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source: trunk/GSASIIspc.py @ 3136

Last change on this file since 3136 was 3136, checked in by vondreele, 6 years ago
make GSAS-II python 3.6 compliant & preserve python 2.7 use;changes: do from future import division, print_function for all GSAS-II py sources all menu items revised to be py 2.7/3.6 compliant all wx.OPEN --> wx.FD_OPEN in file dialogs all integer divides (typically for image pixel math) made explicit with ; ambiguous ones made floats as appropriate all print "stuff" --> print (stuff) all print >> pFile,'stuff' --> pFile.writeCIFtemplate('stuff') all read file opens made explicit 'r' or 'rb' all cPickle imports made for py2.7 or 3.6 as cPickle or _pickle; test for '2' platform.version_tuple[0] for py 2.7 define cPickleload to select load(fp) or load(fp,encoding='latin-1') for loading gpx files; provides cross compatibility between py 2.7/3.6 gpx files make dict.keys() as explicit list(dict.keys()) as needed (NB: possible source of remaining py3.6 bugs) make zip(a,b) as explicit list(zip(a,b)) as needed (NB: possible source of remaining py3.6 bugs) select unichr/chr according test for '2' platform.version_tuple[0] for py 2.7 (G2pwdGUI * G2plot) for special characters select wg.EVT_GRID_CELL_CHANGE (classic) or wg.EVT_GRID_CELL_CHANGED (phoenix) in grid Bind maxint --> maxsize; used in random number stuff raise Exception,"stuff" --> raise Exception("stuff") wx 'classic' sizer.DeleteWindows?() or 'phoenix' sizer.Clear(True) wx 'classic' SetToolTipString?(text) or 'phoenix' SetToolTip?(wx.ToolTip?(text)); define SetToolTipString?(self,text) to handle the choice in plots status.SetFields? --> status.SetStatusText? 'classic' AddSimpleTool? or 'phoenix' self.AddTool? for plot toolbar; Bind different as well define GetItemPydata? as it doesn't exist in wx 'phoenix' allow python versions 2.7 & 3.6 to run GSAS-II Bind override commented out - no logging capability (NB: remove all logging code?) all import ContentsValidator? open filename & test if valid then close; filepointer removed from Reader binary importers (mostly images) test for 'byte' type & convert as needed to satisfy py 3.6 str/byte rules
Property svn:eol-style set to `native` Property svn:keywords set to `Date Author Revision URL Id`
File size: 172.6 KB

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1	# -- coding: utf-8 --
2	"""
3	GSASIIspc: Space group module
4	-------------------------------
5
6	Space group interpretation routines. Note that space group information is
7	stored in a :ref:`Space Group (SGData)<SGData_table>` object.
8
9	"""
10	########### SVN repository information ###################
11	# $Date: 2017-10-23 16:39:16 +0000 (Mon, 23 Oct 2017) $
12	# $Author: vondreele $
13	# $Revision: 3136 $
14	# $URL: trunk/GSASIIspc.py $
15	# $Id: GSASIIspc.py 3136 2017-10-23 16:39:16Z vondreele $
16	########### SVN repository information ###################
17	import numpy as np
18	import numpy.linalg as nl
19	import scipy.optimize as so
20	import sys
21	import copy
22	import os.path as ospath
23
24	import GSASIIpath
25	GSASIIpath.SetVersionNumber("$Revision: 3136 $")
26
27	npsind = lambda x: np.sin(x*np.pi/180.)
28	npcosd = lambda x: np.cos(x*np.pi/180.)
29	DEBUG = False
30
31	################################################################################
32	#### Space group codes
33	################################################################################
34
35	def SpcGroup(SGSymbol):
36	"""
37	Determines cell and symmetry information from a short H-M space group name
38
39	:param SGSymbol: space group symbol (string) with spaces between axial fields
40	:returns: (SGError,SGData)
41
42	* SGError = 0 for no errors; >0 for errors (see SGErrors below for details)
43	* SGData - is a dict (see :ref:`Space Group object<SGData_table>`) with entries:
44
45	* 'SpGrp': space group symbol, slightly cleaned up
46	* 'SGLaue': one of '-1', '2/m', 'mmm', '4/m', '4/mmm', '3R',
47	'3mR', '3', '3m1', '31m', '6/m', '6/mmm', 'm3', 'm3m'
48	* 'SGInv': boolean; True if centrosymmetric, False if not
49	* 'SGLatt': one of 'P', 'A', 'B', 'C', 'I', 'F', 'R'
50	* 'SGUniq': one of 'a', 'b', 'c' if monoclinic, '' otherwise
51	* 'SGCen': cell centering vectors [0,0,0] at least
52	* 'SGOps': symmetry operations as [M,T] so that M*x+T = x'
53	* 'SGSys': one of 'triclinic', 'monoclinic', 'orthorhombic',
54	'tetragonal', 'rhombohedral', 'trigonal', 'hexagonal', 'cubic'
55	* 'SGPolax': one of ' ', 'x', 'y', 'x y', 'z', 'x z', 'y z',
56	'xyz', '111' for arbitrary axes
57	* 'SGPtGrp': one of 32 point group symbols (with some permutations), which
58	is filled by SGPtGroup, is external (KE) part of supersymmetry point group
59	* 'SSGKl': default internal (Kl) part of supersymmetry point group; modified
60	in supersymmetry stuff depending on chosen modulation vector for Mono & Ortho
61
62	"""
63	LaueSym = ('-1','2/m','mmm','4/m','4/mmm','3R','3mR','3','3m1','31m','6/m','6/mmm','m3','m3m')
64	LattSym = ('P','A','B','C','I','F','R')
65	UniqSym = ('','','a','b','c','',)
66	SysSym = ('triclinic','monoclinic','orthorhombic','tetragonal','rhombohedral','trigonal','hexagonal','cubic')
67	SGData = {}
68	if ':R' in SGSymbol:
69	SGSymbol = SGSymbol.replace(':',' ') #get rid of ':' in R space group symbols from some cif files
70	SGSymbol = SGSymbol.split(':')[0] #remove :1/2 setting symbol from some cif files
71	import pyspg
72	SGInfo = pyspg.sgforpy(SGSymbol)
73	SGData['SpGrp'] = SGSymbol.strip().lower().capitalize()
74	SGData['SGLaue'] = LaueSym[SGInfo[0]-1]
75	SGData['SGInv'] = bool(SGInfo[1])
76	SGData['SGLatt'] = LattSym[SGInfo[2]-1]
77	SGData['SGUniq'] = UniqSym[SGInfo[3]+1]
78	if SGData['SGLatt'] == 'P':
79	SGData['SGCen'] = np.array(([0,0,0],))
80	elif SGData['SGLatt'] == 'A':
81	SGData['SGCen'] = np.array(([0,0,0],[0,.5,.5]))
82	elif SGData['SGLatt'] == 'B':
83	SGData['SGCen'] = np.array(([0,0,0],[.5,0,.5]))
84	elif SGData['SGLatt'] == 'C':
85	SGData['SGCen'] = np.array(([0,0,0],[.5,.5,0,]))
86	elif SGData['SGLatt'] == 'I':
87	SGData['SGCen'] = np.array(([0,0,0],[.5,.5,.5]))
88	elif SGData['SGLatt'] == 'F':
89	SGData['SGCen'] = np.array(([0,0,0],[0,.5,.5],[.5,0,.5],[.5,.5,0,]))
90	elif SGData['SGLatt'] == 'R':
91	SGData['SGCen'] = np.array(([0,0,0],[1./3.,2./3.,2./3.],[2./3.,1./3.,1./3.]))
92	SGData['SGOps'] = []
93	SGData['SGGen'] = []
94	SGData['SGSpin'] = []
95	for i in range(SGInfo[5]):
96	Mat = np.array(SGInfo[6][i])
97	Trns = np.array(SGInfo[7][i])
98	SGData['SGOps'].append([Mat,Trns])
99	if 'array' in str(type(SGInfo[8])): #patch for old fortran bin?
100	SGData['SGGen'].append(int(SGInfo[8][i]))
101	SGData['SGSpin'].append(1)
102	if SGData['SGLaue'] == '2/m' and SGData['SGLatt'] != 'P' and '/' in SGData['SpGrp']:
103	SGData['SGSpin'].append(1) #fix bug in fortran
104	if 'F' in SGData['SpGrp']:
105	SGData['SGSpin'] += [1,1,1,1]
106	elif 'R' in SGData['SpGrp']:
107	SGData['SGSpin'] += [1,1,1]
108	elif SGData['SpGrp'][0] in ['A','B','C','I']:
109	SGData['SGSpin'] += [1,]
110	if SGData['SGInv']:
111	if SGData['SGLaue'] in ['-1','2/m','mmm']:
112	Ibar = 7
113	elif SGData['SGLaue'] in ['4/m','4/mmm']:
114	Ibar = 1
115	elif SGData['SGLaue'] in ['3R','3mR','3','3m1','31m','6/m','6/mmm']:
116	Ibar = 15 #8+4+2+1
117	else:
118	Ibar = 4
119	Ibarx = Ibar&14
120	else:
121	Ibarx = 8
122	if SGData['SGLaue'] in ['-1','2/m','mmm','m3','m3m']:
123	Ibarx = 0
124	moregen = []
125	for i,gen in enumerate(SGData['SGGen']):
126	if SGData['SGLaue'] in ['m3','m3m']:
127	if gen in [1,2,4]:
128	SGData['SGGen'][i] = 4
129	elif gen < 7:
130	SGData['SGGen'][i] = 0
131	elif SGData['SGLaue'] in ['4/m','4/mmm','3R','3mR','3','3m1','31m','6/m','6/mmm']:
132	if gen == 2:
133	SGData['SGGen'][i] = 4
134	elif gen in [3,5]:
135	SGData['SGGen'][i] = 3
136	elif gen == 6:
137	if SGData['SGLaue'] in ['4/m','4/mmm']:
138	SGData['SGGen'][i] = 128
139	else:
140	SGData['SGGen'][i] = 16
141	elif not SGData['SGInv'] and gen == 12:
142	SGData['SGGen'][i] = 8
143	elif (not SGData['SGInv']) and (SGData['SGLaue'] in ['3','3m1','31m','6/m','6/mmm']) and (gen == 1):
144	SGData['SGGen'][i] = 24
145	gen = SGData['SGGen'][i]
146	if gen == 99:
147	gen = 8
148	if SGData['SGLaue'] in ['3m1','31m','6/m','6/mmm']:
149	gen = 3
150	elif SGData['SGLaue'] == 'm3m':
151	gen = 12
152	SGData['SGGen'][i] = gen
153	elif gen == 98:
154	gen = 8
155	if SGData['SGLaue'] in ['3m1','31m','6/m','6/mmm']:
156	gen = 4
157	SGData['SGGen'][i] = gen
158	elif not SGData['SGInv'] and gen in [23,] and SGData['SGLaue'] in ['m3','m3m']:
159	SGData['SGGen'][i] = 24
160	elif gen >= 16 and gen != 128:
161	if not SGData['SGInv']:
162	gen = 31
163	else:
164	gen ^= Ibarx
165	SGData['SGGen'][i] = gen
166	if SGData['SGInv']:
167	if gen < 128:
168	moregen.append(SGData['SGGen'][i]^Ibar)
169	else:
170	moregen.append(1)
171	SGData['SGGen'] += moregen
172	# GSASIIpath.IPyBreak()
173	if SGData['SGLaue'] in '-1':
174	SGData['SGSys'] = SysSym[0]
175	elif SGData['SGLaue'] in '2/m':
176	SGData['SGSys'] = SysSym[1]
177	elif SGData['SGLaue'] in 'mmm':
178	SGData['SGSys'] = SysSym[2]
179	elif SGData['SGLaue'] in ['4/m','4/mmm']:
180	SGData['SGSys'] = SysSym[3]
181	elif SGData['SGLaue'] in ['3R','3mR']:
182	SGData['SGSys'] = SysSym[4]
183	elif SGData['SGLaue'] in ['3','3m1','31m']:
184	SGData['SGSys'] = SysSym[5]
185	elif SGData['SGLaue'] in ['6/m','6/mmm']:
186	SGData['SGSys'] = SysSym[6]
187	elif SGData['SGLaue'] in ['m3','m3m']:
188	SGData['SGSys'] = SysSym[7]
189	SGData['SGPolax'] = SGpolar(SGData)
190	SGData['SGPtGrp'],SGData['SSGKl'] = SGPtGroup(SGData)
191	return SGInfo[-1],SGData
192
193	def SGErrors(IErr):
194	'''
195	Interprets the error message code from SpcGroup. Used in SpaceGroup.
196
197	:param IErr: see SGError in :func:`SpcGroup`
198	:returns:
199	ErrString - a string with the error message or "Unknown error"
200	'''
201
202	ErrString = [' ',
203	'Less than 2 operator fields were found',
204	'Illegal Lattice type, not P, A, B, C, I, F or R',
205	'Rhombohedral lattice requires a 3-axis',
206	'Minus sign does not preceed 1, 2, 3, 4 or 6',
207	'Either a 5-axis anywhere or a 3-axis in field not allowed',
208	' ',
209	'I for COMPUTED GO TO out of range.',
210	'An a-glide mirror normal to A not allowed',
211	'A b-glide mirror normal to B not allowed',
212	'A c-glide mirror normal to C not allowed',
213	'D-glide in a primitive lattice not allowed',
214	'A 4-axis not allowed in the 2nd operator field',
215	'A 6-axis not allowed in the 2nd operator field',
216	'More than 24 matrices needed to define group',
217	' ',
218	'Improper construction of a rotation operator',
219	'Mirror following a / not allowed',
220	'A translation conflict between operators',
221	'The 2bar operator is not allowed',
222	'3 fields are legal only in R & m3 cubic groups',
223	'Syntax error. Expected I -4 3 d at this point',
224	' ',
225	'A or B centered tetragonal not allowed',
226	' ','unknown error in sgroup',' ',' ',' ',
227	'Illegal character in the space group symbol',
228	]
229	try:
230	return ErrString[IErr]
231	except:
232	return "Unknown error"
233
234	def SGpolar(SGData):
235	'''
236	Determine identity of polar axes if any
237	'''
238	POL = ('','x','y','x y','z','x z','y z','xyz','111')
239	NP = [1,2,4]
240	NPZ = [0,1]
241	for M,T in SGData['SGOps']:
242	for i in range(3):
243	if M[i][i] <= 0.: NP[i] = 0
244	if M[0][2] > 0: NPZ[0] = 8
245	if M[1][2] > 0: NPZ[1] = 0
246	NPol = (NP[0]+NP[1]+NP[2]+NPZ[0]NPZ[1])(1-int(SGData['SGInv']))
247	return POL[NPol]
248
249	def SGPtGroup(SGData):
250	'''
251	Determine point group of the space group - done after space group symbol has
252	been evaluated by SpcGroup. Only short symbols are allowed
253
254	:param SGData: from :func SpcGroup
255	:returns: SSGPtGrp & SSGKl (only defaults for Mono & Ortho)
256	'''
257	Flds = SGData['SpGrp'].split()
258	if len(Flds) < 2:
259	return '',[]
260	if SGData['SGLaue'] == '-1': #triclinic
261	if '-' in Flds[1]:
262	return '-1',[-1,]
263	else:
264	return '1',[1,]
265	elif SGData['SGLaue'] == '2/m': #monoclinic - default for 2D modulation vector
266	if '/' in SGData['SpGrp']:
267	return '2/m',[-1,1]
268	elif '2' in SGData['SpGrp']:
269	return '2',[-1,]
270	else:
271	return 'm',[1,]
272	elif SGData['SGLaue'] == 'mmm': #orthorhombic
273	if SGData['SpGrp'].count('2') == 3:
274	return '222',[-1,-1,-1]
275	elif SGData['SpGrp'].count('2') == 1:
276	if SGData['SGPolax'] == 'x':
277	return '2mm',[-1,1,1]
278	elif SGData['SGPolax'] == 'y':
279	return 'm2m',[1,-1,1]
280	elif SGData['SGPolax'] == 'z':
281	return 'mm2',[1,1,-1]
282	else:
283	return 'mmm',[1,1,1]
284	elif SGData['SGLaue'] == '4/m': #tetragonal
285	if '/' in SGData['SpGrp']:
286	return '4/m',[1,-1]
287	elif '-' in Flds[1]:
288	return '-4',[-1,]
289	else:
290	return '4',[1,]
291	elif SGData['SGLaue'] == '4/mmm':
292	if '/' in SGData['SpGrp']:
293	return '4/mmm',[1,-1,1,1]
294	elif '-' in Flds[1]:
295	if '2' in Flds[2]:
296	return '-42m',[-1,-1,1]
297	else:
298	return '-4m2',[-1,1,-1]
299	elif '2' in Flds[2:]:
300	return '422',[1,-1,-1]
301	else:
302	return '4mm',[1,1,1]
303	elif SGData['SGLaue'] in ['3','3R']: #trigonal/rhombohedral
304	if '-' in Flds[1]:
305	return '-3',[-1,]
306	else:
307	return '3',[1,]
308	elif SGData['SGLaue'] == '3mR' or 'R' in Flds[0]:
309	if '2' in Flds[2]:
310	return '32',[1,-1]
311	elif '-' in Flds[1]:
312	return '-3m',[-1,1]
313	else:
314	return '3m',[1,1]
315	elif SGData['SGLaue'] == '3m1':
316	if '2' in Flds[2]:
317	return '321',[1,-1,1]
318	elif '-' in Flds[1]:
319	return '-3m1',[-1,1,1]
320	else:
321	return '3m1',[1,1,1]
322	elif SGData['SGLaue'] == '31m':
323	if '2' in Flds[3]:
324	return '312',[1,1,-1]
325	elif '-' in Flds[1]:
326	return '-31m',[-1,1,1]
327	else:
328	return '31m',[1,1,1]
329	elif SGData['SGLaue'] == '6/m': #hexagonal
330	if '/' in SGData['SpGrp']:
331	return '6/m',[1,-1]
332	elif '-' in SGData['SpGrp']:
333	return '-6',[-1,]
334	else:
335	return '6',[1,]
336	elif SGData['SGLaue'] == '6/mmm':
337	if '/' in SGData['SpGrp']:
338	return '6/mmm',[1,-1,1,1]
339	elif '-' in Flds[1]:
340	if '2' in Flds[2]:
341	return '-62m',[-1,-1,1]
342	else:
343	return '-6m2',[-1,1,-1]
344	elif '2' in Flds[2:]:
345	return '622',[1,-1,-1]
346	else:
347	return '6mm',[1,1,1]
348	elif SGData['SGLaue'] == 'm3': #cubic - no (3+1) supersymmetry
349	if '2' in Flds[1]:
350	return '23',[]
351	else:
352	return 'm3',[]
353	elif SGData['SGLaue'] == 'm3m':
354	if '4' in Flds[1]:
355	if '-' in Flds[1]:
356	return '-43m',[]
357	else:
358	return '432',[]
359	else:
360	return 'm-3m',[]
361
362	def SGPrint(SGData,AddInv=False):
363	'''
364	Print the output of SpcGroup in a nicely formatted way. Used in SpaceGroup
365
366	:param SGData: from :func:`SpcGroup`
367	:returns:
368	SGText - list of strings with the space group details
369	SGTable - list of strings for each of the operations
370	'''
371	Mult = len(SGData['SGCen'])len(SGData['SGOps'])(int(SGData['SGInv'])+1)
372	SGText = []
373	SGText.append(' Space Group: '+SGData['SpGrp'])
374	CentStr = 'centrosymmetric'
375	if not SGData['SGInv']:
376	CentStr = 'non'+CentStr
377	if SGData['SGLatt'] in 'ABCIFR':
378	SGText.append(' The lattice is '+CentStr+' '+SGData['SGLatt']+'-centered '+SGData['SGSys'].lower())
379	else:
380	SGText.append(' The lattice is '+CentStr+' '+'primitive '+SGData['SGSys'].lower())
381	SGText.append(' The Laue symmetry is '+SGData['SGLaue'])
382	if 'SGPtGrp' in SGData: #patch
383	SGText.append(' The lattice point group is '+SGData['SGPtGrp'])
384	SGText.append(' Multiplicity of a general site is '+str(Mult))
385	if SGData['SGUniq'] in ['a','b','c']:
386	SGText.append(' The unique monoclinic axis is '+SGData['SGUniq'])
387	if SGData['SGInv']:
388	SGText.append(' The inversion center is located at 0,0,0')
389	if SGData['SGPolax']:
390	SGText.append(' The location of the origin is arbitrary in '+SGData['SGPolax'])
391	SGText.append(' ')
392	if SGData['SGLatt'] == 'P':
393	SGText.append(' The equivalent positions are:\n')
394	else:
395	SGText.append(' The equivalent positions are:')
396	SGText.append(' ('+Latt2text(SGData['SGLatt'])+')+\n')
397	SGTable = []
398	for i,Opr in enumerate(SGData['SGOps']):
399	SGTable.append('(%2d) %s'%(i+1,MT2text(Opr)))
400	if AddInv and SGData['SGInv']:
401	for i,Opr in enumerate(SGData['SGOps']):
402	IOpr = [-Opr[0],-Opr[1]]
403	SGTable.append('(%2d) %s'%(i+1,MT2text(IOpr)))
404	return SGText,SGTable
405
406	def AllOps(SGData):
407	'''
408	Returns a list of all operators for a space group, including those for
409	centering and a center of symmetry
410
411	:param SGData: from :func:`SpcGroup`
412	:returns: (SGTextList,offsetList,symOpList,G2oprList) where
413
414	* SGTextList: a list of strings with formatted and normalized
415	symmetry operators.
