list[2].name = 'salinity_corrected_nitrate'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/L'
var_list[2].units = 'umol/L'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'NUTNR' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/RID26/07-NUTNRB000/telemetered/suna_dcl_recovered'
var_list[0].name = 'time'
var_list[1].name = 'nitrate_concentration'
var_list[2].name = 'salinity_corrected_nitrate'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/L'
var_list[2].units = 'umol/L'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'NUTNR' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/RID26/07-NUTNRB000/telemetered/suna_dcl_recovered'
var_list[0].name = 'time'
var_list[1].name = 'nitrate_concentration'
var_list[2].name = 'salinity_corrected_nitrate'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/L'
var_list[2].units = 'umol/L'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'NUTNR' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/RID16/07-NUTNRB000/telemetered/suna_dcl_recovered'
var_list[0].name = 'time'
var_list[1].name = 'nitrate_concentration'
var_list[2].name = 'salinity_corrected_nitrate'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/L'
var_list[2].units = 'umol/L'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'NUTNR' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/RID26/07-NUTNRB000/telemetered/suna_dcl_recovered'
var_list[0].name = 'time'
var_list[1].name = 'nitrate_concentration'
var_list[2].name = 'salinity_corrected_nitrate'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/L'
var_list[2].units = 'umol/L'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'NUTNR' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/RID26/07-NUTNRB000/telemetered/suna_dcl_recovered'
var_list[0].name = 'time'
var_list[1].name = 'nitrate_concentration'
var_list[2].name = 'salinity_corrected_nitrate'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/L'
var_list[2].units = 'umol/L'
##
#MOPAK
elif platform_name == 'CE01ISSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/SBD17/01-MOPAK0000/recovered_host/mopak_o_dcl_accel_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/SBD11/01-MOPAK0000/recovered_host/mopak_o_dcl_accel_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/SBD11/01-MOPAK0000/recovered_host/mopak_o_dcl_accel_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE06ISSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/SBD17/01-MOPAK0000/recovered_host/mopak_o_dcl_accel_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/SBD11/01-MOPAK0000/recovered_host/mopak_o_dcl_accel_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/SBD11/01-MOPAK0000/recovered_host/mopak_o_dcl_accel_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSPM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSPM/SBS01/01-MOPAK0000/recovered_host/mopak_o_dcl_accel_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
#METBK
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'METBK1' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/SBD11/06-METBKA000/recovered_host/metbk_a_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'sea_surface_temperature'
var_list[2].name = 'sea_surface_conductivity'
var_list[3].name = 'met_salsurf'
var_list[4].name = 'met_windavg_mag_corr_east'
var_list[5].name = 'met_windavg_mag_corr_north'
var_list[6].name = 'barometric_pressure'
var_list[7].name = 'air_temperature'
var_list[8].name = 'relative_humidity'
var_list[9].name = 'longwave_irradiance'
var_list[10].name = 'shortwave_irradiance'
var_list[11].name = 'precipitation'
var_list[12].name = 'met_heatflx_minute'
var_list[13].name = 'met_latnflx_minute'
var_list[14].name = 'met_netlirr_minute'
var_list[15].name = 'met_sensflx_minute'
var_list[16].name = 'eastward_velocity'
var_list[17].name = 'northward_velocity'
var_list[18].name = 'met_spechum'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[15].data = np.array([])
var_list[16].data = np.array([])
var_list[17].data = np.array([])
var_list[18].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'S/m'
var_list[3].units = 'unitless'
var_list[4].units = 'm/s'
var_list[5].units = 'm/s'
var_list[6].units = 'mbar'
var_list[7].units = 'degC'
var_list[8].units = '#'
var_list[9].units = 'W/m'
var_list[10].units = 'W/m'
var_list[11].units = 'mm'
var_list[12].units = 'W/m'
var_list[13].units = 'W/m'
var_list[14].units = 'W/m'
var_list[15].units = 'W/m'
var_list[16].units = 'm/s'
var_list[17].units = 'm/s'
var_list[18].units = 'g/kg'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'METBK1' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/SBD11/06-METBKA000/recovered_host/metbk_a_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'sea_surface_temperature'
var_list[2].name = 'sea_surface_conductivity'
var_list[3].name = 'met_salsurf'
var_list[4].name = 'met_windavg_mag_corr_east'
var_list[5].name = 'met_windavg_mag_corr_north'
var_list[6].name = 'barometric_pressure'
var_list[7].name = 'air_temperature'
var_list[8].name = 'relative_humidity'
var_list[9].name = 'longwave_irradiance'
var_list[10].name = 'shortwave_irradiance'
var_list[11].name = 'precipitation'
var_list[12].name = 'met_heatflx_minute'
var_list[13].name = 'met_latnflx_minute'
var_list[14].name = 'met_netlirr_minute'
var_list[15].name = 'met_sensflx_minute'
var_list[16].name = 'eastward_velocity'
var_list[17].name = 'northward_velocity'
var_list[18].name = 'met_spechum'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[15].data = np.array([])
var_list[16].data = np.array([])
var_list[17].data = np.array([])
var_list[18].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'S/m'
var_list[3].units = 'unitless'
var_list[4].units = 'm/s'
var_list[5].units = 'm/s'
var_list[6].units = 'mbar'
var_list[7].units = 'degC'
var_list[8].units = '#'
var_list[9].units = 'W/m'
var_list[10].units = 'W/m'
var_list[11].units = 'mm'
var_list[12].units = 'W/m'
var_list[13].units = 'W/m'
var_list[14].units = 'W/m'
var_list[15].units = 'W/m'
var_list[16].units = 'm/s'
var_list[17].units = 'm/s'
var_list[18].units = 'g/kg'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'METBK1' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/SBD11/06-METBKA000/recovered_host/metbk_a_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'sea_surface_temperature'
var_list[2].name = 'sea_surface_conductivity'
var_list[3].name = 'met_salsurf'
var_list[4].name = 'met_windavg_mag_corr_east'
var_list[5].name = 'met_windavg_mag_corr_north'
var_list[6].name = 'barometric_pressure'
var_list[7].name = 'air_temperature'
var_list[8].name = 'relative_humidity'
var_list[9].name = 'longwave_irradiance'
var_list[10].name = 'shortwave_irradiance'
var_list[11].name = 'precipitation'
var_list[12].name = 'met_heatflx_minute'
var_list[13].name = 'met_latnflx_minute'
var_list[14].name = 'met_netlirr_minute'
var_list[15].name = 'met_sensflx_minute'
var_list[16].name = 'eastward_velocity'
var_list[17].name = 'northward_velocity'
var_list[18].name = 'met_spechum'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[15].data = np.array([])
var_list[16].data = np.array([])
var_list[17].data = np.array([])
var_list[18].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'S/m'
var_list[3].units = 'unitless'
var_list[4].units = 'm/s'
var_list[5].units = 'm/s'
var_list[6].units = 'mbar'
var_list[7].units = 'degC'
var_list[8].units = '#'
var_list[9].units = 'W/m'
var_list[10].units = 'W/m'
var_list[11].units = 'mm'
var_list[12].units = 'W/m'
var_list[13].units = 'W/m'
var_list[14].units = 'W/m'
var_list[15].units = 'W/m'
var_list[16].units = 'm/s'
var_list[17].units = 'm/s'
var_list[18].units = 'g/kg'
elif platform_name == 'CE09OSSM' and node == 'BUOY' and instrument_class == 'METBK1' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/SBD11/06-METBKA000/recovered_host/metbk_a_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'sea_surface_temperature'
var_list[2].name = 'sea_surface_conductivity'
var_list[3].name = 'met_salsurf'
var_list[4].name = 'met_windavg_mag_corr_east'
var_list[5].name = 'met_windavg_mag_corr_north'
var_list[6].name = 'barometric_pressure'
var_list[7].name = 'air_temperature'
var_list[8].name = 'relative_humidity'
var_list[9].name = 'longwave_irradiance'
var_list[10].name = 'shortwave_irradiance'
var_list[11].name = 'precipitation'
var_list[12].name = 'met_heatflx_minute'
var_list[13].name = 'met_latnflx_minute'
var_list[14].name = 'met_netlirr_minute'
var_list[15].name = 'met_sensflx_minute'
var_list[16].name = 'eastward_velocity'
var_list[17].name = 'northward_velocity'
var_list[18].name = 'met_spechum'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[15].data = np.array([])
var_list[16].data = np.array([])
var_list[17].data = np.array([])
var_list[18].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'S/m'
var_list[3].units = 'unitless'
var_list[4].units = 'm/s'
var_list[5].units = 'm/s'
var_list[6].units = 'mbar'
var_list[7].units = 'degC'
var_list[8].units = '#'
var_list[9].units = 'W/m'
var_list[10].units = 'W/m'
var_list[11].units = 'mm'
var_list[12].units = 'W/m'
var_list[13].units = 'W/m'
var_list[14].units = 'W/m'
var_list[15].units = 'W/m'
var_list[16].units = 'm/s'
var_list[17].units = 'm/s'
var_list[18].units = 'g/kg'
#FLORT
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/RID16/02-FLORTD000/recovered_host/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE01ISSM' and node == 'BUOY' and instrument_class == 'FLORT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/SBD17/06-FLORTD000/recovered_host/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/RID16/02-FLORTD000/recovered_host/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE06ISSM' and node == 'BUOY' and instrument_class == 'FLORT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/SBD17/06-FLORTD000/recovered_host/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/RID27/02-FLORTD000/recovered_host/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/RID27/02-FLORTD000/recovered_host/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/RID27/02-FLORTD000/recovered_host/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/RID27/02-FLORTD000/recovered_host/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
#FDCHP
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'FDCHP' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/SBD12/08-FDCHPA000/recovered_host/fdchp_a_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
#DOSTA
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/RID16/03-DOSTAD000/recovered_host/dosta_abcdjm_ctdbp_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/RID27/04-DOSTAD000/recovered_host/dosta_abcdjm_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/RID27/04-DOSTAD000/recovered_host/dosta_abcdjm_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/RID16/03-DOSTAD000/recovered_host/dosta_abcdjm_ctdbp_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/RID27/04-DOSTAD000/recovered_host/dosta_abcdjm_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/RID27/04-DOSTAD000/recovered_host/dosta_abcdjm_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'DOSTA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/MFD37/03-DOSTAD000/recovered_host/dosta_abcdjm_ctdbp_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'DOSTA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/MFD37/03-DOSTAD000/recovered_host/dosta_abcdjm_ctdbp_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'DOSTA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/MFD37/03-DOSTAD000/recovered_host/dosta_abcdjm_ctdbp_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'DOSTA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/MFD37/03-DOSTAD000/recovered_host/dosta_abcdjm_ctdbp_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
#ADCP
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'ADCP' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/RID26/01-ADCPTA000/recovered_host/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'ADCP' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/RID26/01-ADCPTC000/recovered_host/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'ADCP' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/RID26/01-ADCPTA000/recovered_host/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'ADCP' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/RID26/01-ADCPTC000/recovered_host/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'ADCP' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/MFD35/04-ADCPTM000/recovered_host/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'ADCP' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/MFD35/04-ADCPTM000/recovered_host/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'ADCP' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/MFD35/04-ADCPTC000/recovered_host/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'ADCP' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/MFD35/04-ADCPSJ000/recovered_host/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
#WAVSS
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'WAVSS_Stats' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/SBD12/05-WAVSSA000/recovered_host/wavss_a_dcl_statistics_recovered'
var_list[0].name = 'time'
var_list[1].name = 'number_zero_crossings'
var_list[2].name = 'average_wave_height'
var_list[3].name = 'mean_spectral_period'
var_list[4].name = 'max_wave_height'
var_list[5].name = 'significant_wave_height'
var_list[6].name = 'significant_period'
var_list[7].name = 'wave_height_10'
var_list[8].name = 'wave_period_10'
var_list[9].name = 'mean_wave_period'
var_list[10].name = 'peak_wave_period'
var_list[11].name = 'wave_period_tp5'
var_list[12].name = 'wave_height_hmo'
var_list[13].name = 'mean_direction'
var_list[14].name = 'mean_spread'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'counts'
var_list[2].units = 'm'
var_list[3].units = 'sec'
var_list[4].units = 'm'
var_list[5].units = 'm'
var_list[6].units = 'sec'
var_list[7].units = 'm'
var_list[8].units = 'sec'
var_list[9].units = 'sec'
var_list[10].units = 'sec'
var_list[11].units = 'sec'
var_list[12].units = 'm'
var_list[13].units = 'degrees'
var_list[14].units = 'degrees'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'WAVSS_Stats' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/SBD12/05-WAVSSA000/recovered_host/wavss_a_dcl_statistics_recovered'
var_list[0].name = 'time'
var_list[1].name = 'number_zero_crossings'
var_list[2].name = 'average_wave_height'
var_list[3].name = 'mean_spectral_period'
var_list[4].name = 'max_wave_height'
var_list[5].name = 'significant_wave_height'
var_list[6].name = 'significant_period'
var_list[7].name = 'wave_height_10'
var_list[8].name = 'wave_period_10'
var_list[9].name = 'mean_wave_period'
var_list[10].name = 'peak_wave_period'
var_list[11].name = 'wave_period_tp5'
var_list[12].name = 'wave_height_hmo'
var_list[13].name = 'mean_direction'
var_list[14].name = 'mean_spread'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'counts'
var_list[2].units = 'm'
var_list[3].units = 'sec'
var_list[4].units = 'm'
var_list[5].units = 'm'
var_list[6].units = 'sec'
var_list[7].units = 'm'
var_list[8].units = 'sec'
var_list[9].units = 'sec'
var_list[10].units = 'sec'
var_list[11].units = 'sec'
var_list[12].units = 'm'
var_list[13].units = 'degrees'
var_list[14].units = 'degrees'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'WAVSS_Stats' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/SBD12/05-WAVSSA000/recovered_host/wavss_a_dcl_statistics_recovered'
var_list[0].name = 'time'
var_list[1].name = 'number_zero_crossings'
var_list[2].name = 'average_wave_height'
var_list[3].name = 'mean_spectral_period'
var_list[4].name = 'max_wave_height'
var_list[5].name = 'significant_wave_height'
var_list[6].name = 'significant_period'
var_list[7].name = 'wave_height_10'
var_list[8].name = 'wave_period_10'
var_list[9].name = 'mean_wave_period'
var_list[10].name = 'peak_wave_period'
var_list[11].name = 'wave_period_tp5'
var_list[12].name = 'wave_height_hmo'
var_list[13].name = 'mean_direction'
var_list[14].name = 'mean_spread'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'counts'
var_list[2].units = 'm'
var_list[3].units = 'sec'
var_list[4].units = 'm'
var_list[5].units = 'm'
var_list[6].units = 'sec'
var_list[7].units = 'm'
var_list[8].units = 'sec'
var_list[9].units = 'sec'
var_list[10].units = 'sec'
var_list[11].units = 'sec'
var_list[12].units = 'm'
var_list[13].units = 'degrees'
var_list[14].units = 'degrees'
elif platform_name == 'CE09OSSM' and node == 'BUOY' and instrument_class == 'WAVSS_Stats' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/SBD12/05-WAVSSA000/recovered_host/wavss_a_dcl_statistics_recovered'
var_list[0].name = 'time'
var_list[1].name = 'number_zero_crossings'
var_list[2].name = 'average_wave_height'
var_list[3].name = 'mean_spectral_period'
var_list[4].name = 'max_wave_height'
var_list[5].name = 'significant_wave_height'
var_list[6].name = 'significant_period'
var_list[7].name = 'wave_height_10'
var_list[8].name = 'wave_period_10'
var_list[9].name = 'mean_wave_period'
var_list[10].name = 'peak_wave_period'
var_list[11].name = 'wave_period_tp5'
var_list[12].name = 'wave_height_hmo'
var_list[13].name = 'mean_direction'
var_list[14].name = 'mean_spread'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'counts'
var_list[2].units = 'm'
var_list[3].units = 'sec'
var_list[4].units = 'm'
var_list[5].units = 'm'
var_list[6].units = 'sec'
var_list[7].units = 'm'
var_list[8].units = 'sec'
var_list[9].units = 'sec'
var_list[10].units = 'sec'
var_list[11].units = 'sec'
var_list[12].units = 'm'
var_list[13].units = 'degrees'
var_list[14].units = 'degrees'
#VELPT
elif platform_name == 'CE01ISSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/SBD17/04-VELPTA000/recovered_host/velpt_ab_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/SBD11/04-VELPTA000/recovered_host/velpt_ab_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/SBD11/04-VELPTA000/recovered_host/velpt_ab_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE06ISSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'RecoveredHost':
#uframe_dataset_name = 'CE06ISSM/RID16/04-VELPTA000/recovered_host/velpt_ab_dcl_instrument_recovered'
uframe_dataset_name = 'CE06ISSM/RID16/04-VELPTA000/recovered_host/velpt_ab_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/SBD11/04-VELPTA000/recovered_host/velpt_ab_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE09OSSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/SBD11/04-VELPTA000/recovered_host/velpt_ab_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'VELPT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/RID16/04-VELPTA000/recovered_host/velpt_ab_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'VELPT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/RID26/04-VELPTA000/recovered_host/velpt_ab_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'VELPT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/RID26/04-VELPTA000/recovered_host/velpt_ab_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'VELPT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/RID16/04-VELPTA000/recovered_host/velpt_ab_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'VELPT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/RID26/04-VELPTA000/recovered_host/velpt_ab_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'VELPT' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/RID26/04-VELPTA000/recovered_host/velpt_ab_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
#PCO2W
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'PCO2W' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/RID16/05-PCO2WB000/recovered_host/pco2w_abc_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'pco2w_thermistor_temperature'
var_list[2].name = 'pco2_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'uatm'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'PCO2W' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/MFD35/05-PCO2WB000/recovered_host/pco2w_abc_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'pco2w_thermistor_temperature'
var_list[2].name = 'pco2_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'uatm'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'PCO2W' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/RID16/05-PCO2WB000/recovered_host/pco2w_abc_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'pco2w_thermistor_temperature'
var_list[2].name = 'pco2_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'uatm'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'PCO2W' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/MFD35/05-PCO2WB000/recovered_host/pco2w_abc_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'pco2w_thermistor_temperature'
var_list[2].name = 'pco2_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'uatm'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'PCO2W' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/MFD35/05-PCO2WB000/recovered_host/pco2w_abc_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'pco2w_thermistor_temperature'
var_list[2].name = 'pco2_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'uatm'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'PCO2W' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/MFD35/05-PCO2WB000/recovered_host/pco2w_abc_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'pco2w_thermistor_temperature'
var_list[2].name = 'pco2_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'uatm'
#PHSEN
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'PHSEN' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/RID16/06-PHSEND000/recovered_host/phsen_abcdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'PHSEN' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/RID26/06-PHSEND000/recovered_host/phsen_abcdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'PHSEN' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/RID26/06-PHSEND000/recovered_host/phsen_abcdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'PHSEN' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/RID16/06-PHSEND000/recovered_host/phsen_abcdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'PHSEN' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/RID26/06-PHSEND000/recovered_host/phsen_abcdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'PHSEN' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/RID26/06-PHSEND000/recovered_host/phsen_abcdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'PHSEN' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/MFD35/06-PHSEND000/recovered_host/phsen_abcdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'PHSEN' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/MFD35/06-PHSEND000/recovered_host/phsen_abcdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'PHSEN' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/MFD35/06-PHSEND000/recovered_host/phsen_abcdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'PHSEN' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/MFD35/06-PHSEND000/recovered_host/phsen_abcdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'phsen_thermistor_temperature'
var_list[2].name = 'phsen_abcdef_ph_seawater'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
#SPKIR
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'SPKIR' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/RID16/08-SPKIRB000/recovered_host/spkir_abj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'spkir_abj_cspp_downwelling_vector'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uW cm-2 nm-1'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'SPKIR' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/RID26/08-SPKIRB000/recovered_host/spkir_abj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'spkir_abj_cspp_downwelling_vector'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uW cm-2 nm-1'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'SPKIR' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/RID26/08-SPKIRB000/recovered_host/spkir_abj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'spkir_abj_cspp_downwelling_vector'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uW cm-2 nm-1'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'SPKIR' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/RID16/08-SPKIRB000/recovered_host/spkir_abj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'spkir_abj_cspp_downwelling_vector'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uW cm-2 nm-1'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'SPKIR' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/RID26/08-SPKIRB000/recovered_host/spkir_abj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'spkir_abj_cspp_downwelling_vector'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uW cm-2 nm-1'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'SPKIR' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/RID26/08-SPKIRB000/recovered_host/spkir_abj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'spkir_abj_cspp_downwelling_vector'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uW cm-2 nm-1'
#PRESF
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'PRESF' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/MFD35/02-PRESFA000/recovered_host/presf_abc_dcl_tide_measurement_recovered'
var_list[0].name = 'time'
var_list[1].name = 'abs_seafloor_pressure'
var_list[2].name = 'seawater_temperature'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'dbar'
var_list[2].units = 'degC'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'PRESF' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/MFD35/02-PRESFA000/recovered_host/presf_abc_dcl_tide_measurement_recovered'
var_list[0].name = 'time'
var_list[1].name = 'abs_seafloor_pressure'
var_list[2].name = 'seawater_temperature'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'dbar'
var_list[2].units = 'degC'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'PRESF' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/MFD35/02-PRESFB000/recovered_host/presf_abc_dcl_tide_measurement_recovered'
var_list[0].name = 'time'
var_list[1].name = 'abs_seafloor_pressure'
var_list[2].name = 'seawater_temperature'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'dbar'
var_list[2].units = 'degC'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'PRESF' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/MFD35/02-PRESFC000/recovered_host/presf_abc_dcl_tide_measurement_recovered'
var_list[0].name = 'time'
var_list[1].name = 'abs_seafloor_pressure'
var_list[2].name = 'seawater_temperature'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'dbar'
var_list[2].units = 'degC'
#CTDBP
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/RID16/03-CTDBPC000/recovered_host/ctdbp_cdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'CTD' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/MFD37/03-CTDBPC000/recovered_host/ctdbp_cdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE01ISSM' and node == 'BUOY' and instrument_class == 'CTD' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/SBD17/06-CTDBPC000/recovered_host/ctdbp_cdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/RID16/03-CTDBPC000/recovered_host/ctdbp_cdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'CTD' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/MFD37/03-CTDBPC000/recovered_host/ctdbp_cdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE06ISSM' and node == 'BUOY' and instrument_class == 'CTD' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/SBD17/06-CTDBPC000/recovered_host/ctdbp_cdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/RID27/03-CTDBPC000/recovered_host/ctdbp_cdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/RID27/03-CTDBPC000/recovered_host/ctdbp_cdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/RID27/03-CTDBPC000/recovered_host/ctdbp_cdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/RID27/03-CTDBPC000/recovered_host/ctdbp_cdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'CTD' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/MFD37/03-CTDBPC000/recovered_host/ctdbp_cdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'CTD' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/MFD37/03-CTDBPE000/recovered_host/ctdbp_cdef_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'temp'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'pressure'
var_list[5].name = 'conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
#VEL3D
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'VEL3D' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/MFD35/01-VEL3DD000/recovered_host/vel3d_cd_dcl_velocity_data_recovered'
var_list[0].name = 'time'
var_list[1].name = 'vel3d_c_eastward_turbulent_velocity'
var_list[2].name = 'vel3d_c_northward_turbulent_velocity'
var_list[3].name = 'vel3d_c_upward_turbulent_velocity'
var_list[4].name = 'seawater_pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = '0.001dbar'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'VEL3D' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/MFD35/01-VEL3DD000/recovered_host/vel3d_cd_dcl_velocity_data_recovered'
var_list[0].name = 'time'
var_list[1].name = 'vel3d_c_eastward_turbulent_velocity'
var_list[2].name = 'vel3d_c_northward_turbulent_velocity'
var_list[3].name = 'vel3d_c_upward_turbulent_velocity'
var_list[4].name = 'seawater_pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = '0.001dbar'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'VEL3D' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/MFD35/01-VEL3DD000/recovered_host/vel3d_cd_dcl_velocity_data_recovered'
var_list[0].name = 'time'
var_list[1].name = 'vel3d_c_eastward_turbulent_velocity'
var_list[2].name = 'vel3d_c_northward_turbulent_velocity'
var_list[3].name = 'vel3d_c_upward_turbulent_velocity'
var_list[4].name = 'seawater_pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = '0.001dbar'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'VEL3D' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/MFD35/01-VEL3DD000/recovered_host/vel3d_cd_dcl_velocity_data_recovered'
var_list[0].name = 'time'
var_list[1].name = 'vel3d_c_eastward_turbulent_velocity'
var_list[2].name = 'vel3d_c_northward_turbulent_velocity'
var_list[3].name = 'vel3d_c_upward_turbulent_velocity'
var_list[4].name = 'seawater_pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = '0.001dbar'
#PCO2A
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'PCO2A' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/SBD12/04-PCO2AA000/recovered_host/pco2a_a_dcl_instrument_water_recovered'
var_list[0].name = 'time'
var_list[1].name = 'partial_pressure_co2_ssw'
var_list[2].name = 'partial_pressure_co2_atm'
var_list[3].name = 'pco2_co2flux'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uatm'
var_list[2].units = 'uatm'
var_list[3].units = 'mol m-2 s-1'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'PCO2A' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/SBD12/04-PCO2AA000/recovered_host/pco2a_a_dcl_instrument_water_recovered'
var_list[0].name = 'time'
var_list[1].name = 'partial_pressure_co2_ssw'
var_list[2].name = 'partial_pressure_co2_atm'
var_list[3].name = 'pco2_co2flux'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uatm'
var_list[2].units = 'uatm'
var_list[3].units = 'mol m-2 s-1'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'PCO2A' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/SBD12/04-PCO2AA000/recovered_host/pco2a_a_dcl_instrument_water_recovered'
var_list[0].name = 'time'
var_list[1].name = 'partial_pressure_co2_ssw'
var_list[2].name = 'partial_pressure_co2_atm'
var_list[3].name = 'pco2_co2flux'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uatm'
var_list[2].units = 'uatm'
var_list[3].units = 'mol m-2 s-1'
elif platform_name == 'CE09OSSM' and node == 'BUOY' and instrument_class == 'PCO2A' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/SBD12/04-PCO2AA000/recovered_host/pco2a_a_dcl_instrument_water_recovered'
var_list[0].name = 'time'
var_list[1].name = 'partial_pressure_co2_ssw'
var_list[2].name = 'partial_pressure_co2_atm'
var_list[3].name = 'pco2_co2flux'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'uatm'
var_list[2].units = 'uatm'
var_list[3].units = 'mol m-2 s-1'
#OPTAA
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'OPTAA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/RID16/01-OPTAAD000/recovered_host/optaa_dj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'OPTAA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/RID27/01-OPTAAD000/recovered_host/optaa_dj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'OPTAA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/RID27/01-OPTAAD000/recovered_host/optaa_dj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'OPTAA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/RID16/01-OPTAAD000/recovered_host/optaa_dj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'OPTAA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/RID27/01-OPTAAD000/recovered_host/optaa_dj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'OPTAA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/RID27/01-OPTAAD000/recovered_host/optaa_dj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'OPTAA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/MFD37/01-OPTAAD000/recovered_host/optaa_dj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'OPTAA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/MFD37/01-OPTAAD000/recovered_host/optaa_dj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'OPTAA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/MFD37/01-OPTAAD000/recovered_host/optaa_dj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'OPTAA' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/MFD37/01-OPTAAC000/recovered_host/optaa_dj_dcl_instrument_recovered'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
#NUTNR
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'NUTNR' and method == 'RecoveredHost':
uframe_dataset_name = 'CE01ISSM/RID16/07-NUTNRB000/recovered_host/suna_dcl_recovered'
var_list[0].name = 'time'
var_list[1].name = 'nitrate_concentration'
var_list[2].name = 'salinity_corrected_nitrate'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/L'
var_list[2].units = 'umol/L'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'NUTNR' and method == 'RecoveredHost':
uframe_dataset_name = 'CE02SHSM/RID26/07-NUTNRB000/recovered_host/suna_dcl_recovered'
var_list[0].name = 'time'
var_list[1].name = 'nitrate_concentration'
var_list[2].name = 'salinity_corrected_nitrate'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/L'
var_list[2].units = 'umol/L'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'NUTNR' and method == 'RecoveredHost':
uframe_dataset_name = 'CE04OSSM/RID26/07-NUTNRB000/recovered_host/suna_dcl_recovered'
var_list[0].name = 'time'
var_list[1].name = 'nitrate_concentration'
var_list[2].name = 'salinity_corrected_nitrate'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/L'
var_list[2].units = 'umol/L'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'NUTNR' and method == 'RecoveredHost':
uframe_dataset_name = 'CE06ISSM/RID16/07-NUTNRB000/recovered_host/suna_dcl_recovered'
var_list[0].name = 'time'
var_list[1].name = 'nitrate_concentration'
var_list[2].name = 'salinity_corrected_nitrate'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/L'
var_list[2].units = 'umol/L'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'NUTNR' and method == 'RecoveredHost':
uframe_dataset_name = 'CE07SHSM/RID26/07-NUTNRB000/recovered_host/suna_dcl_recovered'
var_list[0].name = 'time'
var_list[1].name = 'nitrate_concentration'
var_list[2].name = 'salinity_corrected_nitrate'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/L'
var_list[2].units = 'umol/L'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'NUTNR' and method == 'RecoveredHost':
uframe_dataset_name = 'CE09OSSM/RID26/07-NUTNRB000/recovered_host/suna_dcl_recovered'
var_list[0].name = 'time'
var_list[1].name = 'nitrate_concentration'
var_list[2].name = 'salinity_corrected_nitrate'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/L'
var_list[2].units = 'umol/L'
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'RecoveredInst':
uframe_dataset_name = 'CE01ISSM/RID16/03-CTDBPC000/recovered_inst/ctdbp_cdef_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdbp_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdbp_seawater_pressure'
var_list[5].name = 'ctdbp_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'CTD' and method == 'RecoveredInst':
uframe_dataset_name = 'CE01ISSM/MFD37/03-CTDBPC000/recovered_inst/ctdbp_cdef_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdbp_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdbp_seawater_pressure'
var_list[5].name = 'ctdbp_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE01ISSM' and node == 'BUOY' and instrument_class == 'CTD' and method == 'RecoveredInst':
uframe_dataset_name = 'CE01ISSM/SBD17/06-CTDBPC000/recovered_inst/ctdbp_cdef_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdbp_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdbp_seawater_pressure'
var_list[5].name = 'ctdbp_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'RecoveredInst':
uframe_dataset_name = 'CE06ISSM/RID16/03-CTDBPC000/recovered_inst/ctdbp_cdef_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdbp_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdbp_seawater_pressure'
var_list[5].name = 'ctdbp_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'CTD' and method == 'RecoveredInst':
uframe_dataset_name = 'CE06ISSM/MFD37/03-CTDBPC000/recovered_inst/ctdbp_cdef_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdbp_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdbp_seawater_pressure'
var_list[5].name = 'ctdbp_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE06ISSM' and node == 'BUOY' and instrument_class == 'CTD' and method == 'RecoveredInst':
uframe_dataset_name = 'CE06ISSM/SBD17/06-CTDBPC000/recovered_inst/ctdbp_cdef_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdbp_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdbp_seawater_pressure'
var_list[5].name = 'ctdbp_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'RecoveredInst':
uframe_dataset_name = 'CE02SHSM/RID27/03-CTDBPC000/recovered_inst/ctdbp_cdef_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdbp_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdbp_seawater_pressure'
var_list[5].name = 'ctdbp_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'RecoveredInst':
uframe_dataset_name = 'CE07SHSM/RID27/03-CTDBPC000/recovered_inst/ctdbp_cdef_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdbp_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdbp_seawater_pressure'
var_list[5].name = 'ctdbp_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'RecoveredInst':
uframe_dataset_name = 'CE04OSSM/RID27/03-CTDBPC000/recovered_inst/ctdbp_cdef_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdbp_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdbp_seawater_pressure'
var_list[5].name = 'ctdbp_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'CTD' and method == 'RecoveredInst':
uframe_dataset_name = 'CE09OSSM/RID27/03-CTDBPC000/recovered_inst/ctdbp_cdef_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdbp_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdbp_seawater_pressure'
var_list[5].name = 'ctdbp_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'CTD' and method == 'RecoveredInst':
uframe_dataset_name = 'CE07SHSM/MFD37/03-CTDBPC000/recovered_inst/ctdbp_cdef_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdbp_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdbp_seawater_pressure'
var_list[5].name = 'ctdbp_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'CTD' and method == 'RecoveredInst':
uframe_dataset_name = 'CE09OSSM/MFD37/03-CTDBPE000/recovered_inst/ctdbp_cdef_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdbp_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdbp_seawater_pressure'
var_list[5].name = 'ctdbp_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE09OSPM' and node == 'PROFILER' and instrument_class == 'CTD' and method == 'RecoveredWFP':
uframe_dataset_name = 'CE09OSPM/WFP01/03-CTDPFK000/recovered_wfp/ctdpf_ckl_wfp_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'ctdpf_ckl_seawater_temperature'
var_list[2].name = 'practical_salinity'
var_list[3].name = 'density'
var_list[4].name = 'ctdpf_ckl_seawater_pressure'
var_list[5].name = 'ctdpf_ckl_seawater_conductivity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'unitless'
var_list[3].units = 'kg/m3'
var_list[4].units = 'dbar'
var_list[5].units = 'S/m'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'ADCP' and method == 'RecoveredInst':
uframe_dataset_name = 'CE02SHSM/RID26/01-ADCPTA000/recovered_inst/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'ADCP' and method == 'RecoveredInst':
uframe_dataset_name = 'CE04OSSM/RID26/01-ADCPTC000/recovered_inst/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'ADCP' and method == 'RecoveredInst':
uframe_dataset_name = 'CE07SHSM/RID26/01-ADCPTA000/recovered_inst/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'ADCP' and method == 'RecoveredInst':
uframe_dataset_name = 'CE09OSSM/RID26/01-ADCPTC000/recovered_inst/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'ADCP' and method == 'RecoveredInst':
uframe_dataset_name = 'CE01ISSM/MFD35/04-ADCPTM000/recovered_inst/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'ADCP' and method == 'RecoveredInst':
uframe_dataset_name = 'CE06ISSM/MFD35/04-ADCPTM000/recovered_inst/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'ADCP' and method == 'RecoveredInst':
uframe_dataset_name = 'CE07SHSM/MFD35/04-ADCPTC000/recovered_inst/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'ADCP' and method == 'RecoveredInst':
uframe_dataset_name = 'CE09OSSM/MFD35/04-ADCPSJ000/recovered_inst/adcp_velocity_earth'
var_list[0].name = 'time'
var_list[1].name = 'bin_depths'
var_list[2].name = 'heading'
var_list[3].name = 'pitch'
var_list[4].name = 'roll'
var_list[5].name = 'eastward_seawater_velocity'
var_list[6].name = 'northward_seawater_velocity'
var_list[7].name = 'upward_seawater_velocity'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'meters'
var_list[2].units = 'deci-degrees'
var_list[3].units = 'deci-degrees'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'm/s'
var_list[6].units = 'm/s'
var_list[7].units = 'm/s'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'ZPLSC' and method == 'RecoveredInst':
uframe_dataset_name = 'CE01ISSM/MFD37/07-ZPLSCC000/recovered_inst/zplsc_echogram_data'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'ZPLSC' and method == 'RecoveredInst':
uframe_dataset_name = 'CE06ISSM/MFD37/07-ZPLSCC000/recovered_inst/zplsc_echogram_data'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE07SHSM' and node == 'MFN' and instrument_class == 'ZPLSC' and method == 'RecoveredInst':
uframe_dataset_name = 'CE07SHSM/MFD37/07-ZPLSCC000/recovered_inst/zplsc_echogram_data'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSSM' and node == 'MFN' and instrument_class == 'ZPLSC' and method == 'RecoveredInst':
uframe_dataset_name = 'CE09OSSM/MFD37/07-ZPLSCC000/recovered_inst/zplsc_echogram_data'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE01ISSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'RecoveredInst':
uframe_dataset_name = 'CE01ISSM/SBD17/04-VELPTA000/recovered_inst/velpt_ab_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'RecoveredInst':
uframe_dataset_name = 'CE02SHSM/SBD11/04-VELPTA000/recovered_inst/velpt_ab_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'RecoveredInst':
uframe_dataset_name = 'CE04OSSM/SBD11/04-VELPTA000/recovered_inst/velpt_ab_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE06ISSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'RecoveredInst':
uframe_dataset_name = 'CE06ISSM/SBD17/04-VELPTA000/recovered_inst/velpt_ab_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm/s'
var_list[2].units = 'm/s'
var_list[3].units = 'm/s'
var_list[4].units = 'deci-degrees'
var_list[5].units = 'deci-degrees'
var_list[6].units = 'deci-degrees'
var_list[7].units = '0.01degC'
var_list[8].units = '0.001dbar'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'VELPT' and method == 'RecoveredInst':
uframe_dataset_name = 'CE07SHSM/SBD11/04-VELPTA000/recovered_inst/velpt_ab_instrument_recovered'
var_list[0].name = 'time'
var_list[1].name = 'eastward_velocity'
var_list[2].name = 'northward_velocity'
var_list[3].name = 'upward_velocity'
var_list[4].name = 'heading_decidegree'
var_list[5].name = 'roll_decidegree'
var_list[6].name = 'pitch_decidegree'
var_list[7].name = 'temperature_centidegree'
var_list[8].name = 'pressure_mbar'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = | np.array([]) | numpy.array |
from spreco.common import utils, ops
from spreco.model.sde import sde, posterior_sampler
import argparse
import os
from functools import partial
import numpy as np
import tensorflow.compat.v1 as tf
tf.disable_eager_execution()
def recon(config, workspace, kspace_path, mask_path):
if not os.path.exists(workspace):
os.makedirs(workspace)
model_config = utils.load_config(os.path.join(config['model_folder'], 'config.yaml'))
| np.random.seed(model_config['seed']) | numpy.random.seed |
# CURRENTPASS: this file is going to a different project altogheter and will be importing bioflow
# from a pip install
import pickle
import numpy as np
from scipy.stats import gaussian_kde
from matplotlib import pyplot as plt
from numpy import histogram2d
from csv import reader as csv_reader
# from bioflow.configs.main_configs import interactome_rand_samp_db # deprecated
from bioflow.utils.log_behavior import get_logger
from bioflow.molecular_network.InteractomeInterface import InteractomeInterface
from bioflow.sample_storage.mongodb import find_interactome_rand_samp, count_interactome_rand_samp
from bioflow.algorithms_bank.deprecated_clustering_routines import deprecated_perform_clustering
from bioflow.configs.main_configs import Dumps
from bioflow.utils.top_level import map_and_save_gene_ids
# from bioflow.algorithms_bank.conduction_routines import get_current_through_nodes
from matplotlib.cm import get_cmap
log = get_logger(__name__)
wanted_samples = 1000
essential_genes_file = ''
# 'C:\Users\Andrei\Dropbox\workspaces\JHU\Mehdi_paper_1.inviable_annotations_filtered_by_S288C-filt.tsv'
interactome_interface_instance = InteractomeInterface()
interactome_interface_instance.fast_load()
up_1, up_2 = (interactome_interface_instance._background[0],
interactome_interface_instance._background[1])
md5_hash = interactome_interface_instance.md5_hash()
active_sample_hash = interactome_interface_instance.active_sample_md5_hash(False)
samples_to_test_against = count_interactome_rand_samp({
'active_sample_hash': active_sample_hash,
'sys_hash': md5_hash})
if samples_to_test_against < wanted_samples:
interactome_interface_instance.randomly_sample(wanted_samples - samples_to_test_against,
sparse_rounds=False)
samples_to_test_against = count_interactome_rand_samp({
'active_sample_hash': active_sample_hash,
'sys_hash': md5_hash})
log.info("samples found to test against:\t %d" % samples_to_test_against)
background_samples = find_interactome_rand_samp({
'active_sample_hash': active_sample_hash,
'sys_hash': md5_hash})
essential_genes_bulbs_ids, _, _ = map_and_save_gene_ids(essential_genes_file)
length_width_accumulator = []
essentiality_percentage = []
values = []
for i, sample in enumerate(background_samples):
# if i > 10:
# break
_, nodes_current_dict = pickle.loads(sample['currents'])
tensions = pickle.loads(sample['voltages'])
io_nodes, tension = (tensions.keys()[0], tensions.values()[0])
# this actually should be a multiplication - we divide to normalize to 1 volt, after counting for 1 amp
nodes_current = np.sort(np.array(nodes_current_dict.values()).astype(np.float))[-100:] * tension
# not the most efficient implementation, but oh well
essential_max_current = 0
for gene in essential_genes_bulbs_ids:
if nodes_current_dict[gene]/tension > 0.05:
if nodes_current_dict[gene] > essential_max_current:
essential_max_current = nodes_current_dict[gene] * tension
# delete nodes close to 1 (IO)
# ivide by 2
if tension > .2:
total_resistance = tension # yeah, tension is just a resistance in this context - my labeling error
length_by_width = total_resistance
# nodes_current = nodes_current[np.logical_not(np.isclose(nodes_current, np.ones(nodes_current.shape), rtol=1e-03))]/2
nodes_current = nodes_current[nodes_current < 0.999]
shape_characteristic = 1. / nodes_current
print('\n\n\n>>>>>>>>>>>>>')
print('sample ', i)
print('length/width', length_by_width)
# alternative width is max. But in this case we might to remove everything close enough to 0
# mean_width = 1./np.mean(nodes_current[nodes_current > 0.1])
mean_width = 1. / np.mean(nodes_current[nodes_current > 0.2])
length = mean_width * length_by_width
if length < 1:
mean_width /= length
length = 1
if mean_width < 1:
length /= mean_width
mean_width = 1
print('width', mean_width)
print('length', length)
print('essentiality', essential_max_current)
# print 'io nodes:\t', nodes_current_dict[io_nodes[0]] * tension, nodes_current_dict[io_nodes[1]] * tension
# print 'resistance:\t', total_resistance
# print 'max current:\t', nodes_current[-1]
# print 'tension:\t', tension
# print nodes_current
length_width_accumulator.append((length, mean_width))
values += nodes_current.tolist()
essentiality_percentage.append(min([essential_max_current,1.]))
# if any(nodes_current > 1.1):
# print nodes_current
# raise Exception('debug')
# print 'tension', tension
# print 'total_res', total_resistance
# print 'path_len, nodes_current', np.column_stack((shape_characteristic, nodes_current))
# if tension > 0.1: # (if tension is below, we hit a super closely related cluster - 10 direct connections)
# shape_characteristic = shape_characteristic[shape_characteristic < 20]
# shape_characteristic = shape_characteristic[shape_characteristic > 0.1]
# mean_width = 1.
# mean_length = 1.
#
# w_selected = shape_characteristic[shape_characteristic < 1]
# if np.any(w_selected):
# print 'estimated width distribution:\t', np.mean(1. / w_selected)
# mean_width = np.mean(1. / w_selected)
# width_accumulator += (1. / w_selected).tolist()
# if mean_width < 1:
# raise Exception('unexpected width mean')
# else:
# print 'estimated width distribution:\t', 1.
#
# l_selected = shape_characteristic[shape_characteristic > 1]
# if np.any(l_selected):
# print 'estimated length distribution:\t', np.mean(l_selected)
# mean_length = np.mean(l_selected)
# length_accumulator += l_selected.tolist()
# else:
# print 'estimated length distribution: \t', 1.
#
# # print essential_max_current
# # print nodes_current[-1]
# print "essentiality percentage :\t", essential_max_current/nodes_current[-1]*tension
# essentiality_percentage.append(essential_max_current/nodes_current[-1]*tension)
# if essential_max_current*tension > nodes_current[-1]:
# print essential_max_current
# print nodes_current
#
# length_width_accumulator.append([mean_length, mean_width])
values = np.array(values)
data = values[values > 0.2]
fltr = np.logical_not(np.isnan(data))
density = gaussian_kde(data[fltr].flatten())
xs = np.linspace(data[fltr].min(), data[fltr].max(), 200)
plt.plot(xs, density(xs), 'k')
plt.xlabel('pathway shape parameter')
plt.ylabel('density of distribution')
plt.show()
_length = np.array(length_width_accumulator)[:, 0]
print('average length', np.mean(_length[_length > 1.99]))
print('std length', np.std(_length[_length > 1.99]))
data = np.array(_length[_length > 1.99])
fltr = np.logical_not(np.isnan(data))
density = gaussian_kde(data[fltr].flatten())
xs = np.linspace(data[fltr].min(), data[fltr].max(), 200)
plt.title('Length distribution of non-trivial pathways')
plt.plot(xs, density(xs), 'k')
plt.xlabel('length of the pathway')
plt.ylabel('density of distribution')
plt.show()
_width = | np.array(length_width_accumulator) | numpy.array |
# Copyright (c) 2020 <NAME> <<EMAIL>>, EPFL
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# 3. Neither the name of the copyright holder nor the names of its contributors
# may be used to endorse or promote products derived from this software without
# specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
# BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER
# IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
"""
Base classes to represent experiments
"""
from abc import ABC, abstractmethod
import numpy as np
__all__ = ["ComplexSignal", "MagnitudeSignal", "FittedSignal",
"SignalCollection",
"ComplexSignalCollection", "MagnitudeSignalCollection", "FittedSignalCollection"]
class Signal(ABC):
def __init__(self, tau):
self._tau = tau
@property
def tau(self):
return self._tau
@property
def size(self):
return self._tau.shape[0]
@abstractmethod
def _signal_impl(self):
pass
@property
def signal(self):
return self._signal_impl()
class ComplexSignal(Signal):
"""A complex signal"""
def __init__(self, tau, real, imag):
assert(real.shape[0] == tau.shape[0])
assert(imag.shape[0] == tau.shape[0])
super().__init__(tau)
self._real = real
self._imag = imag
@property
def real(self):
return self._real
@property
def imag(self):
return self._imag
def _signal_impl(self):
return self._real
def phase(self, start_echo, nb_echo):
thetas = []
for i in np.arange(start_echo, start_echo + nb_echo+1):
if self.real[i] < 0:
thetas.append(np.arctan(self.imag[i] / self.real[i]) + np.pi)
else:
thetas.append(np.arctan(self.imag[i] / self.real[i]))
theta = np.array(thetas).mean()
real1 = np.cos(theta)*self.real + np.sin(theta)*self.imag
imag1 = -np.sin(theta)*self.real + np.cos(theta)*self.imag
self._real = real1
self._imag = imag1
def magnitude(self):
signal = np.sqrt( | np.power(self._real, 2) | numpy.power |
# 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]) | numpy.array |
import torch
import os
import sys
import yaml
import numpy as np
import random
random.seed(1337)
import shutil
from utils.multipathvisualizerCombine import DrawpathCombine
from torch import nn
import utils.graphUtils.graphTools as graph
from scipy.spatial.distance import squareform, pdist
from dataloader.statetransformer import AgentState
import scipy.io as sio
# from onlineExpert.ECBS_onlineExpert import ComputeCBSSolution
class multiRobotSim:
def __init__(self, config):
self.config = config
self.AgentState = AgentState(self.config.num_agents)
self.delta_list =[[-1, 0], # go up
[0, -1], # go left
[1, 0], # go down
[0, 1], # go right
[0, 0]] # stop
self.delta = torch.FloatTensor(self.delta_list).to(self.config.device)
# self.onlineExpert = ComputeCBSSolution(self.config)
self.List_MultiAgent_ActionVec_target = None
self.store_MultiAgent = None
self.channel_map = None
self.size_map = None
self.maxstep = None
self.posObstacle = None
self.numObstacle = None
self.posStart = None
self.posGoal = None
self.currentState_predict = None
self.makespanTarget = None
self.flowtimeTarget = None
self.makespanPredict = None
self.flowtimePredict = None
self.count_reachgoal = None
self.count_reachgoalTarget = None
self.fun_Softmax = None
self.zeroTolerance = 1e-9
print("run on multirobotsim with collision shielding")
def setup(self, loadInput, loadTarget, makespanTarget, tensor_map, ID_dataset):
# self.fun_Softmax = nn.Softmax(dim=-1)
self.fun_Softmax = nn.LogSoftmax(dim=-1)
self.ID_dataset = ID_dataset
self.store_GSO = []
self.store_communication_radius = []
self.status_MultiAgent = {}
# setupState = loadInput.permute(3, 4, 2, 1, 0)
target = loadTarget.permute(1, 2, 3, 0)
self.List_MultiAgent_ActionVec_target = target[:, :, :,0]
# self.List_MultiAgent_ActionVec_target = target[:, :, 0]
self.channel_map = tensor_map[0] # setupState[:, :, 0, 0, 0]
self.AgentState.setmap(self.channel_map)
self.posObstacle = self.findpos(self.channel_map).to(self.config.device)
self.numObstacle = self.posObstacle.shape[0]
self.size_map = self.channel_map.shape
# self.communicationRadius = 5 #self.size_map[0] * 0.5
# self.maxstep = self.size_map[0] * self.size_map[1]
if self.config.num_agents >=20:
self.rate_maxstep = 3
else:
self.rate_maxstep = self.config.rate_maxstep
self.maxstep = int(makespanTarget.type(torch.int32) * self.rate_maxstep)
self.check_predictCollsion = False
self.check_moveCollision = True
self.check_predictEdgeCollsion = [False] * self.config.num_agents
self.count_reachgoal = [False] * self.config.num_agents
self.count_reachgoalTarget = [False] * self.config.num_agents
self.allReachGoal_Target = False
self.makespanTarget = 0
self.flowtimeTarget = 0
self.makespanPredict = self.maxstep
self.flowtimePredict = self.maxstep * self.config.num_agents #0
# used for determining flowtimes of non rouge agents
self.nonRogueFlowtimePredict = None
self.stopKeyValue = torch.tensor(4).to(self.config.device)
self.reset_disabled_action = torch.tensor([1.0, 1.0, 1.0, 1.0, 1.0]).float().to(self.config.device)
self.store_goalAgents = loadInput[0, 0, :,:]
self.store_stateAgents = loadInput[0, 1, :, :]
for id_agent in range(self.config.num_agents):
status_CurrentAgent = {}
posGoal = loadInput[:, 0,id_agent,:] #self.findpos(goal_CurrentAgent)
posStart = loadInput[:, 1,id_agent,:] #self.findpos(start_CurrentAgent)
path_predict = {0:posStart}
path_target = {0:posStart}
len_action_predict = 0
list_actionKey_predict = []
actionVec_target_CurrentAgents = self.List_MultiAgent_ActionVec_target[id_agent, :, :]
actionKeyList_target_CurrentAgents = torch.max(actionVec_target_CurrentAgents, 1)[1]
disabled_action_predict_currentAgent = self.reset_disabled_action
startStep_action_currentAgent = None
endStep_action_currentAgent = None
len_action_target = actionKeyList_target_CurrentAgents.shape[0]
status_CurrentAgents = {"goal": posGoal,
"start": posStart,#torch.FloatTensor([[0,0]]).to(self.config.device),
"currentState": posStart,
"path_target": path_target,
"action_target": actionKeyList_target_CurrentAgents,
"len_action_target": len_action_target,
"startStep_action_target": startStep_action_currentAgent,
"endStep_action_target": endStep_action_currentAgent,
"path_predict": path_predict,
"nextState_predict": posStart,
"action_predict": list_actionKey_predict,
"disabled_action_predict": disabled_action_predict_currentAgent,
"len_action_predict": len_action_predict,
"startStep_action_predict": startStep_action_currentAgent,
"endStep_action_predict": endStep_action_currentAgent
}
# print("Agent{} - goal:{} - start:{} - currentState:{}".format(id_agent, posGoal,posStart,posStart))
name_agent = "agent{}".format(id_agent)
self.status_MultiAgent.update({name_agent: status_CurrentAgents})
self.getPathTarget()
pass
def findpos(self, channel):
pos_object = channel.nonzero()
num_object = pos_object.shape[0]
pos = torch.zeros(num_object, 2)
# pos_list = []
for i in range(num_object):
pos[i][0] = pos_object[i][0]
pos[i][1] = pos_object[i][1]
# pos_list.append([pos_object[i][0], pos_object[i][1]])
# pos = torch.FloatTensor(pos_list)
return pos
def getPathTarget(self):
#todo check the length for ground truth, out of index
list_len_action_target = []
for id_agent in range(self.config.num_agents):
name_agent = "agent{}".format(id_agent)
len_actionTarget_currentAgent = self.status_MultiAgent[name_agent]["len_action_target"]
list_len_action_target.append(len_actionTarget_currentAgent)
maxStep = max(list_len_action_target)
for id_agent in range(self.config.num_agents):
name_agent = "agent{}".format(id_agent)
pathTarget_currentAgent = self.status_MultiAgent[name_agent]["path_target"]
currentState_target = self.status_MultiAgent[name_agent]['start']
goal_currentAgent = self.status_MultiAgent[name_agent]['goal']
nextState_target = currentState_target
goalIndexX = int(goal_currentAgent[0][0])
goalIndexY = int(goal_currentAgent[0][1])
for step in range(maxStep):
actionKey_target = self.status_MultiAgent[name_agent]['action_target'][step]
check_move = (actionKey_target != self.stopKeyValue)
check_startStep_action = self.status_MultiAgent[name_agent]["startStep_action_target"]
if check_move == 1 and check_startStep_action is None:
self.status_MultiAgent[name_agent]["startStep_action_target"] = step
else:
currentState_target = nextState_target
action_target = self.delta[actionKey_target]
nextState_target = torch.add(currentState_target, action_target)
pathTarget_currentAgent.update({step+1: nextState_target})
self.status_MultiAgent[name_agent]["path_target"] = pathTarget_currentAgent
if nextState_target[0][0] == goalIndexX and nextState_target[0][1] == goalIndexY and not self.count_reachgoalTarget[id_agent]:
self.count_reachgoalTarget[id_agent] = True
self.status_MultiAgent[name_agent]["endStep_action_target"] = step + 1
self.allReachGoal_Target = all(self.count_reachgoalTarget)
if self.allReachGoal_Target:
List_endStep_target = []
List_startStep_target = []
self.flowtimeTarget = 0
for id_agent in range(self.config.num_agents):
name_agent = "agent{}".format(id_agent)
List_endStep_target.append(self.status_MultiAgent[name_agent]["endStep_action_target"])
List_startStep_target.append(self.status_MultiAgent[name_agent]["startStep_action_target"])
self.flowtimeTarget += self.status_MultiAgent[name_agent]["endStep_action_target"] - \
self.status_MultiAgent[name_agent]["startStep_action_target"]
len_action_predict = self.status_MultiAgent[name_agent]["endStep_action_target"] - \
self.status_MultiAgent[name_agent]["startStep_action_target"]
self.status_MultiAgent[name_agent]["len_action_target"] = len_action_predict
self.makespanTarget = max(List_endStep_target) - min(List_startStep_target)
# print("Makespane(target):{} \n Flowtime(target): {} \n ").format(self.makespanTarget, self.flowtimeTarget)
break
def getOptimalityMetrics(self):
return [self.makespanPredict, self.makespanTarget], [self.flowtimePredict, self.flowtimeTarget]
def getMaxstep(self):
return self.maxstep
def getMapsize(self):
return self.size_map
def initCommunicationRadius(self):
self.communicationRadius = self.config.commR
# self.communicationRadius = 5
# self.communicationRadius = 6
# self.communicationRadius = 7
# self.communicationRadius = 8
# self.communicationRadius = 9
# self.communicationRadius = 10
def reachObstacle(self, state):
reach_obstacle = False
# name_agent = "agent{}".format(id_agent)
currentState_predict = state #self.status_MultiAgent[name_agent]["currentState"]
currentStateIndexX = currentState_predict[0][0]
currentStateIndexY = currentState_predict[0][1]
# print(self.channel_map.shape)
# print(self.channel_map)
# time.sleep(10)
if self.channel_map[int(currentStateIndexX)][int(currentStateIndexY)] == 1:
# print('Reach obstacle.')
reach_obstacle = True
else:
reach_obstacle = False
# if reach_obstacle:
# break
return reach_obstacle
def reachEdge(self, state):
reach_edge = False
# name_agent = "agent{}".format(id_agent)
currentState_predict = state #self.status_MultiAgent[name_agent]["currentState"]
currentStateIndexX = currentState_predict[0][0]
currentStateIndexY = currentState_predict[0][1]
if currentStateIndexX >= self.size_map[0] or currentStateIndexX < 0 or currentStateIndexY >= self.size_map[1] or currentStateIndexY < 0:
# print('Reach edge.')
reach_edge = True
# break
else:
reach_edge = False
return reach_edge
def computeAdjacencyMatrix_fixedCommRadius(self, step, agentPos, CommunicationRadius, graphConnected=False):
len_TimeSteps = agentPos.shape[0] # length of timesteps
nNodes = agentPos.shape[1] # Number of nodes
# Create the space to hold the adjacency matrices
W = np.zeros([len_TimeSteps, nNodes, nNodes])
# Initial matrix
distances = squareform(pdist(agentPos[0])) # nNodes x nNodes
# I will increase the communication radius by 10% each time,
# but I have to do it consistently within the while loop,
# so in order to not affect the first value set of communication radius, I will account for that initial 10% outside
distances = squareform(pdist(agentPos[0])) # nNodes x nNodes
W[0] = (distances < self.communicationRadius).astype(agentPos.dtype)
W[0] = W[0] - np.diag(np.diag(W[0]))
graphConnected = graph.isConnected(W[0])
deg = np.sum(W[0], axis=1) # nNodes (degree vector)
zeroDeg = np.nonzero(np.abs(deg) < self.zeroTolerance)[0]
deg[zeroDeg] = 1.
invSqrtDeg = np.sqrt(1. / deg)
invSqrtDeg[zeroDeg] = 0.
Deg = np.diag(invSqrtDeg)
W[0] = Deg @ W[0] @ Deg
return W, self.communicationRadius, graphConnected
def computeAdjacencyMatrix(self, step, agentPos, CommunicationRadius, graphConnected=False):
len_TimeSteps = agentPos.shape[0] # length of timesteps
nNodes = agentPos.shape[1] # Number of nodes
# Create the space to hold the adjacency matrices
W = np.zeros([len_TimeSteps, nNodes, nNodes])
# Initial matrix
distances = squareform(pdist(agentPos[0])) # nNodes x nNodes
# I will increase the communication radius by 10% each time,
# but I have to do it consistently within the while loop,
# so in order to not affect the first value set of communication radius, I will account for that initial 10% outside
if step == 0:
self.communicationRadius = self.communicationRadius / 1.1
while graphConnected is False:
self.communicationRadius = self.communicationRadius * 1.1
W[0] = (distances < self.communicationRadius).astype(agentPos.dtype)
W[0] = W[0] - np.diag(np.diag(W[0]))
graphConnected = graph.isConnected(W[0])
# And once we have found a connected initial position, we normalize it
deg = np.sum(W[0], axis=1) # nNodes (degree vector)
zeroDeg = np.nonzero(np.abs(deg) < self.zeroTolerance)[0]
deg[zeroDeg] = 1.
invSqrtDeg = np.sqrt(1. / deg)
invSqrtDeg[zeroDeg] = 0.
Deg = | np.diag(invSqrtDeg) | numpy.diag |
import os
import shutil
import numpy as np
from PIL import Image
from MathworksLoader import MathworksLoader
# For 3 unique identities, will create 5 test images, that are 2x2 images, for each identity
# Identity 1
fingerprint_1_1 = np.array([[1, 2], [3, 4]])
fingerprint_1_2 = np.array([[1, 2], [5, 6]])
fingerprint_1_3 = np.array([[1, 2], [7, 8]])
fingerprint_1_4 = np.array([[1, 2], [9, 10]])
fingerprint_1_5 = np.array([[3, 4], [1, 2]])
# Identity 2
fingerprint_2_1 = np.array([[100, 101], [3, 4]])
fingerprint_2_2 = np.array([[100, 101], [5, 6]])
fingerprint_2_3 = np.array([[100, 101], [7, 8]])
fingerprint_2_4 = | np.array([[100, 101], [9, 10]]) | numpy.array |
import numpy as np
import json
import copy
import os
def rotate_box_by_angle_up_direction(box, rotation_angle):
cosval = np.cos(rotation_angle)
sinval = np.sin(rotation_angle)
rotation_matrix = np.array([[cosval, 0, sinval],
[0, 1, 0],
[-sinval, 0, cosval]])
box[0:3] = np.dot(box[0:3], rotation_matrix)
box[6:9] = np.dot(box[6:9], rotation_matrix)
box[9:] = np.dot(box[9:], rotation_matrix)
return box
def rotate_box_by_angle_straight_direction(box, rotation_angle):
cosval = | np.cos(rotation_angle) | numpy.cos |
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import scipy.interpolate
from scipy.spatial import distance
from scipy import ndimage
from PIL import Image, ImageDraw
from skimage import measure
from skimage import morphology
from matplotlib.colors import LinearSegmentedColormap
import time, sys
import numba
import matplotlib.colors as mcolors
import matplotlib.gridspec as gridspec
def update_progress(progress):
"""progress bar from https://stackoverflow.com/questions/3160699/python-progress-bar
update_progress() : Displays or updates a console progress bar
Accepts a float between 0 and 1. Any int will be converted to a float.
A value under 0 represents a 'halt'.
A value at 1 or bigger represents 100%"""
barLength = 20 # Modify this to change the length of the progress bar
status = ""
if isinstance(progress, int):
progress = float(progress)
if not isinstance(progress, float):
progress = 0
status = "error: progress var must be float\r\n"
if progress < 0:
progress = 0
status = "Halt...\r\n"
if progress >= 1:
progress = 1
status = "Done...\r\n"
block = int(round(barLength*progress))
text = "\rPercent: [{0}] {1}% {2}".format( "#"*block + "-"*(barLength-block), progress*100, status)
sys.stdout.write(text)
sys.stdout.flush()
class Channel:
"""class for Channel objects"""
def __init__(self,x,y,z,W,D):
"""initialize Channel object
x, y, z - coordinates of centerline
W - channel width
D - channel depth"""
self.x = x
self.y = y
self.z = z
self.W = W
self.D = D
class Cutoff:
"""class for Cutoff objects"""
def __init__(self,x,y,z,W,D):
"""initialize Cutoff object
x, y, z - coordinates of centerline
W - channel width
D - channel depth"""
self.x = x
self.y = y
self.z = z
self.W = W
self.D = D
class ChannelBelt3D:
"""class for 3D models of channel belts"""
def __init__(self, model_type, topo, strat, facies, facies_code, dx, channels):
"""model_type - can be either 'fluvial' or 'submarine'
topo - set of topographic surfaces (3D numpy array)
strat - set of stratigraphic surfaces (3D numpy array)
facies - facies volume (3D numpy array)
facies_code - dictionary of facies codes, e.g. {0:'oxbow', 1:'point bar', 2:'levee'}
dx - gridcell size (m)
channels - list of channel objects that form 3D model"""
self.model_type = model_type
self.topo = topo
self.strat = strat
self.facies = facies
self.facies_code = facies_code
self.dx = dx
self.channels = channels
def plot_xsection(self, xsec, colors, ve):
"""method for plotting a cross section through a 3D model; also plots map of
basal erosional surface and map of final geomorphic surface
xsec - location of cross section along the x-axis (in pixel/ voxel coordinates)
colors - list of RGB values that define the colors for different facies
ve - vertical exaggeration"""
strat = self.strat
dx = self.dx
fig1 = plt.figure(figsize=(20,5))
ax1 = fig1.add_subplot(111)
r,c,ts = np.shape(strat)
Xv = dx * np.arange(0,r)
for xloc in range(xsec,xsec+1,1):
for i in range(0,ts-1,3):
X1 = np.concatenate((Xv, Xv[::-1]))
Y1 = np.concatenate((strat[:,xloc,i], strat[::-1,xloc,i+1]))
Y2 = np.concatenate((strat[:,xloc,i+1], strat[::-1,xloc,i+2]))
Y3 = np.concatenate((strat[:,xloc,i+2], strat[::-1,xloc,i+3]))
if self.model_type == 'submarine':
ax1.fill(X1, Y1, facecolor=colors[2], linewidth=0.5, edgecolor=[0,0,0]) # oxbow mud
ax1.fill(X1, Y2, facecolor=colors[0], linewidth=0.5, edgecolor=[0,0,0]) # point bar sand
ax1.fill(X1, Y3, facecolor=colors[1], linewidth=0.5) # levee mud
if self.model_type == 'fluvial':
ax1.fill(X1, Y1, facecolor=colors[0], linewidth=0.5, edgecolor=[0,0,0]) # levee mud
ax1.fill(X1, Y2, facecolor=colors[1], linewidth=0.5, edgecolor=[0,0,0]) # oxbow mud
ax1.fill(X1, Y3, facecolor=colors[2], linewidth=0.5) # channel sand
ax1.set_xlim(0,dx*(r-1))
ax1.set_aspect(ve, adjustable='datalim')
fig2 = plt.figure()
ax2 = fig2.add_subplot(111)
ax2.contourf(strat[:,:,ts-1],100,cmap='viridis')
ax2.contour(strat[:,:,ts-1],100,colors='k',linestyles='solid',linewidths=0.1,alpha=0.4)
ax2.plot([xloc, xloc],[0,r],'k',linewidth=2)
ax2.axis([0,c,0,r])
ax2.set_aspect('equal', adjustable='box')
ax2.set_title('final geomorphic surface')
ax2.tick_params(bottom=False,top=False,left=False,right=False,labelbottom=False,labelleft=False)
fig3 = plt.figure()
ax3 = fig3.add_subplot(111)
ax3.contourf(strat[:,:,0],100,cmap='viridis')
ax3.contour(strat[:,:,0],100,colors='k',linestyles='solid',linewidths=0.1,alpha=0.4)
ax3.plot([xloc, xloc],[0,r],'k',linewidth=2)
ax3.axis([0,c,0,r])
ax3.set_aspect('equal', adjustable='box')
ax3.set_title('basal erosional surface')
ax3.tick_params(bottom=False,top=False,left=False,right=False,labelbottom=False,labelleft=False)
return fig1,fig2,fig3
class ChannelBelt:
"""class for ChannelBelt objects"""
def __init__(self, channels, cutoffs, cl_times, cutoff_times):
"""initialize ChannelBelt object
channels - list of Channel objects
cutoffs - list of Cutoff objects
cl_times - list of ages of Channel objects
cutoff_times - list of ages of Cutoff objects"""
self.channels = channels
self.cutoffs = cutoffs
self.cl_times = cl_times
self.cutoff_times = cutoff_times
def migrate(self,nit,saved_ts,deltas,pad,crdist,Cf,kl,kv,dt,dens,t1,t2,t3,aggr_factor,*D):
"""function for computing migration rates along channel centerlines and moving the centerlines accordingly
inputs:
nit - number of iterations
saved_ts - which time steps will be saved
deltas - distance between nodes on centerline
pad - padding (number of nodepoints along centerline)
crdist - threshold distance at which cutoffs occur
Cf - dimensionless Chezy friction factor
kl - migration rate constant (m/s)
kv - vertical slope-dependent erosion rate constant (m/s)
dt - time step (s)
dens - density of fluid (kg/m3)
t1 - time step when incision starts
t2 - time step when lateral migration starts
t3 - time step when aggradation starts
aggr_factor - aggradation factor
D - channel depth (m)"""
channel = self.channels[-1] # first channel is the same as last channel of input
x = channel.x; y = channel.y; z = channel.z
W = channel.W;
if len(D)==0:
D = channel.D
else:
D = D[0]
k = 1.0 # constant in HK equation
xc = [] # initialize cutoff coordinates
# determine age of last channel:
if len(self.cl_times)>0:
last_cl_time = self.cl_times[-1]
else:
last_cl_time = 0
dx, dy, dz, ds, s = compute_derivatives(x,y,z)
slope = np.gradient(z)/ds
# padding at the beginning can be shorter than padding at the downstream end:
pad1 = int(pad/10.0)
if pad1<5:
pad1 = 5
omega = -1.0 # constant in curvature calculation (Howard and Knutson, 1984)
gamma = 2.5 # from Ikeda et al., 1981 and Howard and Knutson, 1984
for itn in range(nit): # main loop
update_progress(itn/nit)
x, y = migrate_one_step(x,y,z,W,kl,dt,k,Cf,D,pad,pad1,omega,gamma)
x,y,z,xc,yc,zc = cut_off_cutoffs(x,y,z,s,crdist,deltas) # find and execute cutoffs
x,y,z,dx,dy,dz,ds,s = resample_centerline(x,y,z,deltas) # resample centerline
slope = np.gradient(z)/ds
# for itn<t1, z is unchanged
if (itn>t1) & (itn<=t2): # incision
if np.min(np.abs(slope))!=0:
z = z + kv*dens*9.81*D*slope*dt
else:
z = z - kv*dens*9.81*D*dt*0.00001
if (itn>t2) & (itn<=t3): # lateral migration
if np.min(np.abs(slope))!=0:
z = z + kv*dens*9.81*D*slope*dt - kv*dens*9.81*D*np.median(slope)*dt
else:
z = z # no change in z
if (itn>t3): # aggradation
if np.min(np.abs(slope))!=0:
z = z + kv*dens*9.81*D*slope*dt - aggr_factor*kv*dens*9.81*D*np.mean(slope)*dt
else:
z = z + aggr_factor*dt
if len(xc)>0: # save cutoff data
self.cutoff_times.append(last_cl_time+(itn+1)*dt/(365*24*60*60.0))
cutoff = Cutoff(xc,yc,zc,W,D) # create cutoff object
self.cutoffs.append(cutoff)
# saving centerlines:
if np.mod(itn,saved_ts)==0:
self.cl_times.append(last_cl_time+(itn+1)*dt/(365*24*60*60.0))
channel = Channel(x,y,z,W,D) # create channel object
self.channels.append(channel)
def plot(self,plot_type,pb_age,ob_age,*end_time):
"""plot ChannelBelt object
plot_type - can be either 'strat' (for stratigraphic plot) or 'morph' (for morphologic plot)
pb_age - age of point bars (in years) at which they get covered by vegetation
ob_age - age of oxbow lakes (in years) at which they get covered by vegetation
end_time (optional) - age of last channel to be plotted (in years)"""
cot = np.array(self.cutoff_times)
sclt = np.array(self.cl_times)
if len(end_time)>0:
cot = cot[cot<=end_time]
sclt = sclt[sclt<=end_time]
times = np.sort(np.hstack((cot,sclt)))
times = np.unique(times)
order = 0 # variable for ordering objects in plot
# set up min and max x and y coordinates of the plot:
xmin = np.min(self.channels[0].x)
xmax = np.max(self.channels[0].x)
ymax = 0
for i in range(len(self.channels)):
ymax = max(ymax, np.max(np.abs(self.channels[i].y)))
ymax = ymax+2*self.channels[0].W # add a bit of space on top and bottom
ymin = -1*ymax
# size figure so that its size matches the size of the model:
fig = plt.figure(figsize=(20,(ymax-ymin)*20/(xmax-xmin)))
if plot_type == 'morph':
pb_crit = len(times[times<times[-1]-pb_age])/float(len(times))
ob_crit = len(times[times<times[-1]-ob_age])/float(len(times))
green = (106/255.0,159/255.0,67/255.0) # vegetation color
pb_color = (189/255.0,153/255.0,148/255.0) # point bar color
ob_color = (15/255.0,58/255.0,65/255.0) # oxbow color
pb_cmap = make_colormap([green,green,pb_crit,green,pb_color,1.0,pb_color]) # colormap for point bars
ob_cmap = make_colormap([green,green,ob_crit,green,ob_color,1.0,ob_color]) # colormap for oxbows
plt.fill([xmin,xmax,xmax,xmin],[ymin,ymin,ymax,ymax],color=(106/255.0,159/255.0,67/255.0))
for i in range(0,len(times)):
if times[i] in sclt:
ind = np.where(sclt==times[i])[0][0]
x1 = self.channels[ind].x
y1 = self.channels[ind].y
W = self.channels[ind].W
xm, ym = get_channel_banks(x1,y1,W)
if plot_type == 'morph':
if times[i]>times[-1]-pb_age:
plt.fill(xm,ym,facecolor=pb_cmap(i/float(len(times)-1)),edgecolor='k',linewidth=0.2)
else:
plt.fill(xm,ym,facecolor=pb_cmap(i/float(len(times)-1)))
else:
order = order+1
plt.fill(xm,ym,sns.xkcd_rgb["light tan"],edgecolor='k',linewidth=0.25,zorder=order)
if times[i] in cot:
ind = np.where(cot==times[i])[0][0]
for j in range(0,len(self.cutoffs[ind].x)):
x1 = self.cutoffs[ind].x[j]
y1 = self.cutoffs[ind].y[j]
xm, ym = get_channel_banks(x1,y1,self.cutoffs[ind].W)
if plot_type == 'morph':
plt.fill(xm,ym,color=ob_cmap(i/float(len(times)-1)))
else:
order = order+1
plt.fill(xm,ym,sns.xkcd_rgb["ocean blue"],edgecolor='k',linewidth=0.25,zorder=order)
x1 = self.channels[len(sclt)-1].x
y1 = self.channels[len(sclt)-1].y
xm, ym = get_channel_banks(x1,y1,self.channels[len(sclt)-1].W)
order = order+1
plt.fill(xm,ym,color=(16/255.0,73/255.0,90/255.0),zorder=order) #,edgecolor='k')
plt.axis('equal')
plt.xlim(xmin,xmax)
plt.ylim(ymin,ymax)
return fig
def create_movie(self,xmin,xmax,plot_type,filename,dirname,pb_age,ob_age,scale,*end_time):
"""method for creating movie frames (PNG files) that capture the plan-view evolution of a channel belt through time
movie has to be assembled from the PNG file after this method is applied
xmin - value of x coodinate on the left side of frame
xmax - value of x coordinate on right side of frame
plot_type = - can be either 'strat' (for stratigraphic plot) or 'morph' (for morphologic plot)
filename - first few characters of the output filenames
dirname - name of directory where output files should be written
pb_age - age of point bars (in years) at which they get covered by vegetation (if the 'morph' option is used for 'plot_type')
ob_age - age of oxbow lakes (in years) at which they get covered by vegetation (if the 'morph' option is used for 'plot_type')
scale - scaling factor (e.g., 2) that determines how many times larger you want the frame to be, compared to the default scaling of the figure
"""
sclt = np.array(self.cl_times)
if len(end_time)>0:
sclt = sclt[sclt<=end_time]
channels = self.channels[:len(sclt)]
ymax = 0
for i in range(len(channels)):
ymax = max(ymax, np.max(np.abs(channels[i].y)))
ymax = ymax+2*channels[0].W # add a bit of space on top and bottom
ymin = -1*ymax
for i in range(0,len(sclt)):
fig = self.plot(plot_type,pb_age,ob_age,sclt[i])
fig_height = scale*fig.get_figheight()
fig_width = (xmax-xmin)*fig_height/(ymax-ymin)
fig.set_figwidth(fig_width)
fig.set_figheight(fig_height)
fig.gca().set_xlim(xmin,xmax)
fig.gca().set_xticks([])
fig.gca().set_yticks([])
plt.plot([xmin+200, xmin+200+5000],[ymin+200, ymin+200], 'k', linewidth=2)
plt.text(xmin+200+2000, ymin+200+100, '5 km', fontsize=14)
fname = dirname+filename+'%03d.png'%(i)
fig.savefig(fname, bbox_inches='tight')
plt.close()
def build_3d_model(self,model_type,h_mud,levee_width,h,w,bth,dcr,dx,delta_s,starttime,endtime,xmin,xmax,ymin,ymax):
"""method for building 3D model from set of centerlines (that are part of a ChannelBelt object)
Inputs:
model_type - model type ('fluvial' or 'submarine')
h_mud - maximum thickness of overbank mud
levee_width - width of overbank mud
h - channel depth
w - channel width
bth - thickness of channel sand (only used in submarine models)
dcr - critical channel depth where sand thickness goes to zero (only used in submarine models)
dx - cell size in x and y directions
delta_s - sampling distance alogn centerlines
starttime - age of centerline that will be used as the first centerline in the model
endtime - age of centerline that will be used as the last centerline in the model
xmin,xmax,ymin,ymax - x and y coordinates that define the model domain; if xmin is set to zero,
a plot of the centerlines is generated and the model domain has to be defined by clicking its upper
left and lower right corners
Returns: a ChannelBelt3D object
"""
sclt = np.array(self.cl_times)
ind1 = np.where(sclt>=starttime)[0][0]
ind2 = np.where(sclt<=endtime)[0][-1]
sclt = sclt[ind1:ind2+1]
channels = self.channels[ind1:ind2+1]
cot = np.array(self.cutoff_times)
if (len(cot)>0) & (len(np.where(cot>=starttime)[0])>0) & (len(np.where(cot<=endtime)[0])>0):
cfind1 = np.where(cot>=starttime)[0][0]
cfind2 = np.where(cot<=endtime)[0][-1]
cot = cot[cfind1:cfind2+1]
cutoffs = self.cutoffs[cfind1:cfind2+1]
else:
cot = []
cutoffs = []
n_steps = len(sclt) # number of events
if xmin == 0: # plot centerlines and define model domain
plt.figure(figsize=(15,4))
maxX, minY, maxY = 0, 0, 0
for i in range(n_steps): # plot centerlines
plt.plot(channels[i].x,channels[i].y,'k')
maxX = max(maxX,np.max(channels[i].x))
maxY = max(maxY,np.max(channels[i].y))
minY = min(minY,np.min(channels[i].y))
plt.axis([0,maxX,minY-10*w,maxY+10*w])
plt.gca().set_aspect('equal', adjustable='box')
plt.tight_layout()
pts = np.zeros((2,2))
for i in range(0,2):
pt = np.asarray(plt.ginput(1))
pts[i,:] = pt
plt.scatter(pt[0][0],pt[0][1])
plt.plot([pts[0,0],pts[1,0],pts[1,0],pts[0,0],pts[0,0]],[pts[0,1],pts[0,1],pts[1,1],pts[1,1],pts[0,1]],'r')
xmin = min(pts[0,0],pts[1,0])
xmax = max(pts[0,0],pts[1,0])
ymin = min(pts[0,1],pts[1,1])
ymax = max(pts[0,1],pts[1,1])
iwidth = int((xmax-xmin)/dx)
iheight = int((ymax-ymin)/dx)
topo = np.zeros((iheight,iwidth,4*n_steps)) # array for storing topographic surfaces
facies = np.zeros((4*n_steps,1))
# create initial topography:
x1 = np.linspace(0,iwidth-1,iwidth)
y1 = np.linspace(0,iheight-1,iheight)
xv, yv = np.meshgrid(x1,y1)
z1 = channels[0].z
z1 = z1[(channels[0].x>xmin) & (channels[0].x<xmax)]
topoinit = z1[0] - ((z1[0]-z1[-1])/(xmax-xmin))*xv*dx # initial (sloped) topography
topo[:,:,0] = topoinit.copy()
surf = topoinit.copy()
facies[0] = np.NaN
# generate surfaces:
channels3D = []
x_pixs = []
y_pixs = []
for i in range(n_steps):
update_progress(i/n_steps)
x = channels[i].x
y = channels[i].y
z = channels[i].z
cutoff_ind = []
# check if there were cutoffs during the last time step and collect indices in an array:
for j in range(len(cot)):
if (cot[j] >= sclt[i-1]) & (cot[j] < sclt[i]):
cutoff_ind = np.append(cutoff_ind,j)
# create distance map:
cl_dist, x_pix, y_pix, z_pix, s_pix, z_map, x1, y1, z1 = dist_map(x,y,z,xmin,xmax,ymin,ymax,dx,delta_s)
if i == 0:
cl_dist_prev = cl_dist
# erosion:
surf = np.minimum(surf,erosion_surface(h,w/dx,cl_dist,z_map))
topo[:,:,4*i] = surf # erosional surface
facies[4*i] = np.NaN
if model_type == 'fluvial':
pb = point_bar_surface(cl_dist,z_map,h,w/dx)
th = np.maximum(surf,pb)-surf
th_oxbows = th.copy()
# setting sand thickness to zero at cutoff locations:
if len(cutoff_ind)>0:
cutoff_dists = 1e10*np.ones(np.shape(th)) #initialize cutoff_dists with a large number
for j in range(len(cutoff_ind)):
cutoff_dist, cfx_pix, cfy_pix = cl_dist_map(cutoffs[int(cutoff_ind[j])].x[0],cutoffs[int(cutoff_ind[j])].y[0],cutoffs[int(cutoff_ind[j])].z[0],xmin,xmax,ymin,ymax,dx)
cutoff_dists = np.minimum(cutoff_dists,cutoff_dist)
th_oxbows[cutoff_dists>=0.9*w/dx] = 0 # set oxbow fill thickness to zero outside of oxbows
th[cutoff_dists<0.9*w/dx] = 0 # set point bar thickness to zero inside of oxbows
else: # no cutoffs
th_oxbows = np.zeros(np.shape(th))
th[th<0] = 0 # eliminate negative th values
surf = surf+th_oxbows # update topographic surface with oxbow deposit thickness
topo[:,:,4*i+1] = surf # top of oxbow mud
facies[4*i+1] = 0
surf = surf+th # update topographic surface with sand thickness
topo[:,:,4*i+2] = surf # top of sand
facies[4*i+2] = 1
surf = surf + mud_surface(h_mud,levee_width/dx,cl_dist,w/dx,z_map,surf) # mud/levee deposition
topo[:,:,4*i+3] = surf # top of levee
facies[4*i+3] = 2
channels3D.append(Channel(x1,y1,z1,w,h))
x_pixs.append(x_pix)
y_pixs.append(y_pix)
if model_type == 'submarine':
surf = surf + mud_surface(h_mud[i],levee_width/dx,cl_dist,w/dx,z_map,surf) # mud/levee deposition
topo[:,:,4*i+1] = surf # top of levee
facies[4*i+1] = 2
# sand thickness:
th, relief = sand_surface(surf,bth,dcr,z_map,h)
th[th<0] = 0 # eliminate negative th values
th[cl_dist>1.0*w/dx] = 0 # eliminate sand outside of channel
th_oxbows = th.copy()
# setting sand thickness to zero at cutoff locations:
if len(cutoff_ind)>0:
cutoff_dists = 1e10*np.ones(np.shape(th)) #initialize cutoff_dists with a large number
for j in range(len(cutoff_ind)):
cutoff_dist, cfx_pix, cfy_pix = cl_dist_map(cutoffs[int(cutoff_ind[j])].x[0],cutoffs[int(cutoff_ind[j])].y[0],cutoffs[int(cutoff_ind[j])].z[0],xmin,xmax,ymin,ymax,dx)
cutoff_dists = np.minimum(cutoff_dists,cutoff_dist)
th_oxbows[cutoff_dists>=0.9*w/dx] = 0 # set oxbow fill thickness to zero outside of oxbows
th[cutoff_dists<0.9*w/dx] = 0 # set point bar thickness to zero inside of oxbows
# adding back sand near the channel axis (submarine only):
# th[cl_dist<0.5*w/dx] = bth*(1 - relief[cl_dist<0.5*w/dx]/dcr)
else: # no cutoffs
th_oxbows = np.zeros(np.shape(th))
surf = surf+th_oxbows # update topographic surface with oxbow deposit thickness
topo[:,:,4*i+2] = surf # top of oxbow mud
facies[4*i+2] = 0
surf = surf+th # update topographic surface with sand thickness
topo[:,:,4*i+3] = surf # top of sand
facies[4*i+3] = 1
cl_dist_prev = cl_dist.copy()
topo = np.concatenate((np.reshape(topoinit,(iheight,iwidth,1)),topo),axis=2) # add initial topography to array
strat = topostrat(topo) # create stratigraphic surfaces
strat = np.delete(strat, np.arange(4*n_steps+1)[1::4], 2) # get rid of unnecessary stratigraphic surfaces (duplicates)
facies = np.delete(facies, np.arange(4*n_steps)[::4]) # get rid of unnecessary facies layers (NaNs)
if model_type == 'fluvial':
facies_code = {0:'oxbow', 1:'point bar', 2:'levee'}
if model_type == 'submarine':
facies_code = {0:'oxbow', 1:'channel sand', 2:'levee'}
chb_3d = ChannelBelt3D(model_type,topo,strat,facies,facies_code,dx,channels3D)
return chb_3d, xmin, xmax, ymin, ymax
def resample_centerline(x,y,z,deltas):
dx, dy, dz, ds, s = compute_derivatives(x,y,z) # compute derivatives
# resample centerline so that 'deltas' is roughly constant
# [parametric spline representation of curve; note that there is *no* smoothing]
tck, u = scipy.interpolate.splprep([x,y,z],s=0)
unew = np.linspace(0,1,1 + np.int(s[-1]/deltas)) # vector for resampling
out = scipy.interpolate.splev(unew,tck) # resampling
x, y, z = out[0], out[1], out[2] # assign new coordinate values
dx, dy, dz, ds, s = compute_derivatives(x,y,z) # recompute derivatives
return x,y,z,dx,dy,dz,ds,s
def migrate_one_step(x,y,z,W,kl,dt,k,Cf,D,pad,pad1,omega,gamma):
ns=len(x)
curv = compute_curvature(x,y)
dx, dy, dz, ds, s = compute_derivatives(x,y,z)
curv = W*curv # dimensionless curvature
R0 = kl*curv # simple linear relationship between curvature and nominal migration rate
alpha = k*2*Cf/D # exponent for convolution function G
R1 = compute_migration_rate(pad,ns,ds,alpha,omega,gamma,R0)
# calculate new centerline coordinates:
dy_ds = dy[pad1:ns-pad+1]/ds[pad1:ns-pad+1]
dx_ds = dx[pad1:ns-pad+1]/ds[pad1:ns-pad+1]
# adjust x and y coordinates (this *is* the migration):
x[pad1:ns-pad+1] = x[pad1:ns-pad+1] + R1[pad1:ns-pad+1]*dy_ds*dt
y[pad1:ns-pad+1] = y[pad1:ns-pad+1] - R1[pad1:ns-pad+1]*dx_ds*dt
return x,y
def generate_initial_channel(W,D,Sl,deltas,pad,n_bends):
"""generate straight Channel object with some noise added that can serve
as input for initializing a ChannelBelt object
W - channel width
D - channel depth
Sl - channel gradient
deltas - distance between nodes on centerline
pad - padding (number of nodepoints along centerline)
n_bends - approximate number of bends to be simulated"""
noisy_len = n_bends*10*W/2.0 # length of noisy part of initial centerline
pad1 = int(pad/10.0) # padding at upstream end can be shorter than padding on downstream end
if pad1<5:
pad1 = 5
x = np.linspace(0, noisy_len+(pad+pad1)*deltas, int(noisy_len/deltas+pad+pad1)+1) # x coordinate
y = 10.0 * (2*np.random.random_sample(int(noisy_len/deltas)+1,)-1)
y = np.hstack((np.zeros((pad1),),y,np.zeros((pad),))) # y coordinate
deltaz = Sl * deltas*(len(x)-1)
z = np.linspace(0,deltaz,len(x))[::-1] # z coordinate
return Channel(x,y,z,W,D)
@numba.jit(nopython=True) # use Numba to speed up the heaviest computation
def compute_migration_rate(pad,ns,ds,alpha,omega,gamma,R0):
"""compute migration rate as weighted sum of upstream curvatures
pad - padding (number of nodepoints along centerline)
ns - number of points in centerline
ds - distances between points in centerline
omega - constant in HK model
gamma - constant in HK model
R0 - nominal migration rate (dimensionless curvature * migration rate constant)"""
R1 = np.zeros(ns) # preallocate adjusted channel migration rate
pad1 = int(pad/10.0) # padding at upstream end can be shorter than padding on downstream end
if pad1<5:
pad1 = 5
for i in range(pad1,ns-pad):
si2 = np.hstack((np.array([0]),np.cumsum(ds[i-1::-1]))) # distance along centerline, backwards from current point
G = np.exp(-alpha*si2) # convolution vector
R1[i] = omega*R0[i] + gamma*np.sum(R0[i::-1]*G)/np.sum(G) # main equation
return R1
def compute_derivatives(x,y,z):
"""function for computing first derivatives of a curve (centerline)
x,y are cartesian coodinates of the curve
outputs:
dx - first derivative of x coordinate
dy - first derivative of y coordinate
ds - distances between consecutive points along the curve
s - cumulative distance along the curve"""
dx = np.gradient(x) # first derivatives
dy = np.gradient(y)
dz = np.gradient(z)
ds = np.sqrt(dx**2+dy**2+dz**2)
s = np.hstack((0,np.cumsum(ds[1:])))
return dx, dy, dz, ds, s
def compute_curvature(x,y):
"""function for computing first derivatives and curvature of a curve (centerline)
x,y are cartesian coodinates of the curve
outputs:
dx - first derivative of x coordinate
dy - first derivative of y coordinate
ds - distances between consecutive points along the curve
s - cumulative distance along the curve
curvature - curvature of the curve (in 1/units of x and y)"""
dx = np.gradient(x) # first derivatives
dy = np.gradient(y)
ddx = np.gradient(dx) # second derivatives
ddy = np.gradient(dy)
curvature = (dx*ddy-dy*ddx)/((dx**2+dy**2)**1.5)
return curvature
def make_colormap(seq):
"""Return a LinearSegmentedColormap
seq: a sequence of floats and RGB-tuples. The floats should be increasing
and in the interval (0,1).
[from: https://stackoverflow.com/questions/16834861/create-own-colormap-using-matplotlib-and-plot-color-scale]
"""
seq = [(None,) * 3, 0.0] + list(seq) + [1.0, (None,) * 3]
cdict = {'red': [], 'green': [], 'blue': []}
for i, item in enumerate(seq):
if isinstance(item, float):
r1, g1, b1 = seq[i - 1]
r2, g2, b2 = seq[i + 1]
cdict['red'].append([item, r1, r2])
cdict['green'].append([item, g1, g2])
cdict['blue'].append([item, b1, b2])
return mcolors.LinearSegmentedColormap('CustomMap', cdict)
def kth_diag_indices(a,k):
"""function for finding diagonal indices with k offset
[from https://stackoverflow.com/questions/10925671/numpy-k-th-diagonal-indices]"""
rows, cols = np.diag_indices_from(a)
if k<0:
return rows[:k], cols[-k:]
elif k>0:
return rows[k:], cols[:-k]
else:
return rows, cols
def find_cutoffs(x,y,crdist,deltas):
"""function for identifying locations of cutoffs along a centerline
and the indices of the segments that will become part of the oxbows
x,y - coordinates of centerline
crdist - critical cutoff distance
deltas - distance between neighboring points along the centerline"""
diag_blank_width = int((crdist+20*deltas)/deltas)
# distance matrix for centerline points:
dist = distance.cdist(np.array([x,y]).T,np.array([x,y]).T)
dist[dist>crdist] = np.NaN # set all values that are larger than the cutoff threshold to NaN
# set matrix to NaN along the diagonal zone:
for k in range(-diag_blank_width,diag_blank_width+1):
rows, cols = kth_diag_indices(dist,k)
dist[rows,cols] = np.NaN
i1, i2 = np.where(~np.isnan(dist))
ind1 = i1[np.where(i1<i2)[0]] # get rid of unnecessary indices
ind2 = i2[np.where(i1<i2)[0]] # get rid of unnecessary indices
return ind1, ind2 # return indices of cutoff points and cutoff coordinates
def cut_off_cutoffs(x,y,z,s,crdist,deltas):
"""function for executing cutoffs - removing oxbows from centerline and storing cutoff coordinates
x,y - coordinates of centerline
crdist - critical cutoff distance
deltas - distance between neighboring points along the centerline
outputs:
x,y,z - updated coordinates of centerline
xc, yc, zc - lists with coordinates of cutoff segments"""
xc = []
yc = []
zc = []
ind1, ind2 = find_cutoffs(x,y,crdist,deltas) # initial check for cutoffs
while len(ind1)>0:
xc.append(x[ind1[0]:ind2[0]+1]) # x coordinates of cutoff
yc.append(y[ind1[0]:ind2[0]+1]) # y coordinates of cutoff
zc.append(z[ind1[0]:ind2[0]+1]) # z coordinates of cutoff
x = np.hstack((x[:ind1[0]+1],x[ind2[0]:])) # x coordinates after cutoff
y = np.hstack((y[:ind1[0]+1],y[ind2[0]:])) # y coordinates after cutoff
z = np.hstack((z[:ind1[0]+1],z[ind2[0]:])) # z coordinates after cutoff
ind1, ind2 = find_cutoffs(x,y,crdist,deltas)
return x,y,z,xc,yc,zc
def get_channel_banks(x,y,W):
"""function for finding coordinates of channel banks, given a centerline and a channel width
x,y - coordinates of centerline
W - channel width
outputs:
xm, ym - coordinates of channel banks (both left and right banks)"""
x1 = x.copy()
y1 = y.copy()
x2 = x.copy()
y2 = y.copy()
ns = len(x)
dx = np.diff(x); dy = np.diff(y)
ds = np.sqrt(dx**2+dy**2)
x1[:-1] = x[:-1] + 0.5*W*np.diff(y)/ds
y1[:-1] = y[:-1] - 0.5*W*np.diff(x)/ds
x2[:-1] = x[:-1] - 0.5*W*np.diff(y)/ds
y2[:-1] = y[:-1] + 0.5*W*np.diff(x)/ds
x1[ns-1] = x[ns-1] + 0.5*W*(y[ns-1]-y[ns-2])/ds[ns-2]
y1[ns-1] = y[ns-1] - 0.5*W*(x[ns-1]-x[ns-2])/ds[ns-2]
x2[ns-1] = x[ns-1] - 0.5*W*(y[ns-1]-y[ns-2])/ds[ns-2]
y2[ns-1] = y[ns-1] + 0.5*W*(x[ns-1]-x[ns-2])/ds[ns-2]
xm = np.hstack((x1,x2[::-1]))
ym = np.hstack((y1,y2[::-1]))
return xm, ym
def dist_map(x,y,z,xmin,xmax,ymin,ymax,dx,delta_s):
"""function for centerline rasterization and distance map calculation
inputs:
x,y,z - coordinates of centerline
xmin, xmax, ymin, ymax - x and y coordinates that define the area of interest
dx - gridcell size (m)
delta_s - distance between points along centerline (m)
returns:
cl_dist - distance map (distance from centerline)
x_pix, y_pix, z_pix - x,y, and z pixel coordinates of the centerline
s_pix - along-channel distance in pixels
z_map - map of reference channel thalweg elevation (elevation of closest point along centerline)
x, y, z - x,y,z centerline coordinates clipped to the 3D model domain"""
y = y[(x>xmin) & (x<xmax)]
z = z[(x>xmin) & (x<xmax)]
x = x[(x>xmin) & (x<xmax)]
dummy,dy,dz,ds,s = compute_derivatives(x,y,z)
if len(np.where(ds>2*delta_s)[0])>0:
inds = np.where(ds>2*delta_s)[0]
inds = np.hstack((0,inds,len(x)))
lengths = np.diff(inds)
long_segment = np.where(lengths==max(lengths))[0][0]
start_ind = inds[long_segment]+1
end_ind = inds[long_segment+1]
if end_ind<len(x):
x = x[start_ind:end_ind]
y = y[start_ind:end_ind]
z = z[start_ind:end_ind]
else:
x = x[start_ind:]
y = y[start_ind:]
z = z[start_ind:]
xdist = xmax - xmin
ydist = ymax - ymin
iwidth = int((xmax-xmin)/dx)
iheight = int((ymax-ymin)/dx)
xratio = iwidth/xdist
# create list with pixel coordinates:
pixels = []
for i in range(0,len(x)):
px = int(iwidth - (xmax - x[i]) * xratio)
py = int(iheight - (ymax - y[i]) * xratio)
pixels.append((px,py))
# create image and numpy array:
img = Image.new("RGB", (iwidth, iheight), "white")
draw = ImageDraw.Draw(img)
draw.line(pixels, fill="rgb(0, 0, 0)") # draw centerline as black line
pix = np.array(img)
cl = pix[:,:,0]
cl[cl==255] = 1 # set background to 1 (centerline is 0)
y_pix,x_pix = np.where(cl==0)
x_pix,y_pix = order_cl_pixels(x_pix,y_pix)
# This next block of code is kind of a hack. Looking for, and eliminating, 'bad' pixels.
img = np.array(img)
img = img[:,:,0]
img[img==255] = 1
img1 = morphology.binary_dilation(img, morphology.square(2)).astype(np.uint8)
if len(np.where(img1==0)[0])>0:
x_pix, y_pix = eliminate_bad_pixels(img,img1)
x_pix,y_pix = order_cl_pixels(x_pix,y_pix)
img1 = morphology.binary_dilation(img, np.array([[1,0,1],[1,1,1]],dtype=np.uint8)).astype(np.uint8)
if len(np.where(img1==0)[0])>0:
x_pix, y_pix = eliminate_bad_pixels(img,img1)
x_pix,y_pix = order_cl_pixels(x_pix,y_pix)
img1 = morphology.binary_dilation(img, np.array([[1,0,1],[0,1,0],[1,0,1]],dtype=np.uint8)).astype(np.uint8)
if len(np.where(img1==0)[0])>0:
x_pix, y_pix = eliminate_bad_pixels(img,img1)
x_pix,y_pix = order_cl_pixels(x_pix,y_pix)
#redo the distance calculation (because x_pix and y_pix do not always contain all the points in cl):
cl[cl==0] = 1
cl[y_pix,x_pix] = 0
cl_dist, inds = ndimage.distance_transform_edt(cl, return_indices=True)
dx,dy,dz,ds,s = compute_derivatives(x,y,z)
dx_pix = np.diff(x_pix)
dy_pix = np.diff(y_pix)
ds_pix = np.sqrt(dx_pix**2+dy_pix**2)
s_pix = np.hstack((0,np.cumsum(ds_pix)))
f = scipy.interpolate.interp1d(s,z)
snew = s_pix*s[-1]/s_pix[-1]
if snew[-1]>s[-1]:
snew[-1]=s[-1]
snew[snew<s[0]]=s[0]
z_pix = f(snew)
# create z_map:
z_map = np.zeros(np.shape(cl_dist))
z_map[y_pix,x_pix]=z_pix
xinds=inds[1,:,:]
yinds=inds[0,:,:]
for i in range(0,len(x_pix)):
z_map[(xinds==x_pix[i]) & (yinds==y_pix[i])] = z_pix[i]
return cl_dist, x_pix, y_pix, z_pix, s_pix, z_map, x, y, z
def erosion_surface(h,w,cl_dist,z):
"""function for creating a parabolic erosional surface
inputs:
h - geomorphic channel depth (m)
w - geomorphic channel width (in pixels, as cl_dist is also given in pixels)
cl_dist - distance map (distance from centerline)
z - reference elevation (m)
returns:
surf - map of the quadratic erosional surface (m)
"""
surf = z + (4*h/w**2)*(cl_dist+w*0.5)*(cl_dist-w*0.5)
return surf
def point_bar_surface(cl_dist,z,h,w):
"""function for creating a Gaussian-based point bar surface
used in 3D fluvial model
inputs:
cl_dist - distance map (distance from centerline)
z - reference elevation (m)
h - channel depth (m)
w - channel width, in pixels, as cl_dist is also given in pixels
returns:
pb - map of the Gaussian surface that can be used to from a point bar deposit (m)"""
pb = z-h*np.exp(-(cl_dist**2)/(2*(w*0.33)**2))
return pb
def sand_surface(surf,bth,dcr,z_map,h):
"""function for creating the top horizontal surface sand-rich deposit in the bottom of the channel
used in 3D submarine channel models
inputs:
surf - current geomorphic surface
bth - thickness of sand deposit in axis of channel (m)
dcr - critical channel depth, above which there is no sand deposition (m)
z_map - map of reference channel thalweg elevation (elevation of closest point along centerline)
h - channel depth (m)
returns:
th - thickness map of sand deposit (m)
relief - map of channel relief (m)"""
relief = abs(surf-z_map+h)
relief = abs(relief-np.amin(relief))
th = bth * (1 - relief/dcr) # bed thickness inversely related to relief
th[th<0] = 0.0 # set negative th values to zero
return th, relief
def mud_surface(h_mud,levee_width,cl_dist,w,z_map,topo):
"""function for creating a map of overbank deposit thickness
inputs:
h_mud - maximum thickness of overbank deposit (m)
levee_width - half-width of overbank deposit (m)
cl_dist - distance map (distance from centerline)
w - channel width (in pixels, as cl_dist is also given in pixels)
z_map - map of reference channel thalweg elevation (elevation of closest point along centerline)
topo - current geomorphic surface
returns:
th - map of overbank deposit thickness (m)"""
surf1 = (-2*h_mud/levee_width)*cl_dist+h_mud;
surf2 = (2*h_mud/levee_width)*cl_dist+h_mud;
surf = np.minimum(surf1,surf2)
surf3 = h_mud + (4*1.5*h_mud/w**2)*(cl_dist+w*0.5)*(cl_dist-w*0.5)
surf = np.minimum(surf,surf3)
surf[surf<0] = 0;
relief = abs(topo-z_map)
fth = 100.0 # critical height above thalweg, above which there is no deposition
th = 1 - relief/fth
th[th<0] = 0 # set negative th values to zero
th = surf * th
return th
def topostrat(topo):
"""function for converting a stack of geomorphic surfaces into stratigraphic surfaces
inputs:
topo - 3D numpy array of geomorphic surfaces
returns:
strat - 3D numpy array of stratigraphic surfaces
"""
r,c,ts = np.shape(topo)
strat = np.copy(topo)
for i in (range(0,ts)):
strat[:,:,i] = np.amin(topo[:,:,i:], axis=2)
return strat
def cl_dist_map(x,y,z,xmin,xmax,ymin,ymax,dx):
"""function for centerline rasterization and distance map calculation (does not return zmap)
used for cutoffs only
inputs:
x,y,z - coordinates of centerline
xmin, xmax, ymin, ymax - x and y coordinates that define the area of interest
dx - gridcell size (m)
returns:
cl_dist - distance map (distance from centerline)
x_pix, y_pix, - x and y pixel coordinates of the centerline
"""
y = y[(x>xmin) & (x<xmax)]
z = z[(x>xmin) & (x<xmax)]
x = x[(x>xmin) & (x<xmax)]
xdist = xmax - xmin
ydist = ymax - ymin
iwidth = int((xmax-xmin)/dx)
iheight = int((ymax-ymin)/dx)
xratio = iwidth/xdist
# create list with pixel coordinates:
pixels = []
for i in range(0,len(x)):
px = int(iwidth - (xmax - x[i]) * xratio)
py = int(iheight - (ymax - y[i]) * xratio)
pixels.append((px,py))
# create image and numpy array:
img = Image.new("RGB", (iwidth, iheight), "white")
draw = ImageDraw.Draw(img)
draw.line(pixels, fill="rgb(0, 0, 0)") # draw centerline as black line
pix = np.array(img)
cl = pix[:,:,0]
cl[cl==255] = 1 # set background to 1 (centerline is 0)
# calculate Euclidean distance map:
cl_dist, inds = ndimage.distance_transform_edt(cl, return_indices=True)
y_pix,x_pix = np.where(cl==0)
return cl_dist, x_pix, y_pix
def eliminate_bad_pixels(img,img1):
x_ind = np.where(img1==0)[1][0]
y_ind = np.where(img1==0)[0][0]
img[y_ind:y_ind+2,x_ind:x_ind+2] = np.ones(1,).astype(np.uint8)
all_labels = measure.label(img,background=1,connectivity=2)
cl=all_labels.copy()
cl[cl==2]=0
cl[cl>0]=1
y_pix,x_pix = np.where(cl==1)
return x_pix, y_pix
def order_cl_pixels(x_pix,y_pix):
dist = distance.cdist(np.array([x_pix,y_pix]).T,np.array([x_pix,y_pix]).T)
dist[np.diag_indices_from(dist)]=100.0
ind = np.argmin(x_pix) # select starting point on left side of image
clinds = [ind]
count = 0
while count<len(x_pix):
t = dist[ind,:].copy()
if len(clinds)>2:
t[clinds[-2]]=t[clinds[-2]]+100.0
t[clinds[-3]]=t[clinds[-3]]+100.0
ind = | np.argmin(t) | numpy.argmin |
from scipy.stats import pearsonr as pho
from scipy.spatial.distance import euclidean as eDist
import time
import numpy as np
import os
import six.moves.urllib as urllib
import tarfile
import tensorflow as tf
tf.logging.set_verbosity(0)
from matplotlib import pyplot as plt
from PIL import Image
from os import path
from utils import label_map_util
from utils import visualization_utils as vis_util
import time
import cv2
def detect_traffic_lights(image_cv2,sess):
# Definite input and output Tensors for detection_graph
image_tensor = detection_graph.get_tensor_by_name('image_tensor:0')
# Each box represents a part of the image where a particular object was detected.
detection_boxes = detection_graph.get_tensor_by_name('detection_boxes:0')
# Each score represent how level of confidence for each of the objects.
# Score is shown on the result image, together with the class label.
detection_scores = detection_graph.get_tensor_by_name('detection_scores:0')
detection_classes = detection_graph.get_tensor_by_name('detection_classes:0')
num_detections = detection_graph.get_tensor_by_name('num_detections:0')
image_np_expanded = np.expand_dims(image_cv2, axis=0)
print (image_np_expanded.shape)
# Actual detection.
(boxes, scores, classes, num) = sess.run(
[detection_boxes, detection_scores, detection_classes, num_detections],
feed_dict={image_tensor: image_np_expanded})
go_flag = False
if classes[0][0] == 2.0:
go_flag = True
im_width=image_cv2.shape[1]
im_height = image_cv2.shape[0]
ymin, xmin, ymax, xmax = boxes[0][0].tolist()
left, right, top, bottom = map(lambda x:int(x),[xmin * im_width, xmax * im_width,ymin * im_height, ymax * im_height])
return go_flag,[left, right, top, bottom]
class vision():
def __init__(self):
# change it to the camera for real application
# self.cap = cv2.VideoCapture("IGVC_2015_Speed_Record.mp4")
self.start_time = time.time()
self.cap = cv2.VideoCapture("stocker1f-test1.mp4")
self.time_stamp = 0
self.go = False
self.magenta2m = False
self.magenta0m = False
def start_engine(self,sess):
# for traffic light detection
ret,self.frame = self.cap.read()
# self.frame = cv2.resize(self.frame,(300,300))
if ret == False:
print ("Nothing read in")
return 0
# frame = cv2.imread("test_images/test3.jpg")
self.go,self.boxes_list = detect_traffic_lights(cv2.cvtColor(self.frame, cv2.COLOR_BGR2RGB),sess)
# self.go = detect_traffic_lights("test_images/test3.jpg")
def detect_end_line(self):
ret, frame = self.cap.read()
if ret == False:
return 0
frame = cv2.cvtColor(frame, cv2.COLOR_BGR2RGB)
mask = detect_magenta_color(frame)
if not self.magenta2m:
self.magenta2m = detect_lane(mask,200,300)
else:
self.magenta0m = detect_lane(mask,100,200)
def detect_lane(mask,bottom,top):
points = []
for j in range(0,1200,50):
patch = mask[bottom:top,j:j+100]
a1,a2 = patch.nonzero()
count = np.count_nonzero(patch)
if count < 500:
continue
pr, pv = pho(a1,a2)
pr = abs(pr)
if pr > 0.7:
points.append(j)
else:
continue
return len(points) > 5
def detect_magenta_color(frame):
# hsv = cv2.cvtColor(frame, cv2.COLOR_BGR2HSV)
r1 = np.array([150,0,130], dtype=np.uint8)
r2 = | np.array([255, 100, 255], dtype=np.uint8) | numpy.array |
"""
Functions to apply the fitting in an MCMC manner.
"""
import numpy as np
from tqdm import tqdm
from .profiles import free_params
# -- MCMC Functions -- #
def lnprior(params, priors):
"""Log-prior function."""
lnp = 0.0
for param, prior in zip(params, priors):
lnp += parse_prior(param, prior)
return lnp
def parse_prior(p, prior):
"""Parse the prior function."""
if prior[-1] == 'flat':
valid = np.logical_and(p >= prior[0], p <= prior[1])
return np.where(valid, -np.log(prior[1] - prior[0]), -np.inf)
elif prior[-1] == 'gaussian':
return -0.5 * ((p - prior[0]) / prior[1])**2
else:
raise ValueError("Unknown prior type '{}'.".format(prior[-1]))
def lnlike(params, x, y, dy, model_function):
"""Log-likelihood function."""
y_mod = model_function(x, *params)
return -0.5 * np.sum(((y - y_mod) / dy)**2)
def lnpost(params, x, y, dy, priors, model_function):
"""Log-posterior function."""
lnp = lnprior(params, priors)
if ~np.isfinite(lnp):
return lnp
return lnp + lnlike(params, x, y, dy, model_function)
# -- Sampling Functions -- #
def fit_cube(velax, data, rms, model_function, indices=None, **kwargs):
"""
Cycle through the provided indices fitting each spectrum. Only spectra
which have more more than twice the number of pixel compared to the number
of free parameters in the model will be fit.
For more information on ``kwargs``, see the ``fit_spectrum`` documentation.
Args:
velax (ndarray): Velocity axis of the cube.
data (ndarray): Intensity or brightness temperature array. The first
axis must be the velocity axis.
rms (float): Noise per pixel in same units as ``data``.
model_function (str): Name of the model function to fit to the data.
Must be a function withing ``profiles.py``.
indices (list): A list of pixels described by ``(y_idx, x_idx)`` tuples
to fit. If none are provided, will fit all pixels.
Returns:
fits (ndarray): A ``(Npix, Ndim, 2)`` shaped array of the fits and
associated uncertainties. The uncertainties will be interleaved
with the best-fit values.
"""
# Check the inputs.
assert velax.size == data.shape[0], "Incorrect velax and data shape."
try:
_ = import_function(model_function)
nparams = free_params(model_function)
except ValueError as error_message:
print(error_message)
if indices is None:
indices = | np.indices(data[0].shape) | numpy.indices |
from timebox.exceptions import *
from timebox.timebox import TimeBox
from timebox.timebox_tag import TimeBoxTag
from ..utils.datetime_utils import DAYS, HOURS
import unittest
import numpy as np
import os
def example_time_box(file_name: str):
tb = TimeBox(file_name)
tb._timebox_version = 1
tb._tag_names_are_strings = False
tb._date_differentials_stored = True
tb._num_points = 4
tb._tags = {
0: TimeBoxTag(0, 1, 'u'),
1: TimeBoxTag(1, 2, 'i'),
2: TimeBoxTag(2, 4, 'f')
}
tb._start_date = np.datetime64('2018-01-01', 's')
tb._tags[0].data = np.array([1, 2, 3, 4], dtype=np.uint8)
tb._tags[1].data = np.array([-4, -2, 0, 2000], dtype=np.int16)
tb._tags[2].data = np.array([5.2, 0.8, 3.1415, 8], dtype=np.float32)
tb._date_differentials = np.array([1, 1, 1], dtype=np.uint8)
tb._date_differential_units = DAYS
tb._bytes_per_date_differential = 1
return tb
class TestTimeBoxDateData(unittest.TestCase):
def test_date_validation_errors(self):
file_name = 'test_date_data.npb'
tb = example_time_box(file_name)
tb._validate_data_for_write() # pass
tb._date_differentials_stored = False
with self.assertRaises(DateDataError):
tb._validate_data_for_write()
tb._date_differentials_stored = True
tb._date_differentials = tb._date_differentials.astype(np.int8)
with self.assertRaises(DateDataError):
tb._validate_data_for_write()
tb._date_differentials = tb._date_differentials.astype(np.uint32)
with self.assertRaises(DateDataError):
tb._validate_data_for_write()
tb._date_differentials = np.array([1, 1, 1, 1], dtype=np.uint8)
with self.assertRaises(DateDataError):
tb._validate_data_for_write()
tb = example_time_box('')
tb._date_differentials = None
tb._dates = np.array(
[
np.datetime64('2018-01-05', 's'),
np.datetime64('2018-01-04', 's'),
np.datetime64('2018-01-03', 's'),
np.datetime64('2018-01-02', 's')
],
dtype=np.datetime64
)
with self.assertRaises(DateDataError):
tb._calculate_date_differentials()
return
def test_date_differential_io(self):
file_name = 'test_date_data.npb'
tb = example_time_box(file_name)
with open(file_name, 'wb') as f:
self.assertEqual(3, tb._write_date_deltas(f))
with open(file_name, 'rb') as f:
self.assertEqual(3, tb._read_date_deltas(f))
self.assertEqual(np.uint8, tb._date_differentials.dtype)
self.assertEqual(3, tb._date_differentials.size)
os.remove(file_name)
return
def test_calculate_date_differentials(self):
tb = example_time_box('')
tb._date_differentials = None
tb._dates = np.array(
[
np.datetime64('2018-01-01', 's'),
np.datetime64('2018-01-02', 's'),
np.datetime64('2018-01-03', 's'),
np.datetime64('2018-01-05', 's')
]
)
tb._calculate_date_differentials()
self.assertEqual(3, tb._date_differentials.size)
self.assertEqual('timedelta64[s]', str(tb._date_differentials.dtype))
self.assertEqual(86400, tb._date_differentials[0].astype(np.int64))
self.assertEqual(86400, tb._date_differentials[1].astype(np.int64))
self.assertEqual(2*86400, tb._date_differentials[2].astype(np.int64))
return
def test_compress_date_differentials(self):
tb = example_time_box('')
tb._date_differentials = None
tb._dates = np.array(
[
np.datetime64('2018-01-01', 's'),
np.datetime64('2018-01-02', 's'),
np.datetime64('2018-01-03', 's'),
np.datetime64('2018-01-05', 's')
]
)
tb._calculate_date_differentials()
tb._compress_date_differentials()
self.assertEqual(3, tb._date_differentials.size)
self.assertEqual(np.uint8, tb._date_differentials.dtype)
self.assertEqual(DAYS, tb._date_differential_units)
self.assertEqual(1, tb._bytes_per_date_differential)
self.assertEqual(1, tb._date_differentials[0])
self.assertEqual(1, tb._date_differentials[1])
self.assertEqual(2, tb._date_differentials[2])
return
def test_time_box_date_io(self):
file_name = 'date_io.npb'
tb = example_time_box(file_name)
tb._date_differentials = None
tb._dates = np.array(
[
np.datetime64('2018-01-01T00:00', 's'),
np.datetime64('2018-01-02T12:00', 's'),
np.datetime64('2018-01-03T05:00', 's'),
| np.datetime64('2018-01-05T00:00', 's') | numpy.datetime64 |
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Oct 31 13:38:02 2019
@author: brsr
"""
import geopandas
import pandas as pd
import shapely
from shapely.geometry import LineString, Polygon, Point
import pyproj
#import homography
import warnings
import numpy as np
from abc import ABC
from scipy.optimize import minimize, minimize_scalar, root_scalar
from scipy.special import hyp2f1, gamma, ellipj, ellipk, ellipkinc
#TODO:
#vectorize all the things
#find a better implementation of conformal
# (some kind of circle-packing thing?)
#repeated subdivision
#arange3 = np.arange(3)
#FIRST AXIS IS SPATIAL
TGTPTS3 = np.eye(3)
TGTPTS4 = np.array([[0, 1, 1, 0],
[0, 0, 1, 1]])
def normalize(vectors, axis=0):
"""Normalizes vectors in n-space. The zero vector remains the zero vector.
Args:
vectors: Array of vectors
axis: Which axis to take the norm over (by default the first axis, 0)
>>> x = np.stack((np.ones(5), np.arange(5)), axis=0)
>>> normalize(x)
array([[1. , 0.70710678, 0.4472136 , 0.31622777, 0.24253563],
[0. , 0.70710678, 0.89442719, 0.9486833 , 0.9701425 ]])
"""
n = np.linalg.norm(vectors, axis=axis, keepdims=True)
return np.where(n <= 0, 0, vectors / n)
def complex_to_float2d(arr):
"""Converts a complex array to a multidimensional float array.
>>> x = np.exp(2j*np.pi*np.linspace(0, 1, 5)).round()
>>> complex_to_float2d(x.round())
array([[ 1., 0.],
[ 0., 1.],
[-1., 0.],
[-0., -1.],
[ 1., -0.]])
"""
return arr.view(float).reshape(list(arr.shape) + [-1])
def float2d_to_complex(arr):
"""Converts a multidimensional float array to a complex array.
Input must be a float type, since there is no integer complex type.
>>> y = np.arange(8, dtype=float).reshape((-1, 2))
>>> float2d_to_complex(y)
array([[0.+1.j],
[2.+3.j],
[4.+5.j],
[6.+7.j]])
"""
return arr.view(complex)
def sqrt(x):
"""Real sqrt clipped to 0 for negative values.
>>> x = np.array([-np.inf, -1, 0, 1, np.inf, np.nan])
>>> sqrt(x)
array([ 0., 0., 0., 1., inf, nan])
"""
return np.where(x < 0, 0, np.sqrt(x))
def geodesics(lon, lat, geod, n=100, includepts=False):
"""Draw geodesics between each adjacent pair of points given by
lon and lat.
"""
lon2 = np.roll(lon, -1, axis=0)
lat2 = np.roll(lat, -1, axis=0)
result = []
for l, t, l2, t2 in zip(lon, lat, lon2, lat2):
g = geod.npts(l, t, l2, t2, n)
g.insert(0, (l, t))
g.append((l2, t2))
result.append(LineString(g))
ctrlboundary = geopandas.GeoSeries(result)
if includepts:
controlpts = arraytoptseries(np.array([lon, lat]))
ctrlpoly = geopandas.GeoSeries(pd.concat([ctrlboundary, controlpts],
ignore_index=True))
return ctrlpoly
else:
return ctrlboundary
def transform_antipode(lon, lat):
"""Transform a point given by lon and lat to its antipode."""
lon2 = lon - 180
np.where(lon2 <= -180, lon2 + 360, lon2)
return lon2, -lat
def ptseriestoarray(ser):
"""Convert a geopandas GeoSeries containing shapely Points
(or LineStrings of all the same length) to an array of
shape (2, n) or (3, n).
"""
return np.stack([x.coords for x in ser], axis=-1).squeeze()
def arraytoptseries(arr, crs={'epsg': '4326'}):
"""Convert an array of shape (2, ...) or (3, ...) to a
geopandas GeoSeries containing shapely Point objects.
"""
if arr.shape[0] == 2:
result = geopandas.GeoSeries([Point(x[0], x[1])
for x in arr.reshape(2, -1).T])
else:
result = geopandas.GeoSeries([Point(x[0], x[1], x[2])
for x in arr.reshape(3, -1).T])
#result.crs = crs
return result
def transeach(func, geoms):
"""Transform each element of geoms using the function func."""
plist = []
for geom in geoms:
if isinstance(geom, Point):
#special logic for points
ll = geom.coords[0]
plist.append(Point(func(*ll)))
else:
plist.append(shapely.ops.transform(func, geom))
return geopandas.GeoSeries(plist)
def graticule(spacing1=15, spacing2=1,
lonrange = [-180, 180], latrange = [-90, 90]):
"""
Create a graticule (or another square grid)
"""
a = int((lonrange[1] - lonrange[0])//spacing2)
b = int((latrange[1] - latrange[0])//spacing1)
c = int((lonrange[1] - lonrange[0])//spacing1)
d = int((latrange[1] - latrange[0])//spacing2)
plx = np.linspace(lonrange[0], lonrange[1], num=a + 1)
ply = np.linspace(latrange[0], latrange[1], num=b + 1)
mex = np.linspace(lonrange[0], lonrange[1], num=c + 1)
mey = np.linspace(latrange[0], latrange[1], num=d + 1)
parallels = np.stack(np.meshgrid(plx, ply), axis=-1).transpose((1,0,2))
meridians = np.stack(np.meshgrid(mex, mey), axis=-1)
gratlist = [parallels[:, i] for i in range(parallels.shape[1])]
gratlist += [meridians[:, i] for i in range(meridians.shape[1])]
gratl2 = [LineString(line) for line in gratlist]
grat = geopandas.GeoSeries(gratl2)
grat.crs = {'init': 'epsg:4326'}
return grat
#%%
def trigivenangles(angles, scale=np.pi/180):
"""Given angles, create the vertices of a triangle with those vertex
angles. Only uses the first 2 angles. The last vertex is always 1, 0.
>>> angles = np.array([45,90,45])
>>> np.round(trigivenangles(angles), decimals=8)
array([[-1., 0., 1.],
[ 0., -1., 0.]])
"""
angles = angles * scale
p0 = [np.cos(2*angles[1]), np.sin(2*angles[1])]
p1 = [np.cos(2*angles[0]), np.sin(-2*angles[0])]
p2 = [1, 0]
return np.array([p0, p1, p2]).T
def anglesgivensides(sides, scale=180/np.pi):
"""Given side lengths of a triangle, determines the interior angle at each
vertex, and the radius of the circumcircle.