416	* offsetList: a tuple of (dx,dy,dz) offsets that relate the GSAS-II
417	symmetry operation to the operator in SGTextList and symOpList.
418	these dx (etc.) values are added to the GSAS-II generated
419	positions to provide the positions that are generated
420	by the normalized symmetry operators.
421	* symOpList: a list of tuples with the normalized symmetry
422	operations as (M,T) values
423	(see ``SGOps`` in the :ref:`Space Group object<SGData_table>`)
424	* G2oprList: The GSAS-II operations for each symmetry operation as
425	a tuple with (center,mult,opnum,opcode), where center is (0,0,0), (0.5,0,0),
426	(0.5,0.5,0.5),...; where mult is 1 or -1 for the center of symmetry
427	where opnum is the number for the symmetry operation, in ``SGOps``
428	(starting with 0) and opcode is mult(100icen+j+1).
429	'''
430	SGTextList = []
431	offsetList = []
432	symOpList = []
433	G2oprList = []
434	G2opcodes = []
435	onebar = (1,)
436	if SGData['SGInv']:
437	onebar += (-1,)
438	for icen,cen in enumerate(SGData['SGCen']):
439	for mult in onebar:
440	for j,(M,T) in enumerate(SGData['SGOps']):
441	offset = [0,0,0]
442	Tprime = (mult*T)+cen
443	for i in range(3):
444	while Tprime[i] < 0:
445	Tprime[i] += 1
446	offset[i] += 1
447	while Tprime[i] >= 1:
448	Tprime[i] += -1
449	offset[i] += -1
450	Opr = [mult*M,Tprime]
451	OPtxt = MT2text(Opr)
452	SGTextList.append(OPtxt.replace(' ',''))
453	offsetList.append(tuple(offset))
454	symOpList.append((mult*M,Tprime))
455	G2oprList.append((cen,mult,j))
456	G2opcodes.append(mult(100icen+j+1))
457	return SGTextList,offsetList,symOpList,G2oprList,G2opcodes
458
459	def MT2text(Opr):
460	"From space group matrix/translation operator returns text version"
461	XYZ = ('-Z','-Y','-X','X-Y','ERR','Y-X','X','Y','Z')
462	TRA = (' ','ERR','1/6','1/4','1/3','ERR','1/2','ERR','2/3','3/4','5/6','ERR')
463	Fld = ''
464	M,T = Opr
465	for j in range(3):
466	IJ = int(round(2M[j][0]+3M[j][1]+4*M[j][2]+4))%12
467	IK = int(round(T[j]*12))%12
468	if IK:
469	if IJ < 3:
470	Fld += (TRA[IK]+XYZ[IJ]).rjust(5)
471	else:
472	Fld += (TRA[IK]+'+'+XYZ[IJ]).rjust(5)
473	else:
474	Fld += XYZ[IJ].rjust(5)
475	if j != 2: Fld += ', '
476	return Fld
477
478	def Latt2text(Latt):
479	"From lattice type ('P',A', etc.) returns ';' delimited cell centering vectors"
480	lattTxt = {'A':'0,0,0; 0,1/2,1/2','B':'0,0,0; 1/2,0,1/2',
481	'C':'0,0,0; 1/2,1/2,0','I':'0,0,0; 1/2,1/2,1/2',
482	'F':'0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0',
483	'R':'0,0,0; 1/3,2/3,2/3; 2/3,1/3,1/3','P':'0,0,0'}
484	return lattTxt[Latt]
485
486	def SpaceGroup(SGSymbol):
487	'''
488	Print the output of SpcGroup in a nicely formatted way.
489
490	:param SGSymbol: space group symbol (string) with spaces between axial fields
491	:returns: nothing
492	'''
493	E,A = SpcGroup(SGSymbol)
494	if E > 0:
495	print (SGErrors(E))
496	return
497	for l in SGPrint(A):
498	print (l)
499	################################################################################
500	#### Magnetic space group stuff
501	################################################################################
502
503	def GetGenSym(SGData):
504	'''
505	Get the space group generator symbols
506	:param SGData: from :func:`SpcGroup`
507	LaueSym = ('-1','2/m','mmm','4/m','4/mmm','3R','3mR','3','3m1','31m','6/m','6/mmm','m3','m3m')
508	LattSym = ('P','A','B','C','I','F','R')
509	UniqSym = ('','','a','b','c','',)
510
511	'''
512	OprNames = [GetOprPtrName(str(irtx))[1] for irtx in PackRot(SGData['SGOps'])]
513	if SGData['SGInv']:
514	OprNames += [GetOprPtrName(str(-irtx))[1] for irtx in PackRot(SGData['SGOps'])]
515	Nsyms = len(SGData['SGOps'])
516	if SGData['SGInv']: Nsyms *= 2
517	UsymOp = []
518	OprFlg = []
519	if Nsyms == 2: #Centric triclinic or acentric monoclinic
520	UsymOp.append(OprNames[1])
521	OprFlg.append(SGData['SGGen'][1])
522	elif Nsyms == 4: #Point symmetry 2/m, 222, 22m, or 4
523	if '4z' in OprNames[1]: #Point symmetry 4 or -4
524	UsymOp.append(OprNames[1])
525	OprFlg.append(SGData['SGGen'][1])
526	elif not SGData['SGInv']: #Acentric Orthorhombic
527	if 'm' in OprNames[1:4]: #22m, 2m2 or m22
528	if '2' in OprNames[1]: #Acentric orthorhombic, 2mm
529	UsymOp.append(OprNames[2])
530	OprFlg.append(SGData['SGGen'][2])
531	UsymOp.append(OprNames[3])
532	OprFlg.append(SGData['SGGen'][3])
533	elif '2' in OprNames[2]: #Acentric orthorhombic, m2m
534	UsymOp.append(OprNames[1])
535	OprFlg.append(SGData['SGGen'][1])
536	UsymOp.append(OprNames[3])
537	OprFlg.append(SGData['SGGen'][3])
538	else: #Acentric orthorhombic, mm2
539	UsymOp.append(OprNames[1])
540	OprFlg.append(SGData['SGGen'][1])
541	UsymOp.append(OprNames[2])
542	OprFlg.append(SGData['SGGen'][2])
543	else: #Acentric orthorhombic, 222
544	SGData['SGGen'][1:] = [4,2,1]
545	UsymOp.append(OprNames[1])
546	OprFlg.append(SGData['SGGen'][1])
547	UsymOp.append(OprNames[2])
548	OprFlg.append(SGData['SGGen'][2])
549	UsymOp.append(OprNames[3])
550	OprFlg.append(SGData['SGGen'][3])
551	else: #Centric Monoclinic
552	UsymOp.append(OprNames[1])
553	OprFlg.append(SGData['SGGen'][1])
554	UsymOp.append(OprNames[3])
555	OprFlg.append(SGData['SGGen'][3])
556	elif Nsyms == 6: #Point symmetry 32, 3m or 6
557	if '6' in OprNames[1]: #Hexagonal 6/m Laue symmetry
558	UsymOp.append(OprNames[1])
559	OprFlg.append(SGData['SGGen'][1])
560	else: #Trigonal
561	UsymOp.append(OprNames[4])
562	OprFlg.append(SGData['SGGen'][3])
563	if '2110' in OprNames[1]: UsymOp[-1] = ' 2100 '
564	elif Nsyms == 8: #Point symmetry mmm, 4/m, or 422, etc
565	if '4' in OprNames[1]: #Tetragonal
566	if SGData['SGInv']: #4/m
567	UsymOp.append(OprNames[1])
568	OprFlg.append(SGData['SGGen'][1])
569	UsymOp.append(OprNames[6])
570	OprFlg.append(SGData['SGGen'][6])
571	else:
572	if 'x' in OprNames[4]: #4mm type group
573	UsymOp.append(OprNames[4])
574	OprFlg.append(6)
575	UsymOp.append(OprNames[7])
576	OprFlg.append(8)
577	else: #-42m, -4m2, and 422 type groups
578	UsymOp.append(OprNames[5])
579	OprFlg.append(8)
580	UsymOp.append(OprNames[6])
581	OprFlg.append(19)
582	else: #Orthorhombic, mmm
583	UsymOp.append(OprNames[1])
584	OprFlg.append(SGData['SGGen'][1])
585	UsymOp.append(OprNames[2])
586	OprFlg.append(SGData['SGGen'][2])
587	UsymOp.append(OprNames[7])
588	OprFlg.append(SGData['SGGen'][7])
589	elif Nsyms == 12 and '3' in OprNames[1] and SGData['SGSys'] != 'cubic': #Trigonal
590	UsymOp.append(OprNames[3])
591	OprFlg.append(SGData['SGGen'][3])
592	UsymOp.append(OprNames[9])
593	OprFlg.append(SGData['SGGen'][9])
594	elif Nsyms == 12 and '6' in OprNames[1]: #Hexagonal
595	if 'mz' in OprNames[9]: #6/m
596	UsymOp.append(OprNames[1])
597	OprFlg.append(SGData['SGGen'][1])
598	UsymOp.append(OprNames[6])
599	OprFlg.append(SGData['SGGen'][6])
600	else: #6mm, -62m, -6m2 or 622
601	UsymOp.append(OprNames[6])
602	OprFlg.append(18)
603	if 'm' in UsymOp[-1]: OprFlg[-1] = 20
604	UsymOp.append(OprNames[7])
605	OprFlg.append(24)
606	elif Nsyms in [16,24]:
607	if '3' in OprNames[1]:
608	UsymOp.append('')
609	OprFlg.append(SGData['SGGen'][3])
610	for i in range(Nsyms):
611	if 'mx' in OprNames[i]:
612	UsymOp[-1] = OprNames[i]
613	elif 'm11' in OprNames[i]:
614	UsymOp[-1] = OprNames[i]
615	elif '211' in OprNames[i]:
616	UsymOp[-1] = OprNames[i]
617	OprFlg[-1] = 24
618	else: #4/mmm or 6/mmm
619	UsymOp.append(' mz ')
620	OprFlg.append(1)
621	if '4' in OprNames[1]: #4/mmm
622	UsymOp.append(' mx ')
623	OprFlg.append(20)
624	UsymOp.append(' m110 ')
625	OprFlg.append(24)
626	else: #6/mmm
627	UsymOp.append(' m110 ')
628	OprFlg.append(4)
629	UsymOp.append(' m+-0 ')
630	OprFlg.append(8)
631	else: #System is cubic
632	if Nsyms == 48:
633	UsymOp.append(' mx ')
634	OprFlg.append(4)
635	UsymOp.append(' m110 ')
636	OprFlg.append(24)
637	ncv = len(SGData['SGCen'])
638	if ncv > 1:
639	for icv in range(ncv):
640	if SGData['SpGrp'] in ['F d d 2','F d 2 d','F 2 d d','F d d d']:
641	break
642	if 'F' in SGData['SpGrp'] and SGData['SGSys'] == 'cubic':
643	break
644	if icv:
645	if SGData['SGCen'][icv][0] == 0.5:
646	if SGData['SGCen'][icv][1] == 0.5:
647	if SGData['SGCen'][icv][2] == 0.5:
648	if not SGData['SpGrp'] in ['I 41/a','I 41 m d',
649	'I 41 c d','I -4 2 d','I -4 3 d',
650	'I a 3 d','I a -3 d','I b 3 d','I b -3 d']:
651	UsymOp.append(' Icen ')
652	else:
653	UsymOp.append(' Ccen ')
654	else:
655	UsymOp.append(' Bcen ')
656	elif SGData['SGCen'][icv][1] == 0.5:
657	UsymOp.append(' Acen ')
658	return UsymOp,OprFlg
659
660	def CheckSpin(isym,SGData):
661	''' Check for exceptions in spin rules
662	'''
663	if SGData['SpGrp'] in ['C c','C 1 c 1','A a','A 1 a 1','B b 1 1','C c 1 1',
664	'A 1 1 a','B 1 1 b','I -4']:
665	if SGData['SGSpin'][:2] == [-1,-1]:
666	SGData['SGSpin'][(isym+1)%2] = 1
667	elif SGData['SpGrp'] in ['C 2/c','C 1 2/c 1','A 2/a','A 1 2/a 1','B 2/b 1 1','C 2/c 1 1',
668	'A 1 1 2/a','B 1 1 2/b']:
669	if SGData['SGSpin'][1:3] == [-1,-1]:
670	SGData['SGSpin'][isym%2+1] = 1
671	elif SGData['SGPtGrp'] in ['222','mm2','2mm','m2m']:
672	if SGData['SGSpin'][0]SGData['SGSpin'][1]SGData['SGSpin'][2] < 0:
673	SGData['SGSpin'][(isym+1)%3] *= -1
674	if SGData['SpGrp'][0] == 'F' and isym > 2:
675	SGData['SGSpin'][(isym+1)%3+3] *= -1
676	elif SGData['SGPtGrp'] == 'mmm':
677	if SGData['SpGrp'][0] == 'F' and isym > 2:
678	SGData['SGSpin'][(isym+1)%3+3] *= -1
679	elif SGData['SGSpin'][3] < 0:
680	if SGData['SpGrp'] in ['C m m a','A b m m','B m c m','B m a m','C m m b','A c m m',
681	'C c c a','A b a a','B b c b','B b a b','C c c b','A c a a','I b c a','I c a b']:
682	for i in [0,1,2]:
683	if i != isym and SGData['SGSpin'][i] < 0:
684	SGData['SGSpin'][i] = 1
685	elif SGData['SpGrp'] in ['I m m a','I b m m','I m c m','I m a m','I m m b','I c m m']:
686	if SGData['SGSpin'][0]SGData['SGSpin'][1]SGData['SGSpin'][2] < 0:
687	SGData['SGSpin'][(isym+1)%3] *= -1
688	elif SGData['SpGrp'] in ['I -4 m 2','I -4 c 2']:
689	if SGData['SGSpin'][2] < 0:
690	if 'm' in SGData['SpGrp']:
691	SGData['SGSpin'][1] = 1
692	elif isym < 2:
693	if SGData['SGSpin'][isym] < 0:
694	SGData['SGSpin'][:2] = [-1,-1]
695	else:
696	SGData['SGSpin'][:2] = [1,1]
697	else:
698	SGData['SGSpin'][:2] = [1,1]
699
700	def MagSGSym(SGData):
701	SGLaue = SGData['SGLaue']
702	SpnFlp = SGData['SGSpin']
703	GenSym = SGData['GenSym']
704	if not len(SpnFlp):
705	SGLaue['MagPtGp'] = SGLaue
706	return SGData['SpGrp']
707	magSym = SGData['SpGrp'].split()
708	if SGLaue in ['-1',]:
709	SGData['MagPtGp'] = SGLaue
710	if SpnFlp[0] == -1:
711	magSym[1] += "'"
712	SGData['MagPtGp'] += "'"
713	if magSym[0] in ['A','B','C','I'] and SGData['SpGrp'] != 'I 41/a':
714	if SpnFlp[1] < 0:
715	magSym[0] += '(P)'
716	elif SGLaue in ['mmm',]:
717	SGData['MagPtGp'] = ''
718	for i in [0,1,2]:
719	SGData['MagPtGp'] += 'm'
720	if SpnFlp[i] < 0:
721	magSym[i+1] += "'"
722	SGData['MagPtGp'] += "'"
723	if len(GenSym) > 3:
724	if magSym[0] == 'F':
725	if SpnFlp[3]+SpnFlp[4]+SpnFlp[5] < 0:
726	if SpnFlp[3] > 0:
727	magSym[0] += '(A)'
728	elif SpnFlp[4] > 0:
729	magSym[0] += '(B)'
730	elif SpnFlp[5] > 0:
731	magSym[0] += '(C)'
732	else:
733	if SpnFlp[3] < 0:
734	magSym[0] += '(P)'
735	elif SGLaue == '6/mmm': #ok
736	if len(GenSym) == 2:
737	magPtGp = ['6','m','m']
738	for i in [0,1]:
739	if SpnFlp[i] < 0:
740	magSym[i+2] += "'"
741	magPtGp[i+1] += "'"
742	if SpnFlp[0]*SpnFlp[1] < 0:
743	magSym[1] += "'"
744	magPtGp[0] += "'"
745	else:
746	sym = magSym[1].split('/')
747	Ptsym = ['6','m']
748	magPtGp = ['','m','m']
749	for i in [0,1,2]:
750	if SpnFlp[i] < 0:
751	if i:
752	magSym[i+1] += "'"
753	magPtGp[i] += "'"
754	else:
755	sym[1] += "'"
756	Ptsym[0] += "'"
757	if SpnFlp[1]*SpnFlp[2] < 0:
758	sym[0] += "'"
759	Ptsym[0] += "'"
760	magSym[1] = '/'.join(sym)
761	magPtGp[0] = '/'.join(Ptsym)
762	SGData['MagPtGp'] = ''.join(magPtGp)
763	elif SGLaue == '4/mmm':
764	if len(GenSym) == 2:
765	magPtGp = ['4','m','m']
766	for i in [0,1]:
767	if SpnFlp[i] < 0:
768	magSym[i+2] += "'"
769	magPtGp[i+1] += "'"
770	if SpnFlp[0]*SpnFlp[1] < 0:
771	magSym[1] += "'"
772	magPtGp[0] += "'"
773	else:
774	if '/' in magSym[1]: #P 4/m m m, etc.
775	sym = magSym[1].split('/')
776	Ptsym = ['4','m']
777	magPtGp = ['','m','m']
778	for i in [0,1,2]:
779	if SpnFlp[i] < 0:
780	if i:
781	magSym[i+1] += "'"
782	magPtGp[i] += "'"
783	else:
784	sym[1] += "'"
785	Ptsym[1] += "'"
786	if SpnFlp[1]*SpnFlp[2] < 0:
787	sym[0] += "'"
788	Ptsym[0] += "'"
789	magSym[1] = '/'.join(sym)
790	magPtGp[0] = '/'.join(Ptsym)
791	if SpnFlp[3] < 0:
792	magSym[0] += '(P)'
793	else:
794	for i in [0,1]:
795	if SpnFlp[i] < 0:
796	magSym[i+2] += "'"
797	if SpnFlp[0]*SpnFlp[1] < 0:
798	magSym[1] += "'"
799	if SpnFlp[2] < 0:
800	magSym[0] += '(P)'
801	SGData['MagPtGp'] = ''.join(magPtGp)
802	elif SGLaue in ['2/m','4/m','6/m']: #all ok
803	Uniq = {'a':1,'b':2,'c':3,'':1}
804	id = [0,1]
805	if len(magSym) > 2:
806	id = [0,Uniq[SGData['SGUniq']]]
807	sym = magSym[id[1]].split('/')
808	Ptsym = SGLaue.split('/')
809	if len(GenSym) == 3:
810	for i in [0,1,2]:
811	if SpnFlp[i] < 0:
812	if i == 2:
813	magSym[0] += '(P)'
814	else:
815	sym[i] += "'"
816	Ptsym[i] += "'"
817	else:
818	for i in range(len(GenSym)):
819	if SpnFlp[i] < 0:
820	if i and magSym[0] in ['A','B','C','I'] and SGData['SpGrp'] != 'I 41/a':
821	magSym[0] += '(P)'
822	else:
823	sym[i] += "'"
824	Ptsym[i] += "'"
825	SGData['MagPtGp'] = '/'.join(Ptsym)
826	magSym[id[1]] = '/'.join(sym)
827	elif SGLaue in ['3','3m1','31m']: #ok
828	# GSASIIpath.IPyBreak()
829	Ptsym = list(SGLaue)
830	if len(GenSym) == 1: #all ok
831	id = 2
832	if (len(magSym) == 4) and (magSym[2] == '1'):
833	id = 3
834	if '3' in GenSym[0]:
835	id = 1
836	magSym[id].strip("'")
837	if SpnFlp[0] < 0:
838	magSym[id] += "'"
839	Ptsym[id-1] += "'"
840	elif len(GenSym) == 2:
841	if 'R' in GenSym[1]:
842	magSym[-1].strip("'")
843	if SpnFlp[0] < 0:
844	magSym[-1] += "'"
845	Ptsym[-1] += "'"
846	else:
847	i,j = [1,2]
848	if magSym[2] == '1':
849	i,j = [1,3]
850	magSym[i].strip("'")
851	Ptsym[i-1].strip("'")
852	magSym[j].strip("'")
853	Ptsym[j-1].strip("'")
854	if SpnFlp[:2] == [1,-1]:
855	magSym[i] += "'"
856	Ptsym[i-1] += "'"
857	elif SpnFlp[:2] == [-1,-1]:
858	magSym[j] += "'"
859	Ptsym[j-1] += "'"
860	elif SpnFlp[:2] == [-1,1]:
861	magSym[i] += "'"
862	Ptsym[i-1] += "'"
863	magSym[j] += "'"
864	Ptsym[j-1] += "'"
865	else:
866	if 'c' not in magSym[2]:
867	i,j = [1,2]
868	magSym[i].strip("'")
869	Ptsym[i-1].strip("'")
870	magSym[j].strip("'")
871	Ptsym[j-1].strip("'")
872	if SpnFlp[:2] == [1,-1]:
873	magSym[i] += "'"
874	Ptsym[i-1] += "'"
875	elif SpnFlp[:2] == [-1,-1]:
876	magSym[j] += "'"
877	Ptsym[j-1] += "'"
878	elif SpnFlp[:2] == [-1,1]:
879	magSym[i] += "'"
880	Ptsym[i-1] += "'"
881	magSym[j] += "'"
882	Ptsym[j-1] += "'"
883	SGData['MagPtGp'] = ''.join(Ptsym)
884	elif SGData['SGPtGrp'] == '23' and len(magSym):
885	SGData['MagPtGp'] = '23'
886	if SpnFlp[0] < 0:
887	magSym[0] += '(P)'
888	elif SGData['SGPtGrp'] == 'm3':
889	SGData['MagPtGp'] = "m3"
890	if SpnFlp[0] < 0:
891	magSym[1] += "'"
892	magSym[2] += "'"
893	SGData['MagPtGp'] = "m'3'"
894	if SpnFlp[1] < 0:
895	magSym[0] += '(P)'
896	if not 'm' in magSym[1]: #only Ia3
897	magSym[1].strip("'")
898	SGData['MagPtGp'] = "m3'"
899	elif SGData['SGPtGrp'] in ['432','-43m']:
900	Ptsym = SGData['SGPtGrp'].split('3')
901	if SpnFlp[0] < 0:
902	magSym[1] += "'"
903	Ptsym[0] += "'"
904	magSym[3] += "'"
905	Ptsym[1] += "'"
906	if SpnFlp[1] < 0:
907	magSym[0] += '(P)'
908	SGData['MagPtGp'] = '3'.join(Ptsym)
909	elif SGData['SGPtGrp'] == 'm-3m':
910	Ptsym = ['m','3','m']
911	if SpnFlp[:2] == [-1,1]:
912	magSym[1] += "'"
913	Ptsym[0] += "'"
914	magSym[2] += "'"
915	Ptsym[1] += "'"
916	elif SpnFlp[:2] == [1,-1]:
917	magSym[3] += "'"
918	Ptsym[2] += "'"
919	elif SpnFlp[:2] == [-1,-1]:
920	magSym[1] += "'"
921	Ptsym[0] += "'"
922	magSym[2] += "'"
923	Ptsym[1] += "'"
924	magSym[3] += "'"
925	Ptsym[2] += "'"
926	if SpnFlp[2] < 0:
927	magSym[0] += '(P)'
928	SGData['MagPtGp'] = ''.join(Ptsym)
929	# print SpnFlp
930	return ' '.join(magSym)
931
932	def GenMagOps(SGData):
933	FlpSpn = SGData['SGSpin']
934	Nsym = len(SGData['SGOps'])
935	Nfl = len(SGData['GenFlg'])
936	Ncv = len(SGData['SGCen'])
937	sgOp = [M for M,T in SGData['SGOps']]
938	OprName = [GetOprPtrName(str(irtx))[1] for irtx in PackRot(SGData['SGOps'])]
939	if SGData['SGInv']:
940	Nsym *= 2
941	sgOp += [-M for M,T in SGData['SGOps']]
942	OprName += [GetOprPtrName(str(-irtx))[1] for irtx in PackRot(SGData['SGOps'])]
943	Nsyms = 0
944	sgOps = []
945	OprNames = []
946	for incv in range(Ncv):
947	Nsyms += Nsym
948	sgOps += sgOp
949	OprNames += OprName
950	SpnFlp = np.ones(Nsym,dtype=np.int)
951	for ieqv in range(Nsym):
952	for iunq in range(Nfl):
953	if SGData['SGGen'][ieqv] & SGData['GenFlg'][iunq]:
954	SpnFlp[ieqv] *= FlpSpn[iunq]
955	# print '\nMagSpGrp:',SGData['MagSpGrp'],Ncv
956	# print 'GenFlg:',SGData['GenFlg']
957	# print 'GenSym:',SGData['GenSym']
958	# print 'FlpSpn:',Nfl,FlpSpn
959	detM = [nl.det(M) for M in sgOp]
960	for incv in range(Ncv):
961	if incv:
962	SpnFlp = np.concatenate((SpnFlp,SpnFlp[:Nsym]*FlpSpn[Nfl+incv-1]))
963	if ' 1bar ' in SGData['GenSym'][0] and FlpSpn[0] < 0:
964	detM[1] = 1.
965	MagMom = SpnFlpnp.array(NcvdetM)
966	SGData['MagMom'] = MagMom
967	# print 'SgOps:',OprNames
968	# print 'SGGen:',SGData['SGGen']
969	# print 'SpnFlp:',SpnFlp
970	# print 'MagMom:',MagMom
971	return OprNames,SpnFlp
972
973	def GetOpNum(Opr,SGData):
974	Nops = len(SGData['SGOps'])
975	opNum = abs(Opr)%100
976	cent = abs(Opr)//100
977	if Opr < 0:
978	opNum += Nops
979	if SGData['SGInv']:
980	Nops *= 2
981	opNum += cent*Nops
982	return opNum
983
984	################################################################################
985	#### Superspace group codes
986	################################################################################
987
988	def SSpcGroup(SGData,SSymbol):
989	"""
990	Determines supersymmetry information from superspace group name; currently only for (3+1) superlattices
991
992	:param SGData: space group data structure as defined in SpcGroup above (see :ref:`SGData<SGData_table>`).
993	:param SSymbol: superspace group symbol extension (string) defining modulation direction & generator info.
994	:returns: (SSGError,SSGData)
995
996	* SGError = 0 for no errors; >0 for errors (see SGErrors below for details)
997	* SSGData - is a dict (see :ref:`Superspace Group object<SSGData_table>`) with entries:
998
999	* 'SSpGrp': superspace group symbol extension to space group symbol, accidental spaces removed
1000	* 'SSGCen': 4D cell centering vectors [0,0,0,0] at least
1001	* 'SSGOps': 4D symmetry operations as [M,T] so that M*x+T = x'
1002
1003	"""
1004
1005	def checkModSym():
1006	'''
1007	Checks to see if proposed modulation form is allowed for Laue group
1008	'''
1009	if LaueId in [0,] and LaueModId in [0,]:
1010	return True
1011	elif LaueId in [1,]:
1012	try:
1013	if modsym.index('1/2') != ['A','B','C'].index(SGData['SGLatt']):
1014	return False
1015	if 'I'.index(SGData['SGLatt']) and modsym.count('1/2') not in [0,2]:
1016	return False
1017	except ValueError:
1018	pass
1019	if SGData['SGUniq'] == 'a' and LaueModId in [5,6,7,8,9,10,]:
1020	return True
1021	elif SGData['SGUniq'] == 'b' and LaueModId in [3,4,13,14,15,16,]:
1022	return True
1023	elif SGData['SGUniq'] == 'c' and LaueModId in [1,2,19,20,21,22,]:
1024	return True
1025	elif LaueId in [2,] and LaueModId in [i+7 for i in range(18)]:
1026	try:
1027	if modsym.index('1/2') != ['A','B','C'].index(SGData['SGLatt']):
1028	return False
1029	if SGData['SGLatt'] in ['I','F',] and modsym.index('1/2'):
1030	return False
1031	except ValueError:
1032	pass
1033	return True
1034	elif LaueId in [3,4,] and LaueModId in [19,22,]:
1035	try:
1036	if SGData['SGLatt'] == 'I' and modsym.count('1/2'):
1037	return False
1038	except ValueError:
1039	pass
1040	return True
1041	elif LaueId in [7,8,9,] and LaueModId in [19,25,]:
1042	if (SGData['SGLatt'] == 'R' or SGData['SGPtGrp'] in ['3m1','-3m1']) and modsym.count('1/3'):
1043	return False
1044	return True
1045	elif LaueId in [10,11,] and LaueModId in [19,]:
1046	return True
1047	return False
1048
1049	def fixMonoOrtho():
1050	mod = ''.join(modsym).replace('1/2','0').replace('1','0')
1051	if SGData['SGPtGrp'] in ['2','m']: #OK
1052	if mod in ['a00','0b0','00g']:
1053	result = [i*-1 for i in SGData['SSGKl']]
1054	else:
1055	result = SGData['SSGKl'][:]
1056	if '/' in mod:
1057	return [i*-1 for i in result]
1058	else:
1059	return result
1060	elif SGData['SGPtGrp'] == '2/m': #OK
1061	if mod in ['a00','0b0','00g']:
1062	result = SGData['SSGKl'][:]
1063	else:
1064	result = [i*-1 for i in SGData['SSGKl']]
1065	if '/' in mod:
1066	return [i*-1 for i in result]
1067	else:
1068	return result
1069	else: #orthorhombic
1070	return [-SSGKl[i] if mod[i] in ['a','b','g'] else SSGKl[i] for i in range(3)]
1071
1072	def extendSSGOps(SSGOps):
1073	for OpA in SSGOps:
1074	OpAtxt = SSMT2text(OpA)
1075	if 't' not in OpAtxt:
1076	continue
1077	for OpB in SSGOps:
1078	OpBtxt = SSMT2text(OpB)
1079	if 't' not in OpBtxt:
1080	continue
1081	OpC = list(SGProd(OpB,OpA))
1082	OpC[1] %= 1.
1083	OpCtxt = SSMT2text(OpC)
1084	# print OpAtxt.replace(' ','')+' * '+OpBtxt.replace(' ','')+' = '+OpCtxt.replace(' ','')
1085	for k,OpD in enumerate(SSGOps):
1086	OpDtxt = SSMT2text(OpD)
1087	if 't' in OpDtxt:
1088	continue
1089	# print ' ('+OpCtxt.replace(' ','')+' = ? '+OpDtxt.replace(' ','')+')'
1090	if OpCtxt == OpDtxt:
1091	continue
1092	elif OpCtxt.split(',')[:3] == OpDtxt.split(',')[:3]:
1093	if 't' not in OpDtxt:
1094	SSGOps[k] = OpC
1095	# print k,' new:',OpCtxt.replace(' ','')
1096	break
1097	else:
1098	OpCtxt = OpCtxt.replace(' ','')
1099	OpDtxt = OpDtxt.replace(' ','')
1100	Txt = OpCtxt+' conflict with '+OpDtxt
1101	print (Txt)
1102	return False,Txt
1103	return True,SSGOps
1104
1105	def findMod(modSym):
1106	for a in ['a','b','g']:
1107	if a in modSym:
1108	return a
1109
1110	def genSSGOps():
1111	SSGOps = SSGData['SSGOps'][:]
1112	iFrac = {}
1113	for i,frac in enumerate(SSGData['modSymb']):
1114	if frac in ['1/2','1/3','1/4','1/6','1']:
1115	iFrac[i] = frac+'.'