>>> sides=np.array( [3,4,5])
>>> anglesgivensides(sides)
"""
#might be more stable to use law of cotangents, but eh
r = np.product(sides)/sqrt(
2*np.sum(sides**2*np.roll(sides,1)**2)
-np.sum(sides**4))
s1 = sides
s2 = np.roll(sides, -1)
s3 = np.roll(sides, 1)
cosangle = (s2**2 + s3**2 - s1**2)/ (2*s2*s3)
angles = np.arccos(cosangle)
return angles*scale, r
def trigivenlengths(sides):
"""Given side lengths, creates the vertices of a triangle with those
side lengths, and having circumcenter at 0,0.
>>> sides=np.array( [3,4,5])
>>> np.round(trigivenlengths(sides), decimals=8)
array([[-2.5, -0.7, 2.5],
[ 0. , -2.4, 0. ]])
"""
angles, r = anglesgivensides(sides, scale=1)
return r*trigivenangles(np.roll(angles, -1), scale=1)
#%%
def central_angle(x, y, signed=False):
"""Central angle between vectors with respect to 0. If vectors have norm
1, this is the spherical distance between them.
Args:
x, y: Coordinates of points on the sphere.
axis: Which axis the vectors lie along. By default, -1.
Returns: Array of central angles.
>>> t = np.linspace(0, np.pi, 5)
>>> c = np.cos(t)
>>> s = np.sin(t)
>>> z = np.zeros(t.shape)
>>> x = np.stack((c, s, z), axis=0)
>>> y = np.stack((c, z, s), axis=0)
>>> np.round(central_angle(x, y)/np.pi*180)
array([ 0., 60., 90., 60., 0.])
"""
cos = np.sum(x*y, axis=0)
sin = np.linalg.norm(np.cross(x, y, axis=0), axis=0)
result = np.arctan2(sin, cos)
return result if signed else abs(result)
def slerp(pt1, pt2, intervals):
"""Spherical linear interpolation.
Args:
pt1: Array of points. When interval is 0, the result is pt1.
pt2: Array of points. When interval is 1, the result is pt2.
intervals: Array of intervals at which to evaluate the
linear interpolation
>>> x = np.array([1, 0, 0])
>>> y = np.array([0, 0, 1])
>>> t = np.linspace(0, 1, 4)[:, np.newaxis]
>>> slerp(x, y, t)
array([[1. , 0. , 0. ],
[0.8660254, 0. , 0.5 ],
[0.5 , 0. , 0.8660254],
[0. , 0. , 1. ]])
"""
t = intervals
angle = central_angle(pt1, pt2)[..., np.newaxis]
return (np.sin((1 - t)*angle)*pt1 + np.sin((t)*angle)*pt2)/np.sin(angle)
def dslerp(pt1, pt2, intervals):
"""The derivative of slerp."""
t = intervals
angle = central_angle(pt1, pt2)[..., np.newaxis]
return (-np.cos((1 - t)*angle)*pt1 + np.cos(t*angle)*pt2)/np.sin(angle)
def triangle_solid_angle(a, b, c, axis=0):
"""Solid angle of a triangle with respect to 0. If vectors have norm 1,
this is the spherical area. Note there are two solid angles defined by
three points, determined by orientation of a, b, c.
Formula is from <NAME>; <NAME> (1983).
"The Solid Angle of a Plane Triangle". IEEE Trans. Biom. Eng.
BME-30 (2): 125–126. doi:10.1109/TBME.1983.325207.
Args:
a, b, c: Coordinates of points on the sphere.
Returns: Array of solid angles.
>>> t = np.linspace(0, np.pi, 5)
>>> a = np.stack([np.cos(t), np.sin(t), np.zeros(5)],axis=0)
>>> b = np.array([0, 1, 1])/np.sqrt(2)
>>> c = np.array([0, -1, 1])/np.sqrt(2)
>>> np.round(triangle_solid_angle(a, b, c), 4)
array([ 1.5708, 1.231 , 0. , -1.231 , -1.5708])
"""
axes = (axis,axis)
top = np.tensordot(a, np.cross(b, c, axis=axis), axes=axes)
na = np.linalg.norm(a, axis=0)
nb = np.linalg.norm(b, axis=0)
nc = np.linalg.norm(c, axis=0)
bottom = (na * nb * nc + np.tensordot(a, b, axes=axes) * nc
+ np.tensordot(b, c, axes=axes) * na
+ np.tensordot(c, a, axes=axes) * nb)
return 2 * np.arctan2(top, bottom)
def shoelace(pts):
"""Find area of polygon in the plane defined by pts, where pts is an
array with shape (2,n).
>>> pts = np.arange(6).reshape(2,-1)%4
>>> shoelace(pts)
2.0
"""
return abs(np.sum(np.cross(pts, np.roll(pts, -1, axis=1), axis=0)))/2
def antipode_v(ll):
"""Antipodes of points given by longitude and latitude."""
antipode = ll.copy()
antipode[0] -= 180
index = antipode[0] < -180
antipode[0, index] += 360
antipode[1] *= -1
return antipode
def omegascale(adegpts, degpts_t, geod, spacing=1):
"""Estimate scale factor and max deformation angle for a map projection
based on a grid of points
"""
#actrlpts, tgtpts,
#ar, p = geod.polygon_area_perimeter(actrlpts[0], actrlpts[1])
#at = shoelace(tgtpts)
es = geod.es
a = geod.a
factor = np.pi/180
#lon = adegpts[0]*factor
lat = adegpts[1]*factor
x = degpts_t[0]
y = degpts_t[1]
dx = np.gradient(x, factor*spacing)
dy = np.gradient(y, factor*spacing)
dxdlat, dxdlon = dx
dydlat, dydlon = dy
J = (dydlat*dxdlon - dxdlat*dydlon)
R = a*np.sqrt(1-es)/(1-es*np.sin(lat)**2)
h = sqrt((dxdlat)**2 + (dydlat)**2)*(1-es*np.sin(lat)**2)**(3/2)/(a*(1-es))
k = sqrt((dxdlon)**2 + (dydlon)**2)*(1-es*np.sin(lat)**2)**(1/2)/(a*np.cos(lat))
scale = J/(R**2*np.cos(lat))
sinthetaprime = np.clip(scale/(h*k), -1, 1)
aprime = sqrt(h**2 + k**2 + 2*h*k*sinthetaprime)
bprime = sqrt(h**2 + k**2 - 2*h*k*sinthetaprime)
sinomegav2 = np.clip(bprime/aprime, -1, 1)
omega = 360*np.arcsin(sinomegav2)/np.pi
return omega, scale
def rodrigues(center, v, theta):
"""Rodrigues formula: rotate vector v around center by angle theta
"""
cxv = np.cross(center, v)
cv = np.sum(center* v, axis=-1, keepdims=True)
cc = v*np.cos(theta) + cxv*np.sin(theta) + center*cv*(1-np.cos(theta))
return cc
#%%
class Projection(ABC):
"""Don't subclass this without subclassing one of
transform and transform_v and one of invtransform and invtransform_v,
or else an infinite regression will occur"""
def transform(self, x, y, z = None, **kwargs):
if z is None:
pts = np.stack([x,y])
else:
pts = np.stack([x,y,z])
vresult = self.transform_v(pts, **kwargs)
return vresult
def invtransform(self, x, y, z=None, **kwargs):
if z is None:
pts = np.stack([x,y])
else:
pts = np.stack([x,y,z])
vresult = self.invtransform_v(pts, **kwargs)
return vresult
def transform_v(self, pts, **kwargs):
rpts = pts.reshape((pts.shape[0],-1)).T
result = []
for xy in rpts:
result.append(self.transform(*xy, **kwargs))
result = np.array(result)
shape = [-1, ] + list(pts.shape[1:])
return result.T.reshape(shape)
def invtransform_v(self, pts, **kwargs):
rpts = pts.reshape((pts.shape[0],-1)).T
result = []
for xy in rpts:
result.append(self.invtransform(*xy, **kwargs))
result = np.array(result)
shape = [-1, ] + list(pts.shape[1:])
return result.T.reshape(shape)
#%%
class UV(Projection):
nctrlpts = 4
@staticmethod
def grid(**kwargs):
"""Create a square grid"""
return graticule(spacing1=1, spacing2=0.01,
lonrange=[0,1], latrange=[0,1])
@staticmethod
def gridpolys(n=11):
poi = np.array(np.meshgrid(np.linspace(0, 1, n),
np.linspace(0, 1, n)))
poilist = []
for i, j in np.ndindex(n-1,n-1):
x = Polygon([poi[:, i, j], poi[:, i, j+1],
poi[:, i+1, j+1], poi[:, i+1, j]])
poilist.append(x)
poiframe = geopandas.geoseries.GeoSeries(poilist)
return poiframe
@staticmethod
def segment(uv):
u, v = uv
index1 = u > v
index2 = u < 1 - v
#1 and 2 = 0
#1 and not 2 = 1
#not 1 and not 2 = 2
#not 1 and 2 = 3
result = np.zeros(u.shape)
result[index1 & ~index2] = 1
result[~index1 & ~index2] = 2
result[~index1 & index2] = 3
return result
class Bilinear(UV):
"""Bilinear interpolation
"""
_bilinear_mat = np.array([[ 1, 1, 1, 1],
[-1, 1, 1,-1],
[-1,-1, 1, 1],
[ 1,-1, 1,-1]])/4
def __init__(self, tgtpts):
self.tgtpts = tgtpts
self.abcd = self._bilinear_mat @ tgtpts.T
def transform(self, u, v):
"""u and v should have the same shape"""
abcd = self.abcd
stack = np.stack([np.ones(u.shape), u, v, u*v])
return (abcd @ stack).T
def transform_v(self, pts, **kwargs):
return self.transform(pts[0], pts[1])
def invtransform_v(self, pts):
abcd = self.abcd
A = abcd[:,0]
B = abcd[:,1]
C = abcd[:,2]
D = abcd[:,3] - pts
AB = np.cross(A,B)
AC = np.cross(A,C)
AD = np.cross(A,D)
BC = np.cross(B,C)
BD = np.cross(B,D)
CD = np.cross(C,D)
ua = 2*BD
ub = AD + BC
uc = 2*AC
va = 2*CD
vb = AD - BC
vc = 2*AB
u1 = (-ub + sqrt(ub**2 - ua*uc) )/ua
#u2 = (-ub - sqrt(ub**2 - ua*uc) )/ua
#v2 = (-vb + sqrt(vb**2 - va*vc) )/va
v1 = (-vb - sqrt(vb**2 - va*vc) )/va
return u1, v1
class Homeomorphism(UV):
"""Homeomorphism"""
def __init__(self, tgtpts):
self.tgtpts = tgtpts
class Barycentric(Projection):
"""Transforms between plane and barycentric coordinates"""
nctrlpts = 3
def __init__(self, tgtpts):
self.tgtpts = tgtpts
m = np.concatenate([self.tgtpts, np.ones((1, 3))])
self.minv = np.linalg.inv(m)
def transform_v(self, bary):
"""Convert barycentric to plane"""
rbary = bary.reshape(3,-1)
result = self.tgtpts @ rbary
shape = [2,] + list(bary.shape[1:])
return result.reshape(shape)
def invtransform_v(self, xy):
"""Convert plane to barycentric"""
rxy = xy.reshape(2,-1)
shape = list(rxy.shape)
shape[0] = 1
xy1 = np.concatenate([rxy, np.ones(shape)])
result = self.minv @ xy1
shape = [3,] + list(xy.shape[1:])
return result.reshape(shape)
@staticmethod
def grid(spacing1=0.1, spacing2=1E-2, rang = [0, 1], eps=1E-8):
"""Create a triangle grid in barycentric coordinates
"""
nx = int((rang[1] - rang[0])/spacing1 + 1)
ny = int((rang[1] - rang[0])/spacing2 + 1)
x = np.linspace(rang[0], rang[1], nx)
y = np.linspace(rang[0], rang[1], ny)
z = 1 - x[..., np.newaxis] - y
#valid = (rang[0] <= z) & (z <= rang[1])
#z[~valid] = np.nan
bary1 = np.stack([np.broadcast_to(x[..., np.newaxis], (nx, ny)),
np.broadcast_to(y, (nx, ny)),
z])
bary = np.concatenate([bary1, np.roll(bary1, -1, axis=0),
np.roll(bary1, -2, axis=0)], axis=1)
gratlist = [bary[:, i] for i in range(nx*3)]
gratl2 = []
for i in range(nx*3):
g = gratlist[i]
valid = np.all((rang[0]-eps <= g) & (g <= rang[1]+eps), axis=0)
if np.sum(valid) > 1:
g = g[..., valid]
gratl2.append(LineString(g.T))
grat = geopandas.GeoSeries(gratl2)
return grat
@staticmethod
def gridpolys(n=11, eps=0.01):
poi = np.meshgrid(np.linspace(0, 1, n), np.linspace(0, 1, n))
poi.append(1 - poi[0] - poi[1])
poi = np.array(poi)
poilist = []
for i,j in np.ndindex(n-1,n-1):
if poi[2, i, j] >= eps:
x = Polygon([poi[:, i, j],poi[:, i, j+1],poi[:, i+1, j]])
poilist.append(x)
if poi[2, i+1, j+1] >= -eps:
y = Polygon([poi[:, i+1, j+1],poi[:, i+1, j],poi[:, i, j+1]])
poilist.append(y)
poiframe = geopandas.geoseries.GeoSeries(poilist)
return poiframe
@staticmethod
def segment(bary):
return np.argmin(bary, axis=0)
class UnitVector(Projection):
"""Convert longitude and latitude to unit vector normals.
The methods of this class are static, and mostly organized in a class
for consistency."""
@staticmethod
def transform(x, y, **kwargs):
pts = np.stack([x,y])
vresult = UnitVector.transform_v(pts, **kwargs)
return vresult
@staticmethod
def invtransform(x, y, z, **kwargs):
pts = np.stack([x,y,z])
vresult = UnitVector.invtransform_v(pts, **kwargs)
return vresult
@staticmethod
def transform_v(ll, scale=np.pi/180):
"""Convert longitude and latitude to 3-vector
>>> ll = np.arange(6).reshape(2,3)*18
>>> UnitVector.transform_v(ll)
array([[5.87785252e-01, 2.93892626e-01, 4.95380036e-17],
[0.00000000e+00, 9.54915028e-02, 3.59914664e-17],
[8.09016994e-01, 9.51056516e-01, 1.00000000e+00]])
"""
lon, lat = ll*scale
x = np.cos(lat)*np.cos(lon)
y = np.cos(lat)*np.sin(lon)
z = np.sin(lat)
return np.stack([x, y, z], axis=0)
@staticmethod
def invtransform_v(pts, scale=180/np.pi):
"""Convert 3-vector to longitude and latitude.
Vector does not have to be normalized.
>>> UnitVector.invtransform_v(np.eye(3))
array([[ 0., 90., 0.],
[ 0., 0., 90.]])
"""
lat = scale*np.arctan2(pts[2], sqrt(pts[1]**2 + pts[0]**2))
lon = scale*np.arctan2(pts[1], pts[0])
return np.stack([lon, lat], axis=0)
_unitsphgeod = pyproj.Geod(a=1, b=1)
class CtrlPtsProjection(Projection, ABC):
"""Subclass for any map projection that uses (2 or more) control points."""
def __init__(self, ctrlpts, geod = _unitsphgeod):
"""Parameters:
ctrlpts: 2x3 or 2x4 Numpy array, latitude and longitude of
each control point
geod= a pyproj.Geod object. For a unit sphere use
pyproj.Geod(a=1,b=1)
"""
n = ctrlpts.shape[1]
if self.nctrlpts != n:
raise ValueError(
'ctrlpts has wrong number of points for this projection')
self.geod = geod
#it's possible to get a geod where this would give the wrong answer,
#but I think it would have to be really weird
area, _ = geod.polygon_area_perimeter([0,120,-120],[0,0,0])
self.totalarea = 2*area
self.ctrlpts = ctrlpts
ctrlpts_v = UnitVector.transform_v(ctrlpts)
self.ctrlpts_v = ctrlpts_v
center_v = ctrlpts_v.sum(axis=1)
self.center_v = center_v / np.linalg.norm(center_v)
self.center = UnitVector.invtransform_v(center_v)
antipode = antipode_v(ctrlpts)
self.antipode = antipode
self.antipode_v = UnitVector.transform_v(antipode)
self.sa = 0
if self.nctrlpts > 2:
faz, baz, sides = self.geod.inv(ctrlpts[0], ctrlpts[1],
np.roll(ctrlpts[0], -1),
np.roll(ctrlpts[1], -1))
self.sides = sides
self.faz = faz
self.baz = baz
self.ctrl_angles = (faz - np.roll(baz, 1))%360
area, _ = geod.polygon_area_perimeter(*ctrlpts)
self.area = area
self.ca = central_angle(ctrlpts_v,
np.roll(ctrlpts_v, -1, axis=1))
for i in range(1, self.nctrlpts-1):
self.sa += triangle_solid_angle(ctrlpts_v[..., 0],
ctrlpts_v[..., i],
ctrlpts_v[..., i+1])
self.edgenormals = np.cross(ctrlpts_v,
np.roll(ctrlpts_v, -1, axis=1), axis=0)
else:
faz, baz, sides = self.geod.inv(ctrlpts[0,0], ctrlpts[1,0],
ctrlpts[0,1], ctrlpts[1,1])
self.sides = sides
self.faz = faz
self.baz = baz
self.area = 0
self.ca = central_angle(ctrlpts_v[..., 0], ctrlpts_v[..., 1])
self.edgenormals = np.cross(ctrlpts_v[..., 0], ctrlpts_v[..., 1])
self.cosca = np.cos(self.ca)
self.sinca = np.sin(self.ca)
if self.sa < 0:
warnings.warn('control polygon is in negative orientation, '
+ 'may cause unusual results')
if self.nctrlpts == 4:
ctrlpts_v = self.ctrlpts_v
v0 = ctrlpts_v[..., 0]
v1 = ctrlpts_v[..., 1]
v2 = ctrlpts_v[..., 2]
v3 = ctrlpts_v[..., 3]
poip1 = np.cross(np.cross(v0, v1), np.cross(v3, v2))
poip2 = np.cross(np.cross(v0, v3), np.cross(v1, v2))
poip = np.stack([[poip1, -poip1],
[poip2, -poip2]]).transpose(2,0,1)
poip = poip / np.linalg.norm(poip, axis=0)
self.poi_v = poip
self.poi = UnitVector.invtransform_v(poip)
self.crossx = np.cross(ctrlpts_v,
np.roll(ctrlpts_v, -2, axis=1),
axis=0)[..., :2]
def orienttgtpts(self, tgtpts, N = (0, 90)):
"""Orient target points so that line from 0 to the projection of N
points up. Will fail if map projection doesn't define tgtpts."""
pN = self.transform(*N)
if np.allclose(pN, [0,0]):
raise ValueError('projection of N too close to 0')
angle = np.arctan2(pN[0],pN[1])
rotm = np.array([[np.cos(angle), -np.sin(angle)],
[np.sin(angle), np.cos(angle)]])
result = rotm @ tgtpts
self.tgtpts = result
def lune(self, lon, lat):
"""
Determine which lune a point or series of points lies in.
Lune 0 is the lune with vertex at the centroid and edges passing through
control points 0 and 1. Lune 1 is the same using control pts 1 and 2,
and Lune 2 uses control pts 2 and 0.
"""
#inexact on ellipsoids but close enough
testpt = UnitVector.transform(lon, lat)
testpt_v = testpt.reshape(3,-1)
ctrlpts_v = self.ctrlpts_v
center_v = self.center_v
cx = np.cross(center_v, ctrlpts_v, axis=0)
sk = cx.T @ testpt_v
sg = sk >= 0
ind = sg & ~np.roll(sg, shift=-1, axis=0)
result = np.argmax(ind, axis=0)
return result.reshape(testpt.shape[1:])
class BarycentricMapProjection(CtrlPtsProjection):
nctrlpts = 3
tweak = False
bcenter = np.ones(3)/3
def fixbary(self, bary):
if self.tweak:
return self.fixbary_normalize(bary)
else:
return self.fixbary_subtract(bary)
@staticmethod
def fixbary_normalize(bary):
"""Converts array bary to an array with sum = 1 by dividing by
bary.sum(). Will return nan if bary.sum() == 0.
>>> fixbary_normalize(np.arange(3))
array([0. , 0.33333333, 0.66666667])
"""
bary = np.array(bary)
return bary / np.sum(bary, axis=0, keepdims=True)
@staticmethod
def fixbary_subtract(bary):
"""Converts array bary to an array with sum = 1 by subtracting
(bary.sum() - 1)/bary.shape[0].
>>> fixbary_subtract(np.arange(3))
array([-0.66666667, 0.33333333, 1.33333333])
"""
bary = np.array(bary)
s = (np.sum(bary, axis=0, keepdims=True) - 1)/bary.shape[0]
return bary - s
def _fix_corners(self, lon, lat, result):
ctrlpts = self.ctrlpts
index0 = (lon == ctrlpts[0,0]) & (lat == ctrlpts[1,0])
index1 = (lon == ctrlpts[0,1]) & (lat == ctrlpts[1,1])
index2 = (lon == ctrlpts[0,2]) & (lat == ctrlpts[1,2])
#print(lon, lat, ctrlpts, result)
#print(index0.shape, result.shape, np.array([1, 0, 0])[..., np.newaxis].shape)
result[..., index0] = np.array([1, 0, 0])[..., np.newaxis]
result[..., index1] = np.array([0, 1, 0])[..., np.newaxis]
result[..., index2] = np.array([0, 0, 1])[..., np.newaxis]
return result
def _fix_corners_inv(self, bary, result):
index0 = (bary[0] == 1)
index1 = (bary[1] == 1)
index2 = (bary[2] == 1)
if np.any(index0):
result[..., index0] = self.ctrlpts_v[..., 0, np.newaxis]
if np.any(index1):
result[..., index1] = self.ctrlpts_v[..., 1, np.newaxis]
if np.any(index2):
result[..., index2] = self.ctrlpts_v[..., 2, np.newaxis]
return result
class UVMapProjection(CtrlPtsProjection):
nctrlpts = 4
bcenter = np.ones(2)/2
def _fix_corners(self, lon, lat, result):
ctrlpts = self.ctrlpts
index0 = (lon == ctrlpts[0,0]) & (lat == ctrlpts[1,0])
index1 = (lon == ctrlpts[0,1]) & (lat == ctrlpts[1,1])
index2 = (lon == ctrlpts[0,2]) & (lat == ctrlpts[1,2])
index3 = (lon == ctrlpts[0,3]) & (lat == ctrlpts[1,3])
result[..., index0] = np.array([ 0, 0])[..., np.newaxis]
result[..., index1] = np.array([ 1, 0])[..., np.newaxis]
result[..., index2] = np.array([ 1, 1])[..., np.newaxis]
result[..., index3] = np.array([ 0, 1])[..., np.newaxis]
return result
def _fix_corners_inv(self, x, y, result):
index0 = (x == 0) & (y == 0)
index1 = (x == 1) & (y == 0)
index2 = (x == 1) & (y == 1)
index3 = (x == 0) & (y == 1)
if np.any(index0):
result[..., index0] = self.ctrlpts_v[..., 0, np.newaxis]
if np.any(index1):
result[..., index1] = self.ctrlpts_v[..., 1, np.newaxis]
if np.any(index2):
result[..., index2] = self.ctrlpts_v[..., 2, np.newaxis]
if np.any(index3):
result[..., index3] = self.ctrlpts_v[..., 3, np.newaxis]
return result
#%% not-polygonal projections
class ChambTrimetric(CtrlPtsProjection):
"""Chamberlin trimetric projection"""
#FIXME this implementation fails for control triangles with
#high aspect ratios
nctrlpts = 3
def __init__(self, ctrlpts, geod=_unitsphgeod):
super().__init__(ctrlpts, geod)
self.tgtpts = trigivenlengths(self.sides)
try:
self.orienttgtpts(self.tgtpts)
except ValueError:
pass
def transform(self, x, y, **kwargs):
if hasattr(x, '__iter__'):
raise TypeError()
tgtpts = self.tgtpts
f, b, rad = self.geod.inv(self.ctrlpts[0], self.ctrlpts[1],
x*np.ones(3), y*np.ones(3))
faz = self.faz
raz1 = (faz - f) % 360
radsq = np.array(rad).squeeze()**2
ctgt = tgtpts.T.copy().view(dtype=complex).squeeze()
a = np.roll(ctgt, -1) - ctgt
b = ctgt
l = abs(a)
lsq = l**2
rsq = radsq/lsq
ssq = np.roll(radsq, -1, axis=-1)/lsq
x0 = (rsq - ssq + 1)/2
y0 = sqrt(-rsq**2 + 2*rsq*(ssq + 1) - (ssq - 1)**2)/2
y0[np.isnan(y0)] = 0
y = np.where(raz1 > 180, -y0, y0)
z0 = x0 +1j*y
pts = (a * z0 + b)
result = np.mean(pts)
return result.real, result.imag
def invtransform(self, *args, **kwargs):
return NotImplemented
class LstSqTrimetric(ChambTrimetric):
"""Least-squares variation of the Chamberlin trimetric projection"""
def transform(self, x, y, **kwargs):
init = super().transform(x, y)
tgtpts = self.tgtpts
f, b, rad = self.geod.inv(self.ctrlpts[0], self.ctrlpts[1],
x*np.ones(3), y*np.ones(3))
def objective(v):
x = v[0]
y = v[1]
a = tgtpts[0]
b = tgtpts[1]
xma = x-a
ymb = y-b
dist = np.sqrt(xma**2 + ymb**2)
result = np.sum((dist - rad)**2 )
f = 1 - rad/dist
f[rad <= 0] = 1
jac = 2*np.array([np.sum(xma*f), np.sum(ymb*f)])
return result, jac
res = minimize(objective, init, jac=True,
method = 'BFGS')
return res.x
class LinearTrimetric(CtrlPtsProjection):
"""The linear variation of the Chamberlin Trimetric projection."""
nctrlpts = 3
matrix1 = np.array([[0,-1],
[1,0]])
matrix2 = np.array([[0, -1, 1],
[1, 0, -1],
[-1, 1, 0]])
matrixinv1 = np.array([[-2,1,1],
[1,-2,1],
[1,1,-2]])*2/3
def __init__(self, ctrlpts, geod=_unitsphgeod):
"""Parameters:
ctrlpts: 2x3 Numpy array, latitude and longitude of each control point
geod= a pyproj.Geod object. For a unit sphere use
pyproj.Geod(a=1,b=1).
"""
super().__init__(ctrlpts, geod)
self.radius = ((geod.a**(3/2) + geod.b**(3/2))/2)**(2/3)
self.tgtpts = trigivenlengths(self.sides)
self.setmat()
# try:
# self.orienttgtpts(self.tgtpts)
# self.setmat()
# except ValueError:
# pass
vctrl = self.ctrlpts_v
self.invctrlvector = np.linalg.pinv(vctrl)
self.invperpmatrix = self.invctrlvector @ self.invctrlvector.T
cosrthmin = 1 / np.sqrt(self.invperpmatrix.sum())
self.hminall = np.arccos(cosrthmin)**2
def setmat(self, tgtpts=None):
"""Set matrices that use tgtpts"""
if tgtpts is None:
tgtpts = self.tgtpts
else:
self.tgtpts = tgtpts
tgtde = np.linalg.det(np.concatenate([tgtpts, np.ones((1,3))], axis=0))
self.m = self.matrix1 @ tgtpts @ self.matrix2 /(2*tgtde)
self.minv = self.matrixinv1 @ tgtpts.T
def transform_v(self, pts):
rpts = pts.reshape((2,-1)).T
rad = []
for x,y in rpts:
f, b, radi = self.geod.inv(x*np.ones(3), y*np.ones(3),
self.ctrlpts[0], self.ctrlpts[1])
rad.append(radi)
shape = list(pts.shape)
shape[0] = 3
rad = np.array(rad).T
radsq = np.array(rad)**2
result = self.m @ radsq
return result.reshape(pts.shape)
def invtransform_v(self, pts, n=20, stop=1E-8):
if not self.geod.sphere:
warnings.warn('inverse transform is approximate on ellipsoids')
rpts = pts.reshape((2,-1))
k = self.minv @ rpts/self.radius**2
hmin = -np.min(k, axis=0)
print('k: ', k)
#hmax = np.pi**2-np.max(k, axis=0)
hminall = self.hminall
h = np.where(hmin < hminall, hminall, hmin)
print('h: ', h)
for i in range(n):
rsq = (k + h)
#pos = rsq > 0
neg = rsq < 0
zer = rsq == 0
c = np.where(neg, np.cosh(np.sqrt(-rsq)), np.cos(np.sqrt(rsq)))
b = np.where(neg, np.sinh(np.sqrt(-rsq)),
np.sin(np.sqrt(rsq)))/np.sqrt(np.abs(rsq))
b[zer] = 1
f = np.einsum('i...,ij,j...', c, self.invperpmatrix, c) - 1
fprime = np.einsum('i...,ij,j...', c, self.invperpmatrix, b)
delta = f/fprime
h += delta
print('delta:', delta)
print('h: ', h)
if np.max(np.abs(delta)) < stop:
break
#h = np.clip(h, hmin, hmax)
rsq = np.clip(k + h, 0, np.pi**2)
c = np.cos(np.sqrt(rsq))
vector = self.invctrlvector.T @ c
print(c)
print(vector)
return UnitVector.invtransform_v(vector).reshape(pts.shape)
def nmforplot(self, pts, n=100):
rpts = pts.reshape((2,-1))
k = self.minv @ rpts/self.radius**2
hmin = -np.min(k, axis=0)
hmax = np.pi**2-np.max(k, axis=0)
h = np.linspace(hmin,hmax,100).T
rsq = (k[..., np.newaxis] + h)
c = np.cos(np.sqrt(rsq))
nm = np.einsum('i...,ij,j...', c, self.invperpmatrix, c)
return h, nm
class Alfredo(BarycentricMapProjection):
"""this doesn't really accomplish anything"""
def __init__(self, ctrlpts, tweak=False):
"""Parameters:
ctrlpts: 2x3 Numpy array, latitude and longitude of each control point
"""
super().__init__(ctrlpts)
ctrlpts_v = self.ctrlpts_v
self.cosADfactor = (np.cross(np.roll(ctrlpts_v, 1, axis=1),
np.roll(ctrlpts_v, -1, axis=1), axis=0) +
ctrlpts_v * np.linalg.det(ctrlpts_v))
self.tweak = tweak
def transform_v(self, ll):
rll = ll.reshape(2, -1)
ctrlpts_v = self.ctrlpts_v
cosADfactor = self.cosADfactor
vtestpt = UnitVector.transform_v(rll)
cosAPi = (vtestpt.T @ ctrlpts_v).T
cosADi = (vtestpt.T @ cosADfactor).T
pli = np.sqrt((1-cosAPi)/(1-cosADi))
b = 1 - pli
result = self.fixbary(b)
shape = (3,) + ll.shape[1:]
return result.reshape(shape)
def invtransform(self, *args, **kwargs):
return NotImplemented
#%%
class Areal(BarycentricMapProjection):
"""Spherical areal projection."""
def __init__(self, ctrlpts, geod=_unitsphgeod):
"""Parameters:
ctrlpts: 2x3 Numpy array, latitude and longitude of each control point
geod: a pyproj.Geod object. For a unit sphere use
pyproj.Geod(a=1,b=1).
"""
super().__init__(ctrlpts, geod)
a_i = np.sum(np.roll(self.ctrlpts_v, -1, axis=1) *
np.roll(self.ctrlpts_v, 1, axis=1), axis=0)
self.a_i = a_i
self.b_i = (np.roll(a_i, -1) + np.roll(a_i, 1))/(1+a_i)
self.tau_c = self.tau(self.area)
def tau(self, area):
"""Convert areas on the geod to tau values for inverse transform"""
return np.tan(area/self.totalarea*2*np.pi)
def transform(self, x, y):
try:
areas = []
for i in range(3):
smtri = self.ctrlpts.copy()
smtri[:, i] = np.array([x,y])
a, _ = self.geod.polygon_area_perimeter(smtri[0],
smtri[1])
areas.append(a)
areas = np.array(areas)
return areas/self.area
except ValueError:
raise TypeError()
def invtransform_v(self, bary):
rbary = bary.reshape(3,-1)
if not self.geod.sphere:
warnings.warn('inverse transform is approximate on ellipsoids')
b_i = self.b_i[:,np.newaxis]
tau = self.tau_c
tau_i = self.tau(self.area*rbary)
t_i = tau_i/tau
c_i = t_i / ((1+b_i) + (1-b_i) * t_i)
f_i = c_i / (1 - np.sum(c_i, axis=0))
vector = self.ctrlpts_v @ f_i
shape = [2] + list(bary.shape[1:])
result = UnitVector.invtransform_v(vector).reshape(shape)
return result
#%%
class BisectTri(BarycentricMapProjection):
"""Inverse is only approximate
"""
def __init__(self, ctrlpts):
"""Parameters:
ctrlpts: 2xn Numpy array, latitude and longitude of each control point
"""
super().__init__(ctrlpts)
ctrlpts_v = self.ctrlpts_v
#v_0 = ctrlpts_v[..., 0]
#v_1 = ctrlpts_v[..., 1]
#v_2 = ctrlpts_v[..., 2]
midpoint_v = np.roll(ctrlpts_v, 1, axis=1) + np.roll(ctrlpts_v, -1, axis=1)
midpoint_v /= np.linalg.norm(midpoint_v, axis=0, keepdims=True)
self.midpoint_v = midpoint_v
self.midpoint = UnitVector.invtransform_v(self.midpoint_v)
aream = []
for i in range(3):
#index = np.roll(np.arange(3), -i)[:2]
#lona = list(ctrlpts[0, index]) + [self.midpoint[0,i],]
#lata = list(ctrlpts[1, index]) + [self.midpoint[1,i],]
#am, _ = self.geod.polygon_area_perimeter(lona, lata)
am = triangle_solid_angle(ctrlpts_v[:,i], ctrlpts_v[:,(i+1)%3],
midpoint_v[:,i])
#vc[:,0], mi, lproj)
aream.append(am)
self.aream = np.array(aream)
def transform(self, lon, lat):
lon + 0
vtestpt = UnitVector.transform(lon, lat)
areas = []
vctrlpts = self.ctrlpts_v
actrlpts = self.ctrlpts
geod = self.geod
area = self.area
for i in range(3):
vc = np.roll(vctrlpts, i, axis=1)
#ac = np.roll(actrlpts, i, axis=1)
mi = self.midpoint_v[:,-i]#?
lproj = -np.cross(np.cross(vc[..., 1], vc[..., 2]),
np.cross(vc[..., 0], vtestpt))
#lllproj = UnitVector.invtransform_v(lproj)
#loni = [ac[0,0], mi[0], lllproj[0]]
#lati = [ac[1,0], mi[1], lllproj[1]]
#a1, _ = geod.polygon_area_perimeter(loni, lati)
a1 = triangle_solid_angle(vc[:,0], mi, lproj)
areas.append(a1)
areas = np.array(areas) + self.aream
aa = areas/area
bx = []
for i in range(3):
x,y,z = np.roll(aa, i, axis=0)
b = (y**2 * x**2 + z**2 * x**2 - y**2 * z**2
- x * y**2 + z * y**2
- 2*y*x**2 - x*z**2 + y*z**2 + x**2
+ 3*y*x + z*x - 2*y*z
- 2*x - y + z + 1)
bx.append(b)
bx = np.array(bx)
betax = bx/bx.sum()
return self._fix_corners(lon, lat, betax)
def invtransform(self, b1, b2, b3):
b1 + 0
beta = np.array([b1,b2,b3])
vctrlpts3 = self.ctrlpts_v
#xs = []
ptts = []
for i in range(3):
beta1, beta2, beta3 = np.roll(beta, -i, axis=0)
x = beta2/(1 - beta1)
#xs.append(x)
a = x * self.area
pt0 = vctrlpts3[:,i]
pt1 = vctrlpts3[:,i-2]
pt2 = vctrlpts3[:,i-1]
cosw = pt1 @ pt2
w = np.arccos(cosw)
sinw = np.sin(w)
p2 = ((np.cos(a/2)* pt2 @ np.cross(pt0, pt1)- np.sin(a/2)*pt2 @ (pt1 + pt0))
+ np.sin(a/2)*cosw*(1 + pt1 @ pt0))
p3 = sinw*np.sin(a/2)*(1 + pt0 @ pt1)
r = 2*p3*p2/(p2**2 - p3**2)
t = np.arctan(r)/w#really close to just x
#print(x, t)
#t = x
ptt = slerp(pt2, pt1, t)
ptts.append(ptt)
ptts = np.array(ptts).T
ns = np.cross(vctrlpts3, ptts, axis=0)
pts = np.cross(ns, np.roll(ns, -1, axis=1), axis=0)
v = pts.sum(axis=1)
v = self._fix_corners_inv(beta, v)
return UnitVector.invtransform_v(v)
class BisectTri2(BarycentricMapProjection):
"""Inverse is only approximate"""
def __init__(self, ctrlpts):
"""Parameters:
ctrlpts: 2xn Numpy array, latitude and longitude of each control point
"""
super().__init__(ctrlpts)
ctrlpts_v = self.ctrlpts_v
#v_0 = ctrlpts_v[..., 0]
#v_1 = ctrlpts_v[..., 1]
#v_2 = ctrlpts_v[..., 2]
midpoint_v = np.roll(ctrlpts_v, 1, axis=1) + np.roll(ctrlpts_v, -1, axis=1)
midpoint_v /= np.linalg.norm(midpoint_v, axis=0, keepdims=True)
self.midpoint_v = midpoint_v
self.midpoint = UnitVector.invtransform_v(self.midpoint_v)
def transform(self, lon, lat):
lon + 0
vtestpt = UnitVector.transform(lon, lat)
aa = []
vctrlpts = self.ctrlpts_v
actrlpts = self.ctrlpts
for i in range(3):
vc = np.roll(vctrlpts, i, axis=1)
ac = np.roll(actrlpts, i, axis=1)
mi = self.midpoint[:,-i]
lproj = -np.cross(np.cross(vc[..., 1], vc[..., 2]),
np.cross(vc[..., 0], vtestpt))
lllproj = UnitVector.invtransform_v(lproj)
dist1x = central_angle(vc[..., 1], lproj)
f, b, dist1x = self.geod.inv(mi[0], mi[1],
lllproj[0],lllproj[1])
f0, b0, _ = self.geod.inv(mi[0], mi[1],
ac[0,2], ac[1,2])
deltaf = (f-f0) % 360
if (deltaf <= 90) | (deltaf > 270):
s = 1
else:
s = -1
t = s*dist1x/self.sides[i] + 1/2
#print(t)
aa.append(t)
bx = []
for i in range(3):
x,y,z = np.roll(aa, i, axis=0)
b = (y**2 * x**2 + z**2 * x**2 - y**2 * z**2
- x * y**2 + z * y**2
- 2*y*x**2 - x*z**2 + y*z**2 + x**2
+ 3*y*x + z*x - 2*y*z
- 2*x - y + z + 1)
bx.append(b)
bx = np.array(bx)
betax = bx/bx.sum()
return self._fix_corners(lon, lat, betax)
def invtransform(self, b1, b2, b3):
b1 + 0
beta = np.array([b1,b2,b3])
vctrlpts3 = self.ctrlpts_v
#xs = []
ptts = []
for i in range(3):
beta1, beta2, beta3 = np.roll(beta, -i, axis=0)
x = beta2/(1 - beta1)
pt1 = vctrlpts3[:,i-2]
pt2 = vctrlpts3[:,i-1]
ptt = slerp(pt2, pt1, x)
ptts.append(ptt)
ptts = np.array(ptts).T
ns = np.cross(vctrlpts3, ptts, axis=0)
pts = np.cross(ns, np.roll(ns, -1, axis=1), axis=0)
v = pts.sum(axis=1)
v = self._fix_corners_inv(beta, v)
return UnitVector.invtransform_v(v)
class FullerEq(BarycentricMapProjection):
def transform_v(self, ll):
vtestpt_pre = UnitVector.transform(*ll)
vtestpt = vtestpt_pre.reshape(3,-1)
ctrlpts_v = self.ctrlpts_v
b = []
for i in range(3):
v0 = ctrlpts_v[..., i]
v1 = ctrlpts_v[..., (i+1)%3]
v2 = ctrlpts_v[..., (i-1)%3]
cosw01 = v0 @ v1
cosw02 = v0 @ v2
w01 = np.arccos(cosw01)
w02 = np.arccos(cosw02)
w = (w01 + w02) / 2
sinw = np.sin(w)
cosw = np.cos(w)
vt01 = np.tensordot(vtestpt, | np.cross(v0, v1) | numpy.cross |
#! /usr/bin/env python
"""
IMU Node. Gets raw IMU data from ABridge and publishes calibrated IMU messages.
Can perform a 2D IMU Calibration as a fallback at the start of a round.
Ellipsoid fit, from:
https://github.com/aleksandrbazhin/ellipsoid_fit_python
Adapted for ROS by <NAME>, Cabrillo College.
The MIT License (MIT)
Copyright (c) 2016 aleksandrbazhin
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.
todo: pick validation thresholds that make sense. Something that means the 2D calibration is likely going to be better.
todo: ok for node to crash if extended cal file is missing or corrupt?
"""
from __future__ import print_function
import math
import numpy
import sys
import tf
import rospy
from diagnostic_msgs.msg import DiagnosticArray, DiagnosticStatus, KeyValue
from geometry_msgs.msg import Quaternion
from sensor_msgs.msg import Imu
from std_msgs.msg import String
from std_srvs.srv import Empty, EmptyRequest, EmptyResponse
from control_msgs.srv import QueryCalibrationState, QueryCalibrationStateResponse
from swarmie_msgs.msg import SwarmieIMU
class IMU:
"""Global State Variables"""
STATE_IDLE = 0
STATE_NORMAL = 1
STATE_VALIDATE = 2
STATE_CAL_GYRO_BIAS = 3
STATE_CAL_GYRO_SCALE = 4
STATE_CAL_MAG = 5
STATE_CAL_MISALIGN = 6
# Mode variables
MODE_3D = 0
MODE_2D = 1
# In case someone forgets to exit either calibration state.
DATA_SIZE_LIMIT = 3000 # 5 min worth of data at 10 Hz
MIN_DATA_SIZE = 50
# For extended file validation
ROLL_PITCH_TOLERANCE = 3.0 # degrees
MAG_VAR_TOLERANCE = 1e-3
ACC_VAR_TOLERANCE = 4e-3
def __init__(self, rover):
self.rover = rover
rospy.init_node(self.rover + '_IMU')
if rospy.has_param('~imu_mode'): # if respawning
self._get_mode()
else:
self.current_mode = IMU.MODE_3D # default to 3D mode
self.current_state = IMU.STATE_IDLE # idle until data file is loaded
self.gyro_timer = None
self.gyro_start_time = None
self.gyro_status_msg = ''
self.cal = {}
self.roll = 0
self.pitch = 0
self.yaw = 0
# used during file validation
self.rolls = []
self.pitches = []
# Default param values. Set to final values after validating
self.finished_validating = False
self.needs_calibration = False
self.DEBUG = rospy.get_param(
'~publish_debug_topic',
default=False
)
self.LOAD_RAW_DATA = rospy.get_param(
'~load_raw_data',
default=False
)
self.RAW_DATA_PATH = rospy.get_param(
'~raw_data_path',
default='/home/swarmie/KSC_extended_calibration.csv'
)
# Raw data collected while in a calibration state is stored in a list
# of lists, which is converted to a numpy array when needed.
self.mag_data = [[], [], []]
self.gyro_data = [[], [], []]
# Default matrices
self.acc_offsets = [[0], [0], [0]]
self.acc_transform = [[1., 0, 0],
[0, 1., 0],
[0, 0, 1.]]
self.mag_offsets = [[0], [0], [0]]
self.mag_transform = [[1., 0, 0],
[0, 1., 0],
[0, 0, 1.]]
self.misalignment = [[1., 0, 0],
[0, 1., 0],
[0, 0, 1.]]
self.gyro_bias = [[0], [0], [0]]
self.gyro_scale = [[1., 0, 0],
[0, 1., 0],
[0, 0, 1.]]
# Subscribers
self.imu_raw_sub = rospy.Subscriber(
self.rover + '/imu/raw',
SwarmieIMU,
self.imu_callback,
queue_size=10
)
# Publishers
self.imu_pub = rospy.Publisher(
self.rover + '/imu',
Imu,
queue_size=10
)
self.imu_diag_pub = rospy.Publisher(
self.rover + '/imu/cal_diag',
DiagnosticArray,
queue_size=10,
latch=True
)
if self.DEBUG:
self.imu_cal_data_pub = rospy.Publisher(
self.rover + '/imu/raw/calibrated',
SwarmieIMU,
queue_size=10
)
self.info_log = rospy.Publisher(
'/infoLog',
String,
queue_size=10
)
self.diags_log = rospy.Publisher(
'/diagsLog',
String,
queue_size=10,
latch=True
)
# Services
self.start_imu_cal = rospy.Service(
self.rover + '/start_imu_calibration',
Empty,
self.start_imu_calibration
)
self.store_cal = rospy.Service(
self.rover + '/store_imu_calibration',
Empty,
self.store_calibration
)
self.start_misalign_cal = rospy.Service(
self.rover + '/start_misalignment_calibration',
Empty,
self.start_misalignment_calibration
)
self.start_gyro_bias_cal = rospy.Service(
self.rover + '/start_gyro_bias_calibration',
Empty,
self.start_gyro_bias_calibration
)
self.start_gyro_scale_cal = rospy.Service(
self.rover + '/start_gyro_scale_calibration',
Empty,
self.start_gyro_scale_calibration
)
self._is_finished_val = rospy.Service(
self.rover + '/imu/is_finished_validating',
QueryCalibrationState,
self._is_finished_validating
)
self._needs_cal = rospy.Service(
self.rover + '/imu/needs_calibration',
QueryCalibrationState,
self._needs_calibration
)
# Try waiting for subscriber on /diagsLog. Helps to make sure first
# message or two actually make it onto the rqt gui.
rate = rospy.Rate(10)
for i in range(20):
if self.diags_log.get_num_connections() > 0:
break
rate.sleep()
# If node is respawning for some reason
if rospy.has_param('~imu_calibration_matrices'):
self.cal = rospy.get_param('~imu_calibration_matrices')
self._get_mode()
self.acc_offsets = self.cal['acc_offsets']
self.acc_transform = self.cal['acc_transform']
self.mag_offsets = self.cal['mag_offsets']
self.mag_transform = self.cal['mag_transform']
self.misalignment = self.cal['misalignment']
self.gyro_bias = self.cal['gyro_bias']
self.gyro_scale = self.cal['gyro_scale']
self.current_state = IMU.STATE_NORMAL
self.finished_validating = True
self.needs_calibration = False
msg = self.rover + ': reloaded calibration matrices after respawn.'
if self.current_mode == IMU.MODE_2D:
msg += ' Using 2D mode.'
elif self.current_mode == IMU.MODE_3D:
msg += ' Using 3D mode.'
rospy.loginfo(msg)
self.diags_log.publish(msg)
elif self.LOAD_RAW_DATA:
self.load_and_validate_calibration()
# Publish current calibration once:
self.publish_diagnostic_msg()
def _set_mode(self, mode):
"""Sets the IMU mode to mode and puts it onto the parameter server.
Useful if node respawns, so it knows which mode (2D/3D) it was in."""
self.current_mode = mode
rospy.set_param('~imu_mode', mode)
def _get_mode(self):
"""Gets the IMU mode from the parameter server. Useful if node
respawns, so it knows which mode (2D/3D) it was in."""
self.current_mode = rospy.get_param('~imu_mode', default=IMU.MODE_3D)
def _is_finished_validating(self, req):
"""Service to allow Swarmie API to wait until extended calibration file
has been loaded and validated."""
response = QueryCalibrationStateResponse()
response.is_calibrated = self.finished_validating
return response
def _needs_calibration(self, req):
"""Service to allow Swarmie API to ask if the IMU needs to be
calibrated using the 2D fallback."""
response = QueryCalibrationStateResponse()
response.is_calibrated = self.needs_calibration
return response
def load_and_validate_calibration(self):
"""Load the extended calibration file.
Raises:
* IOError if calibration file can't be found.
* ValueError if calibration file is corrupt.
"""
try:
data = numpy.loadtxt(self.RAW_DATA_PATH, delimiter=',')
mag_x = data[:,0]
mag_y = data[:,1]
mag_z = data[:,2]
acc_x = data[:,3]
acc_y = data[:,4]
acc_z = data[:,5]
self.cal['mag_offsets'], self.cal['mag_transform'] = \
self.ellipsoid_fit(mag_x, mag_y, mag_z)
self.cal['acc_offsets'], self.cal['acc_transform'] = \
self.ellipsoid_fit(acc_x, acc_y, acc_z)
self.cal['misalignment'] = [[1., 0, 0],
[0, 1., 0],
[0, 0, 1.]]
self.cal['gyro_bias'] = [[0], [0], [0]]
self.cal['gyro_scale'] = [[1., 0, 0],
[0, 1., 0],
[0, 0, 1.]]
rospy.loginfo(
self.rover + ': IMU raw data file loaded from ' +
self.RAW_DATA_PATH
)
except IOError as e:
msg = (self.rover +
': FATAL ERROR. Extended calibration file not found.')
rospy.logfatal(msg)
self.diags_log.publish('<font color=Red>' + msg + '</font>')
raise
except ValueError as e:
msg = (self.rover +
': FATAL ERROR. Error reading extended calibration file.')
rospy.logfatal(msg)
self.diags_log.publish('<font color=Red>' + msg + '</font>')
raise
# Calibration matrices are stored as lists and converted to numpy
# arrays when needed.
self.acc_offsets = self.cal['acc_offsets']
self.acc_transform = self.cal['acc_transform']
self.mag_offsets = self.cal['mag_offsets']
self.mag_transform = self.cal['mag_transform']
self.misalignment = self.cal['misalignment']
self.gyro_bias = self.cal['gyro_bias']
self.gyro_scale = self.cal['gyro_scale']
# Check variance in errors
mag_var_err = self.error(mag_x, mag_y, mag_z,
self.mag_offsets, self.mag_transform)
acc_var_err = self.error(acc_x, acc_y, acc_z,
self.acc_offsets, self.acc_transform)
mag_msg = '{}: Magnetometer v[Err]: {:7.6f}'.format(self.rover,
mag_var_err)
acc_msg = '{}: Accelerometer v[Err]: {:7.6f}'.format(self.rover,
acc_var_err)
self.diags_log.publish(mag_msg)
rospy.loginfo(mag_msg)
self.diags_log.publish(acc_msg)
rospy.loginfo(acc_msg)
if (math.isnan(mag_var_err) or
abs(mag_var_err) >= IMU.MAG_VAR_TOLERANCE):
msg = "{}: The magnetometer fit is too poor to use.".format(
self.rover
)
rospy.logwarn(msg)
self.diags_log.publish('<font color=Red>' + msg + '</font>')
self.needs_calibration = True
self._set_mode(IMU.MODE_2D)
if (math.isnan(acc_var_err) or
abs(acc_var_err) >= IMU.ACC_VAR_TOLERANCE):
msg = "{}: The accelerometer fit is too poor to use.".format(
self.rover
)
rospy.logwarn(msg)
self.diags_log.publish('<font color=Red>' + msg + '</font>')
self.needs_calibration = True
self._set_mode(IMU.MODE_2D)
# Check roll and pitch
self.current_state = IMU.STATE_VALIDATE
try:
rospy.wait_for_message(
self.rover + '/imu/raw',
SwarmieIMU,
timeout=5
)
except rospy.ROSException:
# hopefully this doesn't happen
pass
# wait for 2 seconds for messages to come in and populate
# self.rolls and self.pitches
rospy.sleep(2)
avg_roll = numpy.average(self.rolls) * 180 / math.pi
avg_pitch = numpy.average(self.pitches) * 180 / math.pi
self.diags_log.publish('{}: Average roll: {:6.3f} deg'.format(
self.rover,
avg_roll)
)
self.diags_log.publish('{}: Average pitch: {:6.3f} deg'.format(
self.rover,
avg_pitch)
)
if abs(avg_roll) > IMU.ROLL_PITCH_TOLERANCE:
msg = '{}: Roll exceeds tolerance threshold of {:.1f} deg.'.format(
self.rover,
IMU.ROLL_PITCH_TOLERANCE
)
rospy.logwarn(msg)
self.diags_log.publish('<font color=Red>' + msg + '</font>')
self.needs_calibration = True
self._set_mode(IMU.MODE_2D)
if abs(avg_pitch) > IMU.ROLL_PITCH_TOLERANCE:
msg = '{}: Pitch exceeds tolerance threshold of {:.1f} deg.'.format(
self.rover,
IMU.ROLL_PITCH_TOLERANCE
)
rospy.logwarn(msg)
self.diags_log.publish('<font color=Red>' + msg + '</font>')
self.needs_calibration = True
self._set_mode(IMU.MODE_2D)
self.finished_validating = True
self.store_calibration(EmptyRequest())
self.current_state = IMU.STATE_NORMAL
def error(self, x, y, z, offsets, transform):
"""Compute the variance of errors of data in numpy arrays x,
y, z. Errors are the distances of the calibrated points from the
surface of the unit sphere.
"""
v = numpy.array([x, y, z])
offsets = numpy.array(offsets)
transform = numpy.array(transform)
v = transform.dot(v - offsets)
var_err = numpy.var(numpy.sqrt(numpy.sum(numpy.square(v), 0)) - 1)
return var_err
def ellipsoid_fit(self, x, y, z):
"""Fit the data points contained in numpy arrays x, y and z to a unit
sphere centered at the origin.
Returns a list containing the offset matrix to center the data, and
a list containing the transformation matrix, to map each data point to
its position on the sphere.
Modified from:
http://www.mathworks.com/matlabcentral/fileexchange/24693-ellipsoid-fit
"""
D = numpy.array([x*x,
y*y,
z*z,
2 * x*y,
2 * x*z,
2 * y*z,
2 * x,
2 * y,
2 * z])
DT = D.conj().T
v = numpy.linalg.solve(D.dot(DT), D.dot(numpy.ones(numpy.size(x))))
A = numpy.array([[v[0], v[3], v[4], v[6]],
[v[3], v[1], v[5], v[7]],
[v[4], v[5], v[2], v[8]],
[v[6], v[7], v[8], -1]])
center = numpy.linalg.solve(-A[:3,:3], [[v[6]], [v[7]], [v[8]]])
T = numpy.eye(4)
T[3,:3] = center.T
R = T.dot(A).dot(T.conj().T)
evals, evecs = numpy.linalg.eig(R[:3,:3] / -R[3,3])
radii = numpy.sqrt(1. / evals)
offset = center
a, b, c = radii
D = numpy.array([[1/a, 0., 0.], [0., 1/b, 0.], [0., 0., 1/c]])
transform = evecs.dot(D).dot(evecs.T)
return offset.tolist(), transform.tolist()
def ellipse_fit(self, x, y):
"""Fits the data points in x and y to a circle centered at the x-y
origin.
http://nicky.vanforeest.com/misc/fitEllipse/fitEllipse.html
Returns 3R x 1C offset matrix and a 3x3 transformation matrix. Only the
first 2 rows and columns are calculated in the transformation matrix,
since this is only a 2-D calibration.
"""
x = x[:,numpy.newaxis]
y = y[:,numpy.newaxis]
D = numpy.hstack((x*x, x*y, y*y, x, y, numpy.ones_like(x)))
S = numpy.dot(D.T,D)
C = numpy.zeros([6,6])
C[0,2] = C[2,0] = 2; C[1,1] = -1
E, V = numpy.linalg.eig(numpy.dot(numpy.linalg.inv(S), C))
n = numpy.argmax(numpy.abs(E))
A = V[:,n]
center = self.ellipse_center(A)
beta = self.ellipse_angle_of_rotation(A)
major, minor = self.ellipse_axis_length(A)
# Singular Value Decomposition:
# commons.wikimedia.org/wiki/File:Singular-Value-Decomposition.svg
# CCW rot through beta
U = numpy.array([[math.cos(beta), -math.sin(beta)],
[math.sin(beta), math.cos(beta)]])
phi = math.tan(beta) + 1
alpha = math.atan(phi)
# CW rot through alpha
V_star = numpy.array([[math.cos(alpha), math.sin(alpha)],
[-math.sin(alpha), math.cos(alpha)]])
r = math.sqrt(major * minor) # preserve approximate area
sigma = numpy.diag([r / minor, r / major])
transform = numpy.linalg.inv(U.dot(sigma).dot(V_star))
TR = numpy.eye(3)
TR[0:2, 0:2] = transform
# Append current z-mag_offset value for z-axis
center.append(self.mag_offsets[2][0])
offset = numpy.vstack(center)
return offset.tolist(), TR.tolist()
def ellipse_center(self, A):
"""Returns ellipse's center coordinates, given ellipse parameters in
A."""
b,c,d,f,g,a = A[1]/2, A[2], A[3]/2, A[4]/2, A[5], A[0]
num = b*b-a*c
x0=(c*d-b*f)/num
y0=(a*f-b*d)/num
return [x0,y0]
def ellipse_angle_of_rotation(self, A):
"""Returns ellipse's angle of rotation, given ellipse parameters in
A."""
b,c,d,f,g,a = A[1]/2, A[2], A[3]/2, A[4]/2, A[5], A[0]
if b == 0:
if a > c:
return 0
else:
return numpy.pi/2
else:
if a > c:
return numpy.arctan(2*b/(a-c))/2
else:
return numpy.pi/2 + numpy.arctan(2*b/(a-c))/2
def ellipse_axis_length(self, A):
"""Returns ellipse axes lengths, given ellipse parameters in A."""
b,c,d,f,g,a = A[1]/2, A[2], A[3]/2, A[4]/2, A[5], A[0]
up = 2*(a*f*f+c*d*d+g*b*b-2*b*d*f-a*c*g)
down1=(b*b-a*c)*((c-a)*numpy.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a))
down2=(b*b-a*c)*((a-c)*numpy.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a))
res1=numpy.sqrt(up/down1)
res2=numpy.sqrt(up/down2)
return [res1, res2]
def calc_misalignment(self, H, current_misalign):
"""Misalignment calibration.
From: https://www.pololu.com/file/0J434/LSM303DLH-compass-app-note.pdf
We will only perform calibration for the rotation around the z-axis.
Calculates compensation to align the IMU sensor axis to the rover's
body axis using numpy array, H, the data from a 2D rotation around one
axis.
"""
w = numpy.sqrt(numpy.sum(numpy.square(H), axis=1)).reshape(-1, 1)
try:
(X, residuals, rank, shape) = numpy.linalg.lstsq(H, w)
R = X / numpy.sqrt((numpy.sum(X**2)))
misalignment = numpy.array(current_misalign)
misalignment[:,2] = R.T
misalignment = misalignment.tolist()
except ValueError as e:
rospy.logwarn("Misalignment data can't be fit yet.")
# Z-position of column-z in misalignment matrix should be positive.
# It's calculated as a negative value because spinning the rover in
# place on level ground actually is a z-up rotation, and the
# calibration calculation assumes a z-down rotation, so the sign
# gets reversed.
misalignment[2][2] = abs(misalignment[2][2])
return misalignment
def compute_calibrated_data(self, x, y, z, offset, transform,
use_misalignment=True):
"""Map the raw x, y, z accelerometer or magnetometer vector onto the
calibrated unit sphere. Skips misalignment transformation if we are in
the misalignment calibration state.
"""
v = numpy.array([[x],
[y],
[z]])
offset = numpy.array(offset)
# Misalignment calibration needs to get only hard-iron and soft-iron
# calibrated data.
if self.current_state == IMU.STATE_CAL_MISALIGN or use_misalignment is False:
M_m = numpy.eye(3)
else:
M_m = numpy.array(self.misalignment)
transform = | numpy.array(transform) | numpy.array |
"""
Utilities for regridding with Meshes
"""
import sys
try:
import numpy as np
except:
raise ImportError('The Numpy library cannot be found!')
try:
import ESMF
except:
raise ImportError('The ESMF library cannot be found!')
def mesh_create_5_pentahexa(coord_sys=None):
'''
PRECONDITIONS: None
POSTCONDITIONS: A 5 element Mesh has been created.
RETURN VALUES: \n Mesh :: mesh \n
2.5 8 10 --------11
/ \ / |
2.1 7 9 12
| | 5 /
| 4 | /
| | /
1.0 4 ------- 5 ------- 6
| | \ 3 |
| 1 | \ |
| | 2 \ |
-0.1 1 ------- 2 ------- 3
-0.1 1.0 2.1 2.5
Node Ids at corners
Element Ids in centers
Note: This mesh is not parallel, it can only be used in serial
'''
# Two parametric dimensions, and two spatial dimensions
mesh = ESMF.Mesh(parametric_dim=2, spatial_dim=2, coord_sys=coord_sys)
num_node = 12
num_elem = 5
nodeId = np.array([1,2,3,4,5,6,7,8,9,10,11,12])
nodeCoord = np.array([-0.1,-0.1, #node id 1
1.0,-0.1, #node id 2
2.1,-0.1, #node id 3
0.1, 1.0, #node id 4
1.0, 1.0, #node id 5
2.1, 1.0, #node id 6
0.1, 2.1, #node id 7
0.5, 2.5, #node id 8
1.0, 2.1, #node id 9
1.5, 2.5, #node id 10
2.5, 2.5, #node id 11
2.5, 2.1]) #node id 12
nodeOwner = np.zeros(num_node)
elemId = np.array([1,2,3,4,5])
elemType=np.array([ESMF.MeshElemType.QUAD,
ESMF.MeshElemType.TRI,
ESMF.MeshElemType.TRI, 5, 6])
# I believe python connections are 0-based
# elemConn=np.array([1,2,5,4, # elem id 1
# 2,3,5, # elem id 2
# 3,6,5, # elem id 3
# 4,5,9,8,7, # elem id 4
# 5,6,12,11,10,9]) # elem id 5
elemConn=np.array([0,1,4,3, # elem id 1
1,2,4, # elem id 2
2,5,4, # elem id 3
3,4,8,7,6, # elem id 4
4,5,11,10,9,8]) # elem id 5
mesh.add_nodes(num_node,nodeId,nodeCoord,nodeOwner)
mesh.add_elements(num_elem,elemId,elemType,elemConn)
return mesh, nodeCoord, nodeOwner, elemType, elemConn
def mesh_create_4_ngons():
'''
PRECONDITIONS: None
POSTCONDITIONS: A 4 element Mesh has been created.
RETURN VALUES: \n Mesh :: mesh \n
2.25 6 ------ 7 ----- 8 ------ 9
| \ / |
| \ 4 / |
| \ / |
| \ / |
1.00 | 5 |
| / \ |
| 1 / 2 \ 3 |
| / \ |
0.25 1 ------ 2 ----- 3 ------ 4
0.25 0.75 1.0 1.25 1.75
Node Ids at corners
Element Ids in centers
Note: This mesh is not parallel, it can only be used in serial
'''
# Two parametric dimensions, and two spatial dimensions
mesh = ESMF.Mesh(parametric_dim=2, spatial_dim=2)
num_node = 9
num_elem = 4
nodeId = np.array([1,2,3,4,5,6,7,8,9])
nodeCoord = np.array([0.25, 0.25,
0.25, 0.75,
0.25, 1.25,
0.25, 1.75,
1.0, 1.0,
2.25, 0.25,
2.25, 0.75,
2.25, 1.25,
2.25, 1.75])
nodeOwner = np.zeros(num_node)
elemId = np.array([1,2,3,4])
elemType=np.array([5,3,5,3])
elemConn=np.array([0,1,4,6,5,
1,2,4,
2,5,4,
2,3,8,7,4,
4,7,6])
mesh.add_nodes(num_node,nodeId,nodeCoord,nodeOwner)
mesh.add_elements(num_elem,elemId,elemType,elemConn)
return mesh, nodeCoord, nodeOwner, elemType, elemConn
def mesh_create_5():
'''
PRECONDITIONS: None
POSTCONDITIONS: A 5 element Mesh has been created.
RETURN VALUES: \n Mesh :: mesh \n
4.0 31 ------ 32 ------ 33
| | 22 / |
| 21 | / |
| | / 23 |
2.0 21 ------ 22 ------ 23
| | |
| 11 | 12 |
| | |
0.0 11 ------ 12 ------ 13
0.0 2.0 4.0
Node Ids at corners
Element Ids in centers
Note: This mesh is not parallel, it can only be used in serial
'''
# Two parametric dimensions, and two spatial dimensions
mesh = ESMF.Mesh(parametric_dim=2, spatial_dim=2)
num_node = 9
num_elem = 5
nodeId = np.array([11,12,13,21,22,23,31,32,33])
nodeCoord = np.array([0.0,0.0, # node 11
2.0,0.0, # node 12
4.0,0.0, # node 13
0.0,2.0, # node 21
2.0,2.0, # node 22
4.0,2.0, # node 23
0.0,4.0, # node 31
2.0,4.0, # node 32
4.0,4.0]) # node 33
nodeOwner = np.zeros(num_node)
elemId = np.array([11,12,21,22,23])
elemType=np.array([ESMF.MeshElemType.QUAD,
ESMF.MeshElemType.QUAD,
ESMF.MeshElemType.QUAD,
ESMF.MeshElemType.TRI,
ESMF.MeshElemType.TRI])
elemConn=np.array([0,1,4,3, # element 11
1,2,5,4, # element 12
3,4,7,6, # element 21
4,8,7, # element 22
4,5,8]) # element 23
elemCoord = np.array([1.0, 1.0,
3.0, 1.0,
1.0, 3.0,
2.5, 3.5,
3.5, 2.5])
mesh.add_nodes(num_node,nodeId,nodeCoord,nodeOwner)
mesh.add_elements(num_elem,elemId,elemType,elemConn, element_coords=elemCoord)
return mesh, nodeCoord, nodeOwner, elemType, elemConn, elemCoord
def mesh_create_10():
'''
PRECONDITIONS: None
POSTCONDITIONS: A 10 element Mesh has been created.
RETURN VALUES: \n Mesh :: mesh \n
4.0 41 ------ 42 ------- 43 ------ 44
| | | 33 / |
| 31 | 32 | / |
| | | / 34 |
2.5 31 ------ 32 ------- 33 ------ 34
| | | |
| 21 | 22 | 23 |
| | | |
1.5 21 ------ 22 ------- 23 ------ 24
| | | |
| 11 | 12 | 13 |
| | | |
0.0 11 ------ 12 ------- 13 ------ 14
0.0 1.5 2.5 4.0
Node Ids at corners
Element Ids in centers
Note: This mesh is not parallel, it can only be used in serial
'''
# Two parametric dimensions, and two spatial dimensions
mesh = ESMF.Mesh(parametric_dim=2, spatial_dim=2)
num_node = 16
num_elem = 10
nodeId = np.array([11,12,13,14,21,22,23,24,31,32,33,34,41,42,43,44])
nodeCoord = np.array([0.0,0.0, 1.5,0.0, 2.5,0.0, 4.0,0.0,
0.0,1.5, 1.5,1.5, 2.5,1.5, 4.0,1.5,
0.0,2.5, 1.5,2.5, 2.5,2.5, 4.0,2.5,
0.0,4.0, 1.5,4.0, 2.5,4.0, 4.0,4.0])
nodeOwner = np.zeros(num_node)
elemId = np.array([11,12,13,21,22,23,31,32,33,34])
elemType=np.array([ESMF.MeshElemType.QUAD,
ESMF.MeshElemType.QUAD,
ESMF.MeshElemType.QUAD,
ESMF.MeshElemType.QUAD,
ESMF.MeshElemType.QUAD,
ESMF.MeshElemType.QUAD,
ESMF.MeshElemType.QUAD,
ESMF.MeshElemType.QUAD,
ESMF.MeshElemType.TRI,
ESMF.MeshElemType.TRI])
elemConn = np.array([0,1,5,4,
1,2,6,5,
2,3,7,6,
4,5,9,8,
5,6,10,9,
6,7,11,10,
8,9,13,12,
9,10,14,13,
10,15,14,
10,11,15])
elemCoord = np.array([0.75, 0.75, 2.0, 0.75, 3.25, 0.75,
0.75, 2.0, 2.0, 2.0, 3.25, 2.0,
0.75, 3.25, 2.0, 3.25, 3.0, 3.5, 3.5, 3.0])
mesh.add_nodes(num_node,nodeId,nodeCoord,nodeOwner)
mesh.add_elements(num_elem,elemId,elemType,elemConn, element_coords=elemCoord)
return mesh, nodeCoord, nodeOwner, elemType, elemConn, elemCoord
def mesh_create_50(domask=False, doarea=False):
'''
PRECONDITIONS: None
POSTCONDITIONS: A 50 element Mesh has been created.
RETURN VALUES: \n Mesh :: mesh \n
3.75 81 ------ 82 ----- 83 ------ 84 ------ 85 ------ 86 ------ 87 ------ 88
| | | | | | | 77 / |
| 71 | 72 | 73 | 74 | 75 | 76 | / |
| | | | | | | / 78 |
3.25 71 ------ 72 ----- 73 ------ 74 ------ 75 ------ 76 ------ 77 ------ 78
| | | | | | | |
| 61 | 62 | 63 | 64 | 65 | 66 | 67 |
| | | | | | | |
2.75 61 ------ 62 ----- 63 ------ 64 ------ 65 ------ 66 ------ 67 ------ 68
| | | | | | | |
| 51 | 52 | 53 | 54 | 55 | 56 | 57 |
| | | | | | | |
2.25 51 ------ 52 ----- 53 ------ 54 ------ 55 ------ 56 ------ 57 ------ 58
| | | | | | | |
| 41 | 42 | 43 | 44 | 45 | 46 | 47 |
| | | | | | | |
1.75 41 ------ 42 ----- 43 ------ 44 ------ 45 ------ 46 ------ 47 ------ 48
| | | | | | | |
| 31 | 32 | 33 | 34 | 35 | 36 | 37 |
| | | | | | | |
1.25 31 ------ 32 ----- 33 ------ 34 ------ 35 ------ 36 ------ 37 ------ 38
| | | | | | | |
| 21 | 22 | 23 | 24 | 25 | 26 | 27 |
| | | | | | | |
0.75 21 ------ 22 ----- 23 ------ 24 ------ 25 ------ 26 ------ 27 ------ 28
| | | | | | | |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| | | | | | | |
0.25 11 ------ 12 ----- 13 ------ 14 ------ 15 ------ 16 ------ 17 ------ 18
0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75
Node Ids at corners
Element Ids in centers
Note: This mesh is not parallel, it can only be used in serial
'''
# Two parametric dimensions, and two spatial dimensions
mesh = ESMF.Mesh(parametric_dim=2, spatial_dim=2)
num_node = 64
num_elem = 50
nodeId = np.array([11,12,13,14,15,16,17,18,
21,22,23,24,25,26,27,28,
31,32,33,34,35,36,37,38,
41,42,43,44,45,46,47,48,
51,52,53,54,55,56,57,58,
61,62,63,64,65,66,67,68,
71,72,73,74,75,76,77,78,
81,82,83,84,85,86,87,88])
nodeCoord = np.array([0.25,0.25, 0.25,0.75, 0.25,1.25, 0.25,1.75, 0.25,2.25, 0.25,2.75, 0.25,3.25, 0.25,3.75,
0.75,0.25, 0.75,0.75, 0.75,1.25, 0.75,1.75, 0.75,2.25, 0.75,2.75, 0.75,3.25, 0.75,3.75,
1.25,0.25, 1.25,0.75, 1.25,1.25, 1.25,1.75, 1.25,2.25, 1.25,2.75, 1.25,3.25, 1.25,3.75,
1.75,0.25, 1.75,0.75, 1.75,1.25, 1.75,1.75, 1.75,2.25, 1.75,2.75, 1.75,3.25, 1.75,3.75,
2.25,0.25, 2.25,0.75, 2.25,1.25, 2.25,1.75, 2.25,2.25, 2.25,2.75, 2.25,3.25, 2.25,3.75,
2.75,0.25, 2.75,0.75, 2.75,1.25, 2.75,1.75, 2.75,2.25, 2.75,2.75, 2.75,3.25, 2.75,3.75,
3.25,0.25, 3.25,0.75, 3.25,1.25, 3.25,1.75, 3.25,2.25, 3.25,2.75, 3.25,3.25, 3.25,3.75,
3.75,0.25, 3.75,0.75, 3.75,1.25, 3.75,1.75, 3.75,2.25, 3.75,2.75, 3.75,3.25, 3.75,3.75])
nodeOwner = np.zeros(num_node)
elemId = np.array([11,12,13,14,15,16,17,
21,22,23,24,25,26,27,
31,32,33,34,35,36,37,
41,42,43,44,45,46,47,
51,52,53,54,55,56,57,
61,62,63,64,65,66,67,
71,72,73,74,75,76,77,78])
elemType = np.ones(num_elem-2)*ESMF.MeshElemType.QUAD
elemType = np.append(elemType, [ESMF.MeshElemType.TRI, ESMF.MeshElemType.TRI])
elemConn = np.array([11,12,22,21,12,13,23,22,13,14,24,23,14,15,25,24,15,16,26,25,16,17,27,26,17,18,28,27,
21,22,32,31,22,23,33,32,23,24,34,33,24,25,35,34,25,26,36,35,26,27,37,36,27,28,38,37,
31,32,42,41,32,33,43,42,33,34,44,43,34,35,45,44,35,36,46,45,36,37,47,46,37,38,48,47,
41,42,52,51,42,43,53,52,43,44,54,53,44,45,55,54,45,46,56,55,46,47,57,56,47,48,58,57,
51,52,62,61,52,53,63,62,53,54,64,63,54,55,65,64,55,56,66,65,56,57,67,66,57,58,68,67,
61,62,72,71,62,63,73,72,63,64,74,73,64,65,75,74,65,66,76,75,66,67,77,76,67,68,78,77,
71,72,82,81,72,73,83,82,73,74,84,83,74,75,85,84,75,76,86,85,76,77,87,86,
77,88,87,
77,78,88])
elemConn = np.array([np.where(a==nodeId) for a in elemConn]).flatten()
elemCoord = np.array(
[0.5, 0.5, 1.0, 0.5, 1.5, 0.5, 2.0, 0.5, 2.5, 0.5, 3.0, 0.5, 3.5, 0.5,
0.5, 1.0, 1.0, 1.0, 1.5, 1.0, 2.0, 1.0, 2.5, 1.0, 3.0, 1.0, 3.5, 1.0,
0.5, 1.5, 1.0, 1.5, 1.5, 1.5, 2.0, 1.5, 2.5, 1.5, 3.0, 1.5, 3.5, 1.5,
0.5, 2.0, 1.0, 2.0, 1.5, 2.0, 2.0, 2.0, 2.5, 2.0, 3.0, 2.0, 3.5, 2.0,
0.5, 2.5, 1.0, 2.5, 1.5, 2.5, 2.0, 2.5, 2.5, 2.5, 3.0, 2.5, 3.5, 2.5,
0.5, 3.0, 1.0, 3.0, 1.5, 3.0, 2.0, 3.0, 2.5, 3.0, 3.0, 3.0, 3.5, 3.0,
0.5, 3.5, 1.0, 3.5, 1.5, 3.5, 2.0, 3.5, 2.5, 3.5, 3.0, 3.5, 3.375, 3.625, 3.625, 3.375])
elemMask = None
if domask:
elemMask = np.ones(50)
elemMask[1] = 0
elemArea = None
if doarea:
elemArea = np.ones(48)*5
elemArea = np.append(elemArea, [2.5, 2.5])
mesh.add_nodes(num_node,nodeId,nodeCoord,nodeOwner)
mesh.add_elements(num_elem,elemId,elemType,elemConn,
element_mask=elemMask, element_area=elemArea, element_coords=elemCoord)
# TODO: clean this up!
if domask and doarea:
return mesh, nodeCoord, nodeOwner, elemType, elemConn, elemMask, elemArea
elif domask and not doarea:
return mesh, nodeCoord, nodeOwner, elemType, elemConn, elemMask
elif not domask and doarea:
return mesh, nodeCoord, nodeOwner, elemType, elemConn, elemArea
else:
return mesh, nodeCoord, nodeOwner, elemType, elemConn, elemCoord
def mesh_create_50_ngons(domask=False, doarea=False):
'''
PRECONDITIONS: None
POSTCONDITIONS: A 50 element Mesh has been created.
RETURN VALUES: \n Mesh :: mesh \n
3.75 81 ------ 82 ----- 83 ------ 84 ------ 85 ------ 86 ------ 87 ------ 88
| | | | | | | |
| 71 | 72 | 73 | 74 | 75 | 76 | 77 |
| | | | | | | |
3.25 71 ------ 72 ----- 73 ------ 74 ------ 75 ------ 76 ------ 77 ------ 78
| \ / | | | | |
| \ 64 / | | | | |
| \ / | | | | |
| \ / | | | | |
3.00 | 69 | | | | |
| / \ | | | | |
| 61 / 62 \ 63 | 65 | 66 | 67 | 68 |
| / \ | | | | |
2.75 61 ------ 62 ----- 63 ------ 64 ------ 65 ------ 66 ------ 67 ------ 68
| | | | | | | |
| 51 | 52 | 53 | 54 | 55 | 56 | 57 |
| | | | | | | |
2.25 51 ------ 52 ----- 53 ------ 54 ------ 55 ------ 56 ------ 57 ------ 58
| | | | | | | |
| 41 | 42 | 43 | 44 | 45 | 46 | 47 |
| | | | | | | |
1.75 41 ------ 42 ----- 43 ------ 44 ------ 45 ------ 46 ------ 47 ------ 48
| | | | | | | |
| 31 | 32 | 33 | 34 | 35 | 36 | 37 |
| | | | | | | |
1.25 31 ------ 32 ----- 33 ------ 34 ------ 35 ------ 36 ------ 37 ------ 38
| | | | | | | |
| 21 | 22 | 23 | 24 | 25 | 26 | 27 |
| | | | | | | |
0.75 21 ------ 22 ----- 23 ------ 24 ------ 25 ------ 26 ------ 27 ------ 28
| | | | | | | |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| | | | | | | |
0.25 11 ------ 12 ----- 13 ------ 14 ------ 15 ------ 16 ------ 17 ------ 18
0.25 0.75 1.0 1.25 1.75 2.25 2.75 3.25 3.75
Node Ids at corners
Element Ids in centers
Note: This mesh is not parallel, it can only be used in serial
'''
# Two parametric dimensions, and two spatial dimensions
mesh = ESMF.Mesh(parametric_dim=2, spatial_dim=2)
num_node = 65
num_elem = 50
nodeId = np.array([11,12,13,14,15,16,17,18,
21,22,23,24,25,26,27,28,
31,32,33,34,35,36,37,38,
41,42,43,44,45,46,47,48,
51,52,53,54,55,56,57,58,
61,62,63,64,65,66,67,68,69,
71,72,73,74,75,76,77,78,
81,82,83,84,85,86,87,88])
nodeCoord = np.array([0.25,0.25, 0.75,0.25, 1.25,0.25, 1.75,0.25, 2.25,0.25, 2.75,0.25, 3.25,0.25, 3.75,0.25,
0.25,0.75, 0.75,0.75, 1.25,0.75, 1.75,0.75, 2.25,0.75, 2.75,0.75, 3.25,0.75, 3.75,0.75,
0.25,1.25, 0.75,1.25, 1.25,1.25, 1.75,1.25, 2.25,1.25, 2.75,1.25, 3.25,1.25, 3.75,1.25,
0.25,1.75, 0.75,1.75, 1.25,1.75, 1.75,1.75, 2.25,1.75, 2.75,1.75, 3.25,1.75, 3.75,1.75,
0.25,2.25, 0.75,2.25, 1.25,2.25, 1.75,2.25, 2.25,2.25, 2.75,2.25, 3.25,2.25, 3.75,2.25,
0.25,2.75, 0.75,2.75, 1.25,2.75, 1.75,2.75, 2.25,2.75, 2.75,2.75, 3.25,2.75, 3.75,2.75, 1.0,3.0,
0.25,3.25, 0.75,3.25, 1.25,3.25, 1.75,3.25, 2.25,3.25, 2.75,3.25, 3.25,3.25, 3.75,3.25,
0.25,3.75, 0.75,3.75, 1.25,3.75, 1.75,3.75, 2.25,3.75, 2.75,3.75, 3.25,3.75, 3.75,3.75,])
nodeOwner = np.zeros(num_node)
elemId = np.array([11,12,13,14,15,16,17,
21,22,23,24,25,26,27,
31,32,33,34,35,36,37,
41,42,43,44,45,46,47,
51,52,53,54,55,56,57,
61,62,63,64,65,66,67,68,
71,72,73,74,75,76,77])
elemType = np.ones(num_elem)*ESMF.MeshElemType.QUAD
elemType[35] = 5
elemType[36] = ESMF.MeshElemType.TRI
elemType[37] = 5
elemType[38] = ESMF.MeshElemType.TRI
elemConn = np.array([11,12,22,21,12,13,23,22,13,14,24,23,14,15,25,24,15,16,26,25,16,17,27,26,17,18,28,27,
21,22,32,31,22,23,33,32,23,24,34,33,24,25,35,34,25,26,36,35,26,27,37,36,27,28,38,37,
31,32,42,41,32,33,43,42,33,34,44,43,34,35,45,44,35,36,46,45,36,37,47,46,37,38,48,47,
41,42,52,51,42,43,53,52,43,44,54,53,44,45,55,54,45,46,56,55,46,47,57,56,47,48,58,57,
51,52,62,61,52,53,63,62,53,54,64,63,54,55,65,64,55,56,66,65,56,57,67,66,57,58,68,67,
61, 62, 69, 72, 71, 62, 63, 69, 63, 64, 74, 73, 69, 69, 73, 72, 64, 65, 75, 74, 65, 66, 76, 75,
66, 67, 77, 76, 67, 68, 78, 77,
71,72,82,81,72,73,83,82,73,74,84,83,74,75,85,84,75,76,86,85,76,77,87,86,77,78,88,87])
elemConn = np.array([np.where(a==nodeId) for a in elemConn]).flatten()
# TODO: element coordinates is not supported for meshes containing ngons
elemCoord = np.array(
[0.5, 0.5, 1.0, 0.5, 1.5, 0.5, 2.0, 0.5, 2.5, 0.5, 3.0, 0.5, 3.5, 0.5,
0.5, 1.0, 1.0, 1.0, 1.5, 1.0, 2.0, 1.0, 2.5, 1.0, 3.0, 1.0, 3.5, 1.0,
0.5, 1.5, 1.0, 1.5, 1.5, 1.5, 2.0, 1.5, 2.5, 1.5, 3.0, 1.5, 3.5, 1.5,
0.5, 2.0, 1.0, 2.0, 1.5, 2.0, 2.0, 2.0, 2.5, 2.0, 3.0, 2.0, 3.5, 2.0,
0.5, 2.5, 1.0, 2.5, 1.5, 2.5, 2.0, 2.5, 2.5, 2.5, 3.0, 2.5, 3.5, 2.5,
0.5, 3.0, 1.0, 2.875, 1.5, 3.0, 1.0, 3.12, 2.0, 3.0, 2.5, 3.0, 3.0, 3.0, 3.5, 3.0,
0.5, 3.5, 1.0, 3.5, 1.5, 3.5, 2.0, 3.5, 2.5, 3.5, 3.0, 3.5, 3.5, 3.5])
elemMask = None
if domask:
elemMask = np.ones(num_elem)
elemMask[1] = 0
elemArea = None
if doarea:
elemArea = np.ones(num_elem)*5
elemArea[35] = 6.25
elemArea[36] = 1.25
elemArea[37] = 6.25
elemArea[38] = 1.25
mesh.add_nodes(num_node,nodeId,nodeCoord,nodeOwner)
mesh.add_elements(num_elem,elemId,elemType,elemConn, element_area=elemArea, element_mask=elemMask)
if domask and doarea:
return mesh, nodeCoord, nodeOwner, elemType, elemConn, elemMask, elemArea
elif domask and not doarea:
return mesh, nodeCoord, nodeOwner, elemType, elemConn, elemMask
elif not domask and doarea:
return mesh, nodeCoord, nodeOwner, elemType, elemConn, elemArea
else:
return mesh, nodeCoord, nodeOwner, elemType, elemConn
def mesh_create_4_ngons(domask=False, doarea=False):
'''
PRECONDITIONS: None
POSTCONDITIONS: A 4 element Mesh has been created.
RETURN VALUES: \n Mesh :: mesh \n
3.25 71 ------ 72 ----- 73 ------ 74
| \ / |
| \ 64 / |
| \ / |
| \ / |
3.00 | 69 |
| / \ |
| 61 / 62 \ 63 |
| / \ |
2.75 61 ------ 62 ----- 63 ------ 64
0.25 0.75 1.0 1.25 1.75
Node Ids at corners
Element Ids in centers
Note: This mesh is not parallel, it can only be used in serial
'''
# Two parametric dimensions, and two spatial dimensions
mesh = ESMF.Mesh(parametric_dim=2, spatial_dim=2)
num_node = 9
num_elem = 4
nodeId = np.array([61,62,63,64,69,71,72,73,74,])
nodeCoord = np.array([0.25,2.75, 0.75,2.75, 1.25,2.75, 1.75,2.75,
1.,3.,
0.25, 3.25, 0.75, 3.25, 1.25, 3.25, 1.75, 3.25])
nodeOwner = np.zeros(num_node)
elemId = np.array([61,62,63,64])
elemType = np.ones(num_elem)
elemType[0] = 5
elemType[1] = ESMF.MeshElemType.TRI
elemType[2] = 5
elemType[3] = ESMF.MeshElemType.TRI
elemConn = np.array([61, 62, 69, 72, 71, 62, 63, 69, 63, 64, 74, 73, 69, 69, 73, 72])
elemConn = np.array([np.where(a==nodeId) for a in elemConn]).flatten()
elemMask = None
if domask:
elemMask = np.ones(num_elem)
elemMask[1] = 0
elemArea = None
if doarea:
elemArea = np.ones(num_elem)*5
elemArea[35] = 6.25
elemArea[36] = 1.25
elemArea[37] = 6.25
elemArea[42] = 1.25
mesh.add_nodes(num_node,nodeId,nodeCoord,nodeOwner)
mesh.add_elements(num_elem,elemId,elemType,elemConn,
element_mask=elemMask, element_area=elemArea)
if domask and doarea:
return mesh, nodeCoord, nodeOwner, elemType, elemConn, elemMask, elemArea
elif domask and not doarea:
return mesh, nodeCoord, nodeOwner, elemType, elemConn, elemMask
elif not domask and doarea:
return mesh, nodeCoord, nodeOwner, elemType, elemConn, elemArea
else:
return mesh, nodeCoord, nodeOwner, elemType, elemConn
def mesh_create_5_parallel ():
'''
PRECONDITIONS: None
POSTCONDITIONS: A 5 element Mesh has been created in parallel.
RETURN VALUES: \n Mesh :: mesh \n
# 4.0 31 ------ 32 [32] ----- 33
# | | | 22 / |
# | 21 | | / |
# | | | / 23 |
# 2.0 [21] ---- [22] [22] ---- [23]
#
# 0.0 2.0 2.0 4.0
#
# PET 2 PET 3
#
#
# 2.0 21 ------ 22 [22] ----- 23
# | | | |
# | 11 | | 12 |
# | | | |
# 0.0 11 ------ 12 [12] ----- 13
#
# 0.0 2.0 2.0 4.0
#
# PET 0 PET 1
#
# Node Id labels at corners
# Element Id labels in centers
'''
# Two parametric dimensions, and two spatial dimensions
mesh = ESMF.Mesh(parametric_dim=2, spatial_dim=2)
if ESMF.pet_count() > 1:
if ESMF.pet_count() != 4:
raise NameError('MPI rank must be 4 to build this mesh!')
if (ESMF.local_pet() == 0):
num_node=4
num_elem=1
nodeId=np.array([11,12,21,22])
nodeCoord=np.array([0.0,0.0,
2.0,0.0,
0.0,2.0,
2.0,2.0 ])
nodeOwner=np.zeros(num_node)
elemId=np.array([11])
elemType=np.array([ESMF.MeshElemType.QUAD])
elemConn=np.array([0,1,3,2])
elif (ESMF.local_pet() == 1):
num_node=4
num_elem=1
nodeId=np.array([12,13,22,23])
nodeCoord=np.array([2.0,0.0,
4.0,0.0,
2.0,2.0,
4.0,2.0 ])
nodeOwner=np.array([0,
1,
0,
1])
elemId=np.array([12])
elemType=np.array([ESMF.MeshElemType.QUAD])
elemConn=np.array([0,1,3,2])
elif (ESMF.local_pet() == 2):
num_node=4
num_elem=1
nodeId=np.array([21,22,31,32])
nodeCoord=np.array([0.0,2.0,
2.0,2.0,
0.0,4.0,
2.0,4.0 ])
nodeOwner=np.array([0,
0,
2,
2])
elemId=np.array([21])
elemType=np.array([ESMF.MeshElemType.QUAD])
elemConn=np.array([0,1,3,2])
elif (ESMF.local_pet() == 3):
num_node=4
num_elem=2
nodeId=np.array([22,23,32,33])
nodeCoord=np.array([2.0,2.0,
4.0,2.0,
2.0,4.0,
4.0,4.0 ])
nodeOwner=np.array([0,
1,
2,
3])
elemId=np.array([22,23])
elemType=np.array([ESMF.MeshElemType.TRI,
ESMF.MeshElemType.TRI])
elemConn=np.array([0,3,2,
0,1,3])
# Add nodes and elements to the Mesh
mesh.add_nodes(num_node,nodeId,nodeCoord,nodeOwner)
mesh.add_elements(num_elem,elemId,elemType,elemConn)
return mesh, nodeCoord, nodeOwner, elemType, elemConn
def mesh_create_5_pentahexa_parallel ():
'''
PRECONDITIONS: None
POSTCONDITIONS: A 5 element Mesh has been created in parallel.
RETURN VALUES: \n Mesh :: mesh \n
# 2.1 8 10 --------11
# / \ / |
# 7 9 [9] 12
# | | | 5 /
# | 4 | | /
# | | | /
# 1.0 [4] ----- [5] [5] ----- [6]
#
# -0.1 1.0 1.0 2.1 2.5
#
# PET 2 PET 3
#
#
# 1.0 4 ------- 5 [5] ------- 6
# | | | \ 3 |
# | 1 | | \ |
# | | | 2 \ |
# -0.1 1 ------- 2 [2] ------- 3
#
# -0.1 1.0 1.0 2.1 2.5
#
# PET 0 PET 1
#
# Node Id labels at corners
# Element Id labels in centers
'''
# Two parametric dimensions, and two spatial dimensions
mesh = ESMF.Mesh(parametric_dim=2, spatial_dim=2)
if ESMF.pet_count() > 1:
if ESMF.pet_count() != 4:
raise NameError('MPI rank must be 4 to build this mesh!')
if (ESMF.local_pet() == 0):
num_node=4
num_elem=1
nodeId=np.array([1, 2, 4, 5])
nodeCoord=np.array([-0.1, -0.1,
1.0, -0.1,
- 0.1, 1.0,
1.0, 1.0 ])
nodeOwner=np.zeros(num_node)
elemId=np.array([1])
elemType=np.array([ESMF.MeshElemType.QUAD])
elemConn=np.array([0, 1, 3, 2 ])
elif (ESMF.local_pet() == 1):
num_node=4
num_elem=2
nodeId=np.array([2, 3, 5, 6])
nodeCoord=np.array([1.0, -0.1,
2.1, -0.1,
1.0, 1.0,
2.1, 1.0 ])
nodeOwner=np.array([0,
1,
0,
1])
elemId=np.array([2, 3])
elemType=np.array([ESMF.MeshElemType.TRI, ESMF.MeshElemType.TRI])
elemConn=np.array([0, 1, 2,
1, 3, 2])
elif (ESMF.local_pet() == 2):
num_node=5
num_elem=1
nodeId=np.array([4, 5, 7, 8, 9])
nodeCoord=np.array([-0.1, 1.0,
1.0, 1.0,
-0.1, 2.1,
0.5, 2.5,
1.0, 2.1 ])
nodeOwner=np.array([0,
0,
2,
2,
2])
elemId=np.array([4])
elemType=np.array([5])
elemConn= | np.array([0, 1, 4, 3, 2]) | numpy.array |
from __future__ import print_function
import sys
import os
dir = os.path.dirname(os.path.abspath(__file__))
from FFTLog_integrals import *
import power_FFTLog as power
import numpy as np
from scipy.interpolate import interp1d
from scipy.integrate import quad
import matplotlib.pyplot as plt
import matplotlib as mpl
import matplotlib.ticker
locmin = matplotlib.ticker.LogLocator(base=10.0, subs=np.arange(2, 10) * .1, numticks=100)
def find_ind(k, P):
ipos = P >= 0.0
ineg = P < 0.0
kpos, Ppos = k[ipos], P[ipos]
kneg, Pneg = k[ineg], P[ineg]
return (kpos, Ppos, kneg, Pneg)
def plot_all():
N = 1400
nu = -0.6
with_padding = False
save_matrices = False
kw = {'N':N, 'nu':nu, 'with_padding':with_padding, 'save_matrices':save_matrices}
fft_2G22 = FFT_22(kernel='2G22', **kw)
fft_G13 = FFT_13(kernel='G13', **kw)
fft_2K22 = FFT_22(kernel='2K22', **kw)
fft_4KG22 = FFT_22(kernel='4KG22', **kw)
fft_KG13 = FFT_13(kernel='KG13', **kw)
k = np.exp(fft_2G22.lnk)
PL = fft_2G22.PL(k)
# one-loop
P13 = fft_G13.P13(k, ell=0)
P22 = fft_2G22.P22(k, ell=0)
P_1loop_corr = P22 + 2*P13
P_2K22_ell0 = fft_2K22.DelP0(k) # Note we subract out P_11 !!!
P_2K22_ell2 = fft_2K22.P22(k, ell=2)
P_2K22_ell4 = fft_2K22.P22(k, ell=4)
P_4KG22_ell0 = fft_4KG22.P22(k, ell=0)
P_4KG22_ell2 = fft_4KG22.P22(k, ell=2)
P_KG13_ell0 = fft_KG13.P13(k, ell=0)
P_KG13_ell2 = fft_KG13.P13(k, ell=2)
P_3K13_ell0 = fft_KG13.K3_ell0(k)
P_3K13_ell2 = fft_KG13.K3_ell2(k)
P_1loop = PL + P_1loop_corr # no rsd corrections
P0 = P_2K22_ell0 + P_4KG22_ell0 + P_KG13_ell0 + (P_1loop) + P_3K13_ell0
P2 = P_2K22_ell2 + P_4KG22_ell2 + P_KG13_ell2 + P_3K13_ell2
P4 = P_2K22_ell4
plt.figure(figsize=(6,6))
plt.loglog(k, P0, 'k', lw=1.1) # label=r'$\ell=0$',
# plt.loglog(k, np.abs(P2), 'b', label=r'$\ell=2$', lw=1.2)
kp, P2p, kn, P2n = find_ind(k, P2)
plt.loglog(kp, P2p, 'b', lw=1.4) # label=r'$\ell=2$',
plt.loglog(kn, np.abs(P2n), 'b--', dashes=(5,3), lw=1.4)
plt.loglog(k, P4, 'r', lw=1.4) # label=r'$\ell=4$',
plt.loglog(k, P_1loop, 'k-.', label=r'$P^{1\!-\!loop}_{\theta\theta}$', lw=1.1)
plt.loglog(k, PL, c='gray', ls=':', lw=1.4)
plt.text(x=0.0035, y=7500, s=r'$P^0_{\theta\theta}$')
plt.text(x=0.19, y=2430, s=r'$P_L$')
plt.text(x=3e-2, y=400, s=r'$P^2_{\theta\theta}$', c='b')
plt.text(x=5e-2, y=36, s=r'$P^4_{\theta\theta}$', c='r')
# plt.grid(ls=':')
plt.legend(frameon=False, loc='upper right', fontsize=16)
plt.tick_params(right=True, top=True, which='both')
# plt.xlim(1e-3,3e0)
plt.xlim(3e-3,0.3)
plt.ylim(1e1,4e4)
# plt.xticks([1e-3,1e-2,1e-1,1e0])
plt.xlabel(r'Wavenumber $k$ [h Mpc$^{-1}$]')
plt.ylabel(r'$P^\ell_{\theta\theta}(k)$ [h$^{-3}$ Mpc$^3$]')
plt.show()
def plot_ell0_compts():
N = 1400
nu = -0.6
with_padding = False
save_matrices = False
kw = {'N':N, 'nu':nu, 'with_padding':with_padding, 'save_matrices':save_matrices}
fft_2G22 = FFT_22(kernel='2G22', **kw)
fft_G13 = FFT_13(kernel='G13', **kw)
fft_2K22 = FFT_22(kernel='2K22', **kw)
fft_4KG22 = FFT_22(kernel='4KG22', **kw)
fft_KG13 = FFT_13(kernel='KG13', **kw)
k = np.exp(fft_2G22.lnk)
PL = fft_2G22.PL(k)
# one-loop
P13 = fft_G13.P13(k, ell=0)
P22 = fft_2G22.P22(k, ell=0)
P_1loop_corr = P22 + 2*P13
P_2K22_ell0 = fft_2K22.DelP0(k) # Note we subract out P_11 !!!
P_4KG22_ell0 = fft_4KG22.P22(k, ell=0)
P_KG13_ell0 = fft_KG13.P13(k, ell=0)
# the last term
P_3K13_ell0 = fft_KG13.K3_ell0(k)
P_1loop = PL + P_1loop_corr # no rsd corrections
P0 = P_2K22_ell0 + P_4KG22_ell0 + P_KG13_ell0 + (P_1loop) + P_3K13_ell0
plt.figure(figsize=(6,6))
plt.loglog(k, P0, 'k', lw=1.2)
plt.loglog(k, P_2K22_ell0, 'b', lw=1.2)
plt.loglog(k, P_4KG22_ell0, 'magenta', lw=1.2)
plt.loglog(k, np.abs(P_KG13_ell0), 'r', ls='--', dashes=(5,3), lw=1.2)
plt.loglog(k, np.abs(P_3K13_ell0), 'lime', ls='--', dashes=(5,3), lw=1.2)
plt.loglog(k, np.abs(P22+2*P13), 'turquoise', ls='--', dashes=(5,3), lw=1.2)
plt.loglog(k, PL, c='gray', ls=':', lw=1.2)
plt.text(x=0.0035, y=7500, s=r'$P^0_{\theta\theta}$')
plt.text(x=0.19, y=2430, s=r'$P_L$')
plt.text(x=0.015, y=1100, s=r'$P_{22}+2P_{13}$', c='turquoise')
plt.text(x=0.1, y=74, s=r'$K^{(2)}_S K^{(2)}_S$', c='b')
plt.text(x=0.096, y=283, s=r'$K^{(2)}_S G^{(2)}_S$ (22)', c='magenta', fontsize=13) # 0.0269
plt.text(x=0.0155, y=115, s=r'$K^{(2)}_S G^{(2)}_S$ (13)', c='r', fontsize=13) # label=r'$KG13$',
plt.text(x=0.01, y=16, s=r'$K^{(3)}_S$', c='lime') # label=r'$3K13$'
# plt.grid(ls=':')
# plt.legend(frameon=False, loc='center left', fontsize=14)
# plt.xlim(1e-3,3e0)
plt.xlim(3e-3,0.3)
plt.ylim(1e1,4e4)
plt.tick_params(right=True, top=True, which='both')
# plt.xticks([1e-3,1e-2,1e-1,1e0])
plt.xlabel(r'Wavenumber $k$ [h Mpc$^{-1}$]')
plt.ylabel(r'$P^0_{\theta\theta}(k)\,$ [h$^{-3}$ Mpc$^3$]')
plt.show()
def plot_oneloop_theta():
k, PL, P13, P22, P_1loop = power.Ptt_1loop(k=None, PL=None, get_compts=True, N=1024)
fig, ax = plt.subplots(figsize=(6,6))
ax.loglog(k, P_1loop, 'k', label=r'$P_L+P_{22}+2P_{13}$', lw=1.4)
kp, Pp, kn, Pn = find_ind(k, P22+2*P13)
ax.loglog(kp, Pp, 'b', label=r'$P_{22}+2P_{13}$', lw=1.2)
ax.loglog(kn, np.abs(Pn), 'b--', lw=1.2)
# ax.loglog(k, np.abs(P22+2*P13), 'b', label=r'$|P_{22}+2P_{13}|$', lw=1.2)
ax.loglog(k, P22, 'r', label=r'$P_{22}$', lw=1.2)
ax.loglog(k, np.abs(2*P13), 'lime', ls='--', label=r'$2P_{13}$', lw=1.2)
ax.loglog(k, PL, 'gray', ls=':', label=r'$P_L$', lw=1.4)
ax.legend(frameon=False, loc='upper right', fontsize=13)
ax.set_xlim(2e-4,1e2)
ax.set_ylim(1e0,1e5)
ax.tick_params(right=True, top=True, which='both')
ax.xaxis.set_minor_locator(locmin)
ax.xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
ax.set_xticks([1e-3,1e-2,1e-1,1e0,1e1,1e2])
ax.set_xlabel(r'Wavenumber $k$ [h Mpc$^{-1}$]')
ax.set_ylabel(r'$P_{\theta\theta}(k)$ [h$^{-3}$ Mpc$^3$]')
plt.show()
def plot_oneloop_matter():
k, PL, P13, P22, P_1loop = power.Pmm_1loop(k=None, PL=None, get_compts=True, N=1024)
fig, ax = plt.subplots(figsize=(6,6))
ax.loglog(k, P_1loop, 'k', label=r'$P_L+P_{22}+2P_{13}$', lw=1.4)
kp, Pp, kn, Pn = find_ind(k, P22+2*P13)
ax.loglog(kp, Pp, 'b', label=r'$P_{22}+2P_{13}$', lw=1.2)
ax.loglog(kn, np.abs(Pn), 'b--', lw=1.2)
ax.loglog(k, P22, 'r', label=r'$P_{22}$', lw=1.2)
ax.loglog(k, np.abs(2*P13), 'lime', ls='--', label=r'$2P_{13}$', lw=1.2)
ax.loglog(k, PL, 'gray', ls=':', label=r'$P_L$', lw=1.4)
# ax.grid(ls=':')
ax.legend(frameon=False, loc='upper right', fontsize=13)
ax.set_xlim(2e-4,1e2)
ax.set_ylim(1e0,1e5)
ax.tick_params(right=True, top=True, which='both')
ax.xaxis.set_minor_locator(locmin)
ax.xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
ax.set_xticks([1e-3,1e-2,1e-1,1e0,1e1,1e2])
ax.set_xlabel(r'Wavenumber $k$ [h Mpc$^{-1}$]')
ax.set_ylabel(r'$P_{mm}(k)$ [h$^{-3}$ Mpc$^3$]')
plt.show()
def plot_Ps_vv_with_ratio(N=512): # P(k,mu) for diff mu
H0f = 51.57 # Om^0.55=0.3^0.55=0.5157
kin, plin = np.loadtxt('Pk_Planck15_large.dat', unpack=True, skiprows=4)
F = power.Ps_tt(kin, plin, N=N)
k = F.k
mu1, mu2, mu3, mu4 = 1.0, 0.6, 0.3, 0.1
Pvv1_norsd = F.Pvv_norsd(mu1)
Pvv2_norsd = F.Pvv_norsd(mu2)
Pvv3_norsd = F.Pvv_norsd(mu3)
Pvv4_norsd = F.Pvv_norsd(mu4)
Psvv1 = F.Psvv(mu1, with_fog=False)
Psvv2 = F.Psvv(mu2, with_fog=False)
Psvv3 = F.Psvv(mu3, with_fog=False)
Psvv4 = F.Psvv(mu4, with_fog=False)
fig, ax = plt.subplots(nrows=2, sharex=True, figsize=(6,8), gridspec_kw={'height_ratios': [2.5, 1], 'hspace': 0.0})
ax[0].loglog(k, Psvv1, 'k', lw=1.2, label=r'$\mu=1.0$')
ax[0].loglog(k, Psvv2, 'b', lw=1.2, label=r'$\mu=0.6$')
ax[0].loglog(k, Psvv3, 'r', lw=1.2, label=r'$\mu=0.3$')
ax[0].loglog(k, Psvv4, 'lime', lw=1.2, label=r'$\mu=0.1$')
ax[0].loglog(k, Pvv1_norsd, 'k', ls=':', lw=1.7)
ax[0].loglog(k, Pvv2_norsd, 'b', ls=':', lw=1.7)
ax[0].loglog(k, Pvv3_norsd, 'r', ls=':', lw=1.7)
ax[0].loglog(k, Pvv4_norsd, 'lime', ls=':', lw=1.5)
ax[1].semilogx(k, Psvv1/Pvv1_norsd, 'k', lw=1.2)
ax[1].semilogx(k, Psvv2/Pvv2_norsd, 'b', lw=1.2)
ax[1].semilogx(k, Psvv3/Pvv3_norsd, 'r', lw=1.2)
ax[1].semilogx(k, Psvv4/Pvv4_norsd, 'lime', lw=1.2)
ax[0].legend(frameon=False, loc='upper right', fontsize=16)
ax[1].text(x=4e-3, y=0.4, s=r'$P^s_{vv}(k,\mu)\,/\,P_{vv,no\:RSD}(k,\mu)$', color='k', fontsize=18)
ax[1].set_yticks([0.4,0.6,0.8,1.0])
ax[0].set_xlim(3e-3,0.24)
ax[0].set_ylim(8e0*H0f**2, 2e9*H0f**2)
ax[1].set_ylim(0.3,1.05)
ax[0].tick_params(right=True, top=True, which='both')
ax[1].tick_params(right=True, top=True, which='both')
ax[1].set_xlabel(r'Wavenumber $k$ [h Mpc$^{-1}$]')
ax[0].set_ylabel(r'$P^s_{vv}(k,\mu)$ [$(km/s)^2\, (h^{-1}\, Mpc)^3$]')
ax[1].set_ylabel(r'Ratio')
ax[0].yaxis.set_minor_locator(locmin)
ax[0].yaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
plt.show()
def plot_Ps_vv_with_ratio2(N=512): # Pvv^ell
H0f = 51.57
kin, plin = np.loadtxt('Pk_Planck15_large.dat', unpack=True, skiprows=4)
F = power.Ps_tt(kin, plin, N=N)
P0vv = F.Psvv_ell(ell=0, with_fog=False)
P2vv = F.Psvv_ell(ell=2, with_fog=False)
P4vv = F.Psvv_ell(ell=4, with_fog=False)
P6vv = F.Psvv_ell(ell=6, with_fog=False)
fig, ax = plt.subplots(nrows=2, sharex=True, figsize=(6,8), gridspec_kw={'height_ratios': [2.5, 1], 'hspace': 0.0})
ax[0].loglog(F.k, P0vv, 'k', lw=1.2, label=r'$\ell=0$')
ax[0].loglog(F.k, P2vv, 'b', lw=1.2, label=r'$\ell=2$')
pos_signal = np.ma.masked_where(P4vv<=0.0, P4vv)
neg_signal = np.ma.masked_where(P4vv>0.0, P4vv)
ax[0].loglog(F.k, pos_signal, 'r', lw=1.2, label=r'$\ell=4$')
ax[0].loglog(F.k, np.abs(neg_signal), 'r--', dashes=(5,3), lw=1.2)
ax[0].loglog(F.k, P6vv, 'lime', lw=1.2, label=r'$\ell=6$')
ax[0].loglog(F.k, F.P0vv_norsd, 'k:', lw=1.7)
ax[0].loglog(F.k, F.P2vv_norsd, 'b:', lw=1.7)
ax[1].semilogx(F.k, P0vv/F.P0vv_norsd, 'k', lw=1.2, label=r'$P^0_{vv}\,/\,P^0_{vv,no\:RSD}$')
ax[1].semilogx(F.k, P2vv/F.P2vv_norsd, 'b', lw=1.2, label=r'$P^2_{vv}\,/\,P^2_{vv,no\:RSD}$')
ax[0].legend(frameon=False, loc='upper right', fontsize=18, ncol=1)
ax[1].legend(frameon=False, loc='lower left', fontsize=18, ncol=1)
ax[1].set_yticks([0.4,0.6,0.8,1.0])
ax[0].set_xlim(3e-3,0.24)
ax[0].set_ylim(8e0*H0f**2,2e9*H0f**2)
ax[1].set_ylim(0.3,1.05)
ax[0].tick_params(right=True, top=True, which='both')
ax[1].tick_params(right=True, top=True, which='both')
ax[1].set_xlabel(r'Wavenumber $k$ [h Mpc$^{-1}$]')
ax[0].set_ylabel(r'$P^\ell_{vv}(k)$ [$(km/s)^2\, (h^{-1}\, Mpc)^3$]')
ax[1].set_ylabel(r'Ratio')
ax[0].yaxis.set_minor_locator(locmin)
ax[0].yaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
plt.show()
def plot_Ps_vv_disp_with_ratio(N=512): # P(k,mu) for diff mu
H0f = 51.57 # Om^0.55=0.3^0.55=0.5157
sig_fog = 3.5
kin, plin = np.loadtxt('Pk_Planck15_large.dat', unpack=True, skiprows=4)
F = power.Ps_tt(kin, plin, sig_fog=sig_fog, N=N)
k = F.k
mu1, mu2, mu3, mu4 = 1.0, 0.6, 0.3, 0.1
Pvv1_norsd = F.Pvv_norsd(mu1)
Pvv2_norsd = F.Pvv_norsd(mu2)
Pvv3_norsd = F.Pvv_norsd(mu3)
Pvv4_norsd = F.Pvv_norsd(mu4)
Psvv1_disp = F.Psvv(mu1, with_fog=True)
Psvv2_disp = F.Psvv(mu2, with_fog=True)
Psvv3_disp = F.Psvv(mu3, with_fog=True)
Psvv4_disp = F.Psvv(mu4, with_fog=True)
fig, ax = plt.subplots(nrows=2, sharex=True, figsize=(6,8), gridspec_kw={'height_ratios': [2.5, 1], 'hspace': 0.0})
ax[0].loglog(k, Psvv1_disp, 'k', lw=1.2, label=r'$\mu=1.0$')
ax[0].loglog(k, Psvv2_disp, 'b', lw=1.2, label=r'$\mu=0.6$')
ax[0].loglog(k, Psvv3_disp, 'r', lw=1.2, label=r'$\mu=0.3$')
ax[0].loglog(k, Psvv4_disp, 'lime', lw=1.2, label=r'$\mu=0.1$')
ax[0].loglog(k, Pvv1_norsd, 'k', ls=':', lw=1.7)
ax[0].loglog(k, Pvv2_norsd, 'b', ls=':', lw=1.7)
ax[0].loglog(k, Pvv3_norsd, 'r', ls=':', lw=1.7)
ax[0].loglog(k, Pvv4_norsd, 'lime', ls=':', lw=1.5)
ax[1].semilogx(k, Psvv1_disp/Pvv1_norsd, 'k', lw=1.2)
ax[1].semilogx(k, Psvv2_disp/Pvv2_norsd, 'b', lw=1.2)
ax[1].semilogx(k, Psvv3_disp/Pvv3_norsd, 'r', lw=1.2)
ax[1].semilogx(k, Psvv4_disp/Pvv4_norsd, 'lime', lw=1.2)
# uncomment to add more clutter to the plot
# Ps1 = F.Ps(mu1) * (H0f*mu1/k)**2 # no damping
# Ps2 = F.Ps(mu2) * (H0f*mu2/k)**2
# Ps3 = F.Ps(mu3) * (H0f*mu3/k)**2
# Ps4 = F.Ps(mu4) * (H0f*mu4/k)**2
# ax[1].semilogx(k, Ps1/Pvv1_norsd, 'k:', lw=1.2)
# ax[1].semilogx(k, Ps2/Pvv2_norsd, 'b:', lw=1.2)
# ax[1].semilogx(k, Ps3/Pvv3_norsd, 'r:', lw=1.2)
# ax[1].semilogx(k, Ps4/Pvv4_norsd, 'lime', ls=':', lw=1.2)
ax[0].legend(frameon=False, loc='upper right', fontsize=16)
ax[1].text(x=4e-3, y=0.4, s=r'$P^s_{vv}(k,\mu)\,/\,P_{vv,no\:RSD}(k,\mu)$', color='k', fontsize=18)
ax[1].set_yticks([0.4,0.6,0.8,1.0])
ax[0].set_xlim(3e-3,0.24)
ax[0].set_ylim(8e0*H0f**2,2e9*H0f**2)
ax[1].set_ylim(0.3,1.05)
ax[0].tick_params(right=True, top=True, which='both')
ax[1].tick_params(right=True, top=True, which='both')
ax[1].set_xlabel(r'Wavenumber $k$ [h Mpc$^{-1}$]')
ax[0].set_ylabel(r'$P^s_{vv}(k,\mu)$ [$(km/s)^2\, (h^{-1}\, Mpc)^3$]')
ax[1].set_ylabel(r'Ratio')
ax[0].yaxis.set_minor_locator(locmin)
ax[0].yaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
plt.show()
def plot_Ps_vv_disp_with_ratio2(N=512): # Puu^ell for ell=0,2
H0f = 51.57 # Om^0.55=0.3^0.55=0.5157
sig_fog = 3.5 # 6.a
kin, plin = np.loadtxt('Pk_Planck15_large.dat', unpack=True, skiprows=4)
F = power.Ps_tt(kin, plin, sig_fog=sig_fog, N=N)
P0vv_disp = F.Psvv_ell(ell=0, with_fog=True)
P2vv_disp = F.Psvv_ell(ell=2, with_fog=True)
P4vv_disp = F.Psvv_ell(ell=4, with_fog=True)
P6vv_disp = F.Psvv_ell(ell=6, with_fog=True)
P8vv_disp = F.Psvv_ell(ell=8, with_fog=True)
P10vv_disp = F.Psvv_ell(ell=10, with_fog=True)
P0vv = F.Psvv_ell(ell=0, with_fog=False)
P2vv = F.Psvv_ell(ell=2, with_fog=False)
fig, ax = plt.subplots(nrows=2, sharex=True, figsize=(6,8), gridspec_kw={'height_ratios': [2.5, 1], 'hspace': 0.0})
ax[0].loglog(F.k, P0vv_disp, 'k', lw=1.2, label=r'$\ell=0$')
ax[0].loglog(F.k, P2vv_disp, 'b', lw=1.2, label=r'$\ell=2$')
pos_signal = np.ma.masked_where(P4vv_disp<=0.0, P4vv_disp)
neg_signal = np.ma.masked_where(P4vv_disp>0.0, P4vv_disp)
ax[0].loglog(F.k, pos_signal, 'r', lw=1.2, label=r'$\ell=4$')
ax[0].loglog(F.k, np.abs(neg_signal), 'r--', dashes=(5,3), lw=1.2)
ax[0].loglog(F.k, P6vv_disp, 'lime', lw=1.2, label=r'$\ell=6$')
pos_signal = np.ma.masked_where(P8vv_disp<=0.0, P8vv_disp)
neg_signal = np.ma.masked_where(P8vv_disp>0.0, P8vv_disp)
ax[0].loglog(F.k, pos_signal, 'cyan', lw=1.2, label=r'$\ell=8$')
ax[0].loglog(F.k, np.abs(neg_signal), 'cyan', ls='--', dashes=(5,3), lw=1.2)
pos_signal = np.ma.masked_where(P10vv_disp<=0.0, P10vv_disp)
neg_signal = np.ma.masked_where(P10vv_disp>0.0, P10vv_disp)
ax[0].loglog(F.k, pos_signal, 'magenta', lw=1.2, label=r'$\ell=10$')
ax[0].loglog(F.k, np.abs(neg_signal), 'magenta', ls='--', dashes=(5,3), lw=1.2)
ax[0].loglog(F.k, F.P0vv_norsd, 'k:', lw=1.7)
ax[0].loglog(F.k, F.P2vv_norsd, 'b:', lw=1.7)
ax[1].semilogx(F.k, P0vv_disp/F.P0vv_norsd, 'k', lw=1.2, label=r'$P^0_{vv}\,/\,P^0_{vv,no\:RSD}$')
ax[1].semilogx(F.k, P2vv_disp/F.P2vv_norsd, 'b', lw=1.2, label=r'$P^2_{vv}\,/\,P^2_{vv,no\:RSD}$')
ax[1].semilogx(F.k, P0vv/F.P0vv_norsd, 'k:', lw=1.2)
ax[1].semilogx(F.k, P2vv/F.P2vv_norsd, 'b:', lw=1.2)
# ax[0].text(x=4e-3, y=5e4, s='with damping', color='k', fontsize=18)
ax[0].legend(frameon=False, loc='upper right', fontsize=16, ncol=2, \
columnspacing=0.8, handlelength=1.2, handletextpad=0.5)
ax[1].legend(frameon=False, loc='lower left', fontsize=18, ncol=1)
ax[1].set_yticks([0.4,0.6,0.8,1.0])
ax[0].set_xlim(3e-3,0.24)
ax[0].set_ylim(8e0*H0f**2,2e9*H0f**2)
ax[1].set_ylim(0.3,1.05)
ax[0].tick_params(right=True, top=True, which='both')
ax[1].tick_params(right=True, top=True, which='both')
ax[1].set_xlabel(r'Wavenumber $k$ [h Mpc$^{-1}$]')
ax[0].set_ylabel(r'$P^\ell_{vv}(k)$ [$(km/s)^2\, (h^{-1}\, Mpc)^3$]')
ax[1].set_ylabel(r'Ratio')
ax[0].yaxis.set_minor_locator(locmin)
ax[0].yaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())
plt.show()
# cumulant expansion model
def plot_Pvv_cumexp2(N=1024):
H0f = 100. * 0.3**0.55
kin, plin = np.loadtxt('Pk_Planck15_large.dat', unpack=True, skiprows=4)
F = power.Ps_vv_cumexp(kin, plin, N=N)
k = F.k
# A (bispectrum term = 22 + 13)
P0vv_KA = F.P0uu_KA * F.H0f**2
P2vv_KA = F.P2uu_KA * F.H0f**2
P4vv_KA = F.P4uu_KA * F.H0f**2
P6vv_KA = F.P6uu_KA * F.H0f**2
# B (pure 22 loop)
P0vv_KB = F.P0uu_KB * F.H0f**2
P2vv_KB = F.P2uu_KB * F.H0f**2
P4vv_KB = F.P4uu_KB * F.H0f**2
P6vv_KB = F.P6uu_KB * F.H0f**2
fig, ax = plt.subplots(nrows=1, ncols=3, figsize=(20,6), sharex=True, sharey=True, gridspec_kw={'wspace': 0.05})
ax[0].loglog(k, F.P0vv_norsd, 'k', ls=':', lw=1.7)
ax[1].loglog(k, F.P2vv_norsd, 'k', ls=':', lw=1.7)
# A
color = 'lime'
pos_signal = np.ma.masked_where(P0vv_KA<=0.0, P0vv_KA)
neg_signal = np.ma.masked_where(P0vv_KA>0.0, P0vv_KA)
ax[0].loglog(F.k, pos_signal, c=color, lw=1.4, label=r'$\ell=0$')
ax[0].loglog(F.k, np.abs(neg_signal), c=color, ls='--', dashes=(5,3), lw=1.7)
pos_signal = np.ma.masked_where(P2vv_KA<=0.0, P2vv_KA)
neg_signal = np.ma.masked_where(P2vv_KA>0.0, P2vv_KA)
ax[1].loglog(F.k, pos_signal, c=color, lw=1.4, label=r'$\ell=2$')
ax[1].loglog(F.k, np.abs(neg_signal), c=color, ls='--', dashes=(5,3), lw=1.7)
pos_signal = np.ma.masked_where(P4vv_KA<=0.0, P4vv_KA)
neg_signal = | np.ma.masked_where(P4vv_KA>0.0, P4vv_KA) | numpy.ma.masked_where |
import json
import logging
from pathlib import Path
from typing import Any, Dict, List, Optional, Tuple
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from matplotlib.colors import LogNorm
from pylossmap import BLMData
# from tensorflow.keras.utils import Sequence
from tqdm.auto import tqdm
UFO_LABEL = 1
NON_UFO_LABEL = 0
def augment_mirror(data: np.ndarray) -> np.ndarray:
"""Augment the data with the mirrored data.
Args:
data: data to augment
Returns:
the data with the mirrored data appended to the data.