1116	# print SGData['SpGrp']+SSymbol
1117	# print 'SSGKl',SSGKl,'genQ',genQ,'iFrac',iFrac,'modSymb',SSGData['modSymb']
1118	# set identity & 1,-1; triclinic
1119	SSGOps[0][0][3,3] = 1.
1120	## expand if centrosymmetric
1121	# if SGData['SGInv']:
1122	# SSGOps += [[-1*M,V] for M,V in SSGOps[:]]
1123	# monoclinic - all done & all checked
1124	if SGData['SGPtGrp'] in ['2','m']: #OK
1125	SSGOps[1][0][3,3] = SSGKl[0]
1126	SSGOps[1][1][3] = genQ[0]
1127	for i in iFrac:
1128	SSGOps[1][0][3,i] = -SSGKl[0]
1129	elif SGData['SGPtGrp'] == '2/m': #OK
1130	SSGOps[1][0][3,3] = SSGKl[1]
1131	if gensym:
1132	SSGOps[1][1][3] = 0.5
1133	for i in iFrac:
1134	SSGOps[1][0][3,i] = SSGKl[0]
1135
1136	# orthorhombic - all OK not fully checked
1137	elif SGData['SGPtGrp'] in ['222','mm2','m2m','2mm']: #OK
1138	if SGData['SGPtGrp'] == '222':
1139	OrOps = {'g':{0:[1,3],1:[2,3]},'a':{1:[1,2],2:[1,3]},'b':{2:[3,2],0:[1,2]}} #OK
1140	elif SGData['SGPtGrp'] == 'mm2':
1141	OrOps = {'g':{0:[1,3],1:[2,3]},'a':{1:[2,1],2:[3,1]},'b':{0:[1,2],2:[3,2]}} #OK
1142	elif SGData['SGPtGrp'] == 'm2m':
1143	OrOps = {'b':{0:[1,2],2:[3,2]},'g':{0:[1,3],1:[2,3]},'a':{1:[2,1],2:[3,1]}} #OK
1144	elif SGData['SGPtGrp'] == '2mm':
1145	OrOps = {'a':{1:[2,1],2:[3,1]},'b':{0:[1,2],2:[3,2]},'g':{0:[1,3],1:[2,3]}} #OK
1146	a = findMod(SSGData['modSymb'])
1147	OrFrac = OrOps[a]
1148	for j in iFrac:
1149	for i in OrFrac[j]:
1150	SSGOps[i][0][3,j] = -2.eval(iFrac[j])SSGKl[i-1]
1151	for i in [0,1,2]:
1152	SSGOps[i+1][0][3,3] = SSGKl[i]
1153	SSGOps[i+1][1][3] = genQ[i]
1154	E,SSGOps = extendSSGOps(SSGOps)
1155	if not E:
1156	return E,SSGOps
1157	elif SGData['SGPtGrp'] == 'mmm': #OK
1158	OrOps = {'g':{0:[1,3],1:[2,3]},'a':{1:[2,1],2:[3,1]},'b':{0:[1,2],2:[3,2]}}
1159	a = findMod(SSGData['modSymb'])
1160	if a == 'g':
1161	SSkl = [1,1,1]
1162	elif a == 'a':
1163	SSkl = [-1,1,-1]
1164	else:
1165	SSkl = [1,-1,-1]
1166	OrFrac = OrOps[a]
1167	for j in iFrac:
1168	for i in OrFrac[j]:
1169	SSGOps[i][0][3,j] = -2.eval(iFrac[j])SSkl[i-1]
1170	for i in [0,1,2]:
1171	SSGOps[i+1][0][3,3] = SSkl[i]
1172	SSGOps[i+1][1][3] = genQ[i]
1173	E,SSGOps = extendSSGOps(SSGOps)
1174	if not E:
1175	return E,SSGOps
1176	# tetragonal - all done & checked
1177	elif SGData['SGPtGrp'] == '4': #OK
1178	SSGOps[1][0][3,3] = SSGKl[0]
1179	SSGOps[1][1][3] = genQ[0]
1180	if '1/2' in SSGData['modSymb']:
1181	SSGOps[1][0][3,1] = -1
1182	elif SGData['SGPtGrp'] == '-4': #OK
1183	SSGOps[1][0][3,3] = SSGKl[0]
1184	if '1/2' in SSGData['modSymb']:
1185	SSGOps[1][0][3,1] = 1
1186	elif SGData['SGPtGrp'] in ['4/m',]: #OK
1187	if '1/2' in SSGData['modSymb']:
1188	SSGOps[1][0][3,1] = -SSGKl[0]
1189	for i,j in enumerate([1,3]):
1190	SSGOps[j][0][3,3] = 1
1191	if genQ[i]:
1192	SSGOps[j][1][3] = genQ[i]
1193	E,SSGOps = extendSSGOps(SSGOps)
1194	if not E:
1195	return E,SSGOps
1196	elif SGData['SGPtGrp'] in ['422','4mm','-42m','-4m2',]: #OK
1197	iGens = [1,4,5]
1198	if SGData['SGPtGrp'] in ['4mm','-4m2',]:
1199	iGens = [1,6,7]
1200	for i,j in enumerate(iGens):
1201	if '1/2' in SSGData['modSymb'] and i < 2:
1202	SSGOps[j][0][3,1] = SSGKl[i]
1203	SSGOps[j][0][3,3] = SSGKl[i]
1204	if genQ[i]:
1205	if 's' in gensym and j == 6:
1206	SSGOps[j][1][3] = -genQ[i]
1207	else:
1208	SSGOps[j][1][3] = genQ[i]
1209	E,SSGOps = extendSSGOps(SSGOps)
1210	if not E:
1211	return E,SSGOps
1212	elif SGData['SGPtGrp'] in ['4/mmm',]:#OK
1213	if '1/2' in SSGData['modSymb']:
1214	SSGOps[1][0][3,1] = -SSGKl[0]
1215	SSGOps[6][0][3,1] = SSGKl[1]
1216	if modsym:
1217	SSGOps[1][1][3] = -genQ[3]
1218	for i,j in enumerate([1,2,6,7]):
1219	SSGOps[j][0][3,3] = 1
1220	SSGOps[j][1][3] = genQ[i]
1221	E,Result = extendSSGOps(SSGOps)
1222	if not E:
1223	return E,Result
1224	else:
1225	SSGOps = Result
1226
1227	# trigonal - all done & checked
1228	elif SGData['SGPtGrp'] == '3': #OK
1229	SSGOps[1][0][3,3] = SSGKl[0]
1230	if '1/3' in SSGData['modSymb']:
1231	SSGOps[1][0][3,1] = -1
1232	SSGOps[1][1][3] = genQ[0]
1233	elif SGData['SGPtGrp'] == '-3': #OK
1234	SSGOps[1][0][3,3] = -SSGKl[0]
1235	if '1/3' in SSGData['modSymb']:
1236	SSGOps[1][0][3,1] = -1
1237	SSGOps[1][1][3] = genQ[0]
1238	elif SGData['SGPtGrp'] in ['312','3m','-3m','-3m1','3m1']: #OK
1239	if '1/3' in SSGData['modSymb']:
1240	SSGOps[1][0][3,1] = -1
1241	for i,j in enumerate([1,5]):
1242	if SGData['SGPtGrp'] in ['3m','-3m']:
1243	SSGOps[j][0][3,3] = 1
1244	else:
1245	SSGOps[j][0][3,3] = SSGKl[i+1]
1246	if genQ[i]:
1247	SSGOps[j][1][3] = genQ[i]
1248	elif SGData['SGPtGrp'] in ['321','32']: #OK
1249	for i,j in enumerate([1,4]):
1250	SSGOps[j][0][3,3] = SSGKl[i]
1251	if genQ[i]:
1252	SSGOps[j][1][3] = genQ[i]
1253	elif SGData['SGPtGrp'] in ['31m','-31m']: #OK
1254	ids = [1,3]
1255	if SGData['SGPtGrp'] == '-31m':
1256	ids = [1,3]
1257	if '1/3' in SSGData['modSymb']:
1258	SSGOps[ids[0]][0][3,1] = -SSGKl[0]
1259	for i,j in enumerate(ids):
1260	SSGOps[j][0][3,3] = 1
1261	if genQ[i+1]:
1262	SSGOps[j][1][3] = genQ[i+1]
1263
1264	# hexagonal all done & checked
1265	elif SGData['SGPtGrp'] == '6': #OK
1266	SSGOps[1][0][3,3] = SSGKl[0]
1267	SSGOps[1][1][3] = genQ[0]
1268	elif SGData['SGPtGrp'] == '-6': #OK
1269	SSGOps[1][0][3,3] = SSGKl[0]
1270	elif SGData['SGPtGrp'] in ['6/m',]: #OK
1271	SSGOps[1][0][3,3] = -SSGKl[1]
1272	SSGOps[1][1][3] = genQ[0]
1273	SSGOps[2][1][3] = genQ[1]
1274	elif SGData['SGPtGrp'] in ['622',]: #OK
1275	for i,j in enumerate([1,8,9]):
1276	SSGOps[j][0][3,3] = SSGKl[i]
1277	if genQ[i]:
1278	SSGOps[j][1][3] = genQ[i]
1279	E,SSGOps = extendSSGOps(SSGOps)
1280
1281	elif SGData['SGPtGrp'] in ['6mm','-62m','-6m2',]: #OK
1282	for i,j in enumerate([1,6,7]):
1283	SSGOps[j][0][3,3] = SSGKl[i]
1284	if genQ[i]:
1285	SSGOps[j][1][3] = genQ[i]
1286	E,SSGOps = extendSSGOps(SSGOps)
1287	elif SGData['SGPtGrp'] in ['6/mmm',]: # OK
1288	for i,j in enumerate([1,2,10,11]):
1289	SSGOps[j][0][3,3] = 1
1290	if genQ[i]:
1291	SSGOps[j][1][3] = genQ[i]
1292	E,SSGOps = extendSSGOps(SSGOps)
1293	elif SGData['SGPtGrp'] in ['1','-1']: #triclinic - done
1294	return True,SSGOps
1295	E,SSGOps = extendSSGOps(SSGOps)
1296	return E,SSGOps
1297
1298	def specialGen(gensym,modsym):
1299	sym = ''.join(gensym)
1300	if SGData['SGPtGrp'] in ['2/m',] and 'n' in SGData['SpGrp']:
1301	if 's' in sym:
1302	gensym = 'ss'
1303	if SGData['SGPtGrp'] in ['-62m',] and sym == '00s':
1304	gensym = '0ss'
1305	elif SGData['SGPtGrp'] in ['222',]:
1306	if sym == '00s':
1307	gensym = '0ss'
1308	elif sym == '0s0':
1309	gensym = 'ss0'
1310	elif sym == 's00':
1311	gensym = 's0s'
1312	elif SGData['SGPtGrp'] in ['mmm',]:
1313	if 'g' in modsym:
1314	if sym == 's00':
1315	gensym = 's0s'
1316	elif sym == '0s0':
1317	gensym = '0ss'
1318	elif 'a' in modsym:
1319	if sym == '0s0':
1320	gensym = 'ss0'
1321	elif sym == '00s':
1322	gensym = 's0s'
1323	elif 'b' in modsym:
1324	if sym == '00s':
1325	gensym = '0ss'
1326	elif sym == 's00':
1327	gensym = 'ss0'
1328	return gensym
1329
1330	def checkGen(gensym):
1331	'''
1332	GenSymList = ['','s','0s','s0', '00s','0s0','s00','s0s','ss0','0ss','q00','0q0','00q','qq0','q0q', '0qq',
1333	'q','qqs','s0s0','00ss','s00s','t','t00','t0','h','h00','000s']
1334	'''
1335	sym = ''.join(gensym)
1336	# monoclinic - all done
1337	if str(SSGKl) == '[-1]' and sym == 's':
1338	return False
1339	elif SGData['SGPtGrp'] in ['2/m',]:
1340	if str(SSGKl) == '[-1, 1]' and sym == '0s':
1341	return False
1342	elif str(SSGKl) == '[1, -1]' and sym == 's0':
1343	return False
1344	#orthorhombic - all
1345	elif SGData['SGPtGrp'] in ['222',] and sym not in ['','s00','0s0','00s']:
1346	return False
1347	elif SGData['SGPtGrp'] in ['2mm','m2m','mm2','mmm'] and sym not in ['',]+GenSymList[4:16]:
1348	return False
1349	#tetragonal - all done
1350	elif SGData['SGPtGrp'] in ['4',] and sym not in ['','s','q']:
1351	return False
1352	elif SGData['SGPtGrp'] in ['-4',] and sym not in ['',]:
1353	return False
1354	elif SGData['SGPtGrp'] in ['4/m',] and sym not in ['','s0','q0']:
1355	return False
1356	elif SGData['SGPtGrp'] in ['422',] and sym not in ['','q00','s00']:
1357	return False
1358	elif SGData['SGPtGrp'] in ['4mm',] and sym not in ['','ss0','s0s','0ss','00s','qq0','qqs']:
1359	return False
1360	elif SGData['SGPtGrp'] in ['-4m2',] and sym not in ['','0s0','0q0']:
1361	return False
1362	elif SGData['SGPtGrp'] in ['-42m',] and sym not in ['','0ss','00q',]:
1363	return False
1364	elif SGData['SGPtGrp'] in ['4/mmm',] and sym not in ['','s00s','s0s0','00ss','000s',]:
1365	return False
1366	#trigonal/rhombohedral - all done
1367	elif SGData['SGPtGrp'] in ['3',] and sym not in ['','t']:
1368	return False
1369	elif SGData['SGPtGrp'] in ['-3',] and sym not in ['',]:
1370	return False
1371	elif SGData['SGPtGrp'] in ['32',] and sym not in ['','t0']:
1372	return False
1373	elif SGData['SGPtGrp'] in ['321','312'] and sym not in ['','t00']:
1374	return False
1375	elif SGData['SGPtGrp'] in ['3m','-3m'] and sym not in ['','0s']:
1376	return False
1377	elif SGData['SGPtGrp'] in ['3m1','-3m1'] and sym not in ['','0s0']:
1378	return False
1379	elif SGData['SGPtGrp'] in ['31m','-31m'] and sym not in ['','00s']:
1380	return False
1381	#hexagonal - all done
1382	elif SGData['SGPtGrp'] in ['6',] and sym not in ['','s','h','t']:
1383	return False
1384	elif SGData['SGPtGrp'] in ['-6',] and sym not in ['',]:
1385	return False
1386	elif SGData['SGPtGrp'] in ['6/m',] and sym not in ['','s0']:
1387	return False
1388	elif SGData['SGPtGrp'] in ['622',] and sym not in ['','h00','t00','s00']:
1389	return False
1390	elif SGData['SGPtGrp'] in ['6mm',] and sym not in ['','ss0','s0s','0ss']:
1391	return False
1392	elif SGData['SGPtGrp'] in ['-6m2',] and sym not in ['','0s0']:
1393	return False
1394	elif SGData['SGPtGrp'] in ['-62m',] and sym not in ['','00s']:
1395	return False
1396	elif SGData['SGPtGrp'] in ['6/mmm',] and sym not in ['','s00s','s0s0','00ss']:
1397	return False
1398	return True
1399
1400	LaueModList = [
1401	'abg','ab0','ab1/2','a0g','a1/2g', '0bg','1/2bg','a00','a01/2','a1/20',
1402	'a1/21/2','a01','a10','0b0','0b1/2', '1/2b0','1/2b1/2','0b1','1b0','00g',
1403	'01/2g','1/20g','1/21/2g','01g','10g', '1/31/3g']
1404	LaueList = ['-1','2/m','mmm','4/m','4/mmm','3R','3mR','3','3m1','31m','6/m','6/mmm','m3','m3m']
1405	GenSymList = ['','s','0s','s0', '00s','0s0','s00','s0s','ss0','0ss','q00','0q0','00q','qq0','q0q', '0qq',
1406	'q','qqs','s0s0','00ss','s00s','t','t00','t0','h','h00','000s']
1407	Fracs = {'1/2':0.5,'1/3':1./3,'1':1.0,'0':0.,'s':.5,'t':1./3,'q':.25,'h':1./6,'a':0.,'b':0.,'g':0.}
1408	LaueId = LaueList.index(SGData['SGLaue'])
1409	if SGData['SGLaue'] in ['m3','m3m']:
1410	return '(3+1) superlattices not defined for cubic space groups',None
1411	elif SGData['SGLaue'] in ['3R','3mR']:
1412	return '(3+1) superlattices not defined for rhombohedral settings - use hexagonal setting',None
1413	try:
1414	modsym,gensym = splitSSsym(SSymbol)
1415	except ValueError:
1416	return 'Error in superspace symbol '+SSymbol,None
1417	if ''.join(gensym) not in GenSymList:
1418	return 'unknown generator symbol '+''.join(gensym),None
1419	try:
1420	LaueModId = LaueModList.index(''.join(modsym))
1421	except ValueError:
1422	return 'Unknown modulation symbol '+''.join(modsym),None
1423	if not checkModSym():
1424	return 'Modulation '+''.join(modsym)+' not consistent with space group '+SGData['SpGrp'],None
1425	modQ = [Fracs[mod] for mod in modsym]
1426	SSGKl = SGData['SSGKl'][:]
1427	if SGData['SGLaue'] in ['2/m','mmm']:
1428	SSGKl = fixMonoOrtho()
1429	if len(gensym) and len(gensym) != len(SSGKl):
1430	return 'Wrong number of items in generator symbol '+''.join(gensym),None
1431	if not checkGen(gensym):
1432	return 'Generator '+''.join(gensym)+' not consistent with space group '+SGData['SpGrp'],None
1433	gensym = specialGen(gensym,modsym)
1434	genQ = [Fracs[mod] for mod in gensym]
1435	if not genQ:
1436	genQ = [0,0,0,0]
1437	SSGData = {'SSpGrp':SGData['SpGrp']+SSymbol,'modQ':modQ,'modSymb':modsym,'SSGKl':SSGKl}
1438	SSCen = np.zeros((len(SGData['SGCen']),4))
1439	for icen,cen in enumerate(SGData['SGCen']):
1440	SSCen[icen,0:3] = cen
1441	SSCen[0] = np.zeros(4)
1442	SSGData['SSGCen'] = SSCen
1443	SSGData['SSGOps'] = []
1444	for iop,op in enumerate(SGData['SGOps']):
1445	T = np.zeros(4)
1446	ssop = np.zeros((4,4))
1447	ssop[:3,:3] = op[0]
1448	T[:3] = op[1]
1449	SSGData['SSGOps'].append([ssop,T])
1450	E,Result = genSSGOps()
1451	if E:
1452	SSGData['SSGOps'] = Result
1453	if DEBUG:
1454	print ('Super spacegroup operators for '+SSGData['SSpGrp'])
1455	for Op in Result:
1456	print (SSMT2text(Op).replace(' ',''))
1457	if SGData['SGInv']:
1458	for Op in Result:
1459	Op = [-Op[0],-Op[1]%1.]
1460	print (SSMT2text(Op).replace(' ',''))
1461	return None,SSGData
1462	else:
1463	return Result+'\nOperator conflict - incorrect superspace symbol',None
1464
1465	def splitSSsym(SSymbol):
1466	'''
1467	Splits supersymmetry symbol into two lists of strings
1468	'''
1469	modsym,gensym = SSymbol.replace(' ','').split(')')
1470	if gensym in ['0','00','000','0000']: #get rid of extraneous symbols
1471	gensym = ''
1472	nfrac = modsym.count('/')
1473	modsym = modsym.lstrip('(')
1474	if nfrac == 0:
1475	modsym = list(modsym)
1476	elif nfrac == 1:
1477	pos = modsym.find('/')
1478	if pos == 1:
1479	modsym = [modsym[:3],modsym[3],modsym[4]]
1480	elif pos == 2:
1481	modsym = [modsym[0],modsym[1:4],modsym[4]]
1482	else:
1483	modsym = [modsym[0],modsym[1],modsym[2:]]
1484	else:
1485	lpos = modsym.find('/')
1486	rpos = modsym.rfind('/')
1487	if lpos == 1 and rpos == 4:
1488	modsym = [modsym[:3],modsym[3:6],modsym[6]]
1489	elif lpos == 1 and rpos == 5:
1490	modsym = [modsym[:3],modsym[3],modsym[4:]]
1491	else:
1492	modsym = [modsym[0],modsym[1:4],modsym[4:]]
1493	gensym = list(gensym)
1494	return modsym,gensym
1495
1496	def SSGPrint(SGData,SSGData):
1497	'''
1498	Print the output of SSpcGroup in a nicely formatted way. Used in SSpaceGroup
1499
1500	:param SGData: space group data structure as defined in SpcGroup above.
1501	:param SSGData: from :func:`SSpcGroup`
1502	:returns:
1503	SSGText - list of strings with the superspace group details
1504	SGTable - list of strings for each of the operations
1505	'''
1506	Mult = len(SSGData['SSGCen'])len(SSGData['SSGOps'])(int(SGData['SGInv'])+1)
1507	SSGText = []
1508	SSGText.append(' Superspace Group: '+SSGData['SSpGrp'])
1509	CentStr = 'centrosymmetric'
1510	if not SGData['SGInv']:
1511	CentStr = 'non'+CentStr
1512	if SGData['SGLatt'] in 'ABCIFR':
1513	SSGText.append(' The lattice is '+CentStr+' '+SGData['SGLatt']+'-centered '+SGData['SGSys'].lower())
1514	else:
1515	SSGText.append(' The superlattice is '+CentStr+' '+'primitive '+SGData['SGSys'].lower())
1516	SSGText.append(' The Laue symmetry is '+SGData['SGLaue'])
1517	SSGText.append(' The superlattice point group is '+SGData['SGPtGrp']+', '+''.join([str(i) for i in SSGData['SSGKl']]))
1518	SSGText.append(' The number of superspace group generators is '+str(len(SGData['SSGKl'])))
1519	SSGText.append(' Multiplicity of a general site is '+str(Mult))
1520	if SGData['SGUniq'] in ['a','b','c']:
1521	SSGText.append(' The unique monoclinic axis is '+SGData['SGUniq'])
1522	if SGData['SGInv']:
1523	SSGText.append(' The inversion center is located at 0,0,0')
1524	if SGData['SGPolax']:
1525	SSGText.append(' The location of the origin is arbitrary in '+SGData['SGPolax'])
1526	SSGText.append(' ')
1527	if len(SSGData['SSGCen']) > 1:
1528	SSGText.append(' The equivalent positions are:')
1529	SSGText.append(' ('+SSLatt2text(SSGData['SSGCen'])+')+\n')
1530	else:
1531	SSGText.append(' The equivalent positions are:\n')
1532	SSGTable = []
1533	for i,Opr in enumerate(SSGData['SSGOps']):
1534	SSGTable.append('(%2d) %s'%(i+1,SSMT2text(Opr)))
1535	return SSGText,SSGTable
1536
1537	def SSGModCheck(Vec,modSymb,newMod=True):
1538	''' Checks modulation vector compatibility with supersymmetry space group symbol.
1539	if newMod: Superspace group symbol takes precidence & the vector will be modified accordingly
1540	'''
1541	Fracs = {'1/2':0.5,'1/3':1./3,'1':1.0,'0':0.,'a':0.,'b':0.,'g':0.}
1542	modQ = [Fracs[mod] for mod in modSymb]
1543	if newMod:
1544	newVec = [0.1 if (vec == 0.0 and mod in ['a','b','g']) else vec for [vec,mod] in zip(Vec,modSymb)]
1545	return [Q if mod not in ['a','b','g'] and vec != Q else vec for [vec,mod,Q] in zip(newVec,modSymb,modQ)], \
1546	[True if mod in ['a','b','g'] else False for mod in modSymb]
1547	else:
1548	return Vec,[True if mod in ['a','b','g'] else False for mod in modSymb]
1549
1550	def SSMT2text(Opr):
1551	"From superspace group matrix/translation operator returns text version"
1552	XYZS = ('x','y','z','t') #Stokes, Campbell & van Smaalen notation
1553	TRA = (' ','ERR','1/6','1/4','1/3','ERR','1/2','ERR','2/3','3/4','5/6','ERR')
1554	Fld = ''
1555	M,T = Opr
1556	for j in range(4):
1557	IJ = ''
1558	for k in range(4):
1559	txt = str(int(round(M[j][k])))
1560	txt = txt.replace('1',XYZS[k]).replace('0','')
1561	if '2' in txt:
1562	txt += XYZS[k]
1563	if IJ and M[j][k] > 0:
1564	IJ += '+'+txt
1565	else:
1566	IJ += txt
1567	IK = int(round(T[j]*12))%12
1568	if IK:
1569	if not IJ:
1570	break
1571	if IJ[0] == '-':
1572	Fld += (TRA[IK]+IJ).rjust(8)
1573	else:
1574	Fld += (TRA[IK]+'+'+IJ).rjust(8)
1575	else:
1576	Fld += IJ.rjust(8)
1577	if j != 3: Fld += ', '
1578	return Fld
1579
1580	def SSLatt2text(SSGCen):
1581	"Lattice centering vectors to text"
1582	lattTxt = ''
1583	lattDir = {4:'1/3',6:'1/2',8:'2/3',0:'0'}
1584	for vec in SSGCen:
1585	lattTxt += ' '
1586	for item in vec:
1587	lattTxt += '%s,'%(lattDir[int(item*12)])
1588	lattTxt = lattTxt.rstrip(',')
1589	lattTxt += ';'
1590	lattTxt = lattTxt.rstrip(';').lstrip(' ')
1591	return lattTxt
1592
1593	def SSpaceGroup(SGSymbol,SSymbol):
1594	'''
1595	Print the output of SSpcGroup in a nicely formatted way.
1596
1597	:param SGSymbol: space group symbol with spaces between axial fields.
1598	:param SSymbol: superspace group symbol extension (string).
1599	:returns: nothing
1600	'''
1601
1602	E,A = SpcGroup(SGSymbol)
1603	if E > 0:
1604	print (SGErrors(E))
1605	return
1606	E,B = SSpcGroup(A,SSymbol)
1607	if E > 0:
1608	print (E)
1609	return
1610	for l in SSGPrint(B):
1611	print (l)
1612
1613	def SGProd(OpA,OpB):
1614	'''
1615	Form space group operator product. OpA & OpB are [M,V] pairs;
1616	both must be of same dimension (3 or 4). Returns [M,V] pair
1617	'''
1618	A,U = OpA
1619	B,V = OpB
1620	M = np.inner(B,A.T)
1621	W = np.inner(B,U)+V
1622	return M,W
1623
1624	def MoveToUnitCell(xyz):
1625	'''
1626	Translates a set of coordinates so that all values are >=0 and < 1
1627
1628	:param xyz: a list or numpy array of fractional coordinates
1629	:returns: XYZ - numpy array of new coordinates now 0 or greater and less than 1
1630	'''
1631	XYZ = (np.array(xyz)+10.)%1.
1632	cell = np.asarray(np.rint(xyz-XYZ),dtype=np.int32)
1633	return XYZ,cell
1634
1635	def Opposite(XYZ,toler=0.0002):
1636	'''
1637	Gives opposite corner, edge or face of unit cell for position within tolerance.
1638	Result may be just outside the cell within tolerance
1639
1640	:param XYZ: 0 >= np.array[x,y,z] > 1 as by MoveToUnitCell
1641	:param toler: unit cell fraction tolerance making opposite
1642	:returns:
1643	XYZ: dict of opposite positions; key=unit cell & always contains XYZ
1644	'''
1645	perm3 = [[1,1,1],[0,1,1],[1,0,1],[1,1,0],[1,0,0],[0,1,0],[0,0,1],[0,0,0]]
1646	TB = np.where(abs(XYZ-1)<toler,-1,0)+np.where(abs(XYZ)<toler,1,0)
1647	perm = TB*perm3
1648	cperm = ['%d,%d,%d'%(i,j,k) for i,j,k in perm]
1649	D = dict(zip(cperm,perm))
1650	new = {}
1651	for key in D:
1652	new[key] = np.array(D[key])+np.array(XYZ)
1653	return new
1654
1655	def GenAtom(XYZ,SGData,All=False,Uij=[],Move=True):
1656	'''
1657	Generates the equivalent positions for a specified coordinate and space group
1658
1659	:param XYZ: an array, tuple or list containing 3 elements: x, y & z
1660	:param SGData: from :func:`SpcGroup`
1661	:param All: True return all equivalent positions including duplicates;
1662	False return only unique positions
1663	:param Uij: [U11,U22,U33,U12,U13,U23] or [] if no Uij
1664	:param Move: True move generated atom positions to be inside cell
1665	False do not move atoms
1666	:return: [[XYZEquiv],Idup,[UijEquiv]]
1667
1668	* [XYZEquiv] is list of equivalent positions (XYZ is first entry)
1669	* Idup = [-][C]SS where SS is the symmetry operator number (1-24), C (if not 0,0,0)
1670	* is centering operator number (1-4) and - is for inversion
1671	Cell = unit cell translations needed to put new positions inside cell
1672	[UijEquiv] - equivalent Uij; absent if no Uij given
1673
1674	'''
1675	XYZEquiv = []
1676	UijEquiv = []
1677	Idup = []
1678	Cell = []
1679	X = np.array(XYZ)
1680	if Move:
1681	X = MoveToUnitCell(X)[0]
1682	for ic,cen in enumerate(SGData['SGCen']):
1683	C = np.array(cen)
1684	for invers in range(int(SGData['SGInv']+1)):
1685	for io,[M,T] in enumerate(SGData['SGOps']):
1686	idup = ((io+1)+100ic)(1-2*invers)
1687	XT = np.inner(M,X)+T
1688	if len(Uij):
1689	U = Uij2U(Uij)
1690	U = np.inner(M,np.inner(U,M).T)
1691	newUij = U2Uij(U)
1692	if invers:
1693	XT = -XT
1694	XT += C
1695	cell = np.zeros(3,dtype=np.int32)
1696	cellj = np.zeros(3,dtype=np.int32)
1697	if Move:
1698	newX,cellj = MoveToUnitCell(XT)
1699	else:
1700	newX = XT
1701	cell += cellj
1702	if All:
1703	if np.allclose(newX,X,atol=0.0002):
1704	idup = False
1705	else:
1706	if True in [np.allclose(newX,oldX,atol=0.0002) for oldX in XYZEquiv]:
1707	idup = False
1708	if All or idup:
1709	XYZEquiv.append(newX)
1710	Idup.append(idup)
1711	Cell.append(cell)
1712	if len(Uij):
1713	UijEquiv.append(newUij)
1714	if len(Uij):
1715	return list(zip(XYZEquiv,UijEquiv,Idup,Cell))
1716	else:
1717	return list(zip(XYZEquiv,Idup,Cell))
1718
1719	def GenHKL(HKL,SGData):
1720	''' Generates all equivlent reflections including Friedel pairs
1721	:param HKL: [h,k,l] must be integral values
1722	:param SGData: space group data obtained from SpcGroup
1723	:returns: array Uniq: equivalent reflections
1724	'''
1725
1726	Ops = SGData['SGOps']
1727	OpM = np.array([op[0] for op in Ops])
1728	Uniq = np.inner(OpM,HKL)
1729	Uniq = list(Uniq)+list(-1*Uniq)
1730	return np.array(Uniq)
1731
1732	def GenHKLf(HKL,SGData):
1733	'''
1734	Uses old GSAS Fortran routine genhkl.for
1735
1736	:param HKL: [h,k,l] must be integral values for genhkl.for to work
1737	:param SGData: space group data obtained from SpcGroup
1738	:returns: iabsnt,mulp,Uniq,phi
1739
1740	* iabsnt = True if reflection is forbidden by symmetry
1741	* mulp = reflection multiplicity including Friedel pairs
1742	* Uniq = numpy array of equivalent hkl in descending order of h,k,l
1743	* phi = phase offset for each equivalent h,k,l
1744
1745	'''
1746	hklf = list(HKL)+[0,] #could be numpy array!
1747	Ops = SGData['SGOps']
1748	OpM = np.array([op[0] for op in Ops],order='F')
1749	OpT = np.array([op[1] for op in Ops])
1750	Cen = np.array([cen for cen in SGData['SGCen']],order='F')
1751
1752	import pyspg
1753	Nuniq,Uniq,iabsnt,mulp = pyspg.genhklpy(hklf,len(Ops),OpM,OpT,SGData['SGInv'],len(Cen),Cen)
1754	h,k,l,f = Uniq
1755	Uniq=np.array(list(zip(h[:Nuniq],k[:Nuniq],l[:Nuniq])))
1756	phi = f[:Nuniq]
1757	return iabsnt,mulp,Uniq,phi
1758
1759	def checkSSLaue(HKL,SGData,SSGData):
1760	#Laue check here - Toss HKL if outside unique Laue part
1761	h,k,l,m = HKL
1762	if SGData['SGLaue'] == '2/m':
1763	if SGData['SGUniq'] == 'a':
1764	if 'a' in SSGData['modSymb'] and h == 0 and m < 0:
1765	return False
1766	elif 'b' in SSGData['modSymb'] and k == 0 and l ==0 and m < 0:
1767	return False
1768	else:
1769	return True
1770	elif SGData['SGUniq'] == 'b':
1771	if 'b' in SSGData['modSymb'] and k == 0 and m < 0:
1772	return False
1773	elif 'a' in SSGData['modSymb'] and h == 0 and l ==0 and m < 0:
1774	return False
1775	else:
1776	return True
1777	elif SGData['SGUniq'] == 'c':
1778	if 'g' in SSGData['modSymb'] and l == 0 and m < 0:
1779	return False
1780	elif 'a' in SSGData['modSymb'] and h == 0 and k ==0 and m < 0:
1781	return False
1782	else:
1783	return True
1784	elif SGData['SGLaue'] == 'mmm':
1785	if 'a' in SSGData['modSymb']:
1786	if h == 0 and m < 0:
1787	return False
1788	else:
1789	return True
1790	elif 'b' in SSGData['modSymb']:
1791	if k == 0 and m < 0:
1792	return False
1793	else:
1794	return True
1795	elif 'g' in SSGData['modSymb']:
1796	if l == 0 and m < 0:
1797	return False
1798	else:
1799	return True
1800	else: #tetragonal, trigonal, hexagonal (& triclinic?)