"""
return np.vstack([data, data[:, ::-1]])
def create_labels(
ufo: np.ndarray, non_ufo: np.ndarray
) -> Tuple[np.ndarray, np.ndarray]:
"""Create the label arrays.
Args:
ufo: ufo data
non_ufo: non ufo data
Returns:
The labels of the ufo and non ufo data.
"""
ufo_labels = np.array([UFO_LABEL] * len(ufo))[:, None]
non_ufo_labels = np.array([NON_UFO_LABEL] * len(non_ufo))[:, None]
return ufo_labels, non_ufo_labels
def truncate_data(data: List[pd.DataFrame], target_length: int) -> np.ndarray:
"""Truncate the rows to a given length, centered.
Args:
data: iterable containing vector data to truncate
target_length: the desired length of the vector conatining the blm signals
Returns:
Array containing the truncated data.
"""
truncated_rows = []
for row in data:
length = row.shape[1]
half_delta = (length - target_length) / 2
start_shift = int(np.floor(half_delta))
end_cutoff = int(np.ceil(half_delta))
row_chunk = row.iloc[0, start_shift:-end_cutoff]
truncated_rows.append(row_chunk.to_numpy())
truncated_rows = np.array(truncated_rows)
return truncated_rows
def create_peak_dataset(
ufo_meta: pd.DataFrame,
raw_data_dir: Path,
dcum_around: int = 24000,
target_length: int = 33,
prior_dt: int = 3,
post_dt: int = 3,
non_ufo_threshold: float = 1e-3,
include_meta: bool = True,
) -> Dict[str, np.ndarray]:
"""Create a ufo and non ufo peak dataset.
Args:
ufo_meta: metadata of the ufo events
raw_data_dir: directory containing the raw data
dcum_around: dcum range around the ufo
target_length: the desired length of the vector conatining the blm signals
prior_dt: how many seconds back to get the prior events
post_dt: how many seconds forward to get the post events
non_ufo_threshold: don't include non ufo samples when the max is above threshold
include_meta: include the metadata of the samples in the returned dictionary
Returns:
Dictionary containing the ufo and non ufo data and metadata.
"""
non_ufo_prior = []
non_ufo_prior_meta = []
peaks = []
peaks_meta = []
non_ufo_post = []
non_ufo_post_meta = []
for idx, ufo in tqdm(ufo_meta.iterrows(), total=len(ufo_meta)):
raw_fill_data = BLMData.load(raw_data_dir / f"{ufo.fill}.h5")
raw_fill_data.df = raw_fill_data.df.droplevel("mode")
raw_fill_data.df = raw_fill_data.df.iloc[~raw_fill_data.df.index.duplicated()]
raw_idx = raw_fill_data.df.index.get_loc(ufo.datetime, method="nearest") + 1
around_blms = raw_fill_data.meta[
(raw_fill_data.meta["dcum"] < ufo.dcum + dcum_around)
& (raw_fill_data.meta["dcum"] > ufo.dcum - dcum_around)
]
around_data = raw_fill_data.df[around_blms.index].iloc[raw_idx : raw_idx + 1]
if around_data.shape[1] < target_length:
print("skipping sample, not enough blms.")
continue
peaks.append(around_data)
if include_meta:
peaks_meta.append(ufo)
around_prior_data = raw_fill_data.df[around_blms.index].iloc[
raw_idx - prior_dt : raw_idx + 1 - prior_dt
]
around_post_data = raw_fill_data.df[around_blms.index].iloc[
raw_idx + post_dt : raw_idx + 1 + post_dt
]
print("===============")
print("prior max: ", around_prior_data.max().max())
print("prior min: ", around_prior_data.min().min())
print("prior shape: ", around_prior_data.shape)
if around_prior_data.max().max() > non_ufo_threshold:
print("High value, skipping")
print(idx, ufo)
elif around_prior_data.min().min() == 0:
print("found a zero min value, skipping")
print(idx, ufo)
else:
non_ufo_prior.append(around_prior_data)
if include_meta:
prior_meta = ufo.copy()
prior_meta["datetime"] = prior_meta["datetime"] - pd.Timedelta(
f"{prior_dt}s"
)
non_ufo_prior_meta.append(prior_meta)
print("post max: ", around_post_data.max().max())
print("post min: ", around_post_data.min().min())
print("post shape: ", around_post_data.shape)
if around_post_data.max().max() > non_ufo_threshold:
print("High value, skipping")
print(idx, ufo)
elif around_post_data.min().min() == 0:
print("found a zero min value, skipping")
print(idx, ufo)
else:
non_ufo_post.append(around_post_data)
if include_meta:
post_meta = ufo.copy()
post_meta["datetime"] = post_meta["datetime"] + pd.Timedelta(
f"{post_dt}s"
)
non_ufo_post_meta.append(post_meta)
out = {
"ufo": truncate_data(peaks, target_length=target_length),
"non_ufo_prior": truncate_data(non_ufo_prior, target_length=target_length),
"non_ufo_post": truncate_data(non_ufo_post, target_length=target_length),
}
if include_meta:
out["ufo_meta"] = pd.DataFrame(peaks_meta)
out["non_ufo_prior_meta"] = pd.DataFrame(non_ufo_prior_meta)
out["non_ufo_post_meta"] = pd.DataFrame(non_ufo_post_meta)
return out
def rolling_window(a: np.ndarray, window: int) -> np.ndarray:
"""Create a rolling window over the provided array.
Args:
a: array on which to perform the rolling window
window: the size of the rolling window
Returns:
An array of the rolling window.
"""
shape = a.shape[:-1] + (a.shape[-1] - window + 1, window)
strides = a.strides + (a.strides[-1],)
return | np.lib.stride_tricks.as_strided(a, shape=shape, strides=strides) | numpy.lib.stride_tricks.as_strided |
import argparse
import contextlib
from itertools import product
from math import floor
import os
os.environ.update(
OMP_NUM_THREADS = '1',
OPENBLAS_NUM_THREADS = '1',
NUMEXPR_NUM_THREADS = '1',
MKL_NUM_THREADS = '1',
)
import numpy as np
| np.set_printoptions(precision=3) | numpy.set_printoptions |
from __future__ import division
import gzip
import matplotlib.pyplot as plt
import numpy as np
import random
import math
def Randomize_Weights(weight_vector: np.ndarray):
rand_weights = weight_vector
for j in range(0,len(weight_vector)):
rand_weights[j][::1] = float(random.randint(-100, 100) / 100)
return rand_weights
def Forward_Pass(data: np.ndarray, weights, biases): # a Single Forward Pass, returns a vector output after the softmax
output = [0] * 10
probs = np.zeros(10)
output[::1] = (np.inner(weights[::1], data) + biases[::1])
sum = 0
for index,x in enumerate(output):
exp = math.exp(x)
sum += exp
probs[index] = exp
probs[::1] = probs[::1] * (1/sum)
return probs
def Label_Probs(probabilities): # returns a label, expects normalized data
return np.unravel_index(np.argmax(probabilities, axis=None), probabilities.shape)
def Test_NN(weights, biases): # Tests network and prints accuracy
test_im = np.zeros((10000, 784))
test_lb = None
with open('./data/test_images.gz', 'rb') as f, gzip.GzipFile(fileobj=f) as bytestream:
tmp = bytestream.read()
tmp = np.frombuffer(tmp, dtype= | np.dtype('b') | numpy.dtype |
# 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.
# Lint as: python2, python3
"""Tests for implied_vol_approx."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from absl.testing import parameterized
import numpy as np
import tensorflow as tf
import tf_quant_finance as tff
from tensorflow.python.framework import test_util # pylint: disable=g-direct-tensorflow-import
bs = tff.black_scholes
@test_util.run_all_in_graph_and_eager_modes
class ApproxImpliedVolTest(parameterized.TestCase, tf.test.TestCase):
"""Tests for methods in implied_vol module."""
def test_approx_implied_vol(self):
"""Basic test of the implied vol calculation."""
np.random.seed(6589)
n = 100
dtypes = [np.float32, np.float64]
for dtype in dtypes:
volatilities = np.exp(np.random.randn(n) / 2)
forwards = np.exp(np.random.randn(n))
strikes = forwards * (1 + (np.random.rand(n) - 0.5) * 0.2)
expiries = np.exp(np.random.randn(n))
prices = self.evaluate(
bs.option_price(
volatilities, strikes, expiries, forwards=forwards, dtype=dtype))
implied_vols = self.evaluate(
bs.implied_vol_approx(
prices, strikes, expiries, forwards=forwards, dtype=dtype))
self.assertArrayNear(volatilities, implied_vols, 0.6)
def test_approx_implied_vol_validate(self):
"""Test the Radiocic-Polya approx doesn't raise where it shouldn't."""
np.random.seed(6589)
n = 100
dtypes = [np.float32, np.float64]
for dtype in dtypes:
volatilities = np.exp(np.random.randn(n) / 2)
forwards = np.exp(np.random.randn(n))
strikes = forwards * (1 + (np.random.rand(n) - 0.5) * 0.2)
expiries = np.exp(np.random.randn(n))
prices = self.evaluate(
bs.option_price(
volatilities, strikes, expiries, forwards=forwards, dtype=dtype))
implied_vols = self.evaluate(
bs.implied_vol_approx(
prices,
strikes,
expiries,
forwards=forwards,
validate_args=True,
dtype=dtype))
self.assertArrayNear(volatilities, implied_vols, 0.6)
@parameterized.named_parameters(
# This case should hit the call lower bound since C = F - K.
('call_lower', 0.0, 1.0, 1.0, 1.0, True),
# This case should hit the call upper bound since C = F
('call_upper', 1.0, 1.0, 1.0, 1.0, True),
# This case should hit the put upper bound since C = K
('put_lower', 1.0, 1.0, 1.0, 1.0, False),
# This case should hit the call lower bound since C = F - K.
('put_upper', 0.0, 1.0, 1.0, 1.0, False))
def test_approx_implied_vol_validate_raises(self, price, forward, strike,
expiry, is_call_option):
"""Test the Radiocic-Polya approximation raises appropriately."""
dtypes = [np.float32, np.float64]
for dtype in dtypes:
prices = | np.array([price]) | numpy.array |
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Bioindustrial-Park: BioSTEAM's Premier Biorefinery Models and Results
# Copyright (C) 2020-, <NAME> <<EMAIL>>
#
# This module is under the UIUC open-source license. See
# github.com/BioSTEAMDevelopmentGroup/biosteam/blob/master/LICENSE.txt
# for license details.
'''
References
----------
[1] Humbird et al., Process Design and Economics for Biochemical Conversion of
Lignocellulosic Biomass to Ethanol: Dilute-Acid Pretreatment and Enzymatic
Hydrolysis of Corn Stover; Technical Report NREL/TP-5100-47764;
National Renewable Energy Lab (NREL), 2011.
https://www.nrel.gov/docs/fy11osti/47764.pdf
[2] Davis et al., Process Design and Economics for the Conversion of Lignocellulosic
Biomass to Hydrocarbon Fuels and Coproducts: 2018 Biochemical Design Case Update;
NREL/TP-5100-71949; National Renewable Energy Lab (NREL), 2018.
https://doi.org/10.2172/1483234
[3] Cortes-Peña et al., BioSTEAM: A Fast and Flexible Platform for the Design,
Simulation, and Techno-Economic Analysis of Biorefineries under Uncertainty.
ACS Sustainable Chem. Eng. 2020, 8 (8), 3302–3310.
https://doi.org/10.1021/acssuschemeng.9b07040
'''
# %%
# =============================================================================
# Simulate pretreatment efficacy
# =============================================================================
import numpy as np
import pandas as pd
from biosteam.utils import TicToc
timer_efficacy = TicToc('timer_efficacy')
timer_efficacy.tic()
lignin = np.arange(0, 0.41, 0.01)
conversion_max = np.ones(1000)
conversion_min = np.zeros(1000)
# Liquid hot water (LHW)
np.random.seed(3221)
intercept_LHW_1 = np.random.normal(0.84, 0.04, 1000)
intercept_LHW_2 = np.random.normal(1.32, 0.07, 1000)
slope_LHW_2 = np.random.normal(-2.33, 0.33, 1000)
df_LHW = pd.DataFrame()
# Acid
intercept_acid = np.random.normal(1.04, 0.04, 1000)
slope_acid = np.random.normal(-1.37, 0.18, 1000)
df_acid = pd.DataFrame()
# Explosion (EXP)
intercept_EXP = | np.random.normal(0.83, 0.07, 1000) | numpy.random.normal |
# SPDX-FileCopyrightText: Copyright 2021, <NAME> <<EMAIL>>
# SPDX-License-Identifier: BSD-3-Clause
# SPDX-FileType: SOURCE
#
# This program is free software: you can redistribute it and/or modify it under
# the terms of the license found in the LICENSE.txt file in the root directory
# of this source tree.
# =======
# Imports
# =======
import numpy
import scipy.optimize
from functools import partial
from .._utilities.plot_utilities import * # noqa: F401, F403
from .._utilities.plot_utilities import load_plot_settings, save_plot, plt
# =================
# Direct Likelihood
# =================
class DirectLikelihood(object):
# ==============
# log likelihood
# ==============
@staticmethod
def log_likelihood(z, X, K_mixed, sign_switch, hyperparam):
"""
Here we use direct parameter, sigma and sigma0
sign_switch chnages the sign of the output from lp to -lp. When True,
this is used to minimizing (instad of maximizing) the negative of
log-likelihood function.
"""
# hyperparameters
sigma = hyperparam[0]
sigma0 = hyperparam[1]
n, m = X.shape
# S is the (sigma**2) * K + (sigma0**2) * I, but we don't construct it.
# Instead, we consruct Kn = K + eta I, where eta = (sigma0 / sigma)**2
tol = 1e-8
if numpy.abs(sigma) < tol:
# Ignore (sigma**2 * K) compared to (sigma0**2 * I) term.
logdet_S = n * numpy.log(sigma0**2)
Y = X / sigma0**2
else:
eta = (sigma0 / sigma)**2
logdet_Kn = K_mixed.logdet(eta)
logdet_S = n * numpy.log(sigma**2) + logdet_Kn
Y = K_mixed.solve(eta, X) / sigma**2
# Compute log det (X.T*Sinv*X)
XtSinvX = numpy.matmul(X.T, Y)
logdet_XtSinvX = numpy.log(numpy.linalg.det(XtSinvX))
# Compute zMz
B = numpy.matmul(X.T, Y)
Binv = numpy.linalg.inv(B)
Mz = DirectLikelihood.M_dot(K_mixed, Binv, Y, sigma, sigma0, z)
zMz = numpy.dot(z, Mz)
# Log likelihood
lp = -0.5*(n-m)*numpy.log(2.0*numpy.pi) - 0.5*logdet_S \
- 0.5*logdet_XtSinvX - 0.5*zMz
# If lp is used in scipy.optimize.minimize, change the sign to optain
# the minimum of -lp
if sign_switch:
lp = -lp
return lp
# =======================
# log likelihood jacobian
# =======================
@staticmethod
def log_likelihood_jacobian(z, X, K_mixed, sign_switch, hyperparam):
"""
When both :math:`\\sigma` and :math:`\\sigma_0` are zero, jacobian is
undefined.
"""
# hyperparameters
sigma = hyperparam[0]
sigma0 = hyperparam[1]
n, m = X.shape
# S is the (sigma**2) * K + (sigma0**2) * I, but we don't construct it
# Instead, we construct Kn = K + eta I, where eta = (sigma0 / sigma)**2
# Computing Y=Sinv*X and w=Sinv*z
tol = 1e-8
if numpy.abs(sigma) < tol:
# Ignore (sigma**2 * K) compared to (sigma0**2 * I) term.
Y = X / sigma0**2
else:
eta = (sigma0 / sigma)**2
Y = K_mixed.solve(eta, X) / sigma**2
# B is Xt * Y
B = numpy.matmul(X.T, Y)
Binv = numpy.linalg.inv(B)
# Compute Mz
Mz = DirectLikelihood.M_dot(K_mixed, Binv, Y, sigma, sigma0, z)
# Compute KMz
KMz = K_mixed.dot(0, Mz)
# Compute zMMz and zMKMz
zMMz = numpy.dot(Mz, Mz)
zMKMz = numpy.dot(Mz, KMz)
# Compute trace of M
if numpy.abs(sigma) < tol:
trace_M = (n - m) / sigma0**2
else:
trace_Sinv = K_mixed.traceinv(eta) / sigma**2
YtY = numpy.matmul(Y.T, Y)
trace_BinvYtY = numpy.trace( | numpy.matmul(Binv, YtY) | numpy.matmul |
import argparse
import json
import os
import time
import numpy as np
from sklearn import svm
from sklearn.metrics import classification_report, confusion_matrix
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import FunctionTransformer, StandardScaler
from config import CONFIG_BY_KEY
from text_data_loader import TextDataLoader
from text_data_loader import TextDataHelper
from audio_data_loader import AudioDataLoader
from audio_data_loader import AudioDataHelper
RESULT_FILE = "./output/{}.json"
def parse_args():
parser = argparse.ArgumentParser()
parser.add_argument('--config-key', default='', choices=list(CONFIG_BY_KEY.keys()))
return parser.parse_args()
args = parse_args()
print("Args:", args)
# Load config
config = CONFIG_BY_KEY[args.config_key]
# Load textdata
textdata = TextDataLoader(config)
audiodata = AudioDataLoader(config)
def latefusion(y_pred, y_true):
if config.use_context:
print("Use Context")
if config.use_author:
print("Use Author")
if config.use_target_text:
if config.use_bert:
print("BERT Model")
else:
print("GLOVE Model")
else:
print("Audio Only")
result_string = classification_report(y_true, y_pred, digits=3)
print("Confusion Matrix:")
print(confusion_matrix(y_true, y_pred))
print("Accuracy:")
print(result_string)
print("Runtime:")
print("--- %s seconds ---" % (time.time() - start_time))
return classification_report(y_true, y_pred, output_dict=True, digits=3), result_string
def svm_train_text(text_train_input, text_train_output):
print("SVM Train Text")
textclf = make_pipeline(
StandardScaler() if config.svm_scale else FunctionTransformer(lambda x: x, validate=False),
svm.SVC(C=config.svm_c, gamma='scale', kernel='rbf')
)
return textclf.fit(text_train_input, np.argmax(text_train_output, axis=1))
def svm_test_text(textclf, text_test_input, text_test_output):
print("SVM Test Text")
probas = textclf.predict(text_test_input)
y_pred = probas
y_true = | np.argmax(text_test_output, axis=1) | numpy.argmax |
import numpy as np
import matplotlib.pyplot as plt
import src.solver_helper as helper
from src.traffic_world import TrafficWorld
from src.car_plotting_multiple import plot_multiple_cars
from src.multiagent_mpc import MultiMPC, generate_warm_starts
from src.idm import IDM_acceleration, get_lead_vehicle, MOBIL_lanechange
from contextlib import redirect_stdout
from src.ibr_argument_parser import IBRParser
import datetime, string, random, os, pickle, json, time
import copy as cp
def run_idm_baseline(params, k_politeness, amb_x0, all_other_x0, ambulance, all_other_vehicles, world):
# Current default params
t_start_time = time.time()
idm_params = {
"desired_time_gap": 0.1,
"jam_distance": 4,
}
params["wall_CA"] = 0 # wall_CA by default is zero for IDM since it's only being used for steering
######################################3
i_mpc_start = 0
params["N"] = max(1, int(params["T"] / params["dt"]))
params["number_ctrl_pts_executed"] = max(1, int(np.floor(params["N"] * params["p_exec"])))
n_mpc = params["n_mpc"]
n_sim = params["n_mpc"] * params["number_ctrl_pts_executed"] # corrected since
X_other = [np.zeros((6, n_sim + 1)) for i in range(len(all_other_vehicles))]
X_amb = | np.zeros((6, n_sim + 1)) | numpy.zeros |
from pathlib import Path
from timeit import default_timer as timer
import h5py
import numpy as np
import torch
from methods.utils.data_utilities import (_segment_index, load_dcase_format,
to_metrics2020_format)
from torch.utils.data import Dataset, Sampler
from tqdm import tqdm
from utils.common import int16_samples_to_float32
class UserDataset(Dataset):
""" User defined datset
"""
def __init__(self, args, cfg, dataset, dataset_type='train', overlap=''):
"""
Args:
args: input args
cfg: configurations
dataset: dataset used
dataset_type: 'train' | 'valid' | 'dev_test' | 'eval_test'
overlap: '1' | '2'
"""
super().__init__()
self.dataset_type = dataset_type
self.read_into_mem = args.read_into_mem
self.sample_rate = cfg['data']['sample_rate']
self.clip_length = dataset.clip_length
self.label_resolution = dataset.label_resolution
self.frame_length = int(self.clip_length / self.label_resolution)
self.label_interp_ratio = int(self.label_resolution * self.sample_rate / cfg['data']['hop_length'])
# Chunklen and hoplen and segmentation. Since all of the clips are 60s long, it only segments once here
data = np.zeros((1, self.clip_length * self.sample_rate))
if 'train' in self.dataset_type:
chunklen = int(cfg['data']['train_chunklen_sec'] * self.sample_rate)
hoplen = int(cfg['data']['train_hoplen_sec'] * self.sample_rate)
self.segmented_indexes, self.segmented_pad_width = _segment_index(data, chunklen, hoplen)
elif self.dataset_type in ['valid', 'dev_test', 'eval_test']:
chunklen = int(cfg['data']['test_chunklen_sec'] * self.sample_rate)
hoplen = int(cfg['data']['test_hoplen_sec'] * self.sample_rate)
self.segmented_indexes, self.segmented_pad_width = _segment_index(data, chunklen, hoplen, last_frame_always_paddding=True)
self.num_segments = len(self.segmented_indexes)
# Data and meta path
fold_str_idx = dataset.fold_str_index
ov_str_idx = dataset.ov_str_index
data_sr_folder_name = '{}fs'.format(self.sample_rate)
main_data_dir = Path(cfg['hdf5_dir']).joinpath(cfg['dataset']).joinpath('data').joinpath(data_sr_folder_name)
dev_data_dir = main_data_dir.joinpath('dev').joinpath(cfg['data']['type'])
eval_data_dir = main_data_dir.joinpath('eval').joinpath(cfg['data']['type'])
main_meta_dir = Path(cfg['hdf5_dir']).joinpath(cfg['dataset']).joinpath('meta')
dev_meta_dir = main_meta_dir.joinpath('dev')
eval_meta_dir = main_meta_dir.joinpath('eval')
if self.dataset_type == 'train':
data_dirs = [dev_data_dir]
self.meta_dir = dev_meta_dir
train_fold = [int(fold.strip()) for fold in str(cfg['training']['train_fold']).split(',')]
ov_set = str(cfg['training']['overlap']) if not overlap else overlap
self.paths_list = [path for data_dir in data_dirs for path in sorted(data_dir.glob('*.h5')) \
if int(path.stem[fold_str_idx]) in train_fold and path.stem[ov_str_idx] in ov_set \
and not path.name.startswith('.')]
elif self.dataset_type == 'valid':
if cfg['training']['valid_fold'] != 'eval':
data_dirs = [dev_data_dir]
self.meta_dir = dev_meta_dir
valid_fold = [int(fold.strip()) for fold in str(cfg['training']['valid_fold']).split(',')]
ov_set = str(cfg['training']['overlap']) if not overlap else overlap
self.paths_list = [path for data_dir in data_dirs for path in sorted(data_dir.glob('*.h5')) \
if int(path.stem[fold_str_idx]) in valid_fold and path.stem[ov_str_idx] in ov_set \
and not path.name.startswith('.')]
ori_meta_dir = Path(cfg['dataset_dir']).joinpath('metadata_dev')
else:
data_dirs = [eval_data_dir]
self.meta_dir = eval_meta_dir
ov_set = str(cfg['training']['overlap']) if not overlap else overlap
self.paths_list = [path for data_dir in data_dirs for path in sorted(data_dir.glob('*.h5')) \
if not path.name.startswith('.')]
ori_meta_dir = Path(cfg['dataset_dir']).joinpath('metadata_eval')
frame_begin_index = 0
self.valid_gt_sed_metrics2019 = []
self.valid_gt_doa_metrics2019 = []
self.valid_gt_dcaseformat = {}
for path in self.paths_list:
ori_meta_path = ori_meta_dir.joinpath(path.stem + '.csv')
output_dict, sed_metrics2019, doa_metrics2019 = \
load_dcase_format(ori_meta_path, frame_begin_index=frame_begin_index,
frame_length=self.frame_length, num_classes=len(dataset.label_set))
self.valid_gt_dcaseformat.update(output_dict)
self.valid_gt_sed_metrics2019.append(sed_metrics2019)
self.valid_gt_doa_metrics2019.append(doa_metrics2019)
frame_begin_index += self.frame_length
self.valid_gt_sed_metrics2019 = np.concatenate(self.valid_gt_sed_metrics2019, axis=0)
self.valid_gt_doa_metrics2019 = np.concatenate(self.valid_gt_doa_metrics2019, axis=0)
self.gt_metrics2020_dict = to_metrics2020_format(self.valid_gt_dcaseformat,
self.valid_gt_sed_metrics2019.shape[0], label_resolution=self.label_resolution)
elif self.dataset_type == 'dev_test':
data_dirs = [dev_data_dir]
self.meta_dir = dev_meta_dir
dev_test_fold = [int(fold.strip()) for fold in str(cfg['inference']['test_fold']).split(',')]
ov_set = str(cfg['inference']['overlap']) if not overlap else overlap
self.paths_list = [path for data_dir in data_dirs for path in sorted(data_dir.glob('*.h5')) \
if int(path.stem[fold_str_idx]) in dev_test_fold and path.stem[ov_str_idx] in ov_set \
and not path.name.startswith('.')]
elif self.dataset_type == 'eval_test':
data_dirs = [eval_data_dir]
self.meta_dir = eval_meta_dir
self.paths_list = [path for data_dir in data_dirs for path in sorted(data_dir.glob('*.h5')) \
if not path.name.startswith('.')]
self.paths_list = [Path(str(path) + '%' + str(n)) for path in self.paths_list for n in range(self.num_segments)]
# Read into memory
if self.read_into_mem:
load_begin_time = timer()
print('Start to load dataset: {}, ov={}......\n'.format(self.dataset_type + ' set', ov_set))
iterator = tqdm(self.paths_list, total=len(self.paths_list), unit='clips')
self.dataset_list = []
for path in iterator:
fn, n_segment = path.stem, int(path.name.split('%')[1])
data_path = Path(str(path).split('%')[0])
index_begin = self.segmented_indexes[n_segment][0]
index_end = self.segmented_indexes[n_segment][1]
pad_width_before = self.segmented_pad_width[n_segment][0]
pad_width_after = self.segmented_pad_width[n_segment][1]
with h5py.File(data_path, 'r') as hf:
x = int16_samples_to_float32(hf['waveform'][:, index_begin: index_end])
pad_width = ((0, 0), (pad_width_before, pad_width_after))
x = np.pad(x, pad_width, mode='constant')
if 'test' not in self.dataset_type:
ov = fn[-1]
index_begin_label = int(index_begin / (self.sample_rate * self.label_resolution))
index_end_label = int(index_end / (self.sample_rate * self.label_resolution))
# pad_width_before_label = int(pad_width_before / (self.sample_rate * self.label_resolution))
pad_width_after_label = int(pad_width_after / (self.sample_rate * self.label_resolution))
meta_path = self.meta_dir.joinpath(fn + '.h5')
with h5py.File(meta_path, 'r') as hf:
sed_label = hf['sed_label'][index_begin_label: index_end_label, ...]
doa_label = hf['doa_label'][index_begin_label: index_end_label, ...] # NOTE: this is Catesian coordinates
if pad_width_after_label != 0:
sed_label_new = | np.zeros((pad_width_after_label, 2, 14)) | numpy.zeros |
import numpy as np
import json
import scipy.stats as st
varCount = 0
_floatinfo = np.finfo(np.float64)
_intinfo = np.iinfo(np.int64)
_float_special_values = [0.0, 1.0, _floatinfo.min, _floatinfo.max, _floatinfo.max - 1.0, _floatinfo.min + 1.0,
_floatinfo.eps,
_floatinfo.tiny, 0.00001, -0.00001]
int_special_values = [0, 1, _intinfo.min, _intinfo.max, _intinfo.min + 1, _intinfo.max - 1]
_FUZZERTYPE = 'UNSTR'
def is_unstructured():
return _FUZZERTYPE == 'UNSTR'
def set_fuzzer_type(type):
global _FUZZERTYPE
_FUZZERTYPE = type
def getSupportedDistributions(support, models=None, pps="name"):
if support is None:
return None
if models is None:
models = parse_models()
if support == '[alpha, beta]':
return []
return [model for model in models if pps in model and includes(model["support"], support)]
def getUnSupportedDistributions(support, models=None, pps="name"):
if support is None:
return None
if models is None:
models = parse_models()
if support == '[alpha, beta]':
return [model for model in models if pps in model and model["name"] != "uniform"]
return [model for model in models
if pps in model and notincludes(model["support"], support) and model["name"] != "normal"]
def get_special_values(datatype):
if datatype == 'i':
return np.random.choice(int_special_values)
elif datatype == 'f':
return np.random.choice(_float_special_values)
elif datatype == 'i+':
arr = [x for x in int_special_values if x != 0]
return np.abs(np.random.choice(arr))
elif datatype == "f+":
arr = [x for x in _float_special_values if x > 0.0]
return np.abs(np.random.choice(arr))
elif datatype == "0f+":
arr = [x for x in _float_special_values if x >= 0.0]
return np.abs(np.random.choice(arr))
elif datatype == 'p':
return np.random.choice([0.0, 1.0, 0.5])
elif datatype == '(0,1)':
return np.random.choice([_floatinfo.eps, _floatinfo.tiny])
elif datatype == '0i+':
return np.abs(np.random.choice(int_special_values))
else:
print('Unexpected type ' + datatype)
exit(-1)
def generate_primitives(data_type, size=1, is_special=False):
if is_special and data_type != 'b':
x_data = np.array([get_special_values(data_type) for _ in range(0, size)])
else:
if data_type == 'i':
x_data = np.random.randint(-100, 100, size=size)
elif data_type == 'f':
x_data = np.random.uniform(-100, 100, size=size)
elif data_type == 'p':
x_data = np.random.uniform(0.0, 1.0, size=size)
elif data_type == 'f+':
x_data = np.random.uniform(0.0, 100.0, size=size)
np.place(x_data, x_data == 0.0, 0.1)
elif data_type == '0f+':
x_data = np.random.uniform(0.0, 100.0, size=size)
elif data_type == 'i+':
x_data = np.random.randint(1, 100, size=size)
elif data_type == 'b':
x_data = np.random.randint(2, size=size)
elif data_type == '(0,1)':
arr = np.random.sample(size)
np.place(arr, arr == 0.0, 0.1)
x_data = arr
elif data_type == '0i+':
x_data = np.random.randint(0, 100, size=size, dtype=np.int)
else:
NotImplementedError('Unsupported type ' + str(data_type))
return x_data
def generate_samples(distname, args, samples):
print(args)
if distname == 'bernoulli':
return np.array([st.bernoulli.rvs(*args) for _ in range(0, samples)])
elif distname == 'normal':
return np.array([st.norm.rvs(*args) for _ in range(0, samples)])
elif distname == 'cauchy':
return np.array([st.cauchy.rvs(*args) for _ in range(0, samples)])
elif distname == 'double_exponential':
return np.array([st.laplace.rvs(*args) for _ in range(0, samples)])
elif distname == 'logistic':
return np.array([st.logistic.rvs(*args) for _ in range(0, samples)])
elif distname == 'gumbel':
return np.array([st.gumbel_l.rvs(*args) for _ in range(0, samples)])
elif distname == 'lognormal':
args[0] = np.abs(args[0])
return np.array([st.lognorm.rvs(*args) for _ in range(0, samples)])
elif distname == 'chi_square':
return np.array([st.chi2.rvs(*args) for _ in range(0, samples)])
elif distname == 'inv_chi_square':
return np.array([st.chi2.rvs(*args) for _ in range(0, samples)])
elif distname == 'exponential':
return np.array([st.expon.rvs(*args) for _ in range(0, samples)])
elif distname == 'gamma':
return np.array([st.gamma.rvs(*args) for _ in range(0, samples)])
elif distname == 'invgamma':
return np.array([st.invgamma.rvs(*args) for _ in range(0, samples)])
elif distname == 'weibull':
return np.array([st.weibull_max.rvs(*args) for _ in range(0, samples)])
elif distname == 'beta':
return np.array([st.beta.rvs(*args) for _ in range(0, samples)])
elif distname == 'uniform':
return np.array([st.uniform.rvs(*args) for _ in range(0, samples)])
else:
print(distname)
raise NotImplementedError
def get_new_var_name(prefix=''):
global varCount
varCount += 1
if len(prefix) == 0:
prefix = 'p'
return prefix + str(varCount)
def sigmoid(x):
return 1.0 / (1.0 + np.exp(-x))
def sigmoid_limit(x):
y = sigmoid(x)
y = np.where(y == 0.0, np.finfo(np.float32).eps, y)
y = np.where(y == 1.0, 1.0 - np.finfo(np.float32).eps, y)
return y
def cast_data(y, output_type):
if output_type == 'i':
y = y.astype(np.int32)
elif output_type == 'f':
y = y.astype(np.float32)
elif output_type == 'p':
y = sigmoid(y)
elif output_type == '(0,1)':
y = sigmoid_limit(y)
elif output_type == 'f+':
y = np.abs(y)
y = np.where(y == 0, np.finfo(np.float32).eps, y)
elif output_type == '0f+':
y = | np.abs(y) | numpy.abs |
__all__ = ['extract_ssi', 'extract_ssi_to_file',
'extract_eta', 'extract_eta_to_file',
'extract_Q_channel', 'extract_Q_down',
'extract_overland_volume', 'extract_overland_volume_to_file']
from datetime import timedelta
from configparser import SafeConfigParser
import h5py
import numpy as np
import numpy.ma as ma
# gzip compression flag
comp = 6
def extract_Q_down(control_fname):
"""Extract combined soil and overland out flow rates.
Read a PyTOPKAPI simulation file and return the combined overland
andsoil store outflows in a Numpy array.
Parameters
----------
control_fname : string
The file name of a PyTOPKAPI simulation control file. The name
should contain the full path relative to the current
directory.
Returns
-------
Qdown : Numpy array
A Numpy array containing the simulated outflow flow rates from
the overland and soil store of each cell.
"""
config = SafeConfigParser()
config.read(control_fname)
sim_fname = config.get('output_files', 'file_out')
tkpi_file = h5py.File(sim_fname, 'r')
Qdown = tkpi_file['/Q_down'][...]
tkpi_file.close()
return Qdown
def extract_Q_channel(control_fname):
"""Extract channel flow rates from a PyTOPKAPI simulation file.
Read a PyTOPKAPI simulation file and return the simulated channel
flows in a Numpy masked array.
Parameters
----------
control_fname : string
The file name of a PyTOPKAPI simulation control file. The name
should contain the full path relative to the current
directory.
Returns
-------
Qc : Numpy masked array
A Numpy masked array containing the simulated flow rates for
channel cells.
"""
config = SafeConfigParser()
config.read(control_fname)
param_fname = config.get('input_files', 'file_cell_param')
sim_fname = config.get('output_files', 'file_out')
params = np.loadtxt(param_fname)
tkpi_file = h5py.File(sim_fname, 'r')
Qc = tkpi_file['/Channel/Qc_out'][...]
tkpi_file.close()
channel_mask = params[:, 3]
cond = params[:, 3]*np.ones(Qc.shape, dtype=np.int) != 1
Qc = np.ma.masked_where(cond, Qc)
return Qc
def extract_overland_volume(control_fname):
"""Extract the volumes in the overland stores.
Read a PyTOPKAPI simulation file and return the combined overland
and store volumes in a Numpy array.
Parameters
----------
control_fname : string
The file name of a PyTOPKAPI simulation control file. The name
should contain the full path relative to the current directory
(or the root of the file system).
Returns
-------
Vo : Numpy array
A Numpy array containing the simulated storage volume in the
overland store of each cell.
"""
config = SafeConfigParser()
config.read(control_fname)
sim_fname = config.get('output_files', 'file_out')
tkpi_file = h5py.File(sim_fname, 'r')
Vo = tkpi_file['/Overland/V_o'][...]
tkpi_file.close()
return Vo
def extract_overland_volume_to_file(sim_fname, param_fname,
result_fname, start_dt, timestep):
"""Extract the volumes in the overland stores to a file.
Read a TOPKAPI simulation file and it's associated parameter file
and extract the overland store volumes for each timestep. Store
the results in a new HDF5 file, grouped by date and containing
datasets of latitude, longitude and storage volume.
Parameters
----------
sim_fname : string
The name of a PyTOPKAPI simulation file. This should include
the full or relative path.
param_fname : string
The name of a parameter file describing the catchment. This
should include the full or relative path.
result_fname : string
The name of an HDF5 file to store the output. This should
include the full or relative path.
start_dt : datetime.datetime
The starting date and time of the simulated results in
`sim_fname`.
timestep : int
The length of each model time-step in seconds.
Returns
-------
Nothing
"""
params = np.loadtxt(param_fname)
x = params[:, 1]
y = params[:, 2]
soil_depth = params[:, 8]
soil_depth = ma.masked_values(soil_depth, 0.0)
x = | ma.array(x, mask=soil_depth.mask) | numpy.ma.array |
#!/usr/bin/env python
#
#----------------------------------------------------------------------
# Reference: https://epubs.siam.org/doi/pdf/10.1137/S0036144502417715
# In[1]:
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import lagrange
# mgena
#from pylab import *
print ("")
print ("01 ----------------------------")
#----------------------------------------------------------------------
# In[2]:
def f(t):
return t ** 10 - 1 * t ** 9
ts = np.linspace(0, 1, 6)
fs = f(ts)
print(ts)
print ("02 ----------------------------")
# In[3]:
p4 = lagrange (ts[1:-1], fs[1:-1])
p51 = lagrange (ts[:-1], fs[:-1])
p52 = lagrange (ts[1:], fs[1:])
p6 = lagrange (ts, fs)
ts_cont = np.linspace(0, 1, 100)
# In[4]:
plt.plot (ts_cont, f(ts_cont), ts_cont, p6(ts_cont))
# In[5]:
#----------------------------------------------------------------------
class LagrangeBary:
def __init__(self, ts, fs):
self.ts = np.copy(ts)
self.fs = np.copy(fs)
self.compute_ws()
def compute_ws_j(self, j):
wsj = 1
for k in range(len(self.ts)):
if k == j:
continue
wsj /= self.ts[j] - self.ts[k]
return wsj
def compute_ws(self):
n = len(self.ts)
ws = np.ones(n)
for j in range(n):
ws[j] = self.compute_ws_j(j)
self.ws = ws
def remove_left(self):
t = self.ts[0]
for i in range(len(self.ws)):
self.ws[i] *= self.ts[i] - t
self.ts = np.delete(self.ts, 0)
self.fs = np.delete(self.fs, 0)
self.ws = np.delete(self.ws, 0)
def add_right(self, ti, fi):
self.ts = np.append(self.ts, ti)
self.fs = | np.append(self.fs, fi) | numpy.append |
#!/usr/bin/env python
import numpy as np
import sys
from warnings import warn
class Vertex(object):
def __init__(self, x, y, z, name):
"""
Creates the Vertex Object with Carthesian coordinates
Parameters
----------
x: float
x coordinate
y: float
y coordinate
z: float
z coordinate
coordinates: np array
(x, y, z) coordinates
name: string
Attributes
----------
x: float
x coordinate
y: float
y coordinate
z: float
z coordinate
name: string
single letter name
for example, 'A'
"""
self.x = x
self.y = y
self.z = z
self.coordinates = np.array([self.x, self.y, self.z])
self.name = name
class Face(object):
"""
Face of a polyhedron, defined by its vertices.
Attributes
----------
vertices: list
list of Vertex objects confining the face
ID: int
number identifying the Face
middle: np array
middle of the face
also origin of the local coordinate system
normal: np array
normal vector to the face
u: np array
first axis of the local coordinate system
v: np array
second axis of the local coordinate system
size: float
length of middle to first vertex
"""
def __init__(self, vertices, ID):
"""
Creates a Surface Object from a set of vertices
Parameters
----------
vertices: list
list of Vertex objects confining the face
ID: int
number identifying the Face
"""
self.vertices = vertices
self.numVertices = len(self.vertices)
self.ID = ID
# check that at least three vertices are given
try:
assert(self.numVertices >= 3)
except AssertionError:
print("Can not creatre face with less than three vertices.")
sys.exit(1)
self.calc_system()
def calc_system(self):
"""
Calculates middle of the face, normal vector
and local coordinate system
"""
# middle as average of the vertices
self.middle = np.zeros(self.numVertices)
for v in self.vertices:
self.middle += v.coordinates
self.middle = self.middle / self.numVertices
# normal is in the direction of the origin through the middle
self.normal = self.middle / np.linalg.norm(self.middle)
# pick frist axis from v1 to v2, second from v1 to v3
self.u = self.vertices[1].coordinates - self.vertices[0].coordinates
self.v = self.vertices[2].coordinates - self.vertices[0].coordinates
self.angle = np.arccos(np.dot(self.u, self.v) /
(np.linalg.norm(self.u) * np.linalg.norm(self.v)))
def calc_local_vertices(self):
"""
Get position of the vertices of the face in the local coordinate system
Only works for (triangular) icosahedron surfaces)
hard coded maths
Returns
-------
list
list of 2D arrays of the coordinates of the vertices in the local
coodinate system
"""
D = np.linalg.norm(self.middle - self.vertices[0].coordinates)
v1 = np.array([D, 0])
v2 = np.array([-D*np.cos(self.angle), -D*np.sin(self.angle)])
v3 = np.array([-D*np.cos(self.angle), D*np.sin(self.angle)])
return [v1, v2, v3]
def global_to_lcs(self, point):
"""
Convert a point on the face in global (3D) coordinates to the local
coordinate system of the face (2D)
Paramters
---------
point: array-like
3D global coordinates of a point on the face
Returns
-------
NumPy Array: the point in the lcs of the face
"""
eps = 1.0e-6
# check that point is in the plane of the face
assert(np.dot((point - self.middle), self.normal) < eps)
start_vector = self.vertices[0].coordinates
p = point - start_vector
psize = np.linalg.norm(p)
size = np.linalg.norm(self.u)
# calculate angles between p and basis vectors
# check that total angle is the same as calculated when initializing
cos_angle_u = np.dot(self.u, p) / (psize * size)
cos_angle_v = np.dot(self.v, p) / (psize * size)
tot_angle = np.arccos(cos_angle_u) + np.arccos(cos_angle_v)
cos_tangle = np.cos(self.angle)
assert(abs(np.cos(tot_angle) - cos_tangle) < eps)
factor = psize / (1 - cos_tangle**2.0)
a = factor * (cos_angle_u - np.cos(self.angle)*cos_angle_v) / size
b = factor * (cos_angle_v - | np.cos(self.angle) | numpy.cos |
""" Functions for fetching USarray waveforms. """
from __future__ import print_function, division, absolute_import
import os
import sys
import datetime
import argparse
import copy
import time
# Check version
if sys.version_info.major < 3:
import urllib as urllibrary
else:
import urllib.request as urllibrary
import urllib
import numpy as np
import matplotlib.pyplot as plt
import scipy.signal
import obspy
from wmpl.Utils.Earth import greatCircleDistance
from wmpl.Utils.OSTools import mkdirP
from wmpl.Utils.PlotMap import GroundMap
from wmpl.Utils.Math import subsampleAverage
import pyximport
pyximport.install(setup_args={'include_dirs':[np.get_include()]})
from supra.Fireballs.SeismicTrajectory import timeOfArrival, waveReleasePoint, waveReleasePointWinds, Constants
from supra.Utils.Classes import Position
from supra.Supracenter.cyscan5 import cyscan
from supra.Atmosphere.Parse import parseWeather
DATA_FILE = 'data.txt'
C = ['r', 'g', 'm', 'k', 'y']
'''Reads input config files'''
try:
# Python 2
import ConfigParser as configparser
except:
# Python 3
import configparser
import os
import sys
import datetime
def butterworthBandpassFilter(lowcut, highcut, fs, order=5):
""" Butterworth bandpass filter.
Argument:
lowcut: [float] Lower bandpass frequency (Hz).
highcut: [float] Upper bandpass frequency (Hz).
fs: [float] Sampling rate (Hz).
Keyword arguments:
order: [int] Butterworth filter order.
Return:
(b, a): [tuple] Butterworth filter.
"""
# Calculate the Nyquist frequency
nyq = 0.5*fs
low = lowcut/nyq
high = highcut/nyq
# Init the filter
b, a = scipy.signal.butter(order, [low, high], btype='bandpass')
return b, a
def convolutionDifferenceFilter(waveform_data):
""" Apply the convolution filter on data as suggested in Kalenda et al. (2014). """
# Apply the filter
filtered_data = np.convolve(waveform_data, [-0.5, 1.0, -0.5], mode='same')
# Detrend data
filtered_data = filtered_data - np.mean(filtered_data)
return filtered_data
def plotStationMap(dir_path, data_list, lat_centre, lon_centre, setup, sounding, ax=None, isc_data=None):
""" Plots the map of siesmic stations from loaded data file. """
fig = plt.figure(figsize=plt.figaspect(0.5))
fig.set_size_inches(20.9, 11.7)
if ax is None:
ax = plt.gca()
# Find unique networks
# networks = [entry[0] for entry in data_list]
# stat = [entry[1] for entry in data_list]
# net_isc = []
# lats=[]
# lons=[]
# Extra stations
if isc_data is not None:
all_stns = data_list + isc_data
# Remove duplicates
# k = sorted(isc_data)
# isc_data = [k[i] for i in range(len(k)) if i == 0 or k[i] != k[i-1]]
# for line in isc_data:
# # Only use stations within 5 degrees of lat and lon
# if abs(line[2] - lat_centre) < 5 and abs(line[3] - lon_centre) < 5:
# lats.append(np.radians(line[2]))
# lons.append(np.radians(line[3]))
# net_isc.append(line[5])
# # Extract the list of station locations
# lat_list = [np.radians(entry[2]) for entry in data_list]
# lon_list = [np.radians(entry[3]) for entry in data_list]
if len(all_stns) == 0:
print("ERROR: No stations to plot!")
exit()
lats = []
lons = []
for i in range(len(all_stns)):
lats.append(all_stns[i].position.lat_r)
lons.append(all_stns[i].position.lon_r)
# Plot stations and extra stations
m = GroundMap(lats, lons, ax=ax, color_scheme='light')
# Plot different networks with different colours
for stn in all_stns:
# # Extract the list of station locations
# lat_net_list = [np.radians(entry[2]) for entry in data_list]
# lon_net_list = [np.radians(entry[3]) for entry in data_list]
m.scatter(stn.position.lat_r, stn.position.lon_r, s=2, label=stn.network)
# for i in range(len(lat_net_list)):
x, y = m.m(stn.position.lon, stn.position.lat)
plt.text(x, y, stn.network + '-' + stn.code, horizontalalignment='left', verticalalignment='top', color='k', fontsize=8)
# if stat[i] in setup.rm_stat:
# pass
# # print('Excluding station: {:}'.format(networks[i] + '-' + stat[i]))
# else:
# if stat[i] in setup.high_f:
# m.scatter(lat_net_list[i], lon_net_list[i], s=25, c='g')
# elif stat[i] in setup.high_b:
# m.scatter(lat_net_list[i], lon_net_list[i], s=25, c='b')
# # if len(lats) != 0:
# for i in range(len(net_isc)):
# x, y = m.m(np.degrees(lons[i]), np.degrees(lats[i]))
# plt.text(x, y, net_isc[i], horizontalalignment='left', verticalalignment='top', color='k', fontsize=8)
lx, ly = m.m(lon_centre, lat_centre)
# # All extra stations added
# if isc_data is not None:
# for i in range(len(net_isc)):
# # Convert coordinates to map coordinates
# x, y = m.m(np.degrees(lons[i]), np.degrees(lats[i]))
# # Plot extra stations
# m.scatter(lats[i], lons[i], marker='^', c='k', s=1, )
# # Plot the text
# #plt.text(x, y, net_isc[i], horizontalalignment='left', verticalalignment='top', color='k', fontsize=8)
# data_list.append(isc_data[i])
# Plot source location
m.scatter([np.radians(lat_centre)], [np.radians(lon_centre)], marker='*', c='yellow', edgecolor='k', \
linewidth=0.1, label='Source')
# Plot the trajectory or fragmentation point if given
if setup.show_fragmentation_waveform or setup.show_ballistic_waveform:
if setup.show_fragmentation_waveform:
for i, line in enumerate(setup.fragmentation_point):
# Fragmentation plot
m.scatter([np.radians(float(line[0]))], [np.radians(float(line[1]))], c=C[(i+1)%4], marker='x')
# Extract coordinates of the reference station
ref_pos = position(lat_centre, lon_centre, 0)
# # Calculate the coordinates of the trajectory intersection with the ground
# lat_i, lon_i, elev_i = local2LatLon(float(np.radians(lat0)), float(np.radians(lon0)), float(0), \
# np.array([float(setup.lat_f), float(setup.lon_f), 0]))
# Calculate the coordinate of the beginning of the trajectory
# lat_beg, lon_beg = np.radians(float(np.degrees(setup.lat_i)) - np.cos(np.radians(setup.azim))), \
# np.radians(float(np.degrees(setup.lon_i)) - np.sin(np.radians(setup.azim)))
if setup.show_ballistic_waveform:
# Plot intersection with the ground
m.scatter(setup.traj_f.lat_r, setup.traj_f.lon_r, s=10, marker='x', c='b')
# Plot the trajectory
m.plot([setup.traj_i.lat_r, setup.traj_f.lat_r], [setup.traj_i.lon_r, setup.traj_f.lon_r], c='b')
# Get the limits of the plot
# (approximately a box around the deg_radius)
x_min = setup.traj_f.lon - 100000*setup.deg_radius
x_max = setup.traj_f.lon + 100000*setup.deg_radius
y_min = setup.traj_f.lat - 100000*setup.deg_radius
y_max = setup.traj_f.lat + 100000*setup.deg_radius
# Grid size of the contour plot
img_dim = setup.contour_res
x_data = np.linspace(x_min, x_max, img_dim)
y_data = np.linspace(y_min, y_max, img_dim)
xx, yy = | np.meshgrid(x_data, y_data) | numpy.meshgrid |
import numpy as np
import numpy.linalg as nla
from numpy import cos, sin
import scipy.linalg as sla
import scipy.interpolate
import scipy.optimize
from fym.core import BaseEnv, BaseSystem
from fym.utils.rot import quat2dcm, quat2angle, angle2quat
class Aircraft3Dof(BaseSystem):
g = 9.80665
rho = 1.2215
m = 8.5
S = 0.65
b = 3.44
CD0 = 0.033
CD1 = 0.017
name = 'aircraft'
def __init__(self, initial_state, wind):
super().__init__(initial_state)
self.wind = wind
self.term1 = self.rho*self.S/2/self.m
def external(self, states, controls):
state = states['aircraft']
return dict(wind=self.wind.get(state))
def deriv(self, state, t, control, external):
CL, phi = control
CD = self.CD0 + self.CD1*CL**2
raw_control = CD, CL, phi
return self._raw_deriv(state, t, raw_control, external)
def _raw_deriv(self, state, t, control, external):
x, y, z, V, gamma, psi = state.ravel()
CD, CL, phi = control()
(_, Wy, _), (_, (_, _, dWydz), _) = external['wind']
dxdt = V*np.cos(gamma)*np.cos(psi)
dydt = V*np.cos(gamma)*np.sin(psi) + Wy
dzdt = - V*np.sin(gamma)
dWydt = dWydz * dzdt
dVdt = (-self.term1*V**2*CD - self.g*np.sin(gamma)
- dWydt*np.cos(gamma)*np.sin(psi))
dgammadt = (self.term1*V*CL*np.cos(phi) - self.g*np.cos(gamma)/V
+ dWydt*np.sin(gamma)*np.sin(psi)/V)
dpsidt = (self.term1*V/np.cos(gamma)*CL*np.sin(phi)
- dWydt*np.cos(psi)/V/np.cos(gamma))
return np.vstack([dxdt, dydt, dzdt, dVdt, dgammadt, dpsidt])
class F16LinearLateral(BaseSystem):
"""
Reference:
<NAME> et al. "Aircraft Control and Simulation", 3/e, 2016
Example 5.3-1: LQR Design for F-16 Lateral Regulator
Dynamics:
x_dot = Ax + Bu
State:
x = [beta, phi, p, r, del_a, del_r, x_w]
beta, phi: [rad], p, r: [rad/s], del_a, del_r: [deg]
Control input:
u = [u_a, u_r] (aileron and rudder servo inputs, [deg])
"""
A = np.array([
[-0.322, 0.064, 0.0364, -0.9917, 0.0003, 0.0008, 0],
[0, 0, 1, 0.0037, 0, 0, 0],
[-30.6492, 0, -3.6784, 0.6646, -0.7333, 0.1315, 0],
[8.5396, 0, -0.0254, -0.4764, -0.0319, -0.062, 0],
[0, 0, 0, 0, -20.2, 0, 0],
[0, 0, 0, 0, 0, -20.2, 0],
[0, 0, 0, 57.2958, 0, 0, -1]
])
B = np.array([
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[20.2, 0],
[0, 20.2],
[0, 0]
])
C = np.array([
[0, 0, 0, 57.2958, 0, 0, -1],
[0, 0, 57.2958, 0, 0, 0, 0],
[57.2958, 0, 0, 0, 0, 0, 0],
[0, 57.2958, 0, 0, 0, 0, 0]
])
def __init__(self, initial_state=[1, 0, 0, 0, 0, 0, 0]):
super().__init__(initial_state)
def deriv(self, x, u):
return self.A.dot(x) + self.B.dot(u)
class MorphingPlane(BaseEnv):
g = 9.80665 # [m/s^2]
mass = 10 # [kg]
S = 0.84 # reference area (norminal planform area) [m^2]
# longitudinal reference length (nominal mean aerodynamic chord) [m]
cbar = 0.288
b = 3 # lateral reference length (nominal span) [m]
Tmax = 50 # maximum thrust [N]
control_limits = {
"delt": (0, 1),
"dele": np.deg2rad((-10, 10)),
"dela": (-0.5, 0.5),
"delr": (-0.5, 0.5),
"eta1": (0, 1),
"eta2": (0, 1),
}
coords = {
"eta1": np.linspace(0, 1, 3), # eta1
"eta2": np.linspace(0, 1, 3), # eta2
"dele": np.deg2rad(np.linspace(-10, 10, 3)), # dele
"alpha": np.deg2rad(np.linspace(-10, 20, 61)) # alpha
}
polycoeffs = {
"CD": [0.03802,
[-0.0023543, 0.0113488, -0.00549877, 0.0437561],
[[0.0012769, -0.00220993, 1166.938, 672.113],
[0.00188837, 0.000115637, -203.85818, -149.4225],
[-1166.928, 203.8535, 0.1956192, -115.13404],
[-672.111624, 149.417, 115.76766, 0.994464]]],
"CL": [0.12816,
[0.13625538, 0.1110242, 1.148293, 6.0995634],
[[-0.147822776, 1.064541, 243.35532, -330.0270179],
[-1.13021511, -0.009309088, 166.28991, -146.8964467],
[-243.282881, -166.2709286, 0.071258483, 4480.53564],
[328.541707, 148.945785, -4480.67456545, -0.99765511]]],
"Cm": [0.09406144,
[-0.269902, 0.24346326, -7.46727, -2.7296],
[[0.35794703, -7.433699, 647.83725, -141.0390569],
[6.8532466, -0.0510021, 542.882121, -681.325],
[-647.723162, -542.8638, 0.76322739, 2187.33517],
[135.66547, 678.941, -2186.1196, 0.98880322]]]
}
J_template = np.array([
[9323306930.82, -2622499.75, 56222833.68],
[-2622499.75, 0, 395245.59],
[56222833.68, 395245.59, 105244200037]
]) / 10**9 / 103.47649 * mass
J_yy_data = np.array([
[96180388451.54, 96468774320.55, 97352033548.31],
[96180388451.54, 96720172843.10, 98272328292.52],
[96180388451.54, 97077342563.70, 99566216309.81]
]).T / 10**9 / 103.47649 * mass
J_yy = scipy.interpolate.interp2d(
coords["eta1"], coords["eta2"], J_yy_data
)
def __init__(self, velocity, omega, quaternion, position):
self.vel = BaseSystem(velocity, name="velocity") # 3x1
self.omega = BaseSystem(omega, name="omega") # 3x1
self.quat = BaseSystem(quaternion, name="quaternion") # 4x1
self.pos = BaseSystem(position, name="position") # 3x1
def J(self, eta1, eta2):
J_temp = self.J_template
J_temp[1, 1] = self.J_yy(eta1, eta2)
return J_temp
def _aero_base(self, name, *x):
# x = [eta1, eta2, dele, alp]
a0, a1, a2 = self.polycoeffs[name]
return a0 + np.dot(a1, x) + np.sum(x * np.dot(a2, x), axis=0)
def CD(self, eta1, eta2, dele, alp):
return self._aero_base("CD", eta1, eta2, dele, alp)
def CL(self, eta1, eta2, dele, alp):
return self._aero_base("CL", eta1, eta2, dele, alp)
def Cm(self, eta1, eta2, dele, alp):
return self._aero_base("Cm", eta1, eta2, dele, alp)
def set_dot(self, x, u, eta):
v, omega, q, p = self.observe_list(x)
F, M = self.aerodyn(v, q, p, u, eta)
J = self.J(eta[0], eta[1])
# force equation
self.systems_dict["velocity"].dot = F / self.mass - np.cross(omega, v)
# moment equation
self.systems_dict["omega"].dot = (
nla.inv(J).dot(M - np.cross(omega, J.dot(omega)))
)
# kinematic equation
self.systems_dict["quaternion"].dot = 0.5 * np.append(
-omega.dot(q[1:]),
omega*q[0] - np.cross(omega, q[1:])
)
# navigation equation
self.systems_dict["position"].dot = quat2dcm(q).T.dot(v)
def state_readable(self, v=None, omega=None, q=None, p=None, preset="vel"):
VT = sla.norm(v)
alpha = np.arctan2(v[2], v[0])
beta = np.arcsin(v[1] / VT)
if preset == "vel":
return VT, alpha, beta
else:
_, theta, _ = quat2angle(q)
gamma = theta - alpha
Q = omega[1]
return {'VT': VT, 'gamma': gamma, 'alpha': alpha, 'Q': Q,
'theta': theta, 'beta': beta}
def aerocoeff(self, *args):
# *args: eta1, eta2, dele, alp
# output: CL, CD, Cm, CC, Cl, Cn
return self.CL(*args), self.CD(*args), self.Cm(*args), 0, 0, 0
def aerodyn(self, v, q, p, u, eta):
delt, dele, dela, delr = u
x_cg, z_cg = 0, 0
VT, alp, bet = self.state_readable(v=v, preset="vel")
qbar = 0.5 * get_rho(-p[2]) * VT**2
CL, CD, Cm, CC, Cl, Cn = self.aerocoeff(*eta, dele, alp)
CX = cos(alp)*cos(bet)*(-CD) - cos(alp)*sin(bet)*(-CC) - sin(alp)*(-CL)
CY = sin(bet)*(-CD) + cos(bet)*(-CC) + 0*(-CL)
CZ = cos(bet)*sin(alp)*(-CD) - sin(alp)*sin(bet)*(-CC) + cos(alp)*(-CL)
S, cbar, b, Tmax = self.S, self.cbar, self.b, self.Tmax
X_A = qbar*CX*S # aerodynamic force along body x-axis
Y_A = qbar*CY*S # aerodynamic force along body y-axis
Z_A = qbar*CZ*S # aerodynamic force along body z-axis
# Aerodynamic moment
l_A = qbar*S*b*Cl + z_cg*Y_A # w.r.t. body x-axis
m_A = qbar*S*cbar*Cm + x_cg*Z_A - z_cg*X_A # w.r.t. body y-axis
n_A = qbar*S*b*Cn - x_cg*Y_A # w.r.t. body z-axis
F_A = np.array([X_A, Y_A, Z_A]) # aerodynamic force [N]
M_A = np.array([l_A, m_A, n_A]) # aerodynamic moment [N*m]
# thruster force and moment are computed here
T = Tmax*delt # thrust [N]
X_T, Y_T, Z_T = T, 0, 0 # thruster force body axes component [N]
l_T, m_T, n_T = 0, 0, 0 # thruster moment body axes component [N*m]
# Thruster force, momentum, and gravity force
F_T = np.array([X_T, Y_T, Z_T]) # in body coordinate [N]
M_T = np.array([l_T, m_T, n_T]) # in body coordinate [N*m]
F_G = quat2dcm(q).dot(np.array([0, 0, self.mass*self.g]))
F = F_A + F_T + F_G
M = M_A + M_T
return F, M
def get_trim(self, z0={"alpha": 0.1, "delt": 0.13, "dele": 0},
fixed={"h": 300, "VT": 16, "eta": (0, 0)},
method="SLSQP", options={"disp": True, "ftol": 1e-10}):
z0 = list(z0.values())
fixed = list(fixed.values())
bounds = (
(self.coords["alpha"].min(), self.coords["alpha"].max()),
self.control_limits["delt"],
self.control_limits["dele"]
)
result = scipy.optimize.minimize(
self._trim_cost, z0, args=(fixed,),
bounds=bounds, method=method, options=options)
return self._trim_convert(result.x, fixed)
def _trim_cost(self, z, fixed):
x, u, eta = self._trim_convert(z, fixed)
self.set_dot(x, u, eta)
weight = np.diag([1, 1, 1000])
dxs = np.append(self.vel.dot[(0, 2), ], self.omega.dot[1])
return dxs.dot(weight).dot(dxs)
def _trim_convert(self, z, fixed):
h, VT, eta = fixed
alp = z[0]
v = np.array([VT*cos(alp), 0, VT*sin(alp)])
omega = np.array([0, 0, 0])
q = angle2quat(0, alp, 0)
p = np.array([0, 0, -h])
delt, dele, dela, delr = z[1], z[2], 0, 0
x = np.hstack((v, omega, q, p))
u = np.array([delt, dele, dela, delr])
return x, u, eta
def get_rho(altitude):
pressure = 101325 * (1 - 2.25569e-5 * altitude)**5.25616
temperature = 288.14 - 0.00649 * altitude
return pressure / (287*temperature)
class MorphingLon(BaseSystem, MorphingPlane):
"""
This is a nonlinear simulator of morphing aircraft only considering
the longitudinal dynamics for reduced computational burden.
state (x) : 4x1 vector of (V, alpha, q, gamma)
control (u) : 2x1 vector of (delt, dele)
morph (eta) : 2x1 vector of (eta1, eta2)
"""
rho = get_rho(300)
def __init__(self, init_state=None):
if init_state is None:
init_state, *_ = self.get_trim(verbose=True)
super().__init__(init_state)
self.limits = np.vstack([
self.control_limits[k]
for k in ("delt", "dele", "eta1", "eta2")
])[:, None].transpose(2, 0, 1)
def deriv(self, x, u, eta):
"""Get the state derivative for given (x, u)"""
self._check_control(u)
V, alpha, q, gamma = x.ravel()
delt, dele = u.ravel()
eta1, eta2 = eta.ravel()
S, cbar, Tmax = self.S, self.cbar, self.Tmax
m, g = self.mass, self.g
qbar = self.rho * V**2 / 2
T = Tmax * delt
L = qbar * S * self.CL(eta1, eta2, dele, alpha)
D = qbar * S * self.CD(eta1, eta2, dele, alpha)
M = qbar * cbar * S * self.Cm(eta1, eta2, dele, alpha)
Iy = self.J_yy(eta1, eta2)
dV = 1 / m * (-D + T * cos(alpha) - m * g * sin(gamma))
dalpha = q - 1 / (m * V) * (L + T * sin(alpha) - m * g * cos(gamma))
dq = M / Iy
dgamma = 1 / (m * V) * (L + T * sin(alpha) - m * g * cos(gamma))
return np.vstack((dV, dalpha, dq, dgamma))
def _check_control(self, u):
tlim = self.control_limits["delt"]
elim = self.control_limits["dele"]
if tlim[0] > u[0] or tlim[1] < u[0]:
print("WARN: thrust is over the limits")
if elim[0] > u[1] or elim[1] < u[1]:
print("WARN: elevator is over the limits")
def _trim_cost(self, z, fixed):
x, u, eta = self._trim_convert(z, fixed)
dxs = self.deriv(x, u, eta)
weight = np.diag([1, 1, 100, 1])
return dxs.T.dot(weight).dot(dxs)[0][0]
def _trim_convert(self, z, fixed):
V, _, (eta1, eta2) = fixed
alpha, delt, dele = z
q, gamma = 0, 0
x = np.vstack([V, alpha, q, gamma])
u = np.vstack([delt, dele])
eta = np.vstack([eta1, eta2])
return x, u, eta
def get_trim(self, z0={"alpha": 0.1, "delt": 0.19, "dele": 0},
fixed={"V": 20, "h": 300, "eta": (0.5, 0.5)},
method="SLSQP", options={"disp": False, "ftol": 1e-10},
verbose=False):
z0 = list(z0.values())
fixed = list(fixed.values())
bounds = (
(self.coords["alpha"].min(), self.coords["alpha"].max()),
self.control_limits["delt"],
self.control_limits["dele"]
)
result = scipy.optimize.minimize(
self._trim_cost, z0, args=(fixed,),
bounds=bounds, method=method, options=options)
x, u, eta = self._trim_convert(result.x, fixed)
dx = self.deriv(x, u, eta)
if verbose:
print("=========================================")
print(" Trim point ")
print(" ---------- ")
print("VT: {:5.2f} [m/s] AOA: {:5.2f} [deg]".format(
x[0, 0], x[1, 0] * np.rad2deg(1)))
print("Q: {:5.2f} [deg/s] Gamma: {:5.2f} [deg]".format(
x[2, 0] * np.rad2deg(1), x[3, 0] * np.rad2deg(1)))
print("delt: {:5.2f} [ ] dele: {:5.2f} [deg]".format(
u[0, 0], u[1, 0] * np.rad2deg(1)))
print("eta1: {:5.2f} [ ] eta2: {:5.2f} [ ]".format(
eta[0, 0], eta[1, 0]))
print("")
print(" Derivatives ")
print(" ----------- ")
print("VT: {:9.2e} [m/s] AOA: {:9.2e} [deg]".format(
dx[0, 0], dx[1, 0] * | np.rad2deg(1) | numpy.rad2deg |
# plots.py
import matplotlib
matplotlib.rcParams = matplotlib.rc_params_from_file('../../matplotlibrc')
#================================================
#Plots for the Value Function Iteration Lab
#================================================
import numpy as np
import math
from scipy import stats as st
import discretenorm
from matplotlib import pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
def diff_policies():
def graph_policy(policies, utility_function=np.sqrt, beta=0.9):
# First, create a state space that is the same length as the policy.
states = np.linspace(0,1,len(policies[0]))
# Now calculate the utility accumulated at each step of the policy.
fig = plt.figure()
fig.set_size_inches(8,8)
plt.title('Utility Gained From Various Policies')
for i, policy in enumerate(policies):
total_utility = np.zeros(len(policy))
total_utility[0] = utility_function(policy[0])
for j, consumption_amount in enumerate(policy[1:]):
total_utility[j+1] = total_utility[j] + beta**(j+1)*utility_function(policy[j+1])
l, = plt.plot(np.arange(len(policy)), total_utility, label='Policy ' + str(i+1)
+ ', Utility = ' + str(total_utility[-1])[:3])
print("Total Utility: \t" + str(total_utility[-1]))
plt.legend(loc='upper left')
plt.savefig('./diff_policies.pdf')
policy1 = np.array([1.0, 0, 0, 0, 0])
policy2 = np.array([0, 0, 0, 0, 1.0])
policy3 = np.array([0.2, 0.2, 0.2, 0.2, 0.2])
policy4 = np.array([0.4, 0.3, 0.2, 0.1, 0])
policies = [policy1, policy2, policy3, policy4]
graph_policy(policies)
def eatCake(beta, N, Wmax=1., T=None, finite=True, plot=False):
"""
Solve the finite horizon cake-eating problem using Value Function iteration.
Inputs:
T -- final time period
beta -- discount factor
N -- number of discrete intervals to break up the cake
size -- size of the cake to begin with
plot -- boolean indicating whether to plot value function surface and policy function
surface
Returns:
values -- numpy array of shape (N, T+2) (if finite=True) or shape (N,) (if finite=False)
giving the value function at each time period for each state
psi -- numpy array of shape (N, T+1) (if finite=True) or shape (N,) (if finite=False)
giving the policy at each time period for each state.
"""
states = np.linspace(0,Wmax,N) #state space vector
actions = np.tile(states, N).reshape((N,N)).T
actions = actions - actions.T
actions[actions<0] = 0
rewards = np.sqrt(actions)
rewards[np.triu_indices(N, k=1)] = -1e10 #pre-computed reward function
n_range = np.arange(N) #this is used several times, so initialize it once
if finite:
values = np.zeros((N, T+2))
psi = np.zeros((N, T+1))
for i in xrange(T,-1,-1):
argmaxs = np.argmax(rewards + beta*values[:,i+1].reshape(1,N), axis=1)
values[:,i] = (rewards + beta*values[:,i+1].reshape(1,N))[n_range,argmaxs]
psi[:,i] = states[argmaxs]
x=np.arange(0,N)
if plot:
x=np.arange(0,N)
y=np.arange(0,T+2)
X,Y=np.meshgrid(x,y)
fig1 = plt.figure()
ax1= Axes3D(fig1)
ax1.plot_surface(states[X],Y,values.T, cmap=cm.coolwarm)
plt.show ()
fig2 = plt.figure()
ax2 = Axes3D(fig2)
y = np.arange(0,T+1)
X,Y=np.meshgrid(x,y)
ax2.plot_surface(states[X],Y,psi.T, cmap = cm.coolwarm)
plt.show()
else:
values = np.zeros(N)
psi = np.zeros(N)
delta = 1.
while delta >= 1e-9:
values1 = values.copy()
argmaxs = np.argmax(rewards + beta*values1.reshape(1,N), axis=1)
values = (rewards + beta*values.reshape(1,N))[n_range, argmaxs]
psi = states[argmaxs]
delta = ((values-values1)**2).sum()
if plot:
plt.plot(states, psi)
plt.show()
return values, psi
def finite_horiz():
#First compute solution to problem 1
beta = 0.9;
T = 10;
N = 100;
u = lambda c: np.sqrt(c);
W = np.linspace(0,1,N);
X, Y = np.meshgrid(W,W);
Wdiff = Y-X
index = Wdiff <0;
Wdiff[index] = 0;
util_grid = u(Wdiff);
util_grid[index] = -10**10;
V = np.zeros((N,T+2));
psi = np.zeros((N,T+1));
for k in xrange(T,-1,-1):
val = util_grid + beta*np.tile(V[:,k+1].T,(N,1));
vt = np.amax(val, axis = 1);
psi_ind = np.argmax(val,axis = 1)
V[:,k] = vt;
psi[:,k] = W[psi_ind];
#now create plots
#fixed time plot
plt.figure()
plt.plot(V[:,5])
plt.title(r'Value function for $t = 5$')
plt.ylabel(r'$V$')
plt.xlabel(r'$W$')
plt.savefig('fixed_time.pdf')
#fixed W plot
plt.figure()
plt.plot(V[50,:])
plt.title(r'Value function for $W = 0.505$')
plt.ylabel(r'$V$')
plt.xlabel(r'$t$')
plt.savefig('fixed_w.pdf')
plt.clf()
#plot delta -> 0
def delta():
beta = 0.99
N = 1000
u = lambda c: np.sqrt(c)
W = np.linspace(0,1,N)
X, Y = np.meshgrid(W,W)
Wdiff = (X-Y).T
index = Wdiff <0
Wdiff[index] = 0
util_grid = u(Wdiff)
util_grid[index] = -10**10
Vprime = np.zeros((N,1))
delta = np.ones(1)
tol = 10**-9
it = 0
max_iter = 500
while (delta[-1] >= tol) and (it < max_iter):
V = Vprime
it += 1;
val = util_grid + beta*V.T
Vprime = np.amax(val, axis = 1)
Vprime = Vprime.reshape((N,1))
delta = np.append(delta,np.dot((Vprime-V).T,Vprime-V))
plt.figure()
plt.plot(delta[1:])
plt.ylabel(r'$\delta_k$')
plt.xlabel('iteration')
plt.savefig('convergence.pdf')
plt.clf()
def infiniteHorizon():
"""
Plot policy function for infinite time horizon cake eating problem.
"""
values, psi = eatCake(.9, 100, finite=False)
states = np.linspace(0,1,100)
plt.figure()
plt.title(r'Policy Function')
plt.ylabel(r'$\psi$')
plt.xlabel(r'$W$')
plt.plot(states, psi)
plt.savefig('infiniteHorizon.pdf')
plt.clf()
def disc_norm():
x = np.linspace(-3,3,100)
y = st.norm.pdf(x,0,1)
fig, ax = plt.subplots()
fig.canvas.draw()
ax.plot(x,y)
fill1_x = np.linspace(-2,-1.5,100)
fill1_y = st.norm.pdf(fill1_x,0,1)
fill2_x = | np.linspace(-1.5,-1,100) | numpy.linspace |
#!/usr/bin/env python
# -*- encoding: utf-8 -*-
'''
@Description : 根据路网进一步细化网格
@Date : 2021/11/28 10:49:59
@Author : gz.gong
@Contact : <EMAIL>
@version : 1.0
'''
import numpy as np
from pandas.io import pickle
def path_match(real_roads, car_paths):
""" assign each catr_path one real road in a single grid
Arg:
real_roads: list[ list[ [float: x, float: y], ... ], ... ]
len(real_roads) --> M, M is the number of real road in current grid
car_paths: list[ list[ [float: x, float: y], ... ], ... ]
len(car_paths) --> N, N is the number of car path in current grid
output:
match_index: list[ int: i_0, int: i_1, ... int: i_N-1 ]
len(match_index) --> N
i ~ (i_0, i_N-1) ∈ range(0, M)
example: match_index --> list[ int: i_0 = 5, int: i_1 = 2, ... ] NOTES: now M >= 5
means car_paths[0] matches real_roads[5], car_paths[1] matches real_roads[2]
Description:
Author: @Tu.xk
Date: 2021-11-27
"""
M = len(real_roads)
N = len(car_paths)
roadLength_group = [len(real_roads[i]) for i in range(M)]
roadlength_group = np.array(roadLength_group, dtype=np.int32)
max_roadLength = np.max(roadlength_group)
for i in range(M):
current_roadLen = len(real_roads[i])
if current_roadLen < max_roadLength:
for k in range(max_roadLength - current_roadLen):
real_roads[i].append([0., 0.])
real_roads_np = np.array(real_roads,
dtype=np.float32).reshape(1, M, max_roadLength, 2)
path_match_index = []
for j in range(N):
car_path = car_paths[j]
car_pathLength = len(car_path)
car_path = np.array(car_path, dtype=np.float32).reshape(-1, 1, 1, 2)
real_roads_np_expsion = np.repeat(real_roads_np,
car_pathLength,
axis=0)
path_match_dis = real_roads_np_expsion - car_path
path_match_dis = np.linalg.norm(path_match_dis,
ord=2,
axis=-1,
keepdims=False)
path_match_dis = np.min(path_match_dis, axis=-1)
path_match_dis = | np.sum(path_match_dis, axis=0, keepdims=False) | numpy.sum |
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Interpolation of Amplitude and Phase using the interpolant derived by <NAME>.
For details see - https://doi.org/10.1007/s10236-017-1122-8
TODO:
* Add a wrapper class
* Add type and error check
* Add case for missing value
Author: khan
"""
import numpy as np
import matplotlib.pyplot as plt
class Point(object):
'''
Point(x, y=0, a=None, p=None, isradians=False) is point object to hold point information
including the amplitude and phase.
args:
x (float) : x position
y (float) : y position
a (float) : amplitude
p (float) : phase in degree or radians (default: degrees)
isradians (bool): if input is in degrees or radians (default: false)
returns:
An instance of Point class.
attributes:
x (float) : x position
y (float) : y position
a (float) : amplitude
p (float) : phase in radians
methods:
print() : prints the attributes
TODO:
* add typecheck and error handling
'''
def __init__(self, x, y=0, a=None, p=None, isradians=False):
self.x = float(x)
self.y = float(y)
if a is not None:
self.a = float(a)
else:
self.a = float(0)
self.isradians = isradians
if p is not None:
if self.isradians:
self.p = float(p)
else:
self.p = float(p)*np.pi/180.0
else:
self.p = float(0)
def print(self):
print(self.x, self.y, self.a, self.p)
def __lt__(self, other):
return(self.x < other.x and self.y < other.y)
class Grid(object):
'''
Grid(x, y, A=None, P=None, isradians=False) is the grid object to hold points in a meshgrid.
args:
x ([float]) : x positon array in the structured grid
y ([float]) : y position array in the structured grid
A ([[float]]) : 2D array of size (x, y) containing amplitude
P ([[float]]) : 2D array of size (x, y) containing phase
isradians (bool) : if the phase in in radians
'''
def __init__(self, x, y, A=None, P=None, isradians=False):
# Initiating variables
self.x = x
self.y = y
__X, __Y = np.meshgrid(self.x, self.y, indexing='xy')
self.shape = __X.shape
self.length = len(__X.flat)
self.isradians = isradians
if A is None:
__A = | np.zeros(shape=self.shape) | numpy.zeros |
# -*- coding: utf-8 -*-
"""Face Mask Detector.ipynb
Automatically generated by Colaboratory.
Original file is located at
https://colab.research.google.com/drive/14kYPMO05mqO4AYEyGNxnMlegQuWJ9EmT
"""
# Commented out IPython magic to ensure Python compatibility.
import tensorflow as tf
import keras
from tensorflow.keras.preprocessing.image import ImageDataGenerator
from tensorflow.keras.applications import MobileNetV2
from tensorflow.keras.models import Model
from tensorflow.keras.optimizers import Adam
from tensorflow.keras.applications.mobilenet_v2 import preprocess_input
from tensorflow.keras.preprocessing.image import img_to_array
from tensorflow.keras.preprocessing.image import load_img
from tensorflow.keras.utils import to_categorical
from sklearn.preprocessing import LabelBinarizer
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report
from imutils import paths
import matplotlib.pyplot as plt
# %matplotlib inline
import numpy as np
import argparse
import os
"""## Mounting GDrive"""
from google.colab import drive
drive.mount('/content/drive')
"""### **IMPORTANT NOTE:**
#### If you take a look at Figure you can start to see our training and validation loss start to rapidly divide. When you see training loss falling quickly while validation loss stagnates or even increases, you know you are overfitting.
## What Is **MobileNetV2**?
#### MobileNets are small, low-latency, low-power models parameterised to meet the resource constraints of a variety of use cases. According to the research paper, MobileNetV2 improves the state-of-the-art performance of mobile models on multiple tasks and benchmarks as well as across a spectrum of different model sizes.
#### MobileNetV2 is optimised for mobile devices. The architecture delivers high accuracy results while keeping the parameters and mathematical operations as low as possible to bring deep neural networks to mobile devices.
#### The weights of the pre-trained snippets were learned by the Google team using **ImageNet**.
#### NOTE: **Weights in MobileNetV2:**
One of the following:
* None (random initialization)
* 'imagenet' (pre-training on ImageNet)
* or the path to the weights file to be loaded. Default to imagenet.
---
#### To accomplish **FACE MASK DETECTOR**, we’ll be fine-tuning the MobileNet V2 architecture, a highly efficient architecture that can be applied to embedded devices with limited computational capacity (ex., Raspberry Pi, Google Coral, NVIDIA Jetson Nano, etc.).
---
## Parsing a few command line arguments that are required to launch our script from a terminal
"""
# ap = argparse.ArgumentParser()
# ap.add_argument("-d", "--dataset", required=True,
# help="path to input dataset")
# ap.add_argument("-p", "--plot", type=str, default="plot.png",
# help="path to output loss/accuracy plot")
# ap.add_argument("-m", "--model", type=str,
# default="mask_detector.model",
# help="path to output face mask detector model")
# args = vars(ap.parse_args())
"""## Defining Hyperparameters
#### We will be applying a learning rate decay schedule, which is why we’ve named the learning rate variable INIT_LR.
"""
init_lr = 1e-4 # 0.0001
epochs = 20
bs = 32
"""## Loading and pre-processing our training data"""
imagePaths_mask = []
imagePaths_nomask = []
for filename in os.listdir("/content/drive/My Drive/Kaggle/Face Mask Detector/dataset/with_mask"):
imagePaths_mask.append(filename)
for filename in os.listdir("/content/drive/My Drive/Kaggle/Face Mask Detector/dataset/without_mask"):
imagePaths_nomask.append(filename)
"""**img_to_array()** - Keras provides the img_to_array() function for converting a loaded image in PIL format into a NumPy array for use with deep learning models.
**preprocess_input** - Model specific. The preprocess_input function is meant to adequate your image to the format the model requires
"""
data = []
labels = []
for img in imagePaths_mask:
label = 'with_mask'
image = load_img("/content/drive/My Drive/Kaggle/Face Mask Detector/dataset/with_mask/"+img, target_size=(224,224))
image = img_to_array(image)
image = preprocess_input(image)
data.append(image)
labels.append(label)
for img in imagePaths_nomask:
label = 'without_mask'
image = load_img("/content/drive/My Drive/Kaggle/Face Mask Detector/dataset/without_mask/"+img, target_size=(224,224))
image = img_to_array(image)
image = preprocess_input(image)
data.append(image)
labels.append(label)
# convert the data and labels to NumPy arrays
data = | np.array(data, dtype="float32") | numpy.array |
from __future__ import print_function
import numpy as np
import matplotlib.pyplot as plt
class ISO:
"""
Reads in MIST isochrone files.
"""
def __init__(self, filename, verbose=True):
"""
Args:
filename: the name of .iso file.
Usage:
>> iso = read_mist_models.ISO('MIST_v1.0_feh_p0.00_afe_p0.0_vvcrit0.4.iso')
>> age_ind = iso.age_index(8.0)
>> logTeff = iso.isos[age_ind]['log_Teff']
>> logL = iso.isos[age_ind]['log_L']
>> plt.plot(logTeff, logL) #plot the HR diagram for logage = 8.0
Attributes:
version Dictionary containing the MIST and MESA version numbers.
abun Dictionary containing Yinit, Zinit, [Fe/H], and [a/Fe] values.
rot Rotation in units of surface v/v_crit.
ages List of ages.
num_ages Number of isochrones.
hdr_list List of column headers.
isos Data.
"""
self.filename = filename
if verbose:
print('Reading in: ' + self.filename)
self.version, self.abun, self.rot, self.ages, self.num_ages, self.hdr_list, self.isos = self.read_iso_file()
def read_iso_file(self):
"""
Reads in the isochrone file.
Args:
filename: the name of .iso file.
"""
#open file and read it in
with open(self.filename) as f:
content = [line.split() for line in f]
version = {'MIST': content[0][-1], 'MESA': content[1][-1]}
abun = {content[3][i]:float(content[4][i]) for i in range(1,5)}
rot = float(content[4][-1])
num_ages = int(content[6][-1])
#read one block for each isochrone
iso_set = []
ages = []
counter = 0
data = content[8:]
for i_age in range(num_ages):
#grab info for each isochrone
num_eeps = int(data[counter][-2])
num_cols = int(data[counter][-1])
hdr_list = data[counter+2][1:]
formats = tuple([np.int32]+[np.float64 for i in range(num_cols-1)])
iso = np.zeros((num_eeps),{'names':tuple(hdr_list),'formats':tuple(formats)})
#read through EEPs for each isochrone
for eep in range(num_eeps):
iso_chunk = data[3+counter+eep]
iso[eep]=tuple(iso_chunk)
iso_set.append(iso)
ages.append(iso[0][1])
counter+= 3+num_eeps+2
return version, abun, rot, ages, num_ages, hdr_list, iso_set
def age_index(self, age):
"""
Returns the index for the user-specified age.
Args:
age: the age of the isochrone.
"""
diff_arr = abs(np.array(self.ages) - age)
age_index = np.where(diff_arr == min(diff_arr))[0][0]
if ((age > max(self.ages)) | (age < min(self.ages))):
print('The requested age is outside the range. Try between ' + str(min(self.ages)) + ' and ' + str(max(self.ages)))
return age_index
class ISOCMD:
"""
Reads in MIST CMD files.
"""
def __init__(self, filename, verbose=True):
"""
Args:
filename: the name of .iso.cmd file.
Usage:
>> isocmd = read_mist_models.ISOCMD('MIST_v1.0_feh_p0.00_afe_p0.0_vvcrit0.4.iso.cmd')
>> age_ind = isocmd.age_index(7.0)
>> B = isocmd.isocmds[age_ind]['Bessell_B']
>> V = isocmd.isocmds[age_ind]['Bessell_V']
>> plt.plot(B-V, V) #plot the CMD for logage = 7.0
Attributes:
version Dictionary containing the MIST and MESA version numbers.
photo_sys Photometric system.
abun Dictionary containing Yinit, Zinit, [Fe/H], and [a/Fe] values.
Av_extinction Av for CCM89 extinction.
rot Rotation in units of surface v/v_crit.
ages List of ages.
num_ages Number of ages.
hdr_list List of column headers.
isocmds Data.
"""
self.filename = filename
if verbose:
print('Reading in: ' + self.filename)
self.version, self.photo_sys, self.abun, self.Av_extinction, self.rot, self.ages, self.num_ages, self.hdr_list, self.isocmds = self.read_isocmd_file()
def read_isocmd_file(self):
"""
Reads in the cmd file.
Args:
filename: the name of .iso.cmd file.
"""
#open file and read it in
with open(self.filename) as f:
content = [line.split() for line in f]
version = {'MIST': content[0][-1], 'MESA': content[1][-1]}
photo_sys = ' '.join(content[2][4:])
abun = {content[4][i]:float(content[5][i]) for i in range(1,5)}
rot = float(content[5][-1])
num_ages = int(content[7][-1])
Av_extinction = float(content[8][-1])
#read one block for each isochrone
isocmd_set = []
ages = []
counter = 0
data = content[10:]
for i_age in range(num_ages):
#grab info for each isochrone
num_eeps = int(data[counter][-2])
num_cols = int(data[counter][-1])
hdr_list = data[counter+2][1:]
formats = tuple([np.int32]+[np.float64 for i in range(num_cols-1)])
isocmd = np.zeros((num_eeps),{'names':tuple(hdr_list),'formats':tuple(formats)})
#read through EEPs for each isochrone
for eep in range(num_eeps):
isocmd_chunk = data[3+counter+eep]
isocmd[eep]=tuple(isocmd_chunk)
isocmd_set.append(isocmd)
ages.append(isocmd[0][1])
counter+= 3+num_eeps+2
return version, photo_sys, abun, Av_extinction, rot, ages, num_ages, hdr_list, isocmd_set
def age_index(self, age):
"""
Returns the index for the user-specified age.
Args:
age: the age of the isochrone.
"""
diff_arr = abs( | np.array(self.ages) | numpy.array |
"""
(C) Copyright 2021 IBM Corp.
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.
Created on June 30, 2021
"""
from typing import Tuple
import os
import SimpleITK as sitk
import numpy as np
import torch
import logging
import cv2
from scipy.ndimage.morphology import binary_dilation
from fuse.data.processor.processor_base import FuseProcessorBase
from fuse.data.processor.processor_dicom_mri import FuseDicomMRIProcessor
from fuse_examples.classification.prostate_x.data_utils import FuseProstateXUtilsData
class FusePatchProcessor(FuseProcessorBase):
"""
This processor crops the lesion volume from within 4D MRI volume base on
lesion location as appears in the database.
:returns a sample that includes:
'patient_num': patient id
'lesion_num': one MRI volume may include more than one lesion
'input': vol_tensor as extracted from MRI volume processor
'input_lesion_mask': mask_tensor,
'ggg': row['ggg']: in prostate - lesion grade
'zone': row['zone']: zone in prostate
'ClinSig': row['ClinSig']: Clinical significant ( 0 for benign and 3+3 lesions, 1 for rest)
"""
def __init__(self,
vol_processor: FuseDicomMRIProcessor = FuseDicomMRIProcessor(),
path_to_db: str = None,
data_path: str = None,
ktrans_data_path: str = None,
db_name: str = None,
db_version: str = None,
fold_no : int = None,
lsn_shape: Tuple[int, int, int] = (16, 120, 120),
lsn_spacing: Tuple[float, float, float] = (3, 0.5, 0.5),
longtd_inx: int = 0,
):
"""
:param vol_processor - extracts 4D tensor from path to MRI dicoms
:param path_to_db: path to data pickle
:param data_path: path to directory in which dicom data is located
:param ktrans_data_path: path to directory of Ktrans seq (prostate x)
:param db_name: 'prostatex' for this example
:param fold_no: cross validation fold
:param lsn_shape: shape of volume to extract from full volume (pixels)
:param lsn_spacing: spacing of volume to extract from full volume (mm)
"""
# store input parameters
self.vol_processor = vol_processor
self.path_to_db = path_to_db
self.data_path = data_path
self.ktrans_data_path = ktrans_data_path
self.lsn_shape = lsn_shape
self.lsn_spacing = lsn_spacing
self.db_name = db_name
self.db_ver = db_version
self.fold_no=fold_no
self.prostate_data_path = self.data_path
self.longtd_inx = longtd_inx
# ========================================================================
def create_resample(self,vol_ref:sitk.sitkFloat32, interpolation: str, size:tuple, spacing: tuple):
"""
create_resample create resample operator
:param vol_ref: sitk vol to use as a ref
:param interpolation:['linear','nn','bspline']
:param size: in pixels ()
:param spacing: in mm ()
:return: resample sitk operator
"""
if interpolation == 'linear':
interpolator = sitk.sitkLinear
elif interpolation == 'nn':
interpolator = sitk.sitkNearestNeighbor
elif interpolation == 'bspline':
interpolator = sitk.sitkBSpline
resample = sitk.ResampleImageFilter()
resample.SetReferenceImage(vol_ref)
resample.SetOutputSpacing(spacing)
resample.SetInterpolator(interpolator)
resample.SetSize(size)
return resample
# ========================================================================
def apply_resampling(self,img:sitk.sitkFloat32, mask:sitk.sitkFloat32,
spacing: Tuple[float,float,float] =(0.5, 0.5, 3), size: Tuple[int,int,int] =(160, 160, 32),
transform:sitk=None, interpolation:str='bspline',
label_interpolator:sitk=sitk.sitkLabelGaussian,
):
ref = img if img != [] else mask
size = [int(s) for s in size]
resample = self.create_resample(ref, interpolation, size=size, spacing=spacing)
if ~(transform is None):
resample.SetTransform(transform)
img_r = resample.Execute(img)
resample.SetInterpolator(label_interpolator)
mask_r = resample.Execute(mask)
return img_r, mask_r
# ========================================================================
def crop_lesion_vol(self,vol:sitk.sitkFloat32, position:Tuple[float,float,float], ref:sitk.sitkFloat32, size:Tuple[int,int,int]=(160, 160, 32),
spacing:Tuple[int,int,int]=(1, 1, 3), center_slice=None):
"""
crop_lesion_vol crop tensor around position
:param vol: vol to crop
:param position: point to crop around
:param ref: reference volume
:param size: size in pixels to crop
:param spacing: spacing to resample the col
:param center_slice: z coordinates of position
:return: cropped volume
"""
def get_lesion_mask(position, ref):
mask = np.zeros_like(sitk.GetArrayViewFromImage(ref), dtype=np.uint8)
coords = | np.round(position[::-1]) | numpy.round |
# -*- coding: utf-8 -*-
"""Test probe merging."""
#------------------------------------------------------------------------------
# Imports
#------------------------------------------------------------------------------
import numpy as np
from ..merge import Merger
from phylib.io.alf import EphysAlfCreator
from phylib.io.model import load_model
from phylib.io.tests.conftest import _make_dataset
#------------------------------------------------------------------------------
# Merging tests
#------------------------------------------------------------------------------
def test_probe_merge_1(tempdir):
out_dir = tempdir / 'merged'
# Create two identical datasets.
probe_names = ('probe_left', 'probe_right')
for name in probe_names:
(tempdir / name).mkdir(exist_ok=True, parents=True)
_make_dataset(tempdir / name, param='dense', has_spike_attributes=False)
subdirs = [tempdir / name for name in probe_names]
# Merge them.
m = Merger(subdirs, out_dir)
single = load_model(tempdir / probe_names[0] / 'params.py')
# Test the merged dataset.
merged = m.merge()
for name in ('n_spikes', 'n_channels', 'n_templates'):
assert getattr(merged, name) == getattr(single, name) * 2
assert merged.sample_rate == single.sample_rate
def test_probe_merge_2(tempdir):
out_dir = tempdir / 'merged'
# Create two identical datasets.
probe_names = ('probe_left', 'probe_right')
for name in probe_names:
(tempdir / name).mkdir(exist_ok=True, parents=True)
_make_dataset(tempdir / name, param='dense', has_spike_attributes=False)
subdirs = [tempdir / name for name in probe_names]
# Add small shift in the spike times of the second probe.
single = load_model(tempdir / probe_names[0] / 'params.py')
st_path = tempdir / 'probe_right/spike_times.npy'
np.save(st_path, single.spike_samples + 1)
# make amplitudes unique and growing so they can serve as key and sorting indices
single.amplitudes = np.linspace(5, 15, single.n_spikes)
# single.spike_clusters[single.spike_clusters == 0] = 12
for m, subdir in enumerate(subdirs):
np.save(subdir / 'amplitudes.npy', single.amplitudes + 20 * m)
np.save(subdir / 'spike_clusters.npy', single.spike_clusters)
# Merge them.
m = Merger(subdirs, out_dir)
merged = m.merge()
# Test the merged dataset.
for name in ('n_spikes', 'n_channels', 'n_templates'):
assert getattr(merged, name) == getattr(single, name) * 2
assert merged.sample_rate == single.sample_rate
# Check the spikes.
single = load_model(tempdir / probe_names[0] / 'params.py')
def test_merged_single(merged):
_, im1, i1 = | np.intersect1d(merged.amplitudes, single.amplitudes, return_indices=True) | numpy.intersect1d |
# Authors:
#
# <NAME>
#
# License: BSD 3 clause
import warnings
import itertools
import numpy as np
import numpy.linalg as la
from scipy import sparse, stats
import pytest
from sklearn.utils import gen_batches
from sklearn.utils._testing import assert_almost_equal
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import assert_array_equal
from sklearn.utils._testing import assert_array_less
from sklearn.utils._testing import assert_allclose
from sklearn.utils._testing import assert_allclose_dense_sparse
from sklearn.utils._testing import skip_if_32bit
from sklearn.utils._testing import _convert_container
from sklearn.utils.sparsefuncs import mean_variance_axis
from sklearn.preprocessing import Binarizer
from sklearn.preprocessing import KernelCenterer
from sklearn.preprocessing import Normalizer
from sklearn.preprocessing import normalize
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import scale
from sklearn.preprocessing import MinMaxScaler
from sklearn.preprocessing import minmax_scale
from sklearn.preprocessing import QuantileTransformer
from sklearn.preprocessing import quantile_transform
from sklearn.preprocessing import MaxAbsScaler
from sklearn.preprocessing import maxabs_scale
from sklearn.preprocessing import RobustScaler
from sklearn.preprocessing import robust_scale
from sklearn.preprocessing import add_dummy_feature
from sklearn.preprocessing import PowerTransformer
from sklearn.preprocessing import power_transform
from sklearn.preprocessing._data import _handle_zeros_in_scale
from sklearn.preprocessing._data import BOUNDS_THRESHOLD
from sklearn.exceptions import NotFittedError
from sklearn.base import clone
from sklearn.pipeline import Pipeline
from sklearn.model_selection import cross_val_predict
from sklearn.svm import SVR
from sklearn.utils import shuffle
from sklearn import datasets
iris = datasets.load_iris()
# Make some data to be used many times
rng = np.random.RandomState(0)
n_features = 30
n_samples = 1000
offsets = rng.uniform(-1, 1, size=n_features)
scales = rng.uniform(1, 10, size=n_features)
X_2d = rng.randn(n_samples, n_features) * scales + offsets
X_1row = X_2d[0, :].reshape(1, n_features)
X_1col = X_2d[:, 0].reshape(n_samples, 1)
X_list_1row = X_1row.tolist()
X_list_1col = X_1col.tolist()
def toarray(a):
if hasattr(a, "toarray"):
a = a.toarray()
return a
def _check_dim_1axis(a):
return np.asarray(a).shape[0]
def assert_correct_incr(i, batch_start, batch_stop, n, chunk_size,
n_samples_seen):
if batch_stop != n:
assert (i + 1) * chunk_size == n_samples_seen
else:
assert (i * chunk_size + (batch_stop - batch_start) ==
n_samples_seen)
def test_raises_value_error_if_sample_weights_greater_than_1d():
# Sample weights must be either scalar or 1D
n_sampless = [2, 3]
n_featuress = [3, 2]
for n_samples, n_features in zip(n_sampless, n_featuress):
X = rng.randn(n_samples, n_features)
y = rng.randn(n_samples)
scaler = StandardScaler()
# make sure Error is raised the sample weights greater than 1d
sample_weight_notOK = rng.randn(n_samples, 1) ** 2
with pytest.raises(ValueError):
scaler.fit(X, y, sample_weight=sample_weight_notOK)
@pytest.mark.parametrize(['Xw', 'X', 'sample_weight'],
[([[1, 2, 3], [4, 5, 6]],
[[1, 2, 3], [1, 2, 3], [4, 5, 6]],
[2., 1.]),
([[1, 0, 1], [0, 0, 1]],
[[1, 0, 1], [0, 0, 1], [0, 0, 1], [0, 0, 1]],
np.array([1, 3])),
([[1, np.nan, 1], [np.nan, np.nan, 1]],
[[1, np.nan, 1], [np.nan, np.nan, 1],
[np.nan, np.nan, 1], [np.nan, np.nan, 1]],
np.array([1, 3])),
])
@pytest.mark.parametrize(
"array_constructor", ["array", "sparse_csr", "sparse_csc"]
)
def test_standard_scaler_sample_weight(
Xw, X, sample_weight, array_constructor):
with_mean = not array_constructor.startswith("sparse")
X = _convert_container(X, array_constructor)
Xw = _convert_container(Xw, array_constructor)
# weighted StandardScaler
yw = np.ones(Xw.shape[0])
scaler_w = StandardScaler(with_mean=with_mean)
scaler_w.fit(Xw, yw, sample_weight=sample_weight)
# unweighted, but with repeated samples
y = np.ones(X.shape[0])
scaler = StandardScaler(with_mean=with_mean)
scaler.fit(X, y)
X_test = [[1.5, 2.5, 3.5], [3.5, 4.5, 5.5]]
assert_almost_equal(scaler.mean_, scaler_w.mean_)
assert_almost_equal(scaler.var_, scaler_w.var_)
assert_almost_equal(scaler.transform(X_test), scaler_w.transform(X_test))
def test_standard_scaler_1d():
# Test scaling of dataset along single axis
for X in [X_1row, X_1col, X_list_1row, X_list_1row]:
scaler = StandardScaler()
X_scaled = scaler.fit(X).transform(X, copy=True)
if isinstance(X, list):
X = np.array(X) # cast only after scaling done
if _check_dim_1axis(X) == 1:
assert_almost_equal(scaler.mean_, X.ravel())
assert_almost_equal(scaler.scale_, np.ones(n_features))
assert_array_almost_equal(X_scaled.mean(axis=0),
np.zeros_like(n_features))
assert_array_almost_equal(X_scaled.std(axis=0),
np.zeros_like(n_features))
else:
assert_almost_equal(scaler.mean_, X.mean())
assert_almost_equal(scaler.scale_, X.std())
assert_array_almost_equal(X_scaled.mean(axis=0),
np.zeros_like(n_features))
assert_array_almost_equal(X_scaled.mean(axis=0), .0)
assert_array_almost_equal(X_scaled.std(axis=0), 1.)
assert scaler.n_samples_seen_ == X.shape[0]
# check inverse transform
X_scaled_back = scaler.inverse_transform(X_scaled)
assert_array_almost_equal(X_scaled_back, X)
# Constant feature
X = np.ones((5, 1))
scaler = StandardScaler()
X_scaled = scaler.fit(X).transform(X, copy=True)
assert_almost_equal(scaler.mean_, 1.)
assert_almost_equal(scaler.scale_, 1.)
assert_array_almost_equal(X_scaled.mean(axis=0), .0)
assert_array_almost_equal(X_scaled.std(axis=0), .0)
assert scaler.n_samples_seen_ == X.shape[0]
@pytest.mark.parametrize("sparse_constructor",
[None, sparse.csc_matrix, sparse.csr_matrix])
@pytest.mark.parametrize("add_sample_weight", [False, True])
def test_standard_scaler_dtype(add_sample_weight, sparse_constructor):
# Ensure scaling does not affect dtype
rng = np.random.RandomState(0)
n_samples = 10
n_features = 3
if add_sample_weight:
sample_weight = np.ones(n_samples)
else:
sample_weight = None
with_mean = True
for dtype in [np.float16, np.float32, np.float64]:
X = rng.randn(n_samples, n_features).astype(dtype)
if sparse_constructor is not None:
X = sparse_constructor(X)
with_mean = False
scaler = StandardScaler(with_mean=with_mean)
X_scaled = scaler.fit(X, sample_weight=sample_weight).transform(X)
assert X.dtype == X_scaled.dtype
assert scaler.mean_.dtype == np.float64
assert scaler.scale_.dtype == np.float64
@pytest.mark.parametrize("scaler", [
StandardScaler(with_mean=False),
RobustScaler(with_centering=False),
])
@pytest.mark.parametrize("sparse_constructor",
[np.asarray, sparse.csc_matrix, sparse.csr_matrix])
@pytest.mark.parametrize("add_sample_weight", [False, True])
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
@pytest.mark.parametrize("constant", [0, 1., 100.])
def test_standard_scaler_constant_features(
scaler, add_sample_weight, sparse_constructor, dtype, constant):
if (isinstance(scaler, StandardScaler)
and constant > 1
and sparse_constructor is not np.asarray
and add_sample_weight):
# https://github.com/scikit-learn/scikit-learn/issues/19546
pytest.xfail("Computation of weighted variance is numerically unstable"
" for sparse data. See: #19546.")
if isinstance(scaler, RobustScaler) and add_sample_weight:
pytest.skip(f"{scaler.__class__.__name__} does not yet support"
f" sample_weight")
rng = np.random.RandomState(0)
n_samples = 100
n_features = 1
if add_sample_weight:
fit_params = dict(sample_weight=rng.uniform(size=n_samples) * 2)
else:
fit_params = {}
X_array = np.full(shape=(n_samples, n_features), fill_value=constant,
dtype=dtype)
X = sparse_constructor(X_array)
X_scaled = scaler.fit(X, **fit_params).transform(X)
if isinstance(scaler, StandardScaler):
# The variance info should be close to zero for constant features.
assert_allclose(scaler.var_, np.zeros(X.shape[1]), atol=1e-7)
# Constant features should not be scaled (scale of 1.):
assert_allclose(scaler.scale_, np.ones(X.shape[1]))
if hasattr(X_scaled, "toarray"):
assert_allclose(X_scaled.toarray(), X_array)
else:
assert_allclose(X_scaled, X)
if isinstance(scaler, StandardScaler) and not add_sample_weight:
# Also check consistency with the standard scale function.
X_scaled_2 = scale(X, with_mean=scaler.with_mean)
if hasattr(X_scaled_2, "toarray"):
assert_allclose(X_scaled_2.toarray(), X_scaled_2.toarray())
else:
assert_allclose(X_scaled_2, X_scaled_2)
def test_scale_1d():
# 1-d inputs
X_list = [1., 3., 5., 0.]
X_arr = np.array(X_list)
for X in [X_list, X_arr]:
X_scaled = scale(X)
assert_array_almost_equal(X_scaled.mean(), 0.0)
assert_array_almost_equal(X_scaled.std(), 1.0)
assert_array_equal(scale(X, with_mean=False, with_std=False), X)
@skip_if_32bit
def test_standard_scaler_numerical_stability():
# Test numerical stability of scaling
# np.log(1e-5) is taken because of its floating point representation
# was empirically found to cause numerical problems with np.mean & np.std.
x = np.full(8, np.log(1e-5), dtype=np.float64)
# This does not raise a warning as the number of samples is too low
# to trigger the problem in recent numpy
with pytest.warns(None) as record:
scale(x)
assert len(record) == 0
assert_array_almost_equal(scale(x), np.zeros(8))
# with 2 more samples, the std computation run into numerical issues:
x = np.full(10, np.log(1e-5), dtype=np.float64)
warning_message = (
"standard deviation of the data is probably very close to 0"
)
with pytest.warns(UserWarning, match=warning_message):
x_scaled = scale(x)
assert_array_almost_equal(x_scaled, np.zeros(10))
x = np.full(10, 1e-100, dtype=np.float64)
with pytest.warns(None) as record:
x_small_scaled = scale(x)
assert len(record) == 0
assert_array_almost_equal(x_small_scaled, np.zeros(10))
# Large values can cause (often recoverable) numerical stability issues:
x_big = np.full(10, 1e100, dtype=np.float64)
warning_message = (
"Dataset may contain too large values"
)
with pytest.warns(UserWarning, match=warning_message):
x_big_scaled = scale(x_big)
assert_array_almost_equal(x_big_scaled, np.zeros(10))
assert_array_almost_equal(x_big_scaled, x_small_scaled)
with pytest.warns(UserWarning, match=warning_message):
x_big_centered = scale(x_big, with_std=False)
assert_array_almost_equal(x_big_centered, np.zeros(10))
assert_array_almost_equal(x_big_centered, x_small_scaled)
def test_scaler_2d_arrays():
# Test scaling of 2d array along first axis
rng = np.random.RandomState(0)
n_features = 5
n_samples = 4
X = rng.randn(n_samples, n_features)
X[:, 0] = 0.0 # first feature is always of zero
scaler = StandardScaler()
X_scaled = scaler.fit(X).transform(X, copy=True)
assert not np.any(np.isnan(X_scaled))
assert scaler.n_samples_seen_ == n_samples
assert_array_almost_equal(X_scaled.mean(axis=0), n_features * [0.0])
assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])
# Check that X has been copied
assert X_scaled is not X
# check inverse transform
X_scaled_back = scaler.inverse_transform(X_scaled)
assert X_scaled_back is not X
assert X_scaled_back is not X_scaled
assert_array_almost_equal(X_scaled_back, X)
X_scaled = scale(X, axis=1, with_std=False)
assert not np.any(np.isnan(X_scaled))
assert_array_almost_equal(X_scaled.mean(axis=1), n_samples * [0.0])
X_scaled = scale(X, axis=1, with_std=True)
assert not np.any(np.isnan(X_scaled))
assert_array_almost_equal(X_scaled.mean(axis=1), n_samples * [0.0])
assert_array_almost_equal(X_scaled.std(axis=1), n_samples * [1.0])
# Check that the data hasn't been modified
assert X_scaled is not X
X_scaled = scaler.fit(X).transform(X, copy=False)
assert not np.any(np.isnan(X_scaled))
assert_array_almost_equal(X_scaled.mean(axis=0), n_features * [0.0])
assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])
# Check that X has not been copied
assert X_scaled is X
X = rng.randn(4, 5)
X[:, 0] = 1.0 # first feature is a constant, non zero feature
scaler = StandardScaler()
X_scaled = scaler.fit(X).transform(X, copy=True)
assert not np.any(np.isnan(X_scaled))
assert_array_almost_equal(X_scaled.mean(axis=0), n_features * [0.0])
assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])
# Check that X has not been copied
assert X_scaled is not X
def test_scaler_float16_overflow():
# Test if the scaler will not overflow on float16 numpy arrays
rng = np.random.RandomState(0)
# float16 has a maximum of 65500.0. On the worst case 5 * 200000 is 100000
# which is enough to overflow the data type
X = rng.uniform(5, 10, [200000, 1]).astype(np.float16)
with np.errstate(over='raise'):
scaler = StandardScaler().fit(X)
X_scaled = scaler.transform(X)
# Calculate the float64 equivalent to verify result
X_scaled_f64 = StandardScaler().fit_transform(X.astype(np.float64))
# Overflow calculations may cause -inf, inf, or nan. Since there is no nan
# input, all of the outputs should be finite. This may be redundant since a
# FloatingPointError exception will be thrown on overflow above.
assert np.all(np.isfinite(X_scaled))
# The normal distribution is very unlikely to go above 4. At 4.0-8.0 the
# float16 precision is 2^-8 which is around 0.004. Thus only 2 decimals are
# checked to account for precision differences.
assert_array_almost_equal(X_scaled, X_scaled_f64, decimal=2)
def test_handle_zeros_in_scale():
s1 = np.array([0, 1e-16, 1, 2, 3])
s2 = _handle_zeros_in_scale(s1, copy=True)
assert_allclose(s1, np.array([0, 1e-16, 1, 2, 3]))
assert_allclose(s2, np.array([1, 1, 1, 2, 3]))
def test_minmax_scaler_partial_fit():
# Test if partial_fit run over many batches of size 1 and 50
# gives the same results as fit
X = X_2d
n = X.shape[0]
for chunk_size in [1, 2, 50, n, n + 42]:
# Test mean at the end of the process
scaler_batch = MinMaxScaler().fit(X)
scaler_incr = MinMaxScaler()
for batch in gen_batches(n_samples, chunk_size):
scaler_incr = scaler_incr.partial_fit(X[batch])
assert_array_almost_equal(scaler_batch.data_min_,
scaler_incr.data_min_)
assert_array_almost_equal(scaler_batch.data_max_,
scaler_incr.data_max_)
assert scaler_batch.n_samples_seen_ == scaler_incr.n_samples_seen_
assert_array_almost_equal(scaler_batch.data_range_,
scaler_incr.data_range_)
assert_array_almost_equal(scaler_batch.scale_, scaler_incr.scale_)
assert_array_almost_equal(scaler_batch.min_, scaler_incr.min_)
# Test std after 1 step
batch0 = slice(0, chunk_size)
scaler_batch = MinMaxScaler().fit(X[batch0])
scaler_incr = MinMaxScaler().partial_fit(X[batch0])
assert_array_almost_equal(scaler_batch.data_min_,
scaler_incr.data_min_)
assert_array_almost_equal(scaler_batch.data_max_,
scaler_incr.data_max_)
assert scaler_batch.n_samples_seen_ == scaler_incr.n_samples_seen_
assert_array_almost_equal(scaler_batch.data_range_,
scaler_incr.data_range_)
assert_array_almost_equal(scaler_batch.scale_, scaler_incr.scale_)
assert_array_almost_equal(scaler_batch.min_, scaler_incr.min_)
# Test std until the end of partial fits, and
scaler_batch = MinMaxScaler().fit(X)
scaler_incr = MinMaxScaler() # Clean estimator
for i, batch in enumerate(gen_batches(n_samples, chunk_size)):
scaler_incr = scaler_incr.partial_fit(X[batch])
assert_correct_incr(i, batch_start=batch.start,
batch_stop=batch.stop, n=n,
chunk_size=chunk_size,
n_samples_seen=scaler_incr.n_samples_seen_)
def test_standard_scaler_partial_fit():
# Test if partial_fit run over many batches of size 1 and 50
# gives the same results as fit
X = X_2d
n = X.shape[0]
for chunk_size in [1, 2, 50, n, n + 42]:
# Test mean at the end of the process
scaler_batch = StandardScaler(with_std=False).fit(X)
scaler_incr = StandardScaler(with_std=False)
for batch in gen_batches(n_samples, chunk_size):
scaler_incr = scaler_incr.partial_fit(X[batch])
assert_array_almost_equal(scaler_batch.mean_, scaler_incr.mean_)
assert scaler_batch.var_ == scaler_incr.var_ # Nones
assert scaler_batch.n_samples_seen_ == scaler_incr.n_samples_seen_
# Test std after 1 step
batch0 = slice(0, chunk_size)
scaler_incr = StandardScaler().partial_fit(X[batch0])
if chunk_size == 1:
assert_array_almost_equal(np.zeros(n_features, dtype=np.float64),
scaler_incr.var_)
assert_array_almost_equal(np.ones(n_features, dtype=np.float64),
scaler_incr.scale_)
else:
assert_array_almost_equal(np.var(X[batch0], axis=0),
scaler_incr.var_)
assert_array_almost_equal(np.std(X[batch0], axis=0),
scaler_incr.scale_) # no constants
# Test std until the end of partial fits, and
scaler_batch = StandardScaler().fit(X)
scaler_incr = StandardScaler() # Clean estimator
for i, batch in enumerate(gen_batches(n_samples, chunk_size)):
scaler_incr = scaler_incr.partial_fit(X[batch])
assert_correct_incr(i, batch_start=batch.start,
batch_stop=batch.stop, n=n,
chunk_size=chunk_size,
n_samples_seen=scaler_incr.n_samples_seen_)
assert_array_almost_equal(scaler_batch.var_, scaler_incr.var_)
assert scaler_batch.n_samples_seen_ == scaler_incr.n_samples_seen_
def test_standard_scaler_partial_fit_numerical_stability():
# Test if the incremental computation introduces significative errors
# for large datasets with values of large magniture
rng = np.random.RandomState(0)
n_features = 2
n_samples = 100
offsets = rng.uniform(-1e15, 1e15, size=n_features)
scales = rng.uniform(1e3, 1e6, size=n_features)
X = rng.randn(n_samples, n_features) * scales + offsets
scaler_batch = StandardScaler().fit(X)
scaler_incr = StandardScaler()
for chunk in X:
scaler_incr = scaler_incr.partial_fit(chunk.reshape(1, n_features))
# Regardless of abs values, they must not be more diff 6 significant digits
tol = 10 ** (-6)
assert_allclose(scaler_incr.mean_, scaler_batch.mean_, rtol=tol)
assert_allclose(scaler_incr.var_, scaler_batch.var_, rtol=tol)
assert_allclose(scaler_incr.scale_, scaler_batch.scale_, rtol=tol)
# NOTE Be aware that for much larger offsets std is very unstable (last
# assert) while mean is OK.
# Sparse input
size = (100, 3)
scale = 1e20
X = rng.randint(0, 2, size).astype(np.float64) * scale
X_csr = sparse.csr_matrix(X)
X_csc = sparse.csc_matrix(X)
for X in [X_csr, X_csc]:
# with_mean=False is required with sparse input
scaler = StandardScaler(with_mean=False).fit(X)
scaler_incr = StandardScaler(with_mean=False)
for chunk in X:
# chunk = sparse.csr_matrix(data_chunks)
scaler_incr = scaler_incr.partial_fit(chunk)
# Regardless of magnitude, they must not differ more than of 6 digits
tol = 10 ** (-6)
assert scaler.mean_ is not None
assert_allclose(scaler_incr.var_, scaler.var_, rtol=tol)
assert_allclose(scaler_incr.scale_, scaler.scale_, rtol=tol)
@pytest.mark.parametrize("sample_weight", [True, None])
def test_partial_fit_sparse_input(sample_weight):
# Check that sparsity is not destroyed
X = np.array([[1.], [0.], [0.], [5.]])
X_csr = sparse.csr_matrix(X)
X_csc = sparse.csc_matrix(X)
if sample_weight:
sample_weight = rng.rand(X_csc.shape[0])
null_transform = StandardScaler(with_mean=False, with_std=False, copy=True)
for X in [X_csr, X_csc]:
X_null = null_transform.partial_fit(
X, sample_weight=sample_weight).transform(X)
assert_array_equal(X_null.toarray(), X.toarray())
X_orig = null_transform.inverse_transform(X_null)
assert_array_equal(X_orig.toarray(), X_null.toarray())
assert_array_equal(X_orig.toarray(), X.toarray())
@pytest.mark.parametrize("sample_weight", [True, None])
def test_standard_scaler_trasform_with_partial_fit(sample_weight):
# Check some postconditions after applying partial_fit and transform
X = X_2d[:100, :]
if sample_weight:
sample_weight = rng.rand(X.shape[0])
scaler_incr = StandardScaler()
for i, batch in enumerate(gen_batches(X.shape[0], 1)):
X_sofar = X[:(i + 1), :]
chunks_copy = X_sofar.copy()
if sample_weight is None:
scaled_batch = StandardScaler().fit_transform(X_sofar)
scaler_incr = scaler_incr.partial_fit(X[batch])
else:
scaled_batch = StandardScaler().fit_transform(
X_sofar, sample_weight=sample_weight[:i + 1])
scaler_incr = scaler_incr.partial_fit(
X[batch], sample_weight=sample_weight[batch])
scaled_incr = scaler_incr.transform(X_sofar)
assert_array_almost_equal(scaled_batch, scaled_incr)
assert_array_almost_equal(X_sofar, chunks_copy) # No change
right_input = scaler_incr.inverse_transform(scaled_incr)
assert_array_almost_equal(X_sofar, right_input)
zero = np.zeros(X.shape[1])
epsilon = np.finfo(float).eps
assert_array_less(zero, scaler_incr.var_ + epsilon) # as less or equal
assert_array_less(zero, scaler_incr.scale_ + epsilon)
if sample_weight is None:
# (i+1) because the Scaler has been already fitted
assert (i + 1) == scaler_incr.n_samples_seen_
else:
assert (
np.sum(sample_weight[:i + 1]) ==
pytest.approx(scaler_incr.n_samples_seen_)
)
def test_min_max_scaler_iris():
X = iris.data
scaler = MinMaxScaler()
# default params
X_trans = scaler.fit_transform(X)
assert_array_almost_equal(X_trans.min(axis=0), 0)
assert_array_almost_equal(X_trans.max(axis=0), 1)
X_trans_inv = scaler.inverse_transform(X_trans)
assert_array_almost_equal(X, X_trans_inv)
# not default params: min=1, max=2
scaler = MinMaxScaler(feature_range=(1, 2))
X_trans = scaler.fit_transform(X)
assert_array_almost_equal(X_trans.min(axis=0), 1)
assert_array_almost_equal(X_trans.max(axis=0), 2)
X_trans_inv = scaler.inverse_transform(X_trans)
assert_array_almost_equal(X, X_trans_inv)
# min=-.5, max=.6
scaler = MinMaxScaler(feature_range=(-.5, .6))
X_trans = scaler.fit_transform(X)
assert_array_almost_equal(X_trans.min(axis=0), -.5)
assert_array_almost_equal(X_trans.max(axis=0), .6)
X_trans_inv = scaler.inverse_transform(X_trans)
assert_array_almost_equal(X, X_trans_inv)
# raises on invalid range
scaler = MinMaxScaler(feature_range=(2, 1))
with pytest.raises(ValueError):
scaler.fit(X)
def test_min_max_scaler_zero_variance_features():
# Check min max scaler on toy data with zero variance features
X = [[0., 1., +0.5],
[0., 1., -0.1],
[0., 1., +1.1]]
X_new = [[+0., 2., 0.5],
[-1., 1., 0.0],
[+0., 1., 1.5]]
# default params
scaler = MinMaxScaler()
X_trans = scaler.fit_transform(X)
X_expected_0_1 = [[0., 0., 0.5],
[0., 0., 0.0],
[0., 0., 1.0]]
assert_array_almost_equal(X_trans, X_expected_0_1)
X_trans_inv = scaler.inverse_transform(X_trans)
assert_array_almost_equal(X, X_trans_inv)
X_trans_new = scaler.transform(X_new)
X_expected_0_1_new = [[+0., 1., 0.500],
[-1., 0., 0.083],
[+0., 0., 1.333]]
assert_array_almost_equal(X_trans_new, X_expected_0_1_new, decimal=2)
# not default params
scaler = MinMaxScaler(feature_range=(1, 2))
X_trans = scaler.fit_transform(X)
X_expected_1_2 = [[1., 1., 1.5],
[1., 1., 1.0],
[1., 1., 2.0]]
assert_array_almost_equal(X_trans, X_expected_1_2)
# function interface
X_trans = minmax_scale(X)
assert_array_almost_equal(X_trans, X_expected_0_1)
X_trans = minmax_scale(X, feature_range=(1, 2))
assert_array_almost_equal(X_trans, X_expected_1_2)
def test_minmax_scale_axis1():
X = iris.data
X_trans = minmax_scale(X, axis=1)
assert_array_almost_equal(np.min(X_trans, axis=1), 0)
assert_array_almost_equal(np.max(X_trans, axis=1), 1)
def test_min_max_scaler_1d():
# Test scaling of dataset along single axis
for X in [X_1row, X_1col, X_list_1row, X_list_1row]:
scaler = MinMaxScaler(copy=True)
X_scaled = scaler.fit(X).transform(X)
if isinstance(X, list):
X = np.array(X) # cast only after scaling done
if _check_dim_1axis(X) == 1:
assert_array_almost_equal(X_scaled.min(axis=0),
np.zeros(n_features))
assert_array_almost_equal(X_scaled.max(axis=0),
np.zeros(n_features))
else:
assert_array_almost_equal(X_scaled.min(axis=0), .0)
assert_array_almost_equal(X_scaled.max(axis=0), 1.)
assert scaler.n_samples_seen_ == X.shape[0]
# check inverse transform
X_scaled_back = scaler.inverse_transform(X_scaled)
assert_array_almost_equal(X_scaled_back, X)
# Constant feature
X = np.ones((5, 1))
scaler = MinMaxScaler()
X_scaled = scaler.fit(X).transform(X)
assert X_scaled.min() >= 0.
assert X_scaled.max() <= 1.
assert scaler.n_samples_seen_ == X.shape[0]
# Function interface
X_1d = X_1row.ravel()
min_ = X_1d.min()
max_ = X_1d.max()
assert_array_almost_equal((X_1d - min_) / (max_ - min_),
minmax_scale(X_1d, copy=True))
@pytest.mark.parametrize("sample_weight", [True, None])
def test_scaler_without_centering(sample_weight):
rng = np.random.RandomState(42)
X = rng.randn(4, 5)
X[:, 0] = 0.0 # first feature is always of zero
X_csr = sparse.csr_matrix(X)
X_csc = sparse.csc_matrix(X)
if sample_weight:
sample_weight = rng.rand(X.shape[0])
with pytest.raises(ValueError):
StandardScaler().fit(X_csr)
with pytest.raises(ValueError):
StandardScaler().fit(X_csc)
null_transform = StandardScaler(with_mean=False, with_std=False, copy=True)
X_null = null_transform.fit_transform(X_csr)
assert_array_equal(X_null.data, X_csr.data)
X_orig = null_transform.inverse_transform(X_null)
assert_array_equal(X_orig.data, X_csr.data)
scaler = StandardScaler(with_mean=False).fit(
X, sample_weight=sample_weight)
X_scaled = scaler.transform(X, copy=True)
assert not np.any(np.isnan(X_scaled))
scaler_csr = StandardScaler(with_mean=False).fit(
X_csr, sample_weight=sample_weight)
X_csr_scaled = scaler_csr.transform(X_csr, copy=True)
assert not np.any(np.isnan(X_csr_scaled.data))
scaler_csc = StandardScaler(with_mean=False).fit(
X_csc, sample_weight=sample_weight)
X_csc_scaled = scaler_csc.transform(X_csc, copy=True)
assert not np.any(np.isnan(X_csc_scaled.data))
assert_array_almost_equal(scaler.mean_, scaler_csr.mean_)
assert_array_almost_equal(scaler.var_, scaler_csr.var_)
assert_array_almost_equal(scaler.scale_, scaler_csr.scale_)
assert_array_almost_equal(scaler.n_samples_seen_,
scaler_csr.n_samples_seen_)
assert_array_almost_equal(scaler.mean_, scaler_csc.mean_)
assert_array_almost_equal(scaler.var_, scaler_csc.var_)
assert_array_almost_equal(scaler.scale_, scaler_csc.scale_)
assert_array_almost_equal(scaler.n_samples_seen_,
scaler_csc.n_samples_seen_)
if sample_weight is None:
assert_array_almost_equal(
X_scaled.mean(axis=0), [0., -0.01, 2.24, -0.35, -0.78], 2)
assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])
X_csr_scaled_mean, X_csr_scaled_var = \
mean_variance_axis(X_csr_scaled, 0)
assert_array_almost_equal(X_csr_scaled_mean, X_scaled.mean(axis=0))
assert_array_almost_equal(X_csr_scaled_var, X_scaled.var(axis=0))
# Check that X has not been modified (copy)
assert X_scaled is not X
assert X_csr_scaled is not X_csr
X_scaled_back = scaler.inverse_transform(X_scaled)
assert X_scaled_back is not X
assert X_scaled_back is not X_scaled
assert_array_almost_equal(X_scaled_back, X)
X_csr_scaled_back = scaler_csr.inverse_transform(X_csr_scaled)
assert X_csr_scaled_back is not X_csr
assert X_csr_scaled_back is not X_csr_scaled
assert_array_almost_equal(X_csr_scaled_back.toarray(), X)
X_csc_scaled_back = scaler_csr.inverse_transform(X_csc_scaled.tocsc())
assert X_csc_scaled_back is not X_csc
assert X_csc_scaled_back is not X_csc_scaled
assert_array_almost_equal(X_csc_scaled_back.toarray(), X)
@pytest.mark.parametrize("with_mean", [True, False])
@pytest.mark.parametrize("with_std", [True, False])
@pytest.mark.parametrize("array_constructor",
[np.asarray, sparse.csc_matrix, sparse.csr_matrix])
def test_scaler_n_samples_seen_with_nan(with_mean, with_std,
array_constructor):
X = np.array([[0, 1, 3],
[np.nan, 6, 10],
[5, 4, np.nan],
[8, 0, np.nan]],
dtype=np.float64)
X = array_constructor(X)
if sparse.issparse(X) and with_mean:
pytest.skip("'with_mean=True' cannot be used with sparse matrix.")
transformer = StandardScaler(with_mean=with_mean, with_std=with_std)
transformer.fit(X)
assert_array_equal(transformer.n_samples_seen_, np.array([3, 4, 2]))
def _check_identity_scalers_attributes(scaler_1, scaler_2):
assert scaler_1.mean_ is scaler_2.mean_ is None
assert scaler_1.var_ is scaler_2.var_ is None
assert scaler_1.scale_ is scaler_2.scale_ is None
assert scaler_1.n_samples_seen_ == scaler_2.n_samples_seen_
def test_scaler_return_identity():
# test that the scaler return identity when with_mean and with_std are
# False
X_dense = np.array([[0, 1, 3],
[5, 6, 0],
[8, 0, 10]],
dtype=np.float64)
X_csr = sparse.csr_matrix(X_dense)
X_csc = X_csr.tocsc()
transformer_dense = StandardScaler(with_mean=False, with_std=False)
X_trans_dense = transformer_dense.fit_transform(X_dense)
transformer_csr = clone(transformer_dense)
X_trans_csr = transformer_csr.fit_transform(X_csr)
transformer_csc = clone(transformer_dense)
X_trans_csc = transformer_csc.fit_transform(X_csc)
assert_allclose_dense_sparse(X_trans_csr, X_csr)
assert_allclose_dense_sparse(X_trans_csc, X_csc)
assert_allclose(X_trans_dense, X_dense)
for trans_1, trans_2 in itertools.combinations([transformer_dense,
transformer_csr,
transformer_csc],
2):
_check_identity_scalers_attributes(trans_1, trans_2)
transformer_dense.partial_fit(X_dense)
transformer_csr.partial_fit(X_csr)
transformer_csc.partial_fit(X_csc)
for trans_1, trans_2 in itertools.combinations([transformer_dense,
transformer_csr,
transformer_csc],
2):
_check_identity_scalers_attributes(trans_1, trans_2)
transformer_dense.fit(X_dense)
transformer_csr.fit(X_csr)
transformer_csc.fit(X_csc)
for trans_1, trans_2 in itertools.combinations([transformer_dense,
transformer_csr,
transformer_csc],
2):
_check_identity_scalers_attributes(trans_1, trans_2)
def test_scaler_int():
# test that scaler converts integer input to floating
# for both sparse and dense matrices
rng = np.random.RandomState(42)
X = rng.randint(20, size=(4, 5))
X[:, 0] = 0 # first feature is always of zero
X_csr = sparse.csr_matrix(X)
X_csc = sparse.csc_matrix(X)
null_transform = StandardScaler(with_mean=False, with_std=False, copy=True)
with warnings.catch_warnings(record=True):
X_null = null_transform.fit_transform(X_csr)
assert_array_equal(X_null.data, X_csr.data)
X_orig = null_transform.inverse_transform(X_null)
assert_array_equal(X_orig.data, X_csr.data)
with warnings.catch_warnings(record=True):
scaler = StandardScaler(with_mean=False).fit(X)
X_scaled = scaler.transform(X, copy=True)
assert not np.any(np.isnan(X_scaled))
with warnings.catch_warnings(record=True):
scaler_csr = StandardScaler(with_mean=False).fit(X_csr)
X_csr_scaled = scaler_csr.transform(X_csr, copy=True)
assert not np.any(np.isnan(X_csr_scaled.data))
with warnings.catch_warnings(record=True):
scaler_csc = StandardScaler(with_mean=False).fit(X_csc)
X_csc_scaled = scaler_csc.transform(X_csc, copy=True)
assert not np.any(np.isnan(X_csc_scaled.data))
assert_array_almost_equal(scaler.mean_, scaler_csr.mean_)
assert_array_almost_equal(scaler.var_, scaler_csr.var_)
assert_array_almost_equal(scaler.scale_, scaler_csr.scale_)
assert_array_almost_equal(scaler.mean_, scaler_csc.mean_)
assert_array_almost_equal(scaler.var_, scaler_csc.var_)
assert_array_almost_equal(scaler.scale_, scaler_csc.scale_)
assert_array_almost_equal(
X_scaled.mean(axis=0),
[0., 1.109, 1.856, 21., 1.559], 2)
assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])
X_csr_scaled_mean, X_csr_scaled_std = mean_variance_axis(
X_csr_scaled.astype(float), 0)
assert_array_almost_equal(X_csr_scaled_mean, X_scaled.mean(axis=0))
assert_array_almost_equal(X_csr_scaled_std, X_scaled.std(axis=0))
# Check that X has not been modified (copy)
assert X_scaled is not X
assert X_csr_scaled is not X_csr
X_scaled_back = scaler.inverse_transform(X_scaled)
assert X_scaled_back is not X
assert X_scaled_back is not X_scaled
assert_array_almost_equal(X_scaled_back, X)
X_csr_scaled_back = scaler_csr.inverse_transform(X_csr_scaled)
assert X_csr_scaled_back is not X_csr
assert X_csr_scaled_back is not X_csr_scaled
assert_array_almost_equal(X_csr_scaled_back.toarray(), X)
X_csc_scaled_back = scaler_csr.inverse_transform(X_csc_scaled.tocsc())
assert X_csc_scaled_back is not X_csc
assert X_csc_scaled_back is not X_csc_scaled
assert_array_almost_equal(X_csc_scaled_back.toarray(), X)
def test_scaler_without_copy():
# Check that StandardScaler.fit does not change input
rng = np.random.RandomState(42)
X = rng.randn(4, 5)
X[:, 0] = 0.0 # first feature is always of zero
X_csr = sparse.csr_matrix(X)
X_csc = sparse.csc_matrix(X)
X_copy = X.copy()
StandardScaler(copy=False).fit(X)
assert_array_equal(X, X_copy)
X_csr_copy = X_csr.copy()
StandardScaler(with_mean=False, copy=False).fit(X_csr)
assert_array_equal(X_csr.toarray(), X_csr_copy.toarray())
X_csc_copy = X_csc.copy()
StandardScaler(with_mean=False, copy=False).fit(X_csc)
assert_array_equal(X_csc.toarray(), X_csc_copy.toarray())
def test_scale_sparse_with_mean_raise_exception():
rng = np.random.RandomState(42)
X = rng.randn(4, 5)
X_csr = sparse.csr_matrix(X)
X_csc = sparse.csc_matrix(X)
# check scaling and fit with direct calls on sparse data
with pytest.raises(ValueError):
scale(X_csr, with_mean=True)
with pytest.raises(ValueError):
StandardScaler(with_mean=True).fit(X_csr)
with pytest.raises(ValueError):
scale(X_csc, with_mean=True)
with pytest.raises(ValueError):
StandardScaler(with_mean=True).fit(X_csc)
# check transform and inverse_transform after a fit on a dense array
scaler = StandardScaler(with_mean=True).fit(X)
with pytest.raises(ValueError):
scaler.transform(X_csr)
with pytest.raises(ValueError):
scaler.transform(X_csc)
X_transformed_csr = sparse.csr_matrix(scaler.transform(X))
with pytest.raises(ValueError):
scaler.inverse_transform(X_transformed_csr)
X_transformed_csc = sparse.csc_matrix(scaler.transform(X))
with pytest.raises(ValueError):
scaler.inverse_transform(X_transformed_csc)
def test_scale_input_finiteness_validation():
# Check if non finite inputs raise ValueError
X = [[np.inf, 5, 6, 7, 8]]
with pytest.raises(ValueError, match="Input contains infinity "
"or a value too large"):
scale(X)
def test_robust_scaler_error_sparse():
X_sparse = sparse.rand(1000, 10)
scaler = RobustScaler(with_centering=True)
err_msg = "Cannot center sparse matrices"
with pytest.raises(ValueError, match=err_msg):
scaler.fit(X_sparse)
@pytest.mark.parametrize("with_centering", [True, False])
@pytest.mark.parametrize("with_scaling", [True, False])
@pytest.mark.parametrize("X", [np.random.randn(10, 3),
sparse.rand(10, 3, density=0.5)])
def test_robust_scaler_attributes(X, with_centering, with_scaling):
# check consistent type of attributes
if with_centering and sparse.issparse(X):
pytest.skip("RobustScaler cannot center sparse matrix")
scaler = RobustScaler(with_centering=with_centering,
with_scaling=with_scaling)
scaler.fit(X)
if with_centering:
assert isinstance(scaler.center_, np.ndarray)
else:
assert scaler.center_ is None
if with_scaling:
assert isinstance(scaler.scale_, np.ndarray)
else:
assert scaler.scale_ is None
def test_robust_scaler_col_zero_sparse():
# check that the scaler is working when there is not data materialized in a
# column of a sparse matrix
X = np.random.randn(10, 5)
X[:, 0] = 0
X = sparse.csr_matrix(X)
scaler = RobustScaler(with_centering=False)
scaler.fit(X)
assert scaler.scale_[0] == pytest.approx(1)
X_trans = scaler.transform(X)
assert_allclose(X[:, 0].toarray(), X_trans[:, 0].toarray())
def test_robust_scaler_2d_arrays():
# Test robust scaling of 2d array along first axis
rng = np.random.RandomState(0)
X = rng.randn(4, 5)
X[:, 0] = 0.0 # first feature is always of zero
scaler = RobustScaler()
X_scaled = scaler.fit(X).transform(X)
assert_array_almost_equal(np.median(X_scaled, axis=0), 5 * [0.0])
assert_array_almost_equal(X_scaled.std(axis=0)[0], 0)
@pytest.mark.parametrize("density", [0, 0.05, 0.1, 0.5, 1])
@pytest.mark.parametrize("strictly_signed",
['positive', 'negative', 'zeros', None])
def test_robust_scaler_equivalence_dense_sparse(density, strictly_signed):
# Check the equivalence of the fitting with dense and sparse matrices
X_sparse = sparse.rand(1000, 5, density=density).tocsc()
if strictly_signed == 'positive':
X_sparse.data = np.abs(X_sparse.data)
elif strictly_signed == 'negative':
X_sparse.data = - np.abs(X_sparse.data)
elif strictly_signed == 'zeros':
X_sparse.data = np.zeros(X_sparse.data.shape, dtype=np.float64)
X_dense = X_sparse.toarray()
scaler_sparse = RobustScaler(with_centering=False)
scaler_dense = RobustScaler(with_centering=False)
scaler_sparse.fit(X_sparse)
scaler_dense.fit(X_dense)
assert_allclose(scaler_sparse.scale_, scaler_dense.scale_)
def test_robust_scaler_transform_one_row_csr():
# Check RobustScaler on transforming csr matrix with one row
rng = np.random.RandomState(0)
X = rng.randn(4, 5)
single_row = np.array([[0.1, 1., 2., 0., -1.]])
scaler = RobustScaler(with_centering=False)
scaler = scaler.fit(X)
row_trans = scaler.transform(sparse.csr_matrix(single_row))
row_expected = single_row / scaler.scale_
assert_array_almost_equal(row_trans.toarray(), row_expected)
row_scaled_back = scaler.inverse_transform(row_trans)
assert_array_almost_equal(single_row, row_scaled_back.toarray())
def test_robust_scaler_iris():
X = iris.data
scaler = RobustScaler()
X_trans = scaler.fit_transform(X)
assert_array_almost_equal(np.median(X_trans, axis=0), 0)
X_trans_inv = scaler.inverse_transform(X_trans)
assert_array_almost_equal(X, X_trans_inv)
q = np.percentile(X_trans, q=(25, 75), axis=0)
iqr = q[1] - q[0]
assert_array_almost_equal(iqr, 1)
def test_robust_scaler_iris_quantiles():
X = iris.data
scaler = RobustScaler(quantile_range=(10, 90))
X_trans = scaler.fit_transform(X)
assert_array_almost_equal(np.median(X_trans, axis=0), 0)
X_trans_inv = scaler.inverse_transform(X_trans)
assert_array_almost_equal(X, X_trans_inv)
q = np.percentile(X_trans, q=(10, 90), axis=0)
q_range = q[1] - q[0]
assert_array_almost_equal(q_range, 1)
def test_quantile_transform_iris():
X = iris.data
# uniform output distribution
transformer = QuantileTransformer(n_quantiles=30)
X_trans = transformer.fit_transform(X)
X_trans_inv = transformer.inverse_transform(X_trans)
assert_array_almost_equal(X, X_trans_inv)
# normal output distribution
transformer = QuantileTransformer(n_quantiles=30,
output_distribution='normal')
X_trans = transformer.fit_transform(X)
X_trans_inv = transformer.inverse_transform(X_trans)
assert_array_almost_equal(X, X_trans_inv)
# make sure it is possible to take the inverse of a sparse matrix
# which contain negative value; this is the case in the iris dataset
X_sparse = sparse.csc_matrix(X)
X_sparse_tran = transformer.fit_transform(X_sparse)
X_sparse_tran_inv = transformer.inverse_transform(X_sparse_tran)
assert_array_almost_equal(X_sparse.A, X_sparse_tran_inv.A)
def test_quantile_transform_check_error():
X = np.transpose([[0, 25, 50, 0, 0, 0, 75, 0, 0, 100],
[2, 4, 0, 0, 6, 8, 0, 10, 0, 0],
[0, 0, 2.6, 4.1, 0, 0, 2.3, 0, 9.5, 0.1]])
X = sparse.csc_matrix(X)
X_neg = np.transpose([[0, 25, 50, 0, 0, 0, 75, 0, 0, 100],
[-2, 4, 0, 0, 6, 8, 0, 10, 0, 0],
[0, 0, 2.6, 4.1, 0, 0, 2.3, 0, 9.5, 0.1]])
X_neg = sparse.csc_matrix(X_neg)
err_msg = "Invalid value for 'n_quantiles': 0."
with pytest.raises(ValueError, match=err_msg):
QuantileTransformer(n_quantiles=0).fit(X)
err_msg = "Invalid value for 'subsample': 0."
with pytest.raises(ValueError, match=err_msg):
QuantileTransformer(subsample=0).fit(X)
err_msg = ("The number of quantiles cannot be greater than "
"the number of samples used. Got 1000 quantiles "
"and 10 samples.")
with pytest.raises(ValueError, match=err_msg):
QuantileTransformer(subsample=10).fit(X)
transformer = QuantileTransformer(n_quantiles=10)
err_msg = "QuantileTransformer only accepts non-negative sparse matrices."
with pytest.raises(ValueError, match=err_msg):
transformer.fit(X_neg)
transformer.fit(X)
err_msg = "QuantileTransformer only accepts non-negative sparse matrices."
with pytest.raises(ValueError, match=err_msg):
transformer.transform(X_neg)
X_bad_feat = np.transpose([[0, 25, 50, 0, 0, 0, 75, 0, 0, 100],
[0, 0, 2.6, 4.1, 0, 0, 2.3, 0, 9.5, 0.1]])
err_msg = ("X has 2 features, but QuantileTransformer is expecting "
"3 features as input.")
with pytest.raises(ValueError, match=err_msg):
transformer.inverse_transform(X_bad_feat)
transformer = QuantileTransformer(n_quantiles=10,
output_distribution='rnd')
# check that an error is raised at fit time
err_msg = ("'output_distribution' has to be either 'normal' or "
"'uniform'. Got 'rnd' instead.")
with pytest.raises(ValueError, match=err_msg):
transformer.fit(X)
# check that an error is raised at transform time
transformer.output_distribution = 'uniform'
transformer.fit(X)
X_tran = transformer.transform(X)
transformer.output_distribution = 'rnd'
err_msg = ("'output_distribution' has to be either 'normal' or 'uniform'."
" Got 'rnd' instead.")
with pytest.raises(ValueError, match=err_msg):
transformer.transform(X)
# check that an error is raised at inverse_transform time
err_msg = ("'output_distribution' has to be either 'normal' or 'uniform'."
" Got 'rnd' instead.")
with pytest.raises(ValueError, match=err_msg):
transformer.inverse_transform(X_tran)
# check that an error is raised if input is scalar
with pytest.raises(ValueError,
match='Expected 2D array, got scalar array instead'):
transformer.transform(10)
# check that a warning is raised is n_quantiles > n_samples
transformer = QuantileTransformer(n_quantiles=100)
warn_msg = "n_quantiles is set to n_samples"
with pytest.warns(UserWarning, match=warn_msg) as record:
transformer.fit(X)
assert len(record) == 1
assert transformer.n_quantiles_ == X.shape[0]
def test_quantile_transform_sparse_ignore_zeros():
X = np.array([[0, 1],
[0, 0],
[0, 2],
[0, 2],
[0, 1]])
X_sparse = sparse.csc_matrix(X)
transformer = QuantileTransformer(ignore_implicit_zeros=True,
n_quantiles=5)
# dense case -> warning raise
warning_message = ("'ignore_implicit_zeros' takes effect"
" only with sparse matrix. This parameter has no"
" effect.")
with pytest.warns(UserWarning, match=warning_message):
transformer.fit(X)
X_expected = np.array([[0, 0],
[0, 0],
[0, 1],
[0, 1],
[0, 0]])
X_trans = transformer.fit_transform(X_sparse)
assert_almost_equal(X_expected, X_trans.A)
# consider the case where sparse entries are missing values and user-given
# zeros are to be considered
X_data = np.array([0, 0, 1, 0, 2, 2, 1, 0, 1, 2, 0])
X_col = np.array([0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1])
X_row = np.array([0, 4, 0, 1, 2, 3, 4, 5, 6, 7, 8])
X_sparse = sparse.csc_matrix((X_data, (X_row, X_col)))
X_trans = transformer.fit_transform(X_sparse)
X_expected = np.array([[0., 0.5],
[0., 0.],
[0., 1.],
[0., 1.],
[0., 0.5],
[0., 0.],
[0., 0.5],
[0., 1.],
[0., 0.]])
assert_almost_equal(X_expected, X_trans.A)
transformer = QuantileTransformer(ignore_implicit_zeros=True,
n_quantiles=5)
X_data = np.array([-1, -1, 1, 0, 0, 0, 1, -1, 1])
X_col = np.array([0, 0, 1, 1, 1, 1, 1, 1, 1])
X_row = np.array([0, 4, 0, 1, 2, 3, 4, 5, 6])
X_sparse = sparse.csc_matrix((X_data, (X_row, X_col)))
X_trans = transformer.fit_transform(X_sparse)
X_expected = np.array([[0, 1],
[0, 0.375],
[0, 0.375],
[0, 0.375],
[0, 1],
[0, 0],
[0, 1]])
assert_almost_equal(X_expected, X_trans.A)
assert_almost_equal(X_sparse.A, transformer.inverse_transform(X_trans).A)
# check in conjunction with subsampling
transformer = QuantileTransformer(ignore_implicit_zeros=True,
n_quantiles=5,
subsample=8,
random_state=0)
X_trans = transformer.fit_transform(X_sparse)
assert_almost_equal(X_expected, X_trans.A)
assert_almost_equal(X_sparse.A, transformer.inverse_transform(X_trans).A)
def test_quantile_transform_dense_toy():
X = np.array([[0, 2, 2.6],
[25, 4, 4.1],
[50, 6, 2.3],
[75, 8, 9.5],
[100, 10, 0.1]])
transformer = QuantileTransformer(n_quantiles=5)
transformer.fit(X)
# using the a uniform output, each entry of X should be map between 0 and 1
# and equally spaced
X_trans = transformer.fit_transform(X)
X_expected = np.tile(np.linspace(0, 1, num=5), (3, 1)).T
assert_almost_equal(np.sort(X_trans, axis=0), X_expected)
X_test = np.array([
[-1, 1, 0],
[101, 11, 10],
])
X_expected = np.array([
[0, 0, 0],
[1, 1, 1],
])
assert_array_almost_equal(transformer.transform(X_test), X_expected)
X_trans_inv = transformer.inverse_transform(X_trans)
assert_array_almost_equal(X, X_trans_inv)
def test_quantile_transform_subsampling():
# Test that subsampling the input yield to a consistent results We check
# that the computed quantiles are almost mapped to a [0, 1] vector where
# values are equally spaced. The infinite norm is checked to be smaller
# than a given threshold. This is repeated 5 times.
# dense support
n_samples = 1000000
n_quantiles = 1000
X = np.sort(np.random.sample((n_samples, 1)), axis=0)
ROUND = 5
inf_norm_arr = []
for random_state in range(ROUND):
transformer = QuantileTransformer(random_state=random_state,
n_quantiles=n_quantiles,
subsample=n_samples // 10)
transformer.fit(X)
diff = (np.linspace(0, 1, n_quantiles) -
np.ravel(transformer.quantiles_))
inf_norm = np.max(np.abs(diff))
assert inf_norm < 1e-2
inf_norm_arr.append(inf_norm)
# each random subsampling yield a unique approximation to the expected
# linspace CDF
assert len(np.unique(inf_norm_arr)) == len(inf_norm_arr)
# sparse support
X = sparse.rand(n_samples, 1, density=.99, format='csc', random_state=0)
inf_norm_arr = []
for random_state in range(ROUND):
transformer = QuantileTransformer(random_state=random_state,
n_quantiles=n_quantiles,
subsample=n_samples // 10)
transformer.fit(X)
diff = (np.linspace(0, 1, n_quantiles) -
np.ravel(transformer.quantiles_))
inf_norm = np.max(np.abs(diff))
assert inf_norm < 1e-1
inf_norm_arr.append(inf_norm)
# each random subsampling yield a unique approximation to the expected
# linspace CDF
assert len(np.unique(inf_norm_arr)) == len(inf_norm_arr)
def test_quantile_transform_sparse_toy():
X = np.array([[0., 2., 0.],
[25., 4., 0.],
[50., 0., 2.6],
[0., 0., 4.1],
[0., 6., 0.],
[0., 8., 0.],
[75., 0., 2.3],
[0., 10., 0.],
[0., 0., 9.5],
[100., 0., 0.1]])
X = sparse.csc_matrix(X)
transformer = QuantileTransformer(n_quantiles=10)
transformer.fit(X)
X_trans = transformer.fit_transform(X)
assert_array_almost_equal(np.min(X_trans.toarray(), axis=0), 0.)
assert_array_almost_equal(np.max(X_trans.toarray(), axis=0), 1.)
X_trans_inv = transformer.inverse_transform(X_trans)
assert_array_almost_equal(X.toarray(), X_trans_inv.toarray())
transformer_dense = QuantileTransformer(n_quantiles=10).fit(
X.toarray())
X_trans = transformer_dense.transform(X)
assert_array_almost_equal(np.min(X_trans.toarray(), axis=0), 0.)
assert_array_almost_equal(np.max(X_trans.toarray(), axis=0), 1.)
X_trans_inv = transformer_dense.inverse_transform(X_trans)
assert_array_almost_equal(X.toarray(), X_trans_inv.toarray())
def test_quantile_transform_axis1():
X = np.array([[0, 25, 50, 75, 100],
[2, 4, 6, 8, 10],
[2.6, 4.1, 2.3, 9.5, 0.1]])
X_trans_a0 = quantile_transform(X.T, axis=0, n_quantiles=5)
X_trans_a1 = quantile_transform(X, axis=1, n_quantiles=5)
assert_array_almost_equal(X_trans_a0, X_trans_a1.T)
def test_quantile_transform_bounds():
# Lower and upper bounds are manually mapped. We checked that in the case
# of a constant feature and binary feature, the bounds are properly mapped.
X_dense = np.array([[0, 0],
[0, 0],
[1, 0]])
X_sparse = sparse.csc_matrix(X_dense)
# check sparse and dense are consistent
X_trans = QuantileTransformer(n_quantiles=3,
random_state=0).fit_transform(X_dense)
assert_array_almost_equal(X_trans, X_dense)
X_trans_sp = QuantileTransformer(n_quantiles=3,
random_state=0).fit_transform(X_sparse)
assert_array_almost_equal(X_trans_sp.A, X_dense)
assert_array_almost_equal(X_trans, X_trans_sp.A)
# check the consistency of the bounds by learning on 1 matrix
# and transforming another
X = np.array([[0, 1],
[0, 0.5],
[1, 0]])
X1 = np.array([[0, 0.1],
[0, 0.5],
[1, 0.1]])
transformer = QuantileTransformer(n_quantiles=3).fit(X)
X_trans = transformer.transform(X1)
assert_array_almost_equal(X_trans, X1)
# check that values outside of the range learned will be mapped properly.
X = np.random.random((1000, 1))
transformer = QuantileTransformer()
transformer.fit(X)
assert (transformer.transform([[-10]]) ==
transformer.transform([[np.min(X)]]))
assert (transformer.transform([[10]]) ==
transformer.transform([[np.max(X)]]))
assert (transformer.inverse_transform([[-10]]) ==
transformer.inverse_transform([[np.min(transformer.references_)]]))
assert (transformer.inverse_transform([[10]]) ==
transformer.inverse_transform([[np.max(transformer.references_)]]))
def test_quantile_transform_and_inverse():
X_1 = iris.data
X_2 = np.array([[0.], [BOUNDS_THRESHOLD / 10], [1.5], [2], [3], [3], [4]])
for X in [X_1, X_2]:
transformer = QuantileTransformer(n_quantiles=1000, random_state=0)
X_trans = transformer.fit_transform(X)
X_trans_inv = transformer.inverse_transform(X_trans)
assert_array_almost_equal(X, X_trans_inv, decimal=9)
def test_quantile_transform_nan():
X = np.array([[np.nan, 0, 0, 1],
[np.nan, np.nan, 0, 0.5],
[np.nan, 1, 1, 0]])
transformer = QuantileTransformer(n_quantiles=10, random_state=42)
transformer.fit_transform(X)
# check that the quantile of the first column is all NaN
assert np.isnan(transformer.quantiles_[:, 0]).all()
# all other column should not contain NaN
assert not np.isnan(transformer.quantiles_[:, 1:]).any()
@pytest.mark.parametrize("array_type", ['array', 'sparse'])
def test_quantile_transformer_sorted_quantiles(array_type):
# Non-regression test for:
# https://github.com/scikit-learn/scikit-learn/issues/15733
# Taken from upstream bug report:
# https://github.com/numpy/numpy/issues/14685
X = np.array([0, 1, 1, 2, 2, 3, 3, 4, 5, 5, 1, 1, 9, 9, 9, 8, 8, 7] * 10)
X = 0.1 * X.reshape(-1, 1)
X = _convert_container(X, array_type)
n_quantiles = 100
qt = QuantileTransformer(n_quantiles=n_quantiles).fit(X)
# Check that the estimated quantile threasholds are monotically
# increasing:
quantiles = qt.quantiles_[:, 0]
assert len(quantiles) == 100
assert all(np.diff(quantiles) >= 0)
def test_robust_scaler_invalid_range():
for range_ in [
(-1, 90),
(-2, -3),
(10, 101),
(100.5, 101),
(90, 50),
]:
scaler = RobustScaler(quantile_range=range_)
with pytest.raises(ValueError, match=r'Invalid quantile range: \('):
scaler.fit(iris.data)
def test_scale_function_without_centering():
rng = np.random.RandomState(42)
X = rng.randn(4, 5)
X[:, 0] = 0.0 # first feature is always of zero
X_csr = sparse.csr_matrix(X)
X_scaled = scale(X, with_mean=False)
assert not np.any(np.isnan(X_scaled))
X_csr_scaled = scale(X_csr, with_mean=False)
assert not np.any(np.isnan(X_csr_scaled.data))
# test csc has same outcome
X_csc_scaled = scale(X_csr.tocsc(), with_mean=False)
assert_array_almost_equal(X_scaled, X_csc_scaled.toarray())
# raises value error on axis != 0
with pytest.raises(ValueError):
scale(X_csr, with_mean=False, axis=1)
assert_array_almost_equal(X_scaled.mean(axis=0),
[0., -0.01, 2.24, -0.35, -0.78], 2)
assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])
# Check that X has not been copied
assert X_scaled is not X
X_csr_scaled_mean, X_csr_scaled_std = mean_variance_axis(X_csr_scaled, 0)
assert_array_almost_equal(X_csr_scaled_mean, X_scaled.mean(axis=0))
assert_array_almost_equal(X_csr_scaled_std, X_scaled.std(axis=0))
# null scale
X_csr_scaled = scale(X_csr, with_mean=False, with_std=False, copy=True)
assert_array_almost_equal(X_csr.toarray(), X_csr_scaled.toarray())
def test_robust_scale_axis1():
X = iris.data
X_trans = robust_scale(X, axis=1)
assert_array_almost_equal(np.median(X_trans, axis=1), 0)
q = np.percentile(X_trans, q=(25, 75), axis=1)
iqr = q[1] - q[0]
assert_array_almost_equal(iqr, 1)
def test_robust_scale_1d_array():
X = iris.data[:, 1]
X_trans = robust_scale(X)
assert_array_almost_equal(np.median(X_trans), 0)
q = np.percentile(X_trans, q=(25, 75))
iqr = q[1] - q[0]
assert_array_almost_equal(iqr, 1)
def test_robust_scaler_zero_variance_features():
# Check RobustScaler on toy data with zero variance features
X = [[0., 1., +0.5],
[0., 1., -0.1],
[0., 1., +1.1]]
scaler = RobustScaler()
X_trans = scaler.fit_transform(X)
# NOTE: for such a small sample size, what we expect in the third column
# depends HEAVILY on the method used to calculate quantiles. The values
# here were calculated to fit the quantiles produces by np.percentile
# using numpy 1.9 Calculating quantiles with
# scipy.stats.mstats.scoreatquantile or scipy.stats.mstats.mquantiles
# would yield very different results!
X_expected = [[0., 0., +0.0],
[0., 0., -1.0],
[0., 0., +1.0]]
assert_array_almost_equal(X_trans, X_expected)
X_trans_inv = scaler.inverse_transform(X_trans)
assert_array_almost_equal(X, X_trans_inv)
# make sure new data gets transformed correctly
X_new = [[+0., 2., 0.5],
[-1., 1., 0.0],
[+0., 1., 1.5]]
X_trans_new = scaler.transform(X_new)
X_expected_new = [[+0., 1., +0.],
[-1., 0., -0.83333],
[+0., 0., +1.66667]]
assert_array_almost_equal(X_trans_new, X_expected_new, decimal=3)
def test_robust_scaler_unit_variance():
# Check RobustScaler with unit_variance=True on standard normal data with
# outliers
rng = np.random.RandomState(42)
X = rng.randn(1000000, 1)
X_with_outliers = np.vstack(
[X, np.ones((100, 1)) * 100, np.ones((100, 1)) * -100]
)
quantile_range = (1, 99)
robust_scaler = RobustScaler(
quantile_range=quantile_range, unit_variance=True
).fit(X_with_outliers)
X_trans = robust_scaler.transform(X)
assert robust_scaler.center_ == pytest.approx(0, abs=1e-3)
assert robust_scaler.scale_ == pytest.approx(1, abs=1e-2)
assert X_trans.std() == pytest.approx(1, abs=1e-2)
def test_maxabs_scaler_zero_variance_features():
# Check MaxAbsScaler on toy data with zero variance features
X = [[0., 1., +0.5],
[0., 1., -0.3],
[0., 1., +1.5],
[0., 0., +0.0]]
scaler = MaxAbsScaler()
X_trans = scaler.fit_transform(X)
X_expected = [[0., 1., 1.0 / 3.0],
[0., 1., -0.2],
[0., 1., 1.0],
[0., 0., 0.0]]
assert_array_almost_equal(X_trans, X_expected)
X_trans_inv = scaler.inverse_transform(X_trans)
assert_array_almost_equal(X, X_trans_inv)
# make sure new data gets transformed correctly
X_new = [[+0., 2., 0.5],
[-1., 1., 0.0],
[+0., 1., 1.5]]
X_trans_new = scaler.transform(X_new)
X_expected_new = [[+0., 2.0, 1.0 / 3.0],
[-1., 1.0, 0.0],
[+0., 1.0, 1.0]]
assert_array_almost_equal(X_trans_new, X_expected_new, decimal=2)
# function interface
X_trans = maxabs_scale(X)
assert_array_almost_equal(X_trans, X_expected)
# sparse data
X_csr = sparse.csr_matrix(X)
X_csc = sparse.csc_matrix(X)
X_trans_csr = scaler.fit_transform(X_csr)
X_trans_csc = scaler.fit_transform(X_csc)
X_expected = [[0., 1., 1.0 / 3.0],
[0., 1., -0.2],
[0., 1., 1.0],
[0., 0., 0.0]]
assert_array_almost_equal(X_trans_csr.A, X_expected)
assert_array_almost_equal(X_trans_csc.A, X_expected)
X_trans_csr_inv = scaler.inverse_transform(X_trans_csr)
X_trans_csc_inv = scaler.inverse_transform(X_trans_csc)
assert_array_almost_equal(X, X_trans_csr_inv.A)
assert_array_almost_equal(X, X_trans_csc_inv.A)
def test_maxabs_scaler_large_negative_value():
# Check MaxAbsScaler on toy data with a large negative value
X = [[0., 1., +0.5, -1.0],
[0., 1., -0.3, -0.5],
[0., 1., -100.0, 0.0],
[0., 0., +0.0, -2.0]]
scaler = MaxAbsScaler()
X_trans = scaler.fit_transform(X)
X_expected = [[0., 1., 0.005, -0.5],
[0., 1., -0.003, -0.25],
[0., 1., -1.0, 0.0],
[0., 0., 0.0, -1.0]]
assert_array_almost_equal(X_trans, X_expected)
def test_maxabs_scaler_transform_one_row_csr():
# Check MaxAbsScaler on transforming csr matrix with one row
X = sparse.csr_matrix([[0.5, 1., 1.]])
scaler = MaxAbsScaler()
scaler = scaler.fit(X)
X_trans = scaler.transform(X)
X_expected = sparse.csr_matrix([[1., 1., 1.]])
assert_array_almost_equal(X_trans.toarray(), X_expected.toarray())
X_scaled_back = scaler.inverse_transform(X_trans)
assert_array_almost_equal(X.toarray(), X_scaled_back.toarray())
def test_maxabs_scaler_1d():
# Test scaling of dataset along single axis
for X in [X_1row, X_1col, X_list_1row, X_list_1row]:
scaler = MaxAbsScaler(copy=True)
X_scaled = scaler.fit(X).transform(X)
if isinstance(X, list):
X = np.array(X) # cast only after scaling done
if _check_dim_1axis(X) == 1:
assert_array_almost_equal(np.abs(X_scaled.max(axis=0)),
np.ones(n_features))
else:
assert_array_almost_equal(np.abs(X_scaled.max(axis=0)), 1.)
assert scaler.n_samples_seen_ == X.shape[0]
# check inverse transform
X_scaled_back = scaler.inverse_transform(X_scaled)
assert_array_almost_equal(X_scaled_back, X)
# Constant feature
X = np.ones((5, 1))
scaler = MaxAbsScaler()
X_scaled = scaler.fit(X).transform(X)
assert_array_almost_equal(np.abs(X_scaled.max(axis=0)), 1.)
assert scaler.n_samples_seen_ == X.shape[0]
# function interface
X_1d = X_1row.ravel()
max_abs = np.abs(X_1d).max()
assert_array_almost_equal(X_1d / max_abs, maxabs_scale(X_1d, copy=True))
def test_maxabs_scaler_partial_fit():
# Test if partial_fit run over many batches of size 1 and 50
# gives the same results as fit
X = X_2d[:100, :]
n = X.shape[0]
for chunk_size in [1, 2, 50, n, n + 42]:
# Test mean at the end of the process
scaler_batch = MaxAbsScaler().fit(X)
scaler_incr = MaxAbsScaler()
scaler_incr_csr = MaxAbsScaler()
scaler_incr_csc = MaxAbsScaler()
for batch in gen_batches(n, chunk_size):
scaler_incr = scaler_incr.partial_fit(X[batch])
X_csr = sparse.csr_matrix(X[batch])
scaler_incr_csr = scaler_incr_csr.partial_fit(X_csr)
X_csc = sparse.csc_matrix(X[batch])
scaler_incr_csc = scaler_incr_csc.partial_fit(X_csc)
assert_array_almost_equal(scaler_batch.max_abs_, scaler_incr.max_abs_)
assert_array_almost_equal(scaler_batch.max_abs_,
scaler_incr_csr.max_abs_)
assert_array_almost_equal(scaler_batch.max_abs_,
scaler_incr_csc.max_abs_)
assert scaler_batch.n_samples_seen_ == scaler_incr.n_samples_seen_
assert (scaler_batch.n_samples_seen_ ==
scaler_incr_csr.n_samples_seen_)
assert (scaler_batch.n_samples_seen_ ==
scaler_incr_csc.n_samples_seen_)
assert_array_almost_equal(scaler_batch.scale_, scaler_incr.scale_)
assert_array_almost_equal(scaler_batch.scale_, scaler_incr_csr.scale_)
assert_array_almost_equal(scaler_batch.scale_, scaler_incr_csc.scale_)
assert_array_almost_equal(scaler_batch.transform(X),
scaler_incr.transform(X))
# Test std after 1 step
batch0 = slice(0, chunk_size)
scaler_batch = MaxAbsScaler().fit(X[batch0])
scaler_incr = MaxAbsScaler().partial_fit(X[batch0])
assert_array_almost_equal(scaler_batch.max_abs_, scaler_incr.max_abs_)
assert scaler_batch.n_samples_seen_ == scaler_incr.n_samples_seen_
assert_array_almost_equal(scaler_batch.scale_, scaler_incr.scale_)
assert_array_almost_equal(scaler_batch.transform(X),
scaler_incr.transform(X))
# Test std until the end of partial fits, and
scaler_batch = MaxAbsScaler().fit(X)
scaler_incr = MaxAbsScaler() # Clean estimator
for i, batch in enumerate(gen_batches(n, chunk_size)):
scaler_incr = scaler_incr.partial_fit(X[batch])
assert_correct_incr(i, batch_start=batch.start,
batch_stop=batch.stop, n=n,
chunk_size=chunk_size,
n_samples_seen=scaler_incr.n_samples_seen_)
def test_normalizer_l1():
rng = np.random.RandomState(0)
X_dense = rng.randn(4, 5)
X_sparse_unpruned = sparse.csr_matrix(X_dense)
# set the row number 3 to zero
X_dense[3, :] = 0.0
# set the row number 3 to zero without pruning (can happen in real life)
indptr_3 = X_sparse_unpruned.indptr[3]
indptr_4 = X_sparse_unpruned.indptr[4]
X_sparse_unpruned.data[indptr_3:indptr_4] = 0.0
# build the pruned variant using the regular constructor
X_sparse_pruned = sparse.csr_matrix(X_dense)
# check inputs that support the no-copy optim
for X in (X_dense, X_sparse_pruned, X_sparse_unpruned):
normalizer = Normalizer(norm='l1', copy=True)
X_norm = normalizer.transform(X)
assert X_norm is not X
X_norm1 = toarray(X_norm)
normalizer = Normalizer(norm='l1', copy=False)
X_norm = normalizer.transform(X)
assert X_norm is X
X_norm2 = toarray(X_norm)
for X_norm in (X_norm1, X_norm2):
row_sums = np.abs(X_norm).sum(axis=1)
for i in range(3):
assert_almost_equal(row_sums[i], 1.0)
assert_almost_equal(row_sums[3], 0.0)
# check input for which copy=False won't prevent a copy
for init in (sparse.coo_matrix, sparse.csc_matrix, sparse.lil_matrix):
X = init(X_dense)
X_norm = normalizer = Normalizer(norm='l2', copy=False).transform(X)
assert X_norm is not X
assert isinstance(X_norm, sparse.csr_matrix)
X_norm = toarray(X_norm)
for i in range(3):
assert_almost_equal(row_sums[i], 1.0)
assert_almost_equal(la.norm(X_norm[3]), 0.0)
def test_normalizer_l2():
rng = np.random.RandomState(0)
X_dense = rng.randn(4, 5)
X_sparse_unpruned = sparse.csr_matrix(X_dense)
# set the row number 3 to zero
X_dense[3, :] = 0.0
# set the row number 3 to zero without pruning (can happen in real life)
indptr_3 = X_sparse_unpruned.indptr[3]
indptr_4 = X_sparse_unpruned.indptr[4]
X_sparse_unpruned.data[indptr_3:indptr_4] = 0.0
# build the pruned variant using the regular constructor
X_sparse_pruned = sparse.csr_matrix(X_dense)
# check inputs that support the no-copy optim
for X in (X_dense, X_sparse_pruned, X_sparse_unpruned):
normalizer = Normalizer(norm='l2', copy=True)
X_norm1 = normalizer.transform(X)
assert X_norm1 is not X
X_norm1 = toarray(X_norm1)
normalizer = Normalizer(norm='l2', copy=False)
X_norm2 = normalizer.transform(X)
assert X_norm2 is X
X_norm2 = toarray(X_norm2)
for X_norm in (X_norm1, X_norm2):
for i in range(3):
assert_almost_equal(la.norm(X_norm[i]), 1.0)
assert_almost_equal(la.norm(X_norm[3]), 0.0)
# check input for which copy=False won't prevent a copy
for init in (sparse.coo_matrix, sparse.csc_matrix, sparse.lil_matrix):
X = init(X_dense)
X_norm = normalizer = Normalizer(norm='l2', copy=False).transform(X)
assert X_norm is not X
assert isinstance(X_norm, sparse.csr_matrix)
X_norm = toarray(X_norm)
for i in range(3):
assert_almost_equal(la.norm(X_norm[i]), 1.0)
assert_almost_equal(la.norm(X_norm[3]), 0.0)
def test_normalizer_max():
rng = np.random.RandomState(0)
X_dense = rng.randn(4, 5)
X_sparse_unpruned = sparse.csr_matrix(X_dense)
# set the row number 3 to zero
X_dense[3, :] = 0.0
# set the row number 3 to zero without pruning (can happen in real life)
indptr_3 = X_sparse_unpruned.indptr[3]
indptr_4 = X_sparse_unpruned.indptr[4]
X_sparse_unpruned.data[indptr_3:indptr_4] = 0.0
# build the pruned variant using the regular constructor
X_sparse_pruned = sparse.csr_matrix(X_dense)
# check inputs that support the no-copy optim
for X in (X_dense, X_sparse_pruned, X_sparse_unpruned):
normalizer = Normalizer(norm='max', copy=True)
X_norm1 = normalizer.transform(X)
assert X_norm1 is not X
X_norm1 = toarray(X_norm1)
normalizer = Normalizer(norm='max', copy=False)
X_norm2 = normalizer.transform(X)
assert X_norm2 is X
X_norm2 = toarray(X_norm2)
for X_norm in (X_norm1, X_norm2):
row_maxs = abs(X_norm).max(axis=1)
for i in range(3):
assert_almost_equal(row_maxs[i], 1.0)
assert_almost_equal(row_maxs[3], 0.0)
# check input for which copy=False won't prevent a copy
for init in (sparse.coo_matrix, sparse.csc_matrix, sparse.lil_matrix):
X = init(X_dense)
X_norm = normalizer = Normalizer(norm='l2', copy=False).transform(X)
assert X_norm is not X
assert isinstance(X_norm, sparse.csr_matrix)
X_norm = toarray(X_norm)
for i in range(3):
assert_almost_equal(row_maxs[i], 1.0)
assert_almost_equal(la.norm(X_norm[3]), 0.0)
def test_normalizer_max_sign():
# check that we normalize by a positive number even for negative data
rng = np.random.RandomState(0)
X_dense = rng.randn(4, 5)
# set the row number 3 to zero
X_dense[3, :] = 0.0
# check for mixed data where the value with
# largest magnitude is negative
X_dense[2, abs(X_dense[2, :]).argmax()] *= -1
X_all_neg = -np.abs(X_dense)
X_all_neg_sparse = sparse.csr_matrix(X_all_neg)
for X in (X_dense, X_all_neg, X_all_neg_sparse):
normalizer = Normalizer(norm='max')
X_norm = normalizer.transform(X)
assert X_norm is not X
X_norm = toarray(X_norm)
assert_array_equal(
np.sign(X_norm), np.sign(toarray(X)))
def test_normalize():
# Test normalize function
# Only tests functionality not used by the tests for Normalizer.
X = np.random.RandomState(37).randn(3, 2)
assert_array_equal(normalize(X, copy=False),
normalize(X.T, axis=0, copy=False).T)
with pytest.raises(ValueError):
normalize([[0]], axis=2)
with pytest.raises(ValueError):
normalize([[0]], norm='l3')
rs = | np.random.RandomState(0) | numpy.random.RandomState |
#%% Import Libraries ===============================================
import numpy as np
import torch
import torch.nn as nn
import torch.optim as optim
import torch.nn.functional as F
from torchvision import transforms, datasets
from torch.autograd import Variable
from datetime import datetime
import os
from model import NN_MNIST
# Colab~~~~~~~~~~~~~~~~~
# Set path for model and data locations
path_data = './'
path_model = './'
# Define function for calculating predictions on test data
def calc_test_accy(model, test_loader):
model.eval() # Set model into evaluation mode
correct = 0
with torch.no_grad():
for (data, target) in test_loader:
data, target = data.to(device), target.to(
device) # Move data to GPU
output = model(data) # Calculate Output
pred = output.max(1, keepdim=True)[1] # Calculate Predictions
correct += pred.eq(target.view_as(pred)).sum().item()
return (100.*correct/len(test_loader.dataset))
# Define function for calculating predictions on training data
# n_batches indicates how many training observations to use for training accuracy calculation
# This reduces computation time, instead of using the entire training set.
def calc_train_accy(model, dataloader, n_batches, batch_size):
model.eval()
correct = 0
with torch.no_grad():
data_iterator = iter(dataloader)
for i in range(n_batches): # iterate for the specified number of batches
try:
data, target = next(data_iterator)
except StopIteration:
data_iterator = iter(dataloader)
data, target = next(data_iterator)
data, target = data.to(device), target.to(
device) # Move data to GPU
output = model(data) # Calculate Output
pred = output.max(1, keepdim=True)[1] # Calculate Predictions
correct += pred.eq(target.view_as(pred)).sum().item()
return (100.*correct/(n_batches * batch_size))
#%% Model Parameters ===================================================
load_checkpoint = False
num_epochs = 20
batch_size = 32
optimizer_params = {
'lr': 0.01,
'weight_decay': 0,
'momentum': 0
}
scheduler_params = {
'step_size': 8,
'gamma': 0.1
}
model_params = {
'input_units':28*28,
'num_classes':10,
'hidden_units':500,
'n_layers':3
}
#%% Load Data =================================================
# Define Data Transforms
data_transforms = {
'train': transforms.Compose([
transforms.ToTensor(),
#transforms.Normalize(mean=[0.1307], std=[0.3081])
]),
'test': transforms.Compose([
transforms.ToTensor(),
#transforms.Normalize(mean=[0.1307], std=[0.3081])
])
}
# Training Data
train_set = datasets.MNIST(
root=path_data, train=True, download=True, transform=data_transforms['train'])
train_loader = torch.utils.data.DataLoader(
train_set, batch_size=batch_size, shuffle=True, num_workers=0)
# Test Data
test_set = datasets.MNIST(
root=path_data, train=False, download=True, transform=data_transforms['test'])
test_loader = torch.utils.data.DataLoader(
test_set, batch_size=batch_size, shuffle=False, num_workers=0)
#%% Run Model ==================================================
# Initialize Model
device = torch.device("cuda:0" if torch.cuda.is_available()
else "cpu") # Use GPU if available
model = NN_MNIST(**model_params).to(device)
# Initialize Optimizer
optimizer = torch.optim.SGD(model.parameters(), **optimizer_params)
scheduler = torch.optim.lr_scheduler.StepLR(optimizer, **scheduler_params)
criterion = nn.CrossEntropyLoss()
optimizer.zero_grad()
# Initialize Other Trackers
StartTime = datetime.now() # track training time
# numpy array to track training/test accuracy by epoch
save_accy = np.zeros((num_epochs + 1, 2))
np.random.seed(1)
torch.manual_seed(1)
# Epoch to start calculations (should be zero unless loading previous model checkpoint)
init_epoch = 0
n_batches = np.int(np.floor((len(train_set)*1.)/batch_size))
#~~~~~~~~~~~~~~~~~~~~~~
# If we are starting from a loaded checkpoint, load previous model paramters
if load_checkpoint:
checkpoint = torch.load(os.path.join(path_model, 'checkpoint.pt'))
model = checkpoint['model']
model.load_state_dict(checkpoint['state_dict'])
init_epoch = checkpoint['epoch']
optimizer.load_state_dict(checkpoint['optimizer'])
scheduler.load_state_dict(checkpoint['scheduler'])
model.to(device)
#~~~~~~~~~~~~~~~~~~~~~~~
for epoch in range(init_epoch, num_epochs):
epoch_time_start = datetime.now()
model.train()
for batch_ID, (data, target) in enumerate(train_loader):
data, target = data.to(device), target.to(device) # Move training data to GPU
pred = model(data) # Calculate Predictions
loss = criterion(pred, target) # Calculate Loss
loss.backward() # Calculate Gradients
optimizer.step()
optimizer.zero_grad()
scheduler.step()
# Calculate Train/Test Accuracy
test_accy = calc_test_accy(model, test_loader)
train_accy = calc_train_accy(model, train_loader, | np.minimum(25, n_batches) | numpy.minimum |
# -*- coding: utf-8 -*-
"""
Created on Fri Jun 19 13:16:25 2015
@author: hbanks
Brevity required, prudence preferred
"""
import os
import io
import glob
import errno
import copy
import json
import time
import warnings
import numpy as np
from scipy.optimize import curve_fit
import scipy.interpolate as spi
import scipy.optimize as spo
import scipy.integrate as intgt
import scipy.fftpack as fft
import scipy.special as spl
import matplotlib.pyplot as plt
import scipy.ndimage as ndimage
import itertools as itt
import multiprocessing as mp
import sys
sys.path.append('/Users/marketing/Desktop/HSG-turbo/')
import hsganalysis.QWPProcessing as qwp
from hsganalysis.QWPProcessing.extractMatrices import makeT,saveT
np.set_printoptions(linewidth=500)
# One of the main results is the HighSidebandCCD.sb_results array. These are the
# various mappings between index and real value
# I deally, this code should be converted to pandas to avoid this issue,
# but that's outside the scope of current work.
# [sb number, Freq (eV), Freq error (eV), Gauss area (arb.), Area error, Gauss linewidth (eV), Linewidth error (eV)]
# [ 0 , 1 , 2, , 3 , 4 , 5 , 6 ]
class sbarr(object):
SBNUM = 0
CENFREQ = 1
CENFREQERR = 2
AREA = 3
AREAERR = 4
WIDTH = 5
WIDTHERR = 6
####################
# Objects
####################
class CCD(object):
def __init__(self, fname, spectrometer_offset=None):
"""
This will read the appropriate file and make a basic CCD object. Fancier
things will be handled with the sub classes.
Creates:
self.parameters = Dictionary holding all of the information from the
data file, which comes from the JSON encoded header in the data
file
self.description = string that is the text box from data taking GUI
self.raw_data = raw data output by measurement software, wavelength vs.
data, errors. There may be text for some of the entries
corresponding to text used for Origin imports, but they
should appear as np.nan
self.ccd_data = semi-processed 1600 x 3 array of photon energy vs. data with standard error of mean at that pixel
calculated by taking multiple images. Standard error is calculated from
the data collection software
Most subclasses should make a self.proc_data, which will do whatever
processing is required to the ccd_data, such as normalizing, taking ratios,
etc.
:param fname: file name where the data is saved
:type fname: str
:param spectrometer_offset: if the spectrometer won't go where it's told, use this to correct the wavelengths (nm)
:type spectrometer_offset: float
"""
self.fname = fname
# Checking restrictions from Windows path length limits. Check if you can
# open the file:
try:
with open(fname) as f: pass
except FileNotFoundError:
# Couldn't find the file. Could be you passed the wrong one, but I'm
# finding with a large number of subfolders for polarimetry stuff,
# you end up exceeding Windows' filelength limit.
# Haven't tested on Mac or UNC moutned drives (e.g \\128.x.x.x\Sherwin\)
fname = r"\\?\\" + os.path.abspath(fname)
# Read in the JSON-formatted parameter string.
# The lines are all prepended by '#' for easy numpy importing
# so loop over all those lines
with open(fname, 'r') as f:
param_str = ''
line = f.readline()
while line[0] == '#':
### changed 09/17/18
# This line assumed there was a single '#'
# param_str += line[1:]
# while this one handles everal (because I found old files
# which had '## <text>...'
param_str += line.replace("#", "")
line = f.readline()
# Parse the JSON string
try:
self.parameters = json.loads(param_str)
except json.JSONDecodeError:
# error from _really_ old data where comments were dumped after a
# single-line json dumps
self.parameters=json.loads(param_str.splitlines()[0])
# Spec[trometer] steps are set to define the same physical data, but taken at
# different spectrometer center wavelengths. This value is used later
# for stitching these scans together
try:
self.parameters["spec_step"] = int(self.parameters["spec_step"])
except (ValueError, KeyError):
# If there isn't a spe
self.parameters["spec_step"] = 0
# Slice through 3 to get rid of comments/origin info.
# Would likely be better to check np.isnan() and slicing out those nans.
# I used flipup so that the x-axis is an increasing function of frequency
self.raw_data = np.flipud(np.genfromtxt(fname, comments='#', delimiter=',')[3:])
# The camera chip is 1600 pixels wide. This line was redudent with the [3:]
# slice above and served to make sure there weren't extra stray bad lines
# hanging around.
#
# This should also be updated some day to compensate for any horizontal bining
# on the chip, or masking out points that are bad (cosmic ray making it
# through processing, room lights or monitor lines interfering with signal)
self.ccd_data = np.array(self.raw_data[:1600, :])
# Check to see if the spectrometer offset is set. This isn't specified
# during data collection. This is a value that can be appended
# when processing if it's realized the data is offset.
# This allows the offset to be specified and kept with the data file itself,
# instead of trying to do it in individual processing scripts
#
# It's allowed as a kwarg parameter in this script for trying to determine
# what the correct offset should be
if spectrometer_offset is not None or "offset" in self.parameters:
try:
self.ccd_data[:, 0] += float(self.parameters["offset"])
except:
self.ccd_data[:, 0] += spectrometer_offset
# Convert from nm to eV
# self.ccd_data[:, 0] = 1239.84 / self.ccd_data[:, 0]
self.ccd_data[:, 0] = photon_converter["nm"]["eV"](self.ccd_data[:, 0])
class Photoluminescence(CCD):
def __init__(self, fname):
"""
This object handles PL-type data. The only distinction from the parent class
is that the CCD data gets normalized to the exposure time to make different
exposures directly comparable.
creates:
self.proc_data = self.ccd_data divided by the exposure time
units: PL counts / second
:param fname: name of the file
:type fname: str
"""
super(Photoluminescence, self).__init__(fname)
# Create a copy of the array , and then normalize the signal and the errors
# by the exposure time
self.proc_data = np.array(self.ccd_data)
self.proc_data[:, 1] = self.proc_data[:, 1] / self.parameters['exposure']
self.proc_data[:, 2] = self.proc_data[:, 2] / self.parameters['exposure']
class Absorbance(CCD):
def __init__(self, fname):
"""
There are several ways Absorbance data can be loaded
You could try to load the abs data output from data collection directly,
which has the wavelength, raw, blank and actual absorbance data itself.
This is best way to do it.
Alternatively, you could want to load the raw transmission/reference
data, ignoring (or maybe not even having) the abs calculated
from the data collection software. If you want to do it this way,
you should pass fname as a list where the first element is the
file name for the reference data, and the second is the absorbance data
At first, it didn't really seem to make sense to let you pass just the
raw reference or raw abs data,
Creates:
self.ref_data = np array of the reference,
freq (eV) vs. reference (counts)
self.raw_data = np.array of the raw absorption spectrum,
freq (eV) vs. reference (counts)
self.proc_data = np.array of the absorption spectrum
freq (eV) vs. "absorbance" (dB)
Note, the error bars for this data haven't been defined.
:param fname: either an absorbance filename, or a length 2 list of filenames
:type fname: str
:return: None
"""
if "abs_" in fname:
super(Absorbance, self).__init__(fname)
# Separate into the separate data sets
# The raw counts of the reference data
self.ref_data = np.array(self.ccd_data[:, [0, 1]])
# Raw counts of the sample
self.raw_data = np.array(self.ccd_data[:, [0, 2]])
# The calculated absorbance data (-10*log10(raw/ref))
self.proc_data = np.array(self.ccd_data[:, [0, 3]]) # Already in dB's
else:
# Should be here if you pass the reference/trans filenames
try:
super(Absorbance, self).__init__(fname[0])
self.ref_data = np.array(self.ccd_data)
super(Absorbance, self).__init__(fname[1])
self.raw_data = np.array(self.ccd_data)
except ValueError:
# ValueError gets thrown when importing older data
# which had more headers than data columns. Enforce
# only loading first two columns to avoid numpy trying
# to parse all of the data
# See CCD.__init__ for what's going on.
self.ref_data = np.flipud(np.genfromtxt(fname[0], comments='#',
delimiter=',', usecols=(0, 1)))
self.ref_data = np.array(self.ref_data[:1600, :])
self.ref_data[:, 0] = 1239.84 / self.ref_data[:, 0]
self.raw_data = np.flipud(np.genfromtxt(fname[1], comments='#',
delimiter=',', usecols=(0, 1)))
self.raw_data = np.array(self.raw_data[:1600, :])
self.raw_data[:, 0] = 1239.84 / self.raw_data[:, 0]
except Exception as e:
print("Exception opening absorbance data,", e)
# Calculate the absorbance from the raw camera counts.
self.proc_data = np.empty_like(self.ref_data)
self.proc_data[:, 0] = self.ref_data[:, 0]
self.proc_data[:, 1] = -10*np.log10(self.raw_data[:, 1] / self.ref_data[:,
1])
def abs_per_QW(self, qw_number):
"""
:param qw_number: number of quantum wells in the sample.
:type qw_number: int
:return: None
"""
"""
This method turns the absorption to the absorbance per quantum well. Is
that how this data should be reported?
Also, I'm not sure if columns 1 and 2 are correct.
"""
temp_abs = -np.log(self.proc_data[:, 1] / self.proc_data[:, 2]) / qw_number
self.proc_data = np.hstack((self.proc_data, temp_abs))
def fft_smooth(self, cutoff, inspectPlots=False):
"""
This function removes the Fabry-Perot that affects the absorption data
creates:
self.clean = np.array of the Fourier-filtered absorption data, freq (eV) vs. absorbance (dB!)
self.parameters['fourier cutoff'] = the low pass cutoff frequency, in eV**(-1)
:param cutoff: Fourier frequency of the cut off for the low pass filter
:type cutoff: int or float
:param inspectPlots: Do you want to see the results?
:type inspectPlots: bool
:return: None
"""
# self.fixed = -np.log10(abs(self.raw_data[:, 1]) / abs(self.ref_data[:, 1]))
# self.fixed = np.nan_to_num(self.proc_data[:, 1])
# self.fixed = np.column_stack((self.raw_data[:, 0], self.fixed))
self.parameters['fourier cutoff'] = cutoff
self.clean = low_pass_filter(self.proc_data[:, 0], self.proc_data[:, 1], cutoff, inspectPlots)
def save_processing(self, file_name, folder_str, marker='', index=''):
"""
This bad boy saves the absorption spectrum that has been manipulated.
Saves 100 lines of comments.
:param file_name: The base name of the file to be saved
:type file_name: str
:param folder_str: The name of the folder where the file will be saved
:type folder_str: str
:param marker: A further label that might be the series tag or something
:type marker: str
:param index: If multiple files are being saved with the same name, include an integer to append to the end of the file
:type index: int
:return: None
"""
try:
os.mkdir(folder_str)
except OSError as e:
if e.errno == errno.EEXIST:
pass
else:
raise
spectra_fname = file_name + '_' + marker + '_' + str(index) + '.txt'
self.save_name = spectra_fname
try:
parameter_str = json.dumps(self.parameters, sort_keys=True, indent=4, separators=(',', ': '))
except:
print("Source: EMCCD_image.save_images\nJSON FAILED")
print("Here is the dictionary that broke JSON:\n", self.parameters)
return
parameter_str = parameter_str.replace('\n', '\n#')
num_lines = parameter_str.count('#') # Make the number of lines constant so importing into Origin is easier
# for num in range(99 - num_lines): parameter_str += '\n#'
parameter_str += '\n#' * (99 - num_lines)
origin_import_spec = '\nNIR frequency,Signal,Standard error\neV,arb. u.,arb. u.'
spec_header = '#' + parameter_str + origin_import_spec
# spec_header = '#' + parameter_str + '\n#' + self.description[:-2] + origin_import_spec
np.savetxt(os.path.join(folder_str, spectra_fname), self.proc_data, delimiter=',',
header=spec_header, comments='', fmt='%0.6e')
spectra_fname = 'clean ' + spectra_fname
np.savetxt(os.path.join(folder_str, spectra_fname), self.clean, delimiter=',',
header=spec_header, comments='', fmt='%0.6e')
print("Save image.\nDirectory: {}".format(os.path.join(folder_str, spectra_fname)))
# class LaserLineCCD(HighSidebandCCD):
# """
# Class for use when doing alinging/testing by sending the laser
# directly into the CCD. Modifies how "sidebands" and guess and fit,
# simply looking at the max signal.
# """
# def guess_sidebands(self, cutoff=8, verbose=False, plot=False):
# pass
class NeonNoiseAnalysis(CCD):
"""
This class is used to make handling neon calibration lines easier. It's not great.
"""
def __init__(self, fname, spectrometer_offset=None):
# print 'opening', fname
super(NeonNoiseAnalysis, self).__init__(fname, spectrometer_offset=spectrometer_offset)
self.addenda = self.parameters['addenda']
self.subtrahenda = self.parameters['subtrahenda']
self.noise_and_signal()
self.process_stuff()
def noise_and_signal(self):
"""
This bad boy calculates the standard deviation of the space between the
neon lines.
The noise regions are, in nm:
high: 784-792
low1: 795-806
low2: 815-823
low3: 831-834
the peaks are located at, in nm:
#1, weak: 793.6
#2, medium: 794.3
#3, medium: 808.2
#4, weak: 825.9
#5, strong: 830.0
"""
print('\n\n')
self.ccd_data = np.flipud(self.ccd_data)
# self.high_noise_region = np.array(self.ccd_data[30:230, :])
self.high_noise_region = np.array(self.ccd_data[80:180, :]) # for dark current measurements
self.low_noise_region1 = np.array(self.ccd_data[380:700, :])
self.low_noise_region2 = np.array(self.ccd_data[950:1200, :])
self.low_noise_region3 = np.array(self.ccd_data[1446:1546, :])
# self.high_noise = np.std(self.high_noise_region[:, 1])
self.high_noise_std = np.std(self.high_noise_region[:, 1])
self.high_noise_sig = np.mean(self.high_noise_region[:, 1])
self.low_noise1 = np.std(self.low_noise_region1[:, 1])
self.low_noise2 = np.std(self.low_noise_region2[:, 1])
self.low_noise_std = np.std(self.low_noise_region2[:, 1])
self.low_noise_sig = np.mean(self.low_noise_region2[:, 1])
self.low_noise3 = np.std(self.low_noise_region3[:, 1])
# self.noise_list = [self.high_noise, self.low_noise1, self.low_noise2, self.low_noise3]
self.peak1 = np.array(self.ccd_data[303:323, :])
self.peak2 = np.array(self.ccd_data[319:339, :])
self.peak3 = np.array(self.ccd_data[736:746, :])
self.peak4 = np.array(self.ccd_data[1268:1288, :])
self.peak5 = np.array(self.ccd_data[1381:1421, :])
temp_max = np.argmax(self.peak1[:, 1])
self.signal1 = np.sum(self.peak1[temp_max - 1:temp_max + 2, 1])
self.error1 = np.sqrt(np.sum(self.peak1[temp_max - 1:temp_max + 2, 2] ** 2))
temp_max = np.argmax(self.peak2[:, 1])
self.signal2 = np.sum(self.peak2[temp_max - 1:temp_max + 2, 1])
self.error2 = np.sqrt(np.sum(self.peak2[temp_max - 1:temp_max + 2, 2] ** 2))
temp_max = np.argmax(self.peak3[:, 1])
self.signal3 = np.sum(self.peak3[temp_max - 1:temp_max + 2, 1])
self.error3 = np.sqrt(np.sum(self.peak3[temp_max - 1:temp_max + 2, 2] ** 2))
temp_max = np.argmax(self.peak4[:, 1])
self.signal4 = np.sum(self.peak4[temp_max - 1:temp_max + 2, 1])
self.error4 = np.sqrt(np.sum(self.peak4[temp_max - 1:temp_max + 2, 2] ** 2))
temp_max = np.argmax(self.peak5[:, 1])
self.signal5 = np.sum(self.peak5[temp_max - 1:temp_max + 2, 1])
self.error5 = np.sqrt(np.sum(self.peak5[temp_max - 1:temp_max + 2, 2] ** 2))
self.signal_list = [self.signal1, self.signal2, self.signal3, self.signal4, self.signal5]
self.error_list = [self.error1, self.error2, self.error3, self.error4, self.error5]
print("Signal list:", self.signal_list)
self.ccd_data = np.flipud(self.ccd_data)
def process_stuff(self):
"""
This one puts high_noise, low_noise1, signal2, and error2 in a nice horizontal array
"""
# self.results = np.array([self.high_noise, self.low_noise1, self.signal5, self.error5])
# average = np.mean([self.low_noise1, self.low_noise2, self.low_noise3])
# self.results = np.array([self.high_noise, self.low_noise1, self.low_noise2, self.low_noise3, self.high_noise/average])
self.results = np.array([self.high_noise_sig, self.high_noise_std, self.low_noise_sig, self.low_noise_std])
def collect_noise(neon_list, param_name, folder_name, file_name, name='Signal'):
"""
This function acts like save parameter sweep.
param_name = string that we're gonna save!
"""
# param_array = None
for elem in neon_list:
print("pname: {}".format(elem.parameters[param_name]))
print("results:", elem.results)
temp = np.insert(elem.results, 0, elem.parameters[param_name])
try:
param_array = np.row_stack((param_array, temp))
except UnboundLocalError:
param_array = np.array(temp)
if len(param_array.shape) == 1:
print("I don't think you want this file")
return
# append the relative peak error
print('\n', param_array, '\n')
param_array = np.column_stack((param_array, param_array[:, 4] / param_array[:, 3]))
# append the snr
param_array = np.column_stack((param_array, param_array[:, 3] / param_array[:, 2]))
try:
param_array = param_array[param_array[:, 0].argsort()]
except:
print("param_array shape", param_array.shape)
raise
try:
os.mkdir(folder_name)
except OSError as e:
if e.errno == errno.EEXIST:
pass
else:
raise
file_name = file_name + '.txt'
origin_import1 = param_name + ",Noise,Noise,Signal,error,rel peak error,peak signal-to-noise"
# origin_import1 = param_name + ",Noise,Noise,Noise,Noise,Ratio"
origin_import2 = ",counts,counts,counts,counts,,"
# origin_import2 = ",counts,counts,counts,,"
origin_import3 = ",High noise region,Low noise region,{},{} error,{} rel error, {}".format(name, name, name, name)
# origin_import3 = ",High noise region,Low noise region 1,Low noise region 2,Low noise region 3,High/low"
header_total = origin_import1 + "\n" + origin_import2 + "\n" + origin_import3
# print "Spec header: ", spec_header
print("the param_array is:", param_array)
np.savetxt(os.path.join(folder_name, file_name), param_array, delimiter=',',
header=header_total, comments='', fmt='%0.6e')
print("Saved the file.\nDirectory: {}".format(os.path.join(folder_name, file_name)))
class HighSidebandCCD(CCD):
def __init__(self, hsg_thing, parameter_dict=None, spectrometer_offset=None):
"""
This will read the appropriate file. The header needs to be fixed to
reflect the changes to the output header from the Andor file. Because
another helper file will do the cleaning and background subtraction,
those are no longer part of this init. This also turns all wavelengths
from nm (NIR ones) or cm-1 (THz ones) into eV.
OR, if an array is thrown in there, it'll handle the array and dict
Input:
For post-processing analysis:
hsg_thing = file name of the hsg spectrum from CCD superclass
spectrometer_offset = number of nanometers the spectrometer is off by,
should be 0.0...but can be 0.2 or 1.0
For Live-software:
hsg_thing = np array of spectrum from camera
parameter_dict = equipment dict generated by software
Internal:
self.hsg_thing = the filename
self.parameters = string with all the relevant experimental perameters
self.description = the description we added to the file as the data
was being taken
self.proc_data = processed data that has gone is frequency vs counts/pulse
self.dark_stdev = this is not currently handled appropriately
self.addenda = the list of things that have been added to the file, in
form of [constant, *spectra_added]
self.subtrahenda = the list of spectra that have been subtracted from
the file. Constant subtraction is dealt with with
self.addenda
:param hsg_thing: file name for the file to be opened. OR the actually hsg np.ndarray. Fun!
:type hsg_thing: str OR np.ndarray
:param parameter_dict: If being loaded through the data acquisition GUI, throw the dict in here
:type parameter_dict: dict
:param spectrometer_offset: Number of nm the spectrometer is off by
:type spectrometer_offset: float
:return: None, technically
"""
if isinstance(hsg_thing, str):
super(HighSidebandCCD, self).__init__(hsg_thing, spectrometer_offset=spectrometer_offset)
# TODO: fix addenda bullshit
self.addenda = []
self.subtrahenda = []
elif isinstance(hsg_thing, np.ndarray):
self.parameters = parameter_dict.copy() # Probably shouldn't shoehorn this in this way
self.addenda = []
self.subtrahenda = []
self.ccd_data = np.array(hsg_thing)
self.ccd_data[:, 0] = 1239.84 / self.ccd_data[:, 0]
# This data won't have an error column, so attached a column of ones
self.ccd_data = np.column_stack((self.ccd_data, np.ones_like(self.ccd_data[:,1])))
self.ccd_data = np.flipud(self.ccd_data) # Because turning into eV switches direction
self.fname = "Live Data"
else:
raise Exception("I don't know what this file type is {}, type: {}".format(
hsg_thing, type(hsg_thing)
))
self.proc_data = np.array(self.ccd_data)
# proc_data is now a 1600 long array with [frequency (eV), signal (counts / FEL pulse), S.E. of signal mean]
# self.parameters["nir_freq"] = 1239.84 / float(self.parameters["nir_lambda"])
self.parameters["nir_freq"] = 1239.84 / float(self.parameters.get("nir_lambda", -1))
# self.parameters["thz_freq"] = 0.000123984 * float(self.parameters["fel_lambda"])
self.parameters["thz_freq"] = 0.000123984 * float(self.parameters.get("fel_lambda", -1))
# self.parameters["nir_power"] = float(self.parameters["nir_power"])
self.parameters["nir_power"] = float(self.parameters.get("nir_power", -1))
try: # This is the new way of doing things. Also, now it's power
self.parameters["thz_energy"] = float(self.parameters["pulseEnergies"]["mean"])
self.parameters["thz_energy_std"] = float(self.parameters["pulseEnergies"]["std"])
except: # This is the old way TODO: DEPRECATE THIS
self.parameters["thz_energy"] = float(self.parameters.get("fel_power", -1))
# things used in fitting/guessing
self.sb_list = np.array([])
self.sb_index = np.array([])
self.sb_dict = {}
self.sb_results = np.array([])
self.full_dict = {}
def __add__(self, other):
"""
Add together the image data from self.proc_data, or add a constant to
that np.array. It will then combine the addenda and subtrahenda lists,
as well as add the fel_pulses together. If type(other) is a CCD object,
then it will add the errors as well.
Input:
self = CCD-like object
other = int, float or CCD object
Internal:
ret.proc_data = the self.proc_data + other(.proc_data)
ret.addenda = combination of two input addenda lists
This raises a FutureWarning because these were designed early on and
haven't been used much.
:param other: The thing to be added, it's either a int/float or a HighSidebandCCD object
:type other: int/float or HighSidebandCCD
:return: Sum of self and other
:rtype: HighSidebandCCD
"""
raise FutureWarning
ret = copy.deepcopy(self)
# Add a constant offset to the data
if type(other) in (int, float):
ret.proc_data[:, 1] = self.proc_data[:, 1] + other
ret.addenda[0] = ret.addenda[0] + other
# or add the data of two hsg_spectra together
else:
if np.isclose(ret.parameters['center_lambda'], other.parameters['center_lambda']):
ret.proc_data[:, 1] = self.proc_data[:, 1] + other.proc_data[:, 1]
ret.proc_data[:, 2] = np.sqrt(self.proc_data[:, 1] ** 2 + other.proc_data[:, 1] ** 2)
ret.addenda[0] = ret.addenda[0] + other.addenda[0]
ret.addenda.extend(other.addenda[1:])
ret.subtrahenda.extend(other.subtrahenda)
ret.parameters['fel_pulses'] += other.parameters['fel_pulses']
else:
raise Exception('Source: Spectrum.__add__:\nThese are not from the same grating settings')
return ret
def __sub__(self, other):
"""
This subtracts constants or other data sets between self.proc_data. I
think it even keeps track of what data sets are in the file and how
they got there.
See how __add__ works for more information.
This raises a FutureWarning because these were designed early on and
haven't been used much.
:param other: The thing to be subtracted, it's either a int/float or a HighSidebandCCD object
:type other: int/float or HighSidebandCCD
:return: Sum of self and other
:rtype: HighSidebandCCD
"""
raise FutureWarning
ret = copy.deepcopy(self)
# Subtract a constant offset to the data
if type(other) in (int, float):
ret.proc_data[:, 1] = self.proc_data[:, 1] - other # Need to choose a name
ret.addenda[0] = ret.addenda[0] - other
# Subtract the data of two hsg_spectra from each other
else:
if np.isclose(ret.proc_data[0, 0], other.proc_data[0, 0]):
ret.proc_data[:, 1] = self.proc_data[:, 1] - other.proc_data[:, 1]
ret.proc_data[:, 2] = np.sqrt(self.proc_data[:, 1] ** 2 + other.proc_data[:, 1] ** 2)
ret.subtrahenda.extend(other.addenda[1:])
ret.addenda.extend(other.subtrahenda)
else:
raise Exception('Source: Spectrum.__sub__:\nThese are not from the same grating settings')
return ret
def __repr__(self):
base = """
fname: {},
Series: {series},
spec_step: {spec_step},
fel_lambda: {fel_lambda},
nir_lambda: {nir_lambda}""".format(os.path.basename(self.fname),**self.parameters)
return base
__str__ = __repr__
def calc_approx_sb_order(self, test_nir_freq):
"""
This simple method will simply return a float approximating the order
of the frequency input. We need this because the CCD wavelength
calibration is not even close to perfect. And it shifts by half a nm
sometimes.
:param test_nir_freq: the frequency guess of the nth sideband
:type test_nir_freq: float
:return: The approximate order of the sideband in question
:rtype: float
"""
nir_freq = self.parameters['nir_freq']
thz_freq = self.parameters['thz_freq']
# If thz = 0, prevent error
if not thz_freq: thz_freq = 1
approx_order = (test_nir_freq - nir_freq) / thz_freq
return approx_order
def guess_sidebands(self, cutoff=4.5, verbose=False, plot=False, **kwargs):
"""
Update 05/24/18:
Hunter had two different loops for negative order sidebands,
then positive order sidebands. They're done pretty much identically,
so I've finally merged them into one.
Finds the locations of all the sidebands in the proc_data array to be
able to seed the fitting method. This works by finding the maximum data
value in the array and guessing what sideband it is. It creates an array
that includes this information. It will then step down, initially by one
THz frequency, then by twos after it hasn't found any odd ones. It then
goes up from the max and finds everything above in much the same way.
There is currently no rhyme or reason to a cutoff of 8. I don't know what
it should be changed to, though.
Input:
cutoff = signal-to-noise threshold to count a sideband candidate.
kwargs:
window_size: how big of a window (in pixels) to use for checking for
sidebands. Specified in half-width
default: 15
Internal:
self.sb_list = List of all of the orders the method found
self.sb_index = index of all of the peaks of the sidebands
self.sb_guess = three-part list including the frequency, amplitude and
error guesses for each sideband
"""
# TODO: this isn't commented appropriately. Will it be made more readable first?
if "cutoff" in self.parameters:
cutoff = self.parameters["cutoff"]
else:
self.parameters['cutoff for guess_sidebands'] = cutoff
if verbose:
print("=" * 15)
print()
print("Guessing CCD Sideband parameters")
print(os.path.basename(self.fname))
print("\tCutoff = {}".format(cutoff))
print()
print("=" * 15)
x_axis = np.array(self.proc_data[:, 0])
y_axis = np.array(self.proc_data[:, 1])
try:
error = np.array(self.proc_data[:, 2])
except IndexError:
# Happens on old data where spectra weren't calculated in the live
# software.
error = np.ones_like(x_axis)
min_sb = int(self.calc_approx_sb_order(x_axis[0])) + 1
try:
max_sb = int(self.calc_approx_sb_order(x_axis[-1]))
except ValueError:
print(x_axis)
nir_freq = self.parameters["nir_freq"]
thz_freq = self.parameters["thz_freq"]
if verbose:
print("min_sb: {} | max_sb: {}".format(min_sb, max_sb))
# Find max strength sideband and it's order
global_max = np.argmax(y_axis)
order_init = int(round(self.calc_approx_sb_order(x_axis[global_max])))
# if verbose:
# print "The global max is at index", global_max
if global_max < 15:
check_y = y_axis[:global_max + 15]
check_y = np.concatenate((np.zeros(15 - global_max), check_y))
elif global_max > 1585:
check_y = y_axis[global_max - 15:]
check_y = np.concatenate((check_y, np.zeros(global_max - 1585)))
else:
check_y = y_axis[global_max - 15:global_max + 15]
check_max_index = np.argmax(check_y)
check_max_area = np.sum(check_y[check_max_index - 2:check_max_index + 3])
check_ave = np.mean(check_y[[0, 1, 2, 3, 4, -1, -2, -3, -4, -5]])
check_stdev = np.std(check_y[[0, 1, 2, 3, 4, -1, -2, -3, -4, -5]])
check_ratio = (check_max_area - 3 * check_ave) / check_stdev
if verbose:
print(("{:^16}" * 5).format(
"global_max idx", "check_max_area", "check_ave", "check_stdev",
"check_ratio"))
print(("{:^16.5g}" * 5).format(
global_max, check_max_area, check_ave, check_stdev, check_ratio))
if check_ratio > cutoff:
self.sb_list = [order_init]
self.sb_index = [global_max]
sb_freq_guess = [x_axis[global_max]]
sb_amp_guess = [y_axis[global_max]]
sb_error_est = [
np.sqrt(sum([i ** 2 for i in error[global_max - 2:global_max + 3]])) / (
check_max_area - 5 * check_ave)]
else:
print("There are no sidebands in", self.fname)
raise RuntimeError
if verbose:
print("\t Looking for sidebands with f < {:.6f}".format(sb_freq_guess[0]))
last_sb = sb_freq_guess[0]
index_guess = global_max
# keep track of how many consecutive sidebands we've skipped. Sometimes one's
# noisy or something, so we want to keep looking after skipping one
consecutive_null_sb = 0
consecutive_null_odd = 0
no_more_odds = False
break_condition = False
for order in range(order_init - 1, min_sb - 1, -1):
# Check to make sure we're not looking at an odd when
# we've decided to skip them.
if no_more_odds == True and order % 2 == 1:
last_sb = last_sb - thz_freq
if verbose:
print("I skipped", order)
continue
# Window size to look for next sideband. Needs to be order dependent
# because higher orders get wider, so we need to look at more.
# Values are arbitrary.
window_size = 0.45 + 0.0004 * order # used to be last_sb?
lo_freq_bound = last_sb - thz_freq * (
1 + window_size) # Not sure what to do about these
hi_freq_bound = last_sb - thz_freq * (1 - window_size)
if verbose:
print("\nSideband", order)
print("\t{:.4f} < f_{} < {:.4f}".format(lo_freq_bound, order,
hi_freq_bound))
# Get the indices where the energies lie within the bounds for this SB
sliced_indices = \
np.where((x_axis > lo_freq_bound) & (x_axis < hi_freq_bound))[0]
start_index, end_index = sliced_indices.min(), sliced_indices.max()
# Get a slice of the y_data which is only in the region of interest
check_y = y_axis[sliced_indices]
check_max_index = np.argmax(
check_y) # This assumes that two floats won't be identical
# Calculate the "area" of the sideband by looking at the peak value
# within the range, and the pixel above/below it
check_max_area = np.sum(check_y[check_max_index - 1:check_max_index + 2])
if verbose and plot:
plt.figure("CCD data")
plt.plot([lo_freq_bound] * 2, [0, check_y[check_max_index]], 'b')
plt.plot([hi_freq_bound] * 2, [0, check_y[check_max_index]], 'b')
plt.plot([lo_freq_bound, hi_freq_bound], [check_y[check_max_index]] *
2, 'b', label="{} Box".format(order))
plt.text((lo_freq_bound + hi_freq_bound) / 2, check_y[check_max_index],
order)
# get the slice that doesn't have the peak in it to compare statistics
check_region = np.append(check_y[:check_max_index - 1],
check_y[check_max_index + 2:])
check_ave = check_region.mean()
check_stdev = check_region.std()
# Calculate an effective SNR, where check_ave is roughly the
# background level
check_ratio = (check_max_area - 3 * check_ave) / check_stdev
if order % 2 == 1: # This raises the barrier for odd sideband detection
check_ratio = check_ratio / 1.5
if verbose:
print("\t" + ("{:^14}" * 4).format(
"check_max_area", "check_ave", "check_stdev", "check_ratio"))
print("\t" + ("{:^14.5g}" * 4).format(
check_max_area, check_ave, check_stdev, check_ratio))
if check_ratio > cutoff:
found_index = check_max_index + start_index
self.sb_index.append(found_index)
last_sb = x_axis[found_index]
if verbose:
print("I just found", last_sb)
sb_freq_guess.append(x_axis[found_index])
sb_amp_guess.append(check_max_area - 3 * check_ave)
error_est = np.sqrt(
sum(
[i ** 2 for i in error[found_index - 1:found_index + 2]]
)) / (check_max_area - 3 * check_ave)
if verbose:
print("My error estimate is:", error_est)
sb_error_est.append(error_est)
self.sb_list.append(order)
consecutive_null_sb = 0
if order % 2 == 1:
consecutive_null_odd = 0
else:
# print "I could not find sideband with order", order
last_sb = last_sb - thz_freq
consecutive_null_sb += 1
if order % 2 == 1:
consecutive_null_odd += 1
if consecutive_null_odd == 1 and no_more_odds == False:
# print "I'm done looking for odd sidebands"
no_more_odds = True
if consecutive_null_sb == 2:
# print "I can't find any more sidebands"
break
# Look for higher sidebands
if verbose: print("\nLooking for higher energy sidebands")
last_sb = sb_freq_guess[0]
index_guess = global_max
consecutive_null_sb = 0
consecutive_null_odd = 0
no_more_odds = False
break_condition = False
for order in range(order_init + 1, max_sb + 1):
if no_more_odds == True and order % 2 == 1:
last_sb = last_sb + thz_freq
continue
window_size = 0.45 + 0.001 * order # used to be 0.28 and 0.0004
lo_freq_bound = last_sb + thz_freq * (
1 - window_size) # Not sure what to do about these
hi_freq_bound = last_sb + thz_freq * (1 + window_size)
start_index = False
end_index = False
if verbose:
print("\nSideband", order)
# print "The low frequency bound is", lo_freq_bound
# print "The high frequency bound is", hi_freq_bound
print("\t{:.4f} < f_{} < {:.4f}".format(lo_freq_bound, order,
hi_freq_bound))
for i in range(index_guess, 1600):
if start_index == False and i == 1599:
# print "I'm all out of space, captain!"
break_condition = True
break
elif start_index == False and x_axis[i] > lo_freq_bound:
# print "start_index is", i
start_index = i
elif i == 1599:
end_index = 1599
# print "hit end of data, end_index is 1599"
elif end_index == False and x_axis[i] > hi_freq_bound:
end_index = i
# print "end_index is", i
index_guess = i
break
if break_condition:
break
check_y = y_axis[start_index:end_index]
check_max_index = np.argmax(
check_y) # This assumes that two floats won't be identical
octant = len(check_y) // 8 # To be able to break down check_y into eighths
if octant < 1:
octant = 1
check_max_area = np.sum(
check_y[check_max_index - octant - 1:check_max_index + octant + 1])
if verbose and plot:
plt.figure("CCD data")
plt.plot([lo_freq_bound] * 2, [0, check_y[check_max_index]], 'b')
plt.plot([hi_freq_bound] * 2, [0, check_y[check_max_index]], 'b')
plt.plot([lo_freq_bound, hi_freq_bound], [check_y[check_max_index]] *
2, 'b', label=order)
plt.text((lo_freq_bound + hi_freq_bound) / 2, check_y[check_max_index],
order)
no_peak = (2 * len(
check_y)) // 6 # The denominator is in flux, used to be 5
# if verbose: print "\tcheck_y length", len(check_y)
check_ave = np.mean(np.take(check_y, np.concatenate(
(np.arange(no_peak), np.arange(-no_peak, 0)))))
check_stdev = np.std(np.take(check_y, np.concatenate(
(np.arange(no_peak), np.arange(-no_peak, 0)))))
check_ratio = (check_max_area - (2 * octant + 1) * check_ave) / check_stdev
if verbose:
print("\tIndices: {}->{} (d={})".format(start_index, end_index,
len(check_y)))
# print "check_y is", check_y
# print "\ncheck_max_area is", check_max_area
# print "check_ave is", check_ave
# print "check_stdev is", check_stdev
# print "check_ratio is", check_ratio
print("\t" + ("{:^14}" * 4).format(
"check_max_area", "check_ave", "check_stdev", "check_ratio"))
print("\t" + ("{:^14.6g}" * 4).format(
check_max_area, check_ave, check_stdev, check_ratio))
if order % 2 == 1: # This raises the barrier for odd sideband detection
check_ratio = check_ratio / 2
if check_ratio > cutoff:
found_index = check_max_index + start_index
self.sb_index.append(found_index)
last_sb = x_axis[found_index]
if verbose:
print("\tI'm counting this SB at index {} (f={:.4f})".format(
found_index, last_sb), end=' ')
# print "\tI found", order, "at index", found_index, "at freq", last_sb
sb_freq_guess.append(x_axis[found_index])
sb_amp_guess.append(check_max_area - (2 * octant + 1) * check_ave)
error_est = np.sqrt(sum([i ** 2 for i in error[
found_index - octant:found_index + octant]])) / (
check_max_area - (2 * octant + 1) * check_ave)
# This error is a relative error.
if verbose:
print(". Err = {:.3g}".format(error_est))
# print "\tMy error estimate is:", error_est
# print "My relative error is:", error_est / sb_amp_guess
sb_error_est.append(error_est)
self.sb_list.append(order)
consecutive_null_sb = 0
if order % 2 == 1:
consecutive_null_odd = 0
else:
# print "I could not find sideband with order", order
last_sb = last_sb + thz_freq
consecutive_null_sb += 1
if order % 2 == 1:
consecutive_null_odd += 1
if verbose:
print("\t\tI did not count this sideband")
if consecutive_null_odd == 1 and no_more_odds == False:
# print "I'm done looking for odd sidebands"
no_more_odds = True
if consecutive_null_sb == 2:
# print "I can't find any more sidebands"
break
if verbose:
print("I found these sidebands:", self.sb_list)
print('-' * 15)
print()
print()
self.sb_guess = np.array([np.asarray(sb_freq_guess), np.asarray(sb_amp_guess),
np.asarray(sb_error_est)]).T
# self.sb_guess = [frequency guess, amplitude guess, relative error of amplitude] for each sideband.
def guess_sidebandsOld(self, cutoff=4.5, verbose=False, plot=False, **kwargs):
"""
05/24/18
Old code from Hunter's days (or nearly, I've already started cleaning some
stuff up). keeping it around in case I break too much stuff
Finds the locations of all the sidebands in the proc_data array to be
able to seed the fitting method. This works by finding the maximum data
value in the array and guessing what sideband it is. It creates an array
that includes this information. It will then step down, initially by one
THz frequency, then by twos after it hasn't found any odd ones. It then
goes up from the max and finds everything above in much the same way.
There is currently no rhyme or reason to a cutoff of 8. I don't know what
it should be changed to, though.
Input:
cutoff = signal-to-noise threshold to count a sideband candidate.
kwargs:
window_size: how big of a window (in pixels) to use for checking for
sidebands. Specified in half-width
default: 15
Internal:
self.sb_list = List of all of the orders the method found
self.sb_index = index of all of the peaks of the sidebands
self.sb_guess = three-part list including the frequency, amplitude and
error guesses for each sideband
"""
# TODO: this isn't commented appropriately. Will it be made more readable first?
if "cutoff" in self.parameters:
cutoff = self.parameters["cutoff"]
else:
self.parameters['cutoff for guess_sidebands'] = cutoff
if verbose:
print("=" * 15)
print()
print("Guessing CCD Sideband parameters")
print(os.path.basename(self.fname))
print("\tCutoff = {}".format(cutoff))
print()
print("=" * 15)
x_axis = np.array(self.proc_data[:, 0])
y_axis = np.array(self.proc_data[:, 1])
error = np.array(self.proc_data[:, 2])
min_sb = int(self.calc_approx_sb_order(x_axis[0])) + 1
try:
max_sb = int(self.calc_approx_sb_order(x_axis[-1]))
except ValueError:
print(x_axis)
nir_freq = self.parameters["nir_freq"]
thz_freq = self.parameters["thz_freq"]
if verbose:
print("min_sb: {} | max_sb: {}".format(min_sb, max_sb))
# Find max strength sideband and it's order
global_max = np.argmax(y_axis)
order_init = int(round(self.calc_approx_sb_order(x_axis[global_max])))
# if verbose:
# print "The global max is at index", global_max
if global_max < 15:
check_y = y_axis[:global_max + 15]
check_y = np.concatenate((np.zeros(15 - global_max), check_y))
elif global_max > 1585:
check_y = y_axis[global_max - 15:]
check_y = np.concatenate((check_y, np.zeros(global_max - 1585)))
else:
check_y = y_axis[global_max - 15:global_max + 15]
check_max_index = np.argmax(check_y)
check_max_area = np.sum(check_y[check_max_index - 2:check_max_index + 3])
check_ave = np.mean(check_y[[0, 1, 2, 3, 4, -1, -2, -3, -4, -5]])
check_stdev = np.std(check_y[[0, 1, 2, 3, 4, -1, -2, -3, -4, -5]])
check_ratio = (check_max_area - 3 * check_ave) / check_stdev
if verbose:
print(("{:^16}" * 5).format(
"global_max idx", "check_max_area", "check_ave", "check_stdev",
"check_ratio"))
print(("{:^16.5g}" * 5).format(
global_max, check_max_area, check_ave, check_stdev, check_ratio))
if check_ratio > cutoff:
self.sb_list = [order_init]
self.sb_index = [global_max]
sb_freq_guess = [x_axis[global_max]]
sb_amp_guess = [y_axis[global_max]]
sb_error_est = [
np.sqrt(sum([i ** 2 for i in error[global_max - 2:global_max + 3]])) / (
check_max_area - 5 * check_ave)]
else:
print("There are no sidebands in", self.fname)
raise RuntimeError
if verbose:
print("\t Looking for sidebands with f < {:.6f}".format(sb_freq_guess[0]))
last_sb = sb_freq_guess[0]
index_guess = global_max
# keep track of how many consecutive sidebands we've skipped. Sometimes one's
# noisy or something, so we want to keep looking after skipping one
consecutive_null_sb = 0
consecutive_null_odd = 0
no_more_odds = False
break_condition = False
for order in range(order_init - 1, min_sb - 1, -1):
# Check to make sure we're not looking at an odd when
# we've decided to skip them.
if no_more_odds == True and order % 2 == 1:
last_sb = last_sb - thz_freq
if verbose:
print("I skipped", order)
continue
# Window size to look for next sideband. Needs to be order dependent
# because higher orders get wider, so we need to look at more.
# Values are arbitrary.
window_size = 0.45 + 0.0004 * order # used to be last_sb?
lo_freq_bound = last_sb - thz_freq * (
1 + window_size) # Not sure what to do about these
hi_freq_bound = last_sb - thz_freq * (1 - window_size)
if verbose:
print("\nSideband", order)
print("\t{:.4f} < f_{} < {:.4f}".format(lo_freq_bound, order,
hi_freq_bound))
# Get the indices where the energies lie within the bounds for this SB
sliced_indices = \
np.where((x_axis > lo_freq_bound) & (x_axis < hi_freq_bound))[0]
start_index, end_index = sliced_indices.min(), sliced_indices.max()
# Get a slice of the y_data which is only in the region of interest
check_y = y_axis[sliced_indices]
check_max_index = np.argmax(
check_y) # This assumes that two floats won't be identical
# Calculate the "area" of the sideband by looking at the peak value
# within the range, and the pixel above/below it
check_max_area = np.sum(check_y[check_max_index - 1:check_max_index + 2])
if verbose and plot:
plt.figure("CCD data")
plt.plot([lo_freq_bound] * 2, [0, check_y[check_max_index]], 'b')
plt.plot([hi_freq_bound] * 2, [0, check_y[check_max_index]], 'b')
plt.plot([lo_freq_bound, hi_freq_bound], [check_y[check_max_index]] *
2, 'b', label="{} Box".format(order))
plt.text((lo_freq_bound + hi_freq_bound) / 2, check_y[check_max_index],
order)
# get the slice that doesn't have the peak in it to compare statistics
check_region = np.append(check_y[:check_max_index - 1],
check_y[check_max_index + 2:])
check_ave = check_region.mean()
check_stdev = check_region.std()
# Calculate an effective SNR, where check_ave is roughly the
# background level
check_ratio = (check_max_area - 3 * check_ave) / check_stdev
if order % 2 == 1: # This raises the barrier for odd sideband detection
check_ratio = check_ratio / 1.5
if verbose:
print("\t" + ("{:^14}" * 4).format(
"check_max_area", "check_ave", "check_stdev", "check_ratio"))
print("\t" + ("{:^14.5g}" * 4).format(
check_max_area, check_ave, check_stdev, check_ratio))
if check_ratio > cutoff:
found_index = check_max_index + start_index
self.sb_index.append(found_index)
last_sb = x_axis[found_index]
if verbose:
print("I just found", last_sb)
sb_freq_guess.append(x_axis[found_index])
sb_amp_guess.append(check_max_area - 3 * check_ave)
error_est = np.sqrt(
sum(
[i ** 2 for i in error[found_index - 1:found_index + 2]]
)) / (check_max_area - 3 * check_ave)
if verbose:
print("My error estimate is:", error_est)
sb_error_est.append(error_est)
self.sb_list.append(order)
consecutive_null_sb = 0
if order % 2 == 1:
consecutive_null_odd = 0
else:
# print "I could not find sideband with order", order
last_sb = last_sb - thz_freq
consecutive_null_sb += 1
if order % 2 == 1:
consecutive_null_odd += 1
if consecutive_null_odd == 1 and no_more_odds == False:
# print "I'm done looking for odd sidebands"
no_more_odds = True
if consecutive_null_sb == 2:
# print "I can't find any more sidebands"
break
# Look for higher sidebands
if verbose: print("\nLooking for higher energy sidebands")
last_sb = sb_freq_guess[0]
index_guess = global_max
consecutive_null_sb = 0
consecutive_null_odd = 0
no_more_odds = False
break_condition = False
for order in range(order_init + 1, max_sb + 1):
if no_more_odds == True and order % 2 == 1:
last_sb = last_sb + thz_freq
continue
window_size = 0.45 + 0.001 * order # used to be 0.28 and 0.0004
lo_freq_bound = last_sb + thz_freq * (
1 - window_size) # Not sure what to do about these
hi_freq_bound = last_sb + thz_freq * (1 + window_size)
start_index = False
end_index = False
if verbose:
print("\nSideband", order)
# print "The low frequency bound is", lo_freq_bound
# print "The high frequency bound is", hi_freq_bound
print("\t{:.4f} < f_{} < {:.4f}".format(lo_freq_bound, order,
hi_freq_bound))
for i in range(index_guess, 1600):
if start_index == False and i == 1599:
# print "I'm all out of space, captain!"
break_condition = True
break
elif start_index == False and x_axis[i] > lo_freq_bound:
# print "start_index is", i
start_index = i
elif i == 1599:
end_index = 1599
# print "hit end of data, end_index is 1599"
elif end_index == False and x_axis[i] > hi_freq_bound:
end_index = i
# print "end_index is", i
index_guess = i
break
if break_condition:
break
check_y = y_axis[start_index:end_index]
check_max_index = np.argmax(
check_y) # This assumes that two floats won't be identical
octant = len(check_y) // 8 # To be able to break down check_y into eighths
if octant < 1:
octant = 1
check_max_area = np.sum(
check_y[check_max_index - octant - 1:check_max_index + octant + 1])
if verbose and plot:
plt.figure("CCD data")
plt.plot([lo_freq_bound] * 2, [0, check_y[check_max_index]], 'b')
plt.plot([hi_freq_bound] * 2, [0, check_y[check_max_index]], 'b')
plt.plot([lo_freq_bound, hi_freq_bound], [check_y[check_max_index]] *
2, 'b', label=order)
plt.text((lo_freq_bound + hi_freq_bound) / 2, check_y[check_max_index],
order)
no_peak = (2 * len(
check_y)) // 6 # The denominator is in flux, used to be 5
# if verbose: print "\tcheck_y length", len(check_y)
check_ave = np.mean(np.take(check_y, np.concatenate(
(np.arange(no_peak), np.arange(-no_peak, 0)))))
check_stdev = np.std(np.take(check_y, np.concatenate(
(np.arange(no_peak), np.arange(-no_peak, 0)))))
check_ratio = (check_max_area - (2 * octant + 1) * check_ave) / check_stdev
if verbose:
print("\tIndices: {}->{} (d={})".format(start_index, end_index,
len(check_y)))
# print "check_y is", check_y
# print "\ncheck_max_area is", check_max_area
# print "check_ave is", check_ave
# print "check_stdev is", check_stdev
# print "check_ratio is", check_ratio
print("\t" + ("{:^14}" * 4).format(
"check_max_area", "check_ave", "check_stdev", "check_ratio"))
print("\t" + ("{:^14.6g}" * 4).format(
check_max_area, check_ave, check_stdev, check_ratio))
if order % 2 == 1: # This raises the barrier for odd sideband detection
check_ratio = check_ratio / 2
if check_ratio > cutoff:
found_index = check_max_index + start_index
self.sb_index.append(found_index)
last_sb = x_axis[found_index]
if verbose:
print("\tI'm counting this SB at index {} (f={:.4f})".format(
found_index, last_sb), end=' ')
# print "\tI found", order, "at index", found_index, "at freq", last_sb
sb_freq_guess.append(x_axis[found_index])
sb_amp_guess.append(check_max_area - (2 * octant + 1) * check_ave)
error_est = np.sqrt(sum([i ** 2 for i in error[
found_index - octant:found_index + octant]])) / (
check_max_area - (2 * octant + 1) * check_ave)
# This error is a relative error.
if verbose:
print(". Err = {:.3g}".format(error_est))
# print "\tMy error estimate is:", error_est
# print "My relative error is:", error_est / sb_amp_guess
sb_error_est.append(error_est)
self.sb_list.append(order)
consecutive_null_sb = 0
if order % 2 == 1:
consecutive_null_odd = 0
else:
# print "I could not find sideband with order", order
last_sb = last_sb + thz_freq
consecutive_null_sb += 1
if order % 2 == 1:
consecutive_null_odd += 1
if verbose:
print("\t\tI did not count this sideband")
if consecutive_null_odd == 1 and no_more_odds == False:
# print "I'm done looking for odd sidebands"
no_more_odds = True
if consecutive_null_sb == 2:
# print "I can't find any more sidebands"
break
if verbose:
print("I found these sidebands:", self.sb_list)
print('-' * 15)
print()
print()
self.sb_guess = np.array([np.asarray(sb_freq_guess), np.asarray(sb_amp_guess),
np.asarray(sb_error_est)]).T
# self.sb_guess = [frequency guess, amplitude guess, relative error of amplitude] for each sideband.
def fit_sidebands(self, plot=False, verbose=False):
"""
This takes self.sb_guess and fits to each maxima to get the details of
each sideband. It's really ugly, but it works. The error of the
sideband area is approximated from the data, not the curve fit. All
else is from the curve fit. Which is definitely underestimating the
error, but we don't care too much about those errors (at this point).
self.sb_guess = [frequency guess, amplitude guess, relative error of amplitude] for each sideband.
Temporary stuff:
sb_fits = holder of the fitting results until all spectra have been fit
window = an integer that determines the "radius" of the fit window, proportional to thz_freq.
Attributes created:
self.sb_results = the money maker. Column order:
[sb number, Freq (eV), Freq error (eV), Gauss area (arb.), Area error, Gauss linewidth (eV), Linewidth error (eV)]
[ 0 , 1 , 2, , 3 , 4 , 5 , 6 ]
self.full_dict = a dictionary similar to sb_results, but now the keys
are the sideband orders. Column ordering is otherwise the same.
:param plot: Do you want to see the fits plotted with the data?
:type plot: bool
:param verbose: Do you want to see the details AND the initial guess fits?
:type verbose: bool
:return: None
"""
# print "Trying to fit these"
sb_fits = []
if verbose:
print("=" * 15)
print()
print("Fitting CCD Sidebands")
print(os.path.basename(self.fname))
print()
print("=" * 15)
# pretty sure you want this up here so things don't break
# when no sidebands found
self.full_dict = {}
thz_freq = self.parameters["thz_freq"]
window = 15 + int(15 * thz_freq / 0.0022) # Adjust the fit window based on the sideband spacing
# The 15's are based on empirical knowledge that for
# 540 GHz (2.23 meV), the best window size is 30 and
# that it seems like the window size should grow slowly?
for elem, peakIdx in enumerate(self.sb_index): # Have to do this because guess_sidebands
# doesn't out put data in the most optimized way
if peakIdx < window:
data_temp = self.proc_data[:peakIdx + window, :]
elif (1600 - peakIdx) < window:
data_temp = self.proc_data[peakIdx - window:, :]
else:
data_temp = self.proc_data[peakIdx - window:peakIdx + window, :]
width_guess = 0.0001 + 0.000001 * self.sb_list[elem] # so the width guess gets wider as order goes up
p0 = np.array([self.sb_guess[elem, 0],
self.sb_guess[elem, 1] * width_guess,
width_guess,
0.1])
# print "Let's fit this shit!"
if verbose:
print("Fitting SB {}. Peak index: {}, {}th peak in spectra".format(
self.sb_list[elem], peakIdx, elem
))
# print "\nnumber:", elem, num
# print "data_temp:", data_temp
# print "p0:", p0
print(' '*20 +"p0 = " + np.array_str(p0, precision=4))
# plot_guess = True # This is to disable plotting the guess function
if verbose and plot:
plt.figure('CCD data')
linewidth = 3
x_vals = np.linspace(data_temp[0, 0], data_temp[-1, 0], num=500)
if elem != 0:
try:
plt.plot(x_vals, gauss(x_vals, *p0),
plt.gca().get_lines()[-1].get_color() + '--' # I don't really know. Mostly
# just looked around at what functions
# matplotlib has...
, linewidth=linewidth)
except: # to prevent weird mac issues with the matplotlib things?
plt.plot(x_vals, gauss(x_vals, *p0), '--', linewidth=linewidth)
else:
plt.plot(x_vals, gauss(x_vals, *p0), '--', linewidth=linewidth)
try:
# 11/1/16
# needed to bump maxfev up to 2k because a sideband wasn't being fit
# Fix for sb 106
# 05-23 Loren 10nm\hsg_640_Perp352seq_spectrum.txt
coeff, var_list = curve_fit(
gauss, data_temp[:, 0], data_temp[:, 1], p0=p0, maxfev = 2000)
except Exception as e:
if verbose:
print("\tThe fit failed:")
print("\t\t", e)
print("\tFitting region: {}->{}".format(peakIdx-window, peakIdx+window))
# print "I couldn't fit", elem
# print "It's sideband", num
# print "In file", self.fname
# print "because", e
# print "wanted to fit xindx", peakIdx, "+-", window
self.sb_list[elem] = None
continue # This will ensure the rest of the loop is not run without an actual fit.
coeff[1] = abs(coeff[1]) # The amplitude could be negative if the linewidth is negative
coeff[2] = abs(coeff[2]) # The linewidth shouldn't be negative
if verbose:
print("\tFit successful: ", end=' ')
print("p = " + np.array_str(coeff, precision=4))
# print "coeffs:", coeff
# print "sigma for {}: {}".format(self.sb_list[elem], coeff[2])
if 10e-4 > coeff[2] > 10e-6:
try:
sb_fits.append(np.hstack((self.sb_list[elem], coeff, np.sqrt(np.diag(var_list)))))
except RuntimeWarning:
sb_fits.append(np.hstack((self.sb_list[elem], coeff, np.sqrt(np.abs(np.diag(var_list))))))
# the var_list wasn't approximating the error well enough, even when using sigma and absoluteSigma
# self.sb_guess[elem, 2] is the relative error as calculated by the guess_sidebands method
# coeff[1] is the area from the fit. Therefore, the product should be the absolute error
# of the integrated area of the sideband. The other errors are still underestimated.
#
# 1/12/18 note: So it looks like what hunter did is calculate an error estimate
# for the strength/area by the quadrature sum of errors of the points in the peak
# (from like 813 in guess_sidebands:
# error_est = np.sqrt(sum([i ** 2 for i in error[found_index - 1:found_index + 2]])) / (
# Where the error is what comes from the CCD by averaging 4 spectra. As far as I can tell,
# it doesn't currently pull in the dark counts or anything like that, except maybe
# indirectly since it'll cause the variations in the peaks
sb_fits[-1][6] = self.sb_guess[elem, 2] * coeff[1]
if verbose:
print("\tRel.Err: {:.4e} | Abs.Err: {:.4e}".format(
self.sb_guess[elem, 2], coeff[1] * self.sb_guess[elem, 2]
))
print()
# print "The rel. error guess is", self.sb_guess[elem, 2]
# print "The abs. error guess is", coeff[1] * self.sb_guess[elem, 2]
# The error from self.sb_guess[elem, 2] is a relative error
if plot and verbose:
plt.figure('CCD data')
linewidth = 5
x_vals = np.linspace(data_temp[0, 0], data_temp[-1, 0], num=500)
if elem != 0:
try:
plt.plot(x_vals, gauss(x_vals, *coeff),
plt.gca().get_lines()[-1].get_color() + '--' # I don't really know. Mostly
# just looked around at what functions
# matplotlib has...
, linewidth=linewidth)
except: # to prevent weird mac issues with the matplotlib things?
plt.plot(x_vals, gauss(x_vals, *coeff), '--', linewidth=linewidth)
else:
plt.plot(x_vals, gauss(x_vals, *coeff), '--', linewidth=linewidth)
sb_fits_temp = np.asarray(sb_fits)
reorder = [0, 1, 5, 2, 6, 3, 7, 4, 8]
# Reorder the list to put the error of the i-th parameter as the i+1th.
try:
sb_fits = sb_fits_temp[:, reorder]
# if verbose: print "The abs. error guess is", sb_fits[:, 0:5]
except:
raise RuntimeError("No sidebands to fit?")
# Going to label the appropriate row with the sideband
self.sb_list = sorted(list([x for x in self.sb_list if x is not None]))
sb_names = np.vstack(self.sb_list)
# Sort by SB order
sorter = np.argsort(sb_fits[:, 0])
self.sb_results = np.array(sb_fits[sorter, :7])
if verbose:
print("\tsb_results:")
print("\t\t" + ("{:^5s}" + ("{:^12s}")*(self.sb_results.shape[1]-1)).format(
"SB", "Cen.En.", "", "Area", "", "Width",""))
for line in self.sb_results:
print('\t\t[' + ("{:^5.0f}"+ "{:<12.4g}"*(line.size-1)).format(*line) + ']')
print('-'*19)
self.full_dict = {}
for sb in self.sb_results:
self.full_dict[sb[0]] = np.asarray(sb[1:])
def infer_frequencies(self, nir_units="wavenumber", thz_units="GHz", bad_points=-2):
"""
This guy tries to fit the results from fit_sidebands to a line to get the relevant frequencies
:param nir_units: What units do you want this to output?
:type nir_units: 'nm', 'wavenumber', 'eV', 'THz'
:param thz_units: What units do you want this to output for the THz?
:type thz_units: 'GHz', 'wavenumber', 'meV'
:param bad_points: How many more-positive order sidebands shall this ignore?
:type bad_points: int
:return: freqNIR, freqTHz, the frequencies in the appropriate units
"""
# force same units for in dict
freqNIR, freqTHz = calc_laser_frequencies(self, "wavenumber", "wavenumber", bad_points)
self.parameters["calculated NIR freq (cm-1)"] = "{}".format(freqNIR, nir_units)
self.parameters["calculated THz freq (cm-1)"] = "{}".format(freqTHz, freqTHz)
freqNIR, freqTHz = calc_laser_frequencies(self, nir_units, thz_units, bad_points)
return freqNIR, freqTHz
def save_processing(self, file_name, folder_str, marker='', index='', verbose=''):
"""
This will save all of the self.proc_data and the results from the
fitting of this individual file.
Format:
spectra_fname = file_name + '_' + marker + '_' + str(index) + '.txt'
fit_fname = file_name + '_' + marker + '_' + str(index) + '_fits.txt'
Inputs:
file_name = the beginning of the file name to be saved
folder_str = the location of the folder where the file will be saved,
will create the folder, if necessary.
marker = I...I don't know what this was originally for
index = used to keep these files from overwriting themselves when in a
list
Outputs:
Two files:
self.proc_data = the continuous spectrum
self.sb_results = the individual sideband details
:param file_name: The base name for the saved file
:type file_name: str
:param folder_str: The full name for the folder hte file is saved it. Folder can be created
:type folder_str: str
:param marker: Marker for the file, appended to file_name, often the self.parameters['series']
:type marker: str
:param index: used to keep these files from overwriting themselves when marker is the same
:type index: str or int
:return: None
"""
try:
os.mkdir(folder_str)
except OSError as e:
if e.errno == errno.EEXIST:
pass
else:
raise
temp = np.array(self.sb_results)
ampli = np.array([temp[:, 3] / temp[:, 5]]) # But [:, 3] is already area?
# (The old name was area)
# I think it must be amplitude
temp[:, 5:7] = temp[:, 5:7] * 1000 # For meV linewidths
if verbose:
print("sb_results", self.sb_results.shape)
print("ampli", ampli.shape)
save_results = np.hstack((temp, ampli.T))
spectra_fname = file_name + '_' + marker + '_' + str(index) + '.txt'
fit_fname = file_name + '_' + marker + '_' + str(index) + '_fits.txt'
self.save_name = spectra_fname
self.parameters['addenda'] = self.addenda
self.parameters['subtrahenda'] = self.subtrahenda
try:
parameter_str = json.dumps(self.parameters, sort_keys=True, indent=4, separators=(',', ': '))
except:
print("Source: EMCCD_image.save_images\nJSON FAILED")
print("Here is the dictionary that broke JSON:\n", self.parameters)
return
parameter_str = parameter_str.replace('\n', '\n#')
num_lines = parameter_str.count('#') # Make the number of lines constant so importing is easier
# for num in range(99 - num_lines): parameter_str += '\n#'
parameter_str += '\n#' * (99 - num_lines)
origin_import_spec = '\nNIR frequency,Signal,Standard error\neV,arb. u.,arb. u.'
spec_header = '#' + parameter_str + origin_import_spec
origin_import_fits = '\nSideband,Center energy,error,Sideband strength,error,Linewidth,error,Amplitude'
origin_import_fits += '\norder,eV,,arb. u.,,meV,,arb. u.'
origin_import_fits += "\n{},,,{},,,".format(marker, marker)
fits_header = '#' + parameter_str + origin_import_fits
# print "DEBUG: in saving", folder_str, ",", spectra_fname
np.savetxt(os.path.join(folder_str, spectra_fname), self.proc_data, delimiter=',',
header=spec_header, comments='', fmt='%0.6e')
np.savetxt(os.path.join(folder_str, fit_fname), save_results, delimiter=',',
header=fits_header, comments='', fmt='%0.6e')
if verbose:
print("Save image.\nDirectory: {}".format(os.path.join(folder_str, spectra_fname)))
class HighSidebandCCDRaw(HighSidebandCCD):
"""
This class is meant for passing in an image file (currently supports a 2x1600)
Which it does all the processing on.
"""
def __init__(self, hsg_thing, parameter_dict=None, spectrometer_offset=None):
# let the supers do the hard work of importing the json dict and all that jazz
super(HighSidebandCCDRaw, self).__init__(hsg_thing, parameter_dict=None, spectrometer_offset=None)
self.ccd_data = np.genfromtxt(hsg_thing, delimiter=',').T
self.proc_data = np.column_stack((
self.gen_wavelengths(self.parameters["center_lambda"], self.parameters["grating"]),
np.array(self.ccd_data[:,1], dtype=float)-np.median(self.ccd_data[:,1]),
np.ones_like(self.ccd_data[:,1], dtype=float)
))
self.proc_data[:, 0] = 1239.84 / self.proc_data[:, 0]
self.proc_data = np.flipud(self.proc_data)
@staticmethod
def gen_wavelengths(center_lambda, grating):
'''
This returns a 1600 element list of wavelengths for each pixel in the EMCCD based on grating and center wavelength
grating = which grating, 1 or 2
center = center wavelength in nanometers
'''
b = 0.75 # length of spectrometer, in m
k = -1.0 # order looking at
r = 16.0e-6 # distance between pixles on CCD
if grating == 1:
d = 1. / 1800000.
gamma = 0.213258508834
delta = 1.46389935365
elif grating == 2:
d = 1. / 1200000.
gamma = 0.207412628027
delta = 1.44998344749
elif grating == 3:
d = 1. / 600000.
gamma = 0.213428934011
delta = 1.34584754696
else:
print("What a dick, that's not a valid grating")
return None
center = center_lambda * 10 ** -9
wavelength_list = np.arange(-799.0, 801.0)
output = d * k ** (-1) * ((-1) * np.cos(delta + gamma + (-1) * np.arccos(
(-1 / 4) * (1 / np.cos((1 / 2) * gamma)) ** 2 * (
2 * (np.cos((1 / 2) * gamma) ** 4 * (2 + (-1) * d ** (-2) * k ** 2 * center ** 2 + 2 * np.cos(gamma))) ** (
1 / 2) + d ** (-1) * k * center * np.sin(gamma))) + np.arctan(
b ** (-1) * (r * wavelength_list + b * np.cos(delta + gamma)) * (1 / np.sin(delta + gamma)))) + (
1 + (-1 / 16) * (1 / np.cos((1 / 2) * gamma)) ** 4 * (2 * (
np.cos((1 / 2) * gamma) ** 4 * (
2 + (-1) * d ** (-2) * k ** 2 * center ** 2 + 2 * np.cos(gamma))) ** (1 / 2) + d ** (
-1) * k * center * np.sin(
gamma)) ** 2) ** (1 / 2))
output = (output + center) * 10 ** 9
return output
class PMT(object):
def __init__(self, file_name):
"""
Initializes a SPEX spectrum. It'll open a file, and bring in the details
of a sideband spectrum into the object. There isn't currently any reason
to use inheritance here, but it could be extended later to include PLE or
something of the sort.
attributes:
self.parameters - dictionary of important experimental parameters
this will not necessarily be the same for each
file in the object
self.fname - the current file path
:param file_name: The name of the PMT file
:type file_name: str
:return: None
"""
# print "This started"
self.fname = file_name
# self.files_included = [file_name]
with open(file_name, 'r') as f:
param_str = ''
line = f.readline() # Needed to move past the first line, which is the sideband order. Not generally useful
line = f.readline()
while line[0] == '#':
param_str += line[1:]
line = f.readline()
self.parameters = json.loads(param_str)
class HighSidebandPMT(PMT):
def __init__(self, file_path, verbose=False):
"""
Initializes a SPEX spectrum. It'll open a single file, then read
the data from that file using .add_sideband(). The super's init will handle the parameters
and the description.
attributes:
self.parameters - dictionary of important experimental parameters, created in PMT
self.sb_dict - keys are sideband order, values are PMT data arrays
self.sb_list - sorted list of included sidebands
:param file_path: path to the current file
:type file_path: str
:param verbose: Flag to see the nitty gritty details
:type verbose: bool
:return:
"""
super(HighSidebandPMT, self).__init__(
file_path) # Creates the json parameters dictionary
self.fname = file_path
self.parameters["files included"] = [file_path]
with open(file_path, 'r') as f:
sb_num = int(f.readline()[1:])
raw_temp = np.genfromtxt(file_path, comments='#', delimiter=',')[3:, :]
if self.parameters.get("photon counted", False):
# The scale factor for photon counting to generic
# PMT data depends on... things. It's different each
# day. Unfortunately, the overlap in dynamic range between
# the two is small, and generally only one sideband
# can been seen by both methods. I don't really have
# the motivation to automatically calculate the
# appropriate factor, so this is your reminder to find
# it yourself.
import time
# assert time.strftime("%x") == "03/15/17"
assert self.parameters.get("pc ratio", -1) != -1, self.fname
raw_temp[:,3] *= self.parameters["pc ratio"]
pass
raw_temp[:, 0] = raw_temp[:, 0] / 8065.6 # turn NIR freq into eV
self.parameters["thz_freq"] = 0.000123984 * float(
self.parameters.get("fel_lambda", -1))
self.parameters["nir_freq"] = float(
self.parameters.get("nir_lambda", -1))/8065.6
self.initial_sb = sb_num
self.initial_data = np.array(raw_temp)
self.sb_dict = {sb_num: np.array(raw_temp)}
self.sb_list = [sb_num]
def add_sideband(self, other):
"""
This bad boy will add another PMT sideband object to the sideband spectrum of this object. It handles
when you measure the same sideband twice. It assumes both are equally "good"
NOTE: This means that if both aren't equally "good" (taking a second scan with higher
gain/photon counting because you didn't see it), you need to not add the file
(remove/rename the file, etc.)