1801	if l == 0 and m < 0:
1802	return False
1803	else:
1804	return True
1805
1806
1807	def checkSSextc(HKL,SSGData):
1808	Ops = SSGData['SSGOps']
1809	OpM = np.array([op[0] for op in Ops])
1810	OpT = np.array([op[1] for op in Ops])
1811	HKLS = np.array([HKL,-HKL]) #Freidel's Law
1812	DHKL = np.reshape(np.inner(HKLS,OpM)-HKL,(-1,4))
1813	PHKL = np.reshape(np.inner(HKLS,OpT),(-1,))
1814	for dhkl,phkl in zip(DHKL,PHKL)[1:]: #skip identity
1815	if dhkl.any():
1816	continue
1817	else:
1818	if phkl%1.:
1819	return False
1820	return True
1821
1822	################################################################################
1823	#### Site symmetry tables
1824	################################################################################
1825
1826	OprPtrName = {
1827	'-6643':[ 2,' 1bar ', 1],'6479' :[ 10,' 2z ', 2],'-6479':[ 9,' mz ', 3],
1828	'6481' :[ 7,' my ', 4],'-6481':[ 6,' 2y ', 5],'6641' :[ 4,' mx ', 6],
1829	'-6641':[ 3,' 2x ', 7],'6591' :[ 28,' m+-0 ', 8],'-6591':[ 27,' 2+-0 ', 9],
1830	'6531' :[ 25,' m110 ',10],'-6531':[ 24,' 2110 ',11],'6537' :[ 61,' 4z ',12],
1831	'-6537':[ 62,' -4z ',13],'975' :[ 68,' 3+++1',14],'6456' :[ 114,' 3z1 ',15],
1832	'-489' :[ 73,' 3+-- ',16],'483' :[ 78,' 3-+- ',17],'-969' :[ 83,' 3--+ ',18],
1833	'819' :[ 22,' m+0- ',19],'-819' :[ 21,' 2+0- ',20],'2431' :[ 16,' m0+- ',21],
1834	'-2431':[ 15,' 20+- ',22],'-657' :[ 19,' m101 ',23],'657' :[ 18,' 2101 ',24],
1835	'1943' :[ 48,' -4x ',25],'-1943':[ 47,' 4x ',26],'-2429':[ 13,' m011 ',27],
1836	'2429' :[ 12,' 2011 ',28],'639' :[ 55,' -4y ',29],'-639' :[ 54,' 4y ',30],
1837	'-6484':[ 146,' 2010 ', 4],'6484' :[ 139,' m010 ', 5],'-6668':[ 145,' 2100 ', 6],
1838	'6668' :[ 138,' m100 ', 7],'-6454':[ 148,' 2120 ',18],'6454' :[ 141,' m120 ',19],
1839	'-6638':[ 149,' 2210 ',20],'6638' :[ 142,' m210 ',21], #search ends here
1840	'2223' :[ 68,' 3+++2',39],
1841	'6538' :[ 106,' 6z1 ',40],'-2169':[ 83,' 3--+2',41],'2151' :[ 73,' 3+--2',42],
1842	'2205' :[ 79,'-3-+-2',43],'-2205':[ 78,' 3-+-2',44],'489' :[ 74,'-3+--1',45],
1843	'801' :[ 53,' 4y1 ',46],'1945' :[ 47,' 4x3 ',47],'-6585':[ 62,' -4z3 ',48],
1844	'6585' :[ 61,' 4z3 ',49],'6584' :[ 114,' 3z2 ',50],'6666' :[ 106,' 6z5 ',51],
1845	'6643' :[ 1,' Iden ',52],'-801' :[ 55,' -4y1 ',53],'-1945':[ 48,' -4x3 ',54],
1846	'-6666':[ 105,' -6z5 ',55],'-6538':[ 105,' -6z1 ',56],'-2223':[ 69,'-3+++2',57],
1847	'-975' :[ 69,'-3+++1',58],'-6456':[ 113,' -3z1 ',59],'-483' :[ 79,'-3-+-1',60],
1848	'969' :[ 84,'-3--+1',61],'-6584':[ 113,' -3z2 ',62],'2169' :[ 84,'-3--+2',63],
1849	'-2151':[ 74,'-3+--2',64],'0':[0,' ????',0]
1850	}
1851
1852	OprName = {
1853	'-6643':' -1 ','6479' :' 2(z)','-6479':' m(z)',
1854	'6481' :' m(y)','-6481':' 2(y)','6641' :' m(x)',
1855	'-6641':' 2(x)','6591' :' m(+-0)','-6591':' 2(+-0)',
1856	'6531' :' m(110) ','-6531':' 2(110) ','6537' :' 4(001)',
1857	'-6537':' -4(001)','975' :' 3(111)','6456' :' 3 ',
1858	'-489' :' 3(+--)','483' :' 3(-+-)','-969' :' 3(--+)',
1859	'819' :' m(+0-)','-819' :' 2(+0-)','2431' :' m(0+-)',
1860	'-2431':' 2(0+-)','-657' :' m(xz)','657' :' 2(xz)',
1861	'1943' :' -4(100)','-1943':' 4(100)','-2429':' m(yz)',
1862	'2429' :' 2(yz)','639' :' -4(010)','-639' :' 4(010)',
1863	'-6484':' 2(010) ','6484' :' m(010) ','-6668':' 2(100) ',
1864	'6668' :' m(100) ','-6454':' 2(120) ','6454' :' m(120) ',
1865	'-6638':' 2(210) ','6638' :' m(210) '} #search ends here
1866
1867
1868	KNsym = {
1869	'0' :' 1 ','1' :' -1 ','64' :' 2(x)','32' :' m(x)',
1870	'97' :' 2/m(x)','16' :' 2(y)','8' :' m(y)','25' :' 2/m(y)',
1871	'2' :' 2(z)','4' :' m(z)','7' :' 2/m(z)','134217728' :' 2(yz)',
1872	'67108864' :' m(yz)','201326593' :' 2/m(yz)','2097152' :' 2(0+-)','1048576' :' m(0+-)',
1873	'3145729' :'2/m(0+-)','8388608' :' 2(xz)','4194304' :' m(xz)','12582913' :' 2/m(xz)',
1874	'524288' :' 2(+0-)','262144' :' m(+0-)','796433' :'2/m(+0-)','1024' :' 2(xy)',
1875	'512' :' m(xy)','1537' :' 2/m(xy)','256' :' 2(+-0)','128' :' m(+-0)',
1876	'385' :'2/m(+-0)','76' :' mm2(x)','52' :' mm2(y)','42' :' mm2(z)',
1877	'135266336' :' mm2(yz)','69206048' :'mm2(0+-)','8650760' :' mm2(xz)','4718600' :'mm2(+0-)',
1878	'1156' :' mm2(xy)','772' :'mm2(+-0)','82' :' 222 ','136314944' :' 222(x)',
1879	'8912912' :' 222(y)','1282' :' 222(z)','127' :' mmm ','204472417' :' mmm(x)',
1880	'13369369' :' mmm(y)','1927' :' mmm(z)','33554496' :' 4(100)','16777280' :' -4(100)',
1881	'50331745' :'4/m(100)','169869394' :'422(100)','84934738' :'-42m 100','101711948' :'4mm(100)',
1882	'254804095' :'4/mmm100','536870928 ':' 4(010)','268435472' :' -4(010)','805306393' :'4/m (10)',
1883	'545783890' :'422(010)','272891986' :'-42m 010','541327412' :'4mm(010)','818675839' :'4/mmm010',
1884	'2050' :' 4(001)','4098' :' -4(001)','6151' :'4/m(001)','3410' :'422(001)',
1885	'4818' :'-42m 001','2730' :'4mm(001)','8191' :'4/mmm001','8192' :' 3(111)',
1886	'8193' :' -3(111)','2629888' :' 32(111)','1319040' :' 3m(111)','3940737' :'-3m(111)',
1887	'32768' :' 3(+--)','32769' :' -3(+--)','10519552' :' 32(+--)','5276160' :' 3m(+--)',
1888	'15762945' :'-3m(+--)','65536' :' 3(-+-)','65537' :' -3(-+-)','134808576' :' 32(-+-)',
1889	'67437056' :' 3m(-+-)','202180097' :'-3m(-+-)','131072' :' 3(--+)','131073' :' -3(--+)',
1890	'142737664' :' 32(--+)','71434368' :' 3m(--+)','214040961' :'-3m(--+)','237650' :' 23 ',
1891	'237695' :' m3 ','715894098' :' 432 ','358068946' :' -43m ','1073725439':' m3m ',
1892	'68157504' :' mm2d100','4456464' :' mm2d010','642' :' mm2d001','153092172' :'-4m2 100',
1893	'277348404' :'-4m2 010','5418' :'-4m2 001','1075726335':' 6/mmm ','1074414420':'-6m2 100',
1894	'1075070124':'-6m2 120','1075069650':' 6mm ','1074414890':' 622 ','1073758215':' 6/m ',
1895	'1073758212':' -6 ','1073758210':' 6 ','1073759865':'-3m(100)','1075724673':'-3m(120)',
1896	'1073758800':' 3m(100)','1075069056':' 3m(120)','1073759272':' 32(100)','1074413824':' 32(120)',
1897	'1073758209':' -3 ','1073758208':' 3 ','1074135143':'mmm(100)','1075314719':'mmm(010)',
1898	'1073743751':'mmm(110)','1074004034':' mm2z100','1074790418':' mm2z010','1073742466':' mm2z110',
1899	'1074004004':'mm2(100)','1074790412':'mm2(010)','1073742980':'mm2(110)','1073872964':'mm2(120)',
1900	'1074266132':'mm2(210)','1073742596':'mm2(+-0)','1073872930':'222(100)','1074266122':'222(010)',
1901	'1073743106':'222(110)','1073741831':'2/m(001)','1073741921':'2/m(100)','1073741849':'2/m(010)',
1902	'1073743361':'2/m(110)','1074135041':'2/m(120)','1075314689':'2/m(210)','1073742209':'2/m(+-0)',
1903	'1073741828':' m(001) ','1073741888':' m(100) ','1073741840':' m(010) ','1073742336':' m(110) ',
1904	'1074003968':' m(120) ','1074790400':' m(210) ','1073741952':' m(+-0) ','1073741826':' 2(001) ',
1905	'1073741856':' 2(100) ','1073741832':' 2(010) ','1073742848':' 2(110) ','1073872896':' 2(120) ',
1906	'1074266112':' 2(210) ','1073742080':' 2(+-0) ','1073741825':' -1 '
1907	}
1908
1909	NXUPQsym = {
1910	' 1 ':(28,29,28,28),' -1 ':( 1,29,28, 0),' 2(x)':(12,18,12,25),' m(x)':(25,18,12,25),
1911	' 2/m(x)':( 1,18, 0,-1),' 2(y)':(13,17,13,24),' m(y)':(24,17,13,24),' 2/m(y)':( 1,17, 0,-1),
1912	' 2(z)':(14,16,14,23),' m(z)':(23,16,14,23),' 2/m(z)':( 1,16, 0,-1),' 2(yz)':(10,23,10,22),
1913	' m(yz)':(22,23,10,22),' 2/m(yz)':( 1,23, 0,-1),' 2(0+-)':(11,24,11,21),' m(0+-)':(21,24,11,21),
1914	'2/m(0+-)':( 1,24, 0,-1),' 2(xz)':( 8,21, 8,20),' m(xz)':(20,21, 8,20),' 2/m(xz)':( 1,21, 0,-1),
1915	' 2(+0-)':( 9,22, 9,19),' m(+0-)':(19,22, 9,19),'2/m(+0-)':( 1,22, 0,-1),' 2(xy)':( 6,19, 6,18),
1916	' m(xy)':(18,19, 6,18),' 2/m(xy)':( 1,19, 0,-1),' 2(+-0)':( 7,20, 7,17),' m(+-0)':(17,20, 7,17),
1917	'2/m(+-0)':( 1,20, 17,-1),' mm2(x)':(12,10, 0,-1),' mm2(y)':(13,10, 0,-1),' mm2(z)':(14,10, 0,-1),
1918	' mm2(yz)':(10,13, 0,-1),'mm2(0+-)':(11,13, 0,-1),' mm2(xz)':( 8,12, 0,-1),'mm2(+0-)':( 9,12, 0,-1),
1919	' mm2(xy)':( 6,11, 0,-1),'mm2(+-0)':( 7,11, 0,-1),' 222 ':( 1,10, 0,-1),' 222(x)':( 1,13, 0,-1),
1920	' 222(y)':( 1,12, 0,-1),' 222(z)':( 1,11, 0,-1),' mmm ':( 1,10, 0,-1),' mmm(x)':( 1,13, 0,-1),
1921	' mmm(y)':( 1,12, 0,-1),' mmm(z)':( 1,11, 0,-1),' 4(100)':(12, 4,12, 0),' -4(100)':( 1, 4,12, 0),
1922	'4/m(100)':( 1, 4,12,-1),'422(100)':( 1, 4, 0,-1),'-42m 100':( 1, 4, 0,-1),'4mm(100)':(12, 4, 0,-1),
1923	'4/mmm100':( 1, 4, 0,-1),' 4(010)':(13, 3,13, 0),' -4(010)':( 1, 3,13, 0),'4/m (10)':( 1, 3,13,-1),
1924	'422(010)':( 1, 3, 0,-1),'-42m 010':( 1, 3, 0,-1),'4mm(010)':(13, 3, 0,-1),'4/mmm010':(1, 3, 0,-1,),
1925	' 4(001)':(14, 2,14, 0),' -4(001)':( 1, 2,14, 0),'4/m(001)':( 1, 2,14,-1),'422(001)':( 1, 2, 0,-1),
1926	'-42m 001':( 1, 2, 0,-1),'4mm(001)':(14, 2, 0,-1),'4/mmm001':( 1, 2, 0,-1),' 3(111)':( 2, 5, 2, 0),
1927	' -3(111)':( 1, 5, 2, 0),' 32(111)':( 1, 5, 0, 2),' 3m(111)':( 2, 5, 0, 2),'-3m(111)':( 1, 5, 0,-1),
1928	' 3(+--)':( 5, 8, 5, 0),' -3(+--)':( 1, 8, 5, 0),' 32(+--)':( 1, 8, 0, 5),' 3m(+--)':( 5, 8, 0, 5),
1929	'-3m(+--)':( 1, 8, 0,-1),' 3(-+-)':( 4, 7, 4, 0),' -3(-+-)':( 1, 7, 4, 0),' 32(-+-)':( 1, 7, 0, 4),
1930	' 3m(-+-)':( 4, 7, 0, 4),'-3m(-+-)':( 1, 7, 0,-1),' 3(--+)':( 3, 6, 3, 0),' -3(--+)':( 1, 6, 3, 0),
1931	' 32(--+)':( 1, 6, 0, 3),' 3m(--+)':( 3, 6, 0, 3),'-3m(--+)':( 1, 6, 0,-1),' 23 ':( 1, 1, 0, 0),
1932	' m3 ':( 1, 1, 0, 0),' 432 ':( 1, 1, 0, 0),' -43m ':( 1, 1, 0, 0),' m3m ':( 1, 1, 0, 0),
1933	' mm2d100':(12,13, 0,-1),' mm2d010':(13,12, 0,-1),' mm2d001':(14,11, 0,-1),'-4m2 100':( 1, 4, 0,-1),
1934	'-4m2 010':( 1, 3, 0,-1),'-4m2 001':( 1, 2, 0,-1),' 6/mmm ':( 1, 9, 0,-1),'-6m2 100':( 1, 9, 0,-1),
1935	'-6m2 120':( 1, 9, 0,-1),' 6mm ':(14, 9, 0,-1),' 622 ':( 1, 9, 0,-1),' 6/m ':( 1, 9,14,-1),
1936	' -6 ':( 1, 9,14, 0),' 6 ':(14, 9,14, 0),'-3m(100)':( 1, 9, 0,-1),'-3m(120)':( 1, 9, 0,-1),
1937	' 3m(100)':(14, 9, 0,14),' 3m(120)':(14, 9, 0,14),' 32(100)':( 1, 9, 0,14),' 32(120)':( 1, 9, 0,14),
1938	' -3 ':( 1, 9,14, 0),' 3 ':(14, 9,14, 0),'mmm(100)':( 1,14, 0,-1),'mmm(010)':( 1,15, 0,-1),
1939	'mmm(110)':( 1,11, 0,-1),' mm2z100':(14,14, 0,-1),' mm2z010':(14,15, 0,-1),' mm2z110':(14,11, 0,-1),
1940	'mm2(100)':(12,14, 0,-1),'mm2(010)':(13,15, 0,-1),'mm2(110)':( 6,11, 0,-1),'mm2(120)':(15,14, 0,-1),
1941	'mm2(210)':(16,15, 0,-1),'mm2(+-0)':( 7,11, 0,-1),'222(100)':( 1,14, 0,-1),'222(010)':( 1,15, 0,-1),
1942	'222(110)':( 1,11, 0,-1),'2/m(001)':( 1,16,14,-1),'2/m(100)':( 1,25,12,-1),'2/m(010)':( 1,28,13,-1),
1943	'2/m(110)':( 1,19, 6,-1),'2/m(120)':( 1,27,15,-1),'2/m(210)':( 1,26,16,-1),'2/m(+-0)':( 1,20,17,-1),
1944	' m(001) ':(23,16,14,23),' m(100) ':(26,25,12,26),' m(010) ':(27,28,13,27),' m(110) ':(18,19, 6,18),
1945	' m(120) ':(24,27,15,24),' m(210) ':(25,26,16,25),' m(+-0) ':(17,20, 7,17),' 2(001) ':(14,16,14,23),
1946	' 2(100) ':(12,25,12,26),' 2(010) ':(13,28,13,27),' 2(110) ':( 6,19, 6,18),' 2(120) ':(15,27,15,24),
1947	' 2(210) ':(16,26,16,25),' 2(+-0) ':( 7,20, 7,17),' -1 ':( 1,29,28, 0)
1948	}
1949
1950	CSxinel = [[], # 0th empty - indices are Fortran style
1951	[[0,0,0],[ 0.0, 0.0, 0.0]], #1 0 0 0
1952	[[1,1,1],[ 1.0, 1.0, 1.0]], #2 X X X
1953	[[1,1,1],[ 1.0, 1.0,-1.0]], #3 X X -X
1954	[[1,1,1],[ 1.0,-1.0, 1.0]], #4 X -X X
1955	[[1,1,1],[ 1.0,-1.0,-1.0]], #5 -X X X
1956	[[1,1,0],[ 1.0, 1.0, 0.0]], #6 X X 0
1957	[[1,1,0],[ 1.0,-1.0, 0.0]], #7 X -X 0
1958	[[1,0,1],[ 1.0, 0.0, 1.0]], #8 X 0 X
1959	[[1,0,1],[ 1.0, 0.0,-1.0]], #9 X 0 -X
1960	[[0,1,1],[ 0.0, 1.0, 1.0]], #10 0 Y Y
1961	[[0,1,1],[ 0.0, 1.0,-1.0]], #11 0 Y -Y
1962	[[1,0,0],[ 1.0, 0.0, 0.0]], #12 X 0 0
1963	[[0,1,0],[ 0.0, 1.0, 0.0]], #13 0 Y 0
1964	[[0,0,1],[ 0.0, 0.0, 1.0]], #14 0 0 Z
1965	[[1,1,0],[ 1.0, 2.0, 0.0]], #15 X 2X 0
1966	[[1,1,0],[ 2.0, 1.0, 0.0]], #16 2X X 0
1967	[[1,1,2],[ 1.0, 1.0, 1.0]], #17 X X Z
1968	[[1,1,2],[ 1.0,-1.0, 1.0]], #18 X -X Z
1969	[[1,2,1],[ 1.0, 1.0, 1.0]], #19 X Y X
1970	[[1,2,1],[ 1.0, 1.0,-1.0]], #20 X Y -X
1971	[[1,2,2],[ 1.0, 1.0, 1.0]], #21 X Y Y
1972	[[1,2,2],[ 1.0, 1.0,-1.0]], #22 X Y -Y
1973	[[1,2,0],[ 1.0, 1.0, 0.0]], #23 X Y 0
1974	[[1,0,2],[ 1.0, 0.0, 1.0]], #24 X 0 Z
1975	[[0,1,2],[ 0.0, 1.0, 1.0]], #25 0 Y Z
1976	[[1,1,2],[ 1.0, 2.0, 1.0]], #26 X 2X Z
1977	[[1,1,2],[ 2.0, 1.0, 1.0]], #27 2X X Z
1978	[[1,2,3],[ 1.0, 1.0, 1.0]], #28 X Y Z
1979	]
1980
1981	CSuinel = [[], # 0th empty - indices are Fortran style
1982	[[1,1,1,0,0,0],[ 1.0, 1.0, 1.0, 0.0, 0.0, 0.0],[1,0,0,0,0,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #1 A A A 0 0 0
1983	[[1,1,2,0,0,0],[ 1.0, 1.0, 1.0, 0.0, 0.0, 0.0],[1,0,1,0,0,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #2 A A C 0 0 0
1984	[[1,2,1,0,0,0],[ 1.0, 1.0, 1.0, 0.0, 0.0, 0.0],[1,1,0,0,0,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #3 A B A 0 0 0
1985	[[1,2,2,0,0,0],[ 1.0, 1.0, 1.0, 0.0, 0.0, 0.0],[1,1,0,0,0,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #4 A B B 0 0 0
1986	[[1,1,1,2,2,2],[ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],[1,0,0,1,0,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #5 A A A D D D
1987	[[1,1,1,2,2,2],[ 1.0, 1.0, 1.0, 1.0,-1.0,-1.0],[1,0,0,1,0,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #6 A A A D -D -D
1988	[[1,1,1,2,2,2],[ 1.0, 1.0, 1.0, 1.0,-1.0, 1.0],[1,0,0,1,0,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #7 A A A D -D D
1989	[[1,1,1,2,2,2],[ 1.0, 1.0, 1.0, 1.0, 1.0,-1.0],[1,0,0,1,0,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #8 A A A D D -D
1990	[[1,1,2,1,0,0],[ 1.0, 1.0, 1.0, 0.5, 0.0, 0.0],[1,0,1,0,0,0],[1.0,1.0,1.0,0.5,0.0,0.0]], #9 A A C A/2 0 0
1991	[[1,2,3,0,0,0],[ 1.0, 1.0, 1.0, 0.0, 0.0, 0.0],[1,1,1,0,0,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #10 A B C 0 0 0
1992	[[1,1,2,3,0,0],[ 1.0, 1.0, 1.0, 1.0, 0.0, 0.0],[1,0,1,1,0,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #11 A A C D 0 0
1993	[[1,2,1,0,3,0],[ 1.0, 1.0, 1.0, 0.0, 1.0, 0.0],[1,1,0,0,1,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #12 A B A 0 E 0
1994	[[1,2,2,0,0,3],[ 1.0, 1.0, 1.0, 0.0, 0.0, 1.0],[1,1,0,0,0,1],[1.0,1.0,1.0,0.0,0.0,0.0]], #13 A B B 0 0 F
1995	[[1,2,3,2,0,0],[ 1.0, 1.0, 1.0, 0.5, 0.0, 0.0],[1,1,1,0,0,0],[1.0,1.0,1.0,0.0,0.5,0.0]], #14 A B C B/2 0 0
1996	[[1,2,3,1,0,0],[ 1.0, 1.0, 1.0, 0.5, 0.0, 0.0],[1,1,1,0,0,0],[1.0,1.0,1.0,0.0,0.5,0.0]], #15 A B C A/2 0 0
1997	[[1,2,3,4,0,0],[ 1.0, 1.0, 1.0, 1.0, 0.0, 0.0],[1,1,1,1,0,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #16 A B C D 0 0
1998	[[1,2,3,0,4,0],[ 1.0, 1.0, 1.0, 0.0, 1.0, 0.0],[1,1,1,0,1,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #17 A B C 0 E 0
1999	[[1,2,3,0,0,4],[ 1.0, 1.0, 1.0, 0.0, 0.0, 1.0],[1,1,1,0,0,1],[1.0,1.0,1.0,0.0,0.0,0.0]], #18 A B C 0 0 F
2000	[[1,1,2,3,4,4],[ 1.0, 1.0, 1.0, 1.0, 1.0,-1.0],[1,0,1,1,1,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #19 A A C D E -E
2001	[[1,1,2,3,4,4],[ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],[1,0,1,1,1,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #20 A A C D E E
2002	[[1,2,1,3,4,3],[ 1.0, 1.0, 1.0, 1.0, 1.0,-1.0],[1,1,0,1,1,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #21 A B A D E -D
2003	[[1,2,1,3,4,3],[ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],[1,1,0,1,1,0],[1.0,1.0,1.0,0.0,0.0,0.0]], #22 A B A D E D
2004	[[1,2,2,3,3,4],[ 1.0, 1.0, 1.0, 1.0,-1.0, 1.0],[1,1,0,1,0,1],[1.0,1.0,1.0,0.0,0.0,0.0]], #23 A B B D -D F
2005	[[1,2,2,3,3,4],[ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],[1,1,0,1,0,1],[1.0,1.0,1.0,0.0,0.0,0.0]], #24 A B B D D F
2006	[[1,2,3,2,4,4],[ 1.0, 1.0, 1.0, 0.5, 1.0, 2.0],[1,1,1,0,0,1],[1.0,1.0,1.0,0.5,0.0,0.0]], #25 A B C B/2 F/2 F
2007	[[1,2,3,1,0,4],[ 1.0, 1.0, 1.0, 0.5, 0.0, 1.0],[1,1,1,0,0,1],[1.0,1.0,1.0,0.5,0.0,0.0]], #26 A B C A/2 0 F
2008	[[1,2,3,2,4,0],[ 1.0, 1.0, 1.0, 0.5, 1.0, 0.0],[1,1,1,0,1,0],[1.0,1.0,1.0,0.5,0.0,0.0]], #27 A B C B/2 E 0
2009	[[1,2,3,1,4,4],[ 1.0, 1.0, 1.0, 0.5, 1.0, 0.5],[1,1,1,0,1,0],[1.0,1.0,1.0,0.5,0.0,0.0]], #28 A B C A/2 E E/2
2010	[[1,2,3,4,5,6],[ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],[1,1,1,1,1,1],[1.0,1.0,1.0,0.0,0.0,0.0]], #29 A B C D E F
2011	]
2012
2013	################################################################################
2014	#### Site symmetry routines
2015	################################################################################
2016
2017	def GetOprPtrName(key):
2018	'Needs a doc string'
2019	return OprPtrName[key]
2020
2021	def GetOprName(key):
2022	'Needs a doc string'
2023	return OprName[key]
2024
2025	def GetKNsym(key):
2026	'Needs a doc string'
2027	return KNsym[key]
2028
2029	def GetNXUPQsym(siteSym):
2030	'''
2031	The codes XUPQ are for lookup of symmetry constraints for position(X), thermal parm(U) & magnetic moments (P & Q)
2032	'''
2033	return NXUPQsym[siteSym]
2034
2035	def GetCSxinel(siteSym):
2036	"returns Xyz terms, multipliers, GUI flags"
2037	indx = GetNXUPQsym(siteSym)
2038	return CSxinel[indx[0]]
2039
2040	def GetCSuinel(siteSym):
2041	"returns Uij terms, multipliers, GUI flags & Uiso2Uij multipliers"
2042	indx = GetNXUPQsym(siteSym)
2043	return CSuinel[indx[1]]
2044
2045	def GetCSpqinel(siteSym,SpnFlp,dupDir):
2046	"returns Mxyz terms, multipliers, GUI flags"
2047	CSI = [[1,2,3],[1.0,1.0,1.0]]
2048	for opr in dupDir:
2049	if '-1' in siteSym and SpnFlp[len(SpnFlp)//2-1] < 0:
2050	return [[0,0,0],[0.,0.,0.]]
2051	indx = GetNXUPQsym(opr)
2052	if SpnFlp[dupDir[opr]] > 0.:
2053	csi = CSxinel[indx[2]] #P
2054	else:
2055	csi = CSxinel[indx[3]] #Q
2056	if not len(csi):
2057	return [[0,0,0],[0.,0.,0.]]
2058	for kcs in [0,1,2]:
2059	if csi[0][kcs] == 0 and CSI[0][kcs] != 0:
2060	jcs = CSI[0][kcs]
2061	for ics in [0,1,2]:
2062	if CSI[0][ics] == jcs:
2063	CSI[0][ics] = 0
2064	CSI[1][ics] = 0.
2065	elif CSI[0][ics] > jcs:
2066	CSI[0][ics] = CSI[0][jcs]-1
2067	elif CSI[0][kcs] == csi[0][kcs] and CSI[1][kcs] != csi[1][kcs]:
2068	CSI[1][kcs] = csi[1][kcs]
2069	elif CSI[0][kcs] > csi[0][kcs]:
2070	CSI[0][kcs] = min(CSI[0][kcs],csi[0][kcs])
2071	if CSI[1][kcs] == 1.:
2072	CSI[1][kcs] = csi[1][kcs]
2073	return CSI
2074
2075	def getTauT(tau,sop,ssop,XYZ):
2076	ssopinv = nl.inv(ssop[0])
2077	mst = ssopinv[3][:3]
2078	epsinv = ssopinv[3][3]
2079	sdet = nl.det(sop[0])
2080	ssdet = nl.det(ssop[0])
2081	dtau = mst(XYZ-sop[1])-epsinvssop[1][3]
2082	dT = 1.0
2083	if np.any(dtau%.5):
2084	dT = np.tan(np.pi*np.sum(dtau%.5))
2085	tauT = np.inner(mst,XYZ-sop[1])+epsinv*(tau-ssop[1][3])
2086	return sdet,ssdet,dtau,dT,tauT
2087
2088	def OpsfromStringOps(A,SGData,SSGData):
2089	SGOps = SGData['SGOps']
2090	SSGOps = SSGData['SSGOps']
2091	Ax = A.split('+')
2092	Ax[0] = int(Ax[0])
2093	iC = 1
2094	if Ax[0] < 0:
2095	iC = -1
2096	Ax[0] = abs(Ax[0])
2097	nA = Ax[0]%100-1
2098	return SGOps[nA],SSGOps[nA],iC
2099
2100	def GetSSfxuinel(waveType,nH,XYZ,SGData,SSGData,debug=False):
2101
2102	def orderParms(CSI):
2103	parms = [0,]
2104	for csi in CSI:
2105	for i in [0,1,2]:
2106	if csi[i] not in parms:
2107	parms.append(csi[i])
2108	for csi in CSI:
2109	for i in [0,1,2]:
2110	csi[i] = parms.index(csi[i])
2111	return CSI
2112
2113	def fracCrenel(tau,Toff,Twid):
2114	Tau = (tau-Toff[:,np.newaxis])%1.
2115	A = np.where(Tau<Twid[:,np.newaxis],1.,0.)
2116	return A
2117
2118	def fracFourier(tau,nH,fsin,fcos):
2119	SA = np.sin(2.nHnp.pi*tau)
2120	CB = np.cos(2.nHnp.pi*tau)
2121	A = SA[np.newaxis,np.newaxis,:]*fsin[:,:,np.newaxis]
2122	B = CB[np.newaxis,np.newaxis,:]*fcos[:,:,np.newaxis]
2123	return A+B
2124
2125	def posFourier(tau,nH,psin,pcos):
2126	SA = np.sin(2nHnp.pi*tau)
2127	CB = np.cos(2nHnp.pi*tau)
2128	A = SA[np.newaxis,np.newaxis,:]*psin[:,:,np.newaxis]
2129	B = CB[np.newaxis,np.newaxis,:]*pcos[:,:,np.newaxis]
2130	return A+B
2131
2132	def posSawtooth(tau,Toff,slopes):
2133	Tau = (tau-Toff)%1.
2134	A = slopes[:,np.newaxis]*Tau
2135	return A
2136
2137	def posZigZag(tau,Tmm,XYZmax):
2138	DT = Tmm[1]-Tmm[0]
2139	slopeUp = 2.*XYZmax/DT
2140	slopeDn = 2.*XYZmax/(1.-DT)
2141	A = np.array([np.where(Tmm[0] < t%1. <= Tmm[1],-XYZmax+slopeUp((t-Tmm[0])%1.),XYZmax-slopeDn((t-Tmm[1])%1.)) for t in tau])
2142	return A
2143
2144	def posBlock(tau,Tmm,XYZmax):
2145	A = np.array([np.where(Tmm[0] < t <= Tmm[1],XYZmax,-XYZmax) for t in tau])
2146	return A
2147
2148	def DoFrac():
2149	delt2 = np.eye(2)*0.001
2150	FSC = np.ones(2,dtype='i')
2151	CSI = [np.zeros((2),dtype='i'),np.zeros(2)]
2152	if 'Crenel' in waveType:
2153	dF = np.zeros_like(tau)
2154	else:
2155	dF = fracFourier(tau,nH,delt2[:1],delt2[1:]).squeeze()
2156	dFT = np.zeros_like(dF)
2157	dFTP = []
2158	for i in SdIndx:
2159	sop = Sop[i]
2160	ssop = SSop[i]
2161	sdet,ssdet,dtau,dT,tauT = getTauT(tau,sop,ssop,XYZ)
2162	fsc = np.ones(2,dtype='i')
2163	if 'Crenel' in waveType:
2164	dFT = np.zeros_like(tau)
2165	fsc = [1,1]
2166	else: #Fourier
2167	dFT = fracFourier(tauT,nH,delt2[:1],delt2[1:]).squeeze()
2168	dFT = nl.det(sop[0])*dFT
2169	dFT = dFT[:,np.argsort(tauT)]
2170	dFT[0] *= ssdet
2171	dFT[1] *= sdet
2172	dFTP.append(dFT)
2173
2174	if np.any(dtau%.5) and ('1/2' in SSGData['modSymb'] or '1' in SSGData['modSymb']):
2175	fsc = [1,1]