I'd love to overhall the data collection/analysis so this can be more intelligent
(Effectively offload a lot of the processing (especially not saving 10 arbitrary
points to process later) onto the live software and add sideband strengths alone,
like the CCD works. But this would be a bigger change that I can seem to find
time for).
It currently doesn't do any sort of job combining dictionaries or anything, but it definitely could, if
you have two incomplete dictionaries
:param other: the new sideband data to add to the larger spectrum. Add means append, no additino is performed
:type other: HighSidebandPMT
:return:
"""
"""
This bad boy will add another PMT sideband object to the sideband spectrum of this object
It currently doesn't do any sort of job combining dictionaries or anything, but it definitely could
"""
self.parameters["files included"].append(other.fname)
if other.initial_sb in self.sb_list:
self.sb_list.append(other.initial_sb)
# Make things comma delimited?
try:
self.sb_dict[other.initial_sb] = np.row_stack(
(self.sb_dict[other.initial_sb], other.initial_data)
)
except KeyError:
self.sb_dict[other.initial_sb] = np.array(other.initial_data)
except Exception as e:
print("THIS IS THE OTHER ERROR", e)
raise
def process_sidebands(self, verbose=False, baselineCorr = False):
"""
This bad boy will clean up the garbled mess that is the object before hand,
including clearing out misfired shots and doing the averaging.
Affects:
self.sb_dict = Averages over sidebands
Creates:
self.sb_list = The sideband orders included in this object.
:param verbose: Flag to see the nitty gritty details.
:type verbose: bool
:param baselineCorr: Whether to subtract the average across
the two endpoints
:return: None
"""
for sb_num, sb in list(self.sb_dict.items()):
if sb_num == 0:
fire_condition = -np.inf # This way the FEL doesn't need to be on during laser line measurement
else:
fire_condition = np.mean(sb[:, 2]) / 2 # Say FEL fired if the
# cavity dump signal is
# more than half the mean
# of the cavity dump signal
frequencies = sorted(list(set(sb[:, 0])))
temp = None
for freq in frequencies:
data_temp = np.array([])
for point in sb:
if point[0] == freq and point[2] > fire_condition:
data_temp = np.hstack((data_temp, point[3]))
try:
temp = np.vstack(
(temp, np.array([freq, np.mean(data_temp),
np.std(data_temp) / np.sqrt(len(data_temp))])))
except:
temp = np.array([freq, np.mean(data_temp),
np.std(data_temp) / np.sqrt(len(data_temp))])
# temp[:, 0] = temp[:, 0] / 8065.6 # turn NIR freq into eV
temp = temp[temp[:, 0].argsort()]
if baselineCorr:
x = temp[[0, -1], 0]
y = temp[[0, -1], 1]
p = np.polyfit(x, y, 1)
temp[:, 1] -= np.polyval(p, temp[:,0])
self.sb_dict[sb_num] = np.array(temp)
self.sb_list = sorted(self.sb_dict.keys())
if verbose:
print("Sidebands included", self.sb_list)
def integrate_sidebands(self, verbose=False, cutoff=1.0, **kwargs):
"""
This method will integrate the sidebands to find their strengths, and then
use a magic number to define the width, since they are currently so utterly
undersampled for fitting.
cutoff is the ratio of area/error which must be exceeded to count
It is currently the preferred method for calculating sideband strengths.
self.fit_sidebands is probably better with better-sampled lines.
Creates:
self.sb_results = full list of integrated data. Column order is:
[sb order, Freq (eV), "error" (eV), Integrate area (arb.), area error, "Linewidth" (eV), "Linewidth error" (eV)
self.full_dict = Dictionary where the SB order column is removed and turned into the keys. The values
are the rest of that sideband's results.
:param verbose: Flag to see the nitty gritty details
:type verbose: bool
:return: None
"""
if verbose:
print("="*15)
print()
print("Integrating PMT Sidebands")
print("Cutoff: {}".format(cutoff))
print(os.path.basename(self.fname))
print()
print("=" * 15)
self.full_dict = {}
for sideband in list(self.sb_dict.items()):
index = np.argmax(sideband[1][:, 1])
nir_frequency = sideband[1][index, 0]
# stroff = np.nan_to_num(sideband[1][[0,1,-2,1], 1]).sum()/4.
area = np.trapz(np.nan_to_num(sideband[1][:, 1]), sideband[1][:, 0])
error = np.sqrt(np.sum(np.nan_to_num(
sideband[1][:, 2]) ** 2)) / 8065.6 # Divide by the step size?
if verbose:
print("\torder: {}, area: {:.3g}, error: {:.3g}, ratio: {:.3f}".format(
sideband[0], area, error, area/error
))
details = np.array(
[sideband[0], nir_frequency, 1 / 8065.6, area, error, 2 / 8065.6,
1 / 8065.6])
if area < 0:
if verbose:
print("\t\tarea < 0")
continue
elif area < cutoff/5 * error: # Two seems like a good cutoff?
if verbose:
print("\t\tI did not keep sideband")
continue
try:
self.sb_results = np.vstack((self.sb_results, details))
except:
self.sb_results = np.array(details)
self.full_dict[sideband[0]] = details[1:]
try:
self.sb_results = self.sb_results[self.sb_results[:, 0].argsort()]
except (IndexError, AttributeError):
# IndexError where there's only one sideband
# AttributeError when there aren't any (one sb which wasn't fit)
pass
if verbose:
print('-'*19)
def fit_sidebands(self, plot=False, verbose=False):
"""
This method will fit a gaussian to each of the sidebands provided in
the self.sb_dict and make a list just like in the EMCCD version. It
will also use the standard error of the integral of the PMT peak as the
error of the gaussian area instead of that element from the covariance
matrix. Seems more legit.
attributes:
self.sb_results: the numpy array that contains all of the fit info just
like it does in the CCD class.
self.full_dict = A dictionary version of self.sb_results
:param plot: Flag to see the results plotted
:type plot: bool
:param verbose: Flag to see the nitty gritty details
:type verbose: bool
:return: None
"""
sb_fits = {}
for sideband in list(self.sb_dict.items()):
if verbose:
print("Sideband number", sideband[0])
print("Sideband data:\n", sideband[1])
index = np.argmax(sideband[1][:, 1])
nir_frequency = sideband[1][index, 0]
peak = sideband[1][index, 1]
width_guess = 0.0001 # Yep, another magic number
p0 = [nir_frequency, peak * width_guess, width_guess, 0.00001]
if verbose:
x_vals = np.linspace(np.amin(sideband[1][:, 0]),
np.amax(sideband[1][:, 0]), num=50)
plt.plot(x_vals, gauss(x_vals, *p0),
label="fit :{}".format(sideband[1]))
print("p0:", p0)
try:
coeff, var_list = curve_fit(gauss, sideband[1][:, 0], sideband[1][:, 1],
sigma=sideband[1][:, 2], p0=p0)
coeff[1] = abs(coeff[1])
coeff[2] = abs(coeff[2])
if verbose:
print("coeffs:", coeff)
print("stdevs:", np.sqrt(np.diag(var_list)))
print("integral", np.trapz(sideband[1][:, 1], sideband[1][:, 0]))
if np.sqrt(np.diag(var_list))[0] / coeff[
0] < 0.5: # The error on where the sideband is should be small
sb_fits[sideband[0]] = np.concatenate(
(np.array([sideband[0]]), coeff, np.sqrt(np.diag(var_list))))
# print "error then:", sb_fits[sideband[0]][6]
relative_error = np.sqrt(sum([x ** 2 for x in
sideband[1][index - 1:index + 2,
2]])) / np.sum(
sideband[1][index - 1:index + 2, 1])
if verbose:
print("relative error:", relative_error)
sb_fits[sideband[0]][6] = coeff[1] * relative_error
# print "error now:", sb_fits[sideband[0]][6]
if plot:
x_vals = np.linspace(np.amin(sideband[1][:, 0]),
np.amax(sideband[1][:, 0]), num=50)
plt.plot(x_vals, gauss(x_vals, *coeff))
# plt.plot(x_vals, gauss(x_vals, *p0))
else:
print("what happened?")
except:
print("God damn it, Leroy.\nYou couldn't fit this.")
sb_fits[sideband[0]] = None
for result in sorted(sb_fits.keys()):
try:
self.sb_results = np.vstack((self.sb_results, sb_fits[result]))
except:
self.sb_results = np.array(sb_fits[result])
self.sb_results = self.sb_results[:, [0, 1, 5, 2, 6, 3, 7, 4, 8]]
self.sb_results = self.sb_results[:, :7]
if verbose:
print("And the results, please:\n", self.sb_results)
self.full_dict = {}
for sb in self.sb_results:
self.full_dict[sb[0]] = np.asarray(sb[1:])
def laser_line(self, verbose=False, **kwargs):
"""
This method is designed to scale everything in the PMT to the conversion
efficiency based on our measurement of the laser line with a fixed
attenuation.
Creates:
self.parameters['normalized?'] = Flag to specify if the laser has been
accounted for.
:return: None
"""
if 0 not in self.sb_list:
self.parameters['normalized?'] = False
return
else:
laser_index = np.where(self.sb_results[:,0] == 0)[0][0]
if verbose:
print("sb_results", self.sb_results)
print("laser_index", laser_index)
laser_strength = np.array(self.sb_results[laser_index, 3:5])
if verbose:
print("Laser_strength", laser_strength)
for sb in self.sb_results:
if verbose:
print("\torder {}, strength {}, error {}".format(sb[0], sb[3], sb[4]))
sb[4] = (sb[3] / laser_strength[0]) * np.sqrt(
(sb[4] / sb[3]) ** 2 + (laser_strength[1] / laser_strength[0]) ** 2)
sb[3] = sb[3] / laser_strength[0]
if verbose:
print("\torder {}, strength {}, error {}".format(sb[0], sb[3], sb[4]))
for sb in list(self.full_dict.values()):
sb[3] = (sb[2] / laser_strength[0]) * np.sqrt(
(sb[3] / sb[2]) ** 2 + (laser_strength[1] / laser_strength[0]) ** 2)
sb[2] = sb[2] / laser_strength[0]
self.parameters['normalized?'] = True
def save_processing(self, file_name, folder_str, marker='', index='', verbose=False):
"""
This will save all of the self.proc_data and the results from the
fitting of this individual file.
Format:
spectra_fname = file_name + '_' + marker + '_' + str(index) + '.txt'
fit_fname = file_name + '_' + marker + '_' + str(index) + '_fits.txt'
Inputs:
file_name = the beginning of the file name to be saved
folder_str = the location of the folder where the file will be saved,
will create the folder, if necessary.
marker = I...I don't know what this was originally for
index = used to keep these files from overwriting themselves when in a
list
Outputs:
Two files:
self.proc_data = the continuous spectrum
self.sb_results = the individual sideband details
:param file_name: The base name for the saved file
:type file_name: str
:param folder_str: The full name for the folder hte file is saved it. Folder can be created
:type folder_str: str
:param marker: Marker for the file, appended to file_name, often the self.parameters['series']
:type marker: str
:param index: used to keep these files from overwriting themselves when marker is the same
:type index: str or int
:return: None
"""
try:
os.mkdir(folder_str)
except OSError as e:
if e.errno == errno.EEXIST:
pass
else:
raise
spectra_fname = file_name + '_' + marker + '_' + str(index) + '.txt'
fit_fname = file_name + '_' + marker + '_' + str(index) + '_fits.txt'
self.save_name = spectra_fname
# self.parameters["files included"] = list(self.files)
try:
parameter_str = json.dumps(self.parameters, sort_keys=True, indent=4,
separators=(',', ': '))
except:
print("Source: PMT.save_images\nJSON FAILED")
print("Here is the dictionary that broke JSON:\n", self.parameters)
return
parameter_str = parameter_str.replace('\n', '\n#')
num_lines = parameter_str.count(
'#') # Make the number of lines constant so importing is easier
# for num in range(99 - num_lines): parameter_str += '\n#'
parameter_str += '\n#' * (99 - num_lines)
origin_import_spec = '\nNIR frequency,Signal,Standard error\neV,arb. u.,arb. u.\n,{:.3f},'.format(
self.parameters["fieldStrength"]["mean"])
spec_header = '#' + parameter_str + origin_import_spec
origin_import_fits = '\nIndex,Center energy,error,Amplitude,error,Linewidth,error\nInt,eV,,arb. u.,,eV,,\n,,' # + marker
fits_header = '#' + parameter_str + origin_import_fits
for sideband in sorted(self.sb_dict.keys()):
try:
complete = np.vstack((complete, self.sb_dict[sideband]))
except:
complete = np.array(self.sb_dict[sideband])
np.savetxt(os.path.join(folder_str, spectra_fname), complete, delimiter=',',
header=spec_header, comments='', fmt='%0.6e')
try:
np.savetxt(os.path.join(folder_str, fit_fname), self.sb_results,
delimiter=',',
header=fits_header, comments='', fmt='%0.6e')
except AttributeError:
# Catch the error that happens if you save something without files
print("warning, couldn't save fit file (no sidebands found?)")
if verbose:
print("Saved PMT spectrum.\nDirectory: {}".format(
os.path.join(folder_str, spectra_fname)))
class HighSidebandPMTOld(PMT):
"""
Old version: Replaced March 01, 2017
Class initialized by loading in data set.
Multiple copies of the same sideband were stacked as raw data and combined,
effectively causing (2) 10-pt scans to be treated the same as (1) 20pt scan.
This works well until you have photon counted pulses.
"""
def __init__(self, file_path, verbose=False):
"""
Initializes a SPEX spectrum. It'll open a single file, then read
the data from that file using .add_sideband(). The super's init will handle the parameters
and the description.
attributes:
self.parameters - dictionary of important experimental parameters, created in PMT
self.sb_dict - keys are sideband order, values are PMT data arrays
self.sb_list - sorted list of included sidebands
:param file_path: path to the current file
:type file_path: str
:param verbose: Flag to see the nitty gritty details
:type verbose: bool
:return:
"""
super(HighSidebandPMT, self).__init__(
file_path) # Creates the json parameters dictionary
self.fname = file_path
self.parameters["files included"] = [file_path]
with open(file_path, 'r') as f:
sb_num = int(f.readline()[1:])
raw_temp = np.genfromtxt(file_path, comments='#', delimiter=',')[3:, :]
self.initial_sb = sb_num
self.initial_data = np.array(raw_temp)
self.sb_dict = {sb_num: np.array(raw_temp)}
self.sb_list = [sb_num]
def add_sideband(self, other):
"""
This bad boy will add another PMT sideband object to the sideband spectrum of this object. It handles
when you measure the same sideband twice. It assumes both are equally "good"
It currently doesn't do any sort of job combining dictionaries or anything, but it definitely could, if
you have two incomplete dictionaries
:param other: the new sideband data to add to the larger spectrum. Add means append, no additino is performed
:type other: HighSidebandPMT
:return:
"""
"""
This bad boy will add another PMT sideband object to the sideband spectrum of this object
It currently doesn't do any sort of job combining dictionaries or anything, but it definitely could
"""
self.parameters["files included"].append(other.fname)
if other.initial_sb in self.sb_list:
self.sb_list.append(other.initial_sb)
# Make things comma delimited?
try:
self.sb_dict[other.initial_sb].vstack((other.initial_data))
except:
self.sb_dict[other.initial_sb] = np.array(other.initial_data)
def process_sidebands(self, verbose=False):
"""
This bad boy will clean up the garbled mess that is the object before hand,
including clearing out misfired shots and doing the averaging.
Affects:
self.sb_dict = Averages over sidebands
Creates:
self.sb_list = The sideband orders included in this object.
:param verbose: Flag to see the nitty gritty details.
:type verbose: bool
:return: None
"""
for sb_num, sb in list(self.sb_dict.items()):
if sb_num == 0:
fire_condition = -np.inf # This way the FEL doesn't need to be on during laser line measurement
else:
fire_condition = np.mean(sb[:, 2]) / 2 # Say FEL fired if the
# cavity dump signal is
# more than half the mean
# of the cavity dump signal
frequencies = sorted(list(set(sb[:, 0])))
temp = None
for freq in frequencies:
data_temp = np.array([])
for point in sb:
if point[0] == freq and point[2] > fire_condition:
data_temp = np.hstack((data_temp, point[3]))
try:
temp = np.vstack(
(temp, np.array([freq, np.mean(data_temp),
np.std(data_temp) / np.sqrt(len(data_temp))])))
except:
temp = np.array([freq, np.mean(data_temp),
np.std(data_temp) / np.sqrt(len(data_temp))])
temp[:, 0] = temp[:, 0] / 8065.6 # turn NIR freq into eV
temp = temp[temp[:, 0].argsort()]
self.sb_dict[sb_num] = np.array(temp)
self.sb_list = sorted(self.sb_dict.keys())
if verbose:
print("Sidebands included", self.sb_list)
def integrate_sidebands(self, verbose=False):
"""
This method will integrate the sidebands to find their strengths, and then
use a magic number to define the width, since they are currently so utterly
undersampled for fitting.
It is currently the preferred method for calculating sideband strengths.
self.fit_sidebands is probably better with better-sampled lines.
Creates:
self.sb_results = full list of integrated data. Column order is:
[sb order, Freq (eV), "error" (eV), Integrate area (arb.), area error, "Linewidth" (eV), "Linewidth error" (eV)
self.full_dict = Dictionary where the SB order column is removed and turned into the keys. The values
are the rest of that sideband's results.
:param verbose: Flag to see the nitty gritty details
:type verbose: bool
:return: None
"""
self.full_dict = {}
for sideband in list(self.sb_dict.items()):
index = np.argmax(sideband[1][:, 1])
nir_frequency = sideband[1][index, 0]
area = np.trapz(np.nan_to_num(sideband[1][:, 1]), sideband[1][:, 0])
error = np.sqrt(np.sum(np.nan_to_num(
sideband[1][:, 2]) ** 2)) / 8065.6 # Divide by the step size?
if verbose:
print("order", sideband[0])
print("area", area)
print("error", error)
print("ratio", area / error)
details = np.array(
[sideband[0], nir_frequency, 1 / 8065.6, area, error, 2 / 8065.6,
1 / 8065.6])
if area < 0:
if verbose:
print("area less than 0", sideband[0])
continue
elif area < 1.0 * error: # Two seems like a good cutoff?
if verbose:
print("I did not keep sideband ", sideband[0])
continue
try:
self.sb_results = np.vstack((self.sb_results, details))
except:
self.sb_results = np.array(details)
self.full_dict[sideband[0]] = details[1:]
try:
self.sb_results = self.sb_results[self.sb_results[:, 0].argsort()]
except (IndexError, AttributeError):
# IndexError where there's only one sideband
# AttributeError when there aren't any (one sb which wasn't fit)
pass
def fit_sidebands(self, plot=False, verbose=False):
"""
This method will fit a gaussian to each of the sidebands provided in
the self.sb_dict and make a list just like in the EMCCD version. It
will also use the standard error of the integral of the PMT peak as the
error of the gaussian area instead of that element from the covariance
matrix. Seems more legit.
attributes:
self.sb_results: the numpy array that contains all of the fit info just
like it does in the CCD class.
self.full_dict = A dictionary version of self.sb_results
:param plot: Flag to see the results plotted
:type plot: bool
:param verbose: Flag to see the nitty gritty details
:type verbose: bool
:return: None
"""
sb_fits = {}
for sideband in list(self.sb_dict.items()):
if verbose:
print("Sideband number", sideband[0])
print("Sideband data:\n", sideband[1])
index = np.argmax(sideband[1][:, 1])
nir_frequency = sideband[1][index, 0]
peak = sideband[1][index, 1]
width_guess = 0.0001 # Yep, another magic number
p0 = [nir_frequency, peak * width_guess, width_guess, 0.00001]
if verbose:
x_vals = np.linspace(np.amin(sideband[1][:, 0]),
np.amax(sideband[1][:, 0]), num=50)
plt.plot(x_vals, gauss(x_vals, *p0),
label="fit :{}".format(sideband[1]))
print("p0:", p0)
try:
coeff, var_list = curve_fit(gauss, sideband[1][:, 0], sideband[1][:, 1],
sigma=sideband[1][:, 2], p0=p0)
coeff[1] = abs(coeff[1])
coeff[2] = abs(coeff[2])
if verbose:
print("coeffs:", coeff)
print("stdevs:", np.sqrt(np.diag(var_list)))
print("integral", np.trapz(sideband[1][:, 1], sideband[1][:, 0]))
if np.sqrt(np.diag(var_list))[0] / coeff[
0] < 0.5: # The error on where the sideband is should be small
sb_fits[sideband[0]] = np.concatenate(
(np.array([sideband[0]]), coeff, np.sqrt(np.diag(var_list))))
# print "error then:", sb_fits[sideband[0]][6]
relative_error = np.sqrt(sum([x ** 2 for x in
sideband[1][index - 1:index + 2,
2]])) / np.sum(
sideband[1][index - 1:index + 2, 1])
if verbose:
print("relative error:", relative_error)
sb_fits[sideband[0]][6] = coeff[1] * relative_error
# print "error now:", sb_fits[sideband[0]][6]
if plot:
x_vals = np.linspace(np.amin(sideband[1][:, 0]),
np.amax(sideband[1][:, 0]), num=50)
plt.plot(x_vals, gauss(x_vals, *coeff))
# plt.plot(x_vals, gauss(x_vals, *p0))
else:
print("what happened?")
except:
print("God damn it, Leroy.\nYou couldn't fit this.")
sb_fits[sideband[0]] = None
for result in sorted(sb_fits.keys()):
try:
self.sb_results = np.vstack((self.sb_results, sb_fits[result]))
except:
self.sb_results = np.array(sb_fits[result])
self.sb_results = self.sb_results[:, [0, 1, 5, 2, 6, 3, 7, 4, 8]]
self.sb_results = self.sb_results[:, :7]
if verbose:
print("And the results, please:\n", self.sb_results)
self.full_dict = {}
for sb in self.sb_results:
self.full_dict[sb[0]] = np.asarray(sb[1:])
def laser_line(self, verbose=False):
"""
This method is designed to scale everything in the PMT to the conversion
efficiency based on our measurement of the laser line with a fixed
attenuation.
Creates:
self.parameters['normalized?'] = Flag to specify if the laser has been
accounted for.
:return: None
"""
if 0 not in self.sb_list:
self.parameters['normalized?'] = False
return
else:
laser_index = np.where(self.sb_results[:, 0] == 0)[0][0]
if verbose:
print("sb_results", self.sb_results[laser_index, :])
print("laser_index", laser_index)
laser_strength = np.array(self.sb_results[laser_index, 3:5])
if verbose:
print("Laser_strength", laser_strength)
for sb in self.sb_results:
if verbose:
print("\torder {}, strength {}, error {}".format(sb[0], sb[3], sb[4]))
sb[4] = (sb[3] / laser_strength[0]) * np.sqrt(
(sb[4] / sb[3]) ** 2 + (laser_strength[1] / laser_strength[0]) ** 2)
sb[3] = sb[3] / laser_strength[0]
if verbose:
print("\torder {}, strength {}, error {}".format(sb[0], sb[3], sb[4]))
for sb in list(self.full_dict.values()):
sb[3] = (sb[2] / laser_strength[0]) * np.sqrt(
(sb[3] / sb[2]) ** 2 + (laser_strength[1] / laser_strength[0]) ** 2)
sb[2] = sb[2] / laser_strength[0]
self.parameters['normalized?'] = True
def save_processing(self, file_name, folder_str, marker='', index=''):
"""
This will save all of the self.proc_data and the results from the
fitting of this individual file.
Format:
spectra_fname = file_name + '_' + marker + '_' + str(index) + '.txt'
fit_fname = file_name + '_' + marker + '_' + str(index) + '_fits.txt'
Inputs:
file_name = the beginning of the file name to be saved
folder_str = the location of the folder where the file will be saved,
will create the folder, if necessary.
marker = I...I don't know what this was originally for
index = used to keep these files from overwriting themselves when in a
list
Outputs:
Two files:
self.proc_data = the continuous spectrum
self.sb_results = the individual sideband details
:param file_name: The base name for the saved file
:type file_name: str
:param folder_str: The full name for the folder hte file is saved it. Folder can be created
:type folder_str: str
:param marker: Marker for the file, appended to file_name, often the self.parameters['series']
:type marker: str
:param index: used to keep these files from overwriting themselves when marker is the same
:type index: str or int
:return: None
"""
try:
os.mkdir(folder_str)
except OSError as e:
if e.errno == errno.EEXIST:
pass
else:
raise
spectra_fname = file_name + '_' + marker + '_' + str(index) + '.txt'
fit_fname = file_name + '_' + marker + '_' + str(index) + '_fits.txt'
self.save_name = spectra_fname
# self.parameters["files included"] = list(self.files)
try:
parameter_str = json.dumps(self.parameters, sort_keys=True, indent=4,
separators=(',', ': '))
except:
print("Source: PMT.save_images\nJSON FAILED")
print("Here is the dictionary that broke JSON:\n", self.parameters)
return
parameter_str = parameter_str.replace('\n', '\n#')
num_lines = parameter_str.count(
'#') # Make the number of lines constant so importing is easier
# for num in range(99 - num_lines): parameter_str += '\n#'
parameter_str += '\n#' * (99 - num_lines)
origin_import_spec = '\nNIR frequency,Signal,Standard error\neV,arb. u.,arb. u.\n,{:.3f},'.format(
self.parameters["fieldStrength"]["mean"])
spec_header = '#' + parameter_str + origin_import_spec
origin_import_fits = '\nCenter energy,error,Amplitude,error,Linewidth,error\neV,,arb. u.,,eV,,\n,,' # + marker
fits_header = '#' + parameter_str + origin_import_fits
for sideband in sorted(self.sb_dict.keys()):
try:
complete = np.vstack((complete, self.sb_dict[sideband]))
except:
complete = np.array(self.sb_dict[sideband])
np.savetxt(os.path.join(folder_str, spectra_fname), complete, delimiter=',',
header=spec_header, comments='', fmt='%0.6e')
try:
np.savetxt(os.path.join(folder_str, fit_fname), self.sb_results,
delimiter=',',
header=fits_header, comments='', fmt='%0.6e')
except AttributeError:
# Catch the error that happens if you save something without files
print("warning, couldn't save fit file (no sidebands found?)")
print("Saved PMT spectrum.\nDirectory: {}".format(
os.path.join(folder_str, spectra_fname)))
class TimeTrace(PMT):
"""
This class will be able to handle time traces output by the PMT softare.
"""
def __init__(self, file_path):
super(HighSidebandPMT, self).__init__(file_path)
class FullSpectrum(object):
def __init__(self):
pass
class FullAbsorbance(FullSpectrum):
"""
I'm imagining this will sew up absorption spectra, but I'm not at all sure
how to do that at the moment.
"""
def __init__(self):
pass
class FullHighSideband(FullSpectrum):
"""
I'm imagining this class is created with a base CCD file, then gobbles up
other spectra that belong with it, then grabs the PMT object to normalize
everything, assuming that PMT object exists.
"""
def __init__(self, initial_CCD_piece):
"""
Initialize a full HSG spectrum. Starts with a single CCD image, then
adds more on to itself using stitch_hsg_dicts.
Creates:
self.fname = file name of the initial_CCD_piece
self.sb_results = The sideband details from the initializing data
self.parameters = The parameter dictionary of the initializing data. May
not have all details of spectrum pieces added later.
self.full_dict = a copy of the sb_results without the zeroth column, which
is SB order
:param initial_CCD_piece: The starting part of the spectrum, often the lowest orders seen by CCD
:type initial_CCD_piece: HighSidebandCCD
:return: None
"""
self.fname = initial_CCD_piece.fname
try:
self.sb_results = initial_CCD_piece.sb_results
except AttributeError:
print(initial_CCD_piece.full_dict)
raise
self.parameters = initial_CCD_piece.parameters
self.parameters['files_here'] = [initial_CCD_piece.fname.split('/')[-1]]
self.full_dict = {}
for sb in self.sb_results:
self.full_dict[sb[0]] = np.asarray(sb[1:])
@staticmethod
def parse_sb_array(arr):
"""
Check to make sure the first even order sideband in an array is not weaker
than the second even order. If this happens, it's likely because the SB was in
the short pass filter and isn't work counting.
We cut it out to prevent it from itnerfering with calculating overlaps
:param arr:
:return:
"""
arr = np.array(arr)
if (arr[0, sbarr.SBNUM]>0 and arr[1, sbarr.SBNUM]>0 and # make sure they're both pos
arr[0, sbarr.AREA] < arr[1, sbarr.AREA]): # and the fact the area is less
# print "REMOVING FIRST SIDEBAND FROM FULLSIDEBAND"
# print arr[0]
# print arr[1]
arr = arr[1:]
full_dict = {}
for sb in arr:
full_dict[sb[0]] = np.asarray(sb[1:])
return full_dict, arr
def add_CCD(self, ccd_object, verbose=False, force_calc=None, **kwargs):
"""
This method will be called by the stitch_hsg_results function to add another
CCD image to the spectrum.
:param ccd_object: The CCD object that will be stiched into the current FullHighSideband object
:type ccd_object: HighSidebandCCD
:return: None
"""
if self.parameters["gain"] == ccd_object.parameters["gain"]:
calc = False
else:
calc = True
if force_calc is not None:
calc = force_calc
if "need_ratio" in kwargs: #cascading it through, starting to think
# everything should be in a kwarg
calc = kwargs.pop("need_ratio")
try:
# self.full_dict = stitch_hsg_dicts(self.full_dict, ccd_object.full_dict,
# need_ratio=calc, verbose=verbose)
self.full_dict = stitch_hsg_dicts(self, ccd_object, need_ratio=calc,
verbose=verbose, **kwargs)
self.parameters['files_here'].append(ccd_object.fname.split('/')[-1])
# update sb_results, too
sb_results = [[k]+list(v) for k, v in list(self.full_dict.items())]
sb_results = np.array(sb_results)
self.sb_results = sb_results[sb_results[:,0].argsort()]
except AttributeError:
print('Error, not enough sidebands to fit here! {}, {}, {}, {}'.format(
self.parameters["series"], self.parameters["spec_step"],
ccd_object.parameters["series"], ccd_object.parameters["spec_step"]
))
def add_PMT(self, pmt_object, verbose=True):
"""
This method will be called by the stitch_hsg_results function to add the PMT
data to the spectrum.
"""
# print "I'm adding PMT once"
# self.full_dict = stitch_hsg_dicts(pmt_object.full_dict, self.full_dict,
# need_ratio=True, verbose=False)
self.full_dict = stitch_hsg_dicts(pmt_object, self,
need_ratio=True, verbose=verbose)
# if verbose:
# self.full_dict, ratio = self.full_dict
# print "I'm done adding PMT data"
self.parameters['files_here'].append(pmt_object.parameters['files included'])
self.make_results_array()
# if verbose:
# return ratio
def make_results_array(self):
"""
The idea behind this method is to create the sb_results array from the
finished full_dict dictionary.
"""
self.sb_results = None
# print "I'm making the results array:", sorted(self.full_dict.keys())
for sb in sorted(self.full_dict.keys()):
# print "Going to add this", sb
try:
self.sb_results = np.vstack((self.sb_results, np.hstack((sb, self.full_dict[sb]))))
except ValueError:
# print "It didn't exist yet!"
self.sb_results = np.hstack((sb, self.full_dict[sb]))
# print "and I made this array:", self.sb_results[:, 0]
def save_processing(self, file_name, folder_str, marker='', index='', verbose=''):
"""
This will save all of the self.proc_data and the results from the
fitting of this individual file.
Format:
fit_fname = file_name + '_' + marker + '_' + str(index) + '_full.txt'
Inputs:
file_name = the beginning of the file name to be saved
folder_str = the location of the folder where the file will be saved,
will create the folder, if necessary.
marker = I...I don't know what this was originally for
index = used to keep these files from overwriting themselves when in a
list
Outputs:
Two files, one that is self.proc_data, the other is self.sb_results
"""
try:
os.mkdir(folder_str)
except OSError as e:
if e.errno == errno.EEXIST:
pass
else:
raise
temp = np.array(self.sb_results)
ampli = np.array([temp[:, 3] / temp[:, 5]]) # I'm pretty sure this is
# amplitude, not area
temp[:, 5:7] = temp[:, 5:7] * 1000 # For meV linewidths
if verbose:
print("sb_results", self.sb_results.shape)
print("ampli", ampli.shape)
save_results = np.hstack((temp, ampli.T))
# spectra_fname = file_name + '_' + marker + '_' + str(index) + '.txt'
fit_fname = file_name + '_' + marker + '_' + str(index) + '_full.txt'
# self.save_name = spectra_fname
# self.parameters['addenda'] = self.addenda
# self.parameters['subtrahenda'] = self.subtrahenda
try:
# PMT files add unnecessary number of lines, dump it into one line
# by casting it to a string.
reduced = self.parameters.copy()
reduced["files_here"] = str(reduced["files_here"])
parameter_str = json.dumps(reduced, sort_keys=True, indent=4, separators=(',', ': '))
except Exception as e:
print(e)
print("Source: EMCCD_image.save_images\nJSON FAILED")
print("Here is the dictionary that broke JSON:\n", self.parameters)
return
parameter_str = parameter_str.replace('\n', '\n#')
num_lines = parameter_str.count('#') # Make the number of lines constant so importing is easier
# for num in range(99 - num_lines): parameter_str += '\n#'
parameter_str += '\n#' * (99 - num_lines)
# origin_import_spec = '\nNIR frequency,Signal,Standard error\neV,arb. u.,arb. u.'
# spec_header = '#' + parameter_str + '\n#' + self.description[:-2] + origin_import_spec
origin_import_fits = '\nSideband,Center energy,error,Sideband strength,error,Linewidth,error,Amplitude'+\
'\norder,eV,,arb. u.,,meV,,arb. u.\n' + ','.join([marker]*8)
fits_header = '#' + parameter_str + origin_import_fits
# np.savetxt(os.path.join(folder_str, spectra_fname), self.proc_data, delimiter=',',
# header=spec_header, comments='', fmt='%f')
np.savetxt(os.path.join(folder_str, fit_fname), save_results, delimiter=',',
header=fits_header, comments='', fmt='%0.6e')
if verbose:
print("Save image.\nDirectory: {}".format(os.path.join(folder_str, fit_fname)))
class TheoryMatrix(object):
def __init__(self,ThzField,Thzomega,nir_wl,dephase,peakSplit,temp=60):
'''
This class is designed to handle everything for creating theory
matrices and comparing them to experiement.
Init defines some constants that are used throughout the calculation
and puts somethings in proper units.
Parameters:
:ThzField: Give in kV/cm.
:Thzomega: Give in Ghz.
:nir_wl: Give in nanometers.
:dephase: Dephasing, give in meV.
Should roughly be the width of absorption peaks
:detune: Detuning, give in meV.
Difference between NIR excitation and band gap
:temp: Temperature, give in K
'''
self.F = ThzField * 10**5
self.Thz_w = Thzomega * 10**9 *2*np.pi
self.nir_wl = nir_wl * 10**(-9)
self.nir_ph = .0012398/self.nir_wl #NIR PHOTON ENERGY
self.detune = 1.52 - self.nir_ph
self.peakSplit = peakSplit*1.602*10**(-22)
self.dephase = dephase*1.602*10**(-22)
self.n_ref = 0
self.iterations = 0
self.max_iter = 0
self.hbar = 1.055*10**(-34) # hbar in Js
self.temp = temp
self.kb = 8.617*10**(-5) # Boltzmann constant in eV/K
self.temp_ev = self.temp*self.kb
def mu_generator(self,gamma1,gamma2,phi,beta):
'''
Given gamma1 and gamma2 produces mu+- according to
mu+- = electron mass/(mc^-1+gamma1 -+ 2*gamma2)
Note that this formula is only accurate for THz and NIR
polarized along [010]. The general form requires gamma3 as well
Parameters:
:gamma1: Gamma1 parameter in the luttinger hamiltonian.
Textbook value of 6.85
:gamma2: Gamma2 parameter in the luttinger hamiltonian.
Textbook value of 2.1
:phi: [100] to THz orientation, passed from the data array
:beta: experimentally measured g3/g2 ratio
Returns: mu_p, mu_m effective mass of of mu plus/minus
'''
theta = phi + np.pi/4
emass = 9.109*10**(-31) # bare electron mass in kg
m_cond = 0.0665 # Effective mass of conduction band
mu_p = emass/( 1/m_cond + gamma1 - gamma2*np.sqrt(3*np.sin(2*theta)**2+1+3*np.cos(2*theta)**2*beta**2) ) # Calculates mu_plus
mu_m = emass/( 1/m_cond + gamma1 + gamma2*np.sqrt(3*np.sin(2*theta)**2+1+3*np.cos(2*theta)**2*beta**2) ) # Calculates mu_minus
return mu_p,mu_m
def alpha_value(self,x):
'''
alpha parameter given by Qile's notes on two band model for a given x
Parameters:
:x: the argument of the calculation. Give in radians
Returns:
:alpha_val: the alpha parameter given in Qile's notes
'''
alpha_val = np.cos(x/2) - np.sin(x/2)/(x/2)
# This does the calculation. Pretty straightforward
return alpha_val
def gamma_value(self,x):
'''
gamma parameter given by Qile's notes on two band model
Parameters:
:x: Argument of the calculation. Give in radians
Returns:
:gamma_val: the gamma parameter given in Qile's notes
'''
gamma_val = np.sin(x/2)/(x/2)
# does the calculation
return gamma_val
def Up(self,mu):
'''
Calculates the ponderemotive energy
Ponderemotive energy given by
U = e^2*F_THz^2/(4*mu*w_THz^2)
Parameters:
:F: Thz field. Give in V/m
:mu: effective mass. Give in kg
:w: omega, the THz freqeuncy. Give in angular frequency.
Returns:
:u: The ponderemotive energy
'''
F = self.F
w = self.Thz_w
echarge = 1.602*10**(-19) # electron charge in Coulombs
u = echarge**(2)*F**(2)/(4*mu*w**2) # calculates the ponderemotive energy
return u
def phonon_dephase(self,n):
'''
Step function that will compare the energy gained by the sideband to the
energy of the phonon (36.6meV). If the energy is less than the phonon,
return zero. If it's more return the scattering rate as determined by
Yu and Cordana Eq 5.51
This really should be treated as a full integral, but whatever
'''
thz_omega = self.Thz_w
hbar = self.hbar
thz_ev = n*hbar*thz_omega/(1.602*10**-19) # converts to eV
phonon_ev = 36.6*10**(-3) # phonon energy in Vv
emass = 9.109*10**(-31) # bare electron mass in kg
m_cond = 0.0665 # Effective mass of conduction band
m_eff = emass*m_cond
phonon_n = 1/(np.exp(phonon_ev/self.temp_ev)-1)
if thz_ev<phonon_ev:
# print('No phonon for order',n)
return 0
else:
W0 = 7.7*10**12 # characteristic rate
rate_frac = phonon_n*np.sqrt((thz_ev+phonon_ev)/thz_ev)+(
phonon_n+1)*np.sqrt((thz_ev-phonon_ev)/thz_ev)+(
phonon_ev/thz_ev)*(-phonon_n*np.arcsinh(np.sqrt(
phonon_ev/thz_ev))+(phonon_n+1)*np.arcsinh(np.sqrt(
(thz_ev-phonon_ev)/thz_ev)))
# Got this from Yu and Cordana's book
fullW = W0*rate_frac
return fullW
def integrand(self,x,mu,n):
'''
Calculate the integrand to integrate A_n+- in two_band_model pdf eqn 13.
Given in the new doc pdf from Qile as I_d^(2n)
Parameters:
:x: Argument of integrand equal to omega*t. This is the variable integrated
over.
:dephase: dephasing rate. Should be a few meV, ~the width of the exciton
absorption peak (according to Qile). Should be float
:w: Frequency of THz in radians.
:F: Thz field in V/m
:mu: reduced mass give in kg
:n: Order of the sideband
Returns:
:result: The value of the integrand for a given x value
'''
hbar = self.hbar
F = self.F
w = self.Thz_w
dephase = self.dephase
detune = self.detune
pn_dephase = self.phonon_dephase(n)
exp_arg = (-dephase*x/(hbar*w)-pn_dephase*x/w + 1j*x*self.Up(mu)/(hbar*w)*(self.gamma_value(x)**2-1)+1j*n*x/2-1j*detune*x/(hbar*w))
# Argument of the exponential part of the integrand
bessel_arg = x*self.Up(mu)*self.alpha_value(x)*self.gamma_value(x)/(hbar*w)
# Argument of the bessel function
bessel = spl.jv(n/2,bessel_arg)
# calculates the J_n(bessel_arg) bessel function
result = np.exp(exp_arg)*bessel/x
# This is the integrand for a given x
return result
def Qintegrand(self,x,mu,n):
'''
Calculate the integrand in the expression for Q, with the simplification
that the canonical momentum is zero upon exciton pair creation.
Parameters:
:x: integration variable of dimensionless units. Equal to omega*tau
:dephase: dephasing rate of the electron hole pair as it is accelerated by
the THz field
:w: Frequency of THz is radiams
:F: THz field in V/m
:mu: the effective reduced mass of the electron-hole pair
:n: Order of the sideband
'''
hbar = self.hbar
F = self.F
w = self.Thz_w
dephase = self.dephase
pn_detune = self.phonon_dephase(n)
c0 = 2*(x-np.sin(x))
a = 3*np.sin(2*x)-4*np.sin(w*x)-2*w*x*np.cos(2*x)
b = -3*np.cos(2*w*x)-4*np.cos(x)+2*w*x*np.sin(2*x)+1
c1 = np.sign(a)*np.sqrt(a**2+b**2)
phi = np.arctan2(a,b)
exp_arg = -dephase*x/w-1j*pn_detune*x/w + 1j*(self.Up(mu)*x)/(hbar*w**2)*c0 -1j*n*phi
bessel_arg = self.Up(mu)/(hbar*w)*c1
bessel = spl.jv(n,bessel_arg)
result = np.exp(exp_arg)*bessel*(-1)**(n/2)
return result
def scale_J_n_T(self,Jraw,Jxx,observedSidebands,crystalAngle,saveFileName,
index, save_results=True, scale_to_i=True):
'''
This function takes the raw J from fan_n_Tmat or findJ and scales it with
Jxx found from scaling sideband strengths with the laser line/PMT
In regular processing we actually find all the matrices normalized to Jxx
Now can scale to a given sideband order.
This is to allow comparision between the measured sideband powers,
normalized by the PMT, to the evalueated Path Integral from the two band
model. By normalizing the measured values and integrals to a given
sideband index, we can remove the physical constants from the evaluation.
:param Jraw: set of matrices from findJ
:param Jxx: sb_results from PMT and CCD data
:param observedSidebands: np array of observed sidebands. Data will be
cropped such that these sidebands are included in everything.
:param crystalAngle: (Float) Angle of the sample from the 010 crystal face
:saveFileName: Str of what you want to call the text files to be saved
:save_results: Boolean controls if things are saved to txt files.
Currently saves scaled J and T
:param index: the sideband index to which we want to normalize.
:param saveFileName: Str of what you want to call the text files to be saved.
:param scale_to_i: Boolean that controls to normalize to the ith sideband
True -> Scale to ith | False -> scale to laser line
returns: scaledJ, scaledT matrices scaled by Jxx strengths
'''
# Initialize the array for scaling
Jxx_scales = np.array([ ])
self.n_ref = index
if scale_to_i:
for idx in np.arange(len(Jxx[:,0])):
if Jxx[idx,0] == index:
scale_to = Jxx[idx,3]
print('scale to:',scale_to)
# sets the scale_to to be Jxx for the ith sideband
else:
scale_to = 1 # just makes this 1 if you don't want to scale to i
scaledJ = Jraw # initialize the scaled J matrix
for idx in np.arange(len(Jxx[:,0])):
if Jxx[idx,0] in observedSidebands:
Jxx_scales = np.append(Jxx_scales,Jxx[idx,3]/scale_to)
print('Scaling sb order',Jxx[idx,0])
# Creates scaling factor
for idx in np.arange(len(Jxx_scales)):
scaledJ[:,:,idx] = Jraw[:,:,idx]*Jxx_scales[idx]
# For each sideband scales Jraw by Jxx_scales
scaledT = makeT(scaledJ,crystalAngle)
# Makes scaledT from our new scaledJ
if save_results:
saveT(scaledJ, observedSidebands, "{}_scaledJMatrix.txt".format(saveFileName))
saveT(scaledT, observedSidebands, "{}_scaledTMatrix.txt".format(saveFileName))
# Saves the matrices
return scaledJ, scaledT
def Q_normalized_integrals(self,gamma1,gamma2,n,phi,beta):
'''
Returns Q_n^{HH}/Q_n^{LH} == Integrand_n^{HH}/Integrand_n^{LH}
Unlike the normallized integrals used in early 2020 analysis, these integrals are of a
given Fourier component's intensity from either the HH or LH band, and thus there is no
prefactor related to the energy of the given sideband photon
Parameters:
:dephase: dephasing rate passed to intiallized TMAtrix object
:w: the frequency of the THz field, in GHz
:F: THz field strength in V/m
:gamma1: Gamma1 parameter from Luttinger Hamiltonian
:gamma2: Gamma2 parameter from Luttinger Hamiltonian
:n: Order of the sideband for this integral
:phi: [100] to THz orientation, passed from the cost function funciton (in radians)
:beta: experimentally measured g3/g2 ratio
Returns: QRatio, the ratio of Q_n^{HH}/Q_n^{LH}
'''
mu_p,mu_m = self.mu_generator(gamma1,gamma2,phi,beta)
w = self.Thz_w
hbar = self.hbar
detune = self.detune
U_pp = self.Up(mu_p)
U_pm = self.Up(mu_m)
int_cutoff_HH = ((n*hbar*w-detune)/(8*U_pp))**(1/4)
int_cutoff_LH = ((n*hbar*w-detune)/(8*U_pm))**(1/4)
# Because the integral is complex, the real and imaginary parts have to be
# counted seperatly.
re_Q_HH = intgt.quad(lambda x: self.Qintegrand(x,mu_p,n),
0,int_cutoff_HH)[0]
re_Q_LH = intgt.quad(lambda x: self.Qintegrand(x,mu_m,n),
0,int_cutoff_LH)[0]
im_Q_HH = intgt.quad(lambda x: self.Qintegrand(x,mu_p,n),
0,int_cutoff_HH)[1]
im_Q_LH = intgt.quad(lambda x: self.Qintegrand(x,mu_m,n),
0,int_cutoff_LH)[1]
# Combine the real and imaginary to have the full integral
QRatioRe = re_Q_HH/re_Q_LH
QRatioIm = im_Q_HH/im_Q_LH
return QRatioRe, QRatioIm
def normalized_integrals(self,gamma1,gamma2,n,n_ref,phi,beta):
'''
Returns the plus and minus eta for a given sideband order, normalized
to order n_ref (should probably be 10?). This whole calculation relies
on calculating the ratio of these quantities to get rid of some troubling
constants. So you need a reference integral.
eta(n)+- =
(w_nir + 2*n*w_thz)^2/(w_nir + 2*n_ref*w_thz)^2 *
(mu_+-/mu_ref)^2 * (int(n)+-)^2/(int(n_ref)+)^2
This takes gamma1 and gamma2 and gives the effective mass via mu_generator.
It then calculates the normalized integrals for both mu's and gives eta,
which is the integrals squared with some prefactors.
Then you feed this into a cost function that varies gamma1 and gamma2.
Parameters:
:dephase: dephasing rate. Should be a few meV, ~the width of the exciton
absorption peak (according to Qile). Should be float
:lambda_nir: wavelength of NIR in nm
:w_thz: frequency in GHz of fel. DO NOT give in angular form, the code
does that for you.
:F: THz field strength
:gamma1: Gamma1 parameter in the luttinger hamiltonian.
Textbook value of 6.85
:gamma2: Gamma2 parameter in the luttinger hamiltonian.
Textbook value of 2.1
:n: Order of sideband for this integral
:n_ref: Order of the reference integral which everything will be divided by
:phi: [100] to THz orientation, passed from the data array
:beta: experimentally measured g3/g2 ratio
Returns: eta_p, eta_m the values of the eta parameter normalized to the
appropriate sideband order for plus and minus values of mu.
'''
mu_p,mu_m = self.mu_generator(gamma1,gamma2,phi,beta)
# gets the plus/minus effective mass
omega_thz = self.Thz_w # FEL frequency
omega_nir = 2.998*10**8/(self.nir_wl) *2*np.pi
# NIR frequency, takes nm (wavelength) and gives angular Hz
Field = self.F # THz field
hbar = self.hbar
dephase = self.dephase
int_cutoff = hbar*omega_thz/dephase*10
# This cuts off the integral when x* dephase/hbaromega = 10
# Therefore the values of the integrand will be reduced by a value
# of e^(-10) which is about 4.5*10^(-5)
re_int_ref = intgt.quad(lambda x: np.real(self.integrand(
x,mu_p,n_ref)),0,int_cutoff,limit = 1000000)[0]
re_int_p = intgt.quad(lambda x: np.real(self.integrand(
x,mu_p,n)),0,int_cutoff,limit = 1000000)[0]
re_int_m = intgt.quad(lambda x: np.real(self.integrand(
x,mu_m,n)),0,int_cutoff,limit = 1000000)[0]
# Ok so these integrands are complex valued, but the intgt.quad integration
# does not work with that. So we split the integral up into two parts,
# real and imaginary parts. These lines calculate the real part for the
# reference, plus, and minus integrals.
# The integrals currently are limited to 10,000 iterations. No clue if that's
# a good amount or what. We could potentially make this simpler by doing
# a trapezoidal rule.
# We define the lambda function here to set all the values of the integrand
# function we want except for the variable of integration x
im_int_ref = intgt.quad(lambda x: np.imag(self.integrand(
x,mu_p,n_ref)),0,int_cutoff,limit = 1000000)[0]
im_int_p = intgt.quad(lambda x: np.imag(self.integrand(
x,mu_p,n)),0,int_cutoff,limit = 1000000)[0]
im_int_m = intgt.quad(lambda x: np.imag(self.integrand(
x,mu_m,n)),0,int_cutoff,limit = 1000000)[0]
# Same as above but these are the imaginary parts of the integrals.
int_ref = re_int_ref + 1j*im_int_ref
int_p = re_int_p + 1j*im_int_p
int_m = re_int_m + 1j*im_int_m
# All the king's horses and all the king's men putting together our integrals
# again. :)
prefactor = ((omega_nir +2*n*omega_thz)**2)/((omega_nir +2*n_ref*omega_thz)**2)
# This prefactor is the ratio of energy of the nth sideband to the reference
m_pre = (mu_m/mu_p)**2
# There is a term of mu/mu_ref in the eta expression. For the
eta_p = prefactor*(np.abs(int_p)**2)/(np.abs(int_ref)**2)
eta_m = prefactor*m_pre*(np.abs(int_m)**2)/(np.abs(int_ref)**2)
# Putting everthing together in one tasty little result
return eta_p,eta_m
def cost_func(self,gamma1,gamma2,observedSidebands,n_ref,Jexp,phi,beta,gc_fname,eta_folder):
'''
This will sum up a cost function that takes the difference between
the theory generated eta's and experimental scaled matrices
eta+/eta+_ref = |Jxx|^2
eta-/eta+_ref = |Jyy-Jxx/4|^2/|3/4|^2
The cost function is given as
Sqrt(|eta+(theory)-eta+(experiment)|^2 + |eta-(theory)-eta-(experiment)|^2)
Where the J elements have been scaled to the n_ref sideband (Jxx_nref)
This is designed to run over and over again as you try different
gamma values. On my (Joe) lab computer a single run takes ~300-400 sec.
The function keeps track of values by writing a file with iteration,
gamma1, gamma2, and cost for each run. This lets you keep track of the
results as you run.
Parameters:
:dephase: dephasing rate. Should be a few meV, ~the width of the exciton
absorption peak (according to Qile). Should be float
:lambda_nir: wavelength of NIR in nm
:w_thz: frequency of fel
:F: THz field strength in kV/cm
:gamma1: Gamma1 parameter in the luttinger hamiltonian.
Textbook value of 6.85
:gamma2: Gamma2 parameter in the luttinger hamiltonian.
Textbook value of 2.1
:n_ref: Order of the reference integral which everything will be divided by
:Jexp: Scaled experimental Jones matrices in xy basis that will be compared
to the theoretical values. Pass in the not flattened way.
:phi: [100] to THz orientation, passed from the data array
:beta: experimentally measured g3/g2 ratio
:gc_fname: File name for the gammas and cost results
:eta_folder: Folder name for the eta lists to go in
:i: itteration, for parallel processing output purposes
Returns:
:costs: Cumulative cost function for that run
:i: itteration, for parallel processing output purposes
:eta_list: list of eta for's for each sideband order of the form
sb order | eta_plus theory | eta_plus experiment | eta_minus thoery | eta_minus experiment
.
.
.
'''
costs = 0 # initialize the costs for this run
t_start = time.time() # keeps track of the time the run started.
eta_list = np.array([0,0,0,0,0])
dephase = self.dephase
lambda_nir = self.nir_wl
omega_nir = 2.998*10**8/(self.nir_wl) *2*np.pi
w_thz = self.Thz_w
F = self.F
for idx in np.arrange(len(observedSidebands)):
n = observedSidebands[idx]
eta_p,eta_m = self.normalized_integrals(gamma1,gamma2,n,n_ref,phi,beta)
# calculates eta from the normalized_integrals function
prefactor = ((omega_nir +2*n*w_thz)**2)/((omega_nir +2*n_ref*w_thz)**2)
#Have to hard code the index of the 16th order sideband (8,10,12,14,16)
exp_p = prefactor*np.abs(Jexp[0,0,idx])**2
exp_m = prefactor*np.abs(Jexp[1,1,idx]-(1/4)*Jexp[0,0,idx])**2*(9/16)
# calculates the experimental plus and minus values
# 1/9/20 added prefactor to these bad boys
costs += np.sqrt(np.abs((exp_p-eta_p)/(exp_p))**2 + np.abs((exp_m-eta_m)/(exp_m))**2)
# Adds the cost function for this sideband to the overall cost function
# 1/8/20 Changed cost function to be the diiference of the ratio of the two etas
# 01/30/20 Changed cost function to be relative difference of eta_pm
this_etas = np.array([n,eta_p,exp_p,eta_m,exp_m])
eta_list = np.vstack((eta_list,this_etas))
self.iterations += 1
# Ups the iterations counter
g1rnd = round(gamma1,3)
g2rnd = round(gamma2,3)
costs_rnd = round(costs,5)
# Round gamma1,gamma2,costs to remove float rounding bullshit
g_n_c = str(self.iterations)+','+str(g1rnd)+','+str(g2rnd)+','+str(costs)+'\n'
# String version of iteration, gamma1, gamma2, cost with a new line
gc_file = open(gc_fname,'a') #opens the gamma/cost file in append mode
gc_file.write(g_n_c) # writes the new line to the file
gc_file.close() # closes the file
etas_header = "#\n"*95
etas_header += f'# Dephasing: {self.dephase/(1.602*10**(-22))} eV \n'
etas_header += f'# Detuning: {self.detune/(1.602*10**(-22))} eV \n'
etas_header += f'# Field Strength: {self.F/(10**5)} kV/cm \n'
etas_header += f'# THz Frequency: {self.Thz_w/(10**9 * 2*np.pi)} GHz \n'
etas_header += f'# NIR Wavelength: {self.nir_wl/(10**(-9))} nm \n'
etas_header += 'sb order, eta_plus theory, eta_plus experiment, eta_minus thoery, eta_minus experiment \n'
etas_header += 'unitless, unitless, unitless, unitless, unitless \n'
# Creates origin frienldy header for the eta's
# eta_fname = 'eta_g1_' + str(g1rnd) + '_g2_' + str(g2rnd) + r'.txt'
eta_fname = f'eta_g1_{g1rnd}_g2_{g2rnd}.txt'
eta_path = os.path.join(eta_folder,eta_fname)
#creates the file for this run of etas
eta_list = eta_list[1:,:]
np.savetxt(eta_path,eta_list, delimiter = ',',
header = etas_header, comments = '') #save the etas for these gammas
t_taken = round(time.time()-t_start,5) # calcuates time taken for this run
print(" ")
print("---------------------------------------------------------------------")
print(" ")
print(f'Iteration number {self.iterations} / {self.max_iter} done')
print('for gamma1, gamma2 = ',g1rnd,g2rnd)
print('Cost function is = ',costs_rnd)
print('This calculation took ',t_taken,' seconds')
print(" ")
print("---------------------------------------------------------------------")
print(" ")
# These print statements help you keep track of what's going on as this
# goes on and on and on.
return costs
def Q_cost_func(self,gamma1,gamma2,Gamma_Sidebands,Texp,crystalAngles,
beta,gc_fname,Q_folder,ThetaSweep = True):
'''
This compairs the T Matrix components measured by experiment to the
'''
costs = 0 # Initialize the costs
imcost = 0
recost = 0
t_start = time.time()
Q_list = np.array([0,0,0,0,0])
if ThetaSweep:
for idx in np.arange(len(crystalAngles)):
n = Gamma_Sidebands
phi = float(crystalAngles[idx])
phi_rad = phi*np.pi/180
theta = phi_rad + np.pi/4
#Calculate the Theoretical Q Ratio
QRatioRe, QRatioIm = self.Q_normalized_integrals(gamma1,gamma2,n,phi_rad,beta)
QRatio = QRatioRe + 1j*QRatioIm
#Prefactor for experimental T Matirx algebra
PHI = 5/(3*(np.sin(2*theta) - 1j*beta*np.cos(2*theta)))
THETA = 1/(np.sin(2*theta)-1j*beta*np.cos(2*theta))
ExpQ = (Texp[idx,0,0]+PHI*Texp[idx,0,1])/(Texp[idx,0,0]-THETA*Texp[idx,0,1])
costs += np.abs((ExpQ - QRatio)/QRatio)
imcost += np.abs((np.imag(ExpQ)-QRatioIm)/QRatioIm)
recost += np.abs((np.real(ExpQ)-QRatioRe)/QRatioRe)
this_Qs = np.array([phi,np.real(ExpQ),np.imag(ExpQ),QRatioRe,QRatioIm])
Q_list = np.vstack((Q_list,this_Qs))
else:
for idx in np.arange(len(Gamma_Sidebands)):
n = Gamma_Sidebands[idx]
phi = float(crystalAngles)
phi_rad = phi*np.pi/180
theta = phi_rad + np.pi/4
#Calculate the Theoretical Q Ratio
QRatioRe, QRatioIm = self.Q_normalized_integrals(gamma1,gamma2,n,phi_rad,beta)
QRatio = QRatioRe + 1j*QRatioIm
#Prefactor for experimental T Matirx algebra
PHI = 5/(3*(np.sin(2*theta) - 1j*beta*np.cos(2*theta)))
THETA = 1/(np.sin(2*theta)-1j*beta*np.cos(2*theta))
ExpQ = (Texp[0,0,idx]+PHI*Texp[0,1,idx])/(Texp[0,0,idx]-THETA*Texp[0,1,idx])
costs += np.abs((ExpQ - QRatio)/QRatio)
imcost += np.abs((np.imag(ExpQ)-QRatioIm)/QRatioIm)
recost += np.abs((np.real(ExpQ)-QRatioRe)/QRatioRe)
this_Qs = np.array([n,np.real(ExpQ),np.imag(ExpQ),QRatioRe,QRatioIm])
Q_list = np.vstack((Q_list,this_Qs))
self.iterations += 1
g1rnd = round(gamma1,3)
g2rnd = round(gamma2,3)
costs_rnd = round(costs,5)
imcost_rnd = round(imcost,5)
recost_rnd = round(recost,5)
g_n_c = str(self.iterations) + ',' + str(g1rnd) + ',' + str(g2rnd) + ',' + str(costs) + ',' + str(imcost) + ',' + str(recost) + '\n'
gc_file = open(gc_fname,'a')
gc_file.write(g_n_c)
gc_file.close()
# Origin Header
Q_header = "#\n"*94
Q_header += f'# Crystal Angle: {phi} Deg \n'
Q_header += f'# Dephasing: {self.dephase/(1.602*10**(-22))} eV \n'
Q_header += f'# Detuning: {self.detune/(1.602*10**(-22))} eV \n'
Q_header += f'# Feild Strength: {self.F/(10**5)} kV/cm \n'
Q_header += f'# THz Frequncy {self.Thz_w/(10**9 *2*np.pi)} GHz \n'
Q_header += f'# NIR Wavelength {self.nir_wl/(10**(-9))} nm \n'
Q_header += 'Crystal Angles, QRatio Experiment Real, Imaginary, QRatio Theory Real, Imaginary\n'
Q_header += 'Degrees, unitless, unitless \n'
#Eta File Name
Q_fname = f'Q_g1_{g1rnd}_g2_{g2rnd}.txt'
Q_path = os.path.join(Q_folder,Q_fname)
Q_list = Q_list[1:,:]
np.savetxt(Q_path,Q_list, delimiter = ',',
header = Q_header, comments = '')
t_taken = round(time.time() - t_start,5)
print(" ")
print("---------------------------------------------------------------------")
print(" ")
print(f'Iteration number {self.iterations} / {self.max_iter} done')
print('for gamma1, gamma2 = ',g1rnd,g2rnd)
print('Cost function is = ',costs_rnd)
print('Imaginary Cost function is =',imcost_rnd)
print('Real Cost function is =',recost_rnd)
print('This calculation took ',t_taken,' seconds')
print(" ")
print("---------------------------------------------------------------------")
print(" ")
return costs,imcost,recost
def gamma_sweep(self,gamma1_array,gamma2_array,observedSidebands,n_ref,
Jexp,crystalAngle,gc_fname,eta_folder,save_results = True):
'''
This function calculates the integrals and cost function for an array of
gamma1 and gamma2. You can pass any array of gamma1 and gamma2 values and
this will return the costs for all those values. Let's you avoid the
weirdness of fitting algorithims.
Parameters:
:dephase: dephasing rate. Should be a few meV, ~the width of the exciton
absorption peak (according to Qile). Should be float
:lambda_nir: wavelength of NIR in nm
:w_thz: frequency of fel
:F: THz field strength
:gamma1: Gamma1 parameter in the luttinger hamiltonian.
Textbook value of 6.85
:gamma2: Gamma2 parameter in the luttinger hamiltonian.
Textbook value of 2.1
:n: Order of sideband for this integral
:n_ref: Order of the reference integral which everything will be divided by
:observedSidebands: List or array of observed sidebands. The code will
loop over sidebands in this array.
:Jexp: Scaled experimental Jones matrices in xy basis that will be compared
to the theoretical values. Pass in the not flattened way.
:gc_fname: File name for the gammas and cost functions, include .txt
:eta_folder: Folder name for the eta lists to go in
Returns: gamma_cost_array of form
gamma1 | gamma2 | cost |
. . .
. . .
. . .
This is just running cost_func over and over again essentially.
'''
dephase = self.dephase
lambda_nir = self.nir_wl
w_thz = self.Thz_w
F = self.F
phi = crystalAngle
self.max_iter = len(gamma1_array)*len(gamma2_array)
self.iterations = 0
gamma_cost_array = np.array([0,0,0])
# Initialize the gamma cost array
gammas_costs = np.array([])
# This is just for initializing the gamma costs file
gammacosts_header = "#\n"*95
gammacosts_header += f'# Dephasing: {self.dephase/(1.602*10**(-22))} eV \n'
gammacosts_header += f'# Detuning: {self.detune/(1.602*10**(-22))} eV \n'
gammacosts_header += f'# Field Strength: {self.F/(10**5)} kV/cm \n'
gammacosts_header += f'# THz Frequency: {self.Thz_w/(10**9 * 2*np.pi)} GHz \n'
gammacosts_header += f'# NIR Wavelength: {self.nir_wl/(10**(-9))} nm \n'
gammacosts_header += 'Iteration, Gamma1, Gamma2, Cost Function \n'
gammacosts_header += 'unitless, unitless, unitless, unitless \n'
# Creates origin frienldy header for gamma costs
np.savetxt(gc_fname, gammas_costs, delimiter = ',',
header = gammacosts_header, comments = '')
# create the gamma cost file
data = [gamma1_array,gamma2_array]
for gamma1 in gamma1_array:
for gamma2 in gamma2_array:
cost = self.cost_func(gamma1,gamma2,observedSidebands,
n_ref,Jexp, phi, 1.42, gc_fname,eta_folder)
this_costngamma = np.array([gamma1,gamma2,cost])
gamma_cost_array = np.vstack((gamma_cost_array,this_costngamma))
# calculates the cost for each gamma1/2 and adds the gamma1, gamma2,
# and cost to the overall array.
# gamma_cost_array = gamma_cost_final[1:,:]
# if save_results:
# sweepcosts_header = "#\n"*100
# sweepcosts_header += 'Gamma1, Gamma2, Cost Function \n'
# sweepcosts_header += 'unitless, unitless, unitless \n'
#
# sweep_name = 'sweep_costs_' + gc_fname
# np.savetxt(sweep_name,gamma_cost_array,delimiter = ',',
# header = sweepcosts_header, comments = '')
# Ok so right now I think I am going to get rid of saving this file
# since it has the same information as the file that is saved in
# cost_func but that file is updated every interation where this
# one only works at the end. So if the program gets interrupted
# the other one will still give you some information.
return gamma_cost_array
def gamma_th_sweep(self,gamma1_array,gamma2_array,n,crystalAngles,
Texp,gc_fname,Q_folder,ThetaSweep = True, save_results = True):
'''
This function calculates the integrals and cost function for an array of
gamma1 and gamma2. You can pass any array of gamma1 and gamma2 values and
this will return the costs for all those values. Let's you avoid the
weirdness of fitting algorithims.
Parameters:
:dephase: dephasing rate. Should be a few meV, ~the width of the exciton
absorption peak (according to Qile). Should be float
:lambda_nir: wavelength of NIR in nm
:w_thz: frequency of fel
:F: THz field strength
:gamma1: Gamma1 parameter in the luttinger hamiltonian.
Textbook value of 6.85
:gamma2: Gamma2 parameter in the luttinger hamiltonian.
Textbook value of 2.1
:n: Order of sideband for this integral
:n_ref: Order of the reference integral which everything will be divided by
:observedSidebands: List or array of observed sidebands. The code will
loop over sidebands in this array.
:Jexp: Scaled experimental Jones matrices in xy basis that will be compared
to the theoretical values. Pass in the not flattened way.
:gc_fname: File name for the gammas and cost functions, include .txt
:eta_folder: Folder name for the eta lists to go in
Returns: gamma_cost_array of form
gamma1 | gamma2 | cost |
. . .
. . .
. . .
This is just running cost_func over and over again essentially.
'''
#Hard Coding the experimental g3/g2 factor
beta = 1.42
self.iterations = 0
self.max_iter = len(gamma1_array)*len(gamma2_array)
gamma_cost_array = np.array([0,0,0,0,0])
# Initialize the gamma cost array
gammas_costs = np.array([])
# This is just for initializing the gamma costs file
gammacosts_header = "#\n"*95
gammacosts_header += f'# Detuning: {self.detune/(1.602*10**(-22))} eV \n'
gammacosts_header += f'# Field Strength: {self.F/(10**5)} kV/cm \n'
gammacosts_header += f'# THz Frequency: {self.Thz_w/(10**9 * 2*np.pi)} GHz \n'
gammacosts_header += f'# NIR Wavelength: {self.nir_wl/(10**(-9))} nm \n'
gammacosts_header += 'Iteration, Gamma1, Gamma2, Cost Function, Imaginary, Real \n'
gammacosts_header += 'unitless, unitless, unitless, unitless, unitless \n'
# Creates origin frienldy header for gamma costs
np.savetxt(gc_fname, gammas_costs, delimiter = ',',
header = gammacosts_header, comments = '')
# create the gamma cost file
for gamma1 in gamma1_array:
for gamma2 in gamma2_array:
cost,imcost,recost = self.Q_cost_func(gamma1,gamma2,n,
Texp,crystalAngles,beta,gc_fname,Q_folder,ThetaSweep)
this_costngamma = np.array([gamma1,gamma2,cost,imcost,recost])
gamma_cost_array = np.vstack((gamma_cost_array,this_costngamma))
# calculates the cost for each gamma1/2 and adds the gamma1, gamma2,
# and cost to the overall array.
return gamma_cost_array
####################
# Fitting functions
####################
def gauss(x, *p):
"""
Gaussian fit function.
:param x: The independent variable
:type x: np.array, or int or float
:param p: [mean, area, width, y offset] to be unpacked
:type p: list of floats or ints
:return: Depends on x, returns another np.array or float or int
:rtype: type(x)
"""
mu, A, sigma, y0 = p
return (A / sigma) * np.exp(-(x - mu) ** 2 / (2. * sigma ** 2)) + y0
def lingauss(x, *p):
"""
Gaussian fit function with a linear offset
:param x: The independent variable
:type x: np.array, or int or float
:param p: [mean, area, width, constant offset of background, slope of background] to be unpacked
:type p: list of floats or ints
:return: Depends on x, returns another np.array or float or int
:rtype: type(x)
"""
mu, A, sigma, y0, m = p
return (A / sigma) * np.exp(-(x - mu) ** 2 / (2. * sigma ** 2)) + y0 + m * x
def lorentzian(x, *p):
"""
Lorentzian fit with constant offset
:param x: The independent variable
:type x: np.array, or int or float
:param p: [mean, area, width, constant offset of background, slope of background] to be unpacked
:type p: list of floats or ints
:return: Depends on x, returns another np.array or float or int
:rtype: type(x)
"""
mu, A, gamma, y0 = p
return (A / np.pi) * (gamma / ((x - mu) ** 2 + gamma ** 2)) + y0
def background(x, *p):
"""
Arbitrary pink-noise model background data for absorbance FFT
for the intention of replacing a peak in the FFT
with the background
:param x: The independent variable
:type x: np.array, or int or float
:param p: [proportionality factor, exponent of power law]
:type p: list of floats or ints
:return: Depends on x
:rtype: type(x)
"""
a, b = p
return a * (1 / x) ** b
def gaussWithBackground(x, *p):
"""
Gaussian with pink-noise background function
:param x: independent variable
:type x: np.array, or int or float
:param p: [mean, area, width, constant background, proportionality of power law, exponent of power law]
:type p: list of floats or ints
:return: Depends on x
:rtype: type(x)
"""
pGauss = p[:4]
a, b = p[4:]
return gauss(x, *pGauss) + background(x, a, b)
####################
# Collection functions
####################
def hsg_combine_spectra(spectra_list, verbose = False, **kwargs):
"""
This function is all about smooshing different parts of the same hsg
spectrum together. It takes a list of HighSidebandCCD spectra and turns the
zeroth spec_step into a FullHighSideband object. It then uses the function
stitch_hsg_dicts over and over again for the smooshing.
Input:
spectra_list = list of HighSidebandCCD objects that have sideband spectra
larger than the spectrometer can see.
Returns:
good_list = A list of FullHighSideband objects that have been combined as
much as can be.
:param spectra_list: randomly-ordered list of HSG spectra, some of which can be stitched together
:type spectra_list: List of HighSidebandCCD objects
kwargs gets passed onto add_item
:return: fully combined list of full hsg spectra. No PMT business yet.
:rtype: list of FullHighSideband
"""
good_list = []
spectra_list = spectra_list.copy()
spectra_list.sort(key=lambda x: x.parameters["spec_step"])
# keep a dict for each series' spec step
# This allows you to combine spectra whose spec steps
# change by values other than 1 (2, if you skip, or 0.5 if you
# decide to insert things, or arbitary strings)
spec_steps = {}
for elem in spectra_list:
# if verbose:
# print "Spec_step is", elem.parameters["spec_step"]
current_steps = spec_steps.get(elem.parameters["series"], [])
current_steps.append(elem.parameters["spec_step"])
spec_steps[elem.parameters["series"]] = current_steps
if verbose:
print("I found these spec steps for each series:")
print("\n\t".join("{}: {}".format(*ii) for ii in spec_steps.items()))
# sort the list of spec steps
for series in spec_steps:
spec_steps[series].sort()
same_freq = lambda x,y: x.parameters["fel_lambda"] == y.parameters["fel_lambda"]
for index in range(len(spectra_list)):
try:
temp = spectra_list.pop(0)
if verbose:
print("\nStarting with this guy", temp, "\n")
except:
break
good_list.append(FullHighSideband(temp))
counter = 1
temp_list = list(spectra_list)
for piece in temp_list:
if verbose:
print("\tchecking this spec_step", piece.parameters["spec_step"], end=' ')
print(", the counter is", counter)
if not same_freq(piece, temp):
if verbose:
print("\t\tnot the same fel frequencies ({} vs {})".format(piece.parameters["fel_lambda"], temp.parameters["fel_lambda"]))
continue
if temp.parameters["series"] == piece.parameters["series"]:
if piece.parameters["spec_step"] == spec_steps[temp.parameters["series"]][counter]:
if verbose:
print("I found this one", piece)
counter += 1
good_list[-1].add_CCD(piece, verbose=verbose, **kwargs)
spectra_list.remove(piece)
else:
print("\t\tNot the right spec step?", type(piece.parameters["spec_step"]))
else:
if verbose:
print("\t\tNot the same series ({} vs {}".format(
piece.parameters["series"],temp.parameters["series"]))
good_list[-1].make_results_array()
return good_list
def hsg_combine_spectra_arb_param(spectra_list, param_name="series", verbose = False):
"""
This function is all about smooshing different parts of the same hsg
spectrum together. It takes a list of HighSidebandCCD spectra and turns the
zeroth spec_step into a FullHighSideband object. It then uses the function
stitch_hsg_dicts over and over again for the smooshing.
This is different than hsg_combine_spectra in that you pass which
criteria distinguishes the files to be the "same". Since it can be any arbitrary
value, things won't be exactly the same (field strength will never be identical
between images). It will start with the first (lowest) spec step, then compare the
number of images in the next step. Whichever has
Input:
spectra_list = list of HighSidebandCCD objects that have sideband spectra
larger than the spectrometer can see.
Returns:
good_list = A list of FullHighSideband objects that have been combined as
much as can be.
:param spectra_list: randomly-ordered list of HSG spectra, some of which can be stitched together
:type spectra_list: list of HighSidebandCCD
:return: fully combined list of full hsg spectra. No PMT business yet.
:rtype: list of FullHighSideband
"""
if not spectra_list:
raise RuntimeError("Passed an empty spectra list!")
if isinstance(param_name, list):
# if you pass two things because the param you want
# is in a dict (e.g. field strength has mean/std)
# do it that way
param_name_list = list(param_name)
paramGetter = lambda x: x.parameters[param_name_list[0]][param_name_list[1]]
param_name = param_name[0]
elif isinstance(spectra_list[0].parameters[param_name], dict):
paramGetter = lambda x: x.parameters[param_name]["mean"]
else:
paramGetter = lambda x: x.parameters[param_name]
good_list = []
spectra_list.sort(key=lambda x: x.parameters["spec_step"])
# keep a dict for each spec step.
spec_steps = {}
for elem in spectra_list:
if verbose:
print("Spec_step is", elem.parameters["spec_step"])
current_steps = spec_steps.get(elem.parameters["spec_step"], [])
current_steps.append(elem)
spec_steps[elem.parameters["spec_step"]] = current_steps
# Next, loop over all of the elements. For each element, if it has not
# already been added to a spectra, look at all of the combinations from
# other spec steps to figure out which has the smallest overall deviation
# to make a new full spectrum
good_list = []
already_added = set()
for elem in spectra_list:
if elem in already_added: continue
already_added.add(elem)
good_list.append(FullHighSideband(elem))
other_spec_steps = [v for k, v in list(spec_steps.items()) if
k != good_list[-1].parameters["spec_step"]]
min_distance = np.inf
cur_value = paramGetter(good_list[-1])
best_match = None
for comb in itt.product(*other_spec_steps):
new_values = list(map(paramGetter, comb))
all_values = new_values + [cur_value]
if np.std(all_values) < min_distance:
min_distance = np.std(all_values)
best_match = list(comb)
if best_match is None:
raise RuntimeError("No matches found. Empty lists passed?")
best_values = list(map(paramGetter, best_match))
for spec in best_match:
print("Adding new spec step\n\tStarted with spec={},series={}".format(
good_list[-1].parameters["spec_step"],good_list[-1].parameters["series"]
))
print("\tAdding with spec={},series={}\n".format(
spec.parameters["spec_step"],
spec.parameters["series"]
))
print("\n\nfirst SBs:\n", good_list[-1].sb_results)
print("\n\nsecond SBs:\n", spec.sb_results)
good_list[-1].add_CCD(spec, True)
print("\n\nEnding SBs:\n", good_list[-1].sb_results)
already_added.add(spec)
best_match.append(good_list[-1])
best_values.append(cur_value)
new_value = np.mean(best_values)
new_std = np.std(best_values)
if isinstance(good_list[-1].parameters[param_name], dict):
best_values = np.array([x.parameters[param_name]["mean"] for x in best_match])
best_std = np.array([x.parameters[param_name]["std"] for x in best_match])
new_value = np.average(best_values, weights = best_std)
new_std = np.sqrt(np.average((best_values-new_value)**2, weights=best_std))
good_list[-1].parameters[param_name] = {
"mean": new_value,
"std": new_std
}
return good_list
def pmt_sorter(folder_path, plot_individual = True):
"""
This function will be fed a folder with a bunch of PMT data files in it.
The folder should contain a bunch of spectra with at least one sideband in
them, each differing by the series entry in the parameters dictionary.
This function will return a list of HighSidebandPMT objects.
:param folder_path: Path to a folder containing a bunch of PMT data, can be
part of a parameter sweep
:type folder_path: str
:param plot_individual: Whether to plot each sideband itself
:return: A list of all the possible hsg pmt spectra, organized by series tag
:rtype: list of HighSidebandPMT
"""
file_list = glob.glob(os.path.join(folder_path, '*[0-9].txt'))
pmt_list = []
plot_sb = lambda x: None
if plot_individual:
plt.figure("PMT data")
def plot_sb(spec):
spec = copy.deepcopy(spec)
spec.process_sidebands()
elem = spec.sb_dict[spec.initial_sb]
plt.errorbar(elem[:, 0], elem[:, 1], elem[:, 2],
marker='o',
label="{} {}, {}.{} ".format(
spec.parameters["series"], spec.initial_sb,
spec.parameters["pm_hv"],
't' if spec.parameters.get("photon counted", False) else 'f')
)
for sb_file in file_list:
temp = HighSidebandPMT(sb_file)
plot_sb(temp)
try:
for pmt_spectrum in pmt_list: # pmt_spectrum is a pmt object
if temp.parameters['series'] == pmt_spectrum.parameters['series']:
pmt_spectrum.add_sideband(temp)
break
else: # this will execute IF the break was NOT called
pmt_list.append(temp)
except:
pmt_list.append(temp)
# for sb_file in file_list:
# with open(sb_file,'rU') as f:
# param_str = ''
# line = f.readline()
# line = f.readline()
# while line[0] == '#':
# param_str += line[1:]
# line = f.readline()
#
# parameters = json.loads(param_str)
# try:
# for pmt_spectrum in pmt_list: # pmt_spectrum is a pmt object?
# if parameters['series'] == pmt_spectrum.parameters['series']:
# pmt_spectrum.add_sideband(sb_file)
# break
# else: # this will execute IF the break was NOT called
# pmt_list.append(HighSidebandPMT(sb_file))
# except:
# pmt_list.append(HighSidebandPMT(sb_file))
for pmt_spectrum in pmt_list:
pmt_spectrum.process_sidebands()
return pmt_list
def stitch_abs_results(main, new):
raise NotImplementedError
def hsg_combine_qwp_sweep(path, loadNorm = True, save = False, verbose=False,
skipOdds = True):
"""
Given a path to data taken from rotating the QWP (doing polarimetry),
process the data (fit peaks), and parse it into a matrix of sb strength vs
QWP angle vs sb number.
By default, saves the file into "Processed QWP Dependence"
Return should be passed directly into fitting
-1 | SB1 | SB1 | SB2 | SB2 | ... | ... | SBn | SBn |
angle1 | SB Strength | SB err | SB Strength | SB Err |
angle2 | ... | . |
.
.
.
:param path: Path to load
:param loadNorm: if true, load the normalized data
:param save: Save the processed file or not
:param verbose:
:param skipOdds: Passed on to save sweep; determine whether or not to save
odd orders. Generally, odds are artifacts and I don't want
them messing up the data, so default to True.
:return:
"""
def getData(fname):
"""
Helper function for loading the data and getting the header information for incident NIR stuff
:param fname:
:return:
"""
if isinstance(fname, str):
if loadNorm:
ending = "_norm.txt"
else:
ending = "_snip.txt"
header = ''
with open(os.path.join("Processed QWP Dependence", fname + ending)) as fh:
ln = fh.readline()
while ln[0] == '#':
header += ln[1:]
ln = fh.readline()
data = np.genfromtxt(os.path.join("Processed QWP Dependence", fname + ending),
delimiter=',', dtype=str)
if isinstance(fname, io.BytesIO):
header = b''
ln = fname.readline()
while ln.decode()[0] == '#':
header += ln[1:]
ln = fname.readline()
fname.seek(0)
data = np.genfromtxt(fname,
delimiter=',', dtype=str)
header = json.loads(header)
return data, float(header["lAlpha"]), float(header["lGamma"]), float(header["nir"]), float(header["thz"])
######### End getData
try:
sbData, lAlpha, lGamma, nir, thz = getData(path)
except:
# Do the processing on all the files
specs = proc_n_plotCCD(path, keep_empties=True, verbose=verbose)
for sp in specs:
try:
sp.parameters["series"] = round(float(sp.parameters["rotatorAngle"]), 2)
except KeyError:
# Old style of formatting
sp.parameters["series"] = round(float(sp.parameters["detectorHWP"]), 2)
specs = hsg_combine_spectra(specs, ignore_weaker_lowers=False)
if not save:
# If you don't want to save them, set everything up for doing Bytes objects
# to replacing saving files
full, snip, norm = io.BytesIO(), io.BytesIO(), io.BytesIO()
if "nir_pola" not in specs[0].parameters:
# in the olden days. Force them. Hopefully making them outside of ±360
# makes it obvious
specs[0].parameters["nir_pola"] = 361
specs[0].parameters["nir_polg"] = 361
keyName = "rotatorAngle"
if keyName not in specs[0].parameters:
# from back before I changed the name
keyName = "detectorHWP"
save_parameter_sweep(specs, [full, snip, norm], None,
keyName, "deg", wanted_indices=[3, 4],
header_dict={
"lAlpha": specs[0].parameters["nir_pola"],
"lGamma": specs[0].parameters["nir_polg"],
"nir": specs[0].parameters["nir_lambda"],
"thz": specs[0].parameters["fel_lambda"], },
only_even=skipOdds)
if loadNorm:
sbData, lAlpha, lGamma, nir, thz = getData(norm)
else:
sbData, lAlpha, lGamma, nir, thz = getData(snip)
else:
save_parameter_sweep(specs, os.path.basename(path), "Processed QWP Dependence",
"rotatorAngle", "deg", wanted_indices=[3, 4],
header_dict={
"lAlpha": specs[0].parameters["nir_pola"],
"lGamma": specs[0].parameters["nir_polg"],
"nir": specs[0].parameters["nir_lambda"],
"thz": specs[0].parameters["fel_lambda"], },
only_even=skipOdds)
sbData, lAlpha, lGamma, nir, thz = getData(os.path.basename(path))
laserParams = {
"lAlpha": lAlpha,
"lGamma": lGamma,
"nir": nir,
"thz": thz
}
# get which sidebands were found in this data set
# first two rows are origin header, second is sideband number
# (and empty strings, which is why the "if ii" below, to prevent
# ValueErrors on int('').
foundSidebands = np.array(sorted([float(ii) for ii in set(sbData[2]) if ii]))
# Remove first 3 rows, which are strings for origin header, and cast it to floats
sbData = sbData[3:].astype(float)
# double the sb numbers (to account for sb strength/error) and add a dummy
# number so the array is the same shape
foundSidebands = np.insert(foundSidebands, range(len(foundSidebands)), foundSidebands)
foundSidebands = np.insert(foundSidebands, 0, -1)
return laserParams, np.row_stack((foundSidebands, sbData))
def makeCurve(eta, isVertical):
"""
:param eta: QWP retardance at the wavelength
:return:
"""
cosd = lambda x: np.cos(x * np.pi / 180)
sind = lambda x: np.sin(x * np.pi / 180)
eta = eta * 2 * np.pi
if isVertical:
# vertical polarizer
def analyzerCurve(x, *S):
S0, S1, S2, S3 = S
return S0-S1/2*(1+np.cos(eta)) \
+ S3*np.sin(eta)*sind(2*x) \
+ S1/2*(np.cos(eta)-1)*cosd(4*x) \
+ S2/2*(np.cos(eta)-1)*sind(4*x)
else:
# vertical polarizer
def analyzerCurve(x, *S):
S0, S1, S2, S3 = S
return S0+S1/2*(1+np.cos(eta)) \
- S3*np.sin(eta)*sind(2*x) \
+ S1/2*(1-np.cos(eta))*cosd(4*x) \
+ S2/2*(1-np.cos(eta))*sind(4*x)
return analyzerCurve
def proc_n_fit_qwp_data(data, laserParams = dict(), wantedSBs = None, vertAnaDir = True, plot=False,
save = False, plotRaw = lambda sbidx, sbnum: False, series = '', eta=None, fourier = True,
**kwargs):
"""
Fit a set of sideband data vs QWP angle to get the stoke's parameters
:param data: data in the form of the return of hsg_combine_qwp_sweep
:param laserParams: dictionary of the parameters of the laser, the angles and frequencies. See function for
expected keys. I don't think the errors are used (except for plotting?), or the wavelengths (but
left in for potential future use (wavelength dependent stuff?))
:param wantedSBs: List of the wanted sidebands to fit out.
:param vertAnaDir: direction of the analzyer. True if vertical, false if horizontal.
:param plot: True/False to plot alpha/gamma/dop. Alternatively, a list of "a", "g", "d" to only plot selected ones
:param save: filename to save the files. Accepts BytesIO
:param plotRaw: callable that takes an index of the sb and sb number, returns true to plot the raw curve
:param series: a string to be put in the header for the origin files
:param eta: a function to call to calculate the desired retardance. Input will be the SB order.
:param fourier: Will use Fourier analysis over a fit funciton if True
if saveStokes is in kwargs and False, it will not save the stokes parameters, since I rarely actually use them.
:return:
"""
defaultLaserParams = {
"lAlpha": 90,
"ldAlpha": 0.2,
"lGamma": 0.0,
"ldGamma": 0.2,
"lDOP": 1,
"ldDOP": 0.02,
"nir": 765.7155,
"thz": 21.1
}
defaultLaserParams.update(laserParams)
lAlpha, ldAlpha, lGamma, ldGamma, lDOP, ldDOP = defaultLaserParams["lAlpha"], \
defaultLaserParams["ldAlpha"], \
defaultLaserParams["lGamma"], \
defaultLaserParams["ldGamma"], \
defaultLaserParams["lDOP"], \
defaultLaserParams["ldDOP"]
allSbData = data
angles = allSbData[1:, 0]
# angles += -5
# print("="*20)
# print("\n"*3)
# print(" WARNING")
# print("\n"*3)
# print("ANGLES HAVE BEEN MANUALLY OFFEST IN proc_n_fit_qwp_data")
# print("\n"*3)
# print("="*20)
allSbData = allSbData[:, 1:] # trim out the angles
if wantedSBs is None:
# set to get rid of duplicates, 1: to get rid of the -1 used for
# getting arrays the right shape
wantedSBs = set(allSbData[0, 1:])
if eta is None:
"""
It might be easier for the end user to do this by passing eta(wavelength) instead of eta(sborder),
but then this function would need to carry around wavelengths, which is extra work. It could convert
between NIR/THz wavelengths to SB order, but it's currently unclear whether you'd rather use what the WS6
claims, or what the sidebands say, and you'd probably want to take the extra step to ensure the SB fit rseults
if using the spectromter wavelengths. In general, if you have a function as etal(wavelength), you'd probably
want to pass this as
eta = lambda x: etal(1239.84/(nirEv + x*THzEv))
assuming nirEv/THzEv are the photon energies of the NIR/THz.
"""
eta = lambda x: 0.25
# allow pasing a flag it ignore odds. I think I generally do, so set it to
# default to True
skipOdds = kwargs.get("skip_odds", True)
# Make an array to keep all of the sideband information.
# Start it off by keeping the NIR information (makes for easier plotting into origin)
sbFits = [[0] + [-1] * 8 + [lAlpha, ldAlpha, lGamma, ldGamma, lDOP, ldDOP]]
# Also, for convenience, keep a dictionary of the information.
# This is when I feel like someone should look at porting this over to pandas
sbFitsDict = {}
sbFitsDict["S0"] = [[0, -1, -1]]
sbFitsDict["S1"] = [[0, -1, -1]]
sbFitsDict["S2"] = [[0, -1, -1]]
sbFitsDict["S3"] = [[0, -1, -1]]
sbFitsDict["alpha"] = [[0, lAlpha, ldAlpha]]
sbFitsDict["gamma"] = [[0, lGamma, ldGamma]]
sbFitsDict["DOP"] = [[0, lDOP, ldDOP]]
# Iterate over all sb data. Skip by 2 because error bars are included
for sbIdx in range(0, allSbData.shape[1], 2):
sbNum = allSbData[0, sbIdx]
if sbNum not in wantedSBs: continue
if skipOdds and sbNum%2: continue
# if verbose:
# print("\tlooking at sideband", sbNum)
sbData = allSbData[1:, sbIdx]
sbDataErr = allSbData[1:, sbIdx + 1]
if fourier:
# We want to do Fourier Analysis
# I've hard coded the maximum expected variance from QWP retardance to be
# 5 degrees (converted to radians bc of small angle approximation).
# Not sure how to deal with the fact that this method leaves no variance
# for the S3 paramter.
f0 = 0
f2 = 0
f4 = 0
df0 = 0
df2 = 0
df4 = 0
for k in range(0,16,1):
f0 = f0 + allSbData[k+1,sbIdx]
f2 = f2 + allSbData[k+1,sbIdx]*np.exp(-1j*np.pi*k/4)
f4 = f4 + allSbData[k+1,sbIdx]*np.exp(-1j*np.pi*k/2)
df0 = df0 + allSbData[k+1, sbIdx+1]
df2 = df2 + allSbData[k+1,sbIdx+1]*np.exp(-1j*np.pi*k/4)
df4 = df4 + allSbData[k+1,sbIdx+1]*np.exp(-1j*np.pi*k/2)
phi = 5*2*np.pi/180
# Generate the Stokes parameters from the Fourier Components
S0 = (f0 - 2*f4.real)/(np.pi)
S1 = 4*f4.real/(np.pi)
S2 = -4*f4.imag/(np.pi)
S3 = 2*f2.imag/(np.pi)
# For the Error Propagation, I say phi = 0 and dPhi = 2*phi (value set above)
d0 = np.sqrt(df0**2+2*(4*f4.real**2*phi**2+df4.real**2*(1+phi)**2*(1-1*phi)**2)/(1+phi)**4)/(2*np.pi)
d1 = np.sqrt((f4.real**2*phi**2+df4.real**2*phi**2)/(1+phi)**4)/(np.pi)
d2 = np.sqrt((f4.imag**2*phi**2+df4.imag**2*phi**2)/(1+phi)**4)/(np.pi)
d3 = 2*df2.imag/np.pi
# Calculate the alpha, gamma, DOP and errors from Stokes parameters
thisAlpha = np.arctan2(S2, S1) / 2 * 180. / np.pi
thisAlphaError = np.sqrt(d2 ** 2 * S1 ** 2 + d1 ** 2 * S2 ** 2) / (S1 ** 2 + S2 ** 2) * 180./np.pi
thisGamma = np.arctan2(S3, np.sqrt(S1 ** 2 + S2 ** 2)) / 2 * 180. / np.pi
thisGammaError = np.sqrt((d3 ** 2 * (S1 ** 2 + S2 ** 2) ** 2 + (d1 ** 2 * S1 ** 2 + d2 ** 2 * S2 ** 2) * S3 ** 2) / (
(S1 ** 2 + S2 ** 2) * (S1 ** 2 + S2 ** 2 + S3 ** 2) ** 2)) *180. /np.pi
thisDOP = np.sqrt(S1 ** 2 + S2 ** 2 + S3 ** 2) / S0
thisDOPerror = np.sqrt(((d1 ** 2 * S0 ** 2 * S1 ** 2 + d0 ** 2 * (S1 ** 2 + S2 ** 2 + S3 ** 2) ** 2 + S0 ** 2 * (
d2 ** 2 * S2 ** 2 + d3 ** 2 * S3 ** 2)) / (S0 ** 4 * (S1 ** 2 + S2 ** 2 + S3 ** 2))))
# Append The stokes parameters and errors to the dictionary output.
sbFitsDict["S0"].append([sbNum, S0, d0])
sbFitsDict["S1"].append([sbNum, S1, d1])
sbFitsDict["S2"].append([sbNum, S2, d2])
sbFitsDict["S3"].append([sbNum, S3, d3])
sbFitsDict["alpha"].append([sbNum, thisAlpha, thisAlphaError])
sbFitsDict["gamma"].append([sbNum, thisGamma, thisGammaError])
sbFitsDict["DOP"].append([sbNum, thisDOP, thisDOPerror])
toAppend = [sbNum, S0, d0, S1, d1, S2, d2, S3, d3, thisAlpha, thisAlphaError, thisGamma, thisGammaError, thisDOP, thisDOPerror]
sbFits.append(toAppend)
# Otherwise we will do the normal fit
else:
# try:
# p0 = sbFits[-1][1:8:2]
# except:
# p0 = [1, 1, 0, 0]
p0 = [1, 1, 0, 0]
etan = eta(sbNum)
try:
p, pcov = curve_fit(makeCurve(etan, vertAnaDir), angles, sbData, p0=p0)
except ValueError:
# This is getting tossed around, especially when looking at noisy data,
# especially with the laser line, and it's fitting erroneous values.
# Ideally, I should be cutting this out and not even returning them,
# but that's immedaitely causing
p = np.nan*np.array(p0)
pcov = np.eye(len(p))
if plot and plotRaw(sbIdx, sbNum):
# pg.figure("{}: sb {}".format(dataName, sbNum))
plt.figure("All Curves")
plt.errorbar(angles, sbData, sbDataErr, 'o-', name=f"{series}, {sbNum}")
# plt.plot(angles, sbData,'o-', label="Data")
fineAngles = np.linspace(angles.min(), angles.max(), 300)
# plt.plot(fineAngles,
# makeCurve(eta, "V" in dataName)(fineAngles, *p0), name="p0")
plt.plot(fineAngles,
makeCurve(etan, vertAnaDir)(fineAngles, *p))
# plt.show()
plt.ylim(0, 1)
plt.xlim(0, 360)
plt.ylabel("Normalized Intensity")
plt.xlabel("QWP Angle (θ)")
print(f"\t{series} {sbNum}, p={p}")
# get the errors
d = np.sqrt(np.diag(pcov))
thisData = [sbNum] + list(p) + list(d)
d0, d1, d2, d3 = d
S0, S1, S2, S3 = p
# reorder so errors are after values
thisData = [thisData[i] for i in [0, 1, 5, 2, 6, 3, 7, 4, 8]]
sbFitsDict["S0"].append([sbNum, S0, d0])
sbFitsDict["S1"].append([sbNum, S1, d1])
sbFitsDict["S2"].append([sbNum, S2, d2])
sbFitsDict["S3"].append([sbNum, S3, d3])
# append alpha value
thisData.append(np.arctan2(S2, S1) / 2 * 180. / np.pi)
# append alpha error
variance = (d2 ** 2 * S1 ** 2 + d1 ** 2 * S2 ** 2) / (S1 ** 2 + S2 ** 2) ** 2
thisData.append(np.sqrt(variance) * 180. / np.pi)
sbFitsDict["alpha"].append([sbNum, thisData[-2], thisData[-1]])
# append gamma value
thisData.append(np.arctan2(S3, np.sqrt(S1 ** 2 + S2 ** 2)) / 2 * 180. / np.pi)
# append gamma error
variance = (d3 ** 2 * (S1 ** 2 + S2 ** 2) ** 2 + (d1 ** 2 * S1 ** 2 + d2 ** 2 * S2 ** 2) * S3 ** 2) / (
(S1 ** 2 + S2 ** 2) * (S1 ** 2 + S2 ** 2 + S3 ** 2) ** 2)
thisData.append(np.sqrt(variance) * 180. / np.pi)
sbFitsDict["gamma"].append([sbNum, thisData[-2], thisData[-1]])
# append degree of polarization
thisData.append(np.sqrt(S1 ** 2 + S2 ** 2 + S3 ** 2) / S0)
variance = ((d1 ** 2 * S0 ** 2 * S1 ** 2 + d0 ** 2 * (S1 ** 2 + S2 ** 2 + S3 ** 2) ** 2 + S0 ** 2 * (
d2 ** 2 * S2 ** 2 + d3 ** 2 * S3 ** 2)) / (S0 ** 4 * (S1 ** 2 + S2 ** 2 + S3 ** 2)))
thisData.append(np.sqrt(variance))
sbFitsDict["DOP"].append([sbNum, thisData[-2], thisData[-1]])
sbFits.append(thisData)
sbFits = np.array(sbFits)
sbFitsDict = {k: np.array(v) for k, v in sbFitsDict.items()}
# This chunk used to insert the "alpha deviation", the difference between the angles and the
# nir. I don't think I use this anymore, so stop saving it
# origin_header = 'Sideband,S0,S0 err,S1,S1 err,S2,S2 err,S3,S3 err,alpha,alpha deviation,alpha err,gamma,gamma err,DOP,DOP err\n'
# origin_header += 'Order,arb.u,arb.u,arb.u,arb.u,arb.u,arb.u,arb.u,arb.u,deg,deg,deg,deg,deg,arb.u.,arb.u.\n'
# origin_header += 'Sideband,{},{},{},{},{},{},{},{},{},{},{},{},{},{},{}'.format(*["{}".format(series)] * 15)
# sbFits = np.array(sbFits)
# sbFits = np.insert(sbFits, 10, sbFits[:, 9] - lAlpha, axis=1)
# sbFits = sbFits[sbFits[:, 0].argsort()]
origin_header = "#\n"*100 # to fit all other files for easy origin importing
origin_header += 'Sideband,S0,S0 err,S1,S1 err,S2,S2 err,S3,S3 err,alpha,alpha err,gamma,gamma err,DOP,DOP err\n'
origin_header += 'Order,arb.u,arb.u,arb.u,arb.u,arb.u,arb.u,arb.u,arb.u,deg,deg,deg,deg,arb.u.,arb.u.\n'
origin_header += 'Sideband,{},{},{},{},{},{},{},{},{},{},{},{},{},{}'.format(*["{}".format(series)] * 14)
sbFits = sbFits[sbFits[:, 0].argsort()]
if isinstance(save, str):
sbFitsSave = sbFits
if not kwargs.get("saveStokes", True):
headerlines = origin_header.splitlines()
ln, units, coms = headerlines[-3:]
ln = ','.join([ln.split(',')[0]] + ln.split(',')[9:])
units = ','.join([units.split(',')[0]] + units.split(',')[9:])
coms = ','.join([coms.split(',')[0]] + coms.split(',')[9:])
headerlines[-3:] = ln, units, coms
# remove them from the save data
origin_header = '\n'.join(headerlines)
sbFitsSave = np.delete(sbFits, range(1, 9), axis=1)
if not os.path.exists(os.path.dirname(save)):
os.mkdir(os.path.dirname(save))
np.savetxt(save, np.array(sbFitsSave), delimiter=',', header=origin_header,
comments='', fmt='%.6e')
# print("a = {:.2f} ± {:.2f}".format(sbFits[1, 9], sbFits[1, 10]))
# print("g = {:.2f} ± {:.2f}".format(sbFits[1, 11], sbFits[1, 12]))
if plot:
plt.figure("alpha")
plt.errorbar(sbFitsDict["alpha"][:, 0],
sbFitsDict["alpha"][:, 1],
sbFitsDict["alpha"][:, 2],
'o-', name = series
)
plt.figure("gamma")
plt.errorbar(sbFitsDict["gamma"][:, 0],
sbFitsDict["gamma"][:, 1],
sbFitsDict["gamma"][:, 2],
'o-', name=series
)
return sbFits, sbFitsDict
####################
# Helper functions
####################
def fvb_crr(raw_array, offset=0, medianRatio=1, noiseCoeff=5, debugging=False):
"""
Remove cosmic rays from a sequency of identical exposures
:param raw_array: The array to be cleaned. Successive spectra should
be the columns (i.e. 1600 x n) of the raw_array
:param offset: baseline to add to raw_array.
Not used, but here if it's needed in the future
:param medianRatio: Multiplier to the median when deciding a cutoff
:param noiseCoeff: Multiplier to the noise on the median
May need changing for noisy data
:return:
"""
d = np.array(raw_array)
med = ndimage.filters.median_filter(d, size=(1, d.shape[1]), mode='wrap')
med = np.median(d, axis=1).reshape(d.shape[0], 1)
if debugging:
print("shape of median filter:", med.shape)
meanMedian = med.mean(axis=1)
# meanMedian = med.copy()
if debugging:
print("shape of meaned median filter:", meanMedian.shape)
# Construct a cutoff for each pixel. It was kind of guess and
# check
cutoff = meanMedian * medianRatio + noiseCoeff * np.std(meanMedian[-100:])
if debugging:
print("shape of cutoff criteria:", cutoff.shape)
import pyqtgraph as pg
winlist = []
app = pg.QtGui.QApplication([])
win = pg.GraphicsLayoutWidget()
win.setWindowTitle("Raw Image")
p1 = win.addPlot()
img = pg.ImageItem()
img.setImage(d.copy().T)
p1.addItem(img)
hist = pg.HistogramLUTItem()
hist.setImageItem(img)
win.addItem(hist)
win.nextRow()
p2 = win.addPlot(colspan=2)
p2.setMaximumHeight(250)
p2.addLegend()
for i, v in enumerate(d.T):
p2.plot(v, pen=(i, d.shape[1]), name=str(i))
p2.plot(np.sum(d, axis=1), pen=pg.mkPen('w', width=3))
win.show()
winlist.append(win)
win2 = pg.GraphicsLayoutWidget()
win2.setWindowTitle("Median Image")
p1 = win2.addPlot()
img = pg.ImageItem()
img.setImage(med.T)
p1.addItem(img)
hist = pg.HistogramLUTItem()
hist.setImageItem(img)
win2.addItem(hist)
win2.nextRow()
p2 = win2.addPlot(colspan=2)
p2.setMaximumHeight(250)
p2.plot(np.sum(med, axis=1) / d.shape[1])
win2.show()
winlist.append(win2)
win2 = pg.GraphicsLayoutWidget()
win2.setWindowTitle("d-m")
p1 = win2.addPlot()
img = pg.ImageItem()
img.setImage((d - med).T)
p1.addItem(img)
hist = pg.HistogramLUTItem()
hist.setImageItem(img)
win2.addItem(hist)
win2.nextRow()
p2 = win2.addPlot(colspan=2)
p2.setMaximumHeight(250)
p2.addLegend()
for i, v in enumerate((d - med).T):
p2.plot(v, pen=(i, d.shape[1]), name=str(i))
p2.plot(cutoff, pen=pg.mkPen('w', width=3))
win2.show()
winlist.append(win2)
# Find the bad pixel positions
# Note the [:, None] - needed to cast the correct shapes
badPixs = np.argwhere((d - med) > (cutoff.reshape(len(cutoff), 1)))
for pix in badPixs:
# get the other pixels in the row which aren't the cosmic
if debugging:
print("cleaning pixel", pix)
p = d[pix[0], [i for i in range(d.shape[1]) if not i == pix[1]]]
if debugging:
print("\tRemaining pixels in row are", p)
# Replace the cosmic by the average of the others
# Could get hairy if more than one cosmic per row.
# Maybe when doing many exposures?
d[pix[0], pix[1]] = np.mean(p)
if debugging:
win = pg.GraphicsLayoutWidget()
win.setWindowTitle("Clean Image")
p1 = win.addPlot()
img = pg.ImageItem()
img.setImage(d.copy().T)
p1.addItem(img)
hist = pg.HistogramLUTItem()
hist.setImageItem(img)
win.addItem(hist)
win.nextRow()
p2 = win.addPlot(colspan=2)
p2.setMaximumHeight(250)
p2.plot(np.sum(d, axis=1))
win.show()
winlist.append(win)
app.exec_()
return np.array(d)
def stitchData(dataList, plot=False):
"""
Attempt to stitch together absorbance data. Will translate the second data set
to minimize leastsq between the two data sets.
:param dataList: Iterable of the data sets to be fit. Currently
it only takes the first two elements of the list, but should be fairly
straightforward to recursivly handle a list>2. Shifts the second
data set to overlap the first
elements of dataList can be either np.arrays or Absorbance class,
where it will take the proc_data itself
:param plot: bool whether or not you want the fit iterations to be plotted
(for debugging)
:return: a, a (2,) np.array of the shift
"""
# Data coercsion, make sure we know what we're working wtih
first = dataList[0]
if isinstance(first, Absorbance):
first = first.proc_data
second = dataList[1]
if isinstance(second, Absorbance):
second = second.proc_data
if plot:
# Keep a reference to whatever plot is open at call-time
# Useful if the calling script has plots before and after, as
# omitting this will cause future plots to be added to figures here
firstFig = plt.gcf()
plt.figure("Stitcher")
# Plot the raw input data
plt.plot(*first.T)
plt.plot(*second.T)
# Algorithm is set up such that the "second" data set spans the
# higher domain than first. Need to enforce this, and remember it
# so the correct shift is applied
flipped = False
if max(first[:, 0]) > max(second[:, 0]):
flipped = True
first, second = second, first
def stitch_hsg_dicts(full_obj, new_obj, need_ratio=False, verbose=False, ratios=[1,1],
override_ratio = False, ignore_weaker_lowers = True):
"""
This helper function takes a FullHighSideband and a sideband
object, either CCD or PMT and smushes the new sb_results into the full_dict.
The first input doesn't change, so f there's a PMT set of data involved, it
should be in the full variable to keep the laser normalization intact.
This function almost certainly does not work for stitching many negative orders
in it's current state
11/14/16
--------
This function has been updated to take the CCD objects themselves to be more
intelligent about stitching. Consider two scans, (a) spec step 0 with 1 gain, spec
step 2 with 110 gain and (b) spec step 0 with 50 gain and spec step 1 with 110 gain.
The old version would always take spec step 0 to scale to, so while comparisons
between spec step 0 and 1 for either case is valid, comparison between (a) and (b)
were not, since they were scaled to different gain parameters. This new code will
check what the gain values are and scale to the 110 data set, if present. This seems
valid because we currently always have a 110 gain exposure for higher order
sidebands.
The exception is if the laser is present (sideband 0), as that is an absolute
measure to which all else should be related.
TODO: run some test cases to test this.
06/11/18
--------
That sometimes was breaking if there were only 3-4 sidebands to fit with poor
SNR. I've added the override_ratio to be passed to set a specific ratio to scale
by. From data on 06/03/18, the 50gain to 110gain is a ~3.6 ratio. I haven't done
a clean way of specifying which data set it should be scaled. Right now,
it leaves the laser line data, or the 110 gain data alone.
Inputs:
full = full_dict from FullHighSideband, or HighSidebandPMT. It's important
that it contains lower orders than the new_dict.
new_dict = another full_dict.
need_ratio = If gain or other parameters aren't equal and must resort to
calculating the ratio instead of the measurements being equivalent.
Changing integration time still means N photons made M counts,
but changing gain or using PMT or whatever does affect things.
ratios: Will update with the values to the ratios needed to scale the data.
ratios[0] is the ratio for the "full_obj"
ratios[1] is the ratio for the "new_obj"
one of them will be one, one will be the appropriate scale, since one of
them is unscaled. This is strictly speaking an output
override_ratio: Pass a float to specify the ratio that should be used.
ignore_weaker_lowers: Sometimes, a SB is in the short pass filter so a lower
order is weaker than the next highest. If True, causes script to ignore all
sidebands which are weaker and lower order.
Returns:
full = extended version of the input full. Overlapping sidebands are
averaged because that makes sense?
"""
if isinstance(full_obj, dict) and isinstance(new_obj, dict):
return stitch_hsg_dicts_old(full_obj, new_obj, need_ratio, verbose)
if verbose:
print("=" * 15)
print()
print("Stitching HSG dicts")
print()
print("=" * 15)
# remove potentially offensive SBs, i.e. a 6th order SB being in the SPF for more
# data, but being meaningless to pull intensity information from.
# Note: this might not be the best if you get to higher order stitches where it's
# possible that the sidebands might not be monotonic (from noise?)
if ignore_weaker_lowers:
full_obj.full_dict, full_obj.sb_results = FullHighSideband.parse_sb_array(full_obj.sb_results)
new_obj.new_dict, new_obj.sb_results = FullHighSideband.parse_sb_array(new_obj.sb_results)
# was fucking around with references and causing updates to arrays when it shouldn't
# be
full = copy.deepcopy(full_obj.full_dict)
new_dict = copy.deepcopy(new_obj.full_dict)
# Force a rescaling if you've passed a specified parameter
# if isinstance(override_ratio, float):
# need_ratio = True
# Do some testing to see which dict should be scaled to the other
# I honestly forget why I prioritized the PMT first like this. But the third
# check looks to make a gain 110 prioritize non-110, unless the non-110 includes
# a laser line
scaleTo = ""
if need_ratio:
if isinstance(new_obj, HighSidebandPMT):
scaleTo = "new"
elif isinstance(full_obj, HighSidebandPMT):
scaleTo = "full"
elif new_obj.parameters["gain"] == 110 and full_obj.parameters["gain"] != 110 \
and 0 not in full:
scaleTo = "new"
else:
scaleTo = "full"
if verbose:
print("\tI'm adding these sidebands", new_obj.sb_results[:,0])
print("\t With these:", sorted(full.keys()))
overlap = [] # The list that hold which orders are in both dictionaries
missing = [] # How to deal with sidebands that are missing from full but in new.
for new_sb in new_obj.sb_results[:,0]:
full_sbs = sorted(full.keys())
if new_sb in full_sbs:
overlap.append(new_sb)
elif new_sb not in full_sbs and new_sb < full_sbs[-1]:
# This probably doesn't work with bunches of negative orders
missing.append(new_sb)
if verbose:
print("\t ( overlap:", overlap, ")")
print("\t ( missing:", missing, ")")
# This if-else clause handles how to average together overlapping sidebands
# which are seen in both spectra,
if need_ratio:
# Calculate the appropriate ratio to multiply the new sidebands by.
# I'm not entirely sure what to do with the error of this guy.
ratio_list = []
try:
new_starter = overlap[-1]
if verbose:
print("\n\tadding these ratios,", end=' ')
if len(overlap) > 2:
overlap = [x for x in overlap if (x % 2 == 0)
]# and (x != min(overlap) and (x != max(overlap)))]
if scaleTo == "new":
if verbose:
print("scaling to new :")
for sb in overlap:
ratio_list.append(new_dict[sb][2]/full[sb][2])
if verbose:
print("\t\t{:2.0f}: {:.3e}/{:.3e} ~ {:.3e},".format(sb, new_dict[sb][2],
full[sb][2], ratio_list[-1]))
# new_ratio = 1 06/11/18 Not sure what these were used for
ratio = np.mean(ratio_list)
else:
if verbose:
print("scaling to full:")
for sb in overlap:
ratio_list.append(full[sb][2] / new_dict[sb][2])
if verbose:
print("\t\t{:2.0f}: {:.3e}/{:.3e} ~ {:.3e},".format(sb, full[sb][2],
new_dict[sb][2], ratio_list[-1]))
# new_ratio = np.mean(ratio_list) 06/11/18 Not sure what these were used for
ratio = np.mean(ratio_list)
# Maybe not the best way to do it, performance wise, since you still
# iterate through the list, even though you'll override it.
if isinstance(override_ratio, float):
ratio = override_ratio
if verbose:
print("overriding calculated ratio with user inputted")
error = np.std(ratio_list) / np.sqrt(len(ratio_list))
except IndexError:
# If there's no overlap (which you shouldn't let happen), hardcode a ratio
# and error. I looked at all the ratios for the overlaps from 6/15/16
# (540ghz para) to get the rough average. Hopefully they hold for all data.
if not overlap:
ratio = 0.1695
error = 0.02
# no overlap, so make sure it grabs all the sidebands
new_starter = min(new_dict.keys())
else:
raise
if verbose:
# print "Ratio list\n\t", ("{:.3g}, "*len(ratio_list))[:-2].format(*ratio_list)
# print "Overlap \n\t", [round(ii, 3) for ii in overlap]
print("\t Ratio: {:.3g} +- {:.3g} ({:.2f}%)\n".format(ratio, error, error/ratio*100))
# Adding the new sidebands to the full set and moving errors around.
# I don't know exactly what to do about the other aspects of the sidebands
# besides the strength and its error.
if scaleTo == "full":
ratios[1] = ratio
for sb in overlap:
if verbose:
print("For SB {:02d}, original strength is {:.3g} +- {:.3g} ({:.3f}%)".format(int(sb), new_dict[sb][2], new_dict[sb][3],
new_dict[sb][3]/new_dict[sb][2]*100
))
new_dict[sb][3] = ratio * new_dict[sb][2] * np.sqrt((error / ratio) ** 2 + (new_dict[sb][3] / new_dict[sb][2]) ** 2)
new_dict[sb][2] = ratio * new_dict[sb][2]
if verbose:
print("\t\t scaled\t\t\t\t{:.3g} +- {:.3g} ({:.3f}%)".format(new_dict[sb][2],
new_dict[sb][3],
new_dict[sb][3]/new_dict[sb][2]*100))
print("\t\t full\t\t\t\t\t{:.3g} +- {:.3g} ({:.3f}%)".format(full[sb][2],
full[sb][3],
full[sb][3]/full[sb][2]*100))
sb_error = np.sqrt(full[sb][3] ** (-2) + new_dict[sb][3] ** (-2)) ** (-1)
avg = (full[sb][2] / (full[sb][3] ** 2) + new_dict[sb][2] / (
new_dict[sb][3] ** 2)) / (full[sb][3] ** (-2) + new_dict[sb][3] ** (-2))
full[sb][2] = avg
full[sb][3] = sb_error
if verbose:
print("\t\t replaced with \t\t{:.3g} +- {:.3g} ({:.3f}%)".format(full[sb][2],
full[sb][3],
full[sb][3]/full[sb][2]*100))
print()
lw_error = np.sqrt(full[sb][5] ** (-2) + new_dict[sb][5] ** (-2)) ** (-1)
lw_avg = (full[sb][4] / (full[sb][5] ** 2) + new_dict[sb][4] / (
new_dict[sb][5] ** 2)) / (
full[sb][5] ** (-2) + new_dict[sb][5] ** (-2))
full[sb][4] = lw_avg
full[sb][5] = lw_error # This may not be the exactly right way to calculate the error
else:
ratios[0] = ratio
for sb in overlap:
full[sb][3] = ratio * full[sb][2] * np.sqrt((error / ratio) ** 2 + (full[sb][3] / full[sb][2]) ** 2)
full[sb][2] = ratio * full[sb][2]
sberror = np.sqrt(full[sb][3] ** (-2) + new_dict[sb][3] ** (-2)) ** (-1)
avg = (full[sb][2] / (full[sb][3] ** 2) + new_dict[sb][2] / (
new_dict[sb][3] ** 2)) / (full[sb][3] ** (-2) + new_dict[sb][3] ** (-2))
full[sb][2] = avg
full[sb][3] = sberror
lw_error = np.sqrt(full[sb][5] ** (-2) + new_dict[sb][5] ** (-2)) ** (-1)
lw_avg = (full[sb][4] / (full[sb][5] ** 2) + new_dict[sb][4] / (
new_dict[sb][5] ** 2)) / (
full[sb][5] ** (-2) + new_dict[sb][5] ** (-2))
full[sb][4] = lw_avg
full[sb][5] = lw_error # This may not be the exactly right way to calculate the error
else: # not needing a new ratio
try:
new_starter = overlap[-1] # This grabs the sideband order where only the new dictionary has
# sideband information. It's not clear why it necessarily has to be
# at this line.
overlap = [x for x in overlap if (x % 2 == 0)
] # and (x != min(overlap) and (x != max(overlap)))]
# This cuts out the lowest order sideband in the overlap for mysterious reasons
for sb in overlap: # This for loop average two data points weighted by their relative errors
if verbose:
print("The sideband", sb)
print("Old value", full[sb][4] * 1000)
print("Add value", new_dict[sb][4] * 1000)
try:
error = np.sqrt(full[sb][3] ** (-2) + new_dict[sb][3] ** (-2)) ** (-1)
avg = (full[sb][2] / (full[sb][3] ** 2) + new_dict[sb][2] / (new_dict[sb][3] ** 2)) / (
full[sb][3] ** (-2) + new_dict[sb][3] ** (-2))
full[sb][2] = avg
full[sb][3] = error
except RuntimeWarning:
raise IOError()
lw_error = np.sqrt(full[sb][5] ** (-2) + new_dict[sb][5] ** (-2)) ** (-1)
lw_avg = (full[sb][4] / (full[sb][5] ** 2) + new_dict[sb][4] / (new_dict[sb][5] ** 2)) / (
full[sb][5] ** (-2) + new_dict[sb][5] ** (-2))
full[sb][4] = lw_avg
full[sb][5] = lw_error # This may not be the exactly right way to calculate the error
if verbose:
print("New value", lw_avg * 1000)
except:
new_starter = 0 # I think this makes things work when there's no overlap
if verbose:
print("appending new elements. new_starter={}".format(new_starter))
for sb in [x for x in list(new_dict.keys()) if ((x > new_starter) or (x in missing))]:
full[sb] = new_dict[sb]
if scaleTo == "full":
full[sb][2] = ratio * full[sb][2]
full[sb][3] = full[sb][2] * np.sqrt((error / ratio) ** 2 + (ratio * full[sb][3] / full[sb][2]) ** 2)
if scaleTo == "new":
for sb in set(full.keys()) - set(sorted(new_dict.keys())[:]):
full[sb][2] *= ratio
# TODO: I think this is an invalid error
# propagation (since ratio has error associated with it
full[sb][3] *= ratio
if verbose:
print("I made this dictionary", sorted(full.keys()))
print('-'*19)
return full
return full, ratio #the fuck? Why was this here?
return full
def stitch_hsg_dicts_old(full, new_dict, need_ratio=False, verbose=False):
"""
This helper function takes a FullHighSideband.full_dict attribute and a sideband
object, either CCD or PMT and smushes the new sb_results into the full_dict.
The first input doesn't change, so f there's a PMT set of data involved, it
should be in the full variable to keep the laser normalization intact.
This function almost certainly does not work for stitching many negative orders
in it's current state
11/14/16
--------
The original function has been updated to take the full object (instead of
the dicts alone) to better handle calculating ratios when stitching. This is called
once things have been parsed in the original function (or legacy code where dicts
are passed instead of the object)
Inputs:
full = full_dict from FullHighSideband, or HighSidebandPMT. It's important
that it contains lower orders than the new_dict.
new_dict = another full_dict.
need_ratio = If gain or other parameters aren't equal and must resort to
calculating the ratio instead of the measurements being equivalent.
Changing integration time still means N photons made M counts,
but changing gain or using PMT or whatever does affect things.
Returns:
full = extended version of the input full. Overlapping sidebands are
averaged because that makes sense?
"""
if verbose:
print("I'm adding these sidebands in old stitcher", sorted(new_dict.keys()))
overlap = [] # The list that hold which orders are in both dictionaries
missing = [] # How to deal with sidebands that are missing from full but in new.
for new_sb in sorted(new_dict.keys()):
full_sbs = sorted(full.keys())
if new_sb in full_sbs:
overlap.append(new_sb)
elif new_sb not in full_sbs and new_sb < full_sbs[-1]:
# This probably doesn't work with bunches of negative orders
missing.append(new_sb)
if verbose:
print("overlap:", overlap)
print("missing:", missing)
# This if-else clause handles how to average together overlapping sidebands
# which are seen in both spectra,
if need_ratio:
# Calculate the appropriate ratio to multiply the new sidebands by.
# I'm not entirely sure what to do with the error of this guy.
ratio_list = []
#print '\n1979\nfull[2]', full[0][2]
try:
new_starter = overlap[-1]
if len(overlap) > 2:
overlap = [x for x in overlap if (x % 2 == 0)
]#and (x != min(overlap) and (x != max(overlap)))]
for sb in overlap:
ratio_list.append(full[sb][2] / new_dict[sb][2])
ratio = np.mean(ratio_list)
# print
# print '-'*15
# print "ratio for {}: {}".format()
error = np.std(ratio_list) / np.sqrt(len(ratio_list))
except IndexError:
# If there's no overlap (which you shouldn't let happen),
# hardcode a ratio and error.
# I looked at all the ratios for the overlaps from 6/15/16
# (540ghz para) to get the rough average. Hopefully they hold
# for all data.
if not overlap:
ratio = 0.1695
error = 0.02
# no overlap, so make sure it grabs
# all the sidebands
new_starter = min(new_dict.keys())
else:
raise
if verbose:
print("Ratio list","\n", [round(ii, 3) for ii in ratio_list])
print("Overlap ","\n", [round(ii, 3) for ii in overlap])
print("Ratio", ratio)
print("Error", error)
#print '\n2118\nfull[2]', full[0][2]
# Adding the new sidebands to the full set and moving errors around.
# I don't know exactly what to do about the other aspects of the sidebands
# besides the strength and its error.
for sb in overlap:
full[sb][2] = ratio * new_dict[sb][2]
full[sb][3] = full[sb][2] * np.sqrt((error / ratio) ** 2 + (new_dict[sb][3] / new_dict[sb][2]) ** 2)
#print '\n2125\nfull[2]', full[0][3]
# Now for linewidths
lw_error = np.sqrt(full[sb][5] ** (-2) + new_dict[sb][5] ** (-2)) ** (-1)
lw_avg = (full[sb][4] / (full[sb][5] ** 2) + new_dict[sb][4] / (new_dict[sb][5] ** 2)) / (
full[sb][5] ** (-2) + new_dict[sb][5] ** (-2))
full[sb][4] = lw_avg
full[sb][5] = lw_error
#print '\n2132\nfull[2]', full[0][2]
else:
try:
new_starter = overlap[-1] # This grabs the sideband order where only the new dictionary has
# sideband information. It's not clear why it necessarily has to be
# at this line.
overlap = [x for x in overlap if (x % 2 == 0) and (x != min(overlap) and (x != max(overlap)))]
# This cuts out the lowest order sideband in the overlap for mysterious reasons
for sb in overlap: # This for loop average two data points weighted by their relative errors
if verbose:
print("The sideband", sb)
print("Old value", full[sb][4] * 1000)
print("Add value", new_dict[sb][4] * 1000)
error = np.sqrt(full[sb][3] ** (-2) + new_dict[sb][3] ** (-2)) ** (-1)
avg = (full[sb][2] / (full[sb][3] ** 2) + new_dict[sb][2] / (new_dict[sb][3] ** 2)) / (
full[sb][3] ** (-2) + new_dict[sb][3] ** (-2))
full[sb][2] = avg
full[sb][3] = error
lw_error = np.sqrt(full[sb][5] ** (-2) + new_dict[sb][5] ** (-2)) ** (-1)
lw_avg = (full[sb][4] / (full[sb][5] ** 2) + new_dict[sb][4] / (new_dict[sb][5] ** 2)) / (
full[sb][5] ** (-2) + new_dict[sb][5] ** (-2))
full[sb][4] = lw_avg
full[sb][5] = lw_error # This may not be the exactly right way to calculate the error
if verbose:
print("New value", lw_avg * 1000)
except:
new_starter = 0 # I think this makes things work when there's no overlap
if verbose:
print("appending new elements. new_starter={}".format(new_starter))
# This loop will add the sidebands which were only seen in the second step
for sb in [x for x in list(new_dict.keys()) if ((x >= new_starter) or (x in missing))]:
full[sb] = new_dict[sb]
if need_ratio:
full[sb][2] = ratio * full[sb][2]
full[sb][3] = full[sb][2] * np.sqrt((error / ratio) ** 2 + (ratio * full[sb][3] / full[sb][2]) ** 2)
#print '\n2164\nfull[2]', full[0][2]
if verbose:
print("I made this dictionary", sorted(full.keys()))
return full
def save_parameter_sweep_no_sb(spectrum_list, file_name, folder_str, param_name, unit,
verbose=False):
"""
This function will take a fully processed list of spectrum objects and
slice Spectrum.sb_fits appropriately to get an output like:
"Parameter" | SB1 freq | err | SB1 amp | error | SB1 linewidth | error | SB2...| SBn...|
param1 | . |
param2 | . |
.
.
.
Currently I'm thinking fuck the offset y0
After constructing this large matrix, it will save it somewhere.
"""
spectrum_list.sort(key=lambda x: x.parameters[param_name])
included_spectra = dict()
param_array = None
sb_included = []
for spec in spectrum_list:
sb_included = sorted(list(set(sb_included + list(spec.full_dict.keys()))))
included_spectra[spec.fname.split('/')[-1]] = spec.parameters[param_name]
# If these are from summed spectra, then only the the first file name
# from that sum will show up here, which should be fine?
if verbose:
# print "full name:", spectrum_list[0].fname
print("included names:", included_spectra)
print("sb_included:", sb_included)
for spec in spectrum_list:
temp_dict = {} # This is different from full_dict in that the list has the
# sideband order as the zeroth element.
if verbose:
print("the sb_results:", spec.sb_results)
if spec.sb_results.ndim == 1: continue
for index in range(len(spec.sb_results[:, 0])):
if verbose:
print("my array slice:", spec.sb_results[index, :])
temp_dict[int(round(spec.sb_results[index, 0]))] = np.array(
spec.sb_results[index, 1:])
if verbose:
print(temp_dict)
for sb in sb_included:
blank = np.zeros(6)
# print "checking sideband order:", sb
# print "blank", blank
if sb not in temp_dict:
# print "\nNeed to add sideband order:", sb
temp_dict[sb] = blank
try: # Why is this try-except here?
spec_data = np.array([float(spec.parameters[param_name])])
except:
spec_data = np.array([float(spec.parameters[param_name][:2])])
for key in sorted(temp_dict.keys()):
# print "I am going to hstack this:", temp_dict[key]
spec_data = np.hstack((spec_data, temp_dict[key]))
try:
param_array = np.vstack((param_array, spec_data))
except:
param_array = np.array(spec_data)
if verbose:
print("The shape of the param_array is:", param_array.shape)
# print "The param_array itself is:", param_array
'''
param_array_norm = np.array(param_array).T # python iterates over rows
for elem in [x for x in xrange(len(param_array_norm)) if (x-1)%7 == 3]:
temp_max = np.max(param_array_norm[elem])
param_array_norm[elem] = param_array_norm[elem] / temp_max
param_array_norm[elem + 1] = param_array_norm[elem + 1] / temp_max
'''
snipped_array = param_array[:, 0]
norm_array = param_array[:, 0]
if verbose:
print("Snipped_array is", snipped_array)
for ii in range(len(param_array.T)):
if (ii - 1) % 6 == 0:
if verbose:
print("param_array shape", param_array[:, ii])
snipped_array = np.vstack((snipped_array, param_array[:, ii]))
norm_array = np.vstack((norm_array, param_array[:, ii]))
elif (ii - 1) % 6 == 2:
snipped_array = np.vstack((snipped_array, param_array[:, ii]))
temp_max = np.max(param_array[:, ii])
norm_array = np.vstack((norm_array, param_array[:, ii] / temp_max))
elif (ii - 1) % 6 == 3:
snipped_array = np.vstack((snipped_array, param_array[:, ii]))
norm_array = np.vstack((norm_array, param_array[:, ii] / temp_max))
snipped_array = snipped_array.T
norm_array = norm_array.T
try:
os.mkdir(folder_str)
except OSError as e:
if e.errno == errno.EEXIST:
pass
else:
raise
norm_name = file_name + '_norm.txt'
snip_name = file_name + '_snip.txt'
file_name = file_name + '.txt'
try:
included_spectra_str = json.dumps(included_spectra, sort_keys=True, indent=4,
separators=(',', ': '))
except:
print("Source: save_parameter_sweep\nJSON FAILED")
return
included_spectra_str = included_spectra_str.replace('\n', '\n#')
included_spectra_str += '\n#' * (99 - included_spectra_str.count('\n'))
origin_import1 = param_name
origin_import2 = unit
origin_import3 = ""
for order in sb_included:
origin_import1 += "Frequency,error,Sideband strength,error,Linewidth,error"
origin_import2 += ",eV,,arb. u.,,meV,"
origin_import3 += ",{0},,{0},,{0},".format(order)
origin_total = origin_import1 + "\n" + origin_import2 + "\n" + origin_import3
origin_import1 = param_name
origin_import2 = unit
origin_import3 = ""
for order in sb_included:
origin_import1 += ",Frequency,Sideband strength,error"
origin_import2 += ",eV,arb. u.,"
origin_import3 += ",{0},{0},".format(order)
origin_snip = origin_import1 + "\n" + origin_import2 + "\n" + origin_import3
header_total = '#' + included_spectra_str + '\n' + origin_total
header_snip = '#' + included_spectra_str + '\n' + origin_snip
# print "Spec header: ", spec_header
if verbose:
print("the param_array is:", param_array)
np.savetxt(os.path.join(folder_str, file_name), param_array, delimiter=',',
header=header_total, comments='', fmt='%0.6e')
np.savetxt(os.path.join(folder_str, snip_name), snipped_array, delimiter=',',
header=header_snip, comments='', fmt='%0.6e')
np.savetxt(os.path.join(folder_str, norm_name), norm_array, delimiter=',',
header=header_snip, comments='', fmt='%0.6e')
if verbose:
print("Saved the file.\nDirectory: {}".format(
os.path.join(folder_str, file_name)))
def save_parameter_sweep(spectrum_list, file_name, folder_str, param_name, unit,
wanted_indices = [1, 3, 4], skip_empties = False, verbose=False,
header_dict = {}, only_even=False):
"""
This function will take a fully processed list of spectrum objects and
slice Spectrum.sb_fits appropriately to get an output like:
"Parameter" | SB1 freq | err | SB1 amp | error | SB1 linewidth | error | SB2...| SBn...|
param1 | . |
param2 | . |
.
.
.
Currently I'm thinking fuck the offset y0
After constructing this large matrix, it will save it somewhere.
Thus function has been update to pass a list of indices to slice for the return
values
skip_empties: If False, will add a row of zeroes for the parameter even if no sidebands
are found. If True, will not add a line for that parameter
only_even: don't include odd orders in the saved sweep
[sb number, Freq (eV), Freq error (eV), Gauss area (arb.), Area error, Gauss linewidth (eV), Linewidth error (eV)]
[ 0 , 1 , 2, , 3 , 4 , 5 , 6 ]
"""
if isinstance(param_name, list):
# if you pass two things because the param you want
# is in a dict (e.g. field strength has mean/std)
# do it that way
param_name_list = list(param_name) # keep reference to old one
paramGetter = lambda x: x.parameters[param_name_list[0]][param_name_list[1]]
# Keep the name for labeling things later on
param_name = param_name[0]
else:
paramGetter = lambda x: x.parameters[param_name]
# Sort all of the spectra based on the desired key
spectrum_list.sort(key=paramGetter)
# keep track of which file name corresponds to which parameter which gets put in
included_spectra = dict()
# The big array which will be stacked up to keep all of the sideband details vs desired parameter
param_array = None
# list of which sidebands are seen throughout.
sb_included = []
# how many parameters (area, strength, linewidth, pos, etc.) are there?
# Here incase software changes and more things are kept in
# sb results. Needed to handle how to slice the arrays
try:
num_params = spectrum_list[0].sb_results.shape[1]
except IndexError:
# There's a file with only 1 sb and it happens to be first
# in the list.
num_params = spectrum_list[0].sb_results.shape[0]
except AttributeError:
# The first file has no sidebands, so just hardcode it, as stated below.
num_params=0
# Rarely, there's an issue where I'm doing some testing and there's a set
# where the first file has no sidebands in it, so the above thing returns 0
# It seems really silly to do a bunch of testing to try and correct for that, so
# I'm going to hardcode the number of parameters.
if num_params == 0:
num_params = 7
# loop through all of them once to figure out which sidebands are seen in all spectra
for spec in spectrum_list:
try:
# use sets to keep track of only unique sidebands
sb_included = sorted(list(set(sb_included + list(spec.full_dict.keys()))))
except AttributeError:
print("No full dict?", spec.fname)
print(spec.sb_list)
# If these are from summed spectra, then only the the first file name
# from that sum will show up here, which should be fine?
included_spectra[spec.fname.split('/')[-1]] = paramGetter(spec)
if only_even:
sb_included = [ii for ii in sb_included if not ii%2]
if verbose:
print("included names:", included_spectra)
print("sb_included:", sb_included)
for spec in spectrum_list:
# Flag to keep whethere there are no sidebands or not. Used to skip
# issues when trying to index on empty arrays
noSidebands = False
if verbose:
print("the sb_results:", spec.sb_results)
# if no sidebands were found, skip this one
try:
# TODO: (08/14/18) the .ndim==1 isn't the correct check, since it fails
# when looking at the laser line. Need to test this with a real
# empty data set, vs data set with 1 sb
#
#
# (08/28/18) I'm not sure what the "not spec" is trying to handle
# spec.sb_results is None occurs when _no_ sidebands were fit
# spec.sb_results.ndim == 1 happens when only one sideband is found
if not spec or spec.sb_results is None or spec.sb_results.ndim == 1:
if spec.sb_results is None:
# Flag no sidebands are afound
noSidebands = True
elif spec.sb_results[0] == 0:
# Cast it to 2d to allow slicing later on. Not sure hwy this is
# only done if the laser line is the one found.
spec.sb_results = np.atleast_2d(spec.sb_results)
elif skip_empties:
continue
else:
noSidebands = True
except (AttributeError, TypeError):
# continue
raise
# Make an sb_results of all zeroes where we'll fill
# in the sideband info we found
new_spec = np.zeros((len(sb_included), num_params))
if not noSidebands:
sb_results = spec.sb_results.copy()
saw_sbs = sb_results[:, 0]
found_sb = sorted(list(set(sb_included) & set(saw_sbs)))
found_idx = [sb_included.index(ii) for ii in found_sb]
try:
new_spec[:, 0] = sb_included
except:
print("new_spec", new_spec)
raise
try:
if only_even:
new_spec[found_idx, :] = sb_results[sb_results[:,0]%2==0]
else:
new_spec[found_idx, :] = sb_results
except ValueError:
print(spec.fname)
print("included:", sb_included)
print("found:", found_sb, found_idx)
print(new_spec.shape, sb_results.shape)
print(sb_results)
print(new_spec)
raise
spec_data = np.insert(new_spec.flatten(), 0, float(paramGetter(spec)))
try:
param_array = np.row_stack((param_array, spec_data))
except:
param_array = np.array(spec_data)
if param_array.ndim == 1: # if you only pass one spectra
param_array = param_array[None, :] # recast it to 2D for slicing
# the indices we want from the param array from the passed argument
snip = wanted_indices
N = len(sb_included)
# run it out across all of the points across the param_array
snipped_indices = [0] + list(
1+np.array(snip * N) + num_params * np.array(sorted(list(range(N)) * len(snip))))
snipped_array = param_array[:, snipped_indices]
norm_array = snipped_array.copy()
# normalize the area if it's requested
if 3 in snip:
num_snip = len(snip)
strength_idx = snip.index(3)
if 4 in snip:
#normalize error first if it was requested
idx = snip.index(4)
norm_array[:, 1 + idx + np.arange(N) * num_snip] /= norm_array[:,1 + strength_idx + np.arange(N) * num_snip].max(axis=0)
strength_idx = snip.index(3)
norm_array[:, 1+strength_idx+np.arange(N)*num_snip]/=norm_array[:, 1+strength_idx+np.arange(N)*num_snip].max(axis=0)
try:
os.mkdir(folder_str)
except TypeError:
pass # if you pass None as folder_str (for using byteIO)
except OSError as e:
if e.errno == errno.EEXIST:
pass
else:
raise
included_spectra.update(header_dict)
try:
included_spectra_str = json.dumps(included_spectra, sort_keys=True, indent=4,
separators=(',', ': '))
except:
print("Source: save_parameter_sweep\nJSON FAILED")
return
included_spectra_str = included_spectra_str.replace('\n', '\n#')
included_spectra_str += '\n#' * (99 - included_spectra_str.count('\n'))
# this will make the header chunk for the full, un-sliced data set
# TODO: fix naming so you aren't looping twice
### 1/9/18 This isn't needed, right? Why isn't it deleted?
origin_import1 = param_name
origin_import2 = unit
origin_import3 = ""
for order in sb_included:
origin_import1 += ",sideband,Frequency,error,Sideband strength,error,Linewidth,error"
origin_import2 += ",order,eV,eV,arb. u.,arb.u.,meV,meV"
origin_import3 += ",,{0},,{0},,{0},".format(order)
origin_total = origin_import1 + "\n" + origin_import2 + "\n" + origin_import3
# This little chunk will make a chunk block of header strings for the sliced
# data set which can be looped over
origin_import1 = param_name
origin_import2 = unit
origin_import3 = ""
wanted_titles = ["Sideband", "Frequency", "error", "Sideband strength","error","Linewidth","error"]
wanted_units = ["order", "eV", "eV", "arb. u.", "arb. u.", "eV", "eV"]
wanted_comments = ["", "{0}", "", "{0}", "", "{0}", ""]
wanted_titles = ",".join([wanted_titles[ii] for ii in wanted_indices])
wanted_units = ",".join([wanted_units[ii] for ii in wanted_indices])
wanted_comments = ",".join([wanted_comments[ii] for ii in wanted_indices])
for order in sb_included:
origin_import1 += ","+wanted_titles
origin_import2 += ","+wanted_units
origin_import3 += ","+wanted_comments.format(order)
origin_snip = origin_import1 + "\n" + origin_import2 + "\n" + origin_import3
header_total = '#' + included_spectra_str + '\n' + origin_total
header_snip = '#' + included_spectra_str + '\n' + origin_snip
# print "Spec header: ", spec_header
if verbose:
print("the param_array is:", param_array)
if isinstance(file_name, list):
if isinstance(file_name[0], io.BytesIO):
np.savetxt(file_name[0], param_array, delimiter=',',
header=header_total, comments='', fmt='%0.6e')
np.savetxt(file_name[1], snipped_array, delimiter=',',
header=header_snip, comments='', fmt='%0.6e')
np.savetxt(file_name[2], norm_array, delimiter=',',
header=header_snip, comments='', fmt='%0.6e')
# Need to reset the file position if you want to read them immediately
# Is it better to do that here, or assume you'll do it later?
# I'm gonna assume here, because I can't currently think of a time when I'd want
# to be at the end of the file
[ii.seek(0) for ii in file_name]
if verbose:
print("Saved the file to bytes objects")
else:
if file_name:
norm_name = file_name + '_norm.txt'
snip_name = file_name + '_snip.txt'
file_name = file_name + '.txt'
np.savetxt(os.path.join(folder_str, file_name), param_array, delimiter=',',
header=header_total, comments='', fmt='%0.6e')
np.savetxt(os.path.join(folder_str, snip_name), snipped_array, delimiter=',',
header=header_snip, comments='', fmt='%0.6e')
np.savetxt(os.path.join(folder_str, norm_name), norm_array, delimiter=',',
header=header_snip, comments='', fmt='%0.6e')
if verbose:
print("Saved the file.\nDirectory: {}".format(os.path.join(folder_str, file_name)))
else:
if verbose:
print("Didn't save")
return sb_included, param_array, snipped_array, norm_array
def save_parameter_sweep_vs_sideband(spectrum_list, file_name,
folder_str, param_name, unit, verbose=False,
wanted_indices = [1, 3, 4]):
"""
Similar to save_parameter_sweep, but the data[:,0] column is sideband number instead of
series, and each set of columns correspond to a series step. Pretty much compiles
all of the fit parameters from the files that are already saved and puts it into
one file to keep from polluting the Origin folder
:param spectrum_list:
:param file_name:
:param folder_str:
:param param_name:
:param unit:
:param verbose:
sb number is automatically prepended, so do not include in slicing list
[sb number, Freq (eV), Freq error (eV), Gauss area (arb.), Area error, Gauss linewidth (eV), Linewidth error (eV)]
[ 0 , 1 , 2, , 3 , 4 , 5 , 6 ]
:return:
"""
spectrum_list.sort(key=lambda x: x.parameters[param_name])
included_spectra = dict()
param_array = None
sb_included = []
# what parameters were included (for headers)
params = sorted([x.parameters[param_name] for x in spectrum_list])
for spec in spectrum_list:
sb_included = sorted(list(set(sb_included + list(spec.full_dict.keys()))))
included_spectra[spec.fname.split('/')[-1]] = spec.parameters[param_name]
# If these are from summed spectra, then only the the first file name
# from that sum will show up here, which should be fine?
if verbose:
# print "full name:", spectrum_list[0].fname
print("included names:", included_spectra)
print("sb_included:", sb_included)
param_array = np.array(sb_included)
for spec in spectrum_list:
temp_dict = spec.full_dict.copy()
#prevent breaking if no sidebands in spectrum
if not temp_dict:
if verbose:
print("No sidebands here? {}, {}".format(spec.parameters["series"],
spec.parameters["spec_step"]))
continue
if verbose:
print(temp_dict)
# matrix for holding all of the sb information
# for a given spectrum
spec_matrix = None
for sb in sb_included:
blank = np.zeros(6)
# print "checking sideband order:", sb
# print "blank", blank
sb_data = temp_dict.get(sb, blank)
try:
spec_matrix = np.row_stack((spec_matrix, sb_data))
except:
spec_matrix = sb_data
param_array = np.column_stack((param_array, spec_matrix))
# the indices we want from the param array
# 1- freq, 3-area, 4-area error
snip = wanted_indices
N = len(spectrum_list)
# run it out across all of the points across the param_array
snipped_indices = [0] + list( np.array(snip*N) + 6*np.array(sorted(list(range(N))*len(snip))) )
snipped_array = param_array[:, snipped_indices]
try:
os.mkdir(folder_str)
except OSError as e:
if e.errno == errno.EEXIST:
pass
else:
raise
snip_name = file_name + '_snip.txt'
file_name = file_name + '.txt'
try:
included_spectra_str = json.dumps(included_spectra, sort_keys=True, indent=4, separators=(',', ': '))
except:
print("Source: save_parameter_sweep\nJSON FAILED")
return
included_spectra_str = included_spectra_str.replace('\n', '\n#')
included_spectra_str += '\n#' * (99 - included_spectra_str.count('\n'))
origin_import1 = "Sideband"
origin_import2 = "Order"
origin_import3 = "SB"
for param in params:
origin_import1 += ",Frequency,error,Sideband strength,error,Linewidth,error"
origin_import2 += ",eV,,arb. u.,,meV,"
origin_import3 += ",{0},,{0},,{0},".format(param)
origin_total = origin_import1 + "\n" + origin_import2 + "\n" + origin_import3
# This little chunk will make a chunk block of header strings for the sliced
# data set which can be looped over
origin_import1 = "Sideband"
origin_import2 = "Order"
origin_import3 = "SB"
wanted_titles = ["Sideband", "Frequency", "error", "Sideband strength", "error",
"Linewidth", "error"]
wanted_units = ["order", "eV", "eV", "arb. u.", "arb. u.", "eV", "eV"]
wanted_comments = ["", "{0}", "", "{0}", "", "{0}", ""]
wanted_titles = ",".join([wanted_titles[ii] for ii in wanted_indices])
wanted_units = ",".join([wanted_units[ii] for ii in wanted_indices])
wanted_comments = ",".join([wanted_comments[ii] for ii in wanted_indices])
for param in params:
origin_import1 += "," + wanted_titles
origin_import2 += "," + wanted_units
origin_import3 += "," + wanted_comments.format(param)
origin_snip = origin_import1 + "\n" + origin_import2 + "\n" + origin_import3
header_total = '#' + included_spectra_str + '\n' + origin_total
header_snip = '#' + included_spectra_str + '\n' + origin_snip
# print "Spec header: ", spec_header
if verbose:
print("the param_array is:", param_array)
if file_name: # allow passing false (or empty string) to prevent saving
np.savetxt(os.path.join(folder_str, file_name), param_array, delimiter=',',
header=header_total, comments='', fmt='%0.6e')
np.savetxt(os.path.join(folder_str, snip_name), snipped_array, delimiter=',',
header=header_snip, comments='', fmt='%0.6e')
if verbose:
print("Saved the file.\nDirectory: {}".format(os.path.join(folder_str, file_name)))
return None
def stitchData(dataList, plot=False):
"""
Attempt to stitch together absorbance data. Will translate the second data set
to minimize leastsq between the two data sets.
:param dataList: Iterable of the data sets to be fit. Currently
it only takes the first two elements of the list, but should be fairly
straightforward to recursivly handle a list>2. Shifts the second
data set to overlap the first
elements of dataList can be either np.arrays or Absorbance class,
where it will take the proc_data itself
:param plot: bool whether or not you want the fit iterations to be plotted
(for debugging)
:return: a, a (2,) np.array of the shift
"""
# Data coercsion, make sure we know what we're working wtih
first = dataList[0]
if isinstance(first, Absorbance):
first = first.proc_data
second = dataList[1]
if isinstance(second, Absorbance):
second = second.proc_data
if plot:
# Keep a reference to whatever plot is open at call-time
# Useful if the calling script has plots before and after, as
# omitting this will cause future plots to be added to figures here
firstFig = plt.gcf()
plt.figure("Stitcher")
# Plot the raw input data
plt.plot(*first.T)
plt.plot(*second.T)
# Algorithm is set up such that the "second" data set spans the
# higher domain than first. Need to enforce this, and remember it
# so the correct shift is applied
flipped = False
if max(first[:, 0]) > max(second[:, 0]):
flipped = True
first, second = second, first
def fitter(p, shiftable, immutable):
# designed to over
# Get the shifts
dx = p[0]
dy = p[1]
# Don't want pass-by-reference nonsense, recast our own refs
shiftable = np.array(shiftable)
immutable = np.array(immutable)
# Shift the data set
shiftable[:, 1] += dy
shiftable[:, 0] += dx
# Create an interpolator. We want a
# direct comparision for subtracting the two functions
# Different spec grating positions have different wavelengths
# so they're not directly comparable.
shiftF = spi.interp1d(*shiftable.T)
# Find the bounds of where the two data sets overlap
overlap = (min(shiftable[:, 0]), max(immutable[:, 0]))
print("overlap", overlap)
# Determine the indices of the immutable function
# where it overlaps. argwhere returns 2-d thing,
# requiring the [0] at the end of each call
fOlIdx = (min(np.argwhere(immutable[:, 0] >= overlap[0]))[0],
max(np.argwhere(immutable[:, 0] <= overlap[1]))[0])
print("fOlIdx", fOlIdx)
# Get the interpolated values of the shiftable function at the same
# x-coordinates as the immutable case
newShift = shiftF(immutable[fOlIdx[0]:fOlIdx[1], 0])
if plot:
plt.plot(*immutable[fOlIdx[0]:fOlIdx[1], :].T, marker='o', label="imm", markersize=10)
plt.plot(immutable[fOlIdx[0]:fOlIdx[1], 0], newShift, marker='o', label="shift")
imm = immutable[fOlIdx[0]:fOlIdx[1], 1]
shift = newShift
return imm - shift
a, _, _, msg, err = spo.leastsq(fitter, [0.0001, 0.01 * max(first[:, 1])], args=(second, first), full_output=1)
# print "a", a
if plot:
# Revert back to the original figure, as per top comments
plt.figure(firstFig.number)
# Need to invert the shift if we flipped which
# model we're supposed to move
if flipped: a *= -1
return a
def integrateData(data, t1, t2, ave=False):
"""
Integrate a discrete data set for a
given time period. Sums the data between
the given bounds and divides by dt. Optional
argument to divide by T = t2-t1 for calculating
averages.
data = 2D array. data[:,0] = t, data[:,1] = y
t1 = start of integration
t2 = end of integration
if data is a NxM, with M>=3, it will take the
third column to be the errors of the points,
and return the error as the quadrature sum
"""
t = data[:, 0]
y = data[:, 1]
if data.shape[0] >= 3:
errors = data[:, 2]
else:
errors = np.ones_like(y) * np.nan
gt = set(np.where(t > t1)[0])
lt = set(np.where(t < t2)[0])
# find the intersection of the sets
vals = list(gt & lt)
# Calculate the average
tot = | np.sum(y[vals]) | numpy.sum |
# general imports
import abc
import numpy as np
import logging
import math
import copy
import warnings
# bag imports
import bag.io
from bag.layout.template import TemplateBase
from bag.layout.util import transform_point, BBox, BBoxArray, transform_loc_orient
from BPG.photonic_core import PhotonicBagLayout
# Photonic object imports
from BPG.port import PhotonicPort
from BPG.objects import PhotonicRect, PhotonicPolygon, PhotonicAdvancedPolygon, PhotonicInstance, PhotonicRound, \
PhotonicPath
# Typing imports
from typing import TYPE_CHECKING, Dict, Any, List, Set, Optional, Tuple, Iterable
from BPG.bpg_custom_types import *
if TYPE_CHECKING:
from BPG.bpg_custom_types import layer_or_lpp_type, lpp_type, coord_type, dim_type
from bag.layout.objects import Instance
from BPG.photonic_core import PhotonicTechInfo
from BPG.db import PhotonicTemplateDB
class PhotonicTemplateBase(TemplateBase, metaclass=abc.ABCMeta):
def __init__(self,
temp_db: "PhotonicTemplateDB",
lib_name: str,
params: Dict[str, Any],
used_names: Set[str],
**kwargs,
) -> None:
use_cybagoa: bool = kwargs.get('use_cybagoa', False)
assert isinstance(use_cybagoa, bool)
TemplateBase.__init__(self, temp_db, lib_name, params, used_names, **kwargs)
logging.debug(f'Initializing master {self.__class__.__name__}')
self._photonic_ports: Dict[str, PhotonicPort] = {}
self._layout = PhotonicBagLayout(self._grid, use_cybagoa=use_cybagoa)
if temp_db.photonic_tech_info is None:
raise ValueError("temp_db.photonic_tech_info was None")
self.photonic_tech_info: 'PhotonicTechInfo' = temp_db.photonic_tech_info
# Feature flag that when False, prevents users from creating rotated masters that contain other
# rotated masters
self.allow_rotation_hierarchy = False
# This stores the angular offset from the cardinal axes that this master is drawn at
self._angle = self.params.get('_angle', 0.0)
self._layout.mod_angle = self.angle
@property
def angle(self) -> float:
return self._angle
@abc.abstractmethod
def draw_layout(self) -> None:
pass
def photonic_ports_names_iter(self) -> Iterable[str]:
return self._photonic_ports.keys()
def add_obj(self, obj) -> None:
"""
Takes a provided layout object and adds it to the db. Automatically detects what type of object is
being added, and sends it to the appropriate category in the layoutDB.
Also accepts a list of layout objects.
TODO: Provide support for directly adding photonic ports and simulation objects
"""
if isinstance(obj, PhotonicRect):
self._layout.add_rect(obj)
elif isinstance(obj, PhotonicPolygon):
self._layout.add_polygon(obj)
elif isinstance(obj, PhotonicRound):
self._layout.add_round(obj)
elif isinstance(obj, PhotonicPath):
self._layout.add_path(obj)
elif isinstance(obj, PhotonicAdvancedPolygon):
self._layout.add_polygon(obj)
elif isinstance(obj, PhotonicInstance):
self._layout.add_instance(obj)
elif isinstance(obj, list):
for layout_obj in obj:
self.add_obj(layout_obj)
else:
raise ValueError("{} is not a valid layout object type, and cannot be added to the db".format(type(obj)))
def add_rect(self,
layer: layer_or_lpp_type,
coord1: coord_type = None,
coord2: coord_type = None,
bbox: Union[BBox, BBoxArray] = None,
nx: int = 1,
ny: int = 1,
spx: dim_type = 0,
spy: dim_type = 0,
unit_mode: bool = False,
) -> PhotonicRect:
"""
Creates a new rectangle based on the user provided arguments and adds it to the db. User can either provide a
pair of coordinates representing opposite corners of the rectangle, or a BBox/BBoxArray. This rectangle can
also be arrayed with the number and spacing parameters.
Parameters
----------
layer : Union[str, Tuple[str, str]]
the layer name, or the (layer, purpose) pair.
coord1 : Tuple[Union[int, float], Union[int, float]]
point defining one corner of rectangle boundary.
coord2 : Tuple[Union[int, float], Union[int, float]]
opposite corner from coord1 defining rectangle boundary.
bbox : bag.layout.util.BBox or bag.layout.util.BBoxArray
the base bounding box. If this is a BBoxArray, the BBoxArray's
arraying parameters are used.
nx : int
number of columns.
ny : int
number of rows.
spx : float
column pitch.
spy : float
row pitch.
unit_mode : bool
True if layout dimensions are specified in resolution units.
Returns
-------
rect : PhotonicRect
the added rectangle.
"""
# If coordinates are provided, use them to define a BBox for the rectangle
if coord1 is not None or coord2 is not None:
# Ensure both points are defined
if coord1 is None or coord2 is None:
raise ValueError("If defining by two points, both must be specified.")
# Define the BBox
bbox = BBox(
left=min(coord1[0], coord2[0]),
right=max(coord1[0], coord2[0]),
bottom=min(coord1[1], coord2[1]),
top=max(coord1[1], coord2[1]),
resolution=self.grid.resolution,
unit_mode=unit_mode
)
rect = PhotonicRect(layer, bbox, nx=nx, ny=ny, spx=spx, spy=spy, unit_mode=unit_mode)
self._layout.add_rect(rect)
self._used_tracks.record_rect(self.grid, layer, rect.bbox_array)
return rect
def add_polygon(self,
layer: layer_or_lpp_type = None,
points: List[coord_type] = None,
resolution: Optional[float] = None,
unit_mode: bool = False,
) -> PhotonicPolygon:
"""
Creates a new polygon from the user provided points and adds it to the db
Parameters
----------
layer : Union[str, Tuple[str, str]]
the layer of the polygon
resolution : float
the layout grid resolution
points : List[coord_type]
the points defining the polygon
unit_mode : bool
True if the points are given in resolution units
Returns
-------
polygon : PhotonicPolygon
the added polygon object
"""
# Ensure proper arguments are passed
if layer is None or points is None:
raise ValueError("If adding polygon by layer and points, both layer and points list must be defined.")
if resolution is None:
resolution = self.grid.resolution
assert isinstance(resolution, float)
polygon = PhotonicPolygon(
resolution=resolution,
layer=layer,
points=points,
unit_mode=unit_mode,
)
self._layout.add_polygon(polygon)
return polygon
def add_round(self,
layer: layer_or_lpp_type,
resolution: float,
rout: dim_type,
center: coord_type = (0, 0),
rin: dim_type = 0,
theta0: dim_type = 0,
theta1: dim_type = 360,
nx: int = 1,
ny: int = 1,
spx: dim_type = 0,
spy: dim_type = 0,
unit_mode: bool = False
):
""" Creates a PhotonicRound object based on the provided arguments and adds it to the db """
new_round = PhotonicRound(layer=layer,
resolution=resolution,
rout=rout,
center=center,
rin=rin,
theta0=theta0,
theta1=theta1,
nx=nx,
ny=ny,
spx=spx,
spy=spy,
unit_mode=unit_mode)
self._layout.add_round(new_round)
return new_round
def add_path(self,
layer: layer_or_lpp_type,
width: dim_type,
points: List[coord_type],
resolution: float,
unit_mode: bool = False,
) -> PhotonicPath:
"""
Create a PhotonicPath object based on the provided arguments
and add it to the db.
"""
new_path = PhotonicPath(layer=layer,
width=width,
points=points,
resolution=resolution,
unit_mode=unit_mode)
self._layout.add_path(new_path)
return new_path
def finalize(self):
""" Call the old finalize method, but then also grab the bounding box from the layout content """
TemplateBase.finalize(self)
if self._layout._inst_list != [] and self.angle != 0:
logging.warning(f"{self.__class__.__name__} requires hierarchical non-cardinal rotation. This feature is "
f"currently experimental. Please raise an issue if incorrect results occur")
self.prim_bound_box = self._layout.bound_box
def add_photonic_port(self,
name: Optional[str] = None,
center: Optional[coord_type] = None,
orient: Optional[str] = None,
angle: Optional[float] = 0.0,
width: Optional[dim_type] = None,
layer: Optional[layer_or_lpp_type] = None,
overwrite_purpose: bool = False,
resolution: Optional[float] = None,
unit_mode: bool = False,
port: Optional[PhotonicPort] = None,
overwrite: bool = False,
show: bool = True
) -> PhotonicPort:
"""
Add a photonic port to the current hierarchy. A PhotonicPort
object can be passed, or will be constructed if the proper
arguments are passed to this function.
Parameters
----------
name :
name to give the new port
center :
(x, y) location of the port
orient :
orientation pointing INTO the port
angle :
angle of a unit vector pointing into the port. This is used in combination with orient to place the port
width :
the port width
layer :
the layer on which the port should be added. If only a string, the purpose is defaulted to 'port'
overwrite_purpose :
True to overwrite the 'port' purpose if an LPP is passed. If False (default), the purpose of a passed LPP
is stripped away and the 'port' purpose is used.
resolution :
the grid resolution
unit_mode :
True if layout dimensions are specified in resolution units
port :
the PhotonicPort object to add. This argument can be provided in lieu of all the others.
overwrite :
True to add the port with the specified name even if another port with that name already exists in this
level of the design hierarchy.
show :
True to draw the port indicator shape
Returns
-------
port : PhotonicPort
the added photonic port object
"""
# TODO: Add support for renaming?
# TODO: Remove force append?
# Create a temporary port object unless one is passed as an argument
if port is None:
if layer is None:
raise TypeError("layer is required when creating a port")
if name is None:
raise TypeError("name is required when creating a port")
if center is None:
raise TypeError("center is required when creating a port")
if orient is None:
raise TypeError("orient is required when creating a port")
if width is None:
raise TypeError("width is required when creating a port")
if angle is None:
raise TypeError("angle is required when creating a port")
if resolution is None:
resolution = self.grid.resolution
assert isinstance(resolution, float)
if overwrite_purpose:
if isinstance(layer, str):
raise ValueError(f'Calling add_photonic_port with overwrite_purpose=True requires a LPP to be '
f'pased in the \'layer\' argument.')
else:
layer = (layer[0], layer[1])
else:
if isinstance(layer, str):
layer = (layer, 'port')
else:
layer = (layer[0], 'port')
# Check arguments for validity
if all([name, center, orient, width, layer]) is False:
raise ValueError('User must define name, center, orient, width, and layer')
port = PhotonicPort(name=name,
center=center,
orient=orient,
angle=angle,
width=width,
layer=layer,
resolution=resolution,
unit_mode=unit_mode)
# Add port to port list. If name already is taken, remap port if overwrite is true
if port.name not in self._photonic_ports.keys() or overwrite:
self._photonic_ports[port.name] = port
else:
raise ValueError('Port "{}" already exists in cell.'.format(port.name))
if port.name is not None:
self.add_label(
label=port.name,
layer=port.layer,
bbox=BBox(
bottom=port.center_unit[1],
left=port.center_unit[0],
top=port.center_unit[1] + self.grid.resolution,
right=port.center_unit[0] + self.grid.resolution,
resolution=port.resolution,
unit_mode=True
),
)
if show is True:
# Draw port shape
center_vec = port.center_unit
orient_vec = np.array(port.width_vec_unit)
perp_vec = np.array([-1 * orient_vec[1], orient_vec[0]])
self.add_polygon(
layer=port.layer,
points=[center_vec,
center_vec + orient_vec / 2 + perp_vec / 2,
center_vec + 2 * orient_vec,
center_vec + orient_vec / 2 - perp_vec / 2,
center_vec],
resolution=port.resolution,
unit_mode=True,
)
return port
def has_photonic_port(self,
port_name: str,
) -> bool:
"""Checks if the given port name exists in the current hierarchy level.
Parameters
----------
port_name : str
the name of the port
Returns
-------
: boolean
true if port exists in current hierarchy level
"""
return port_name in self._photonic_ports
def get_photonic_port(self,
port_name: Optional[str] = '',
) -> PhotonicPort:
""" Return the photonic port object with the given name.
Parameters
----------
port_name : Optional[str]
the photonic port terminal name. If None or empty, check if this photonic template has only one port,
and return it
Returns
-------
port : PhotonicPort
The photonic port object
"""
if not port_name:
if len(self._photonic_ports) == 1:
port_name = list(self._photonic_ports.keys())[0]
else:
raise ValueError(
'Template "{}" has {} ports != 1. Must get port by name.'.format(self.__class__.__name__,
len(self._photonic_ports)
)
)
else:
if not self.has_photonic_port(port_name):
raise ValueError('Port "{}" does not exist in {}'.format(port_name, self.__class__.__name__))
return self._photonic_ports[port_name]
def add_instance(self: "PhotonicTemplateBase",
master: "PhotonicTemplateBase",
inst_name: Optional[str] = None,
loc: coord_type = (0, 0),
orient: str = "R0",
angle: float = 0.0,
reflect: bool = False,
nx: int = 1,
ny: int = 1,
spx: dim_type = 0,
spy: dim_type = 0,
unit_mode: bool = False,
) -> PhotonicInstance:
"""Adds a new (arrayed) instance to layout.
Parameters
----------
master :
the master template object.
inst_name :
instance name. If None or an instance with this name already exists,
a generated unique name is used.
loc :
instance location.
orient :
instance orientation. Defaults to "R0"
angle :
angle in radians to rotate this instance
reflect :
True to mirror reflect the instance
nx :
number of columns. Must be positive integer.
ny :
number of rows. Must be positive integer.
spx :
column pitch. Used for arraying given instance.
spy :
row pitch. Used for arraying given instance.
unit_mode :
True if dimensions are given in resolution units.
Returns
-------
inst : PhotonicInstance
the added instance.
"""
res = self.grid.resolution
if not unit_mode:
loc = int(round(loc[0] / res)), int(round(loc[1] / res))
spx = int(round(spx / res))
spy = int(round(spy / res))
inst = PhotonicInstance(self.grid, self._lib_name, master, loc=loc, orient=orient, angle=angle,
mirrored=reflect, name=inst_name, nx=nx, ny=ny, spx=spx, spy=spy, unit_mode=True)
self._layout.add_instance(inst)
return inst
def add_sim_obj(self, sim_obj):
""" Add a new Lumerical simulation object to the db """
self._layout.add_sim_obj(sim_obj)
def add_source_obj(self, source_obj):
""" Add a new Lumerical source object to the db """
self._layout.add_source_obj(source_obj)
def add_monitor_obj(self, monitor_obj):
""" Add a new Lumerical monitor object to the db """
self._layout.add_monitor_obj(monitor_obj)
def add_instances_port_to_port(self,
inst_master: "PhotonicTemplateBase",
instance_port_name: str,
self_port: Optional[PhotonicPort] = None,
self_port_name: Optional[str] = None,
instance_name: Optional[str] = None,
reflect: bool = False,
) -> PhotonicInstance:
warnings.warn(f'PhotonicTemplateBase.add_instances_port_to_port was renamed to '
f'add_instance_port_to_port (no "s"). '
f'The old method name will be removed in V1.0',
DeprecationWarning)
return self.add_instance_port_to_port(
inst_master=inst_master,
instance_port_name=instance_port_name,
self_port=self_port,
self_port_name=self_port_name,
instance_name=instance_name,
reflect=reflect
)
def add_instance_port_to_port(self,
inst_master: "PhotonicTemplateBase",
instance_port_name: str,
self_port: Optional[PhotonicPort] = None,
self_port_name: Optional[str] = None,
instance_name: Optional[str] = None,
reflect: bool = False,
) -> PhotonicInstance:
"""
Instantiates a new instance of the inst_master template.
The new instance is placed such that its port named 'instance_port_name' is aligned-with and touching the
'self_port' or 'self_port_name' port of the current hierarchy level.
The new instance is rotated about the new instance's master's origin until desired port is aligned.
Optional reflection is performed after rotation, about the port axis.
The self port being connected to can be specified either by passing a self_port PhotonicPort object,
or by passing the self_port_name, which refers to a port that must exist in the current hierarchy level.
Parameters
----------
inst_master : PhotonicTemplateBase
the template master to be added
instance_port_name : str
the name of the port in the added instance to connect to
self_port : Optional[PhotonicPort]
the photonic port object in the current hierarchy to connect to. Has priority over self_port_name
self_port_name : Optional[str]
the name of the port in the current hierarchy to connect to
instance_name : Optional[str]
the name to give the new instance
reflect : bool
True to flip the added instance after rotation
Returns
-------
new_inst : PhotonicInstance
the newly added instance
"""
# Get the reference port that we will be aligning the new instance to
# TODO: If ports dont have same width/layer, do we return error?
if self_port is None and self_port_name is None:
raise ValueError('Either self_port or self_port_name must be specified')
if self_port_name and not self.has_photonic_port(self_port_name):
raise ValueError('Photonic port ' + self_port_name + ' does not exist in '
+ self.__class__.__name__)
if not inst_master.has_photonic_port(instance_port_name):
raise ValueError('Photonic port ' + instance_port_name + ' does not exist in '
+ inst_master.__class__.__name__)
# self_port has priority over self_port_name if both are specified
if self_port:
my_port = self_port
else:
my_port = self.get_photonic_port(self_port_name)
new_port = inst_master.get_photonic_port(instance_port_name)
# Compute the angle that the instance must be rotated by in order to have its port align to my_port
# Assuming self.angle = 0 We want the port to point to my_port.angle + math.pi
# Without reflection, inst_master.angle + new_port.angle + diff_angle gives the mod_angle of the
# newly instances port. If no reflection:
# inst_master.angle + new_port.angle + diff_angle = my_port.angle + math.pi
# if the instance is reflected... -(inst_master.angle + new_port.angle) + diff_angle = my_port.angle + math.pi
if reflect:
diff_angle = inst_master.angle + new_port.angle + my_port.angle + math.pi
else:
diff_angle = -1 * (inst_master.angle + new_port.angle) + my_port.angle + math.pi
# Place a rotated PhotonicInstance that is rotated but not in the correct location
new_inst: "PhotonicInstance" = self.add_instance(
master=inst_master,
inst_name=instance_name,
loc=(0, 0),
orient='R0',
angle=diff_angle,
reflect=reflect,
unit_mode=True,
)
# Translate the new instance
translation_vec = my_port.center_unit - new_inst.get_photonic_port(instance_port_name).center_unit
new_inst.move_by(dx=translation_vec[0], dy=translation_vec[1], unit_mode=True)
return new_inst
def delete_port(self,
port_names: Union[str, List[str]],
) -> None:
"""
Removes the given ports from this instances list of ports. Raises error if given port does not exist.
Parameters
----------
port_names : Union[str, List[str]]
"""
if isinstance(port_names, str):
port_names = [port_names]
for port_name in port_names:
if self.has_photonic_port(port_name):
del self._photonic_ports[port_name]
else:
raise ValueError('Photonic port ' + port_name + ' does not exist in '
+ self.__class__.__name__)
def update_port(self):
# TODO: Implement me. Deal with matching here?
pass
def _get_unused_port_name(self,
port_name: Optional[str],
) -> str:
"""Returns a new unique name for a port in the current hierarchy level
Parameters
----------
port_name : Optional[str]
base port name. If no value is supplied, 'PORT' is used as the base name
Returns
-------
new_name : str
new unique port name
"""
if port_name is None:
port_name = 'PORT'
new_name = port_name
if port_name in self._photonic_ports:
cnt = 0
new_name = port_name + '_' + str(cnt)
while new_name in self._photonic_ports:
cnt += 1
new_name = port_name + '_' + str(cnt)
return new_name
def extract_photonic_ports(self,
inst: Union[PhotonicInstance, "Instance"],
port_names: Optional[Union[str, List[str]]] = None,
port_renaming: Optional[Union[str, List[str], Dict[str, str]]] = None,
show: bool = True,
) -> List["PhotonicPort"]:
"""
Brings ports from lower level of hierarchy to the current hierarchy level
Parameters
----------
inst : PhotonicInstance
the instance that contains the ports to be extracted
port_names : Optional[Union[str, List[str]]
the port name or list of port names re-export. If not supplied, all ports of the inst will be extracted
port_renaming : Optional[Dict[str, str]]
a dictionary containing key-value pairs mapping inst's port names (key)
to the new desired port names (value).
If not supplied, extracted ports will be given their original names
show : bool
"""
if port_names is None:
port_names = list(inst.master.photonic_ports_names_iter())
if isinstance(port_names, str):
port_names = [port_names]
if port_renaming is None:
port_renaming = {}
if isinstance(port_renaming, str):
port_renaming = [port_renaming]
if isinstance(port_renaming, list):
if len(port_renaming) != len(port_names):
raise ValueError(f'If port_renaming is a list, must be same length as port_names')
ports_out = []
for ind, port_name in enumerate(port_names):
old_port = inst[port_name]
translation = inst.location_unit
orientation = inst.orientation
# Get new desired name
if isinstance(port_renaming, dict):
if port_name in port_renaming.keys():
new_name = port_renaming[port_name]
else:
new_name = port_name
else:
new_name = port_renaming[ind]
# If name is already used
if new_name in self._photonic_ports:
# Append unique number
new_name = self._get_unused_port_name(new_name)
ports_out.append(
self.add_photonic_port(
name=new_name,
center=old_port.center_unit.tolist(),
orient='R0',
angle=old_port.angle,
width=old_port.width_unit,
layer=old_port.layer,
unit_mode=True,
show=show
)
)
return ports_out
def _find_metal_pairs(self,
bot_layer,
top_layer,
metal_info,
):
"""
Creates an ordered list of metal pairs required to generate a via stack between rect1 and rect2
Metal ordering algorithm
------------------------
1) Map each rectangle's layer to index in the metal stack
2) Determine which rect is lower/higher in the stack based on the index
3) Add each metal pair in the stack between rect1 and rect2 to the metal_pair list, starting with the lower
rectangle and traversing up the metal stack
"""
metal_pairs = []
# 1) Map each rectangle layer to index in the metal stack
index_bottom = metal_info[bot_layer]['index']
index_top = metal_info[top_layer]['index']
# Check if layer order needs to be swapped
if index_bottom > index_top:
top_layer, bot_layer = bot_layer, top_layer
top_layer_fixed = metal_info[top_layer].get('base_name', top_layer)
# 2) Add each layer pair (layer names) between bot_metal and top_metal to a metal_pair list
cur_bot = metal_info[bot_layer].get('base_name', bot_layer)
while True:
# Try to find the metal layer that the current bot layer connects to
try:
cur_top = metal_info[cur_bot]['connect_to']
except KeyError:
raise ValueError(f'Could not complete via stack from {bot_layer} to {top_layer}')
metal_pairs.append((cur_bot, cur_top))
if cur_top == top_layer_fixed:
# If we have made it from the bottom to the top of the via stack, break out of the loop
break
else:
# Otherwise continue traversing the via stack
cur_bot = cur_top
return metal_pairs
def add_via_stack(self,
bot_layer: layer_or_lpp_type,
top_layer: layer_or_lpp_type,
loc: coord_type,
min_area_on_bot_top_layer: bool = False,
unit_mode: bool = False,
):
"""
Adds a via stack with one via in each layer at the provided location.
All intermediate layers will be enclosed with an enclosure that satisfies both via rules and min area rules
Parameters
----------
bot_layer : Union[str, Tuple[str, str]]
Layer name or layer LPP of the bottom layer in the via stack
top_layer : Union[str, Tuple[str, str]]
Layer name or layer LPP of the top layer in the via stack
loc : coord_type
Coordinate of the center of the via stack
min_area_on_bot_top_layer : bool
True to have enclosures on top and bottom layer satisfy minimum area constraints
unit_mode : bool
True if input arguments are specified in layout resolution units
Returns
-------
"""
# If the bottom layer and top layer are the same, do not draw any vias
if bot_layer == top_layer:
return
if not unit_mode:
loc = (int(round(loc[0] / self.grid.resolution)), int(round(loc[1] / self.grid.resolution)))
if isinstance(bot_layer, tuple):
bot_layer = bot_layer[0]
if isinstance(top_layer, tuple):
top_layer = top_layer[0]
bot_layer = bag.io.fix_string(bot_layer)
top_layer = bag.io.fix_string(top_layer)
metal_info = self.photonic_tech_info.dataprep_parameters['MetalStack']
metal_pairs = self._find_metal_pairs(bot_layer=bot_layer,
top_layer=top_layer,
metal_info=metal_info,
)
bot_layer_id_global = self.grid.tech_info.get_layer_id(metal_pairs[0][0])
top_layer_id_global = self.grid.tech_info.get_layer_id((metal_pairs[-1][1]))
for bot_lay_name, top_lay_name in metal_pairs:
bot_lay_type = self.grid.tech_info.get_layer_type(bot_lay_name)
top_lay_type = self.grid.tech_info.get_layer_type(top_lay_name)
bot_lay_id = self.grid.tech_info.get_layer_id(bot_lay_name)
via_name = self.grid.tech_info.get_via_name(bot_lay_id)
via_type_list = self.grid.tech_info.get_via_types(bmtype=bot_lay_type,
tmtype=top_lay_type)
for via_type, weight in via_type_list:
try:
(sp, sp2_list, sp3, sp6, dim, enc_b_list, arr_enc_b, arr_test_b) = self.grid.tech_info.get_via_drc_info(
vname=via_name,
vtype=via_type,
mtype=bot_lay_type,
mw_unit=0,
is_bot=True,
)
(_, _, _, _, _, enc_t_list, arr_enc_t, arr_test_t) = self.grid.tech_info.get_via_drc_info(
vname=via_name,
vtype=via_type,
mtype=top_lay_type,
mw_unit=0,
is_bot=True,
)
# Didnt get valid via info
except ValueError:
continue
# Want to use the via with symmetric enclosure, if available.
enc_b = enc_b_list[0]
enc_t = enc_t_list[0]
for enc in enc_b_list:
if enc[0] == enc[1]:
enc_b = enc
break
for enc in enc_t_list:
if enc[0] == enc[1]:
enc_t = enc
# Fix minimum area violations:
if bot_lay_id > bot_layer_id_global or min_area_on_bot_top_layer:
min_area_unit = self.grid.tech_info.get_min_area_unit(bot_lay_type)
if (2 * enc_b[0] + dim[0]) * (2 * enc_b[1] + dim[1]) < min_area_unit:
min_side_len_unit = int(np.ceil(np.sqrt(min_area_unit)))
enc_b = [np.ceil((min_side_len_unit - dim[0]) / 2), | np.ceil((min_side_len_unit - dim[1]) / 2) | numpy.ceil |
import os
import pickle
import argparse
from tqdm import tqdm
import numpy as np
import numpy.random as npr
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
from matplotlib.font_manager import FontProperties
from pybasicbayes.models import FactorAnalysis
from pybasicbayes.distributions import \
Regression, Gaussian, DiagonalRegression, AutoRegression
from pyhsmm.util.general import relabel_by_permutation
from autoregressive.models import ARWeakLimitStickyHDPHMM
from pyslds.util import get_empirical_ar_params
from pyslds.models import HMMSLDS
from pypolyagamma.distributions import MultinomialRegression
from pypolyagamma.binary_trees import decision_list
from rslds.decision_list import DecisionList
from rslds.models import PGRecurrentSLDS, StickyPGRecurrentSLDS, \
PGRecurrentOnlySLDS, StickyPGRecurrentOnlySLDS
from rslds.util import compute_psi_cmoments
import rslds.plotting as rplt
# Constants
K_true = 4
D_latent = 2
# Parse command line arguments
parser = argparse.ArgumentParser(description='Synthetic NASCAR Example')
parser.add_argument('--T', type=int, default=10000,
help='number of training time steps')
parser.add_argument('--T_sim', type=int, default=2000,
help='number of simulation time steps')
parser.add_argument('--K', type=int, default=4,
help='number of inferred states')
parser.add_argument('--D_obs', type=int, default=10,
help='number of observed dimensions')
parser.add_argument('--mask_start', type=int, default=0,
help='time index of start of mask')
parser.add_argument('--mask_stop', type=int, default=0,
help='time index of end of mask')
parser.add_argument('--N_samples', type=int, default=1000,
help='number of iterations to run the Gibbs sampler')
parser.add_argument('--seed', type=int, default=0,
help='random seed (default: 0)')
parser.add_argument('--cache', action='store_true', default=False,
help='whether or not to cache the results')
parser.add_argument('-o', '--output-dir', default='.',
help='where to store the results')
args = parser.parse_args()
print("Setting seed to ", args.seed)
npr.seed(args.seed)
# Cache results if requested
def cached(results_name):
if args.cache:
def _cache(func):
def func_wrapper(*args, **kwargs):
results_file = os.path.join(args.output_dir, results_name)
if not results_file.endswith(".pkl"):
results_file += ".pkl"
if os.path.exists(results_file):
with open(results_file, "rb") as f:
results = pickle.load(f)
else:
results = func(*args, **kwargs)
with open(results_file, "wb") as f:
pickle.dump(results, f)
return results
return func_wrapper
else:
_cache = lambda func: func
return _cache
# Make an example with 2D latent states and 4 discrete states
def simulate_nascar():
assert K_true == 4
def random_rotation(n, theta):
rot = np.array([[np.cos(theta), -np.sin(theta)],
[np.sin(theta), np.cos(theta)]])
out = np.zeros((n,n))
out[:2,:2] = rot
q = np.linalg.qr(np.random.randn(n,n))[0]
# q = np.eye(n)
return q.dot(out).dot(q.T)
As = [random_rotation(D_latent, np.pi/24.),
random_rotation(D_latent, np.pi/48.)]
# Set the center points for each system
centers = [np.array([+2.0, 0.]),
np.array([-2.0, 0.])]
bs = [-(A - np.eye(D_latent)).dot(center) for A, center in zip(As, centers)]
# Add a "right" state
As.append(np.eye(D_latent))
bs.append(np.array([+0.1, 0.]))
# Add a "right" state
As.append( | np.eye(D_latent) | numpy.eye |
import datetime
import math
import os
import random
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import tensorflow as tf
from PIL import Image
from skimage.transform import rescale
from sklearn import preprocessing
from sklearn.preprocessing import OneHotEncoder, OrdinalEncoder
class RawData:
""" Keeps imported data, their paths and visualization parameters together.
"""
def __init__(self, HYPER):
""" Initializes paths and miscellaneous other values """
# provide the path to where data is stored
path_to_data = '../data/'
# provide the path to where images are stored
self.path_to_images = '../images/'
if not os.path.exists(self.path_to_images):
os.mkdir(self.path_to_images)
# provide the saving path to where computational graph images are stored
self.path_to_computational_graphs = self.path_to_images + 'computational graphs/'
if not os.path.exists(self.path_to_computational_graphs):
os.mkdir(self.path_to_computational_graphs)
# determines how many exemplar subplots to show for load profiles
self.n_subplots = 10
# set the range of the histogram bins and the total number of bins.
self.histo_range = (0, 1)
# set the number of channels
if HYPER.GREY_SCALE:
self.n_channels = 1
else:
self.n_channels = 3
# set the path to electric load profile data
if HYPER.LABELS == 'feature_scaled' or HYPER.LABELS == 'random_scaled':
self.path_to_building_year_profile_folder = (
path_to_data
+ 'public/'
+ HYPER.PROFILE_SET
+ '/building-year profiles/'
+ HYPER.LABELS
+ '/'
)
else:
self.path_to_building_year_profile_folder = (
path_to_data
+ 'private/'
+ HYPER.PROFILE_SET
+ '/building-year profiles/'
+ HYPER.LABELS
+ '/'
)
# set the path to meteo data
self.path_to_meteo_data_folder = (
path_to_data
+ 'public/'
+ HYPER.PROFILE_SET
+ '/meteo data/'
)
# set the path to aerial imagery data
if HYPER.PRIVATE_DATA_ACCESS:
self.path_to_aerial_imagery_folder = (
path_to_data
+ 'private/'
+ HYPER.PROFILE_SET
+ '/building imagery/'
+ 'padded/'
)
else:
if HYPER.SPATIAL_FEATURES == 'histogram':
self.path_to_aerial_imagery_folder = (
path_to_data
+ 'public/'
+ HYPER.PROFILE_SET
+ '/building imagery/'
+ 'histogram/'
)
elif HYPER.SPATIAL_FEATURES == 'average':
self.path_to_aerial_imagery_folder = (
path_to_data
+ 'public/'
+ HYPER.PROFILE_SET
+ '/building imagery/'
+ 'average/'
)
if HYPER.GREY_SCALE:
self.path_to_aerial_imagery_folder = (
self.path_to_aerial_imagery_folder
+ 'greyscale/'
)
else:
self.path_to_aerial_imagery_folder = (
self.path_to_aerial_imagery_folder
+ 'rgb/'
)
# create the experiment name string for saving models and results
if HYPER.RED_CAND_DATA_ACT_LRN:
self.experiment_name = 'delta1'
else:
self.experiment_name = 'delta0'
if HYPER.UPD_VAL_DATA_ACT_LRN:
self.experiment_name += '_valup1'
else:
self.experiment_name += '_valup0'
# create a results folder if not existent
path_to_results = '../results/'
if not os.path.exists(path_to_results):
os.mkdir(path_to_results)
path_to_results += (
HYPER.PROFILE_SET
+ '/'
)
if not os.path.exists(path_to_results):
os.mkdir(path_to_results)
# set the path to the folder for saving trained encoders
self.path_to_encoder_weights = path_to_results + 'encoder weights/'
if not os.path.exists(self.path_to_encoder_weights):
os.mkdir(self.path_to_encoder_weights)
self.path_to_encoder_weights += self.experiment_name + '/'
if not os.path.exists(self.path_to_encoder_weights):
os.mkdir(self.path_to_encoder_weights)
# set the path to the folder for saving trained AL models
if HYPER.SAVE_ACT_LRN_MODELS:
self.path_to_AL_models = path_to_results +'models/'
if not os.path.exists(self.path_to_AL_models):
os.mkdir(self.path_to_AL_models)
self.path_to_AL_models += self.experiment_name + '/'
if not os.path.exists(self.path_to_AL_models):
os.mkdir(self.path_to_AL_models)
# set the path to the folder for saving AL test results or hyper params
if HYPER.SAVE_ACT_LRN_RESULTS or HYPER.SAVE_HYPER_PARAMS:
self.path_to_AL_results = path_to_results + 'values/'
if not os.path.exists(self.path_to_AL_results):
os.mkdir(self.path_to_AL_results)
self.path_to_AL_results += self.experiment_name + '/'
if not os.path.exists(self.path_to_AL_results):
os.mkdir(self.path_to_AL_results)
# set the path to the folder for saving AL test results or hyper params
if HYPER.SAVE_ACT_LRN_TEST_SAMPLE:
self.path_to_AL_test_samples = path_to_results + 'samples/'
if not os.path.exists(self.path_to_AL_test_samples):
os.mkdir(self.path_to_AL_test_samples)
self.path_to_AL_test_samples += self.experiment_name + '/'
if not os.path.exists(self.path_to_AL_test_samples):
os.mkdir(self.path_to_AL_test_samples)
def show_attributes(self):
""" Prints out the attribute names of this class when called.
"""
for attr, value in self.__dict__.items():
print(attr)
class Dataset:
""" Keeps a dataset together that contains multiple elements of X_t, X_s,
X_s1, X_st and Y.
"""
def __init__(self, X_t_ord_1D, X_t, X_s, X_s1, X_st, Y):
""" Initializes a complete set of attributes for a new Dataset object.
Note that missing values should conventionally be passed with a zero.
"""
self.X_t_ord_1D = X_t_ord_1D
self.X_t = X_t
self.X_s = X_s
self.X_s1 = X_s1
self.X_st = X_st
self.Y = Y
self.n_datapoints = len(X_t)
def randomize(self):
""" Randomizes all data entries.
"""
# create random array
random_array = np.arange(len(self.X_t))
# shuffle random array
np.random.shuffle(random_array)
if type(self.X_t_ord_1D) != int and type(self.X_t_ord_1D) != float:
self.X_t_ord_1D = self.X_t_ord_1D[random_array]
if type(self.X_t) != int and type(self.X_t) != float:
self.X_t = self.X_t[random_array]
if type(self.X_s) != int and type(self.X_s) != float:
self.X_s = self.X_s[random_array]
if type(self.X_s1) != int and type(self.X_s1) != float:
self.X_s1 = self.X_s1[random_array]
if type(self.X_st) != int and type(self.X_st) != float:
self.X_st = self.X_st[random_array]
if type(self.Y) != int and type(self.Y) != float:
self.Y = self.Y[random_array]
if hasattr(self, "Y_copy"):
if type(self.Y_copy) != int and type(self.Y_copy) != float:
self.Y_copy = self.Y_copy[random_array]
def show_attributes(self):
""" Prints out the attribute names of this class when called.
"""
for attr, value in self.__dict__.items():
print(attr)
def import_consumption_profiles(HYPER, raw_data, silent=False, plot=True):
""" Imports consumption profiles and appends the following lists to the
raw_data object: building_year_profiles_list, building_id_list,
cluster_id_list, year_id_list, building_id_set, cluster_id_set, year_id_set,
cluster_year_set.
"""
if not silent:
# tell us what we are doing
print('Importing consumption profiles')
# create a progress bar
progbar = tf.keras.utils.Progbar(len(HYPER.PROFILE_YEARS))
# save dataframes here instead of under distinct names
building_year_profiles_list = []
memory_demand_GB = 0
# iterate over the list of years for which we want to import load profiles
for index_year, year in enumerate(HYPER.PROFILE_YEARS):
# get the path to currently iterated building-year profiles file
path_to_building_year_profile_files = (
raw_data.path_to_building_year_profile_folder
+ str(year)
+ ' building-year profiles.csv'
)
# load currently iterated file
df = pd.read_csv(path_to_building_year_profile_files)
# get the building IDs of profiles
building_ids = df.columns.values[1:]
# get the cluster IDs of profiles and drop the row
cluster_ids = df.iloc[0, 1:].values.astype(int)
# get the years of profiles and replace them with the year ID used here
years = df.iloc[1, 1:].values.astype(int)
year_ids = years
year_ids[:] = index_year
# drop the cluder id and year rows
df = df.drop([0, 1])
# rename the 'building ID' column name to 'local_time' so as to match
# the meteo files' column name for search later
df = df.rename(columns={'building ID': 'local_time'})
# get the time stamp of the imported meters
time_stamp_profiles = df.pop('local_time')
# set the new time stamp as index
df = df.set_index(time_stamp_profiles)
# create a random array
randomize = np.arange(len(building_ids))
np.random.shuffle(randomize)
# shuffle ID orders with same random array
building_ids = building_ids[randomize]
cluster_ids = cluster_ids[randomize]
year_ids = year_ids[randomize]
# shorten the considered ID lists according to your chosen number of
# considerable profiles per year
n_profiles = math.ceil(HYPER.PROFILES_PER_YEAR * len(building_ids))
building_ids = building_ids[: n_profiles]
cluster_ids = cluster_ids[: n_profiles]
year_ids = year_ids[: n_profiles]
# shorten dataframe accordingly
df = df[building_ids]
# check if first iteration
if year == HYPER.PROFILE_YEARS[0]:
# if yes, set the id lists equal to currently iterated lists
building_id_list = building_ids
cluster_id_list = cluster_ids
year_id_list = year_ids
else:
# if not, concatenate previous lists with currently iterated lists
building_id_list = np.concatenate((building_id_list, building_ids))
cluster_id_list = np.concatenate((cluster_id_list, cluster_ids))
year_id_list = np.concatenate((year_id_list, year_ids))
# append dataframe
building_year_profiles_list.append(df)
# accumulate the memory demand of building-year profiles we imported
memory_demand_GB = memory_demand_GB + df.memory_usage().sum() * 1e-9
if not silent:
# increment the progress bar
progbar.add(1)
# get the set of building IDs, i.e. drop the duplicate entries
building_id_set = set(building_id_list)
# get the set of building IDs, i.e. drop the duplicate entries
cluster_id_set = set(cluster_id_list)
# get the set of year IDs. Note: this should be equal to PROFILE_YEARS
year_id_set = set(year_id_list)
# get set of cluster-year ID combinations
cluster_year_set = set(list(zip(cluster_id_list, year_id_list)))
raw_data.building_year_profiles_list = building_year_profiles_list
raw_data.building_id_list = building_id_list
raw_data.cluster_id_list = cluster_id_list
raw_data.year_id_list = year_id_list
raw_data.building_id_set = building_id_set
raw_data.cluster_id_set = cluster_id_set
raw_data.year_id_set = year_id_set
raw_data.cluster_year_set = cluster_year_set
# Tell us how much RAM we are occupying with the just imported profiles
print(
'The',
len(building_id_list),
'imported electric load profiles demand a total amount of',
memory_demand_GB,
'GB of RAM',
)
if plot:
# set the number of subplots to the minimum of the desired value and the
# actually available profiles for plotting
n_subplots = min(raw_data.n_subplots, len(df.columns))
# Visualize some profiles
_ = df.iloc[:, :n_subplots].plot(
title='Exemplar electric load profiles (labels/ground truth data)',
subplots=True,
layout=(math.ceil(n_subplots / 2), 2),
figsize=(16, n_subplots),
)
return raw_data
def import_building_images(HYPER, raw_data, silent=False, plot=True):
""" Imports building-scale aerial imagery and appends the following to the
raw_data object: building_imagery_data_list, building_imagery_id_list.
"""
if not silent:
# tell us what we do
print('Importing building-scale aerial imagery:')
# create a progress bar
progbar = tf.keras.utils.Progbar(len(raw_data.building_id_set))
# create a variabl to iteratively add the memory of imported files
memory_demand_GB = 0
# create a empty lists for aerial image data and building ids
building_imagery_data_list = []
building_imagery_id_list = []
if HYPER.PRIVATE_DATA_ACCESS:
# iterate over set of building ID
for building_id in raw_data.building_id_set:
# get the file name first
file_name = 'building ' + building_id + '.png'
# create the entire path to the currently iterated file
path_to_file = raw_data.path_to_aerial_imagery_folder + file_name
# import image
image = Image.open(path_to_file)
# convert to grey scale if this is chosen so and add channel
if HYPER.GREY_SCALE == True:
# convert to grey-scale
image = image.convert('L')
# transform the image to a numeric array
image = | np.asarray(image) | numpy.asarray |
import numpy as np
from tsyplov_stats.wolfram_functions import *
from tsyplov_stats.autoregression_model import *
from tsyplov_stats.arma_model import *
def diff(ts, d):
'''Gives (1 - B)^d y, the list of
first values each of y, (1 - B) y, (1 - B)^2 y, ...
and the list of last values each of y, (1 - B) y, (1 - B)^2 y
'''
start, end, dts = list(), list(), ts.copy()
for _ in range(d):
start.append(dts[0])
end.append(dts[-1])
dts = np.diff(dts)
return dts, start[::-1], end[::-1]
def accumulate(dts, start):
'''Returns back y using (1 - B)^d y and [y_0, (1 - B) y_1, ...]
dts – (1 - B)^d y
'''
integrate = lambda dy, y0: np.cumsum(np.insert(dy, 0, y0))
return fold(integrate, dts, start)
class ARIMA(AutoRegression):
def __init__(self, p=1, d=1, q=1):
self.p = p
self.d = d
self.q = q
self.true_values = np.zeros(2)
self.fitted_values = np.zeros(2)
self.residuals = np.zeros(2)
self.coef = | np.zeros(p + q + 1) | numpy.zeros |
import os
import sys
import yaml
import numpy as np
import torch
import torch.utils.data as data
import numpy as np
import numpy.random as npr
import cv2
import copy
import glob
import scipy
import datasets
from config.config import cfg
from transforms3d.quaternions import mat2quat, quat2mat
from utils.se3 import *
from utils.pose_error import *
from utils.cython_bbox import bbox_overlaps
_SUBJECTS = [
'20200709-subject-01',
'20200813-subject-02',
'20200820-subject-03',
'20200903-subject-04',
'20200908-subject-05',
'20200918-subject-06',
'20200928-subject-07',
'20201002-subject-08',
'20201015-subject-09',
'20201022-subject-10',
]
_SERIALS = [
'836212060125',
'839512060362',
'840412060917',
'841412060263',
'932122060857',
'932122060861',
'932122061900',
'932122062010',
]
_YCB_CLASSES = {
1: '002_master_chef_can',
2: '003_cracker_box',
3: '004_sugar_box',
4: '005_tomato_soup_can',
5: '006_mustard_bottle',
6: '007_tuna_fish_can',
7: '008_pudding_box',
8: '009_gelatin_box',
9: '010_potted_meat_can',
10: '011_banana',
11: '019_pitcher_base',
12: '021_bleach_cleanser',
13: '024_bowl',
14: '025_mug',
15: '035_power_drill',
16: '036_wood_block',
17: '037_scissors',
18: '040_large_marker',
19: '051_large_clamp',
20: '052_extra_large_clamp',
21: '061_foam_brick',
}
_MANO_JOINTS = [
'wrist',
'thumb_mcp',
'thumb_pip',
'thumb_dip',
'thumb_tip',
'index_mcp',
'index_pip',
'index_dip',
'index_tip',
'middle_mcp',
'middle_pip',
'middle_dip',
'middle_tip',
'ring_mcp',
'ring_pip',
'ring_dip',
'ring_tip',
'little_mcp',
'little_pip',
'little_dip',
'little_tip'
]
_MANO_JOINT_CONNECT = [
[0, 1], [ 1, 2], [ 2, 3], [ 3, 4],
[0, 5], [ 5, 6], [ 6, 7], [ 7, 8],
[0, 9], [ 9, 10], [10, 11], [11, 12],
[0, 13], [13, 14], [14, 15], [15, 16],
[0, 17], [17, 18], [18, 19], [19, 20],
]
_BOP_EVAL_SUBSAMPLING_FACTOR = 4
class dex_ycb_dataset(data.Dataset):
def __init__(self, setup, split, obj_list):
self._setup = setup
self._split = split
self._color_format = "color_{:06d}.jpg"
self._depth_format = "aligned_depth_to_color_{:06d}.png"
self._label_format = "labels_{:06d}.npz"
self._height = 480
self._width = 640
# paths
self._name = 'dex_ycb_' + setup + '_' + split
self._image_set = split
self._dex_ycb_path = self._get_default_path()
path = os.path.join(self._dex_ycb_path, 'data')
self._data_dir = path
self._calib_dir = os.path.join(self._data_dir, "calibration")
self._model_dir = os.path.join(self._data_dir, "models")
self._obj_file = {
k: os.path.join(self._model_dir, v, "textured_simple.obj")
for k, v in _YCB_CLASSES.items()
}
# define all the classes
self._classes_all = ('002_master_chef_can', '003_cracker_box', '004_sugar_box', '005_tomato_soup_can', '006_mustard_bottle', \
'007_tuna_fish_can', '008_pudding_box', '009_gelatin_box', '010_potted_meat_can', '011_banana', '019_pitcher_base', \
'021_bleach_cleanser', '024_bowl', '025_mug', '035_power_drill', '036_wood_block', '037_scissors', '040_large_marker', \
'051_large_clamp', '052_extra_large_clamp', '061_foam_brick')
self._num_classes_all = len(self._classes_all)
self._class_colors_all = [(255, 0, 0), (0, 255, 0), (0, 0, 255), (255, 255, 0), (255, 0, 255), (0, 255, 255), \
(128, 0, 0), (0, 128, 0), (0, 0, 128), (128, 128, 0), (128, 0, 128), (0, 128, 128), \
(64, 0, 0), (0, 64, 0), (0, 0, 64), (64, 64, 0), (64, 0, 64), (0, 64, 64),
(192, 0, 0), (0, 192, 0), (0, 0, 192)]
self._extents_all = self._load_object_extents()
self._posecnn_class_indexes = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21]
# compute class index
class_index = []
for name in obj_list:
for i in range(self._num_classes_all):
if name == self._classes_all[i]:
class_index.append(i)
break
print('class index:', class_index)
self._class_index = class_index
# select a subset of classes
self._classes = obj_list
self._num_classes = len(self._classes)
self._class_colors = [self._class_colors_all[i] for i in class_index]
self._extents = self._extents_all[class_index]
self._points, self._points_all = self._load_object_points(self._classes, self._extents)
# Seen subjects, camera views, grasped objects.
if self._setup == 's0':
if self._split == 'train':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = [i for i in range(100) if i % 5 != 4]
if self._split == 'val':
subject_ind = [0, 1]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = [i for i in range(100) if i % 5 == 4]
if self._split == 'test':
subject_ind = [2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = [i for i in range(100) if i % 5 == 4]
# Unseen subjects.
if self._setup == 's1':
if self._split == 'train':
subject_ind = [0, 1, 2, 3, 4, 5, 9]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = list(range(100))
if self._split == 'val':
subject_ind = [6]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = list(range(100))
if self._split == 'test':
subject_ind = [7, 8]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = list(range(100))
# Unseen camera views.
if self._setup == 's2':
if self._split == 'train':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [0, 1, 2, 3, 4, 5]
sequence_ind = list(range(100))
if self._split == 'val':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [6]
sequence_ind = list(range(100))
if self._split == 'test':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [7]
sequence_ind = list(range(100))
# Unseen grasped objects.
if self._setup == 's3':
if self._split == 'train':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = [
i for i in range(100) if i // 5 not in (3, 7, 11, 15, 19)
]
if self._split == 'val':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = [i for i in range(100) if i // 5 in (3, 19)]
if self._split == 'test':
subject_ind = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
serial_ind = [0, 1, 2, 3, 4, 5, 6, 7]
sequence_ind = [i for i in range(100) if i // 5 in (7, 11, 15)]
self._subjects = [_SUBJECTS[i] for i in subject_ind]
self._serials = [_SERIALS[i] for i in serial_ind]
self._intrinsics = []
for s in self._serials:
intr_file = os.path.join(self._calib_dir, "intrinsics", "{}_{}x{}.yml".format(s, self._width, self._height))
with open(intr_file, 'r') as f:
intr = yaml.load(f, Loader=yaml.FullLoader)
intr = intr['color']
self._intrinsics.append(intr)
# build mapping
self._sequences = []
self._mapping = []
self._ycb_ids = []
offset = 0
for n in self._subjects:
seq = sorted(os.listdir(os.path.join(self._data_dir, n)))
seq = [os.path.join(n, s) for s in seq]
assert len(seq) == 100
seq = [seq[i] for i in sequence_ind]
self._sequences += seq
for i, q in enumerate(seq):
meta_file = os.path.join(self._data_dir, q, "meta.yml")
with open(meta_file, 'r') as f:
meta = yaml.load(f, Loader=yaml.FullLoader)
c = np.arange(len(self._serials))
f = np.arange(meta['num_frames'])
f, c = np.meshgrid(f, c)
c = c.ravel()
f = f.ravel()
s = (offset + i) * np.ones_like(c)
m = np.vstack((s, c, f)).T
self._mapping.append(m)
self._ycb_ids.append(meta['ycb_ids'])
offset += len(seq)
self._mapping = np.vstack(self._mapping)
# sample a subset for training
if split == 'train':
self._mapping = self._mapping[::10]
# dataset size
self._size = len(self._mapping)
print('dataset %s with images %d' % (self._name, self._size))
def __len__(self):
return self._size
def get_bop_id_from_idx(self, idx):
s, c, f = map(lambda x: x.item(), self._mapping[idx])
scene_id = s * len(self._serials) + c
im_id = f
return scene_id, im_id
def __getitem__(self, idx):
s, c, f = self._mapping[idx]
is_testing = f % _BOP_EVAL_SUBSAMPLING_FACTOR == 0
if self._split == 'test' and not is_testing:
sample = {'is_testing': is_testing}
return sample
scene_id, im_id = self.get_bop_id_from_idx(idx)
video_id = '%04d' % (scene_id)
image_id = '%06d' % (im_id)
# posecnn result path
posecnn_result_path = os.path.join(self._dex_ycb_path, 'results_posecnn', self._name, 'vgg16_dex_ycb_epoch_16.checkpoint.pth',
video_id + '_' + image_id + '.mat')
d = os.path.join(self._data_dir, self._sequences[s], self._serials[c])
roidb = {
'color_file': os.path.join(d, self._color_format.format(f)),
'depth_file': os.path.join(d, self._depth_format.format(f)),
'label_file': os.path.join(d, self._label_format.format(f)),
'intrinsics': self._intrinsics[c],
'ycb_ids': self._ycb_ids[s],
'posecnn': posecnn_result_path,
}
# Get the input image blob
im_color, im_depth = self._get_image_blob(roidb['color_file'], roidb['depth_file'])
# build the label blob
im_label, intrinsic_matrix, poses, gt_boxes, poses_result, rois_result, labels_result \
= self._get_label_blob(roidb, self._num_classes)
is_syn = 0
im_scale = 1.0
im_info = np.array([im_color.shape[1], im_color.shape[2], im_scale, is_syn], dtype=np.float32)
sample = {'image_color': im_color[:, :, (2, 1, 0)],
'image_depth': im_depth,
'label': im_label,
'intrinsic_matrix': intrinsic_matrix,
'gt_poses': poses,
'gt_boxes': gt_boxes,
'poses_result': poses_result,
'rois_result': rois_result,
'labels_result': labels_result,
'extents': self._extents,
'points': self._points_all,
'im_info': im_info,
'video_id': video_id,
'image_id': image_id}
if self._split == 'test':
sample['is_testing'] = is_testing
return sample
def _get_image_blob(self, color_file, depth_file):
# rgba
rgba = cv2.imread(color_file, cv2.IMREAD_UNCHANGED)
if rgba.shape[2] == 4:
im = np.copy(rgba[:,:,:3])
alpha = rgba[:,:,3]
I = np.where(alpha == 0)
im[I[0], I[1], :] = 0
else:
im = rgba
im_color = im.astype('float') / 255.0
# depth image
im_depth = cv2.imread(depth_file, cv2.IMREAD_UNCHANGED)
im_depth = im_depth.astype('float') / 1000.0
return im_color, im_depth
def _get_label_blob(self, roidb, num_classes):
""" build the label blob """
# parse data
cls_indexes = roidb['ycb_ids']
classes = np.array(self._class_index)
fx = roidb['intrinsics']['fx']
fy = roidb['intrinsics']['fy']
px = roidb['intrinsics']['ppx']
py = roidb['intrinsics']['ppy']
intrinsic_matrix = np.eye(3, dtype=np.float32)
intrinsic_matrix[0, 0] = fx
intrinsic_matrix[1, 1] = fy
intrinsic_matrix[0, 2] = px
intrinsic_matrix[1, 2] = py
label = np.load(roidb['label_file'])
# label image
im_label = label['seg']
# poses
poses = label['pose_y']
if len(poses.shape) == 2:
poses = np.reshape(poses, (1, 3, 4))
num = poses.shape[0]
assert num == len(cls_indexes), 'number of poses not equal to number of objects'
# bounding boxes
gt_boxes = np.zeros((num, 5), dtype=np.float32)
for i in range(num):
cls = int(cls_indexes[i]) - 1
ind = np.where(classes == cls)[0]
if len(ind) > 0:
R = poses[i, :, :3]
T = poses[i, :, 3]
# compute box
x3d = np.ones((4, self._points_all.shape[1]), dtype=np.float32)
x3d[0, :] = self._points_all[ind,:,0]
x3d[1, :] = self._points_all[ind,:,1]
x3d[2, :] = self._points_all[ind,:,2]
RT = np.zeros((3, 4), dtype=np.float32)
RT[:3, :3] = R
RT[:, 3] = T
x2d = np.matmul(intrinsic_matrix, np.matmul(RT, x3d))
x2d[0, :] = np.divide(x2d[0, :], x2d[2, :])
x2d[1, :] = np.divide(x2d[1, :], x2d[2, :])
gt_boxes[i, 0] = np.min(x2d[0, :])
gt_boxes[i, 1] = np.min(x2d[1, :])
gt_boxes[i, 2] = np.max(x2d[0, :])
gt_boxes[i, 3] = np.max(x2d[1, :])
gt_boxes[i, 4] = ind
# load posecnn result if available
if os.path.exists(roidb['posecnn']):
result = scipy.io.loadmat(roidb['posecnn'])
n = result['poses'].shape[0]
poses_result = np.zeros((n, 9), dtype=np.float32)
poses_result[:, 0] = 1
poses_result[:, 1] = result['rois'][:, 1]
poses_result[:, 2:] = result['poses']
rois_result = result['rois'].copy()
labels_result = result['labels'].copy()
# select the classes, one object per class
index = []
flags = np.zeros((self._num_classes, ), dtype=np.int32)
for i in range(poses_result.shape[0]):
cls = self._posecnn_class_indexes[int(poses_result[i, 1])] - 1
ind = np.where(classes == cls)[0]
if len(ind) > 0 and flags[ind] == 0:
index.append(i)
poses_result[i, 1] = ind
rois_result[i, 1] = ind
flags[ind] = 1
poses_result = poses_result[index, :]
rois_result = rois_result[index, :]
else:
# print('no posecnn result %s' % (roidb['posecnn']))
poses_result = np.zeros((0, 9), dtype=np.float32)
rois_result = np.zeros((0, 7), dtype=np.float32)
labels_result = np.zeros((0, 1), dtype=np.float32)
poses = poses.transpose((1, 2, 0))
return im_label, intrinsic_matrix, poses, gt_boxes, poses_result, rois_result, labels_result
def _get_default_path(self):
"""
Return the default path where YCB_Video is expected to be installed.
"""
return os.path.join(datasets.ROOT_DIR, 'data', 'DEX_YCB')
def _load_object_extents(self):
extents = np.zeros((self._num_classes_all, 3), dtype=np.float32)
for i in range(self._num_classes_all):
point_file = os.path.join(self._model_dir, self._classes_all[i], 'points.xyz')
print(point_file)
assert os.path.exists(point_file), 'Path does not exist: {}'.format(point_file)
points = np.loadtxt(point_file)
extents[i, :] = 2 * np.max(np.absolute(points), axis=0)
return extents
def _load_object_points(self, classes, extents):
points = [[] for _ in range(len(classes))]
num = np.inf
num_classes = len(classes)
for i in range(num_classes):
point_file = os.path.join(self._model_dir, classes[i], 'points.xyz')
print(point_file)
assert os.path.exists(point_file), 'Path does not exist: {}'.format(point_file)
points[i] = np.loadtxt(point_file)
if points[i].shape[0] < num:
num = points[i].shape[0]
points_all = np.zeros((num_classes, num, 3), dtype=np.float32)
for i in range(num_classes):
points_all[i, :, :] = points[i][:num, :]
return points, points_all
def write_dop_results(self, output_dir, modality):
# only write the result file
filename = os.path.join(output_dir, 'poserbpf_' + self._name + '_' + modality + '.csv')
f = open(filename, 'w')
f.write('scene_id,im_id,obj_id,score,R,t,time\n')
# list the mat file
filename = os.path.join(output_dir, '*.mat')
files = sorted(glob.glob(filename))
# for each image
for i in range(len(files)):
filename = os.path.basename(files[i])
# parse filename
pos = filename.find('_')
scene_id = int(filename[:pos])
im_id = int(filename[pos+1:-4])
# load result
print(files[i])
result = scipy.io.loadmat(files[i])
if len(result['rois']) == 0:
continue
rois = result['rois']
num = rois.shape[0]
for j in range(num):
obj_id = self._class_index[int(rois[j, 1])] + 1
if obj_id == 0:
continue
score = rois[j, -1]
run_time = -1
# pose from network
R = quat2mat(result['poses'][j, :4].flatten())
t = result['poses'][j, 4:] * 1000
line = '{scene_id},{im_id},{obj_id},{score},{R},{t},{time}\n'.format(
scene_id=scene_id,
im_id=im_id,
obj_id=obj_id,
score=score,
R=' '.join(map(str, R.flatten().tolist())),
t=' '.join(map(str, t.flatten().tolist())),
time=run_time)
f.write(line)
# close file
f.close()
# compute box
def compute_box(self, cls, intrinsic_matrix, RT):
ind = np.where(self._class_index == cls)[0]
x3d = np.ones((4, self._points_all.shape[1]), dtype=np.float32)
x3d[0, :] = self._points_all[ind,:,0]
x3d[1, :] = self._points_all[ind,:,1]
x3d[2, :] = self._points_all[ind,:,2]
x2d = np.matmul(intrinsic_matrix, np.matmul(RT, x3d))
x2d[0, :] = np.divide(x2d[0, :], x2d[2, :])
x2d[1, :] = np.divide(x2d[1, :], x2d[2, :])
x1 = np.min(x2d[0, :])
y1 = np.min(x2d[1, :])
x2 = np.max(x2d[0, :])
y2 = np.max(x2d[1, :])
return [x1, y1, x2, y2]
def evaluation(self, output_dir, modality):
self.write_dop_results(output_dir, modality)
filename = os.path.join(output_dir, 'results_poserbpf.mat')
if os.path.exists(filename):
results_all = scipy.io.loadmat(filename)
print('load results from file')
print(filename)
distances_sys = results_all['distances_sys']
distances_non = results_all['distances_non']
errors_rotation = results_all['errors_rotation']
errors_translation = results_all['errors_translation']
results_seq_id = results_all['results_seq_id'].flatten()
results_frame_id = results_all['results_frame_id'].flatten()
results_object_id = results_all['results_object_id'].flatten()
results_cls_id = results_all['results_cls_id'].flatten()
else:
# save results
num_max = 200000
num_results = 1
distances_sys = np.zeros((num_max, num_results), dtype=np.float32)
distances_non = | np.zeros((num_max, num_results), dtype=np.float32) | numpy.zeros |
import sklearn.base
from abc import abstractmethod, ABC
from sklearn.utils import check_array, check_random_state
import pandas as pd
import os
import pickle
import numpy as np
import warnings
import logging
with warnings.catch_warnings():
warnings.filterwarnings("ignore", category=FutureWarning)
try:
import keras
from keras.backend import clear_session
except (ModuleNotFoundError, ImportError) as e:
pass
try:
import tensorflow.keras as keras
from tensorflow.keras.backend import clear_session
except (ModuleNotFoundError, ImportError) as e:
raise ModuleNotFoundError('Could not find a working distribution of Keras and Tensorflow! Please install to use this module.')
_DEFAULT_PREDICTION_BATCH_SIZE = 50000
### Abstract base class for AD models
class AnomalyDetectionBase(sklearn.base.BaseEstimator, ABC):
"""base class which inherits from the sklearn base estimator. Provides broad functionality for
declaring new model classes, including defining save and load functions.
A subclass should provide the following:
1. an __init__ method which passes all relevant estimator parameters to the
_inputs_to_attributes function, most easily by way of calling locals()
2. A function override for the "fit" function, taking as inputs the arrays
x, y_sim, y_sr, w, and m, and returning a reference to the class instance (self)
3. A function override for the "predict" function, taking as inputs an x-array
and returning an array of predictions
4. A function override for the "_model_names" function, returning a list of the
names of all keras models used for the estimator. This ensures proper saving
Additional helper functions may be defined as necessary, though good practice is
to prefix them with "_" to avoid namespace pollution.
"""
#
# ADDED FUNCTIONALITY (saving and loading)
#
def save(self, path, mkdirs=True,):
"""
Save estimator information to a directory
Parameters
----------
path : str, required
specifies the directory in which to save the model
mkdirs : bool, default=True
whether or not to create the directory given, if it doesn't exist
Returns
-------
self : class instance
useful for cascading object calls
"""
if not os.path.exists(path):
if mkdirs:
os.makedirs(path)
else:
raise FileNotFoundError('pathname "{}" not found. Set <mkdirs=True> to create directories.'.format(path))
save_dict = self.get_params(exact_models=True)
if hasattr(self, '_history'):
save_dict['_history'] = self._history
save_dict['classname'] = self.__class__.__name__
models = dict()
for k in list(save_dict.keys()):
if k in self._model_names():
models[k] = save_dict.pop(k)
for k,model in models.items():
mpath = '{}/{}'.format(path,k)
model = _validate_model(model, k)
save_dict[k] = model.to_json()
model.save(mpath)
with open('{}/params.pkl'.format(path), 'wb') as f:
pickle.dump(save_dict, f, protocol=pickle.HIGHEST_PROTOCOL)
return self
def load(self, path):
"""
Load saved information into estimator from a file
Parameters
----------
path : str, required
specifies a directory in which the desired model was saved.
should have at least the "params.pkl" pickle file in it.
Returns
-------
self : class instance
useful for cascading object calls
"""
save_dict, classname = self._load_params(path)
if classname != self.__class__.__name__:
raise ValueError('tried to load savefile of class "{}" into object with class "{}"!'.format(classname, self.__class__.__name__))
self._load_models(path, save_dict, classname)
return self
def get_params(self, deep=True, copy_models=False, exact_models=False):
"""
Get parameters for this estimator.
Parameters
----------
deep : bool, default=True
If True, will return the parameters for this estimator and
contained subobjects that are estimators.
copy_models : bool, default=False
If True, will return an identical (but copied) keras model
as the ones specified by the class variables of the return of _model_names.
Preserves model weights.
exact_models : bool, default=False
If True, will return the exact keras model as the one specified
by the class variables of the return of _model_names. Overrides
parameter <copy_models>. If both copy_models and exact_models are false,
then the model is cloned using keras.models.clone_model.
Returns
-------
params : dict
Parameter names mapped to their values.
"""
out = dict()
for key in self._get_param_names():
value = getattr(self, key)
if deep and hasattr(value, 'get_params'):
deep_items = value.get_params().items()
out.update((key + '__' + k, val) for k, val in deep_items)
if key in self._model_names():
if isinstance(value, str):
out[key] = value
elif value is None:
out[key] = None
else:
# then it is a keras model
if exact_models:
out[key] = value
elif copy_models:
out[key] = keras.models.model_from_json(value.to_json())
out[key].set_weights(value.get_weights())
else:
out[key] = keras.models.clone_model(value)
else:
out[key] = value
return out
def copy(self, copy_models=True, exact_models=False):
"""
copy this model
Parameters
----------
copy_models : bool, default=False
If True, will return an identical (but copied) keras model
as the ones specified by the class variables of the return of _model_names.
Preserves model weights.
exact_models : bool, default=False
If True, will return the exact keras model as the one specified
by the class variables of the return of _model_names. Overrides
parameter <copy_models>. If both copy_models and exact_models are false,
then the model is cloned using keras.models.clone_model.
Returns
-------
__class__ : copy of this class
"""
return self.__class__(**self.get_params(copy_models=copy_models, exact_models=exact_models))
#
# ABSTRACT METHODS (need to be redefined by derived classes)
#
@abstractmethod
def fit(self):
return self
@abstractmethod
def predict(self):
return None
@abstractmethod
def _model_names(self):
return []
#
# HELPER FUNCTIONS (just for init, basically)
#
def _inputs_to_attributes(self, local_variables):
"""
Set local variable dictionary as attributes; lazy __init__
Parameters
----------
local_variables : dict, required
dictionary of key value pairs to set as class attributes to this
instance of self
Returns
-------
"""
for k,v in local_variables.items():
if k != 'self':
setattr(self, k, v)
@staticmethod
def _load_params(path):
"""
Load saved information into estimator from a file
Parameters. Useful for loading generic models.
----------
path : str, required
specifies a directory in which the desired model was saved.
should have at least the "params.pkl" pickle file in it.
Returns
-------
save_dict : dict
dictionary of parameters from found file
classname : str
classname of class of saved model
"""
if not os.path.exists(path):
raise FileNotFoundError('pathname "{}" not found.'.format(path))
pkl_path = '{}/params.pkl'.format(path)
if not os.path.exists(pkl_path):
raise FileNotFoundError('file "{}" not found. cannot load model.'.format(pkl_path))
with open(pkl_path, 'rb') as f:
save_dict = pickle.load(f)
classname = save_dict.pop('classname')
return save_dict, classname
def _load_models(self, path, save_dict, classname):
"""
Load saved information into estimator from a file
Parameters
----------
path : str, required
specifies a directory in which the desired model was saved.
should have at least the "params.pkl" pickle file in it.
save_dict : dict, required
dictionary of parameters from found file
classname : str, required
classname of class of saved model
Returns
-------
self : class instance
useful for cascading object calls
"""
for k in self._model_names():
model_path = '{}/{}'.format(path, k)
# if k in save_dict:
if os.path.exists(model_path):
model = keras.models.load_model(model_path)
elif k in save_dict:
model = keras.models.model_from_json(save_dict[k])
else:
model = None
save_dict[k] = model
if '_history' in save_dict:
self._history = save_dict.pop('_history')
self.set_params(**save_dict)
return self
def __copy__(self):
return self.copy(exact_models=False)
### Helper functions for class definitions
def _check_array_type(x):
if isinstance(x, pd.DataFrame):
return x.values
elif isinstance(x, np.ndarray):
return x
raise AttributeError('input array is of type "{}"; should be array'.format(type(x)))
def _check_training_params(model, x, *y_args):
"""
checks training dataset parameters x, y, and w against model <model>, including shapes and types
"""
x = _check_array_type(x)
y_args = list(y_args)
arg_shapes = []
for i in range(len(y_args)):
arg = y_args[i]
if arg is not None:
arg = _check_array_type(arg)
if len(np.squeeze(arg).shape) > 1:
raise AttributeError('one of the input y-style arrays is non-vector valued!')
arg_shapes.append(arg.size)
y_args[i] = arg
if len(np.unique(np.array(arg_shapes))) > 1:
raise AttributeError('input y value array shapes do not match')
# if not isinstance(model, keras.Model):
# raise AttributeError('model is not a keras.Model instance!')
input_match = model.input_shape[1] == np.array(x.shape)
if not input_match.any():
raise AttributeError('x array shape {} does not match model input shape {}'.format(x.shape, model.input_shape))
if len(input_match) > 2:
raise AttributeError('input array must have less than 3 dimensions')
if np.where(input_match)[0][0] == 0:
x = x.T
return tuple([x] + y_args)
def _validate_model(model, name):
if model is None:
raise ValueError('parameter <{}> is None. Please set it to a valid keras model/keras json architecture.'.format(name))
elif isinstance(model, str):
print('decoding')
try:
model = keras.models.model_from_json(model)
except JSONDecodeError:
raise ValueError('parameter <{}> with value "{}" could not be decoded.'.format(name, model))
return model
### functions for user usage
def autoload(path, **kwargs):
"""
Dynamically load a model without a specified base class. Class used must be included in
this module, or else specified by name in as a keyword argument.
Parameters
----------
path : str, required
specifies a directory in which the desired model was saved.
should have at least the "params.pkl" pickle file in it.
Returns
-------
AnomalyDetectionBase derived class
loaded model, if its correct classname could be found
"""
params, classname = AnomalyDetectionBase._load_params(path)
if classname in globals():
return globals()[classname]()._load_models(path, params, classname)
else:
raise AttributeError('classname "{}" from model at path {} not known!'.format(classname, path))
### Predefined class definitions for common model types
class SALAD(AnomalyDetectionBase):
def __init__(
self, sb_model=None, model=None,
optimizer='adam', metrics=[], loss='binary_crossentropy',
epochs=10, sb_epochs=10, batch_size=1000, sb_batch_size=1000,
compile=True, callbacks=[], test_size=0., verbose=False,
dctr_epsilon=1e-5,
):
self._inputs_to_attributes(locals())
def fit(
self, x, y_sim=None, y_sr=None, w=None, m=None
):
if y_sim is None:
raise ValueError('parameter <y_sim> must hold simulation/data tags!')
if y_sr is None:
raise ValueError('parameter <y_sr> must hold signal region/sideband tags!')
if m is None:
raise ValueError('parameter <m> must be a localizing feature for SALAD!')
sb_tag, sr_tag = ~y_sr.astype(bool), y_sr.astype(bool)
sb_hist = self._fit_sb(x[sb_tag], y_sim[sb_tag], w=(w[sb_tag] if w is not None else w), m=m[sb_tag])
sr_hist = self._fit_sr(x[sr_tag], y_sim[sr_tag], w=(w[sr_tag] if w is not None else w), m=m[sr_tag])
self._history = sb_hist.history, sr_hist.history
return self
def predict(
self, x
):
return self.model.predict(x, batch_size=_DEFAULT_PREDICTION_BATCH_SIZE).squeeze()
def predict_weight(
self, x
):
yhat = self.sb_model.predict(x, batch_size=_DEFAULT_PREDICTION_BATCH_SIZE)
return np.squeeze(yhat/(1 + self.dctr_epsilon - yhat))
def _fit_sb(
self, x, y_sim, w=None, m=None
):
self.sb_model = _validate_model(self.sb_model, 'sb_model')
if len(m.shape) < 2:
m = m[:,np.newaxis]
x = | np.concatenate([m, x], axis=1) | numpy.concatenate |
import numpy as np
import random
import math
def normalize_table(t):
return t / | np.sum(t, 0) | numpy.sum |
import numpy as np
def random_augmentation(img, mask):
#you can add any augmentations you need
return img, mask
def batch_generator(image, mask,
batch_size=1,
crop_size=0,
patch_size=256,
bbox= None,
augmentation=False):
'''
image: nparray, must have 3 dimension
mask: nparray, 2 dimensions, same size as image
batch_size: int, number of images in a batch
patch_size: int, size of the image returned, patch is square
crop_size: int, how much pixels should be cropped off the mask
bbox: None or tuple of 4 ints, (min_y, max_y, min_x, max_x), the data is selected from within the bbox
augmentation: turn on/off data augmentation. The augmentation function is random_augmentation() above
returns batch of image and mask patches, image is turned to 'channels last' as required by unet
'''
if np.ndim(mask) != 2 or | np.ndim(image) | numpy.ndim |
# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
# 《机器学习实战》 - 第5章 - Logistic回归
# 示例1:采用梯度上升法找到Logistic回归分类器的最佳回归系数
def loadDataSet():
"""
读取数据集
"""
dataMat = []
labelMat = []
fr = open('TestSet.txt')
for line in fr.readlines():
lineArr = line.strip().split()
# X0设为1.0
dataMat.append([1.0,float(lineArr[0]),float(lineArr[1])])
labelMat.append(int(lineArr[2]))
return dataMat,labelMat
def sigmoid(z):
"""
sigmoid函数
"""
return 1.0 / (1 + | np.exp(-z) | numpy.exp |
import os
import sys
import numpy as np
import time
import matplotlib.pyplot as plt
import pandas as pd
from utils import *
def sliding_dot_product(q, t):
n = t.size
m = q.size
# Append t with n zeros
ta = np.append(t, np.zeros(n))
# Reverse Q
qr = np.flip(q, 0)
# Append qra
qra = np.append(qr, np.zeros(2 * n - m))
# Compute FFTs
qraf = np.fft.fft(qra)
taf = np.fft.fft(ta)
# Compute the inverse FFT to the element-wise multiplication of qraf and taf
qt = np.fft.ifft(np.multiply(qraf, taf))
return qt[m:n]
def sliding_dot_product_stomp(q, t):
n = t.size
m = q.size
# Append t with n zeros
ta = np.append(t, np.zeros(n))
# Reverse Q
qr = np.flip(q, 0)
# Append qra
qra = np.append(qr, np.zeros(2 * n - m))
# Compute FFTs
qraf = np.fft.fft(qra)
taf = np.fft.fft(ta)
# Compute the inverse FFT to the element-wise multiplication of qraf and taf
qt = np.fft.ifft(np.multiply(qraf, taf))
return qt[m - 1:n]
def calculate_distance_profile(q, t, qt, a, sum_q, sum_q2, mean_t, sigma_t):
n = t.size
m = q.size
b = np.zeros(n - m)
dist = np.zeros(n - m)
for i in range(0, n - m):
b[i] = -2 * (qt[i].real - sum_q * mean_t[i]) / sigma_t[i]
dist[i] = a[i] + b[i] + sum_q2
return np.sqrt(np.abs(dist))
# The code below takes O(m) for each subsequence
# you should replace it for MASS
def compute_mean_std_for_query(Q):
# Compute Q stats -- O(n)
sumQ = np.sum(Q)
sumQ2 = np.sum(np.power(Q, 2))
return sumQ, sumQ2
def pre_compute_mean_std_for_TS(ta, m):
na = len(ta)
sum_t = np.zeros(na - m)
sum_t2 = np.zeros(na - m)
# Compute the stats for t
cumulative_sum_t = np.cumsum(ta)
cumulative_sum_t2 = np.cumsum(np.power(ta, 2))
for i in range(na - m):
sum_t[i] = cumulative_sum_t[i + m] - cumulative_sum_t[i]
sum_t2[i] = cumulative_sum_t2[i + m] - cumulative_sum_t2[i]
mean_t = np.divide(sum_t, m)
mean_t2 = np.divide(sum_t2, m)
mean_t_p2 = np.power(mean_t, 2)
sigma_t2 = np.subtract(mean_t2, mean_t_p2)
sigma_t = np.sqrt(sigma_t2)
return sum_t, sum_t2, mean_t, mean_t2, mean_t_p2, sigma_t, sigma_t2
def pre_compute_mean_std_for_TS_stomp(ta, m):
na = len(ta)
# Compute the stats for t
cumulative_sum_t = np.cumsum(ta)
cumulative_sum_t2 = np.cumsum(np.power(ta, 2))
sum_t = (cumulative_sum_t[m - 1:na] - np.concatenate(([0], cumulative_sum_t[0:na - m])))
sum_t2 = (cumulative_sum_t2[m - 1:na] - np.concatenate(([0], cumulative_sum_t2[0:na - m])))
mean_t = np.divide(sum_t, m)
mean_t2 = np.divide(sum_t2, m)
mean_t_p2 = np.power(mean_t, 2)
sigma_t2 = np.subtract(mean_t2, mean_t_p2)
sigma_t = np.sqrt(sigma_t2)
return sum_t, sum_t2, mean_t, mean_t2, mean_t_p2, sigma_t, sigma_t2
# MUEEN’S ALGORITHM FOR SIMILARITY SEARCH (MASS)
def mass(Q, T, a, meanT, sigmaT):
# Z-Normalisation
if np.std(Q) != 0:
Q = (Q - np.mean(Q)) / np.std(Q)
QT = sliding_dot_product(Q, T)
sumQ, sumQ2 = compute_mean_std_for_query(Q)
return calculate_distance_profile(Q, T, QT, a, sumQ, sumQ2, meanT, sigmaT)
def element_wise_min(Pab, Iab, D, idx, ignore_trivial, m):
for i in range(0, len(D)):
if not ignore_trivial or (
np.abs(idx - i) > m / 2.0): # if it's a self-join, ignore trivial matches in [-m/2,m/2]
if D[i] < Pab[i]:
Pab[i] = D[i]
Iab[i] = idx
return Pab, Iab
def stamp(Ta, Tb, m):
"""
Compute the Matrix Profile between time-series Ta and Tb.
If Ta==Tb, the operation is a self-join and trivial matches are ignored.
:param Ta: time-series, np.array
:param Tb: time-series, np.array
:param m: subsequence length
:return: Matrix Profile, Nearest-Neighbor indexes
"""
nb = len(Tb)
na = len(Ta)
Pab = np.ones(na - m) * np.inf
Iab = np.zeros(na - m)
idxes = np.arange(nb - m + 1)
sumT, sumT2, meanT, meanT_2, meanTP2, sigmaT, sigmaT2 = pre_compute_mean_std_for_TS(Ta, m)
a = np.zeros(na - m)
for i in range(0, na - m):
a[i] = (sumT2[i] - 2 * sumT[i] * meanT[i] + m * meanTP2[i]) / sigmaT2[i]
ignore_trivial = np.atleast_1d(Ta == Tb).all()
for idx in idxes:
D = mass(Tb[idx: idx + m], Ta, a, meanT, sigmaT)
if (ignore_trivial):
# ignore trivial minimum and maximum
minIdx = int(np.maximum(idx - m / 2.0, 0))
maxIdx = int(np.minimum(idx + m / 2.0, len(D)))
D[minIdx:maxIdx:1] = np.inf
Iab[Pab > D] = i
Pab = np.minimum(Pab, D)
return Pab, Iab
def stomp(T, m):
"""
Compute the Matrix Profile with self join for T
:param T: time-series, np.array
:param Tb: time-series, np.array
:param m: subsequence length
:return: Matrix Profile, Nearest-Neighbor indexes
"""
epsilon = 1e-10
n = len(T)
seq_l = n - m
_, _, meanT, _, _, sigmaT, _ = pre_compute_mean_std_for_TS_stomp(T, m)
Pab = np.full(seq_l + 1, np.inf)
Iab = np.zeros(n - m + 1)
ignore_trivial = True
for idx in range(0, seq_l):
# There's somthing with normalization
Q_std = sigmaT[idx] if sigmaT[idx] > epsilon else epsilon
if idx == 0:
QT = sliding_dot_product_stomp(T[0:m], T).real
QT_first = np.copy(QT)
else:
QT[1:] = QT[0:-1] - (T[0:seq_l] * T[idx - 1]) + (T[m:n] * T[idx + m - 1])
QT[0] = QT_first[idx]
# Calculate distance profile
D = (2 * (m - (QT - m * meanT * meanT[idx]) / (Q_std * sigmaT)))
D[D < epsilon] = 0
if (ignore_trivial):
# ignore trivial minimum and maximum
minIdx = int(np.maximum(idx - m / 2.0, 0))
maxIdx = int(np.minimum(idx + m / 2.0, len(D)))
D[minIdx:maxIdx:1] = np.inf
Iab[Pab > D] = idx
np.minimum(Pab, D, Pab)
np.sqrt(Pab, Pab)
return Pab, Iab
# Quick Test
# def test_stomp(Ta, m):
# start_time = time.time()
#
# Pab, Iab = stomp(Ta, m)
# print("--- %s seconds ---" % (time.time() - start_time))
# plot_motif(Ta, Pab, Iab, m)
# return Pab, Iab
# Quick Test
# def test_stamp(Ta, Tb, m):
# start_time = time.time()
#
# Pab, Iab = stamp(Ta, Tb, m)
# print("--- %s seconds ---" % (time.time() - start_time))
#
# plot_discord(Ta, Pab, Iab, m, )
# return Pab, Iab
def plot_motif(Ta, values, indexes, m):
from matplotlib import gridspec
plt.figure(figsize=(8, 4))
plt.subplot(211)
plt.plot(Ta, linestyle='--', alpha=0.5)
plt.xlim((0, len(Ta)))
print(np.argmax(values))
plt.plot(range(np.argmin(values), np.argmin(values) + m), Ta[np.argmin(values):np.argmin(values) + m], c='g',
label='Top Motif')
plt.plot(range( | np.argmax(values) | numpy.argmax |
import matplotlib.pyplot as plt
import xarray as xr
import xarray.ufuncs as uf
import numpy as np
import warnings
import gsw
import traceback
from .coast import Coast
from .gridded import Gridded
from scipy import interpolate
from scipy.integrate import cumtrapz
from sklearn.neighbors import BallTree
from skimage import measure
from .logging_util import warn, error
# =============================================================================
# The contour module is a place for code related to contours only
# =============================================================================
class Contour:
# TODO Should these be module-level variables?
GRAVITY = 9.8 # m s^-2
EARTH_ROT_RATE = 7.2921 * 10 ** (-5) # rad/s
@staticmethod
def get_contours(gridded: Coast, contour_depth: int):
"""
A method to obtain the continuous isbobath contours within a supplied
gridded domain as a set of y indices and x indices for the model grid.
Parameters
----------
gridded : Coast
The gridded object containing the dataset with the 'bathymetry' variable
contour_depth : int
Depth of desired contours
Returns
-------
List of 2d ndarrays
Each item of the list contains a different continuous isobath contour as a
2d ndarray of indicies, i.e. for each list item:
contour[:,0] contains the y indices for the contour on the model grid
contour[:,1] contains the x indices for the contour on the model grid
"""
contours = measure.find_contours(gridded.dataset.bathymetry.data, contour_depth)
# The find_contours method returns indices that have been interpolated
# between grid points so we must round and cast to integer
contours = [np.round(contour).astype(int) for contour in contours]
return contours, len(contours)
@staticmethod
def plot_contour(gridded: Coast, contour: np.ndarray):
"""
Quick plot method to plot a contour over a pcolormesh of the
model bathymetry
Parameters
----------
gridded : Coast
The gridded object containing the dataset with the 'bathymetry' variable
contour : 2d array
contour[:,0] contains the y indices for the contour on the model grid
contour[:,1] contains the x indices for the contour on the model grid
i.e. contour = np.vstack((y_indices,x_indices)).T
Returns
-------
None
"""
fig, ax = plt.subplots()
lat = gridded.dataset.latitude[xr.DataArray(contour[:, 0]), xr.DataArray(contour[:, 1])]
lon = gridded.dataset.longitude[xr.DataArray(contour[:, 0]), xr.DataArray(contour[:, 1])]
gridded.dataset.bathymetry.where(gridded.dataset.bathymetry > 0, np.nan).plot.pcolormesh(
y="latitude", x="longitude", ax=ax
)
ax.scatter(lon, lat, s=0.5, color="r")
@staticmethod
def get_contour_segment(gridded: Coast, contour: np.ndarray, start_coords: np.ndarray, end_coords: np.ndarray):
"""
Method that will take a contour from the list of contours generated by
coast.Contour.get_contours() and trim it to start at supplied (lat,lon)
coordinates and end at supplied (lat, lon) coordinates.
Parameters
----------
gridded : Coast
The gridded object containing the dataset with the 'bathymetry' variable
contour : numpy.ndarray
contour[:,0] contains the y indices for the contour on the model grid
contour[:,1] contains the x indices for the contour on the model grid
start_coords : numpy.ndarray
1d array containing [latitude,longitude] of the start point of the contour
end_coords : numpy.ndarray
1d array containing [latitude,longitude] of the end point of the contour
Returns
-------
y_ind : numpy.ndarray
y indices of the contour on the model grid
x_ind : numpy.ndarray
x indices of the contour on the model grid
contour : numpy.ndarray
For the convenience of plotting using coast.Contour.plot_contour()
contour[:,0] = y_ind
contour[:,1] = x_ind
"""
y_ind = contour[:, 0]
x_ind = contour[:, 1]
# Create tree of lat and lon on the pre-processed contour
ball_tree = BallTree(
np.deg2rad(
list(zip(gridded.dataset.latitude.values[y_ind, x_ind], gridded.dataset.longitude.values[y_ind, x_ind]))
),
metric="haversine",
)
# Get start and end indices for contour and subset accordingly
start_idx = ball_tree.query(np.deg2rad([start_coords]))[1][0][0]
end_idx = ball_tree.query(np.deg2rad([end_coords]))[1][0][0]
if start_idx > end_idx:
y_ind = y_ind[end_idx : start_idx + 1]
x_ind = x_ind[end_idx : start_idx + 1]
else:
y_ind = y_ind[start_idx : end_idx + 1]
x_ind = x_ind[start_idx : end_idx + 1]
# Ensure that the start point is closer to southern boundary of domain.
# If start and end point have same latitude then ensure start point is
# closer to the western boundary of the domain.
if y_ind[0] > y_ind[-1]:
y_ind = y_ind[::-1]
x_ind = x_ind[::-1]
elif y_ind[0] == y_ind[-1]:
if x_ind[0] > x_ind[-1]:
y_ind = y_ind[::-1]
x_ind = x_ind[::-1]
return y_ind, x_ind, np.vstack((y_ind, x_ind)).T
def __init__(self, gridded: Coast, y_ind, x_ind, depth: int):
"""
Class defining a Contour type, which is a 3d dataset of points between a point A and
a point B defining an isobath contour. The dataset has a time, depth and contour dimension.
The contour dimension defines the points along the contour.
The supplied model Data is subsetted in its entirety along these dimensions and
calculations can be performed on this dataset.
Parameters
----------
gridded : Coast
gridded object containing the model dataset.
y_ind : numpy.ndarray
1d array of y indices defining the contour on the model grid
x_ind : numpy.ndarray
1d array of x indices defining the contour on the model grid
depth : int
Depth of contour isobath
"""
try:
if y_ind[0] > y_ind[-1]:
raise ValueError(
"Start point of the contour "
"must be closer than the end point of the "
"contour to the southern boundary of the model "
"domain."
)
elif y_ind[0] == y_ind[-1]:
if x_ind[0] > x_ind[-1]:
raise ValueError(
"Start and end points of the contour "
"have the same latitudes, the start point must "
"be the closer of the two points to the western "
"boundary of the model domain."
)
self.depth = depth
self.y_ind, self.x_ind = self.process_contour(gridded.dataset, y_ind, x_ind)
self.len = len(self.y_ind)
self.filename_domain = gridded.filename_domain
da_y_ind = xr.DataArray(self.y_ind, dims=["r_dim"])
da_x_ind = xr.DataArray(self.x_ind, dims=["r_dim"])
self.data_contour = gridded.dataset.isel(y_dim=da_y_ind, x_dim=da_x_ind)
except ValueError:
print(traceback.format_exc())
def process_contour(self, dataset: xr.Dataset, y_ind, x_ind):
"""Redefine contour so that each point on the contour defined by
y_ind and x_ind is seperated from its neighbours by a single index change
in y or x, but not both.
example: convert y_ind = [10,11], x_ind = [1,2] to y_ind = [10,10], x_ind = [1,2]
or y_ind = [10,11], x_ind = [1,1]
Parameters
----------
dataset : xarray.Dataset
xarray Dataset from supplied gridded object
y_ind : numpy.ndarray
1d array of y indices defining the contour on the model grid
x_ind : numpy.ndarray
1d array of x indices defining the contour on the model grid
Returns
-------
y_ind : numpy.ndarray
processed y indices of the contour on the model grid
x_ind : numpy.ndarray
processed x indices of the contour on the model grid
"""
try:
y_ind = np.asarray(y_ind)
x_ind = np.asarray(x_ind)
# When replacing diagonal segments in the contour, pick the path that is
# closest to the contour isobath depth
option1 = np.fabs(dataset.bathymetry[xr.DataArray(y_ind + 1), xr.DataArray(x_ind)] - self.depth)
option0 = np.fabs(dataset.bathymetry[xr.DataArray(y_ind), xr.DataArray(x_ind + 1)] - self.depth)
add_new_y_point = xr.where(option1 <= option0, 1, 0)
spacing = np.abs(np.diff(y_ind)) + np.abs(np.diff(x_ind))
if spacing.max() > 2:
raise ValueError(
"The contour is not continuous. The contour must be defined on " "adjacent grid points."
)
spacing[spacing != 2] = 0
double_spacing = np.nonzero(spacing)[0]
for space_index in double_spacing[::-1]:
if add_new_y_point[space_index]:
y_ind = np.insert(y_ind, space_index + 1, y_ind[space_index + 1])
x_ind = np.insert(x_ind, space_index + 1, x_ind[space_index])
else:
y_ind = np.insert(y_ind, space_index + 1, y_ind[space_index])
x_ind = np.insert(x_ind, space_index + 1, x_ind[space_index + 1])
# Remove any repeated points caused by the rounding of the indices
non_repeated_idx = np.nonzero(np.abs(np.diff(y_ind)) + np.abs(np.diff(x_ind)))
y_ind = np.concatenate((y_ind[non_repeated_idx], [y_ind[-1]]))
x_ind = np.concatenate((x_ind[non_repeated_idx], [x_ind[-1]]))
return y_ind, x_ind
except ValueError:
error(traceback.format_exc())
@staticmethod
def gen_z_levels(max_depth):
"""Generates a pre-defined 1d vertical depth coordinates,
i.e. horizontal z-level vertical coordinates up to a supplied
maximum depth, 'max_depth'"""
max_depth = max_depth + 650
z_levels_0_50 = np.arange(0, 55, 5)
z_levels_60_290 = np.arange(60, 300, 10)
z_levels_300_600 = np.arange(300, 650, 50)
z_levels_650_ = np.arange(650, max_depth + 150, 150)
z_levels = np.concatenate((z_levels_0_50, z_levels_60_290, z_levels_300_600, z_levels_650_))
z_levels = z_levels[z_levels <= max_depth]
return z_levels
class ContourF(Contour):
"""
Class defining a Contour type on the f-grid, which is a 3d dataset of points between a point A and
a point B defining an isobath contour. The dataset has a time, depth and contour dimension.
The contour dimension defines the points along the contour.
The supplied model f-grid Data is subsetted in its entirety along these dimensions
within Contour_f.data_contour of type xarray.Dataset
Parameters
----------
gridded_f : Coast
f-grid gridded object containing the model dataset.
y_ind : numpy.ndarray
1d array of y indices defining the contour on the model grid
x_ind : numpy.ndarray
1d array of x indices defining the contour on the model grid
depth : int
Depth of contour isobath
"""
def __init__(self, gridded_f: Coast, y_ind, x_ind, depth):
super().__init__(gridded_f, y_ind, x_ind, depth)
self.data_cross_flow = xr.Dataset()
def calc_cross_contour_flow(self, gridded_u: Coast, gridded_v: Coast):
"""
Method that will calculate the flow across the contour and store this data
within Contour_f.data_cross_flow, which is an xarray.Dataset. Specifically
Contour_f.normal_velocities are the velocities across the contour
(time, depth, position along contour) in m/s
Contour_f.depth_integrated_normal_transport are the depth integrated
volume transports across the contour (time, position along contour) in Sv
If the time dependent cell thicknesses (e3) on the u and v grids are
present in the gridded_u and gridded_v datasets they will be used, if they
are not then the initial cell thicknesses (e3_0) will be used.
Parameters
----------
gridded_u : Coast
The gridded object containing the model data on the u-grid.
gridded_v : Coast
The gridded object containing the model data on the v-grid.
Returns
-------
None.
"""
# compute transports flag; set to false if suitable e3 not found
compute_transports = True
# subset the u and v datasets
da_y_ind = xr.DataArray(self.y_ind, dims=["r_dim"])
da_x_ind = xr.DataArray(self.x_ind, dims=["r_dim"])
u_ds = gridded_u.dataset.isel(y_dim=da_y_ind, x_dim=da_x_ind)
v_ds = gridded_v.dataset.isel(y_dim=da_y_ind, x_dim=da_x_ind)
# use time varying if e3 is present, if not default to e3_0
if "e3" not in u_ds.data_vars:
if "e3_0" not in u_ds.data_vars:
warn("e3 not found, transports will not be calculated")
compute_transports = False
else:
u_ds["e3"] = u_ds.e3_0.broadcast_like(u_ds.u_velocity)
if "e3" not in v_ds.data_vars:
if "e3_0" not in v_ds.data_vars:
warn("e3 not found, transports will not be calculated")
compute_transports = False
else:
v_ds["e3"] = v_ds.e3_0.broadcast_like(v_ds.v_velocity)
# If time dimension is missing it can throw off the indexing so expand dims
if "t_dim" not in u_ds.dims:
u_ds["u_velocity"] = u_ds.u_velocity.expand_dims("t_dim", axis=0)
if compute_transports:
u_ds["e3"] = u_ds.e3.expand_dims("t_dim", axis=0)
if "t_dim" not in v_ds.dims:
v_ds["v_velocity"] = v_ds.v_velocity.expand_dims("t_dim", axis=0)
if compute_transports:
v_ds["e3"] = v_ds.e3.expand_dims("t_dim", axis=0)
dr_n = np.where(np.diff(self.y_ind) > 0, np.arange(0, u_ds.r_dim.size - 1), np.nan)
dr_n = dr_n[~np.isnan(dr_n)].astype(int)
dr_s = np.where(np.diff(self.y_ind) < 0, np.arange(0, u_ds.r_dim.size - 1), np.nan)
dr_s = dr_s[~np.isnan(dr_s)].astype(int)
dr_e = np.where(np.diff(self.x_ind) > 0, np.arange(0, v_ds.r_dim.size - 1), np.nan)
dr_e = dr_e[~np.isnan(dr_e)].astype(int)
dr_w = np.where(np.diff(self.x_ind) < 0, np.arange(0, v_ds.r_dim.size - 1), np.nan)
dr_w = dr_w[~np.isnan(dr_w)].astype(int)
# Note that subsetting the dataset first instead of subsetting each array seperately,
# as we do here, is neater but significantly slower.
tmp_velocities = xr.full_like(u_ds.u_velocity, np.nan)
tmp_velocities[:, :, dr_n] = u_ds.u_velocity.data[:, :, dr_n + 1]
tmp_velocities[:, :, dr_s] = -u_ds.u_velocity.data[:, :, dr_s]
tmp_velocities[:, :, dr_e] = -v_ds.v_velocity.data[:, :, dr_e + 1]
tmp_velocities[:, :, dr_w] = v_ds.v_velocity.data[:, :, dr_w]
self.data_cross_flow["normal_velocities"] = tmp_velocities[:, :, :-1]
self.data_cross_flow["normal_velocities"].attrs = {"units": "m/s", "standard_name": "contour-normal velocities"}
# Store the length of the contour segement (calling it e4) on the cross-contour velocity grid
tmp_e4 = xr.full_like(u_ds.e1, np.nan)
tmp_e4[dr_n] = u_ds.e2.data[dr_n + 1]
tmp_e4[dr_s] = u_ds.e2.data[dr_s]
tmp_e4[dr_e] = v_ds.e1.data[dr_e + 1]
tmp_e4[dr_w] = v_ds.e1.data[dr_w]
self.data_cross_flow["e4"] = tmp_e4[:-1]
self.data_cross_flow["e4"].attrs = {
"units": "m",
"standard_name": "length of contour segment at the cross-contour velocity grid points",
}
if compute_transports:
# calculate the transport across the contour
tmp_transport = xr.full_like(u_ds.u_velocity, np.nan)
tmp_transport[:, :, dr_n] = (
u_ds.u_velocity.data[:, :, dr_n + 1] * u_ds.e2.data[dr_n + 1] * u_ds.e3.data[:, :, dr_n + 1]
)
tmp_transport[:, :, dr_s] = (
-u_ds.u_velocity.data[:, :, dr_s] * u_ds.e2.data[dr_s] * u_ds.e3.data[:, :, dr_s]
)
tmp_transport[:, :, dr_e] = (
-v_ds.v_velocity.data[:, :, dr_e + 1] * v_ds.e1.data[dr_e + 1] * v_ds.e3.data[:, :, dr_e + 1]
)
tmp_transport[:, :, dr_w] = v_ds.v_velocity.data[:, :, dr_w] * v_ds.e1.data[dr_w] * v_ds.e3.data[:, :, dr_w]
self.data_cross_flow["normal_transport"] = tmp_transport[:, :, :-1]
self.data_cross_flow["normal_transport"].attrs = {
"units": "m^3/s",
"standard_name": "contour-normal volume transport",
}
# calculate the depth integrated transport across the contour
self.data_cross_flow["depth_integrated_normal_transport"] = (
self.data_cross_flow.normal_transport.sum(dim="z_dim") / 1000000.0
)
self.data_cross_flow["depth_integrated_normal_transport"].attrs = {
"units": "Sv",
"standard_name": "contour-normal depth integrated volume transport",
}
self._update_cross_flow_vars("depth_0", u_ds.depth_0, v_ds.depth_0, dr_n, dr_s, dr_e, dr_w, 1)
self._update_cross_flow_latlon(u_ds, v_ds, dr_n, dr_s, dr_e, dr_w)
self._update_cross_flow_vars("bathymetry", u_ds.bathymetry, v_ds.bathymetry, dr_n, dr_s, dr_e, dr_w, 0)
self._update_cross_flow_vars("e1", u_ds.e1, v_ds.e1, dr_n, dr_s, dr_e, dr_w, 0)
self._update_cross_flow_vars("e2", u_ds.e2, v_ds.e2, dr_n, dr_s, dr_e, dr_w, 0)
if compute_transports:
self._update_cross_flow_vars("e3", u_ds.e3, v_ds.e3, dr_n, dr_s, dr_e, dr_w, 2)
self.data_cross_flow["depth_0"].attrs = {
"standard_name": "Depth at time zero on the contour-normal velocity grid points"
}
self.data_cross_flow = self.data_cross_flow.squeeze()
def _update_cross_flow_vars(self, var, u_var, v_var, dr_n, dr_s, dr_e, dr_w, pos):
"""This method will pull variable data at specific points along the contour
from the u and v grid datasets and put them into the self.data_cross_flow dataset"""
tmp_var = xr.full_like(u_var, np.nan)
if pos == 0:
tmp_var[dr_n] = u_var.data[dr_n + 1]
tmp_var[dr_s] = u_var.data[dr_s]
tmp_var[dr_e] = v_var.data[dr_e + 1]
tmp_var[dr_w] = v_var.data[dr_w]
self.data_cross_flow[var] = tmp_var[:-1]
elif pos == 1:
tmp_var[:, dr_n] = u_var.data[:, dr_n + 1]
tmp_var[:, dr_s] = u_var.data[:, dr_s]
tmp_var[:, dr_e] = v_var.data[:, dr_e + 1]
tmp_var[:, dr_w] = v_var.data[:, dr_w]
self.data_cross_flow[var] = tmp_var[:, :-1]
elif pos == 2:
tmp_var[:, :, dr_n] = u_var.data[:, :, dr_n + 1]
tmp_var[:, :, dr_s] = u_var.data[:, :, dr_s]
tmp_var[:, :, dr_e] = v_var.data[:, :, dr_e + 1]
tmp_var[:, :, dr_w] = v_var.data[:, :, dr_w]
self.data_cross_flow[var] = tmp_var[:, :, :-1]
def _update_cross_flow_latlon(self, ds_u, ds_v, dr_n, dr_s, dr_e, dr_w):
"""This method will pull the latitude and longitude data at specific points along the
contour from the u and v grid datasets and put them into the self.data_cross_flow dataset"""
for var in ["longitude", "latitude"]:
tmp_var = xr.full_like(ds_u[var], np.nan)
tmp_var[dr_n] = ds_u[var].data[dr_n + 1]
tmp_var[dr_s] = ds_u[var].data[dr_s]
tmp_var[dr_e] = ds_v[var].data[dr_e + 1]
tmp_var[dr_w] = ds_v[var].data[dr_w]
tmp_var.attrs = {"standard_name": var.capitalize() + " at the contour-normal velocity grid points"}
self.data_cross_flow.assign_coords({var: tmp_var[:-1]})
@staticmethod
def _pressure_gradient_fpoint2(ds_t, ds_t_j1, ds_t_i1, ds_t_j1i1, r_ind, velocity_component):
"""
Calculates the hydrostatic and surface pressure gradients at a set of f-points
along the contour, i.e. at a set of specific values of r_dim (but for all time and depth).
The caller must supply four datasets that contain the variables which define
the hydrostatic and surface pressure at all vertical z_levels and all time
on the t-points around the contour i.e. for a set of f-points on the contour
defined each defined at (j+1/2, i+1/2), we want t-points at (j,i), (j+1,i), (j,i+1), (j+1,i+1),
corresponding to ds_t, ds_t_j1, ds_t_i1, ds_t_j1i1, respectively.
ds_t, ds_t_j1, ds_t_i1, ds_t_j1i1 will have dimensions in time and depth.
The velocity_component defines whether u or v is normal to the contour
for the segments of the contour. A segment of contour is
defined as being r_dim to r_dim+1 where r_dim is the along contour dimension.
Returns
-------
hpg_f : DataArray with dimensions in time and depth and along contour
hydrostatic pressure gradient at a set of f-points along the contour
for all time and depth
spg_f : DataArray with dimensions in time and depth and along contour
surface pressure gradient at a set of f-points along the contour
"""
if velocity_component == "u":
# required scale factors for derivative and averaging
e2v = 0.5 * (ds_t_j1.e2.data[r_ind] + ds_t.e2.data[r_ind])
e2v_i1 = 0.5 * (ds_t_j1i1.e2.data[r_ind] + ds_t_i1.e2.data[r_ind])
e1v = 0.5 * (ds_t_j1.e1.data[r_ind] + ds_t.e1.data[r_ind])
e1v_i1 = 0.5 * (ds_t_j1i1.e1.data[r_ind] + ds_t_i1.e1.data[r_ind])
e1f = 0.5 * (e1v + e1v_i1)
# calculate gradients at v-points either side of f-point
hpg = (ds_t_j1.pressure_h_zlevels.data[:, :, r_ind] - ds_t.pressure_h_zlevels.data[:, :, r_ind]) / e2v
hpg_i1 = (
ds_t_j1i1.pressure_h_zlevels.data[:, :, r_ind] - ds_t_i1.pressure_h_zlevels.data[:, :, r_ind]
) / e2v_i1
# average onto f-point
hpg_f = 0.5 * ((e1v * hpg) + (e1v_i1 * hpg_i1)) / e1f
# as aboave
spg = (ds_t_j1.pressure_s.data[:, r_ind] - ds_t.pressure_s.data[:, r_ind]) / e2v
spg_i1 = (ds_t_j1i1.pressure_s.data[:, r_ind] - ds_t_i1.pressure_s.data[:, r_ind]) / e2v_i1
spg_f = 0.5 * ((e1v * spg) + (e1v_i1 * spg_i1)) / e1f
elif velocity_component == "v": # TODO No else? What should happen if both conditions are False?
# required scale factors for derivative and averaging
e1u = 0.5 * (ds_t_i1.e1.data[r_ind] + ds_t.e1.data[r_ind])
e1u_j1 = 0.5 * (ds_t_j1i1.e1.data[r_ind] + ds_t_j1.e1.data[r_ind])
e2u = 0.5 * (ds_t_i1.e2.data[r_ind] + ds_t.e2.data[r_ind])
e2u_j1 = 0.5 * (ds_t_j1i1.e2.data[r_ind] + ds_t_j1.e2.data[r_ind])
e2f = 0.5 * (e2u + e2u_j1)
# calculate gradients at u-points either side of f-point
hpg = (ds_t_i1.pressure_h_zlevels.data[:, :, r_ind] - ds_t.pressure_h_zlevels.data[:, :, r_ind]) / e1u
hpg_j1 = (
ds_t_j1i1.pressure_h_zlevels.data[:, :, r_ind] - ds_t_j1.pressure_h_zlevels.data[:, :, r_ind]
) / e1u_j1
# average onto f-point
hpg_f = 0.5 * ((e2u * hpg) + (e2u_j1 * hpg_j1)) / e2f
# as above
spg = (ds_t_i1.pressure_s.data[:, r_ind] - ds_t.pressure_s.data[:, r_ind]) / e1u
spg_j1 = (ds_t_j1i1.pressure_s.data[:, r_ind] - ds_t_j1.pressure_s.data[:, r_ind]) / e1u_j1
spg_f = 0.5 * ((e2u * spg) + (e2u_j1 * spg_j1)) / e2f
return hpg_f, spg_f
def calc_geostrophic_flow(
self,
gridded_t: Coast,
ref_density=None,
config_u="config/example_nemo_grid_u.json",
config_v="config/example_nemo_grid_v.json",
):
"""
This method will calculate the geostrophic velocity and volume transport
(due to the geostrophic current) across the contour.
Four variables are added to the Contour.data_cross_flow dataset:
1. normal_velocity_hpg (t_dim, depth_z_levels, r_dim)
This is the velocity due to the hydrostatic pressure gradient
2. normal_velocity_spg (t_dim, r_dim)
This is the velocity due to the surface pressure gradient
3. transport_across_AB_hpg (t_dim, r_dim)
This is the volume transport due to the hydrostatic pressure gradient
4. transport_across_AB_spg (t_dim, r_dim
This is the volume transport due to the surface pressure gradient
This implementation works by regridding vertically onto horizontal z_levels in order
to perform the horizontal gradients. Currently s_level depths are
assumed fixed at their initial depths, i.e. at time zero.
Requirements: The gridded t-grid dataset, gridded_t, must contain the sea surface height,
Practical Salinity and the Potential Temperature variables. The depth_0
field must also be supplied. The GSW package is used to calculate
The Absolute Pressure, Absolute Salinity and Conservate Temperature.
Parameters
----------
gridded_t : Coast
This is the gridded model data on the t-grid for the entire domain.
ref_density : TYPE, optional
reference density value. If not supplied a mean in time, depth and
along the contour will be used as the mean reference value.
config_u : file
configuration file for u-grid object
config_v : file
configuration file for v-grid object
Returns
-------
None.
"""
# If there is no time dimension, add one then remove at end. This is so
# indexing can assume a time dimension exists
gridded_t_local = gridded_t.copy()
if "t_dim" not in gridded_t_local.dataset.dims:
gridded_t_local.dataset = gridded_t_local.dataset.expand_dims(dim={"t_dim": 1}, axis=0)
# We need to calculate the pressure at four t-points to get an
# average onto the pressure gradient at the f-points, which will then
# be averaged onto the normal velocity points. Here we subset the gridded_t
# data around the contour so we have these four t-grid points at each
# point along the contour
cont_t = ContourT(gridded_t_local, self.y_ind, self.x_ind, self.depth) # j,i
cont_t_j1 = ContourT(gridded_t_local, self.y_ind + 1, self.x_ind, self.depth) # j+1,i
cont_t_i1 = ContourT(gridded_t_local, self.y_ind, self.x_ind + 1, self.depth) # j,i+1
cont_t_j1i1 = ContourT(gridded_t_local, self.y_ind + 1, self.x_ind + 1, self.depth) # j+1,i+1
bath_max = np.max(
[
cont_t.data_contour.bathymetry.max().item(),
cont_t_j1.data_contour.bathymetry.max().item(),
cont_t_i1.data_contour.bathymetry.max().item(),
cont_t_j1i1.data_contour.bathymetry.max().item(),
]
)
z_levels = self.gen_z_levels(bath_max)
cont_t.construct_pressure(ref_density, z_levels, extrapolate=True)
cont_t_j1.construct_pressure(ref_density, z_levels, extrapolate=True)
cont_t_i1.construct_pressure(ref_density, z_levels, extrapolate=True)
cont_t_j1i1.construct_pressure(ref_density, z_levels, extrapolate=True)
# Remove the mean hydrostatic pressure on each z_level from the hydrostatic pressure.
# This helps to reduce the noise when taking the horizontal gradients of hydrostatic pressure.
# Also catch and ignore nan-slice warning
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=RuntimeWarning)
pressure_h_zlevel_mean = xr.concat(
(
cont_t.data_contour.pressure_h_zlevels,
cont_t_j1.data_contour.pressure_h_zlevels,
cont_t_i1.data_contour.pressure_h_zlevels,
cont_t_j1i1.data_contour.pressure_h_zlevels,
),
dim="concat_dim",
).mean(dim=("concat_dim", "r_dim", "t_dim"), skipna=True)
if ref_density is None:
ref_density = (
xr.concat(
(
cont_t.data_contour.density_zlevels,
cont_t_j1.data_contour.density_zlevels,
cont_t_i1.data_contour.density_zlevels,
cont_t_j1i1.data_contour.density_zlevels,
),
dim="concat_dim",
)
.mean(dim=("concat_dim", "r_dim", "t_dim", "depth_z_levels"), skipna=True)
.item()
)
cont_t.data_contour["pressure_h_zlevels"] = cont_t.data_contour.pressure_h_zlevels - pressure_h_zlevel_mean
cont_t_j1.data_contour["pressure_h_zlevels"] = (
cont_t_j1.data_contour.pressure_h_zlevels - pressure_h_zlevel_mean
)
cont_t_i1.data_contour["pressure_h_zlevels"] = (
cont_t_i1.data_contour.pressure_h_zlevels - pressure_h_zlevel_mean
)
cont_t_j1i1.data_contour["pressure_h_zlevels"] = (
cont_t_j1i1.data_contour.pressure_h_zlevels - pressure_h_zlevel_mean
)
# Coriolis parameter
f = 2 * self.EARTH_ROT_RATE * np.sin(np.deg2rad(self.data_contour.latitude))
# Find the indices where the derivative of the contour in the north, south, east and west
# directions are positive.
dr_n = np.where(np.diff(self.y_ind) > 0, np.arange(0, self.data_contour.r_dim.size - 1), np.nan)
dr_s = np.where(np.diff(self.y_ind) < 0, | np.arange(0, self.data_contour.r_dim.size - 1) | numpy.arange |
import os
from numba import njit, types
from numba.typed import Dict
import numpy as np
from scipy.interpolate import interp1d
from .template import Model
from .. import units as u
from .. import utils
from pysm.utils import trapz_step_inplace
import healpy as hp
class InterpolatingComponent(Model):
def __init__(
self,
path,
input_units,
nside,
interpolation_kind="linear",
has_polarization=True,
map_dist=None,
verbose=False,
):
"""PySM component interpolating between precomputed maps
In order to save memory, maps are converted to float32, if this is not acceptable, please
open an issue on the PySM repository.
When you create the model, PySM checks the folder of the templates and stores a list of
available frequencies. Once you call `get_emission`, maps are read, ud_graded to the target
nside and stored for future use. This is useful if you are running many channels with a similar
bandpass.
If not, you can call `cached_maps.clear()` to remove the cached maps.
Parameters
----------
path : str
Path should contain maps named as the frequency in GHz e.g. 20.fits or 20.5.fits or 00100.fits
input_units : str
Any unit available in PySM (see `pysm.convert_units` e.g. `Jysr`, `MJsr`, `uK_RJ`, `K_CMB`).
nside : int
HEALPix NSIDE of the output maps
interpolation_kind : string
Currently only linear is implemented
has_polarization : bool
whether or not to simulate also polarization maps
map_dist : pysm.MapDistribution
Required for partial sky or MPI, see the PySM docs
verbose : bool
Control amount of output
"""
super().__init__(nside=nside, map_dist=map_dist)
self.maps = {}
self.maps = self.get_filenames(path)
# use a numba typed Dict so we can used in JIT compiled code
self.cached_maps = Dict.empty(
key_type=types.float32, value_type=types.float32[:, :]
)
self.freqs = np.array(list(self.maps.keys()))
self.freqs.sort()
self.input_units = input_units
self.has_polarization = has_polarization
self.interpolation_kind = interpolation_kind
self.verbose = verbose
def get_filenames(self, path):
# Override this to implement name convention
filenames = {}
for f in os.listdir(path):
if f.endswith(".fits"):
freq = float(os.path.splitext(f)[0])
filenames[freq] = os.path.join(path, f)
return filenames
@u.quantity_input
def get_emission(self, freqs: u.GHz, weights=None) -> u.uK_RJ:
nu = freqs.to(u.GHz).value
weights = utils.normalize_weights(freqs, weights)
if not np.isscalar(nu) and len(nu) == 1:
nu = nu[0]
if np.isscalar(nu):
# special case: we request only 1 frequency and that is among the ones
# available as input
check_isclose = np.isclose(self.freqs, nu)
if | np.any(check_isclose) | numpy.any |
import numpy as np
import os
from six.moves import cPickle as pickle
import cv2
dirs = ['Dataset/yawnMouth', 'Dataset/normalMouth']
countYawn = 40
countNormal = 34
def generate_dataset():
'''countYawn = 0
countNormal = 0
maxY = 0
maxX = 0
minX = 1000
minY = 1000
pos = 0
for dir in dirs:
for filename in os.listdir(dir):
if filename.endswith('.png'):
im = cv2.imread(dir + '/' + filename)
maxX = max(maxX, im.shape[0])
minX = min(minX, im.shape[0])
maxY = max(maxY, im.shape[1])
minY = min(minY, im.shape[1])
if pos == 0:
countYawn +=1
else:
countNormal += 1
pos += 1
print(minX, maxX, minY, maxY, countYawn, countNormal)'''
maxX = 60
maxY = 60
dataset = np.ndarray([countYawn + countNormal, maxY, maxX, 1], dtype='float32')
i = 0
j = 0
pos = 0
for dir in dirs:
for filename in os.listdir(dir):
if filename.endswith('.png'):
im = cv2.imread(dir + '/' + filename)
im = cv2.resize(im, (maxX, maxY))
im = np.dot(np.array(im, dtype='float32'), [[0.2989], [0.5870], [0.1140]])/255
#print(i)
dataset[i, :, :, :] = im[:, :, :]
i += 1
if pos == 0:
labels = np.ones([i, 1], dtype=int)
j = i
pos += 1
else:
labels = np.concatenate((labels, np.zeros([i-j, 1], dtype=int)))
return dataset, labels
dataset, labels = generate_dataset()
print("Total = ", len(dataset))
totalCount = countYawn + countNormal
split = int(countYawn*0.8)
splitEnd = countYawn
split2 = countYawn + int(countNormal*0.8)
train_dataset = dataset[:split]
train_labels = | np.ones([split, 1], dtype=int) | numpy.ones |
from statistics import mean
import networkx as nx
from numpy import empty, asarray
from numpy.random import seed, exponential
from conference_scrapper.conference.models import ConferenceGraphEdge, Conference
def get_graph_data(slugs=None):
conf_list_db = (Conference
.objects
.filter(slug__in=slugs)
.values('x_coord', 'y_coord', 'id', 'degree', 'slug'))
conf_list, title_to_id = [], {}
for i in conf_list_db:
conf_list.append(
[i['x_coord'], i['y_coord'], i['id'], {'title': i['slug'], 'degree': i['degree']}]
)
title_to_id[i['slug']] = i['id']
edges = ConferenceGraphEdge.objects.filter(conf_1__in=slugs, conf_2__in=slugs)
edge_list = [
[title_to_id[i.conf_1], title_to_id[i.conf_2], i.matches_len, i.matches] for i in edges
]
return conf_list, edge_list
def get_graph_meta(conf_list, edge_list):
g = nx.Graph()
for i in conf_list:
g.add_node(i[2])
for i in edge_list:
g.add_edge(i[0], i[1])
graph_info = {}
graph_info['degree'] = mean([i[1] for i in nx.degree(g)])
graph_info['density'] = nx.classes.function.density(g)
graph_info['degree_centrality'] = mean(nx.algorithms.centrality.degree_centrality(g).values())
graph_info['closeness_centrality'] = mean(nx.algorithms.centrality.closeness_centrality(g).values())
graph_info['betweenness_centrality'] = mean(nx.algorithms.centrality.betweenness_centrality(g).values())
return graph_info
seed(154)
canvas_size = 1000
padding = 20
g = nx.gnm_random_graph(50, 100)
ws = exponential(size=g.number_of_edges())
edge_list_n = {}
for i, (u, v, w) in enumerate(g.edges(data=True)):
tw = (round(ws[i]) % 4) + 1
w['weight'] = tw
edge_list_n[i] = (u, v, tw, "")
pos = nx.kamada_kawai_layout(g)
degrees = dict()
for node, val in g.degree():
degrees[node] = val
ids = list(g.nodes())
x = []
y = []
degree = []
for elem in ids:
degree.append(degrees[elem])
x.append(pos[elem][0])
y.append(pos[elem][1])
p = empty(shape=(len(x), 2))
p[:, 0] = | asarray(x) | numpy.asarray |
import numpy as np
from .ant import AntEnv
import itertools
from . import register_env
@register_env('ant-legs-var-length')
class AntLegsVarLength(AntEnv):
def __init__(self, n_tasks):
self.tasks = self.get_tasks(n_tasks)
super(AntLegsVarLength, self).__init__()
self.unit_geom_size = np.round_( | np.sqrt(2) | numpy.sqrt |
import numpy as np
class MriPfPocs(object):
"""Calculate POCs Partial Fourier reconstruction.
This calculates a POCs partial Fourier image estimate. Only operates on
'dat'.
Args:
cent_size (tuple): Sice of k-space center used for phase estimation.
niter (int): Number of POCs iterations.
"""
def __init__(self, cent_size, niter=5):
self.cent_size = cent_size
self.niter = niter
def __call__(self, sample):
"""
Args:
sample (dict): a sample with 'target' and 'dat' numpy arrays ('dat'
to be POCs'd).
Returns:
sample (dict): a sample with 'target' and 'dat' numpy arrays, as
well as new 'pocs_image' array.
"""
dat = sample['dat']
nx = dat.shape[1]
ny = dat.shape[2]
fftaxes = tuple(range(1, len(dat.shape)))
pf_cutoff = self.cent_size[1] // 2 + dat.shape[2] // 2
phase_est = np.fft.ifftshift(dat, axes=fftaxes)
phase_est = np.fft.fftn(phase_est, axes=fftaxes)
phase_est = np.fft.fftshift(phase_est, axes=fftaxes)
kdata = phase_est.copy()
window = np.expand_dims(np.hamming(self.cent_size[0]), 1) * \
np.expand_dims(np.hamming(self.cent_size[1]), 0)
ny1 = ny//2 - self.cent_size[1]//2
ny2 = ny - ny1 - self.cent_size[1]
window = np.concatenate((
np.zeros(shape=(nx, ny1)),
window,
np.zeros(shape=(nx, ny2))),
1
)
window = | np.expand_dims(window, 0) | numpy.expand_dims |
import torch
import numpy as np
import cv2
from torchvision.transforms import Compose, Normalize
device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')
cifar_mean = [0.5, 0.5, 0.5]
cifar_std = [0.5, 0.5, 0.5]
image_net_mean = torch.Tensor([0.485, 0.456, 0.406])
image_net_std = torch.Tensor([0.229, 0.224, 0.225])
cifar10_mean = torch.Tensor(cifar_std)
cifar10_std = torch.Tensor(cifar_std)
tiny_image_net_mean = [0.48043722, 0.44820285, 0.39760238]
tiny_image_net_std = [0.27698976, 0.26908714, 0.2821603]
import matplotlib.pyplot as plt
class NormalizeInverse(Normalize):
"""
Undoes the normalization and returns the reconstructed images in the input domain.
"""
def __init__(self, mean, std):
mean = torch.Tensor(mean)
std = torch.Tensor(std)
std_inv = 1 / (std + 1e-7)
mean_inv = -mean * std_inv
super().__init__(mean=mean_inv, std=std_inv)
def __call__(self, tensor):
return super().__call__(tensor.clone())
image_net_preprocessing = Compose([
Normalize(
mean=image_net_mean,
std=image_net_std
)
])
image_net_postprocessing = Compose([
NormalizeInverse(
mean=image_net_mean,
std=image_net_std)
])
cifar10_preprocessing = Compose([
Normalize(
mean=cifar10_mean,
std=cifar10_std
)
])
cifar10_postprocessing = Compose([
NormalizeInverse(
mean=cifar10_mean,
std=cifar10_std)
])
def tensor2cam(image, cam):
image_with_heatmap = image2cam(image.squeeze().permute(1, 2, 0).cpu().numpy(),
cam.detach().cpu().numpy())
return torch.from_numpy(image_with_heatmap).permute(2, 0, 1)
def image2cam(image, cam):
h, w, c = image.shape
cam -= np.min(cam)
cam /= np.max(cam) # Normalize between 0-1
cam = cv2.resize(cam, (w, h))
cam = np.uint8(cam * 255.0)
img_with_cam = cv2.applyColorMap(cam, cv2.COLORMAP_JET)
img_with_cam = cv2.cvtColor(img_with_cam, cv2.COLOR_BGR2RGB)
img_with_cam = img_with_cam + (image * 255)
img_with_cam /= | np.max(img_with_cam) | numpy.max |
"""
For panda (two-finger) gripper: pushing, pushing-left, pushing-up, pulling, pulling-left, pulling-up
50% all parts closed, 50% middle (for each part, 50% prob. closed, 50% prob. middle)
Simulate until static before starting
REPLAY
"""
import os
import sys
import shutil
import numpy as np
from utils import get_global_position_from_camera
import json
import h5py
from sapien.core import Pose
from env import Env, ContactError
from camera import Camera
from robots.panda_robot import Robot
from PIL import Image
from subprocess import call
json_fn = sys.argv[1]
out_dir = '/'.join(json_fn.split('/')[:-1])
with open(json_fn, 'r') as fin:
replay_data = json.load(fin)
shape_id, _, _, primact_type, _ = json_fn.split('/')[-2].split('_')
# setup env
env = Env()
# setup camera
cam_theta = replay_data['camera_metadata']['theta']
cam_phi = replay_data['camera_metadata']['phi']
cam = Camera(env, theta=cam_theta, phi=cam_phi)
env.set_controller_camera_pose(cam.pos[0], cam.pos[1], cam.pos[2], np.pi+cam_theta, -cam_phi)
# load shape
object_urdf_fn = '../data/where2act_original_sapien_dataset/%s/mobility_vhacd.urdf' % shape_id
object_material = env.get_material(4, 4, 0.01)
state = replay_data['object_state']
print( 'Object State: %s' % state)
env.load_object(object_urdf_fn, object_material, state=state)
env.set_object_joint_angles(replay_data['joint_angles'])
cur_qpos = env.get_object_qpos()
# simulate some steps for the object to stay rest
still_timesteps = 0
wait_timesteps = 0
while still_timesteps < 5000 and wait_timesteps < 20000:
env.step()
env.render()
cur_new_qpos = env.get_object_qpos()
invalid_contact = False
for c in env.scene.get_contacts():
for p in c.points:
if abs(p.impulse @ p.impulse) > 1e-4:
invalid_contact = True
break
if invalid_contact:
break
if np.max(np.abs(cur_new_qpos - cur_qpos)) < 1e-6 and (not invalid_contact):
still_timesteps += 1
else:
still_timesteps = 0
cur_qpos = cur_new_qpos
wait_timesteps += 1
if still_timesteps < 5000:
print('Object Not Still!')
env.close()
exit(1)
### use the GT vision
rgb, depth = cam.get_observation()
object_link_ids = env.movable_link_ids
gt_movable_link_mask = cam.get_movable_link_mask(object_link_ids)
# load the pixel to interact
x, y = replay_data['pixel_locs'][0], replay_data['pixel_locs'][1]
env.set_target_object_part_actor_id(object_link_ids[gt_movable_link_mask[x, y]-1])
# load the random direction in the hemisphere
gripper_direction_cam = np.array(replay_data['gripper_direction_camera'], dtype=np.float32)
gripper_direction_cam /= np.linalg.norm(gripper_direction_cam)
gripper_forward_direction_cam = np.array(replay_data['gripper_forward_direction_camera'], dtype=np.float32)
gripper_left_direction_cam = np.cross(gripper_direction_cam, gripper_forward_direction_cam)
gripper_left_direction_cam /= np.linalg.norm(gripper_left_direction_cam)
gripper_forward_direction_cam = np.cross(gripper_left_direction_cam, gripper_direction_cam)
gripper_forward_direction_cam /= np.linalg.norm(gripper_forward_direction_cam)
# convert to world space
mat44 = np.array(replay_data['camera_metadata']['mat44'], dtype=np.float32).reshape(4, 4)
gripper_direction_world = mat44[:3, :3] @ gripper_direction_cam
gripper_forward_direction_world = mat44[:3, :3] @ gripper_forward_direction_cam
# get pixel 3D position (cam/world)
with h5py.File(json_fn.replace('result.json', 'cam_XYZA.h5'), 'r') as fin:
cam_XYZA_id1 = fin['id1'][:].astype(np.int64)
cam_XYZA_id2 = fin['id2'][:].astype(np.int64)
cam_XYZA_pts = fin['pc'][:].astype(np.float32)
cam_XYZA = cam.compute_XYZA_matrix(cam_XYZA_id1, cam_XYZA_id2, cam_XYZA_pts, depth.shape[0], depth.shape[1])
position_cam = cam_XYZA[x, y, :3]
position_cam_xyz1 = np.ones((4), dtype=np.float32)
position_cam_xyz1[:3] = position_cam
position_world_xyz1 = mat44 @ position_cam_xyz1
position_world = position_world_xyz1[:3]
# compute final pose
up = np.array(gripper_direction_world, dtype=np.float32)
up /= np.linalg.norm(up)
forward = np.array(gripper_forward_direction_world, dtype=np.float32)
left = np.cross(up, forward)
left /= np.linalg.norm(left)
forward = np.cross(left, up)
forward /= | np.linalg.norm(forward) | numpy.linalg.norm |
import torch
import numpy as np
import numba
import copy
from ...utils import common_utils
from ...ops.roiaware_pool3d import roiaware_pool3d_utils
from ...ops.iou3d_nms import iou3d_nms_utils
import warnings
try:
from numba.errors import NumbaPerformanceWarning
warnings.filterwarnings("ignore", category=NumbaPerformanceWarning)
except:
pass
def random_flip_along_x(gt_boxes, points):
"""
Args:
gt_boxes: (N, 7), [x, y, z, dx, dy, dz, heading]
points: (M, 3 + C)
Returns:
"""
enable = np.random.choice([False, True], replace=False, p=[0.5, 0.5])
if enable:
gt_boxes[:, 1] = -gt_boxes[:, 1]
gt_boxes[:, 6] = -gt_boxes[:, 6]
points[:, 1] = -points[:, 1]
return gt_boxes, points
def random_flip_along_y(gt_boxes, points):
"""
Args:
gt_boxes: (N, 7), [x, y, z, dx, dy, dz, heading]
points: (M, 3 + C)
Returns:
"""
enable = | np.random.choice([False, True], replace=False, p=[0.5, 0.5]) | numpy.random.choice |
import os
import numpy as np
import matplotlib.pyplot as plt
import cv2
import torch
import torch.nn as nn
import torchvision.models as models
from model import Unet
from utils.dataloader import read_data_path, MaskDataset
from torch.utils.data import DataLoader
from utils.config import Config
from utils.loss import dice_score
# Hyperparameter
config = Config()
TRAIN_TEST_SPLIT = config.TRAIN_TEST_SPLIT
BATCH_SIZE_VALIDATION = config.BATCH_SIZE_VALIDATION
BATCH_SIZE_TESTING = config.BATCH_SIZE_TESTING
PRED_SAVE_DIR = config.PRED_SAVE_DIR
os.makedirs(PRED_SAVE_DIR, exist_ok=True)
INFERENCE_WEIGHT = config.INFERENCE_WEIGHT
# Use torch cuda
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
# Import Resnet-50 as base network, modify first layer
model_ft = models.resnet50(pretrained=True)
model_ft.conv1 = nn.Conv2d(1, 64, kernel_size=(3, 3), stride=(2, 2), padding=(3, 3), bias=False)
# Add Residual layer in unet
model = Unet(model_ft)
model.to(device)
if INFERENCE_WEIGHT:
model.load_state_dict(torch.load(INFERENCE_WEIGHT))
# Read data path, make in dataloader
"""
read_data_path
input: (float), the split of train and test
return: (list, list, list), train & valid & test file path list
list -> (img_path, mask_path)
"""
training_list, validation_list, testing_list = read_data_path(TRAIN_TEST_SPLIT)
val_dataset = MaskDataset(validation_list)
val_loader = DataLoader(val_dataset, batch_size=BATCH_SIZE_VALIDATION, shuffle=False, drop_last=True)
# Erosion and Dilation
def ero_and_dil(image):
kernel = np.ones((3,3), np.uint8)
erosion = cv2.erode(image.copy(), kernel, iterations = 1)
kernel = | np.ones((7,7), np.uint8) | numpy.ones |
import numpy as np
from desdeov2.problem.Problem import ScalarConstraint
from desdeov2.solver.ASF import SimpleASF
from desdeov2.solver.NumericalMethods import DiscreteMinimizer
from desdeov2.solver.ScalarSolver import (
ASFScalarSolver,
EpsilonConstraintScalarSolver,
WeightingMethodScalarSolver,
)
def test_weighting(simple_data_problem):
solver = WeightingMethodScalarSolver(
simple_data_problem, DiscreteMinimizer()
)
res1 = solver.solve(np.array([1, 1]))
assert np.all(np.isclose(res1[0], [-1.05, -2.05, 3.1]))
assert np.all(np.isclose(res1[1], [0, 3.861994]))
res2 = solver.solve(np.array([0, 0.5]))
assert np.all(np.isclose(res2[0], [2, 2, 2]))
assert np.all(np.isclose(res2[1], [6, 3.464101]))
def test_epsilon(simple_data_problem):
solver = EpsilonConstraintScalarSolver(
simple_data_problem, DiscreteMinimizer()
)
solver.epsilons = np.array([10.0, 5.0])
res1 = solver.solve(0)
assert np.all(np.isclose(res1[0], [-1.05, -2.05, 3.1]))
assert np.all(np.isclose(res1[1], [0, 3.861994]))
solver.epsilons = np.array([5.0, 10.0])
res2 = solver.solve(1)
assert np.all(np.isclose(res2[0], [-1.05, -2.05, 3.1]))
assert np.all(np.isclose(res2[1], [0, 3.861994]))
solver.epsilons = np.array([20, 20])
res3 = solver.solve(1)
assert np.all(np.isclose(res3[0], [2, 2, 2]))
assert np.all(np.isclose(res3[1], [6, 3.464101]))
def test_asf(simple_data_problem):
solver = ASFScalarSolver(simple_data_problem, DiscreteMinimizer())
solver.asf = SimpleASF([1, 1])
res1 = solver.solve(np.array([6, 3.4]))
assert np.all(np.isclose(res1[0], [2, 2, 2]))
assert np.all(np.isclose(res1[1], [6, 3.464101]))
res2 = solver.solve(np.array([0, 0]))
assert np.all(np.isclose(res2[0], [-1.05, -2.05, 3.1]))
assert np.all( | np.isclose(res2[1], [0, 3.861994]) | numpy.isclose |
from typing import Iterable
from fv3fit.keras._models.loss import _pack_weights, _weighted_mse, _weighted_mae
from fv3fit._shared import ArrayPacker
import numpy as np
import xarray as xr
import pytest
SAMPLE_DIM = "sample"
FEATURE_DIM = "z"
@pytest.fixture
def names(request):
return request.param
@pytest.fixture
def weights(request):
return request.param
@pytest.fixture
def features(request):
return request.param
@pytest.fixture
def dataset(features) -> xr.Dataset:
data_vars = {}
for name, n_features in features.items():
if n_features == 1:
data_vars[name] = ([SAMPLE_DIM], np.zeros([1]))
else:
data_vars[name] = (
[SAMPLE_DIM, f"{name}_{FEATURE_DIM}"],
np.zeros([1, n_features]),
)
return xr.Dataset(data_vars)
@pytest.fixture
def packer(names: Iterable[str], dataset: xr.Dataset) -> ArrayPacker:
packer = ArrayPacker(SAMPLE_DIM, names)
packer.to_array(dataset) # must let packer know about array shapes
return packer
@pytest.mark.parametrize(
"names,weights,features,reference",
[
pytest.param(
["a"], {"a": 1.0}, {"a": 1}, np.array([[1]]), id="one_scalar_weight_1",
),
pytest.param(
["a"], {"a": 2.0}, {"a": 1}, np.array([[2]]), id="one_scalar_weight_2",
),
pytest.param(
["a"],
{"a": 4.0},
{"a": 4},
np.array([[1.0, 1.0, 1.0, 1.0]]),
id="one_vector_weight_4",
),
pytest.param(
["a", "b"],
{"a": 1.0, "b": 2.0},
{"a": 1, "b": 1},
np.array([[1.0, 2.0]]),
id="two_scalars",
),
pytest.param(
["a", "b"],
{"a": 1.0, "b": 2.0},
{"a": 2, "b": 1},
np.array([[0.5, 0.5, 2]]),
id="one_scalar_one_vector",
),
pytest.param(
["b", "a"],
{"a": 1.0, "b": 2.0},
{"a": 2, "b": 1},
np.array([[2.0, 0.5, 0.5]]),
id="one_scalar_one_vector_reverse_order",
),
],
indirect=["names", "weights", "features"],
)
def test_pack_weights(packer, weights, reference):
result = _pack_weights(packer, **weights)
np.testing.assert_array_equal(result, reference)
@pytest.mark.parametrize(
"weights, std, y_true, y_pred, reference",
[
pytest.param(
np.array([2.0]),
np.array([1.0]),
np.array([0.0]),
np.array([1.0]),
2.0,
id="double_single_feature_loss",
),
pytest.param(
np.array([2.0]),
np.array([0.5]),
np.array([0.0]),
np.array([1.0]),
8.0,
id="double_single_feature_loss_low_std",
),
pytest.param(
np.array([0.5, 1.0, 2.0]),
np.array([1.0, 1.0, 1.0]),
np.array([0.0, 0, 0]),
np.array([1.0, 10, 100]),
20100.5 / 3.0,
id="varying_weight_loss",
),
pytest.param(
np.array([1.0, 1.0, 1.0]),
np.array([0.5, 1.0, 2.0]),
| np.array([0.0, 0, 0]) | numpy.array |
"""
Visual example showing how to test frozen model on
single large image using sliding window. Saves results
(bboxes, scores, name of filepath) in giga1_od_results.pkl
that can later be fully processed using bb_extract.py.
Part of gigadetector repo:
https://github.com/EricThomson/gigadetector
"""
import os
import sys
import joblib
os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2' #set to 3 to print nothing
import tensorflow as tf
#tf.enable_eager_execution()
import numpy as np
import cv2
import logging
logging.basicConfig(level = logging.WARNING)
from object_detection.utils import label_map_util
base_path = os.path.expanduser("~") + r"/gigadetector/"
sys.path.append(base_path + r'/gigadetector/')
import utils
#%% set paths
image_dir = base_path + r'data/'
save_dir = image_dir + r'processed/'
image_path = image_dir + r'giga1.png'
model_dir = base_path + r'models/'
model_path = model_dir + r'fish_frcnn_graph.pb'
labels_path = model_dir + r'fish_classes.pbtxt'
print(f"\nBeginning analysis of {image_path}\nClick Esc over movie to halt progress.")
od_filepath = save_dir + r'giga1_od_results.pkl' #previously used datetime.now().strftime("%Y%m%d_%H%M%S"
if os.path.isdir(save_dir):
pass
else:
os.mkdir(save_dir)
#%% set basic runtime params
win_size = 1024
step_size = win_size//2
edge_min = 29 #at edges, if moving window width or height is this size or less, discard
#verbosity: 0: show nothing just save data, 1: show progress on image
verbosity = 1
if verbosity == 0:
logging.info("\n***Note verbosity is 0, you will only see text feedback.***\n")
#save_data: toggle for test runs
save_data = 1
COLORS = (255, 255, 255)
num_classes = 1
min_confidence = 0.95
#%% tensorflow fix for nvidia gpu cards
from tensorflow.compat.v1 import ConfigProto
#from tensorflow.compat.v1 import InteractiveSession
config = ConfigProto()
config.gpu_options.allow_growth = True
#config.gpu_options.per_process_gpu_memory_fraction = 0.9
session = tf.compat.v1.Session(config=config) #InteractiveSession(config=config)
#%% Initialize model and create context manager to load model from disk
model = tf.Graph()
# create a context manager that makes this model the default one for execution
with model.as_default():
# initialize the graph definition
graphDef = tf.compat.v1.GraphDef()
# load the graph from disk
with tf.io.gfile.GFile(model_path, "rb") as f:
serializedGraph = f.read()
graphDef.ParseFromString(serializedGraph)
tf.import_graph_def(graphDef, name="")
# load the class labels from disk
labelMap = label_map_util.load_labelmap(labels_path)
categories = label_map_util.convert_label_map_to_categories(labelMap,
max_num_classes = num_classes,
use_display_name=True)
categoryIdx = label_map_util.create_category_index(categories)
#%% Load image and set up window parameters
rois_all = []
boxes_all = []
scores_all = []
image = cv2.imread(image_path, cv2.IMREAD_GRAYSCALE)
(h,w) = image.shape
winW = win_size
winH = win_size
try:
assert(step_size < max([winW, winH]))
except AssertionError:
logging.error(" Attempt to step in increment larger than sub-image window size. This won't end well.")
if winW >= w and winH >= h:
logging.warning(" Moving window is as large as the image. This is an unuusal case.")
if winW > w:
winW = w
if winH > h:
winH = h
inbounds_x = True #could rename to inbounds
inbounds_xy = True
final_plot = False
#%% Cycle through applying model to each bit
if verbosity:
("Running analysis. Press escape to quit.")
clone = image.copy()
line_width = clone.shape[1]//300
if verbosity:
cv2.namedWindow('image', cv2.WINDOW_NORMAL)
cv2.resizeWindow('image', 600, 800) #width, height
cv2.moveWindow('image', 500, 70) #x y pos on screen
cv2.imshow("image", clone)
cv2.namedWindow('col_subimage', cv2.WINDOW_NORMAL)
cv2.moveWindow('col_subimage', 75, 70) #x y pos on screen
with model.as_default():
with tf.compat.v1.Session(graph=model) as sess:
for (x, y, sub_image) in utils.sliding_window(image, stepSize = step_size, windowSize=(winW, winH)):
# if the window does not meet our desired window size, ignore it
#if window.shape[0] != winH or window.shape[1] != winW:
# continue
logging.debug(f"inbounds_x: {inbounds_x}")
# Check on subimage size: if smaller than min, skip
(y_sub, x_sub) = sub_image.shape
if y_sub < edge_min or x_sub < edge_min:
continue
# check to see if x was inbounds, but goes out of bounds
if x + winW > w and inbounds_x and inbounds_xy:
logging.debug("\tSliding window resetting x next iteration")
inbounds_x = False #x window has gone out of bounds, so don't go next time
if y + winH > h and inbounds_xy: # y window has gone out of bounds, so maybe don't go next time (depending on x)
inbounds_xy = False
logging.debug(inbounds_xy)
logging.debug("xy out of bounds set")
continue
else:
inbounds_x = True
# create a session to perform inference
# from pyimagesearch: grab a reference to the input image tensor and the boxes tensor
# if the window does not meet our desired window size, ignore it
imageTensor = model.get_tensor_by_name("image_tensor:0")
boxesTensor = model.get_tensor_by_name("detection_boxes:0")
# for each bounding box we would like to know the score (i.e., probability) and class label
scoresTensor = model.get_tensor_by_name("detection_scores:0")
classesTensor = model.get_tensor_by_name("detection_classes:0")
numDetections = model.get_tensor_by_name("num_detections:0")
if verbosity:
k = cv2.waitKey(1)
else:
k = -1
if k == 27:
break
else:
current_roi = np.array([y, y+winH, x, x+winW])
#sub_image = clone[current_roi[0]: current_roi[1], current_roi[2]: current_roi[3]]
logging.info(f"sub_image roi: {current_roi}")
if verbosity:
#for showing the moving window over the original image
copy_big = image.copy()
cv2.rectangle(copy_big, (x, y), (x + winW, y + winH), COLORS, line_width)
cv2.imshow("image", copy_big)
#load subimage
#cv2.imshow('subimage', sub_image)
#NOW APPLY PREVIOUS STUFF TO SUB_IMAGE
(H, W) = sub_image.shape
logging.debug(f"Subimage shape: {H, W}")
# prepare the image for display (output) and detection (image_color), respectively
display_image = sub_image.copy()
image_color = cv2.cvtColor(display_image, cv2.COLOR_BGR2RGB)
image_color = np.expand_dims(image_color, axis=0)
# perform inference and compute the bounding boxes, probabilities, and class labels
(boxes, scores, labels, N) = sess.run([boxesTensor, scoresTensor, classesTensor, numDetections],
feed_dict = {imageTensor: image_color})
# squeeze the lists into a single dimension
boxes = np.squeeze(boxes)
scores = np.squeeze(scores)
labels = | np.squeeze(labels) | numpy.squeeze |
import array
import json as _json
import os
from glob import glob
import numpy as np
from numpy.testing import assert_array_almost_equal, assert_array_equal
import pytest
from numcodecs.compat import ensure_bytes, ensure_ndarray
from numcodecs.registry import get_codec
# star import needed for repr tests so eval finds names
from numcodecs import * # noqa
greetings = ['¡Hola mundo!', '<NAME>!', 'Servus Woid!', 'Hei maailma!',
'Xin chào thế giới', 'Njatjeta Botë!', 'Γεια σου κόσμε!',
'こんにちは世界', '世界，你好！', 'Helló, világ!', 'Zdravo svete!',
'เฮลโลเวิลด์']
def compare_arrays(arr, res, precision=None):
# ensure numpy array with matching dtype
res = ensure_ndarray(res).view(arr.dtype)
# convert to correct shape
if arr.flags.f_contiguous:
order = 'F'
else:
order = 'C'
res = res.reshape(arr.shape, order=order)
# exact compare
if precision is None:
assert_array_equal(arr, res)
# fuzzy compare
else:
assert_array_almost_equal(arr, res, decimal=precision)
def check_encode_decode(arr, codec, precision=None):
# N.B., watch out here with blosc compressor, if the itemsize of
# the source buffer is different then the results of encoding
# (i.e., compression) may be different. Hence we *do not* require that
# the results of encoding be identical for all possible inputs, rather
# we just require that the results of the encode/decode round-trip can
# be compared to the original array.
# encoding should support any object exporting the buffer protocol
# test encoding of numpy array
enc = codec.encode(arr)
dec = codec.decode(enc)
compare_arrays(arr, dec, precision=precision)
# test encoding of bytes
buf = arr.tobytes(order='A')
enc = codec.encode(buf)
dec = codec.decode(enc)
compare_arrays(arr, dec, precision=precision)
# test encoding of bytearray
buf = bytearray(arr.tobytes(order='A'))
enc = codec.encode(buf)
dec = codec.decode(enc)
compare_arrays(arr, dec, precision=precision)
# test encoding of array.array
buf = array.array('b', arr.tobytes(order='A'))
enc = codec.encode(buf)
dec = codec.decode(enc)
compare_arrays(arr, dec, precision=precision)
# decoding should support any object exporting the buffer protocol,
# setup
enc_bytes = ensure_bytes(enc)
# test decoding of raw bytes
dec = codec.decode(enc_bytes)
compare_arrays(arr, dec, precision=precision)
# test decoding of bytearray
dec = codec.decode(bytearray(enc_bytes))
compare_arrays(arr, dec, precision=precision)
# test decoding of array.array
buf = array.array('b', enc_bytes)
dec = codec.decode(buf)
compare_arrays(arr, dec, precision=precision)
# test decoding of numpy array
buf = np.frombuffer(enc_bytes, dtype='u1')
dec = codec.decode(buf)
compare_arrays(arr, dec, precision=precision)
# test decoding directly into numpy array
out = np.empty_like(arr)
codec.decode(enc_bytes, out=out)
compare_arrays(arr, out, precision=precision)
# test decoding directly into bytearray
out = bytearray(arr.nbytes)
codec.decode(enc_bytes, out=out)
# noinspection PyTypeChecker
compare_arrays(arr, out, precision=precision)
def assert_array_items_equal(res, arr):
assert isinstance(res, np.ndarray)
res = res.reshape(-1, order='A')
arr = arr.reshape(-1, order='A')
assert res.shape == arr.shape
assert res.dtype == arr.dtype
# numpy asserts don't compare object arrays
# properly; assert that we have the same nans
# and values
arr = arr.ravel().tolist()
res = res.ravel().tolist()
for a, r in zip(arr, res):
if isinstance(a, np.ndarray):
assert_array_equal(a, r)
elif a != a:
assert r != r
else:
assert a == r
def check_encode_decode_array(arr, codec):
enc = codec.encode(arr)
dec = codec.decode(enc)
assert_array_items_equal(arr, dec)
out = np.empty_like(arr)
codec.decode(enc, out=out)
assert_array_items_equal(arr, out)
enc = codec.encode(arr)
dec = codec.decode(ensure_ndarray(enc))
assert_array_items_equal(arr, dec)
def check_config(codec):
config = codec.get_config()
# round-trip through JSON to check serialization
config = _json.loads(_json.dumps(config))
assert codec == get_codec(config)
def check_repr(stmt):
# check repr matches instantiation statement
codec = eval(stmt)
actual = repr(codec)
assert stmt == actual
def check_backwards_compatibility(codec_id, arrays, codecs, precision=None, prefix=None):
# setup directory to hold data fixture
if prefix:
fixture_dir = os.path.join('fixture', codec_id, prefix)
else:
fixture_dir = os.path.join('fixture', codec_id)
if not os.path.exists(fixture_dir): # pragma: no cover
os.makedirs(fixture_dir)
# save fixture data
for i, arr in enumerate(arrays):
arr_fn = os.path.join(fixture_dir, 'array.{:02d}.npy'.format(i))
if not os.path.exists(arr_fn): # pragma: no cover
np.save(arr_fn, arr)
# load fixture data
for arr_fn in glob(os.path.join(fixture_dir, 'array.*.npy')):
# setup
i = int(arr_fn.split('.')[-2])
arr = np.load(arr_fn, allow_pickle=True)
arr_bytes = arr.tobytes(order='A')
if arr.flags.f_contiguous:
order = 'F'
else:
order = 'C'
for j, codec in enumerate(codecs):
# setup a directory to hold encoded data
codec_dir = os.path.join(fixture_dir, 'codec.{:02d}'.format(j))
if not os.path.exists(codec_dir): # pragma: no cover
os.makedirs(codec_dir)
# file with codec configuration information
codec_fn = os.path.join(codec_dir, 'config.json')
# one time save config
if not os.path.exists(codec_fn): # pragma: no cover
with open(codec_fn, mode='w') as cf:
_json.dump(codec.get_config(), cf, sort_keys=True, indent=4)
# load config and compare with expectation
with open(codec_fn, mode='r') as cf:
config = _json.load(cf)
assert codec == get_codec(config)
enc_fn = os.path.join(codec_dir, 'encoded.{:02d}.dat'.format(i))
# one time encode and save array
if not os.path.exists(enc_fn): # pragma: no cover
enc = codec.encode(arr)
enc = ensure_bytes(enc)
with open(enc_fn, mode='wb') as ef:
ef.write(enc)
# load and decode data
with open(enc_fn, mode='rb') as ef:
enc = ef.read()
dec = codec.decode(enc)
dec_arr = ensure_ndarray(dec).reshape(-1, order='A')
dec_arr = dec_arr.view(dtype=arr.dtype).reshape(arr.shape, order=order)
if precision and precision[j] is not None:
assert_array_almost_equal(arr, dec_arr, decimal=precision[j])
elif arr.dtype == 'object':
assert_array_items_equal(arr, dec_arr)
else:
assert_array_equal(arr, dec_arr)
assert arr_bytes == ensure_bytes(dec)
def check_err_decode_object_buffer(compressor):
# cannot decode directly into object array, leads to segfaults
a = np.arange(10)
enc = compressor.encode(a)
out = np.empty(10, dtype=object)
with pytest.raises(TypeError):
compressor.decode(enc, out=out)
def check_err_encode_object_buffer(compressor):
# compressors cannot encode object array
a = np.array(['foo', 'bar', 'baz'], dtype=object)
with pytest.raises(TypeError):
compressor.encode(a)
def check_max_buffer_size(codec):
for max_buffer_size in [4, 64, 1024]:
old_max_buffer_size = codec.max_buffer_size
try:
codec.max_buffer_size = max_buffer_size
# Just up the max_buffer_size is fine.
codec.encode( | np.zeros(max_buffer_size - 1, dtype=np.int8) | numpy.zeros |
# 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 states.py submodule"""
import pytest
import numpy as np
from scipy.special import factorial as fac
from strawberryfields import backends
from strawberryfields import utils
a = 0.3 + 0.1j
r = 0.23
phi = 0.123
class TestBackendStateCreation:
"""Test the backends properly create states"""
def test_full_state_creation(self, hbar, cutoff, setup_backend):
"""Test backend returns a properly formed state object"""
backend = setup_backend(3)
state = backend.state(modes=None)
assert state.num_modes == 3
assert state.hbar == hbar
assert state.mode_names == {0: "q[0]", 1: "q[1]", 2: "q[2]"}
assert state.mode_indices == {"q[0]": 0, "q[1]": 1, "q[2]": 2}
if isinstance(backend, backends.BaseFock):
assert state.cutoff_dim == cutoff
def test_reduced_state_creation(self, setup_backend):
"""Test backend returns a properly formed reduced state object"""
backend = setup_backend(3)
state = backend.state(modes=[0, 2])
assert state.num_modes == 2
assert state.mode_names == {0: "q[0]", 1: "q[2]"}
assert state.mode_indices == {"q[0]": 0, "q[2]": 1}
def test_reduced_state_fidelity(self, setup_backend, tol):
"""Test backend calculates correct fidelity of reduced coherent state"""
backend = setup_backend(2)
backend.prepare_coherent_state(np.abs(a), np.angle(a), 0)
backend.prepare_squeezed_state(r, phi, 1)
state = backend.state(modes=[0])
f = state.fidelity_coherent([a])
assert np.allclose(f, 1, atol=tol, rtol=0)
def test_reduced_state_fock_probs(self, cutoff, setup_backend, batch_size, tol):
"""Test backend calculates correct fock prob of reduced coherent state"""
backend = setup_backend(2)
backend.prepare_coherent_state(np.abs(a), np.angle(a), 0)
backend.prepare_squeezed_state(r, phi, 1)
state = backend.state(modes=[0])
probs = np.array([state.fock_prob([i]) for i in range(cutoff)]).T
n = np.arange(cutoff)
ref_state = np.exp(-0.5 * np.abs(a) ** 2) * a**n / np.sqrt(fac(n))
ref_probs = np.abs(ref_state) ** 2
if batch_size is not None:
ref_probs = np.tile(ref_probs, batch_size)
assert np.allclose(probs.flatten(), ref_probs.flatten(), atol=tol, rtol=0)
class TestBaseStateMeanPhotonNumber:
"""Tests for the mean photon number method"""
def test_mean_photon_coherent(self, setup_backend, tol, batch_size):
"""Test that E(n) = |a|^2 and var(n) = |a|^2 for a coherent state"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(1)
backend.displacement(np.abs(a), np.angle(a), 0)
state = backend.state()
mean_photon, var = state.mean_photon(0)
assert np.allclose(mean_photon, np.abs(a) ** 2, atol=tol, rtol=0)
assert np.allclose(var, np.abs(a) ** 2, atol=tol, rtol=0)
def test_mean_photon_squeezed(self, setup_backend, tol, batch_size):
"""Test that E(n)=sinh^2(r) and var(n)=2(sinh^2(r)+sinh^4(r)) for a squeezed state"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(1)
r = 0.1
a = 0.3 + 0.1j
backend.squeeze(r, phi, 0)
state = backend.state()
mean_photon, var = state.mean_photon(0)
assert np.allclose(mean_photon, np.sinh(r) ** 2, atol=tol, rtol=0)
assert np.allclose(var, 2 * (np.sinh(r) ** 2 + np.sinh(r) ** 4), atol=tol, rtol=0)
def test_mean_photon_displaced_squeezed(self, setup_backend, tol, batch_size):
"""Test that E(n) = sinh^2(r)+|a|^2 for a displaced squeezed state"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(1)
nbar = 0.123
a = 0.12 - 0.05j
r = 0.195
backend.squeeze(r, phi, 0)
backend.displacement(np.abs(a), np.angle(a), 0)
state = backend.state()
mean_photon, var = state.mean_photon(0)
mag_a = np.abs(a)
phi_a = np.angle(a)
magnitude_squared = np.abs(a) ** 2
mean_ex = magnitude_squared + np.sinh(r) ** 2
var_ex = (
-magnitude_squared
+ magnitude_squared**2
+ 2 * magnitude_squared * np.cosh(2 * r)
- np.exp(-1j * phi) * a**2 * np.cosh(r) * np.sinh(r)
- np.exp(1j * phi) * np.conj(a) ** 2 * np.cosh(r) * np.sinh(r)
+ np.sinh(r) ** 4
- (magnitude_squared + np.conj(np.sinh(r)) * np.sinh(r)) ** 2
+ np.cosh(r) * np.sinh(r) * np.sinh(2 * r)
)
assert np.allclose(mean_photon, mean_ex, atol=tol, rtol=0)
assert np.allclose(var, var_ex, atol=tol, rtol=0)
def test_mean_photon_displaced_thermal(self, setup_backend, tol, batch_size):
"""Test that E(n)=|a|^2+nbar and var(n)=var_th+|a|^2(1+2nbar)"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(1)
nbar = 0.123
backend.prepare_thermal_state(nbar, 0)
backend.displacement(np.abs(a), np.angle(a), 0)
state = backend.state()
mean_photon, var = state.mean_photon(0)
mean_ex = np.abs(a) ** 2 + nbar
var_ex = nbar**2 + nbar + np.abs(a) ** 2 * (1 + 2 * nbar)
assert np.allclose(mean_photon, mean_ex, atol=tol, rtol=0)
assert np.allclose(var, var_ex, atol=tol, rtol=0)
@pytest.mark.backends("fock", "tf", "gaussian")
class TestBaseFockKetDensityMatrix:
"""Tests for the ket, dm, and reduced density matrix function."""
def test_rdm(self, setup_backend, tol, cutoff, batch_size):
"""Test reduced density matrix of a coherent state is as expected
This is supported by all backends, since it returns
the reduced density matrix of a single mode."""
backend = setup_backend(2)
backend.prepare_coherent_state(np.abs(a), np.angle(a), 0)
backend.prepare_coherent_state(0.1, 0, 1)
state = backend.state()
rdm = state.reduced_dm(0, cutoff=cutoff)
n = np.arange(cutoff)
ket = np.exp(-0.5 * np.abs(a) ** 2) * a**n / np.sqrt(fac(n))
rdm_exact = np.outer(ket, ket.conj())
if batch_size is not None:
np.tile(rdm_exact, [batch_size, 1])
assert np.allclose(rdm, rdm_exact, atol=tol, rtol=0)
def test_ket(self, setup_backend, pure, cutoff, batch_size, tol):
"""Test that the ket of a displaced state matches analytic result"""
backend = setup_backend(2)
backend.displacement(np.abs(a), np.angle(a), 0)
state = backend.state()
if not pure and backend.short_name != "gaussian":
assert state.is_pure == False
pytest.skip("Test only works with pure states.")
assert state.is_pure == True
ket = np.sum(state.ket(cutoff=cutoff), axis=-1)
n = np.arange(cutoff)
expected = np.exp(-0.5 * np.abs(a) ** 2) * a**n / np.sqrt(fac(n))
if batch_size is not None:
ket = np.tile(ket, [batch_size, 1])
assert np.allclose(ket, expected, atol=tol, rtol=0)
def test_density_matrix_thermal_state(self, setup_backend, cutoff, batch_size, tol):
"""Test that a thermal state returns the correct density matrix, using
both the dm() and reduced_dm() methods."""
backend = setup_backend(1)
backend.prepare_thermal_state(r, 0)
state = backend.state()
assert not state.is_pure
rho1 = state.dm(cutoff=cutoff)
rho2 = state.reduced_dm(0, cutoff=cutoff)
assert np.allclose(rho1, rho2, atol=tol, rtol=0)
n = np.arange(cutoff)
expected = np.diag((r**n) / ((1 + r) ** (n + 1)))
if batch_size is not None:
expected = np.tile(expected, [batch_size, 1]).reshape(-1, cutoff, cutoff)
assert np.allclose(rho1, expected, atol=tol, rtol=0)
@pytest.mark.backends("gaussian")
class TestBaseGaussianMethods:
"""This tests state methods unique to the BaseGaussian
class, including is_coherent, displacement, is_squeezed,
and squeezing."""
def test_coherent_methods(self, setup_backend, tol):
"""Test that the ket of a displaced state matches analytic result"""
backend = setup_backend(2)
a = 1 + 0.5j
r = 2
phi = -0.5
backend.prepare_coherent_state(np.abs(a), np.angle(a), 0)
backend.prepare_squeezed_state(r, phi, 1)
state = backend.state()
coherent_check = []
for i in range(2):
coherent_check.append(state.is_coherent(i))
alpha_list = state.displacement()
assert np.all(coherent_check == [True, False])
assert np.allclose(alpha_list, [a, 0.0], atol=tol, rtol=0)
def test_squeezing_methods(self, setup_backend, tol):
"""Test that the ket of a displaced state matches analytic result"""
backend = setup_backend(2)
a = 1 + 0.5j
r = 2
phi = -0.5
backend.prepare_coherent_state(np.abs(a), np.angle(a), 0)
backend.prepare_squeezed_state(r, phi, 1)
state = backend.state()
squeezing_check = []
for i in range(2):
squeezing_check.append(state.is_squeezed(i))
z_list = np.array(state.squeezing())
assert np.all(squeezing_check == [False, True])
assert np.allclose(z_list, [[0.0, 0.0], [r, phi]], atol=tol, rtol=0)
class TestQuadratureExpectations:
"""Test quad_expectation methods"""
def test_vacuum(self, setup_backend, hbar, batch_size, tol):
"""Test vacuum state has zero mean and hbar/2 variance"""
backend = setup_backend(1)
state = backend.state()
res = np.array(state.quad_expectation(0, phi=np.pi / 4)).T
res_exact = np.array([0, hbar / 2.0])
if batch_size is not None:
res_exact = np.tile(res_exact, batch_size)
assert np.allclose(res.flatten(), res_exact.flatten(), atol=tol, rtol=0)
def test_squeezed_coherent(self, setup_backend, hbar, batch_size, tol):
"""Test squeezed coherent state has correct mean and variance"""
# quadrature rotation angle
backend = setup_backend(1)
qphi = 0.78
backend.prepare_displaced_squeezed_state(np.abs(a), np.angle(a), r, phi, 0)
state = backend.state()
res = np.array(state.quad_expectation(0, phi=qphi)).T
xphi_mean = (a.real * np.cos(qphi) + a.imag * np.sin(qphi)) * np.sqrt(2 * hbar)
xphi_var = (np.cosh(2 * r) - np.cos(phi - 2 * qphi) * np.sinh(2 * r)) * hbar / 2
res_exact = np.array([xphi_mean, xphi_var])
if batch_size is not None:
res_exact = np.tile(res_exact, batch_size)
assert np.allclose(res.flatten(), res_exact.flatten(), atol=tol, rtol=0)
@pytest.mark.backends("fock", "tf", "gaussian")
class TestNumberExpectation:
"""Multimode photon-number expectation value tests"""
def test_number_expectation_vacuum(self, setup_backend, tol, batch_size):
"""Tests the expectation value of any photon number in vacuum is zero,
and the variance is also 0."""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(2)
state = backend.state()
expected = (0, 0)
assert np.allclose(state.number_expectation([0, 1]), expected, atol=tol, rtol=0)
assert np.allclose(state.number_expectation([0]), expected, atol=tol, rtol=0)
assert np.allclose(state.number_expectation([1]), expected, atol=tol, rtol=0)
def test_number_expectation_displaced_squeezed(self, setup_backend, tol, batch_size):
"""Tests the expectation value of photon numbers when there is no correlation"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(2)
state = backend.state()
a0 = 0.2 + 0.1 * 1j
r0 = 0.2
phi0 = 0.6
a1 = 0.1 + 0.1 * 1j
r1 = 0.1
phi1 = 0.4
backend.prepare_displaced_squeezed_state(np.abs(a0), np.angle(a0), r0, phi0, 0)
backend.prepare_displaced_squeezed_state(np.abs(a1), np.angle(a1), r1, phi1, 1)
state = backend.state()
n0 = np.sinh(r0) ** 2 + np.abs(a0) ** 2
n1 = np.sinh(r1) ** 2 + np.abs(a1) ** 2
def squared_term(a, r, phi):
magnitude_squared = np.abs(a) ** 2
squared_term = (
-magnitude_squared
+ magnitude_squared**2
+ 2 * magnitude_squared * np.cosh(2 * r)
- 2 * np.real(np.exp(-1j * phi) * a**2 * np.cosh(r) * np.sinh(r))
+ np.sinh(r) ** 4
+ np.cosh(r) * np.sinh(r) * np.sinh(2 * r)
)
return squared_term
res = state.number_expectation([0, 1])
var = squared_term(a0, r0, phi0) * squared_term(a1, r1, phi1) - n0**2 * n1**2
assert np.allclose(res[0], n0 * n1, atol=tol, rtol=0)
assert np.allclose(res[1], var, atol=tol, rtol=0)
res = state.number_expectation([0])
var = squared_term(a0, r0, phi0) - n0**2
assert np.allclose(res[0], n0, atol=tol, rtol=0)
assert np.allclose(res[1], var, atol=tol, rtol=0)
res = state.number_expectation([1])
var = squared_term(a1, r1, phi1) - n1**2
assert np.allclose(res[0], n1, atol=tol, rtol=0)
assert np.allclose(res[1], var, atol=tol, rtol=0)
def test_number_expectation_repeated_modes(self, setup_backend, tol):
"""Tests that the correct exception is raised for repeated modes"""
backend = setup_backend(2)
state = backend.state()
with pytest.raises(ValueError, match="There can be no duplicates in the modes specified."):
state.number_expectation([0, 0])
def test_number_expectation_two_mode_squeezed(self, setup_backend, tol, batch_size):
"""Tests the expectation value of photon numbers when there is correlation"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(3)
state = backend.state()
r = 0.2
phi = 0.0
backend.prepare_squeezed_state(r, phi, 0)
backend.prepare_squeezed_state(-r, phi, 2)
backend.beamsplitter(np.pi / 4, np.pi, 0, 2)
state = backend.state()
nbar = np.sinh(r) ** 2
res = state.number_expectation([2, 0])
assert np.allclose(res[0], 2 * nbar**2 + nbar, atol=tol, rtol=0)
res = state.number_expectation([0])
assert np.allclose(res[0], nbar, atol=tol, rtol=0)
res = state.number_expectation([2])
assert np.allclose(res[0], nbar, atol=tol, rtol=0)
def test_number_expectation_photon_displaced_thermal(self, setup_backend, tol, batch_size):
"""Test that E(n)=|a|^2+nbar and var(n)=var_th+|a|^2(1+2nbar)
for uncorrelated displaced thermal states."""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(2)
a0 = 0.1
nbar0 = 0.123
a1 = 0.05
nbar1 = 0.21
backend.prepare_thermal_state(nbar0, 0)
backend.displacement(a0, 0.0, 0)
backend.prepare_thermal_state(nbar1, 1)
backend.displacement(a1, 0.0, 1)
state = backend.state()
res = state.number_expectation([0])
mean0 = np.abs(a0) ** 2 + nbar0
var0 = nbar0**2 + nbar0 + np.abs(a0) ** 2 * (1 + 2 * nbar0)
assert np.allclose(res[0], mean0, atol=tol, rtol=0)
assert np.allclose(res[1], var0, atol=tol, rtol=0.01)
res = state.number_expectation([1])
mean1 = np.abs(a1) ** 2 + nbar1
var1 = nbar1**2 + nbar1 + np.abs(a1) ** 2 * (1 + 2 * nbar1)
assert np.allclose(res[0], mean1, atol=tol, rtol=0)
assert np.allclose(res[1], var1, atol=tol, rtol=0.01)
# test uncorrelated result
res = state.number_expectation([0, 1])
expected_mean = mean0 * mean1
assert np.allclose(res[0], expected_mean, atol=tol, rtol=0)
expected_var = mean0**2 * var1 + mean1**2 * var0 + var0 * var1
assert np.allclose(res[1], expected_var, atol=tol, rtol=0.01)
@pytest.mark.backends("fock", "tf")
def test_number_expectation_four_modes(self, setup_backend, tol, batch_size):
"""Tests the expectation value of photon numbers when there is correlation"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(4)
state = backend.state()
r = 0.2
phi = 0.0
backend.prepare_squeezed_state(r, phi, 0)
backend.prepare_squeezed_state(r, phi + np.pi, 1)
backend.beamsplitter(np.pi / 4, np.pi, 0, 1)
backend.prepare_squeezed_state(r, phi, 2)
backend.prepare_squeezed_state(r, phi + np.pi, 3)
backend.beamsplitter(np.pi / 4, np.pi, 2, 3)
state = backend.state()
nbar = np.sinh(r) ** 2
assert np.allclose(
state.number_expectation([0, 1, 2, 3])[0],
(2 * nbar**2 + nbar) ** 2,
atol=tol,
rtol=0,
)
assert np.allclose(
state.number_expectation([0, 1, 3])[0],
nbar * (2 * nbar**2 + nbar),
atol=tol,
rtol=0,
)
assert np.allclose(
state.number_expectation([3, 1, 2])[0],
nbar * (2 * nbar**2 + nbar),
atol=tol,
rtol=0,
)
class TestParityExpectation:
@pytest.mark.backends("fock", "tf")
def test_parity_fock(self, setup_backend, tol, batch_size):
"""Tests the parity operator for an even superposition of the first two number states"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(2)
state = backend.state()
n1 = 3
n2 = 2
backend.prepare_fock_state(n1, 0)
backend.prepare_fock_state(n2, 1)
backend.beamsplitter(np.pi / 4, 0, 0, 1)
state = backend.state()
assert np.allclose(state.parity_expectation([0]), 0, atol=tol, rtol=0)
@pytest.mark.backends("fock", "tf")
def test_two_mode_fock(self, setup_backend, tol, batch_size):
"""Tests the product of parity operators for two number states"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(2)
state = backend.state()
n1 = 3
n2 = 5
backend.prepare_fock_state(n1, 0)
backend.prepare_fock_state(n2, 1)
state = backend.state()
assert np.allclose(state.parity_expectation([0, 1]), 1, atol=tol, rtol=0)
def test_coherent(self, setup_backend, tol, batch_size):
"""Tests the parity operator for a coherent state"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(1)
state = backend.state()
r = 0.2
backend.prepare_coherent_state(r, 0, 0)
state = backend.state()
assert np.allclose(
state.parity_expectation([0]), np.exp(-2 * (np.abs(r) ** 2)), atol=tol, rtol=0
)
def test_squeezed(self, setup_backend, tol, batch_size):
"""Tests the parity operator for a squeezed state"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(1)
state = backend.state()
r = 0.2
phi = 0
backend.prepare_squeezed_state(r, phi, 0)
state = backend.state()
assert np.allclose(state.parity_expectation([0]), 1, atol=tol, rtol=0)
def test_two_mode_squeezed(self, setup_backend, tol, batch_size):
"""Tests the parity operator for a two-mode squeezed state"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(2)
state = backend.state()
r = 0.2
phi = 0
backend.beamsplitter(np.sqrt(0.5), -np.sqrt(0.5), 0, 1)
backend.prepare_squeezed_state(r, phi, 0)
backend.prepare_squeezed_state(-1 * r, phi, 1)
backend.beamsplitter(np.sqrt(0.5), -np.sqrt(0.5), 0, 1)
state = backend.state()
assert np.allclose(state.parity_expectation([0, 1]), 1, atol=tol, rtol=0)
@pytest.mark.backends("fock", "tf")
def test_thermal(self, setup_backend, tol, batch_size):
"""Tests the parity operator for a thermal state"""
if batch_size is not None:
pytest.skip("Does not support batch mode")
backend = setup_backend(1)
state = backend.state()
m = 0.2
backend.prepare_thermal_state(m, 0)
state = backend.state()
assert np.allclose(state.parity_expectation([0]), (1 / ((2 * m) + 1)), atol=tol, rtol=0)
@pytest.mark.backends("fock", "tf", "gaussian")
class TestFidelities:
"""Fidelity tests."""
def test_vacuum(self, setup_backend, tol):
backend = setup_backend(2)
state = backend.state()
assert np.allclose(state.fidelity_vacuum(), 1, atol=tol, rtol=0)
def test_coherent_fidelity(self, setup_backend, cutoff, tol, hbar):
backend = setup_backend(2)
backend.prepare_coherent_state(np.abs(a), | np.angle(a) | numpy.angle |
import attr
import numpy as np
import scipy.sparse
from tectosaur.fmm.tsfmm import TSFMM
import tectosaur.util.geometry as geometry
import tectosaur.util.gpu as gpu
from tectosaur.farfield import farfield_pts_direct
from tectosaur.util.quadrature import gauss2d_tri, gauss4d_tri
from tectosaur.util.timer import Timer
from tectosaur.kernels import kernels
import logging
logger = logging.getLogger(__name__)
class TriToTriDirectFarfieldOp:
def __init__(self, nq_far, K_name, params, pts, tris,
float_type, obs_subset, src_subset):
self.shape = (obs_subset.shape[0] * 9, src_subset.shape[0] * 9)
self.dim = pts.shape[1]
self.tensor_dim = kernels[K_name].tensor_dim
self.n_obs = obs_subset.shape[0]
self.n_src = src_subset.shape[0]
in_size = self.n_src * self.dim * self.tensor_dim
out_size = self.n_obs * self.dim * self.tensor_dim
self.gpu_in = gpu.empty_gpu(in_size, float_type)
self.gpu_out = gpu.empty_gpu(out_size, float_type)
self.q = gauss2d_tri(nq_far)
self.gpu_pts = gpu.to_gpu(pts, float_type)
self.gpu_obs_tris = gpu.to_gpu(tris[obs_subset], np.int32)
self.gpu_src_tris = gpu.to_gpu(tris[src_subset], np.int32)
self.gpu_params = gpu.to_gpu(np.array(params), float_type)
self.block_size = 128
self.n_blocks = int(np.ceil(self.n_obs / self.block_size))
self.module = gpu.load_gpu(
'matrix_free.cl',
tmpl_args = dict(
block_size = self.block_size,
float_type = gpu.np_to_c_type(float_type),
quad_pts = self.q[0],
quad_wts = self.q[1]
)
)
self.fnc = getattr(self.module, "farfield_tris_to_tris" + K_name)
def dot(self, v):
self.gpu_in[:] = v[:].astype(self.gpu_in.dtype)
self.fnc(
self.gpu_out, self.gpu_in,
self.gpu_pts, self.gpu_obs_tris, self.gpu_src_tris,
self.gpu_params,
np.int32(self.n_obs), | np.int32(self.n_src) | numpy.int32 |
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Copyright (c) BaseDetection, Inc. and its affiliates. All Rights Reserved
import json
import os
import numpy as np
PERSON_CLASSES = ['background', 'person']
class Image(object):
def __init__(self, mode):
self.ID = None
self._width = None
self._height = None
self.dtboxes = None
self.gtboxes = None
self.eval_mode = mode
self._ignNum = None
self._gtNum = None
self._dtNum = None
def load(self, record, body_key, head_key, class_names, gtflag):
"""
:meth: read the object from a dict
"""
if "ID" in record and self.ID is None:
self.ID = record['ID']
if "width" in record and self._width is None:
self._width = record["width"]
if "height" in record and self._height is None:
self._height = record["height"]
if gtflag:
self._gtNum = len(record["gtboxes"])
body_bbox, head_bbox = self.load_gt_boxes(record, 'gtboxes', class_names)
if self.eval_mode == 0:
self.gtboxes = body_bbox
self._ignNum = (body_bbox[:, -1] == -1).sum()
elif self.eval_mode == 1:
self.gtboxes = head_bbox
self._ignNum = (head_bbox[:, -1] == -1).sum()
elif self.eval_mode == 2:
gt_tag = np.array(
[body_bbox[i, -1] != -1 and head_bbox[i, -1] != -1
for i in range(len(body_bbox))]
)
self._ignNum = (gt_tag == 0).sum()
self.gtboxes = np.hstack(
(body_bbox[:, :-1], head_bbox[:, :-1], gt_tag.reshape(-1, 1))
)
else:
raise Exception('Unknown evaluation mode!')
if not gtflag:
self._dtNum = len(record["dtboxes"])
if self.eval_mode == 0:
self.dtboxes = self.load_det_boxes(record, 'dtboxes', body_key, 'score')
elif self.eval_mode == 1:
self.dtboxes = self.load_det_boxes(record, 'dtboxes', head_key, 'score')
elif self.eval_mode == 2:
body_dtboxes = self.load_det_boxes(record, 'dtboxes', body_key)
head_dtboxes = self.load_det_boxes(record, 'dtboxes', head_key, 'score')
self.dtboxes = np.hstack((body_dtboxes, head_dtboxes))
else:
raise Exception('Unknown evaluation mode!')
def compare_caltech(self, thres):
"""
:meth: match the detection results with the groundtruth by Caltech matching strategy
:param thres: iou threshold
:type thres: float
:return: a list of tuples (dtbox, imageID), in the descending sort of dtbox.score
"""
if self.dtboxes is None or self.gtboxes is None:
return list()
dtboxes = self.dtboxes if self.dtboxes is not None else list()
gtboxes = self.gtboxes if self.gtboxes is not None else list()
dt_matched = np.zeros(dtboxes.shape[0])
gt_matched = np.zeros(gtboxes.shape[0])
dtboxes = np.array(sorted(dtboxes, key=lambda x: x[-1], reverse=True))
gtboxes = np.array(sorted(gtboxes, key=lambda x: x[-1], reverse=True))
if len(dtboxes):
overlap_iou = self.box_overlap_opr(dtboxes, gtboxes, True)
overlap_ioa = self.box_overlap_opr(dtboxes, gtboxes, False)
else:
return list()
scorelist = list()
for i, dt in enumerate(dtboxes):
maxpos = -1
maxiou = thres
for j, gt in enumerate(gtboxes):
if gt_matched[j] == 1:
continue
if gt[-1] > 0:
overlap = overlap_iou[i][j]
if overlap > maxiou:
maxiou = overlap
maxpos = j
else:
if maxpos >= 0:
break
else:
overlap = overlap_ioa[i][j]
if overlap > thres:
maxiou = overlap
maxpos = j
if maxpos >= 0:
if gtboxes[maxpos, -1] > 0:
gt_matched[maxpos] = 1
dt_matched[i] = 1
scorelist.append((dt, 1, self.ID))
else:
dt_matched[i] = -1
else:
dt_matched[i] = 0
scorelist.append((dt, 0, self.ID))
return scorelist
def compare_caltech_union(self, thres):
"""
:meth: match the detection results with the groundtruth by Caltech matching strategy
:param thres: iou threshold
:type thres: float
:return: a list of tuples (dtbox, imageID), in the descending sort of dtbox.score
"""
dtboxes = self.dtboxes if self.dtboxes is not None else list()
gtboxes = self.gtboxes if self.gtboxes is not None else list()
if len(dtboxes) == 0:
return list()
dt_matched = np.zeros(dtboxes.shape[0])
gt_matched = np.zeros(gtboxes.shape[0])
dtboxes = np.array(sorted(dtboxes, key=lambda x: x[-1], reverse=True))
gtboxes = np.array(sorted(gtboxes, key=lambda x: x[-1], reverse=True))
dt_body_boxes = np.hstack((dtboxes[:, :4], dtboxes[:, -1][:, None]))
dt_head_boxes = dtboxes[:, 4:8]
gt_body_boxes = np.hstack((gtboxes[:, :4], gtboxes[:, -1][:, None]))
gt_head_boxes = gtboxes[:, 4:8]
overlap_iou = self.box_overlap_opr(dt_body_boxes, gt_body_boxes, True)
overlap_head = self.box_overlap_opr(dt_head_boxes, gt_head_boxes, True)
overlap_ioa = self.box_overlap_opr(dt_body_boxes, gt_body_boxes, False)
scorelist = list()
for i, dt in enumerate(dtboxes):
maxpos = -1
maxiou = thres
for j, gt in enumerate(gtboxes):
if gt_matched[j] == 1:
continue
if gt[-1] > 0:
o_body = overlap_iou[i][j]
o_head = overlap_head[i][j]
if o_body > maxiou and o_head > maxiou:
maxiou = o_body
maxpos = j
else:
if maxpos >= 0:
break
else:
o_body = overlap_ioa[i][j]
if o_body > thres:
maxiou = o_body
maxpos = j
if maxpos >= 0:
if gtboxes[maxpos, -1] > 0:
gt_matched[maxpos] = 1
dt_matched[i] = 1
scorelist.append((dt, 1, self.ID))
else:
dt_matched[i] = -1
else:
dt_matched[i] = 0
scorelist.append((dt, 0, self.ID))
return scorelist
def box_overlap_opr(self, dboxes: np.ndarray, gboxes: np.ndarray, if_iou):
eps = 1e-6
assert dboxes.shape[-1] >= 4 and gboxes.shape[-1] >= 4
N, K = dboxes.shape[0], gboxes.shape[0]
dtboxes = np.tile(np.expand_dims(dboxes, axis=1), (1, K, 1))
gtboxes = np.tile( | np.expand_dims(gboxes, axis=0) | numpy.expand_dims |
import numpy as np
import matplotlib as mpl
mpl.use("Agg")
import seaborn as sns
import matplotlib.pyplot as plt
from utils import *
from torch.nn.utils.rnn import pad_sequence
from sklearn.preprocessing import QuantileTransformer
import os
import torch.nn.functional as F
from utils import *
def get_free_gpu():
os.system('nvidia-smi -q -d Memory |grep -A4 GPU|grep Free > ./tmp')
memory_available = [int(x.split()[2]) for x in open('tmp', 'r').readlines()]
if len(memory_available) > 0:
id = int(np.argmax(memory_available))
print("setting to gpu:%d" % id)
torch.cuda.set_device(id)
return "cuda:%d" % id
else:
return
if torch.cuda.is_available():
current_device = get_free_gpu()
else:
current_device = 'cpu'
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
def proba2matrix(sample, weight=None, proba=None, intra=True):
sample_left = sample
weight_left = weight
if intra:
sample_left -= np.min(sample_left)
size = int(np.max(sample_left) + 1 )
m = np.zeros((size, size), dtype='float32')
if weight is not None:
for i in range(sample_left.shape[-1] - 1):
for j in range( i +1, sample_left.shape[-1]):
m[sample_left[: ,i], sample_left[: ,j]] += np.maximum(proba * weight_left, proba)
else:
for i in range(sample_left.shape[-1] - 1):
for j in range(i + 1, sample_left.shape[-1]):
m[sample_left[:, i], sample_left[:, j]] += proba
m = m + m.T
else:
size1 = int(np.max(sample_left[:, 0]) - np.min(sample_left[:, 0]) + 1)
size2 = int(np.max(sample_left[:, 1]) - np.min(sample_left[:, 1]) + 1)
m = np.zeros((size1, size2), dtype='float32')
if weight is not None:
m[sample_left[:, 0] - np.min(sample_left[:, 0]), sample_left[:, 1]- np.min(sample_left[:, 1])] += np.maximum(proba * weight_left, proba)
else:
m[sample_left[:, 0] - np.min(sample_left[:, 0]), sample_left[:, 1] - np.min(sample_left[:, 1])] += proba
return m
def generate_pair_wise(chrom_id):
samples = []
for i in range(chrom_range[chrom_id ,0] ,chrom_range[chrom_id ,1]):
for j in range( i +min_dis, chrom_range[chrom_id ,1]):
samples.append([i ,j])
samples = | np.array(samples) | numpy.array |
"""Train the model"""
from __future__ import print_function
import os
import sys
import numpy as np
import time
from metrics import mcor,recall,f1,precision
from keras.preprocessing.text import Tokenizer
from keras.preprocessing.sequence import pad_sequences
from keras.utils import to_categorical
from keras.layers import Dense, Input, GlobalMaxPooling1D
from keras.layers import Conv1D, MaxPooling1D, Embedding, LSTM, Dropout, Activation, Bidirectional
from keras.models import Model
from keras.callbacks import TensorBoard, ModelCheckpoint
import keras.backend as K
from time import localtime, strftime
BASE_DIR = ''
GLOVE_DIR = './data/GloVe/glove.6B.100d.txt'
TEXT_DATA_DIR = './data/kaggle'
TENSORBOARD_BASE_DIR = 'experiments/tensorboard'
#MODEL_CP_DIR = 'experiments/weights/weights.best.hdf5'
#MODEL_FINAL_DIR = 'experiments/weights/weights.final.hdf5'
MAX_SEQUENCE_LENGTH = 1000
MAX_NUM_WORDS = 20000
EMBEDDING_DIM = 100
NUM_CLASSES = 'binary_'
TESTS = [('conv', 1), ('conv', 2), ('conv', 3), ('conv', 4), ('lstm', 1), ('lstm', 2), ('lstm', 3), ('bidirectional', 1), ('bidirectional', 2), ('bidirectional', 3)]
#MODEL = 'bidirectional'
# LSTM_CP_DIR = 'experiments/weights/lstm_weights.best.hdf5'
# CONV_CP_DIR = 'experiments/weights/conv_weights.best.hdf5'
# CONV_CP_DIR = '{}{}{}'.format('experiments/weights/',NUM_LAYERS,'conv_weights.best.hdf5')
# LSTM_FINAL_DIR = 'experiments/weights/lstm_weights.final.hdf5'
# CONV_FINAL_DIR = 'experiments/weights/conv_weights.final.hdf5'
def index_glove_embeddings(fname):
# first, build index mapping words in the embeddings set
# to their embedding vector
embeddings_index = {}
with open(fname) as f:
for line in f:
values = line.split()
word = values[0]
coefs = | np.asarray(values[1:], dtype='float32') | numpy.asarray |
"""
2D Disc models
==============
Classes: Rosenfeld2d, General2d, Velocity, Intensity, Cube, Tools
"""
#TODO in show(): Perhaps use text labels on line profiles to distinguish profiles for more than 2 cubes.
#TODO in make_model(): Find a smart way to detect and pass only the coords needed by a prop attribute.
#TODO in run_mcmc(): Enable an arg to allow the user see the position of parameter walkers every 'arg' steps.
#TODO in General2d: Implement irregular grids (see e.g. meshio from nschloe on github) for the disc grid.
#TODO in General2d: Compute props in the interpolated grid (not in the original grid) to avoid interpolation of props and save time.
#TODO in General2d: Allow the lower surface to have independent intensity and line width parametrisations.
#TODO in General2d: Implement pressure support term
#TODO in make_model(): Allow for warped emitting surfaces, check notes for ideas as to how to solve for multiple intersections between l.o.s and emission surface.
#TODO in __main__(): show intro message when python -m disc2d
#TODO in run_mcmc(): use get() methods instead of allowing the user to use self obj attributes.
#TODO in make_model(): Allow R_disc to be a free parameter.
#TODO in make_model(): Enable 3D velocities too when subpixel algorithm is used
#TODO in v1.0: migrate to astropy units
from __future__ import print_function
from ..utils import constants as sfc
from ..utils import units as sfu
from astropy.convolution import Gaussian2DKernel, convolve
from scipy.interpolate import griddata, interp1d
from scipy.special import ellipk, ellipe
from scipy.optimize import curve_fit
from scipy.integrate import quad
import matplotlib.patches as patches
import matplotlib.pyplot as plt
from matplotlib import ticker
import numpy as np
import matplotlib
import itertools
import warnings
import numbers
import pprint
import copy
import time
import sys
import os
from multiprocessing import Pool
os.environ["OMP_NUM_THREADS"] = "1"
try:
import termtables
found_termtables = True
except ImportError:
print ("\n*** For nicer outputs we recommend installing 'termtables' by typing in terminal: pip install termtables ***")
found_termtables = False
#warnings.filterwarnings("error")
__all__ = ['Cube', 'Tools', 'Intensity', 'Velocity', 'General2d', 'Rosenfeld2d']
path_file = os.path.dirname(os.path.realpath(__file__))+'/'
"""
matplotlib.rcParams['font.family'] = 'monospace'
matplotlib.rcParams['font.weight'] = 'normal'
matplotlib.rcParams['lines.linewidth'] = 1.5
matplotlib.rcParams['axes.linewidth'] = 3.0
matplotlib.rcParams['xtick.major.width']=1.6
matplotlib.rcParams['ytick.major.width']=1.6
matplotlib.rc('font', size=MEDIUM_SIZE) # controls default text sizes
matplotlib.rc('axes', titlesize=MEDIUM_SIZE) # fontsize of axes title
matplotlib.rc('axes', labelsize=MEDIUM_SIZE) # fontsize of x and y labels
matplotlib.rc('xtick', labelsize=MEDIUM_SIZE-2) # fontsize of y tick labels
matplotlib.rc('ytick', labelsize=MEDIUM_SIZE-2) # fontsize of x tick labels
matplotlib.rc('legend', fontsize=SMALL_SIZE-1) # legend fontsize
matplotlib.rc('figure', titlesize=BIGGER_SIZE) # fontsize of figure title
params = {'xtick.major.size': 6.5,
'ytick.major.size': 6.5
}
matplotlib.rcParams.update(params)
"""
SMALL_SIZE = 10
MEDIUM_SIZE = 15
BIGGER_SIZE = 22
hypot_func = lambda x,y: np.sqrt(x**2 + y**2) #Slightly faster than np.hypot<np.linalg.norm<scipydistance. Checked precision up to au**2 orders and seemed ok.
class InputError(Exception):
"""Exception raised for errors in the input.
Attributes:
expression -- input expression in which the error occurred
message -- explanation of the error
"""
def __init__(self, expression, message):
self.expression = expression
self.message = message
def __str__(self):
return '%s --> %s'%(self.expression, self.message)
class Tools:
@staticmethod
def _rotate_sky_plane(x, y, ang):
xy = np.array([x,y])
cos_ang = np.cos(ang)
sin_ang = np.sin(ang)
rot = np.array([[cos_ang, -sin_ang],
[sin_ang, cos_ang]])
return np.dot(rot, xy)
@staticmethod
def _rotate_sky_plane3d(x, y, z, ang, axis='z'):
xyz = np.array([x,y,z])
cos_ang = np.cos(ang)
sin_ang = np.sin(ang)
if axis == 'x':
rot = np.array([[1, 0, 0],
[0, cos_ang, -sin_ang],
[0, sin_ang, cos_ang]])
if axis == 'y':
rot = np.array([[cos_ang, 0, -sin_ang],
[0, 1, 0],
[sin_ang, 0, cos_ang]])
if axis == 'z':
rot = np.array([[cos_ang, -sin_ang , 0],
[sin_ang, cos_ang, 0],
[0, 0, 1]])
return np.dot(rot, xyz)
@staticmethod
def _project_on_skyplane(x, y, z, cos_incl, sin_incl):
x_pro = x
y_pro = y * cos_incl - z * sin_incl
z_pro = y * sin_incl + z * cos_incl
return x_pro, y_pro, z_pro
@staticmethod
def get_sky_from_disc_coords(R, az, z, incl, PA):
xp = R*np.cos(az)
yp = R*np.sin(az)
zp = z
xp, yp, zp = Tools._project_on_skyplane(xp, yp, zp, np.cos(incl), np.sin(incl))
xp, yp = Tools._rotate_sky_plane(xp, yp, PA)
return xp, yp, zp
@staticmethod #should be a bound method, self.grid is constant except for z_upper, z_lower
def _compute_prop(grid, prop_funcs, prop_kwargs):
n_funcs = len(prop_funcs)
props = [{} for i in range(n_funcs)]
for side in ['upper', 'lower']:
x, y, z, R, phi, R_1d, z_1d = grid[side]
coord = {'x': x, 'y': y, 'z': z, 'phi': phi, 'R': R, 'R_1d': R_1d, 'z_1d': z_1d}
for i in range(n_funcs): props[i][side] = prop_funcs[i](coord, **prop_kwargs[i])
return props
@staticmethod
def _progress_bar(percent=0, width=50):
left = width * percent // 100
right = width - left
"""
print('\r[', '#' * left, ' ' * right, ']',
f' {percent:.0f}%',
sep='', end='', flush=True)
"""
print('\r[', '#' * left, ' ' * right, ']', ' %.0f%%'%percent, sep='', end='') #compatible with python2 docs
sys.stdout.flush()
@staticmethod
def _break_line(init='', border='*', middle='=', end='\n', width=100):
print('\r', init, border, middle * width, border, sep='', end=end)
@staticmethod
def _print_logo(filename=path_file+'logo.txt'):
logo = open(filename, 'r')
print(logo.read())
logo.close()
@staticmethod
def _get_beam_from(beam, dpix=None, distance=None, frac_pixels=1.0):
"""
beam must be str pointing to fits file to extract beam from header or radio_beam Beam object.
If radio_beam Beam instance is provided, pixel size (in SI units) will be extracted from grid obj. Distance (in pc) must be provided.
#frac_pixels: number of averaged pixels on the data (useful to reduce computing time)
"""
from radio_beam import Beam
from astropy.io import fits
from astropy import units as u
sigma2fwhm = np.sqrt(8*np.log(2))
if isinstance(beam, str):
header = fits.getheader(beam)
beam = Beam.from_fits_header(header)
pix_scale = header['CDELT2'] * u.Unit(header['CUNIT2']) * frac_pixels
elif isinstance(beam, Beam):
if distance is None: raise InputError(distance, 'Wrong input distance. Please provide a value for the distance (in pc) to transform grid pix to arcsec')
pix_radians = np.arctan(dpix / (distance*sfu.pc)) #dist*ang=projdist
pix_scale = (pix_radians*u.radian).to(u.arcsec)
#print (pix_scale, pix_radians)
else: raise InputError(beam, 'beam object must either be str or Beam instance')
x_stddev = ((beam.major/pix_scale) / sigma2fwhm).value
y_stddev = ((beam.minor/pix_scale) / sigma2fwhm).value
#print (x_stddev, beam.major, pix_scale)
angle = (90*u.deg+beam.pa).to(u.radian).value
gauss_kern = Gaussian2DKernel(x_stddev, y_stddev, angle)
#gauss_kern = beam.as_kernel(pix_scale) #as_kernel() is slowing down the run when used in astropy.convolve
return beam, gauss_kern
@staticmethod
def average_pixels_cube(data, frac_pixels, av_method=np.median):
"""
data: datacube with shape (nchan, nx0, ny0)
frac_pixels: number of pixels to average
av_method: function to compute average
"""
nchan, nx0, ny0 = np.shape(data)
nx = int(round(nx0/frac_pixels))
ny = int(round(ny0/frac_pixels))
av_data = np.zeros((nchan, nx, ny))
progress = Tools._progress_bar
if frac_pixels>1:
di = frac_pixels
dj = frac_pixels
print ('Averaging %dx%d pixels from data cube...'%(di, dj))
for k in range(nchan):
progress(int(100*k/nchan))
for i in range(nx):
for j in range(ny):
av_data[k,i,j] = av_method(data[k,i*di:i*di+di,j*dj:j*dj+dj])
progress(100)
return av_data
else:
print('frac_pixels is <= 1, no average was performed...')
return data
@staticmethod
def weighted_std(prop, weights, weighted_mean=None):
sum_weights = np.sum(weights)
if weighted_mean is None:
weighted_mean = np.sum(weights*prop)/sum_weights
n = np.sum(weights>0)
w_std = np.sqrt(np.sum(weights*(prop-weighted_mean)**2)/((n-1)/n * sum_weights))
return w_std
#define a fit_double_bell func, with a model input as an optional arg to constrain initial guesses better
@staticmethod
def fit_one_gauss_cube(data, vchannels, lw_chan=1.0, sigma_fit=None):
"""
Fit Gaussian profile along velocity axis to input data
lw_chan: initial guess for line width is lw_chan*np.mean(dvi).
sigma_fit: cube w/ channel weights for each pixel, passed to curve_fit
"""
gauss = lambda x, *p: p[0]*np.exp(-(x-p[1])**2/(2.*p[2]**2))
nchan, nx, ny = np.shape(data)
peak, dpeak = np.zeros((nx, ny)), np.zeros((nx, ny))
centroid, dcent = np.zeros((nx, ny)), np.zeros((nx, ny))
linewidth, dlinew = np.zeros((nx, ny)), np.zeros((nx, ny))
nbad = 0
ind_max = np.nanargmax(data, axis=0)
I_max = np.nanmax(data, axis=0)
vel_peak = vchannels[ind_max]
dv = lw_chan*np.mean(vchannels[1:]-vchannels[:-1])
progress = Tools._progress_bar
if sigma_fit is None: sigma_func = lambda i,j: None
else: sigma_func = lambda i,j: sigma_fit[:,i,j]
print ('Fitting Gaussian profile to pixels (along velocity axis)...')
for i in range(nx):
for j in range(ny):
isfin = np.isfinite(data[:,i,j])
try: coeff, var_matrix = curve_fit(gauss, vchannels[isfin], data[:,i,j][isfin],
p0=[I_max[i,j], vel_peak[i,j], dv],
sigma=sigma_func(i,j))
except RuntimeError:
nbad+=1
continue
peak[i,j] = coeff[0]
centroid[i,j] = coeff[1]
linewidth[i,j] = coeff[2]
dpeak[i,j], dcent[i,j], dlinew[i,j] = np.sqrt(np.diag(var_matrix))
progress(int(100*i/nx))
progress(100)
print ('\nGaussian fit did not converge for %.2f%s of the pixels'%(100.0*nbad/(nx*ny),'%'))
return peak, centroid, linewidth, dpeak, dcent, dlinew
@staticmethod
def get_tb(I, nu, beam, full=True):
"""
nu in GHz
Intensity in mJy/beam
beam object from radio_beam
if full: use full Planck law, else use rayleigh-jeans approximation
"""
from astropy import units as u
bmaj = beam.major.to(u.arcsecond).value
bmin = beam.minor.to(u.arcsecond).value
beam_area = sfu.au**2*np.pi*(bmaj*bmin)/(4*np.log(2)) #area of gaussian beam
#beam solid angle: beam_area/(dist*pc)**2. dist**2 cancels out with beamarea's dist**2 from conversion or bmaj, bmin to mks units.
beam_solid = beam_area/sfu.pc**2
mJy_to_SI = 1e-3*1e-26
nu = nu*1e9
if full:
Tb = np.sign(I)*(np.log((2*sfc.h*nu**3)/(sfc.c**2*np.abs(I)*mJy_to_SI/beam_solid)+1))**-1*sfc.h*nu/(sfc.kb)
else:
wl = sfc.c/nu
Tb = 0.5*wl**2*I*mJy_to_SI/(beam_solid*sfc.kb)
#(1222.0*I/(nu**2*(beam.minor/1.0).to(u.arcsecond)*(beam.major/1.0).to(u.arcsecond))).value #nrao RayJeans
return Tb
@staticmethod
def _get_tb(*args, **kwargs): return Tools.get_tb(*args, **kwargs)
class Residuals:
pass
class PlotTools:
@staticmethod
def mod_nticks_cbars(cbars, nbins=5):
for cb in cbars:
cb.locator = ticker.MaxNLocator(nbins=nbins)
cb.update_ticks()
@staticmethod
def mod_major_ticks(ax, axis='both', nbins=6):
ax.locator_params(axis=axis, nbins=nbins)
@staticmethod
def mod_minor_ticks(ax):
ax.minorticks_on()
ax.xaxis.set_minor_locator(ticker.AutoMinorLocator(2)) #1 minor tick per major interval
ax.yaxis.set_minor_locator(ticker.AutoMinorLocator(2))
@classmethod
def make_up_ax(cls, ax, xlims=(None, None), ylims=(None, None),
mod_minor=True, mod_major=True, **kwargs_tick_params):
kwargs_t = dict(labeltop=True, labelbottom=False, top=True, right=True, which='both', direction='in')
kwargs_t.update(kwargs_tick_params)
if mod_major: cls.mod_major_ticks(ax)
if mod_minor: cls.mod_minor_ticks(ax)
ax.set_xlim(*xlims)
ax.set_ylim(*ylims)
ax.tick_params(**kwargs_t)
@staticmethod
def truncate_colormap(cmap, minval=0.0, maxval=1.0, n=256):
new_cmap = matplotlib.colors.LinearSegmentedColormap.from_list(
'trunc({n},{a:.2f},{b:.2f})'.format(n=cmap.name, a=minval, b=maxval),
cmap(np.linspace(minval, maxval, n)))
return new_cmap
@staticmethod
def get_cmap_from_color(color, lev=3):
cmap = matplotlib.colors.to_rgba(color)
newcolors = np.tile(cmap, lev).reshape(lev,4) #Repeats the colour lev times
newcolors[:,-1] = np.linspace(0.25, 0.95, lev) #Modifies alpha only
new_cmap = ListedColormap(newcolors)
return new_cmap
@staticmethod
def mask_cmap_interval(cmap, cmap_lims, mask_lims, mask_color=np.ones(4), append=False):
if isinstance(cmap, str): cmap = plt.get_cmap(cmap)
cmap0, cmap1 = cmap_lims
mask0, mask1 = mask_lims
c0 = (mask0-cmap0)/(cmap1-cmap0)
c1 = (mask1-cmap0)/(cmap1-cmap0)
id0 = int(round(c0*(cmap.N)))
id1 = int(round(c1*(cmap.N)))
new_cmap = copy.copy(cmap)
new_cmap._init()
"""#The following does not work, plt does not know where to locate the newly added colorss
if append:
mask_color_arr = np.broadcast_to(mask_color, (id1-id0, 4))
new_cmap._lut = np.insert(new_cmap._lut, id0, mask_color_arr, axis=0)
new_cmap.N = cmap.N + id1-id0
#Next line redoes the continuous linearsegmented colormap, thus the masked color block is reduced to a single color
#new_cmap = new_cmap._resample(new_cmap.N)
"""
new_cmap._lut[id0:id1,:] = mask_color
return new_cmap
@staticmethod
def get_continuous_cmap(hex_list, float_list=None):
"""
Taken from https://github.com/KerryHalupka/custom_colormap
creates and returns a color map that can be used in heat map figures.
If float_list is not provided, colour map graduates linearly between each color in hex_list.
If float_list is provided, each color in hex_list is mapped to the respective location in float_list.
Parameters
----------
hex_list: list of hex code strings
float_list: list of floats between 0 and 1, same length as hex_list. Must start with 0 and end with 1.
Returns
----------
matplotlib cmap
Examples
----------
fig, ax = plt.subplots(1,1)
hex_list = ['#0091ad', '#fffffc', '#ffd166']
x, y = np.mgrid[-5:5:0.05, -5:5:0.05]
z = (np.sqrt(x**2 + y**2) + np.sin(x**2 + y**2))
im = ax.imshow(z, cmap=get_continuous_cmap(hex_list))
fig.colorbar(im)
ax.yaxis.set_major_locator(plt.NullLocator()) # remove y axis ticks
ax.xaxis.set_major_locator(plt.NullLocator()) # remove x axis ticks
plt.show()
"""
rgb_list = [matplotlib.colors.to_rgb(i) for i in hex_list]
if float_list is None: float_list = np.linspace(0,1,len(rgb_list))
cdict = dict()
for num, col in enumerate(['red', 'green', 'blue']):
col_list = [[float_list[i], rgb_list[i][num], rgb_list[i][num]] for i in range(len(float_list))]
cdict[col] = col_list
cmap_new = matplotlib.colors.LinearSegmentedColormap('my_cmp', segmentdata=cdict, N=256)
return cmap_new
@staticmethod
def append_stddev_panel(ax, prop, weights=None, hist=False, fit_gauss_hist=False): #attach significance panel to ax, based on dist. of points prop
gauss = lambda x, A, mu, sigma: A*np.exp(-(x-mu)**2/(2.*sigma**2))
ax1_ylims = ax[-2].get_ylim()
for axi in ax[:-1]: axi.tick_params(which='both', right=False, labelright=False)
ax[-1].tick_params(which='both', top=False, bottom=False, labelbottom=False,
left=False, labelleft=False, right=True, labelright=True)
ax[-1].yaxis.set_label_position('right')
ax[-1].spines['left'].set_color('0.6')
ax[-1].spines['left'].set_linewidth(3.5)
if weights is not None:
prop_mean = np.sum(weights*prop)/np.sum(weights)
prop_std = Tools.weighted_std(prop, weights, weighted_mean=prop_mean)
else:
prop_mean = np.mean(prop)
prop_std = np.std(prop)
max_y = 1.0
if hist:
n, bins, patches = ax[-1].hist(prop, bins=2*int(round(len(prop)**(1/3.)))-1, orientation='horizontal',
density=True, linewidth=1.5, facecolor='0.95', edgecolor='k', alpha=1.0)
max_y = np.max(n)
if fit_gauss_hist: #Fit Gaussian to histogram to compare against data distribution
coeff, var_matrix = curve_fit(gauss, 0.5*(bins[1:]+bins[:-1]), n, p0=[max_y, prop_mean, prop_std])
prop_x = np.linspace(prop_mean-4*prop_std, prop_mean+4*prop_std, 100)
prop_y = gauss(prop_x, *coeff)
ax[-1].plot(prop_y, prop_x, color='tomato', ls='--', lw=2.0)
prop_x = np.linspace(prop_mean-4*prop_std, prop_mean+4*prop_std, 100)
prop_pars = [max_y, prop_mean, prop_std]
prop_y = gauss(prop_x, *prop_pars)
ax[-1].plot(prop_y, prop_x, color='limegreen', lw=3.5)
ax[-1].set_xlim(-0.2*max_y, 1.2*max_y)
#ax[-1].plot([-0.2, 1.0], [prop_mean]*2, color='0.6', lw=2.5)
#for axi in ax[:-1]: axi.axhline(prop_mean, color='0.6', lw=2.5)
for i in range(0,4):
prop_stdi = prop_mean+i*prop_std
gauss_prop_stdi = gauss(prop_stdi, *prop_pars)
ax[-1].plot([-0.2*max_y, gauss_prop_stdi], [prop_stdi]*2, color='0.6', ls=':', lw=2.)
for axi in ax[:-1]: axi.axhline(prop_stdi, color='0.6', ls=':', lw=2.)
if prop_stdi < ax1_ylims[-1] and i>0:
ax[-1].text(gauss_prop_stdi+0.2*max_y, prop_stdi, r'%d$\sigma$'%i,
fontsize=14, ha='center', va='center', rotation=-90)
for axi in ax: axi.set_ylim(*ax1_ylims)
class Canvas3d:
pass
class Contours(PlotTools):
@staticmethod
def emission_surface(ax, R, phi, R_lev=None, phi_lev=None, extent=None, proj_offset=None, X=None, Y=None, kwargs_R={}, kwargs_phi={}):
kwargs_phif = dict(linestyles=':', linewidths=1.0, colors='k')
kwargs_Rf = dict(linewidths=1.4, colors='k')
kwargs_phif.update(kwargs_phi)
kwargs_Rf.update(kwargs_R)
near_nonan = ~np.isnan(R['upper'])
Rmax = np.max(R['upper'][near_nonan])
if extent is None:
extent = np.array([-Rmax, Rmax, -Rmax, Rmax])/sfu.au
kwargs_phif.update({'extent': extent})
kwargs_Rf.update({'extent': extent})
if R_lev is None: R_lev = np.linspace(0.06, 0.97, 4)*Rmax
else: R_lev = np.sort(R_lev)
if phi_lev is None: phi_lev = np.linspace(-np.pi*0.95, np.pi, 11, endpoint=False)
#Splitting phi into pos and neg to try and avoid ugly contours close to -pi and pi
phi_lev_neg = phi_lev[phi_lev<0]
phi_lev_pos = phi_lev[phi_lev>0]
phi_neg_near = np.where((phi['upper']<0) & (R['upper']>R_lev[0]) & (R['upper']<R_lev[-1]), phi['upper'], np.nan)
phi_pos_near = np.where((phi['upper']>0) & (R['upper']>R_lev[0]) & (R['upper']<R_lev[-1]), phi['upper'], np.nan)
phi_neg_far = np.where((phi['lower']<0) & (R['lower']>R_lev[0]) & (R['lower']<R_lev[-1]), phi['lower'], np.nan)
phi_pos_far = np.where((phi['lower']>0) & (R['lower']>R_lev[0]) & (R['lower']<R_lev[-1]), phi['lower'], np.nan)
if proj_offset is not None: #For 3d projections
ax.contour(X, Y, R['upper'], offset=proj_offset, levels=R_lev, **kwargs_Rf)
ax.contour(X, Y, np.where(near_nonan, np.nan, R['lower']), offset=proj_offset, levels=R_lev, **kwargs_Rf)
ax.contour(X, Y, phi_pos_near, offset=proj_offset, levels=phi_lev_pos, **kwargs_phif)
ax.contour(X, Y, phi_neg_near, offset=proj_offset, levels=phi_lev_neg, **kwargs_phif)
ax.contour(X, Y, np.where(near_nonan, np.nan, phi_pos_far), offset=proj_offset, levels=phi_lev_pos, **kwargs_phif)
ax.contour(X, Y, | np.where(near_nonan, np.nan, phi_neg_far) | numpy.where |
import numpy as np
import scipy as sp
import scipy.constants
import cPickle
import echolect as el
import radarmodel
import prx
with open('three_targets_data.pkl', 'rb') as f:
store = cPickle.load(f)
y = store['y']
s = store['s']
ts = store['ts']
t0 = store['t0']
f0 = store['f0']
noise_sigma = store['noise_sigma']
m = len(y)
r = 1
n = 200#len(s)
filt = el.filtering.MatchedDoppler(s, n, m, xdtype=np.complex_)
A = radarmodel.point.Forward(s, n, m, r)
Astar = radarmodel.point.Adjoint(s, n, m, r)
# matched filter recovery
h_matched = filt(y)[:, filt.nodelay]
# compressed sensing recovery
x0 = np.zeros(A.inshape, A.indtype)
x1 = prx.l1rls(A, Astar, y, lmbda=.125, x0=x0, printrate=10)
x = x1/np.sqrt(n) + Astar(y - A(x1))* | np.sqrt(n) | numpy.sqrt |
#This code is based on the implementation of calibration functions available here: https://github.com/dirichletcal/experiments_neurips/blob/master/calib/utils/functions.py
import numpy as np
from scipy.stats import rankdata
from scipy.stats import friedmanchisquare
from scipy.stats import wilcoxon
from scipy.stats import beta
from scipy.stats import percentileofscore
from scipy.optimize import fmin
from scipy.optimize import minimize_scalar
import scipy.integrate as integrate
from scipy.special import gamma as gamma_func
from scipy.stats import gamma
from scipy.stats import percentileofscore
#from sklearn.metrics import brier_score_loss # Only for one-class
from sklearn.metrics import mean_squared_error
from sklearn.metrics import log_loss
# To check of serializable objects
import json
import pickle
def cross_entropy(y_hat, y):
'''
y_hat : predicted y
y : true y
'''
return log_loss(y, y_hat)
def brier_score(y_hat, y):
'''
y_hat : predicted y
y : true y
'''
return mean_squared_error(y, y_hat)
def get_sets(x, y, test_fold_id, test_folds):
x_test = x[test_folds == test_fold_id, :]
y_test = y[test_folds == test_fold_id]
train_indices = test_folds != test_fold_id
x_train = x[train_indices, :]
y_train = y[train_indices]
return [x_train, y_train, x_test, y_test]
def p_value(values):
if values.shape[1] > 2:
return friedmanchisquare(*[values[:, x] for x in np.arange(
values.shape[1])])
else:
return wilcoxon(values[:, 0], values[:, 1])
def _draw_labels(scores):
return np.array([np.random.binomial(1, p) for p in scores])
def df_normalise(df, columns=True):
'''
rows: bool
Normalize each column to sum to one, or each row to sum to one
'''
if columns:
return df/df.sum(axis=0)
return (df.T/df.sum(axis=1)).T
def is_serializable(x):
try:
pickle.dumps(x)
return True
except:
return False
def serializable_or_string(x):
try:
pickle.dumps(x)
return x
except:
return str(x)
# Markus functions
from sklearn.preprocessing import label_binarize
def guo_ECE(probs, y_true, bins=15):
"""
Calculate ECE score based on model output probabilities and true labels
Params:
probs: a list containing probabilities for all the classes with a shape of (samples, classes)
y_true: - a list containing the actual class labels
- ndarray shape (n_samples) with a list containing actual class
labels
- ndarray shape (n_samples, n_classes) with largest value in
each row for the correct column class.
bins: (int) - into how many bins are probabilities divided (default = 15)
Returns:
ece - expected calibration error
"""
return ECE(probs, y_true, normalize=False, bins=bins, ece_full=False)
def ECE(probs, y_true, normalize = False, bins = 15, ece_full = True):
"""
Calculate ECE score based on model output probabilities and true labels
Params:
probs: a list containing probabilities for all the classes with a shape of (samples, classes)
y_true: - a list containing the actual class labels
- ndarray shape (n_samples) with a list containing actual class
labels
- ndarray shape (n_samples, n_classes) with largest value in
each row for the correct column class.
normalize: (bool) in case of 1-vs-K calibration, the probabilities need to be normalized. (default = False)
bins: (int) - into how many bins are probabilities divided (default = 15)
ece_full: (bool) - whether to use ECE-full or ECE-max.
Returns:
ece - expected calibration error
"""
probs = np.array(probs)
y_true = np.array(y_true)
if len(y_true.shape) == 2 and y_true.shape[1] > 1:
y_true = y_true.argmax(axis=1).reshape(-1, 1)
# Prepare predictions, confidences and true labels for ECE calculation
if ece_full:
preds, confs, y_true = get_preds_all(probs, y_true, normalize=normalize, flatten=True)
else:
preds = | np.argmax(probs, axis=1) | numpy.argmax |
#!/usr/bin/python
# coding=utf-8
"""
@version:
@author: <NAME>
@license: Apache Licence
@contact: <EMAIL>
@site:
@software: PyCharm Community Edition
@file: batchmk.py
@time: 09/04/17 21:10
"""
import src.io.fea as fea
import tensorflow as tf
import numpy as np
import time
LONGEST_FRMS = 2000
class lstm_batch(object):
def __init__(self, num_streams, num_steps, input_dim):
self.sample_feat_list = [np.zeros([LONGEST_FRMS, input_dim]) for _ in range(num_streams)]
self.sample_label_list = [np.zeros([LONGEST_FRMS]) for _ in range(num_streams)]
self.sample_mask_list = [np.zeros([LONGEST_FRMS]) for _ in range(num_streams)]
self.curt = np.zeros(num_streams, dtype=int)
self.lent = np.zeros(num_streams, dtype=int)
self.reset_flag = np.zeros(num_streams, dtype=bool)
self.num_streams = num_streams
self.num_steps = num_steps
self.input_dim = input_dim
self.handled_utt_num = 0
self.handled_frm_num = 0
self.cur_epoch_finish = False
def set_stream_num(self, num_streams):
self.num_streams = num_streams
self.sample_feat_list = [np.zeros([LONGEST_FRMS, self.input_dim]) for _ in range(num_streams)]
self.sample_label_list = [np.zeros([LONGEST_FRMS]) for _ in range(num_streams)]
self.sample_mask_list = [np.zeros([LONGEST_FRMS]) for _ in range(num_streams)]
self.curt = np.zeros(num_streams, dtype=int)
self.lent = np.zeros(num_streams, dtype=int)
self.reset_flag = np.zeros(num_streams, dtype=bool)
def reset(self):
self.sample_feat_list = [np.zeros([LONGEST_FRMS, self.input_dim]) for _ in range(self.num_streams)]
self.sample_label_list = [np.zeros([LONGEST_FRMS]) for _ in range(self.num_streams)]
self.sample_mask_list = [np.zeros([LONGEST_FRMS]) for _ in range(self.num_streams)]
self.curt = np.zeros(self.num_streams, dtype=int)
self.lent = np.zeros(self.num_streams, dtype=int)
self.reset_flag = | np.zeros(self.num_streams, dtype=bool) | numpy.zeros |
"""
This modules implements the bulk of Bot Evolution.
"""
import numpy as np
import copy
import settings
from utility import seq_is_equal, distance_between, angle_is_between, find_angle
from neural_network import NNetwork, sigmoid, softmax
class Population:
"""
The environment of bots and food.
"""
def __init__(self, size, mutation_rate):
assert(size >= 5)
assert(0 < mutation_rate < 1)
self.SIZE = size
self.mutation_rate = mutation_rate
self.bots = []
self.food = []
self.time_since_last_death = 0.0
# The neural network will have 1 neuron in the input layer, 1 hidden
# layer with 2 neurons, and 4 neurons in the output layer. The sigmoid
# activation function will be used on the hidden layer, and a softmax
# activation function will be used on the output layer. Input consists
# of the bot's direction and if there is or isn't food in the bots field
# of vision. Output consists of whether or not to move foward, turn
# left, turn right, or do nothing.
for i in range(size):
random_rgb = (np.random.randint(30, 256), np.random.randint(30, 256), np.random.randint(30, 256))
self.bots.append(Bot(NNetwork((1, 2, 4), (sigmoid, softmax)), random_rgb, self))
self.food.append(Food(self))
def eliminate(self, bot, replace = False):
self.time_since_last_death = 0.0
self.bots.remove(bot)
if replace:
random_rgb = (np.random.randint(30, 256), np.random.randint(30, 256), np.random.randint(30, 256))
self.bots.append(Bot(NNetwork((1, 2, 4), (sigmoid, softmax)), random_rgb, self))
def feed(self, bot, food):
bot.score = 1.0
self.food.remove(food)
self.food.append(Food(self))
num_to_replace = int(self.SIZE / 7 - 1)
if num_to_replace < 2:
num_to_replace = 2
for i in range(num_to_replace):
weakest = self.bots[0]
for other in self.bots:
if other.score < weakest.score:
weakest = other
self.eliminate(weakest)
for i in range(num_to_replace):
if np.random.uniform(0, 1) <= self.mutation_rate:
new_rgb = [bot.RGB[0], bot.RGB[1], bot.RGB[2]]
new_rgb[np.random.choice((0, 1, 2))] = np.random.uniform(30, 256)
new_bot = Bot(bot.nnet, new_rgb, self)
new_bot.x = bot.x + Bot.HITBOX_RADIUS * 4 * np.random.uniform(0, 1) * np.random.choice((-1, 1))
new_bot.y = bot.y + Bot.HITBOX_RADIUS * 4 * np.random.uniform(0, 1) * np.random.choice((-1, 1))
nb_c = new_bot.nnet.connections
mutated = False
while not mutated:
for k in range(len(nb_c)):
for i in range(nb_c[k].FROM.SIZE):
for j in range(nb_c[k].TO.SIZE):
if np.random.uniform(0, 1) <= self.mutation_rate:
nb_c[k].weights[i][j] = nb_c[k].weights[i][j] * np.random.normal(1, 0.5) + np.random.standard_normal()
mutated = True
self.bots.append(new_bot)
else:
new_bot = Bot(bot.nnet, bot.RGB, self)
new_bot.x = bot.x + Bot.HITBOX_RADIUS * 4 * | np.random.uniform(0, 1) | numpy.random.uniform |
# 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]) | numpy.array |
#!/usr/bin/env python
from __future__ import print_function
import argparse
import numpy as np
import os, sys, shutil, subprocess, glob
import re
from numpy import pi
from scipy import *
import json
from tabulate import tabulate
from itertools import chain
import flapwmbpt_ini
import prepare_realaxis
# from scipy.interpolate import interp1d
# trans_basis_mode: 0, use wannier function as basis set
# trans_basis_mode: 1, use transformation matrix to rotate the basis set. this matrix doesn't change as a function of iteration.
# trans_basis_mode: 2, use transformation matrix to rotate the basis set. this matrix does change as a function of iteration. this matrix diagonalize the spectral function at the chemical potential.
def open_h_log(control):
if (control['restart']):
control['h_log']=open('./cmd.log', 'a')
else:
control['h_log']=open('./cmd.log', 'w')
print('', file=control['h_log'],flush=True)
print('*********************************',file=control['h_log'],flush=True)
print(' ComDMFT', file=control['h_log'],flush=True)
print('*********************************',file=control['h_log'],flush=True)
print('', file=control['h_log'],flush=True)
#DEBUG
control['h_log'].flush()
os.fsync(control['h_log'].fileno())
#DEBUG
return None
def close_h_log(control):
control['h_log'].close()
return None
def read_comdmft_ini_control():
vglobl={}
vlocal={}
with open('comdmft.ini') as f_ini:
code = compile(f_ini.read(), "comdmft.ini", 'exec')
exec(code, vglobl, vlocal)
f_ini.close()
control=vlocal['control']
return control
def read_comdmft_ini_postprocessing():
vglobl={}
vlocal={}
with open('comdmft.ini') as f_ini:
code = compile(f_ini.read(), "comdmft.ini", 'exec')
exec(code, vglobl, vlocal)
f_ini.close()
control=vlocal['control']
postprocessing_dict=vlocal['postprocessing']
check_key_in_string('mpi_prefix', control)
check_key_in_string('comsuite_dir', postprocessing_dict)
if (control['method']=='spectral') | (control['method']=='band'):
with open(postprocessing_dict['comsuite_dir']+'/comdmft.ini') as f_ini:
code = compile(f_ini.read(), "comdmft.ini", 'exec')
exec(code, vglobl, vlocal)
f_ini.close()
control_temp=vlocal['control']
postprocessing_dict['kpoints']=postprocessing_dict.get('kpoints', os.path.abspath(postprocessing_dict['comsuite_dir']+'/'+control_temp['initial_lattice_dir'])+'/kpoints')
if ((control['method']=='dos') | (control['method']=='dos_qp')):
check_key_in_string('kmesh', postprocessing_dict)
if ((control['method']=='spectral') | (control['method']=='dos')):
check_key_in_string('self energy', postprocessing_dict)
postprocessing_dict['broadening']=postprocessing_dict.get('broadening', 0.01)
return control, postprocessing_dict
def read_comdmft_ini():
vglobl={}
vlocal={}
with open('comdmft.ini') as f_ini:
code = compile(f_ini.read(), "comdmft.ini", 'exec')
exec(code, vglobl, vlocal)
f_ini.close()
# print vglobl
# print 'here'
control=vlocal['control']
wan_hmat=vlocal['wan_hmat']
imp=vlocal['imp']
control['name']='control'
wan_hmat['name']='wan_hmat'
imp['name']='imp'
control['restart']=control.get('restart', False)
open_h_log(control)
control['comsuitedir']=os.environ.get('COMSUITE_BIN')
if not control['comsuitedir']:
print("Error: Environment variable COMSUITE_BIN is not defined.", file=control['h_log'],flush=True)
sys.exit()
print('comsuitedir', control['comsuitedir'])
control['conv_table']=[]
### in control
control['cal_mu']=control.get('cal_mu', True)
control['top_dir']=os.path.abspath('./')
check_key_in_string('method', control)
control['sigma_mix_ratio']=control.get('sigma_mix_ratio', 0.5)
control['doping']=control.get('doping', 0.0)
control['dc_mode']=control.get('dc_mode', 'dc_at_gw')
control['u_mode']=control.get('u_mode', 'bnse')
control['trans_basis_mode']=control.get('trans_basis_mode', 0)
if (control['trans_basis_mode']==1):
check_key_in_string('trans_basis', control)
elif (control['trans_basis_mode']==2):
check_key_in_string('metal_threshold', control)
check_key_in_string('spin_orbit', control)
check_key_in_string('impurity_problem', control)
check_key_in_string('impurity_problem_equivalence', control)
check_key_in_string('initial_lattice_dir', control)
control['initial_lattice_dir']=os.path.abspath(control['initial_lattice_dir'])
control['allfile']=find_allfile(control['initial_lattice_dir'])
if ('dc_directory' not in control):
control['dc_directory']='./dc'
control['dc_directory']=os.path.abspath(control['dc_directory'])
if ('impurity_directory' not in control):
control['impurity_directory']='./impurity'
control['impurity_directory']=os.path.abspath(control['impurity_directory'])
if ('lowh_directory' not in control):
control['lowh_directory']='./lowh'
control['lowh_directory']=os.path.abspath(control['lowh_directory'])
if ('wannier_directory' not in control):
control['wannier_directory']='./wannier'
control['wannier_directory']=os.path.abspath(control['wannier_directory'])
if ('initial_self_energy' in control):
control['initial_self_energy'] =os.path.abspath(control['initial_self_energy'])
if (control['trans_basis_mode']!=0):
check_key_in_string('trans_basis', control)
if ('dc_mat_to_read' in control):
control['dc_mat_to_read'] =os.path.abspath(control['dc_mat_to_read'])
if (control['method']=='lda+dmft'):
control['convergence_header']=['step','i_outer','i_latt','i_imp','causality','delta_rho','w_sp_min','w_sp_max', 'mu', 'std_sig', 'n_imp', 'histo_1', 'histo_2', 'ctqmc_sign']
if (control['method']=='lqsgw+dmft'):
control['convergence_header']=['step','i_imp','causality','static_f0','w_sp_min','w_sp_max', 'mu', 'std_sig', 'n_imp', 'histo_1', 'histo_2', 'ctqmc_sign']
# mpi_prefix
if ('mpi_prefix' in control):
control['mpi_prefix_flapwmbpt']=control.get('mpi_prefix_flapwmbpt', control['mpi_prefix'])
control['mpi_prefix_lowh']=control.get('mpi_prefix_lowh', control['mpi_prefix'])
control['mpi_prefix_impurity']=control.get('mpi_prefix_impurity', control['mpi_prefix'])
control['mpi_prefix_wannier']=control.get('mpi_prefix_wannier', control['mpi_prefix'])
if (control['method']=='lda+dmft'):
control['mpi_prefix_lattice']=control.get('mpi_prefix_lattice', control['mpi_prefix'])
if (control['method']=='lqsgw+dmft'):
control['mpi_prefix_dc']=control.get('mpi_prefix_dc', control['mpi_prefix'])
# mpi_prefix_coulomb
if ('mpi_prefix_coulomb' in control):
check_key_in_string('nproc_k_coulomb', control)
check_key_in_string('nproc_tau_coulomb', control)
else:
# temp=[int(x) for x in np.loadtxt(control['initial_lattice_dir']+'/k_tau_freq.dat')]
temp=list(map(int,np.loadtxt(control['initial_lattice_dir']+'/k_tau_freq.dat')))
control['mpi_prefix_coulomb'], control['nproc_k_coulomb'],control['nproc_tau_coulomb']=optimized_nproc_for_comcoulomb(control['mpi_prefix'], temp[0], temp[1],temp[2],temp[3])
# print('mpi_prefix_coulomb', control['mpi_prefix_coulomb'], file=control['h_log'],flush=True)
# max iteration
if (control['method']=='lda+dmft'):
control['max_iter_num_impurity']=control.get('max_iter_num_impurity', 1)
control['max_iter_num_outer']=control.get('max_iter_num_outer', 50)
elif (control['method']=='lqsgw+dmft'):
control['max_iter_num_impurity']=control.get('max_iter_num_impurity', 50)
# directory_name
if (control['method']=='lda+dmft'):
if ('lattice_directory' not in control):
control['lattice_directory']='./lattice'
control['lattice_directory']=os.path.abspath(control['lattice_directory'])
if (control['method']=='lqsgw+dmft'):
if ('coulomb_directory' not in control):
control['coulomb_directory']='./coulomb'
control['coulomb_directory']=os.path.abspath(control['coulomb_directory'])
if (control['method']=='lqsgw+dmft'):
control['do_wannier']=True
control['do_coulomb']=True
control['do_dc']=True
control['iter_num_impurity']=1
control['iter_num_outer']=1
elif (control['method']=='lda+dmft'):
control['iter_num_outer']=1
control['iter_num_impurity']=0
if (control['restart']):
find_place_to_restart(control)
if (control['method']=='lqsgw+dmft'):
print('do_wannier', control['do_wannier'], file=control['h_log'],flush=True)
print('do_coulomb', control['do_coulomb'], file=control['h_log'],flush=True)
print('do_dc', control['do_dc'], file=control['h_log'],flush=True)
# in wan_hmat
check_key_in_string('kgrid', wan_hmat)
check_key_in_string('froz_win_min', wan_hmat)
check_key_in_string('froz_win_max', wan_hmat)
wan_hmat['write_wan']=wan_hmat.get('write_wan', False)
wan_hmat['dis_win_min']=wan_hmat.get('dis_win_min', wan_hmat['froz_win_min'])
wan_hmat['dis_win_max']=wan_hmat.get('dis_win_max', wan_hmat['froz_win_max']+40.0)
control['proj_win_min']=control.get('proj_win_min', wan_hmat['dis_win_min'])
control['proj_win_max']=control.get('proj_win_max', wan_hmat['dis_win_max'])
wan_hmat['num_iter']=wan_hmat.get('num_iter', 0)
wan_hmat['dis_num_iter']=wan_hmat.get('dis_num_iter', 100)
wan_hmat['cut_low']=wan_hmat.get('cut_low', 0.4)
wan_hmat['cut_froz']=wan_hmat.get('cut_froz', 0.10)
wan_hmat['cut_total']=wan_hmat.get('cut_total', 0.0)
if (control['method']=='lqsgw+dmft'):
wan_hmat['rmode']=wan_hmat.get('rmode', 0)
wan_hmat['radfac']=wan_hmat.get('radfac', 1.0)
if (control['method']=='lda+dmft'):
wan_hmat['rmode']=wan_hmat.get('rmode', 0)
wan_hmat['radfac']=wan_hmat.get('radfac', 1.0)
# in imp
check_key_in_string('temperature', imp)
imp['beta']=1.0/(8.6173303*10**-5*imp['temperature'])
if ('initial_self_energy' in control):
control['n_omega']=np.shape(np.loadtxt(control['initial_self_energy']))[0]
else:
control['n_omega']=int(300.0/(2*pi/imp['beta']))
control['omega']=(np.arange(control['n_omega'])*2+1)*pi/imp['beta']
for key, value in imp.items():
if (not (isinstance(imp[key], dict))):
continue
imp[key]['name']=key
# imp[key]['para']=True
# for ktemp in control['impurity_problem_equivalence'] :
# if (ktemp == -1):
# imp[key]['para']=False
if (-1*int(key) in control['impurity_problem_equivalence']):
imp[key]['para']=False
else:
imp[key]['para']=True
imp[key]['problem']=control['impurity_problem'][control['impurity_problem_equivalence'].index(int(key))][1]
if (control['method']=='lda+dmft'):
check_key_in_string('f0', imp[key])
if ((imp[key]['problem']=='p') | (imp[key]['problem']=='d') | (imp[key]['problem']=='f')):
check_key_in_string('f2', imp[key])
if ((imp[key]['problem']=='d') | (imp[key]['problem']=='f')):
check_key_in_string('f4', imp[key])
if (imp[key]['problem']=='f'):
check_key_in_string('f6', imp[key])
# elif (control['method']=='lqsgw+dmft'):
# check_key_in_string('boson_low_truncation', imp[key])
check_key_in_string('thermalization_time', imp[key])
check_key_in_string('measurement_time', imp[key])
check_key_in_string('impurity_matrix', imp[key])
if (control['trans_basis_mode']<2):
imp[key]['impurity_matrix']=np.array(imp[key]['impurity_matrix'])
else:
print("impurity_matrix reset", file=control['h_log'],flush=True)
nimp_orb=len(imp[key]['impurity_matrix'])
imp[key]['impurity_matrix']=np.zeros((nimp_orb,nimp_orb), dtype='int')
for ii in range(nimp_orb):
imp[key]['impurity_matrix'][ii,ii]=ii+1
print('here', file=control['h_log'],flush=True)
print(type(imp[key]['impurity_matrix']), file=control['h_log'],flush=True)
print(imp[key]['impurity_matrix'], file=control['h_log'],flush=True)
print('here', file=control['h_log'],flush=True)
if (control['method']=='lda+dmft'):
check_key_in_string('nominal_n', imp[key])
check_key_in_string('green_cutoff', imp[key])
imp[key]['susceptibility_cutoff']=imp[key].get('susceptibility_cutoff', 50)
imp[key]['susceptibility_tail']=imp[key].get('susceptibility_tail', 300)
if ('coulomb' not in imp[key]):
imp[key]["coulomb"]='full'
control['sig_header']=['# omega(eV)']
for ii in sorted(set(control['impurity_problem_equivalence'])):
for jj in sorted(set(imp[str(abs(ii))]['impurity_matrix'].flatten().tolist())-{0}):
control['sig_header'].append("Re Sig_{"+str(ii)+','+str(jj)+'}(eV)')
control['sig_header'].append("Im Sig_{"+str(ii)+','+str(jj)+'}(eV)')
# check hdf5
if (os.path.isdir(control['initial_lattice_dir']+"/checkpoint/")):
control['hdf5']=False
else:
control['hdf5']=True
print('hdf5', control['hdf5'],file=control['h_log'],flush=True)
# print
print('top_dir', control['top_dir'], file=control['h_log'],flush=True)
if (control['method']=='lda+dmft'):
print('lattice_directory', control['lattice_directory'], file=control['h_log'],flush=True)
elif (control['method']=='lqsgw+dmft'):
print('coulomb_directory', control['coulomb_directory'], file=control['h_log'],flush=True)
print('wannier_directory', control['wannier_directory'], file=control['h_log'],flush=True)
print('dc_directory', control['dc_directory'], file=control['h_log'],flush=True)
print('impurity_directory', control['impurity_directory'], file=control['h_log'],flush=True)
print('lowh_directory', control['lowh_directory'], file=control['h_log'],flush=True)
return control,wan_hmat,imp
def find_impurity_wan(control, wan_hmat):
num_wann=np.shape(wan_hmat['basis'])[0]
control['impurity_wan']=[]
for ip in range(np.shape(control['impurity_problem'])[0]):
if (control['spin_orbit']):
if (control['impurity_problem'][ip][1].lower()=='f'):
control['impurity_wan'].append([0]*14)
for iwan in range(num_wann):
if ((wan_hmat['basis'][iwan]['atom']==control['impurity_problem'][ip][0]) and (wan_hmat['basis'][iwan]['l']==3)):
if (int(wan_hmat['basis'][iwan]['i']*2)==-1):
if (int(wan_hmat['basis'][iwan]['m']*2)==-5):
control['impurity_wan'][ip][0]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['m']*2)==-3):
control['impurity_wan'][ip][1]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['m']*2)==-1):
control['impurity_wan'][ip][2]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['m']*2)==1):
control['impurity_wan'][ip][3]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['m']*2)==3):
control['impurity_wan'][ip][4]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['m']*2)==5):
control['impurity_wan'][ip][5]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['i']*2)==1):
if (int(wan_hmat['basis'][iwan]['m']*2)==-7):
control['impurity_wan'][ip][6]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['m']*2)==-5):
control['impurity_wan'][ip][7]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['m']*2)==-3):
control['impurity_wan'][ip][8]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['m']*2)==-1):
control['impurity_wan'][ip][9]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['m']*2)==1):
control['impurity_wan'][ip][10]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['m']*2)==3):
control['impurity_wan'][ip][11]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['m']*2)==5):
control['impurity_wan'][ip][12]=wan_hmat['basis'][iwan]['ind']
elif (int(wan_hmat['basis'][iwan]['m']*2)==7):
control['impurity_wan'][ip][13]=wan_hmat['basis'][iwan]['ind']
if (control['impurity_wan'][ip].count(0) !=0):
print('something wrong in find_impurity_wan', file=control['h_log'],flush=True)
sys.exit()
else:
if (control['impurity_problem'][ip][1].lower()=='s'):
control['impurity_wan'].append([0]*1)
for iwan in range(num_wann):
if ((wan_hmat['basis'][iwan]['atom']==control['impurity_problem'][ip][0]) and (wan_hmat['basis'][iwan]['l']==0)):
if (wan_hmat['basis'][iwan]['m']==-0):
control['impurity_wan'][ip][0]=wan_hmat['basis'][iwan]['ind']
if (control['impurity_wan'][ip].count(0) !=0):
print('something wrong in find_impurity_wan', file=control['h_log'],flush=True)
sys.exit()
elif (control['impurity_problem'][ip][1].lower()=='p'):
control['impurity_wan'].append([0]*3)
for iwan in range(num_wann):
if ((wan_hmat['basis'][iwan]['atom']==control['impurity_problem'][ip][0]) and (wan_hmat['basis'][iwan]['l']==1)):
if (wan_hmat['basis'][iwan]['m']==-1):
control['impurity_wan'][ip][0]=wan_hmat['basis'][iwan]['ind']
elif (wan_hmat['basis'][iwan]['m']==-0):
control['impurity_wan'][ip][1]=wan_hmat['basis'][iwan]['ind']
elif (wan_hmat['basis'][iwan]['m']==1):
control['impurity_wan'][ip][2]=wan_hmat['basis'][iwan]['ind']
if (control['impurity_wan'][ip].count(0) !=0):
print('something wrong in find_impurity_wan', file=control['h_log'],flush=True)
sys.exit()
elif (control['impurity_problem'][ip][1].lower()=='d'):
control['impurity_wan'].append([0]*5)
for iwan in range(num_wann):
if ((wan_hmat['basis'][iwan]['atom']==control['impurity_problem'][ip][0]) and (wan_hmat['basis'][iwan]['l']==2)):
if (wan_hmat['basis'][iwan]['m']==-2):
control['impurity_wan'][ip][0]=wan_hmat['basis'][iwan]['ind']
elif (wan_hmat['basis'][iwan]['m']==-1):
control['impurity_wan'][ip][1]=wan_hmat['basis'][iwan]['ind']
elif (wan_hmat['basis'][iwan]['m']==-0):
control['impurity_wan'][ip][2]=wan_hmat['basis'][iwan]['ind']
elif (wan_hmat['basis'][iwan]['m']==1):
control['impurity_wan'][ip][3]=wan_hmat['basis'][iwan]['ind']
elif (wan_hmat['basis'][iwan]['m']==2):
control['impurity_wan'][ip][4]=wan_hmat['basis'][iwan]['ind']
if (control['impurity_wan'][ip].count(0) !=0):
print('something wrong in find_impurity_wan', file=control['h_log'],flush=True)
sys.exit()
elif (control['impurity_problem'][ip][1].lower()=='f'):
control['impurity_wan'].append([0]*7)
for iwan in range(num_wann):
if ((wan_hmat['basis'][iwan]['atom']==control['impurity_problem'][ip][0]) and (wan_hmat['basis'][iwan]['l']==3)):
if (wan_hmat['basis'][iwan]['m']==-3):
control['impurity_wan'][ip][0]=wan_hmat['basis'][iwan]['ind']
elif (wan_hmat['basis'][iwan]['m']==-2):
control['impurity_wan'][ip][1]=wan_hmat['basis'][iwan]['ind']
elif (wan_hmat['basis'][iwan]['m']==-1):
control['impurity_wan'][ip][2]=wan_hmat['basis'][iwan]['ind']
elif (wan_hmat['basis'][iwan]['m']==-0):
control['impurity_wan'][ip][3]=wan_hmat['basis'][iwan]['ind']
elif (wan_hmat['basis'][iwan]['m']==1):
control['impurity_wan'][ip][4]=wan_hmat['basis'][iwan]['ind']
elif (wan_hmat['basis'][iwan]['m']==2):
control['impurity_wan'][ip][5]=wan_hmat['basis'][iwan]['ind']
elif (wan_hmat['basis'][iwan]['m']==3):
control['impurity_wan'][ip][6]=wan_hmat['basis'][iwan]['ind']
if (control['impurity_wan'][ip].count(0) !=0):
print('something wrong in find_impurity_wan', file=control['h_log'],flush=True)
sys.exit()
return None
def initial_file_directory_setup(control):
directory_setup(control)
if (control['method'] == 'lda+dmft'):
print('iter_num_impurity', control['iter_num_impurity'], ' max_iter_num_impurity', control['max_iter_num_impurity'], file=control['h_log'],flush=True)
print('iter_num_outer', control['iter_num_outer'], ' max_iter_num_outer', control['max_iter_num_outer'], file=control['h_log'],flush=True)
elif (control['method'] == 'lqsgw+dmft'):
print('iter_num_impurity', control['iter_num_impurity'], file=control['h_log'],flush=True)
print('max_iter_num_impurity', control['max_iter_num_impurity'], file=control['h_log'],flush=True)
return None
def find_place_to_restart(control):
if (control['method']=='lqsgw+dmft'):
control['conv_table']=read_convergence_table(control)
# print(control['conv_table'], file=control['h_log'],flush=True)
if (len(control['conv_table'])>0):
n_imp_problem=np.amax(control['impurity_problem_equivalence'])
last_step=control['conv_table'][-1][0].strip().split('_')[0]
last_imp_iter=control['conv_table'][-1][1].strip()
if (len(control['conv_table'][-1][0].strip().split('_')) > 1):
last_imp=control['conv_table'][-1][0].strip().split('_')[1]
print(last_step, last_imp, last_imp_iter, file=control['h_log'],flush=True)
else:
print(last_step, last_imp_iter, file=control['h_log'],flush=True)
if last_step == 'wannier':
control['do_wannier']=False
control['do_coulomb']=True
control['do_dc']=True
control['iter_num_impurity']=1
elif last_step == 'coulomb':
control['do_wannier']=False
control['do_coulomb']=False
control['do_dc']=True
control['iter_num_impurity']=1
elif last_step == 'dc':
if (int(last_imp) == n_imp_problem):
control['do_wannier']=False
control['do_coulomb']=False
control['do_dc']=False
control['iter_num_impurity']=1
else:
control['do_wannier']=False
control['do_coulomb']=False
control['do_dc']=True
control['iter_num_impurity']=1
for ii in range(int(last_imp)):
control['conv_table'].pop(-1)
elif (last_step == 'delta'):
control['do_wannier']=False
control['do_coulomb']=False
control['do_dc']=False
control['iter_num_impurity']=int(last_imp_iter)
control['conv_table'].pop(-1)
elif (last_step == 'impurity'):
if (int(last_imp) == n_imp_problem):
control['do_wannier']=False
control['do_coulomb']=False
control['do_dc']=False
control['iter_num_impurity']=int(last_imp_iter)+1
else:
control['do_wannier']=False
control['do_coulomb']=False
control['do_dc']=True
control['iter_num_impurity']=int(last_imp_iter)
for ii in range(int(last_imp)):
control['conv_table'].pop(-1)
else:
control['do_wannier']=True
control['do_coulomb']=True
control['do_dc']=True
control['iter_num_impurity']=1
else:
control['do_wannier']=True
control['do_coulomb']=True
control['do_dc']=True
control['iter_num_impurity']=1
elif (control['method']=='lda+dmft'):
control['conv_table']=read_convergence_table(control)
if (len(control['conv_table'])>0):
linecnt=0
for ii in range(np.shape(control['conv_table'])[0]):
if control['conv_table'][ii][0].strip()=='dft':
linecnt=ii
control['iter_num_outer']=int(control['conv_table'][ii][1])
for ii in range(linecnt, np.shape(control['conv_table'])[0]):
control['conv_table'].pop(-1)
return None
# def find_iter_num_for_restart(control):
# if (control['restart']):
# line_count=sum(1 for line in open(control['top_dir']+'/convergence.log'))
# if (line_count <=1):
# if (control['method']=='lda+dmft'):
# iter_num_outer=1
# elif (control['method']=='lqsgw+dmft'):
# iter_num_impurity=1
# else:
# if (control['method']=='lda+dmft'):
# iter_num_outer=1
# ff=open(control['top_dir']+'/convergence.log', 'r')
# firstline=ff.readline()
# for line in ff:
# temp=line.split()
# if (temp[0] == 'dft'):
# iter_num_outer=int(temp[1])
# ff.close()
# elif (control['method']=='lqsgw+dmft'):
# iter_num_impurity=1
# ff=open(control['top_dir']+'/convergence.log', 'r')
# firstline=ff.readline()
# for line in ff:
# temp=line.split()
# temp1=temp[0]
# if (temp1 == 'impurity'):
# iter_num_impurity=int(temp[2])
# ff.close()
# else:
# if (control['method']=='lda+dmft'):
# iter_num_outer=1
# elif (control['method']=='lqsgw+dmft'):
# iter_num_impurity=1
# if (control['method']=='lda+dmft'):
# return iter_num_outer
# elif (control['method']=='lqsgw+dmft'):
# return iter_num_impurity
def initial_lattice_directory_setup(control):
os.chdir(control['lattice_directory'])
if control['hdf5']:
files = glob.iglob(control['initial_lattice_dir']+"/*.rst")
for filename in files:
shutil.copy(filename, './')
else:
files = glob.iglob(control['initial_lattice_dir']+"/checkpoint/*.rst")
for filename in files:
shutil.copy(filename, './checkpoint/')
files = glob.iglob(control['initial_lattice_dir']+"/*el_density")
for filename in files:
shutil.copy(filename, './')
if os.path.exists(control['initial_lattice_dir']+'/kpath'):
shutil.copy(control['initial_lattice_dir']+'/kpath', './')
if os.path.exists(control['initial_lattice_dir']+'/ini'):
shutil.copy(control['initial_lattice_dir']+'/ini', './')
if os.path.exists(control['initial_lattice_dir']+'/symmetry_operations'):
shutil.copy(control['initial_lattice_dir']+'/symmetry_operations', './')
if os.path.exists(control['initial_lattice_dir']+'/kpoints'):
shutil.copy(control['initial_lattice_dir']+'/symmetry_operations', './')
files = glob.iglob(control['initial_lattice_dir']+"/*.cif")
for filename in files:
shutil.copy(filename, './')
iter_string='_'+str(control['iter_num_outer'])
shutil.copy(control['initial_lattice_dir']+'/'+control['allfile']+'.out', control['allfile']+iter_string+'.out')
print("initial dft directory setup done", file=control['h_log'],flush=True)
os.chdir(control['top_dir'])
return None
def create_comwann_ini(control, wan_hmat):
f=open('comwann.ini','w')
if (control['method']=='lda+dmft'):
f.write(control['lattice_directory']+'\n')
f.write('dft\n')
elif (control['method']=='lqsgw+dmft'):
f.write(control['initial_lattice_dir']+'\n')
f.write('qp\n')
elif (control['method']=='dft'):
f.write('../\n')
f.write('dft\n')
elif (control['method']=='lqsgw'):
f.write('../\n')
f.write('qp\n')
f.write(str(wan_hmat['dis_win_max'])+'\n')
f.write(str(wan_hmat['dis_win_min'])+'\n')
f.write(str(wan_hmat['froz_win_max'])+'\n')
f.write(str(wan_hmat['froz_win_min'])+'\n')
f.write(str(wan_hmat['num_iter'])+'\n')
f.write(str(wan_hmat['dis_num_iter'])+'\n')
if (wan_hmat['write_wan']):
f.write('1\n')
else:
f.write('0\n')
f.write(str(wan_hmat['cut_low'])+'\n')
f.write(str(wan_hmat['cut_froz'])+'\n')
f.write(str(wan_hmat['cut_total'])+'\n')
f.write(str(wan_hmat['rmode'])+'\n')
f.write(str(wan_hmat['radfac'])+'\n')
f.close()
def create_comcoulomb_ini(control):
f=open('comcoulomb.ini','w')
f.write(control['initial_lattice_dir']+'\n')
f.write(control['wannier_directory']+'\n')
f.write(str(control['nproc_tau_coulomb'])+'\n')
f.write(str(control['nproc_k_coulomb'])+'\n')
f.write(str(control['proj_win_min'])+'\n')
f.write(str(control['proj_win_max'])+'\n')
f.write('F\n')
f.write(control['u_mode']+'\n')
nimp_orb=0
natom=len(control['impurity_wan'])
for ii in range(natom):
nimp_orb=nimp_orb+len(control['impurity_wan'][ii])
f.write(str(nimp_orb)+'\n')
for iatom in range(natom):
f.write(' '.join(map(str,control['impurity_wan'][iatom]))+' ')
f.write('\n')
f.write('1\n')
f.write('F\n')
f.write('3.0\n')
f.write('F\n')
f.close()
# def create_wannier_inip(wan_hmat):
# # in the wannier directory
# g=open('wannier.inip', 'w')
# num_wann=np.shape(wan_hmat['basis'])[0]
# g.write(str(num_wann)+'\n')
# for ii in range(num_wann):
# if (control['spin_orbit']==False):
# tempstr=[wan_hmat['basis'][ii]['atom'], wan_hmat['basis'][ii]['l'], wan_hmat['basis'][ii]['m'], wan_hmat['basis'][ii]['xaxis'][0], wan_hmat['basis'][ii]['xaxis'][1], wan_hmat['basis'][ii]['xaxis'][2], wan_hmat['basis'][ii]['zaxis'][0], wan_hmat['basis'][ii]['zaxis'][1], wan_hmat['basis'][ii]['zaxis'][2]]
# else:
# tempstr=[wan_hmat['basis'][ii]['atom'], wan_hmat['basis'][ii]['l'], wan_hmat['basis'][ii]['i'], wan_hmat['basis'][ii]['m'], wan_hmat['basis'][ii]['xaxis'][0], wan_hmat['basis'][ii]['xaxis'][1], wan_hmat['basis'][ii]['xaxis'][2], wan_hmat['basis'][ii]['zaxis'][0], wan_hmat['basis'][ii]['zaxis'][1], wan_hmat['basis'][ii]['zaxis'][2]]
# g.write(' '.join(map(str, tempstr))+'\n')
# g.close()
# return None
def read_wan_hmat_basis(control):
# in the wannier directory
inip=np.loadtxt(control['wannier_directory']+'/wannier.inip')
basis_info=[]
if (control['spin_orbit']):
for ii in range(np.shape(inip)[0]):
basis_info.append({'atom':int(inip[ii,0]), 'l':int(inip[ii,1]), 'i':inip[ii,2],'m':inip[ii,3],'xaxis':inip[ii,4:7],'zaxis':inip[ii,7:10], 'ind':ii+1})
else:
for ii in range(np.shape(inip)[0]):
basis_info.append({'atom':int(inip[ii,0]), 'l':int(inip[ii,1]), 'm':int(inip[ii,2]),'xaxis':inip[ii,3:6],'zaxis':inip[ii,6:9], 'ind':ii+1})
print(basis_info, file=control['h_log'],flush=True)
print('reading wannier.inip to get basis information', file=control['h_log'],flush=True)
return basis_info
def check_key_in_string(key,dictionary):
if (key not in dictionary):
print('missing \''+key+'\' in '+dictionary['name'],flush=True)
sys.exit()
return None
def overwrite_key_in_string(key,dictionary,dictionaryname,value,h_log):
if (key in dictionary):
print('\''+key+'\' in '+dictionaryname+' is overwritten', file=control['h_log'],flush=True)
return value
# def dft_rst_file_check():
# check_for_files('*acc_core_dft.rst', h_log)
# check_for_files('*chemical_potential_dft.rst', h_log)
# check_for_files('*cor_norm_dft.rst', h_log)
# check_for_files('*dfi_dft.rst', h_log)
# check_for_files('*dfidot2_dft.rst', h_log)
# check_for_files('*dfidot_dft.rst', h_log)
# check_for_files('*e_bnd_dft.rst', h_log)
# check_for_files('*e_core_dft.rst', h_log)
# check_for_files('*el_density_dft.rst', h_log)
# check_for_files('*eny_dft.rst', h_log)
# check_for_files('*etot_dft.rst', h_log)
# check_for_files('*ev_bnd_*_dft.rst', h_log)
# check_for_files('*ffsmt_dft.rst', h_log)
# check_for_files('*fi_dft.rst', h_log)
# check_for_files('*fidot2_dft.rst', h_log)
# check_for_files('*fidot_dft.rst', h_log)
# check_for_files('*g_full_00_*_dft.rst', h_log)
# check_for_files('*g_loc_0_dft.rst', h_log)
# check_for_files('*gfun_dft.rst', h_log)
# check_for_files('*gfun_old_dft.rst', h_log)
# check_for_files('*gfund_dft.rst', h_log)
# check_for_files('*gfund_old_dft.rst', h_log)
# check_for_files('*n_bnd_dft.rst', h_log)
# check_for_files('*p_f_dft.rst', h_log)
# check_for_files('*pcor_dft.rst', h_log)
# check_for_files('*pcor_old_dft.rst', h_log)
# check_for_files('*pd2_f_dft.rst', h_log)
# check_for_files('*pd_f_dft.rst', h_log)
# check_for_files('*ptnl_dft.rst', h_log)
# check_for_files('*q_f_dft.rst', h_log)
# check_for_files('*qcor_dft.rst', h_log)
# check_for_files('*qcor_old_dft.rst', h_log)
# check_for_files('*qd2_f_dft.rst', h_log)
# check_for_files('*qd_f_dft.rst', h_log)
# check_for_files('*restart_ubi.rst', h_log)
# check_for_files('*ro_core_dft.rst', h_log)
# check_for_files('*v_intr_h_dft.rst', h_log)
# check_for_files('*v_intr_xc_dft.rst', h_log)
# check_for_files('*v_mt_h_dft.rst', h_log)
# check_for_files('*v_mt_xc_dft.rst', h_log)
# check_for_files('*z_bnd_*_dft.rst', h_log)
# return None
# def string_addwhitespace(string, stringsize):
# stringout=string
# if stringsize > len(string):
# stringout=string+' '*(stringsize-len(string))
# return stringout
def find_all_in_string(str, ch):
for i, ltr in enumerate(str):
if ltr == ch:
yield i
def read_convergence_table(control):
if os.path.exists(control['top_dir']+'/convergence.log'):
with open(control['top_dir']+'/convergence.log', 'r') as logfile:
tmp=logfile.readlines()
nstep=len(tmp)-2
if (nstep>0):
endind=list(find_all_in_string(tmp[1],' '))[::2]+[len(tmp[1])-1]
startind=[0]+(np.array(list(find_all_in_string(tmp[1],' '))[1::2])+1).tolist()
ncolumn=len(endind)
f=open('./convergence.log', 'r')
f.readline()
f.readline()
convergence_table=[]
for lines in f:
eachline=[]
for ii in range(ncolumn):
eachline.append(lines.rstrip()[startind[ii]:endind[ii]])
if (len(eachline[0])>0):
convergence_table.append(eachline)
f.close()
else:
convergence_table=[]
else:
convergence_table=[]
return convergence_table
def generate_initial_self_energy(control,imp):
os.chdir(control['impurity_directory'])
if ('initial_self_energy' in control):
shutil.copy(control['initial_self_energy'], './sig.dat')
if ('initial_impurity_dir' in control):
initial_impurity_dirname=os.path.abspath(os.path.dirname(control['initial_impurity_dir']))
directories = glob.glob(initial_impurity_dirname+"/*/")
for directory_name in directories:
dest_dir=directory_name.split('/')[-2]
files = glob.iglob(os.path.abspath(directory_name)+"/config*")
for filename in files:
shutil.copy(filename, control['impurity_directory']+'/'+dest_dir)
else:
dc=np.loadtxt(control['dc_directory']+'/dc.dat')
beta=imp['beta']
n_omega=control['n_omega']
omega=control['omega']
cnt=0
dclist=[]
for ii in sorted(set(control['impurity_problem_equivalence'])):
for jj in sorted(set(imp[str(abs(ii))]['impurity_matrix'].flatten().tolist())-{0}):
if (imp[str(abs(ii))]['para']):
dclist=dclist+list(dc[(2*cnt):(2*cnt+2)])
else:
dclist=dclist+list(dc[(2*cnt):(2*cnt+2)]-np.array([0.001*np.sign(ii), 0.0]))
cnt=cnt+1
sig_table=[]
for jj in range(control['n_omega']):
sig_omega=[control['omega'][jj]]+dclist
sig_table.append(sig_omega)
with open('./sig.dat', 'w') as outputfile:
outputfile.write(tabulate(sig_table, headers=control['sig_header'], floatfmt=".12f", numalign="right", tablefmt="plain"))
if (control['method']=='lqsgw+dmft'):
iter_string='_0'
elif (control['method']=='lda+dmft'):
iter_string='_'+str(control['iter_num_outer'])+'_0'
labeling_file('./sig.dat', iter_string)
print('initial_self_energy generation done', file=control['h_log'],flush=True)
os.chdir(control['top_dir'])
return None
def prepare_initial_ef(control):
os.chdir(control['lowh_directory'])
f=open('ef.dat','w')
f.write('0.0\n')
f.close()
os.chdir(control['top_dir'])
return None
def delta_postprocessing(control,imp):
write_transformation_matrix(control,control['lowh_directory']+'/local_spectral_matrix_ef.dat')
cal_projected_mean_field_diagonal(control,imp)
cal_dc_diagonal(control)
cal_zinv_m1_diagonal(control)
cal_e_imp_diagonal(control)
delta_causality=cal_hyb_diagonal(control,imp)
if (delta_causality ==0):
print('delta causality broken', file=control['h_log'],flush=True)
sys.exit()
return delta_causality
def cal_dc_diagonal(control):
os.chdir(control['dc_directory'])
dc_mat=read_impurity_mat_static(control,control['dc_directory']+'/dc_mat.dat')
h=open('./dc.dat', 'w')
for ii in sorted(set(control['impurity_problem_equivalence'])):
dc_vec=imp_from_mat_to_array(dc_mat[str(ii)],imp[str(abs(ii))]['impurity_matrix'])
for jj in range(len(dc_vec)):
h.write(str(np.real(dc_vec[jj]))+' '+str(np.imag(dc_vec[jj]))+' ')
h.close()
if (control['method']=='lqsgw+dmft'):
iter_string='_'+str(control['iter_num_impurity'])
elif (control['method']=='lda+dmft'):
iter_string='_'+str(control['iter_num_outer'])+'_'+str(control['iter_num_impurity'])
labeling_file('./dc.dat', iter_string)
print('dc.dat generation done', file=control['h_log'],flush=True)
os.chdir(control['top_dir'])
return None
# def cal_dc_diagonal_new(control):
# os.chdir(control['dc_directory'])
# dc_mat=read_impurity_mat_static(control,control['dc_directory']+'/dc_mat.dat')
# h=open('./dc.dat', 'w')
# for ii in sorted(set(control['impurity_problem_equivalence'])):
# dc_vec=imp_from_mat_to_array(dc_mat[str(ii)],imp[str(abs(ii))]['impurity_matrix'])
# for jj in range(len(dc_vec)):
# h.write(str(np.real(dc_vec[jj]))+' '+str(np.imag(dc_vec[jj]))+' ')
# h.close()
# if (control['method']=='lqsgw+dmft'):
# iter_string='_'+str(control['iter_num_impurity'])
# elif (control['method']=='lda+dmft'):
# iter_string='_'+str(control['iter_num_outer'])+'_'+str(control['iter_num_impurity'])
# labeling_file('./dc.dat', iter_string)
# print('dc.dat generation done', file=control['h_log'],flush=True)
# os.chdir(control['top_dir'])
# return None
def cal_zinv_m1_diagonal(control):
os.chdir(control['dc_directory'])
if os.path.isfile(control['dc_directory']+'/zinv_m1_mat.dat'):
zinv_m1_mat=read_impurity_mat_static(control,control['dc_directory']+'/zinv_m1_mat.dat')
h=open('./zinv_m1.dat', 'w')
for ii in sorted(set(control['impurity_problem_equivalence'])):
zinv_m1_vec=imp_from_mat_to_array(zinv_m1_mat[str(ii)],imp[str(abs(ii))]['impurity_matrix'])
for jj in range(len(zinv_m1_vec)):
h.write(str(np.real(zinv_m1_vec[jj]))+' '+str(np.imag(zinv_m1_vec[jj]))+' ')
h.close()
if (control['method']=='lqsgw+dmft'):
iter_string='_'+str(control['iter_num_impurity'])
elif (control['method']=='lda+dmft'):
iter_string='_'+str(control['iter_num_outer'])+'_'+str(control['iter_num_impurity'])
labeling_file('./zinv_m1.dat', iter_string)
print('zinv_m1.dat generation done', file=control['h_log'],flush=True)
os.chdir(control['top_dir'])
return None
def vec_from_mat_dynamic(mat,trans):
vec=np.zeros(np.shape(mat, 0), np.shape(mat, 1))
for ii in range(np.shape(mat, 0)):
vec[ii,:]=np.diag(dot(np.transpose(np.conj(trans)), np.dot(mat[ii,:,:], trans)))
return vec
def prepare_impurity_solver(control,wan_hmat,imp):
# cal_trans_from_patrick(control, imp)
delta=array_impurity_dynamic(control,imp,control['lowh_directory']+'/delta.dat')
write_json_all(control,imp,delta,'hyb.json')
e_imp=generate_mat_from_array_impurity_static(control,imp,control['lowh_directory']+'/e_imp.dat')
trans_basis=read_impurity_mat_static(control,control['lowh_directory']+'/trans_basis.dat')
for key, value in imp.items():
if (not (isinstance(imp[key], dict))):
continue
nimp_orb=len(imp[key]['impurity_matrix'])
os.chdir(control['impurity_directory']+'/'+key)
if (control['spin_orbit']):
ndim=nimp_orb
e_imp_key=np.zeros((ndim, ndim))
trans_key=np.zeros((ndim, ndim))
# equivalence_key=np.zeros((ndim,ndim),dtype='int')
e_imp_key=np.real(e_imp[key])
trans_key=np.real(trans_basis[key])
# equivalence_key=array([[(lambda ii: str(ii) if str(ii)!='0' else '')(ii) for ii in row] for row in imp[key]['impurity_matrix']])
equivalence_key=list(map(lambda row: list(map(lambda x: str(x) if x!='0' else '', list(map(str, row)))), imp[key]['impurity_matrix']))
else:
ndim=nimp_orb*2
e_imp_key=np.zeros((ndim, ndim))
trans_key=np.zeros((ndim, ndim))
equivalence_key_int_mat=np.array(imp[key]['impurity_matrix'])
equivalence_key_int_mat_all=np.zeros((ndim, ndim),dtype='int')
if (imp[key]['para']):
mkey=key
shiftval=0
else:
mkey=str(-int(key))
shiftval=np.amax(equivalence_key_int_mat)
print(mkey, shiftval, file=control['h_log'],flush=True)
#
# On the next line ii>0 evaluates to 1 if ii>0 and evaluates to 0 otherwise
# equivalence_mkey_int_mat=equivalence_key_int_mat+shiftval*array([[(lambda ii: ii>0)(ii) for ii in row] for row in equivalence_key_int_mat])
# equivalence_mkey_int_mat=equivalence_key_int_mat+shiftval*array(map(lambda row: map(int,row), equivalence_key_int_mat>0))
equivalence_mkey_int_mat=equivalence_key_int_mat+shiftval*(equivalence_key_int_mat>0)
e_imp_key[0:nimp_orb,0:nimp_orb]=np.real(e_imp[key])
e_imp_key[nimp_orb:(2*nimp_orb),nimp_orb:(2*nimp_orb)]=np.real(e_imp[mkey])
trans_key[0:nimp_orb,0:nimp_orb]=np.real(trans_basis[key])
trans_key[nimp_orb:(2*nimp_orb),nimp_orb:(2*nimp_orb)]=np.real(trans_basis[mkey])
equivalence_key_int_mat_all[0:nimp_orb,0:nimp_orb]=equivalence_key_int_mat
equivalence_key_int_mat_all[nimp_orb:(2*nimp_orb),nimp_orb:(2*nimp_orb)]=equivalence_mkey_int_mat
equivalence_key=list(map(lambda row: list(map(lambda x: str(x) if x!='0' else '', list(map(str, row)))), equivalence_key_int_mat_all))
write_params_json(control,imp[key],e_imp_key,trans_key,equivalence_key,imp['beta'])
if (control['method']=='lqsgw+dmft'):
write_dynamical_f0_json(imp[key])
os.chdir(control['top_dir'])
return None
def run_impurity_solver(control,imp):
green={}
sigma_bare={}
sigma={}
sigma_to_delta={}
for key, value in imp.items():
if (not (isinstance(imp[key], dict))):
continue
os.chdir(control['impurity_directory']+'/'+key)
solve_impurity_patrick(control)
measure_impurity_patrick(control)
green[key], sigma_bare[key], sigma[key], sigma_to_delta[key]=impurity_postprocessing(control, imp, key)
os.chdir(control['impurity_directory'])
green_table=[]
sigma_table=[]
sigma_to_delta_table=[]
sigma_bare_table=[]
for jj in range(control['n_omega']):
green_omega=[control['omega'][jj]]
sigma_omega=[control['omega'][jj]]
sigma_to_delta_omega=[control['omega'][jj]]
sigma_bare_omega=[control['omega'][jj]]
for ii in sorted(set(control['impurity_problem_equivalence'])):
n_iio=np.amax(imp[str(abs(ii))]['impurity_matrix'])
for kk in range(n_iio):
if (ii<0):
pp=kk+n_iio
else:
pp=kk
green_omega=green_omega+[np.real(green[str(abs(ii))][jj,pp]),np.imag(green[str(abs(ii))][jj,pp])]
sigma_omega=sigma_omega+[np.real(sigma[str(abs(ii))][jj,pp]),np.imag(sigma[str(abs(ii))][jj,pp])]
sigma_to_delta_omega=sigma_to_delta_omega+[np.real(sigma_to_delta[str(abs(ii))][jj,pp]),np.imag(sigma_to_delta[str(abs(ii))][jj,pp])]
sigma_bare_omega=sigma_bare_omega+[np.real(sigma_bare[str(abs(ii))][jj,pp]),np.imag(sigma_bare[str(abs(ii))][jj,pp])]
green_table.append(green_omega)
sigma_table.append(sigma_omega)
sigma_to_delta_table.append(sigma_to_delta_omega)
sigma_bare_table.append(sigma_bare_omega)
with open('./gimp.dat', 'w') as outputfile:
outputfile.write(tabulate(green_table, headers=control['sig_header'], floatfmt=".12f", numalign="right", tablefmt="plain"))
with open('./sig_bare.dat', 'w') as outputfile:
outputfile.write(tabulate(sigma_bare_table, headers=control['sig_header'], floatfmt=".12f", numalign="right", tablefmt="plain"))
with open('./sig_smth.dat', 'w') as outputfile:
outputfile.write(tabulate(sigma_table, headers=control['sig_header'], floatfmt=".12f", numalign="right", tablefmt="plain"))
with open('./sig.dat', 'w') as outputfile:
outputfile.write(tabulate(sigma_to_delta_table, headers=control['sig_header'], floatfmt=".12f", numalign="right", tablefmt="plain"))
shutil.copy('./sig.dat', control['top_dir'])
if (control['method']=='lqsgw+dmft'):
iter_string='_'+str(control['iter_num_impurity'])
elif (control['method']=='lda+dmft'):
iter_string='_'+str(control['iter_num_outer'])+'_'+str(control['iter_num_impurity'])
labeling_file('./gimp.dat',iter_string)
labeling_file('./sig_bare.dat',iter_string)
labeling_file('./sig_smth.dat',iter_string)
labeling_file('./sig.dat',iter_string)
os.chdir(control['top_dir'])
def generate_mat_from_array_impurity_dynamic(control,imp, filename):
os.chdir(control['impurity_directory'])
dat=np.loadtxt(filename)
start_array={}
end_array={}
last_index=1
for ii in sorted(set(control['impurity_problem_equivalence'])):
n_iio=np.amax(imp[str(abs(ii))]['impurity_matrix'])
start_array[ii]=last_index
end_array[ii]=last_index+2*n_iio
last_index=last_index+2*n_iio
# print(start_array)
# print(end_array)
matout={}
for ii in sorted(set(control['impurity_problem_equivalence'])):
nimp_orb=len(imp[str(abs(ii))]['impurity_matrix'])
tempmat=np.zeros((control['n_omega'],nimp_orb,nimp_orb), dtype='complex')
for iomega in range(control['n_omega']):
tempmat2=dat[iomega,start_array[ii]:end_array[ii]]
tempmat[iomega,:,:]=imp_from_array_to_mat(tempmat2[0::2]+tempmat2[1::2]*1j,imp[str(abs(ii))]['impurity_matrix'])
matout[str(ii)]=tempmat
return matout
def generate_mat_from_array_impurity_static(control,imp, filename):
os.chdir(control['impurity_directory'])
dat=np.loadtxt(filename)
start_array={}
end_array={}
last_index=0
for ii in sorted(set(control['impurity_problem_equivalence'])):
n_iio=np.amax(imp[str(abs(ii))]['impurity_matrix'])
start_array[ii]=last_index
end_array[ii]=last_index+2*n_iio
last_index=last_index+2*n_iio
# print(start_array)
# print(end_array)
matout={}
for ii in sorted(set(control['impurity_problem_equivalence'])):
tempmat2=dat[start_array[ii]:end_array[ii]]
matout[str(ii)]=imp_from_array_to_mat(tempmat2[0::2]+tempmat2[1::2]*1j,imp[str(abs(ii))]['impurity_matrix'])
return matout
def array_impurity_static(control,imp, filename):
os.chdir(control['impurity_directory'])
dat=np.loadtxt(filename)
start_array={}
end_array={}
last_index=0
for ii in sorted(set(control['impurity_problem_equivalence'])):
n_iio=np.amax(imp[str(abs(ii))]['impurity_matrix'])
start_array[ii]=last_index
end_array[ii]=last_index+2*n_iio
last_index=last_index+2*n_iio
# print(start_array)
# print(end_array)
matout={}
for ii in sorted(set(control['impurity_problem_equivalence'])):
tempmat2=dat[start_array[ii]:end_array[ii]]
matout[str(ii)]=tempmat2[0::2]+tempmat2[1::2]*1j
return matout
def array_impurity_dynamic(control,imp, filename):
os.chdir(control['impurity_directory'])
dat=np.loadtxt(filename)
start_array={}
end_array={}
last_index=1
for ii in sorted(set(control['impurity_problem_equivalence'])):
n_iio=np.amax(imp[str(abs(ii))]['impurity_matrix'])
start_array[ii]=last_index
end_array[ii]=last_index+2*n_iio
last_index=last_index+2*n_iio
# print(start_array)
# print(end_array)
matout={}
for ii in sorted(set(control['impurity_problem_equivalence'])):
n_iio=np.amax(imp[str(abs(ii))]['impurity_matrix'])
tempmat=np.zeros((control['n_omega'],n_iio), dtype='complex')
for iomega in range(control['n_omega']):
tempmat2=dat[iomega,start_array[ii]:end_array[ii]]
tempmat[iomega,:]=tempmat2[0::2]+tempmat2[1::2]*1j
matout[str(ii)]=tempmat
return matout
def cal_projected_mean_field_diagonal(control,imp):
os.chdir(control['lowh_directory'])
hmat=read_impurity_mat_static(control,control['lowh_directory']+'/e_projected_mat.dat')
h=open('./projected_eig.dat', 'w')
for ii in sorted(set(control['impurity_problem_equivalence'])):
h_vec=imp_from_mat_to_array(hmat[str(ii)],imp[str(abs(ii))]['impurity_matrix'])
for jj in range(len(h_vec)):
h.write(str(np.real(h_vec[jj]))+' '+str(np.imag(h_vec[jj]))+' ')
h.close()
if (control['method']=='lqsgw+dmft'):
iter_string='_'+str(control['iter_num_impurity'])
elif (control['method']=='lda+dmft'):
iter_string='_'+str(control['iter_num_outer'])+'_'+str(control['iter_num_impurity'])
labeling_file('./projected_eig.dat', iter_string)
print('projected_eig.dat generation done', file=control['h_log'],flush=True)
os.chdir(control['top_dir'])
return None
def cal_e_imp_diagonal(control):
os.chdir(control['lowh_directory'])
eig=np.loadtxt('projected_eig.dat')
dc=np.loadtxt(control['dc_directory']+'/dc.dat')
f=open('e_imp.dat', 'w')
f.write(" ".join(map(str, eig-dc))+'\n')
f.close()
if (control['method']=='lqsgw+dmft'):
iter_string='_'+str(control['iter_num_impurity'])
elif (control['method']=='lda+dmft'):
iter_string='_'+str(control['iter_num_outer'])+'_'+str(control['iter_num_impurity'])
labeling_file('./e_imp.dat', iter_string)
print('e_imp.dat generation done', file=control['h_log'],flush=True)
os.chdir(control['top_dir'])
return None
def imp_from_array_to_mat(vecin,equivalence_mat):
nimp_orb=len(equivalence_mat)
matout=np.zeros((nimp_orb, nimp_orb), dtype='complex')
for ii in range(nimp_orb):
for jj in range(nimp_orb):
if (equivalence_mat[ii,jj]!=0):
matout[ii,jj]=vecin[equivalence_mat[ii,jj]-1]
return matout
def imp_from_mat_to_array(matin,equivalence_mat):
n_iio=np.amax(equivalence_mat)
vecout=np.zeros(n_iio, dtype='complex')
degen_vec=np.zeros(n_iio, dtype='int')
nimp_orb=len(matin)
# print(nimp_orb)
# print(equivalence_mat)
# print(type(equivalence_mat))
# print(matin)
# print(type(matin))
for ii in range(nimp_orb):
for jj in range(nimp_orb):
print(ii, jj)
if (equivalence_mat[ii,jj]!=0):
ind=equivalence_mat[jj,jj]-1
vecout[ind]=vecout[ind]+matin[ii,jj]
degen_vec[ind]=degen_vec[ind]+1
vecout=vecout/(degen_vec*1.0)
return vecout
# def read_trans_basis(control,filename):
# trans_basis={}
# g=open(filename, 'r')
# for ii in sorted(set(control['impurity_problem_equivalence'])):
# prob_ind=con3trol['impurity_problem_equivalence'].index(ii)
# nimp_orb=len(control['impurity_wan'][prob_ind])
# transmat=np.zeros((nimp_orb,nimp_orb), dtype='complex')
# for jj in range(nimp_orb):
# transmat2=array(map(float,g.readline().split()))
# transmat[jj,:]=transmat2[0::2]+transmat2[1::2]*1j
# trans_basis[str(ii)]=transmat
# return trans_basis
# def read_impurity_vec_static(control,filename):
# imp_basis={}
# g=open(filename, 'r')
# for ii in sorted(set(control['impurity_problem_equivalence'])):
# prob_ind=control['impurity_problem_equivalence'].index(ii)
# nimp_orb=len(control['impurity_wan'][prob_ind])
# impmat=np.zeros((nimp_orb,nimp_orb), dtype='complex')
# for jj in range(nimp_orb):
# impmat2=array(map(float,g.readline().split()))
# impmat[jj,:]=impmat2[0::2]+impmat2[1::2]*1j
# imp_basis[str(ii)]=impmat
# return imp_basis
def read_impurity_mat_static(control,filename):
imp_basis={}
g=open(filename, 'r')
for ii in sorted(set(control['impurity_problem_equivalence'])):
prob_ind=control['impurity_problem_equivalence'].index(ii)
nimp_orb=len(control['impurity_wan'][prob_ind])
impmat=np.zeros((nimp_orb,nimp_orb), dtype='complex')
# for jj in range(nimp_orb):
# impmat2=array([float(x) for x in g.readline().split()])
# for kk in range(0,nimp_orb*2,2):
# impmat[jj,kk]=impmat2[kk]+impmat2[kk+1]*1j
for jj in range(nimp_orb):
impmat2=np.array(list(map(float,g.readline().split())))
impmat[jj,:]=impmat2[0::2]+impmat2[1::2]*1j
imp_basis[str(ii)]=impmat
return imp_basis
def read_impurity_mat_dynamic(control,filename):
imp_basis={}
dat=np.loadtxt(filename)
print(np.shape(dat))
start_array={}
end_array={}
last_index=1
for ii in sorted(set(control['impurity_problem_equivalence'])):
prob_ind=control['impurity_problem_equivalence'].index(ii)
nimp_orb=len(control['impurity_wan'][prob_ind])
start_array[ii]=last_index
end_array[ii]=last_index+2*nimp_orb**2
last_index=last_index+2*nimp_orb**2
# print(start_array)
# print(end_array)
for ii in sorted(set(control['impurity_problem_equivalence'])):
prob_ind=control['impurity_problem_equivalence'].index(ii)
nimp_orb=len(control['impurity_wan'][prob_ind])
dat3=np.reshape(dat[:,start_array[ii]:end_array[ii]], (control['n_omega'], 2, nimp_orb,nimp_orb), order='F')
imp_basis[str(ii)]=dat3[:,0,:,:]+dat3[:,1,:,:]*1j
return imp_basis
def cal_hyb_diagonal(control,imp):
os.chdir(control['lowh_directory'])
hyb_mat=read_impurity_mat_dynamic(control,control['lowh_directory']+'/delta_mat.dat')
# print hyb_mat
hyb_table=[]
for jj in range(control['n_omega']):
hyb_omega=[control['omega'][jj]]
for ii in sorted(set(control['impurity_problem_equivalence'])):
hyb_vec=imp_from_mat_to_array(hyb_mat[str(ii)][jj,:,:],imp[str(abs(ii))]['impurity_matrix'])
hyb_omega=hyb_omega+np.reshape(np.stack((np.real(hyb_vec), np.imag(hyb_vec)), 0), (len(hyb_vec)*2), order='F').tolist()
hyb_table.append(hyb_omega)
with open(control['lowh_directory']+'/delta.dat', 'w') as outputfile:
outputfile.write(tabulate(hyb_table, headers=control['sig_header'], floatfmt=".12f", numalign="right", tablefmt="plain"))
if (control['method']=='lqsgw+dmft'):
iter_string='_'+str(control['iter_num_impurity'])
elif (control['method']=='lda+dmft'):
iter_string='_'+str(control['iter_num_outer'])+'_'+str(control['iter_num_impurity'])
labeling_file('./delta.dat', iter_string)
shutil.copy('./delta.dat', control['top_dir'])
print('delta.dat generation done', file=control['h_log'],flush=True)
causality=test_causality('./delta.dat')
os.chdir(control['lowh_directory'])
return causality
# def cal_sig_dc_diagonal(control,imp):
# os.chdir(control['dc_directory'])
# trans_basis=read_impurity_mat_static(control,control['lowh_directory']+'/trans_basis.dat')
# sig_mat=read_impurity_mat_dynamic(control,control['dc_directory']+'/delta_mat.dat')
# h=open('./Delta.inp', 'w')
# print hyb_mat
# for jj in range(control['n_omega']):
# h.write(str(control['omega'][jj])+' ')
# for ii in sorted(set(control['impurity_problem_equivalence'])):
# hyb_mat_new=dot(dot(trans_basis[str(ii)], hyb_mat[str(ii)][jj,:,:]), conj(np.transpose(trans_basis[str(ii)])))
# hyb_vec=imp_from_mat_to_array(hyb_mat_new,imp[str(abs(ii))]['impurity_matrix'])
# for kk in range(len(hyb_vec)):
# h.write(str(np.real(hyb_vec[kk]))+' '+str(np.imag(hyb_vec[kk]))+' ')
# h.write('\n')
# h.close()
# if (control['method']=='lqsgw+dmft'):
# iter_string='_'+str(control['iter_num_impurity'])
# elif (control['method']=='lda+dmft'):
# iter_string='_'+str(control['iter_num_outer'])+'_'+str(control['iter_num_impurity'])
# labeling_file('./Delta.inp', iter_string)
# print('Delta.inp generation done', file=control['h_log'],flush=True)
# causality=test_causality('./Delta.inp')
# return causality
def labeling_file(filename,iter_string):
dirname=os.path.abspath(os.path.dirname(filename))
filenameonly=os.path.basename(filename)
temp=filenameonly.split('.')
shutil.copy(dirname+'/'+filenameonly, dirname+"/"+'.'.join(temp[0:-1])+iter_string+'.'+temp[-1])
return None
def directory_setup(control):
if (control['method'] =='lda+dmft'):
#lattice
tempdir=control['lattice_directory']
if len(glob.glob(tempdir))==0 : os.mkdir(tempdir)
if not control['hdf5']:
if len(glob.glob(tempdir+'/checkpoint'))==0 : os.mkdir(tempdir+'/checkpoint')
elif (control['method'] =='lqsgw+dmft'):
tempdir=control['coulomb_directory']
if len(glob.glob(tempdir))==0 : os.mkdir(tempdir)
#wannier90 directory
tempdir=control['wannier_directory']
if len(glob.glob(tempdir))==0 : os.mkdir(tempdir)
tempdir=control['dc_directory']
if len(glob.glob(tempdir))==0 : os.mkdir(tempdir)
# ctqmc
tempdir=control['impurity_directory']
if len(glob.glob(tempdir))==0 : os.mkdir(tempdir)
for ii in range(1,np.amax(control['impurity_problem_equivalence'])+1):
tempdir=control['impurity_directory']+'/'+str(ii)
if len(glob.glob(tempdir))==0 : os.mkdir(tempdir)
tempdir=control['dc_directory']+'/'+str(ii)
if len(glob.glob(tempdir))==0 : os.mkdir(tempdir)
# delta
tempdir=control['lowh_directory']
if len(glob.glob(tempdir))==0 : os.mkdir(tempdir)
return None
def check_for_files(filepath, h_log):
if len(glob.glob(filepath))==0:
print('missing:', filepath, file=control['h_log'],flush=True)
quit()
return None
def gaussian_broadening_linear(x, y, w1, temperature, cutoff):
# broadening starts at the second matsubara points
print(np.shape(x))
print(np.shape(y))
print(x)
print(y)
w0=(1.0-3.0*w1)*np.pi*temperature*8.6173303*10**-5
width_array=w0+w1*x
cnt=0
ynew=np.zeros(len(y), dtype='complex')
for x0 in x:
if (x0>cutoff+(w0+w1*cutoff)*3.0):
ynew[cnt]=y[cnt]
else:
if ((x0>3*width_array[cnt]) and ((x[-1]-x0)>3*width_array[cnt])):
dist=1.0/np.sqrt(2*pi)/width_array[cnt]*np.exp(-(x-x0)**2/2.0/width_array[cnt]**2)
ynew[cnt]=np.sum(dist*y)/np.sum(dist)
else:
ynew[cnt]=y[cnt]
cnt=cnt+1
return ynew
def solve_impurity_patrick(control):
# execute CTQMC
# chdir_string='cd '+control['top_dir']+'/impurity; '
print('-----------------------', file = sys.stdout, flush=True)
print('run CTQMC', file = sys.stdout, flush=True)
print('-----------------------', file = sys.stdout, flush=True)
print('-----------------------', file = sys.stderr, flush=True)
print('run CTQMC', file = sys.stderr, flush=True)
print('-----------------------', file = sys.stderr, flush=True)
run_string=control['mpi_prefix_impurity']+' '+control['comsuitedir']+"/CTQMC params"
cmd = run_string
print(cmd, file=control['h_log'],flush=True)
# with open('./ctqmc.out', 'w') as logfile, open('./ctqmc.err', 'w') as errfile:
# ret = subprocess.call(cmd, shell=True,stdout = logfile, stderr = errfile)
ret = subprocess.call(cmd, shell=True)
if ret != 0:
print("Error in CTQMC. Check standard error file for error message.", file=control['h_log'],flush=True)
sys.exit()
return None
def measure_impurity_patrick(control):
print('-----------------------', file = sys.stdout, flush=True)
print('run EVALSYM', file = sys.stdout, flush=True)
print('-----------------------', file = sys.stdout, flush=True)
print('-----------------------', file = sys.stderr, flush=True)
print('run EVALSYM', file = sys.stderr, flush=True)
print('-----------------------', file = sys.stderr, flush=True)
run_string= control['mpi_prefix_impurity']+' '+control['comsuitedir']+"/EVALSIM params"
cmd = run_string
print(cmd, file=control['h_log'],flush=True)
# with open('./evalsim.out', 'w') as logfile, open('./evalsim.err', 'w') as errfile :
# ret = subprocess.call(cmd,shell=True, stdout=logfile, stderr=errfile)
ret = subprocess.call(cmd,shell=True)
if ret != 0:
print("Error in EVALSIM. Check standard error file for error message.", file=control['h_log'],flush=True)
sys.exit()
print("measure self-energy done", file=control['h_log'],flush=True)
if (control['method']=='lqsgw+dmft'):
iter_string='_'+str(control['iter_num_impurity'])
elif (control['method']=='lda+dmft'):
iter_string='_'+str(control['iter_num_outer'])+'_'+str(control['iter_num_impurity'])
# shutil.copy("./evalsim.out", "./evalsim"+iter_string+'.log')
return None
def write_json_all(control,imp,data_array,json_name):
# assume that it is diagonal matrix
for key, value in imp.items(): # for the ordered phase this part should be fixed
json_dict={}
if (not (isinstance(imp[key], dict))):
continue
n_iio=np.amax(imp[key]['impurity_matrix'])
if (imp[key]['para']):
for kk in range(n_iio):
orb_name=str(kk+1)
json_dict[orb_name]={}
json_dict[orb_name]['beta']=imp['beta']
json_dict[orb_name]['real']=np.real(data_array[key][:,kk]).tolist()
json_dict[orb_name]['imag']=np.imag(data_array[key][:,kk]).tolist()
else:
mkey=str(-int(key))
for kk in range(n_iio):
orb_name=str(kk+1)
json_dict[orb_name]={}
json_dict[orb_name]['beta']=imp['beta']
json_dict[orb_name]['real']=np.real(data_array[key][:,kk]).tolist()
json_dict[orb_name]['imag']=np.imag(data_array[key][:,kk]).tolist()
orb_name=str(kk+1+n_iio)
json_dict[orb_name]={}
json_dict[orb_name]['beta']=imp['beta']
json_dict[orb_name]['real']=np.real(data_array[mkey][:,kk]).tolist()
json_dict[orb_name]['imag']=np.imag(data_array[mkey][:,kk]).tolist()
with open(control['impurity_directory']+'/'+key+'/'+json_name,'w') as outfile:
json.dump(json_dict, outfile,sort_keys=True, indent=4, separators=(',', ': '))
print(json_name+" written", file=control['h_log'],flush=True)
return None
def read_json(jsonfile):
Sig_temp=json.load(open(jsonfile))
n_omega=len(Sig_temp['1']['real'])
n_iio=len(Sig_temp.keys())
dat1=np.zeros((n_omega, n_iio), dtype='complex')
for key, value in Sig_temp.items():
dat1[:,int(key)-1]=np.array(Sig_temp[key]['real'])+np.array(Sig_temp[key]['imag'])*1j
return dat1
def read_function_from_jsonfile(jsonfile, dict_name):
Sig_temp=json.load(open(jsonfile))['partition'][dict_name]
n_omega=len(Sig_temp['1']["function"]['real'])
n_iio=len(Sig_temp.keys())
dat1=np.zeros((n_omega, n_iio), dtype='complex')
for key, value in Sig_temp.items():
dat1[:,int(key)-1]=np.array(Sig_temp[key]["function"]['real'])+np.array(Sig_temp[key]["function"]['imag'])*1j
return dat1
def impurity_postprocessing(control, imp, key):
if (control['method']=='lqsgw+dmft'):
iter_string='_'+str(control['iter_num_impurity'])
elif (control['method']=='lda+dmft'):
iter_string='_'+str(control['iter_num_outer'])+'_'+str(control['iter_num_impurity'])
labeling_file('./params.obs.json',iter_string)
labeling_file('./params.meas.json',iter_string)
histo_temp=json.load(open('params.obs.json'))['partition']["expansion histogram"]
histo=np.zeros((np.shape(histo_temp)[0], 2))
histo[:,0]=np.arange(np.shape(histo_temp)[0])
histo[:,1]=histo_temp
nn=json.load(open('params.obs.json'))['partition']["scalar"]["N"][0]
ctqmc_sign=json.load(open('params.obs.json'))['partition']["sign"][0]
# histogram
firstmoment=np.sum(histo[:,0]*histo[:,1])/np.sum(histo[:,1])
secondmoment=np.sum((histo[:,0]-firstmoment)**2*histo[:,1])/np.sum(histo[:,1])
thirdmoment=np.sum((histo[:,0]-firstmoment)**3*histo[:,1])/np.sum(histo[:,1])/secondmoment**(3.0/2.0)
print('histogram information for impurity_'+imp['name'], file=control['h_log'],flush=True)
print('first moment', firstmoment, file=control['h_log'],flush=True)
print('second moment', secondmoment, file=control['h_log'],flush=True)
print('third moment', thirdmoment, file=control['h_log'],flush=True)
# previous_iter_string='_'.join(map(str,iter_string.split('_')[:-1]))+'_'+str(int(iter_string.split('_')[-1])-1)
green=read_function_from_jsonfile('./params.obs.json',"green")
sigma_bare=read_function_from_jsonfile('./params.obs.json',"self-energy")
sigma_old=array_impurity_dynamic(control,imp,control['impurity_directory']+'/sig.dat')
sigma=np.zeros(np.shape(sigma_bare), dtype='complex')
sigma_to_delta=np.zeros(np.shape(sigma_bare), dtype='complex')
n_iio=np.amax(imp[key]['impurity_matrix'])
sig_causality=1
for jj in range(n_iio):
sigma[:,jj]=gaussian_broadening_linear(control['omega'], sigma_bare[:,jj], 0.05, imp['temperature'], imp[key]['green_cutoff'])
if ((np.imag(sigma[:,jj])>0.0).any()):
sig_causality=0
sigma_to_delta[:,jj]=sigma_old[key][:,jj]
else:
sigma_to_delta[:,jj]=(sigma_old[key][:,jj])*(1.0-control['sigma_mix_ratio'])+(sigma[:,jj])*control['sigma_mix_ratio']
if (not imp[key]['para']):
for jj in range(n_iio, n_iio*2):
mkey=str(-int(key))
sigma[:,jj]=gaussian_broadening_linear(control['omega'], sigma_bare[:,jj], 0.05, imp['temperature'], imp[key]['green_cutoff'])
if ((np.imag(sigma[:,jj])>0.0).any()):
sig_causality=0
sigma_to_delta[:,jj]=sigma_old[mkey][:,jj-n_iio]
else:
sigma_to_delta[:,jj]=(sigma_old[mkey][:,jj-n_iio])*(1.0-control['sigma_mix_ratio'])+(sigma[:,jj])*control['sigma_mix_ratio']
if (imp[key]['para']):
sig_diff_ave=np.sqrt(np.mean(np.absolute((sigma_to_delta-sigma_old[key]))**2))
else:
mkey=str(-int(key))
sig_diff_ave=np.sqrt(np.mean((np.absolute((sigma_to_delta[:,0:n_iio]-sigma_old[key]))+np.absolute((sigma_to_delta[:,n_iio:]-sigma_old[mkey])))**2)/2.0)
if (sig_causality==1):
causality_flag='good'
else:
causality_flag='broken'
if (control['method']=='lda+dmft'):
control['conv_table'].append(['impurity_'+key,control['iter_num_outer'], '', control['iter_num_impurity'],causality_flag,'','','','',sig_diff_ave,nn,firstmoment,secondmoment,ctqmc_sign])
with open(control['top_dir']+'/convergence.log', 'w') as outputfile:
outputfile.write(tabulate(control['conv_table'], headers=control['convergence_header'], numalign="right", floatfmt=".5f"))
elif (control['method']=='lqsgw+dmft'):
control['conv_table'].append(['impurity_'+key,control['iter_num_impurity'],causality_flag,'','','','',sig_diff_ave,nn,firstmoment,secondmoment,ctqmc_sign])
with open(control['top_dir']+'/convergence.log', 'w') as outputfile:
outputfile.write(tabulate(control['conv_table'], headers=control['convergence_header'], numalign="right", floatfmt=".5f"))
return green, sigma_bare, sigma, sigma_to_delta
def test_causality(filename):
causality=1
dat=np.loadtxt(filename)
if ((dat[:,2::2]>0.0).any()):
causality=0
np.savetxt(filename+'b', dat)
labeling_file(filename+'b',iter_string)
print("Causality in "+filename+" is broken", file=control['h_log'],flush=True)
else:
print("Causality in "+filename+" is good", file=control['h_log'],flush=True)
return causality
def write_transformation_matrix(control, filename):
os.chdir(control['lowh_directory'])
if (control['trans_basis_mode']==2):
f=open('trans_basis.dat', 'w')
g=open(filename, 'r')
for ii in sorted(set(control['impurity_problem_equivalence'])):
prob_ind=control['impurity_problem_equivalence'].index(ii)
nimp_orb=len(control['impurity_wan'][prob_ind])
tempmat=np.zeros((nimp_orb,nimp_orb))
for jj in nimp_orb:
tempmat[jj,:]=np.array(list(map(float,g.readline().split())))
if (trace(tempmat) > control['metal_threshold']):
w, v=np.linalg.eigh(tempmat)
v=tranpose(v)
else:
v=np.identity(nimp_orb)
for iorb in range(nimp_orb):
for jorb in range(nimp_orb):
f.write(str(v[iorb,jorb])+' 0.0 ')
f.write("\n")
f.close()
g.close()
shutil.copy('trans_basis.dat', control['top_dir'])
if (control['method']=='lqsgw+dmft'):
iter_string='_'+str(control['iter_num_impurity'])
elif (control['method']=='lda+dmft'):
iter_string='_'+str(control['iter_num_outer'])+'_'+str(control['iter_num_impurity'])
labeling_file('./trans_basis.dat', iter_string)
os.chdir(control['top_dir'])
return None
def run_comlowh(control):
os.chdir(control['lowh_directory'])
run_string=control['mpi_prefix_lowh']+' '+control['comsuitedir']+"/ComLowH"
logfilename=control['lowh_directory']+'/comlowh.out'
errfilename=control['lowh_directory']+'/comlowh.err'
errormessage="Error in comlowh. Check standard error file for error message."
cmd = run_string
print(cmd, file=control['h_log'],flush=True)
print('-----------------------', file = sys.stdout, flush=True)
print('run ComLowh', file = sys.stdout, flush=True)
print('-----------------------', file = sys.stdout, flush=True)
print('-----------------------', file = sys.stderr, flush=True)
print('run ComLowH', file = sys.stderr, flush=True)
print('-----------------------', file = sys.stderr, flush=True)
# with open(logfilename, 'w') as logfile, open(errfilename, 'w') as errfile:
# ret = subprocess.call(cmd, shell=True,stdout = logfile, stderr = errfile)
ret = subprocess.call(cmd, shell=True)
if ret != 0:
print(errormessage, file=control['h_log'],flush=True)
sys.exit()
if (control['method']=='lqsgw+dmft'):
iter_string="_"+str(control['iter_num_impurity'])
elif (control['method']=='lda+dmft'):
iter_string="_"+str(control['iter_num_outer'])+"_"+str(control['iter_num_impurity'])
# labeling_file('./wannier_den_matrix.dat',iter_string)
labeling_file('./comlowh.log',iter_string)
# labeling_file('./comlowh.out',iter_string)
labeling_file('./delta_mat.dat',iter_string)
labeling_file('./g_loc_mat.dat',iter_string)
labeling_file('./local_spectral_matrix_ef.dat',iter_string)
labeling_file('./e_projected_mat.dat',iter_string)
labeling_file('./ef.dat',iter_string)
os.chdir(control['top_dir'])
print("comlowh done", file=control['h_log'],flush=True)
return None
def run_comcoulomb(control,imp):
print('-----------------------', file = sys.stdout, flush=True)
print('run ComCoulomb', file = sys.stdout, flush=True)
print('-----------------------', file = sys.stdout, flush=True)
print('-----------------------', file = sys.stderr, flush=True)
print('run ComCoulomb', file = sys.stderr, flush=True)
print('-----------------------', file = sys.stderr, flush=True)
os.chdir(control['coulomb_directory'])
run_string=control['mpi_prefix_coulomb']+' '+control['comsuitedir']+"/ComCoulomb"
logfilename=control['coulomb_directory']+'/comcoulomb.out'
errfilename=control['coulomb_directory']+'/comcoulomb.err'
errormessage="Error in comcomcoulomb. Check standard error file for error message."
cmd = run_string
print(cmd, file=control['h_log'],flush=True)
# with open(logfilename, 'w') as logfile, open(errfilename, 'w') as errfile:
# ret = subprocess.call(cmd, shell=True,stdout = logfile, stderr = errfile)
ret = subprocess.call(cmd, shell=True)
if ret != 0:
print(errormessage, file=control['h_log'],flush=True)
sys.exit()
iter_string="_"+str(control['iter_num_outer'])
# labeling_file('./comcoulomb.out',iter_string)
labeling_file('./comcoulomb.ini',iter_string)
files = glob.iglob(control['coulomb_directory']+"/*u_Slater*.rst")
for filename in files:
labeling_file(filename, iter_string)
os.chdir(control['top_dir'])
return None
def comcoulomb_postprocessing(control,imp):
slater_v={}
slater_u={}
slater_w={}
for ii in sorted(set(control['impurity_problem_equivalence'])):
if (ii>0):
jj=control['impurity_problem_equivalence'].index(ii)
iatom=control['impurity_problem'][jj][0]
shell=control['impurity_problem'][jj][1]
if (shell=='s'):
l_char='0'
elif (shell=='p'):
l_char='1'
elif (shell=='d'):
l_char='2'
elif (shell=='f'):
l_char='3'
files = glob.iglob(control['coulomb_directory']+"/*_v_Slater_*"+str(iatom)+'_'+l_char+'.dat')
for filename in files:
# Conditional reshape to avoid a singleton numpy array
# (i.e., maps np.array(x) -> np.array([x]))
data = np.loadtxt(filename)
slater_v[str(ii)] = data if data.ndim > 0 else data.reshape(1,)
# slater_v[str(ii)]=np.loadtxt(filename)
imp[str(ii)]['f0']=slater_v[str(ii)][0]
if (int(l_char) >0):
imp[str(ii)]['f2']=slater_v[str(ii)][1]
if (int(l_char) >1):
imp[str(ii)]['f4']=slater_v[str(ii)][2]
if (int(l_char) >2):
imp[str(ii)]['f6']=slater_v[str(ii)][3]
files = glob.iglob(control['coulomb_directory']+"/*_w_Slater_*"+str(iatom)+'_'+l_char+'.dat')
for filename in files:
tempmat=np.loadtxt(filename)
n_nu=int(np.floor((tempmat[-1,0])/(2*pi/imp['beta'])))
nu=np.arange(n_nu)*(2*pi/imp['beta'])
dynamical_f0=cubic_interp1d(nu,tempmat[:,0], tempmat[:,1])
if (int(l_char) >0):
dynamical_f2=cubic_interp1d(nu,tempmat[:,0], tempmat[:,2])
if (int(l_char) >1):
dynamical_f4=cubic_interp1d(nu,tempmat[:,0], tempmat[:,3])
if (int(l_char) >2):
dynamical_f6=cubic_interp1d(nu,tempmat[:,0], tempmat[:,4])
if (int(l_char)==0):
# Avoids a shape error in the column stack at line 1831,
# which seems to occur for Li because the monoatomic s-orbital
# problem is a special case where the RHS is effectively 1D
# (shape (n_nu, 1) before transposition).
slater_w[str(ii)]=np.vstack((dynamical_f0))
# slater_w[str(ii)]=np.transpose(np.vstack((dynamical_f0)))
elif (int(l_char)==1):
slater_w[str(ii)]=np.transpose(np.vstack((dynamical_f0, dynamical_f2)))
elif (int(l_char)==2):
slater_w[str(ii)]=np.transpose(np.vstack((dynamical_f0, dynamical_f2, dynamical_f4)))
elif (int(l_char)==3):
slater_w[str(ii)]=np.transpose(np.vstack((dynamical_f0, dynamical_f2, dynamical_f4, dynamical_f6)))
files = glob.iglob(control['coulomb_directory']+"/*_u_Slater_*"+str(iatom)+'_'+l_char+'.dat')
for filename in files:
tempmat=np.loadtxt(filename)
n_nu=int(np.floor((tempmat[-1,0])/(2*pi/imp['beta'])))
nu=np.arange(n_nu)*(2*pi/imp['beta'])
dynamical_f0=cubic_interp1d(nu,tempmat[:,0], tempmat[:,1])
if (int(l_char) >0):
dynamical_f2=cubic_interp1d(nu,tempmat[:,0], tempmat[:,2])
if (int(l_char) >1):
dynamical_f4=cubic_interp1d(nu,tempmat[:,0], tempmat[:,3])
if (int(l_char) >2):
dynamical_f6=cubic_interp1d(nu,tempmat[:,0], tempmat[:,4])
if (int(l_char)==0):
# Avoids a shape error in the column stack at line 1830,
# which seems to occur for Li because the monoatomic s-orbital
# problem is a special case where the RHS is effectively 1D
# (shape (n_nu, 1) before transposition).
slater_u[str(ii)]=np.vstack((dynamical_f0))
# slater_u[str(ii)]=np.transpose(np.vstack((dynamical_f0)))
elif (int(l_char)==1):
slater_u[str(ii)]=np.transpose(np.vstack((dynamical_f0, dynamical_f2)))
elif (int(l_char)==2):
slater_u[str(ii)]=np.transpose(np.vstack((dynamical_f0, dynamical_f2, dynamical_f4)))
elif (int(l_char)==3):
slater_u[str(ii)]=np.transpose(np.vstack((dynamical_f0, dynamical_f2, dynamical_f4, dynamical_f6)))
imp[str(ii)]['dynamical_f0']=dynamical_f0-imp[str(ii)]['f0']
u_table=nu
w_table=nu
# u_table=np.hstack((u_table, nu))
# w_table=np.hstack((w_table, nu))
v_table=[]
slater_header=['# nu(eV)']
for ii in sorted(set(control['impurity_problem_equivalence'])):
jj=control['impurity_problem_equivalence'].index(ii)
iatom=control['impurity_problem'][jj][0]
shell=control['impurity_problem'][jj][1]
if (ii>0):
if (shell=='s'):
l_char='0'
elif (shell=='p'):
l_char='1'
elif (shell=='d'):
l_char='2'
elif (shell=='f'):
l_char='3'
u_table=np.column_stack((u_table, slater_u[str(ii)]))
w_table=np.column_stack((w_table, slater_w[str(ii)]))
v_table=np.hstack((v_table, slater_v[str(ii)]))
slater_header.append(str(ii)+':f0(eV)')
if (int(l_char)>0):
slater_header.append(str(ii)+':f2(eV)')
if (int(l_char)>1):
slater_header.append(str(ii)+':f4(eV)')
if (int(l_char)>2):
slater_header.append(str(ii)+':f6(eV)')
with open(control['top_dir']+'/u_slater.dat', 'w') as outputfile:
outputfile.write(tabulate(u_table, headers=slater_header, numalign="right", floatfmt=".12f", tablefmt="plain"))
with open(control['top_dir']+'/w_slater.dat', 'w') as outputfile:
outputfile.write(tabulate(w_table, headers=slater_header, numalign="right", floatfmt=".12f", tablefmt="plain"))
slater_header=slater_header[1:]
slater_header[0]='# '+slater_header[0]
# print('v_table shape'+str(shape(v_table)), file=control['h_log'],flush=True)
# print('v_table header shape'+str(shape(slater_header)), file=control['h_log'],flush=True)
# print(v_table, file=control['h_log'],flush=True)
# print(slater_header, file=control['h_log'],flush=True)
# print('v_table header shape'+str(shape(slater_header)), file=control['h_log'],flush=True)
with open(control['top_dir']+'/v_slater.dat', 'w') as outputfile:
outputfile.write(tabulate([v_table], headers=slater_header, numalign="right", floatfmt=".12f", tablefmt="plain"))
print("comcoulomb done", file=control['h_log'],flush=True)
return None
# def write_updates_json(control,imp):
# if (control['spin_orbit']):
# if (imp['problem']=='f'):
# updates_json={
# "InsertEraseCSQ": {
# "Weight": 1.,
# "Moves": [
# [1.,"5/2,-5/2"],
# [1.,"5/2,-3/2"],
# [1.,"5/2,-1/2"],
# [1.,"5/2,+1/2"],
# [1.,"5/2,+3/2"],
# [1.,"5/2,+5/2"],
# [1.,"7/2,-7/2"],
# [1.,"7/2,-5/2"],
# [1.,"7/2,-3/2"],
# [1.,"7/2,-1/2"],
# [1.,"7/2,+1/2"],
# [1.,"7/2,+3/2"],
# [1.,"7/2,+5/2"],
# [1.,"7/2,+7/2"]
# ]
# }
# }
# else:
# if (imp['problem']=='d'):
# updates_json={
# "InsertEraseCSQ": {
# "Weight": 1.,
# "Moves": [
# [1., "yzUp"],
# [1., "zxUp"],
# [1., "xyUp"],
# [1., "3z2r2Up"],
# [1., "x2y2Up"],
# [1., "yzDown"],
# [1., "zxDown"],
# [1., "xyDown"],
# [1., "3z2r2Down"],
# [1., "x2y2Down"]
# ]
# }
# }
# with open('Updates.json','w') as outfile:
# json.dump(updates_json,outfile,sort_keys=True, indent=4, separators=(',', ': '))
# print("Updates.json written" , file=control['h_log'],flush=True)
# return None
# def write_link_json(control, imp, key, equivalence_orb_mat):
# # prob_ind=control['impurity_problem_equivalence'].index(int(key))
# # nimp_orb=len(control['impurity_wan'][prob_ind])
# if (control['spin_orbit']):
# if (imp[key]['problem']=='f'):
# link_json=[
# {
# "Irreps": ["5/2,-5/2"],
# "Flavors": [["5/2,-5/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[0,0])+"+"]
# ]
# },
# {
# "Irreps": ["5/2,-3/2"],
# "Flavors": [["5/2,-3/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[1,1])+"+"]
# ]
# },
# {
# "Irreps": ["5/2,-1/2"],
# "Flavors": [["5/2,-1/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[2,2])+"+"]
# ]
# },
# {
# "Irreps": ["5/2,+1/2"],
# "Flavors": [["5/2,+1/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[3,3])+"+"]
# ]
# },
# {
# "Irreps": ["5/2,+3/2"],
# "Flavors": [["5/2,+3/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[4,4])+"+"]
# ]
# },
# {
# "Irreps": ["5/2,+5/2"],
# "Flavors": [["5/2,+5/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[5,5])+"+"]
# ]
# },
# {
# "Irreps": ["7/2,-7/2"],
# "Flavors": [["7/2,-7/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[6,6])+"+"]
# ]
# },
# {
# "Irreps": ["7/2,-5/2"],
# "Flavors": [["7/2,-5/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[7,7])+"+"]
# ]
# },
# {
# "Irreps": ["7/2,-3/2"],
# "Flavors": [["7/2,-3/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[8,8])+"+"]
# ]
# },
# {
# "Irreps": ["7/2,-1/2"],
# "Flavors": [["7/2,-1/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[9,9])+"+"]
# ]
# },
# {
# "Irreps": ["7/2,+1/2"],
# "Flavors": [["7/2,+1/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[10,10])+"+"]
# ]
# },
# {
# "Irreps": ["7/2,+3/2"],
# "Flavors": [["7/2,+3/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[11,11])+"+"]
# ]
# },
# {
# "Irreps": ["7/2,+5/2"],
# "Flavors": [["7/2,+5/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[12,12])+"+"]
# ]
# },
# {
# "Irreps": ["7/2,+7/2"],
# "Flavors": [["7/2,+7/2"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[13,13])+"+"]
# ]
# }
# ]
# else:
# if (imp[key]['problem']=='d'):
# if (imp[key]['para']):
# index_shift=0
# else:
# index_shift=np.amax(equivalence_orb_mat)
# link_json=[
# {
# "Irreps": ["yzUp"],
# "Flavors": [["yzUp"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[0,0])+"+"]
# ]
# },
# {
# "Irreps": ["zxUp"],
# "Flavors": [["zxUp"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[1,1])+"+"]
# ]
# },
# {
# "Irreps": ["xyUp"],
# "Flavors": [["xyUp"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[2,2])+"+"]
# ]
# },
# {
# "Irreps": ["3z2r2Up"],
# "Flavors": [["3z2r2Up"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[3,3])+"+"]
# ]
# },
# {
# "Irreps": ["x2y2Up"],
# "Flavors": [["x2y2Up"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[4,4])+"+"]
# ]
# },
# {
# "Irreps": ["yzDown"],
# "Flavors": [["yzDown"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[0,0]+index_shift)+"+"]
# ]
# },
# {
# "Irreps": ["zxDown"],
# "Flavors": [["zxDown"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[1,1]+index_shift)+"+"]
# ]
# },
# {
# "Irreps": ["xyDown"],
# "Flavors": [["xyDown"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[2,2]+index_shift)+"+"]
# ]
# },
# {
# "Irreps": ["3z2r2Down"],
# "Flavors": [["3z2r2Down"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[3,3]+index_shift)+"+"]
# ]
# },
# {
# "Irreps": ["x2y2Down"],
# "Flavors": [["x2y2Down"]],
# "Matrix": [
# ["+"+str(equivalence_orb_mat[4,4]+index_shift)+"+"]
# ]
# }
# ]
# with open('Link.json','w') as outfile:
# json.dump(link_json,outfile,sort_keys=True, indent=4, separators=(',', ': '))
# print("Link.json written" , file=control['h_log'],flush=True)
# return None
def write_params_json(control,imp,e_imp_key,trans_key,equivalence_key,beta):
mu_ctqmc=-e_imp_key[0,0]
nimp_orb=len(imp['impurity_matrix'])
e_ctqmc=(e_imp_key+np.identity(len(e_imp_key))*mu_ctqmc)
params_json={}
# basis
params_json["basis"]={}
params_json["basis"]["orbitals"]=imp['problem'].lower()
if (control['spin_orbit']):
params_json["basis"]["type"]="coupled"
else:
params_json["basis"]["type"]="product"
params_json["basis"]["transformation"]=trans_key.tolist()
# beta
params_json["beta"]=beta
# green basis
params_json["green basis"]="matsubara"
# hloc
params_json["hloc"]={}
params_json["hloc"]["one body"]=e_ctqmc.tolist()
params_json["hloc"]["two body"]={}
params_json["hloc"]["two body"]["parametrisation"]="slater-condon"
params_json["hloc"]["two body"]["F0"]=imp['f0']
if (params_json["basis"]["orbitals"]=='p') or (params_json["basis"]["orbitals"]=='d') or (params_json["basis"]["orbitals"]=='f') :
params_json["hloc"]["two body"]["F2"]=imp['f2']
if (params_json["basis"]["orbitals"]=='d') or (params_json["basis"]["orbitals"]=='f') :
params_json["hloc"]["two body"]["F4"]=imp['f4']
if (params_json["basis"]["orbitals"]=='f') :
params_json["hloc"]["two body"]["F6"]=imp['f6']
if imp["coulomb"]=="full":
params_json["hloc"]["two body"]["approximation"]="none"
elif imp["coulomb"]=="ising":
params_json["hloc"]["two body"]["approximation"]="ising"
# params_json["hloc"]["quantum numbers"]={}
# params_json["hloc"]["quantum numbers"]["N"]={}
# if (control['spin_orbit']):
# params_json["hloc"]["quantum numbers"]["Jz"]={}
# else:
# params_json["hloc"]["quantum numbers"]["Sz"]={}
# hybridization
params_json["hybridisation"]={}
params_json["hybridisation"]["matrix"]=equivalence_key
params_json["hybridisation"]["functions"]="hyb.json"
# measurement time
params_json["measurement time"]=imp['measurement_time']
# mu
params_json["mu"]=mu_ctqmc
# occupation susceptibility direct
params_json["occupation susceptibility direct"]=True
# thermalisation time
params_json["thermalisation time"]=imp['thermalization_time']
if (control['method']=='lqsgw+dmft'):
params_json["dyn"]={}
params_json["dyn"]['functions']="dyn.json"
params_json["dyn"]['matrix']=[['1']]
params_json["dyn"]['quantum numbers']=[[1]*len(equivalence_key)]
params_json['partition']={}
params_json['partition']["green bulla"]=True
params_json['partition']["green matsubara cutoff"]=imp['green_cutoff']
params_json['partition']["observables"]={}
params_json['partition']["probabilities"]={}
params_json['partition']["quantum numbers"]={}
if (control['spin_orbit']):
params_json['partition']["observables"]["J2"]={}
params_json['partition']["probabilities"]=["N", "energy", "J2", "Jz"]
params_json['partition']["quantum numbers"]["Jz"]={}
else:
params_json['partition']["observables"]["S2"]={}
params_json['partition']["probabilities"]=["N", "energy", "S2", "Sz"]
params_json['partition']["quantum numbers"]["Sz"]={}
params_json['partition']["occupation susceptibility bulla"]=True
params_json['partition']["print density matrix"]=True
params_json['partition']["print eigenstates"]=True
params_json['partition']["density matrix precise"]=True
params_json['partition']["quantum number susceptibility"]=True
params_json['partition']["susceptibility cutoff"]=imp['susceptibility_cutoff']
params_json['partition']["susceptibility tail"]=imp['susceptibility_tail']
for key, value in params_json.items():
print(key, value, type(value))
print("prepare_ctqmc:e_imp_done", file=control['h_log'],flush=True)
with open('params.json','w') as outfile:
json.dump(params_json,outfile, sort_keys=True, indent=4, separators=(',', ': '))
print("params.json written", file=control['h_log'],flush=True)
return None
def write_dynamical_f0_json(imp):
dyn_dict={}
dyn_dict['1']=imp['dynamical_f0'].tolist()
with open('dyn.json','w') as outfile:
json.dump(dyn_dict,outfile,sort_keys=True, indent=4, separators=(',', ': '))
print("DynF0.json written" , file=control['h_log'],flush=True)
# os.chdir(control['top_dir'])
return None
# def atom_run_patrick(control, imp):
# # prob_ind=control['impurity_problem_equivalence'].index(int(key))
# # nimp_orb=len(control['impurity_wan'][prob_ind])
# if control['spin_orbit']:
# if imp['problem']=='f':
# atom_exe = control['comsuitedir'] + '/GA_F'
# else:
# if imp['problem']=='d':
# atom_exe = control['comsuitedir'] + '/GA_D'
# # run_string=atom_exe+' params'
# run_string='aprun -n 1 '+atom_exe+' params'
# cmd = run_string
# print(cmd, file=control['h_log'],flush=True)
# with open('./atom.out', 'w') as logfile:
# ret = subprocess.call(cmd,shell=True, stdout=logfile, stderr=logfile)
# if ret != 0:
# print("Error in atom. Check atom.out for error message.", file=control['h_log'],flush=True)
# sys.exit()
# print("prepare_ctqmc:atom done", file=control['h_log'],flush=True)
# if (control['method']=='lqsgw+dmft'):
# iter_string='_'+str(control['iter_num_impurity'])
# elif (control['method']=='lda+dmft'):
# iter_string='_'+str(control['iter_num_outer'])+'_'+str(control['iter_num_impurity'])
# shutil.copy("./atom.out", "./atom"+iter_string+'.log')
# return None
def write_conv_dft(control):
os.chdir(control['lattice_directory'])
iter_string='_'+str(control['iter_num_outer'])
f=open('./convergence.log')
cnt=0
for line in f:
temp=line.split()
if (len(temp)==4):
if temp[2]=='self-consistency=':
cnt=cnt+1
delta_rho=float(temp[3])
control['conv_table'].append(['dft',control['iter_num_outer'],cnt,'', '', delta_rho, '','','','','','',''])
with open(control['top_dir']+'/convergence.log', 'w') as outputfile:
outputfile.write(tabulate(control['conv_table'], headers=control['convergence_header'], numalign="right", floatfmt=".5f"))
f.close()
os.chdir(control['top_dir'])
return None
def write_conv_coulomb(control,imp):
os.chdir(control['coulomb_directory'])
for ii in sorted(set(control['impurity_problem_equivalence'])):
if (ii>0):
control['conv_table'].append(['coulomb_'+str(ii),'', '', str(imp[str(ii)]['dynamical_f0'][0]+imp[str(ii)]['f0']), '','','','','','',''])
with open(control['top_dir']+'/convergence.log', 'w') as outputfile:
outputfile.write(tabulate(control['conv_table'], headers=control['convergence_header'], numalign="right", floatfmt=".5f"))
os.chdir(control['top_dir'])
return None
def write_conv_wan(control):
iter_string='_'+str(control['iter_num_outer'])
os.chdir(control['wannier_directory'])
f=open('./wannier'+iter_string+'.wout')
pp1=re.compile('Final State')
cnt=0
startline=0
for line in f:
mm1=pp1.search(line)
if mm1:
startline=cnt
cnt=cnt+1 # start from 0
f.close()
f=open('./wannier'+iter_string+'.wout')
lines=f.readlines()
spmin=10000000.0
spmax=0.0
num_wann=np.shape(wan_hmat['basis'])[0]
wan_info=np.zeros((4,num_wann), order='F')
cnt=0
for ii in range(startline+1,startline+num_wann+1):
wan_info[3,cnt]=float(lines[ii].split()[-1])
temp1=lines[ii].split('(')[1]
temp2=temp1.split(')')[0]
# wan_info[:3,cnt]=[float(x) for x in temp2.split(',')]
wan_info[:3,cnt]=list(map(float,temp2.split(',')))
cnt=cnt+1
f.close()
# print wan_info
f=open('./wannier'+iter_string+'.wout')
lines=f.readlines()
spmax=np.amax(wan_info[3,:])
spmin=np.amin(wan_info[3,:])
if (control['method']=='lda+dmft'):
control['conv_table'].append(['wannier',control['iter_num_outer'],'','','','', spmin,spmax,'','','','','',''])
with open(control['top_dir']+'/convergence.log', 'w') as outputfile:
outputfile.write(tabulate(control['conv_table'], headers=control['convergence_header'], numalign="right", floatfmt=".5f"))
if (control['method']=='lqsgw+dmft'):
control['conv_table'].append(['wannier','','','', spmin,spmax,'','','','','',''])
with open(control['top_dir']+'/convergence.log', 'w') as outputfile:
outputfile.write(tabulate(control['conv_table'], headers=control['convergence_header'], numalign="right", floatfmt=".5f"))
os.chdir(control['top_dir'])
return None
def write_conv_delta(control,delta_causality):
os.chdir(control['lowh_directory'])
ef=float(np.loadtxt('ef.dat'))
if (delta_causality==1):
causality_flag='good'
else:
causality_flag='broken'
if (control['method']=='lda+dmft'):
control['conv_table'].append(['delta',control['iter_num_outer'],'',control['iter_num_impurity'],causality_flag,'','','', ef,'','','','',''])
with open(control['top_dir']+'/convergence.log', 'w') as outputfile:
outputfile.write(tabulate(control['conv_table'], headers=control['convergence_header'], numalign="right", floatfmt=".5f"))
if (control['method']=='lqsgw+dmft'):
control['conv_table'].append(['delta',control['iter_num_impurity'],causality_flag,'','','', ef,'','','','',''])
with open(control['top_dir']+'/convergence.log', 'w') as outputfile:
outputfile.write(tabulate(control['conv_table'], headers=control['convergence_header'], numalign="right", floatfmt=".5f"))
os.chdir(control['top_dir'])
return None
# def write_conv_imp(control,iter_string,iter_num_outer,iter_num_impurity,firstmoment,secondmoment,sig_causality,h_conv,h_log):
# if (sig_causality==1):
# causality_flag='good'
# else:
# causality_flag='broken'
# os.chdir(control['impurity_directory'])
# sig_ave=np.loadtxt('sig'+iter_string+'.dat')
# sig=np.loadtxt('sig'+iter_string+'.dat')
# sig_diff_ave=np.mean(np.absolute((sig_ave[:,1::2]+sig_ave[:,2::2]*1j)-(sig[:,1::2]+sig[:,2::2]*1j)))
# nimp=read_nimp(imp_solver)
# if (control['method']=='lda+dmft'):
# control['h_conv'].write('%1s%10s%10d%10s%10d%10s%10s%10s%10s%10s%10.7f%10.5f%10.3f%10.3f\n'%('','impurity',iter_num_outer,'',iter_num_impurity,causality_flag,'','','','',sig_diff_ave,nimp,firstmoment,secondmoment))
# elif (control['method']=='lqsgw+dmft'):
# control['h_conv'].write('%1s%10s%10d%10s%10s%10.7f%10.5f%10.3f%10.3f\n'%('','impurity',iter_num_impurity,causality_flag,'',sig_diff_ave,nimp,firstmoment,secondmoment))
# os.chdir(control['top_dir'])
# return None
# def read_nimp(imp_solver):
# # if imp_solver['solver']=='ctqmc_patrick':
# nimp=np.loadtxt('N.dat')
# # else:
# # f=open('sig.dat', 'r')
# # nimp=float((f.readline().split('=')[1]).split()[0])
# # f.close()
# return nimp
def check_wannier_function_input(control,wan_hmat):
os.chdir(control['wannier_directory'])
create_comwann_ini(control, wan_hmat)
if ('local_axis' in wan_hmat):
# print('local_axis',file=control['h_log'],flush=True)
natom=len(json.load(open(control['initial_lattice_dir']+'/crystal_structure.json'))['sites'])
global_xaxis=[1.0, 0.0, 0.0]
global_zaxis=[0.0, 0.0, 1.0]
f=open('local_axis.dat', 'w')
for ii in range(1,natom+1):
if ii in wan_hmat['local_axis']:
f.write('%3d %20.12f %20.12f %20.12f %20.12f %20.12f %20.12f\n' %(ii, wan_hmat['local_axis'][ii]['x'][0], wan_hmat['local_axis'][ii]['x'][1], wan_hmat['local_axis'][ii]['x'][2], wan_hmat['local_axis'][ii]['z'][0], wan_hmat['local_axis'][ii]['z'][1], wan_hmat['local_axis'][ii]['z'][2]))
# print('%3d %20.12f %20.12f %20.12f %20.12f %20.12f %20.12f\n' %(ii, wan_hmat['local_axis'][ii]['x'][0], wan_hmat['local_axis'][ii]['x'][1], wan_hmat['local_axis'][ii]['x'][2], wan_hmat['local_axis'][ii]['z'][0], wan_hmat['local_axis'][ii]['z'][1], wan_hmat['local_axis'][ii]['z'][2]),file=control['h_log'],flush=True)
else:
f.write('%3d %20.12f %20.12f %20.12f %20.12f %20.12f %20.12f\n' %(ii, global_xaxis[0], global_xaxis[1], global_xaxis[2], global_zaxis[0], global_zaxis[1], global_zaxis[2]))
# print('%3d %20.12f %20.12f %20.12f %20.12f %20.12f %20.12f\n' %(ii, global_xaxis[0], global_xaxis[1], global_xaxis[2], global_zaxis[0], global_zaxis[1], global_zaxis[2]),file=control['h_log'],flush=True)
f.close()
return None
# def create_local_axis(control,wan_hmat):
# os.chdir(control['top_dir'])
# return None
def check_coulomb_input(control):
os.chdir(control['coulomb_directory'])
create_comcoulomb_ini(control)
os.chdir(control['top_dir'])
return None
def run_dft(control):
print('-----------------------', file = sys.stdout, flush=True)
print('run FlapwMBPT', file = sys.stdout, flush=True)
print('-----------------------', file = sys.stdout, flush=True)
print('-----------------------', file = sys.stderr, flush=True)
print('run FlapwMBPT', file = sys.stderr, flush=True)
print('-----------------------', file = sys.stderr, flush=True)
os.chdir(control['lattice_directory'])
iter_string='_'+str(control['iter_num_outer'])
run_string=control['mpi_prefix_lattice']+' '+control['comsuitedir']+"/rspflapw.exe"
cmd = run_string
# with open(control['lattice_directory']+'/flapwmbpt.out', 'w') as logfile, open(control['lattice_directory']+'/flapwmbpt.err', 'w') as errfile:
# ret = subprocess.call(cmd, shell=True,stdout = logfile, stderr = errfile)x
ret = subprocess.call(cmd, shell=True)
if ret != 0:
print("Error in dft. Check standard error file for error message.", file=control['h_log'],flush=True)
sys.exit()
allfile=control['allfile']
labeling_file('./'+allfile+'.out',iter_string)
# shutil.move('./dft.out', './dft'+iter_string+'.out')
print("dft calculation done", file=control['h_log'],flush=True)
os.chdir(control['top_dir'])
return None
# def get_param_from_ini(param,stringstart,stringend,val_length,control):
# f=open('ini', 'r')
# pp=re.compile(param)
# cnt=0
# for line in f:
# mm=pp.search(line)
# if mm:
# cnt=cnt+1
# returnval=line[stringend:(stringend+val_length)]
# if (cnt !=0):
# return returnval.strip()
# else:
# print('couldn\'t find ', param, file=control['h_log'],flush=True)
# quit()
# def modify_chemical_potential_ubi(ef,h_log):
# allfile=get_param_from_ini('allfile',1,10,72,control)
# allfile_out=string_addwhitespace(allfile, 72)
# ef_old, ef_new=overwrite_rst.add_chemical_potential(allfile, 'dft', ef)
# print('update, ef in dft', ef_old, ef_new, file=control['h_log'],flush=True)
# return None
def prepare_dft_input(control):
os.chdir(control['lattice_directory'])
shutil.copy(control['lowh_directory']+"/wannier_den_matrix.dat", './')
print("prepare_dft_input done", file=control['h_log'],flush=True)
os.chdir(control['top_dir'])
return None
# def overwrite_restart_ubi(control):
# f=open(control['allfile']+'.rst')
# f.write('dft'+ ' 0\n')
# f.close()
# def check_nominal_dc_input(h_log):
# check_for_files(control['top_dir']+'/dc/n_imp.dat', h_log)
def cal_nominal_dc(imp,control):
os.chdir(control['dc_directory'])
f=open('dc_mat.dat', 'w')
for ii in sorted(set(control['impurity_problem_equivalence'])):
if (control['spin_orbit']):
if (imp[str(abs(ii))]['problem']=='f'):
nimp_orb=14
uval=imp[str(abs(ii))]['f0']
jval=(imp[str(abs(ii))]['f2']+imp[str(abs(ii))]['f4']+imp[str(abs(ii))]['f6'])/(6435.0/(286+195*0.668+250*0.494)*(1.0+0.668+0.494))
else:
if (imp[str(abs(ii))]['problem']=='f'):
nimp_orb=7
uval=imp[str(abs(ii))]['f0']
jval=(imp[str(abs(ii))]['f2']+imp[str(abs(ii))]['f4']+imp[str(abs(ii))]['f6'])/(6435.0/(286+195*0.668+250*0.494)*(1.0+0.668+0.494))
elif (imp[str(abs(ii))]['problem']=='d'):
nimp_orb=5
uval=imp[str(abs(ii))]['f0']
jval=(imp[str(abs(ii))]['f2']+imp[str(abs(ii))]['f4'])/14.0
elif (imp[str(abs(ii))]['problem']=='p'):
# from https://www.cond-mat.de/events/correl16/manuscripts/eder.pdf
nimp_orb=3
uval=imp[str(abs(ii))]['f0']
jval=imp[str(abs(ii))]['f2']*5.0/25.0
elif (imp[str(abs(ii))]['problem']=='s'):
nimp_orb=1
uval=imp[str(abs(ii))]['f0']
jval=0.0
dcval=(uval*(imp[str(abs(ii))]['nominal_n']-0.5)-jval*(imp[str(abs(ii))]['nominal_n']-1)*0.5)
dcmat=np.identity(nimp_orb)*dcval
for jj in range(nimp_orb):
for kk in range(nimp_orb):
f.write(str(dcmat[jj,kk])+' 0.0 ')
f.write('\n')
f.close()
os.chdir(control['top_dir'])
return None
def prepare_seed_dc_sig_and_wannier_dat(control,wan_hmat,imp):
os.chdir(control['lowh_directory'])
generate_comlowh_ini(control,wan_hmat,imp,1)
natom=len(control['impurity_wan'])
nimp_orb=0
for ii in sorted(set(control['impurity_problem_equivalence'])):
nimp_orb=nimp_orb+len(set(list(chain.from_iterable(imp[str(abs(ii))]['impurity_matrix'])))-{0})
np.savetxt('dc.dat', np.zeros((1,nimp_orb*2)))
aa=np.zeros((control['n_omega'],nimp_orb*2))
bb=np.zeros((control['n_omega'],1))
bb[:,0]=control['omega']
np.savetxt('sig.dat',np.hstack((bb,aa)), header=' ')
shutil.copy(control['wannier_directory']+"/wannier.dat", './')
# make sig.dat
os.chdir(control['top_dir'])
return None
# def impurity_equivalence(control,imp):
# imp_equivalence={}
# num_atom=len(control['impurity_problem_equivalence'])
# num_orb=zeros(num_atom, dtype=integer)
# for ii in range(num_atom):
# num_orb[ii]=len(control['impurity_wan'][ii])
# iac=imp['impurity_atom_equivalence']
# if (np.amin(iac) <0):
# n_iac=np.amax(iac)*2
# n_iac_nm=np.amax(iac)
# n_iac_mat=n_iac+1
# n_iac_mat_i=-n_iac_nm
# n_iac_mat_f=n_iac_nm
# is_magnetic=1
# else:
# n_iac=np.amax(iac)
# n_iac_nm=np.amax(iac)
# n_iac_mat=n_iac
# n_iac_mat_i=1
# n_iac_mat_f=n_iac_nm
# is_magnetic=0
# num_orb_max=np.amax(num_orb)
# ndeg_iac=zeros(n_iac_mat_f-n_iac_mat_i+1, dtype=integer)
# norb_iac=zeros(n_iac_mat_f-n_iac_mat_i+1, dtype=integer)
# ioac=zeros((num_orb_max,num_orb_max,n_iac_mat_f-n_iac_mat_i+1), dtype=integer)
# n_ioac=np.amax(ioac)
# iiiio=zeros((n_ioac,n_iac_mat_f-n_iac_mat_i+1), dtype=integer)
# iio_diagonal=zeros((n_ioac,n_iac_mat_f-n_iac_mat_i+1), dtype=integer)
# ndeg_ioac=zeros((n_ioac,n_iac_mat_f-n_iac_mat_i+1), dtype=integer)
# ndeg_itot=zeros((n_ioac,n_iac_mat_f-n_iac_mat_i+1), dtype=integer)
# ndeg_ioac_max=np.amax(ndeg_ioac)
# for iatom in range(num_atom):
# norb_iac[iac[iatom]-n_iac_mat_i]=num_orb[iatom]
# ndeg_iac[iac[iatom]-n_iac_mat_i]=ndeg_iac[iac[iatom]-n_iac_mat_i]+1
# for ii in (n_iac_mat_i, n_iac_mat_f):
# if ((is_magnetic .eq. 1) .and. (ii .eq. 0)) cycle
# do iorb=1, norb_iac(ii)
# read(10,*) (ioac(iorb,jorb,ii),
# $ jorb=1, norb_iac(ii))
# enddo
# enddo
def generate_comlowh_ini(control,wan_hmat,imp,is_recal_ef):
f=open('comlowh.ini', 'w')
f.write('1\n')
natom=len(control['impurity_wan'])
# nimp_orb=np.shape(control['impurity_wan'])[1]
nimp_orb=np.zeros(natom, dtype=int)
for ii in range(natom):
nimp_orb[ii]=len(control['impurity_wan'][ii])
f.write(str(natom)+'\n')
f.write(' '.join(map(str,nimp_orb))+'\n')
f.write(' '.join(map(str,control['impurity_problem_equivalence']))+'\n')
for ii in sorted(set(control['impurity_problem_equivalence'])):
prob_ind=control['impurity_problem_equivalence'].index(ii)
nimp_orb=len(control['impurity_wan'][prob_ind])
for jj in range(nimp_orb):
f.write(' '.join(map(str,imp[str(abs(ii))]['impurity_matrix'][jj]))+'\n')
for iatom in range(natom):
f.write(' '.join(map(str,control['impurity_wan'][iatom]))+' ')
f.write('\n')
f.write(str(control['proj_win_min'])+' '+str(control['proj_win_max'])+'\n')
n_omega=control['n_omega']
f.write(str(n_omega)+'\n')
f.write('0.0\n')
f.write('0.0\n')
f.write(str(imp['beta'])+'\n')
f.write(str(control['doping'])+'\n')
if is_recal_ef:
f.write('1\n')
else:
f.write('0\n')
f.write('bnd\n')
if (control['spin_orbit']):
f.write('1\n')
else:
f.write('0\n')
# if (control['update_mu_dmft_scf']):
# f.write('1\n')
# else:
# f.write('0\n')
f.write(' '.join(map(str,wan_hmat['kgrid']))+'\n')
f.close()
return None
def prepare_dc(control,wan_hmat,imp):
if ('dc_mat_to_read' not in control):
if (control['method']=='lqsgw+dmft'):
if (control['dc_mode'] == 'dc_at_gw'):
gloc_mat=read_impurity_mat_dynamic(control,control['lowh_directory']+'/g_loc_mat.dat')
elif (control['dc_mode'] == 'dc_scf'):
gloc_mat=generate_mat_from_array_impurity_dynamic(control,imp, control['impurity_directory']+'/gimp.dat')
trans_basis=read_impurity_mat_static(control,control['lowh_directory']+'/trans_basis.dat')
print(trans_basis)
for key, value in imp.items(): # for the ordered phase this part should be fixed
if (not (isinstance(imp[key], dict))):
continue
nimp_orb=len(imp[key]['impurity_matrix'])
os.chdir(control['dc_directory']+'/'+key)
f=open('comdc.ini', 'w')
f.write(str(nimp_orb)+'\n')
if (control['spin_orbit']):
f.write('1\n')
else:
f.write('0\n')
f.write('0\n')
f.close()
f=open('g_loc.dat', 'w')
for ii in range(control['n_omega']):
f.write(str(control['omega'][ii])+' '+' '.join(map("{:.12f}".format, np.reshape(np.stack(( | np.real(gloc_mat[key][ii,:,:]) | numpy.real |
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