2176	CSI = [[[1,0],[1,0]],[[1.,0.],[1/dT,0.]]]
2177	FSC = np.zeros(2,dtype='i')
2178	return CSI,dF,dFTP
2179	else:
2180	for i in range(2):
2181	if np.allclose(dF[i,:],dFT[i,:],atol=1.e-6):
2182	fsc[i] = 1
2183	else:
2184	fsc[i] = 0
2185	FSC &= fsc
2186	if debug: print (SSMT2text(ssop).replace(' ',''),sdet,ssdet,epsinv,fsc)
2187	n = -1
2188	for i,F in enumerate(FSC):
2189	if F:
2190	n += 1
2191	CSI[0][i] = n+1
2192	CSI[1][i] = 1.0
2193
2194	return CSI,dF,dFTP
2195
2196	def DoXYZ():
2197	delt4 = np.ones(4)*0.001
2198	delt5 = np.ones(5)*0.001
2199	delt6 = np.eye(6)*0.001
2200	if 'Fourier' in waveType:
2201	dX = posFourier(tau,nH,delt6[:3],delt6[3:]) #+np.array(XYZ)[:,np.newaxis,np.newaxis]
2202	#3x6x12 modulated position array (X,Spos,tau)& force positive
2203	CSI = [np.zeros((6,3),dtype='i'),np.zeros((6,3))]
2204	elif waveType == 'Sawtooth':
2205	dX = posSawtooth(tau,delt4[0],delt4[1:])
2206	CSI = [np.array([[1,0,0],[2,0,0],[3,0,0],[4,0,0]]),
2207	np.array([[1.0,.0,.0],[1.0,.0,.0],[1.0,.0,.0],[1.0,.0,.0]])]
2208	elif waveType in ['ZigZag','Block']:
2209	if waveType == 'ZigZag':
2210	dX = posZigZag(tau,delt5[:2],delt5[2:])
2211	else:
2212	dX = posBlock(tau,delt5[:2],delt5[2:])
2213	CSI = [np.array([[1,0,0],[2,0,0],[3,0,0],[4,0,0],[5,0,0]]),
2214	np.array([[1.0,.0,.0],[1.0,.0,.0],[1.0,.0,.0],[1.0,.0,.0],[1.0,.0,.0]])]
2215	XSC = np.ones(6,dtype='i')
2216	dXTP = []
2217	for i in SdIndx:
2218	sop = Sop[i]
2219	ssop = SSop[i]
2220	sdet,ssdet,dtau,dT,tauT = getTauT(tau,sop,ssop,XYZ)
2221	xsc = np.ones(6,dtype='i')
2222	if 'Fourier' in waveType:
2223	dXT = posFourier(np.sort(tauT),nH,delt6[:3],delt6[3:]) #+np.array(XYZ)[:,np.newaxis,np.newaxis]
2224	elif waveType == 'Sawtooth':
2225	dXT = posSawtooth(tauT,delt4[0],delt4[1:])+np.array(XYZ)[:,np.newaxis,np.newaxis]
2226	elif waveType == 'ZigZag':
2227	dXT = posZigZag(tauT,delt5[:2],delt5[2:])+np.array(XYZ)[:,np.newaxis,np.newaxis]
2228	elif waveType == 'Block':
2229	dXT = posBlock(tauT,delt5[:2],delt5[2:])+np.array(XYZ)[:,np.newaxis,np.newaxis]
2230	dXT = np.inner(sop[0],dXT.T) # X modulations array(3x6x49) -> array(3x49x6)
2231	dXT = np.swapaxes(dXT,1,2) # back to array(3x6x49)
2232	dXT[:,:3,:] = (ssdetsdet) # modify the sin component
2233	dXTP.append(dXT)
2234	if waveType == 'Fourier':
2235	for i in range(3):
2236	if not np.allclose(dX[i,i,:],dXT[i,i,:]):
2237	xsc[i] = 0
2238	if not np.allclose(dX[i,i+3,:],dXT[i,i+3,:]):
2239	xsc[i+3] = 0
2240	if np.any(dtau%.5) and ('1/2' in SSGData['modSymb'] or '1' in SSGData['modSymb']):
2241	xsc[3:6] = 0
2242	CSI = [[[1,0,0],[2,0,0],[3,0,0], [1,0,0],[2,0,0],[3,0,0]],
2243	[[1.,0.,0.],[1.,0.,0.],[1.,0.,0.], [1.,0.,0.],[1.,0.,0.],[1.,0.,0.]]]
2244	if '(x)' in siteSym:
2245	CSI[1][3:] = [1./dT,0.,0.],[-dT,0.,0.],[-dT,0.,0.]
2246	if 'm' in siteSym and len(SdIndx) == 1:
2247	CSI[1][3:] = [-dT,0.,0.],[1./dT,0.,0.],[1./dT,0.,0.]
2248	elif '(y)' in siteSym:
2249	CSI[1][3:] = [-dT,0.,0.],[1./dT,0.,0.],[-dT,0.,0.]
2250	if 'm' in siteSym and len(SdIndx) == 1:
2251	CSI[1][3:] = [1./dT,0.,0.],[-dT,0.,0.],[1./dT,0.,0.]
2252	elif '(z)' in siteSym:
2253	CSI[1][3:] = [-dT,0.,0.],[-dT,0.,0.],[1./dT,0.,0.]
2254	if 'm' in siteSym and len(SdIndx) == 1:
2255	CSI[1][3:] = [1./dT,0.,0.],[1./dT,0.,0.],[-dT,0.,0.]
2256	if '4/mmm' in laue:
2257	if np.any(dtau%.5) and '1/2' in SSGData['modSymb']:
2258	if '(xy)' in siteSym:
2259	CSI[0] = [[1,0,0],[1,0,0],[2,0,0], [1,0,0],[1,0,0],[2,0,0]]
2260	CSI[1][3:] = [[1./dT,0.,0.],[1./dT,0.,0.],[-dT,0.,0.]]
2261	if '(xy)' in siteSym or '(+-0)' in siteSym:
2262	mul = 1
2263	if '(+-0)' in siteSym:
2264	mul = -1
2265	if np.allclose(dX[0,0,:],dXT[1,0,:]):
2266	CSI[0][3:5] = [[11,0,0],[11,0,0]]
2267	CSI[1][3:5] = [[1.,0,0],[mul,0,0]]
2268	xsc[3:5] = 0
2269	if np.allclose(dX[0,3,:],dXT[0,4,:]):
2270	CSI[0][:2] = [[12,0,0],[12,0,0]]
2271	CSI[1][:2] = [[1.,0,0],[mul,0,0]]
2272	xsc[:2] = 0
2273	XSC &= xsc
2274	if debug: print (SSMT2text(ssop).replace(' ',''),sdet,ssdet,epsinv,xsc)
2275	if waveType == 'Fourier':
2276	n = -1
2277	if debug: print (XSC)
2278	for i,X in enumerate(XSC):
2279	if X:
2280	n += 1
2281	CSI[0][i][0] = n+1
2282	CSI[1][i][0] = 1.0
2283
2284	return CSI,dX,dXTP
2285
2286	def DoUij():
2287	tau = np.linspace(0,1,49,True)
2288	delt12 = np.eye(12)*0.0001
2289	dU = posFourier(tau,nH,delt12[:6],delt12[6:]) #Uij modulations - 6x12x12 array
2290	CSI = [np.zeros((12,3),dtype='i'),np.zeros((12,3))]
2291	USC = np.ones(12,dtype='i')
2292	dUTP = []
2293	for i in SdIndx:
2294	sop = Sop[i]
2295	ssop = SSop[i]
2296	sdet,ssdet,dtau,dT,tauT = getTauT(tau,sop,ssop,XYZ)
2297	usc = np.ones(12,dtype='i')
2298	dUT = posFourier(tauT,nH,delt12[:6],delt12[6:]) #Uij modulations - 6x12x49 array
2299	dUijT = np.rollaxis(np.rollaxis(np.array(Uij2U(dUT)),3),3) #convert dUT to 12x49x3x3
2300	dUijT = np.rollaxis(np.inner(np.inner(sop[0],dUijT),sop[0].T),3) #transform by sop - 3x3x12x49
2301	dUT = np.array(U2Uij(dUijT)) #convert to 6x12x49
2302	dUT = dUT[:,:,np.argsort(tauT)]
2303	dUT[:,:6,:] =(ssdetsdet)
2304	dUTP.append(dUT)
2305	if np.any(dtau%.5) and ('1/2' in SSGData['modSymb'] or '1' in SSGData['modSymb']):
2306	CSI = [[[1,0,0],[2,0,0],[3,0,0],[4,0,0],[5,0,0],[6,0,0],
2307	[1,0,0],[2,0,0],[3,0,0],[4,0,0],[5,0,0],[6,0,0]],
2308	[[1.,0.,0.],[1.,0.,0.],[1.,0.,0.], [1.,0.,0.],[1.,0.,0.],[1.,0.,0.],
2309	[1./dT,0.,0.],[1./dT,0.,0.],[1./dT,0.,0.], [1.,0.,0.],[1.,0.,0.],[1.,0.,0.]]]
2310	if 'mm2(x)' in siteSym:
2311	CSI[1][9:] = [0.,0.,0.],[-dT,0.,0.],[0.,0.,0.]
2312	USC = [1,1,1,0,1,0,1,1,1,0,1,0]
2313	elif '(xy)' in siteSym:
2314	CSI[0] = [[1,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0],[4,0,0],
2315	[1,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0],[4,0,0]]
2316	CSI[1][9:] = [[1./dT,0.,0.],[-dT,0.,0.],[-dT,0.,0.]]
2317	USC = [1,1,1,1,1,1,1,1,1,1,1,1]
2318	elif '(x)' in siteSym:
2319	CSI[1][9:] = [-dT,0.,0.],[-dT,0.,0.],[1./dT,0.,0.]
2320	elif '(y)' in siteSym:
2321	CSI[1][9:] = [-dT,0.,0.],[1./dT,0.,0.],[-dT,0.,0.]
2322	elif '(z)' in siteSym:
2323	CSI[1][9:] = [1./dT,0.,0.],[-dT,0.,0.],[-dT,0.,0.]
2324	for i in range(6):
2325	if not USC[i]:
2326	CSI[0][i] = [0,0,0]
2327	CSI[1][i] = [0.,0.,0.]
2328	CSI[0][i+6] = [0,0,0]
2329	CSI[1][i+6] = [0.,0.,0.]
2330	else:
2331	for i in range(6):
2332	if not np.allclose(dU[i,i,:],dUT[i,i,:]): #sin part
2333	usc[i] = 0
2334	if not np.allclose(dU[i,i+6,:],dUT[i,i+6,:]): #cos part
2335	usc[i+6] = 0
2336	if np.any(dUT[1,0,:]):
2337	if '4/m' in siteSym:
2338	CSI[0][6:8] = [[12,0,0],[12,0,0]]
2339	if ssop[1][3]:
2340	CSI[1][6:8] = [[1.,0.,0.],[-1.,0.,0.]]
2341	usc[9] = 1
2342	else:
2343	CSI[1][6:8] = [[1.,0.,0.],[1.,0.,0.]]
2344	usc[9] = 0
2345	elif '4' in siteSym:
2346	CSI[0][6:8] = [[12,0,0],[12,0,0]]
2347	CSI[0][:2] = [[11,0,0],[11,0,0]]
2348	if ssop[1][3]:
2349	CSI[1][:2] = [[1.,0.,0.],[-1.,0.,0.]]
2350	CSI[1][6:8] = [[1.,0.,0.],[-1.,0.,0.]]
2351	usc[2] = 0
2352	usc[8] = 0
2353	usc[3] = 1
2354	usc[9] = 1
2355	else:
2356	CSI[1][:2] = [[1.,0.,0.],[1.,0.,0.]]
2357	CSI[1][6:8] = [[1.,0.,0.],[1.,0.,0.]]
2358	usc[2] = 1
2359	usc[8] = 1
2360	usc[3] = 0
2361	usc[9] = 0
2362	elif 'xy' in siteSym or '+-0' in siteSym:
2363	if np.allclose(dU[0,0,:],dUT[0,1,:]*sdet):
2364	CSI[0][4:6] = [[12,0,0],[12,0,0]]
2365	CSI[0][6:8] = [[11,0,0],[11,0,0]]
2366	CSI[1][4:6] = [[1.,0.,0.],[sdet,0.,0.]]
2367	CSI[1][6:8] = [[1.,0.,0.],[sdet,0.,0.]]
2368	usc[4:6] = 0
2369	usc[6:8] = 0
2370
2371	if debug: print (SSMT2text(ssop).replace(' ',''),sdet,ssdet,epsinv,usc)
2372	USC &= usc
2373	if debug: print (USC)
2374	if not np.any(dtau%.5):
2375	n = -1
2376	for i,U in enumerate(USC):
2377	if U:
2378	n += 1
2379	CSI[0][i][0] = n+1
2380	CSI[1][i][0] = 1.0
2381
2382	return CSI,dU,dUTP
2383
2384	if debug: print ('super space group: '+SSGData['SSpGrp'])
2385	CSI = {'Sfrac':[[[1,0],[2,0]],[[1.,0.],[1.,0.]]],
2386	'Spos':[[[1,0,0],[2,0,0],[3,0,0], [4,0,0],[5,0,0],[6,0,0]],
2387	[[1.,0.,0.],[1.,0.,0.],[1.,0.,0.], [1.,0.,0.],[1.,0.,0.],[1.,0.,0.]]], #sin & cos
2388	'Sadp':[[[1,0,0],[2,0,0],[3,0,0],[4,0,0],[5,0,0],[6,0,0],
2389	[7,0,0],[8,0,0],[9,0,0],[10,0,0],[11,0,0],[12,0,0]],
2390	[[1.,0.,0.],[1.,0.,0.],[1.,0.,0.], [1.,0.,0.],[1.,0.,0.],[1.,0.,0.],
2391	[1.,0.,0.],[1.,0.,0.],[1.,0.,0.], [1.,0.,0.],[1.,0.,0.],[1.,0.,0.]]],
2392	'Smag':[[[1,0,0],[2,0,0],[3,0,0], [4,0,0],[5,0,0],[6,0,0]],
2393	[[1.,0.,0.],[1.,0.,0.],[1.,0.,0.], [1.,0.,0.],[1.,0.,0.],[1.,0.,0.]]],}
2394	xyz = np.array(XYZ)%1.
2395	SGOps = copy.deepcopy(SGData['SGOps'])
2396	laue = SGData['SGLaue']
2397	siteSym = SytSym(XYZ,SGData)[0].strip()
2398	if debug: print ('siteSym: '+siteSym)
2399	if siteSym == '1': #"1" site symmetry
2400	if debug:
2401	return CSI,None,None,None,None
2402	else:
2403	return CSI
2404	elif siteSym == '-1': #"-1" site symmetry
2405	CSI['Sfrac'][0] = [[1,0],[0,0]]
2406	CSI['Spos'][0] = [[1,0,0],[2,0,0],[3,0,0], [0,0,0],[0,0,0],[0,0,0]]
2407	CSI['Sadp'][0] = [[0,0,0],[0,0,0],[0,0,0],[0,0,0],[0,0,0],[0,0,0],
2408	[1,0,0],[2,0,0],[3,0,0],[4,0,0],[5,0,0],[6,0,0]]
2409	if debug:
2410	return CSI,None,None,None,None
2411	else:
2412	return CSI
2413	SSGOps = copy.deepcopy(SSGData['SSGOps'])
2414	#expand ops to include inversions if any
2415	if SGData['SGInv']:
2416	for op,sop in zip(SGData['SGOps'],SSGData['SSGOps']):
2417	SGOps.append([-op[0],-op[1]%1.])
2418	SSGOps.append([-sop[0],-sop[1]%1.])
2419	#build set of sym ops around special position
2420	SSop = []
2421	Sop = []
2422	Sdtau = []
2423	for iop,Op in enumerate(SGOps):
2424	nxyz = (np.inner(Op[0],xyz)+Op[1])%1.
2425	if np.allclose(xyz,nxyz,1.e-4) and iop and MT2text(Op).replace(' ','') != '-X,-Y,-Z':
2426	SSop.append(SSGOps[iop])
2427	Sop.append(SGOps[iop])
2428	ssopinv = nl.inv(SSGOps[iop][0])
2429	mst = ssopinv[3][:3]
2430	epsinv = ssopinv[3][3]
2431	Sdtau.append(np.sum(mst(XYZ-SGOps[iop][1])-epsinvSSGOps[iop][1][3]))
2432	SdIndx = np.argsort(np.array(Sdtau)) # just to do in sensible order
2433	if debug: print ('special pos super operators: ',[SSMT2text(ss).replace(' ','') for ss in SSop])
2434	#setup displacement arrays
2435	tau = np.linspace(-1,1,49,True)
2436	#make modulation arrays - one parameter at a time
2437	#site fractions
2438	CSI['Sfrac'],dF,dFTP = DoFrac()
2439	#positions
2440	CSI['Spos'],dX,dXTP = DoXYZ()
2441	#anisotropic thermal motion
2442	CSI['Sadp'],dU,dUTP = DoUij()
2443	CSI['Spos'][0] = orderParms(CSI['Spos'][0])
2444	CSI['Sadp'][0] = orderParms(CSI['Sadp'][0])
2445	if debug:
2446	return CSI,tau,[dF,dFTP],[dX,dXTP],[dU,dUTP]
2447	else:
2448	return CSI
2449
2450	def MustrainNames(SGData):
2451	'Needs a doc string'
2452	laue = SGData['SGLaue']
2453	uniq = SGData['SGUniq']
2454	if laue in ['m3','m3m']:
2455	return ['S400','S220']
2456	elif laue in ['6/m','6/mmm','3m1']:
2457	return ['S400','S004','S202']
2458	elif laue in ['31m','3']:
2459	return ['S400','S004','S202','S211']
2460	elif laue in ['3R','3mR']:
2461	return ['S400','S220','S310','S211']
2462	elif laue in ['4/m','4/mmm']:
2463	return ['S400','S004','S220','S022']
2464	elif laue in ['mmm']:
2465	return ['S400','S040','S004','S220','S202','S022']
2466	elif laue in ['2/m']:
2467	SHKL = ['S400','S040','S004','S220','S202','S022']
2468	if uniq == 'a':
2469	SHKL += ['S013','S031','S211']
2470	elif uniq == 'b':
2471	SHKL += ['S301','S103','S121']
2472	elif uniq == 'c':
2473	SHKL += ['S130','S310','S112']
2474	return SHKL
2475	else:
2476	SHKL = ['S400','S040','S004','S220','S202','S022']
2477	SHKL += ['S310','S103','S031','S130','S301','S013']
2478	SHKL += ['S211','S121','S112']
2479	return SHKL
2480
2481	def HStrainVals(HSvals,SGData):
2482	laue = SGData['SGLaue']
2483	uniq = SGData['SGUniq']
2484	DIJ = np.zeros(6)
2485	if laue in ['m3','m3m']:
2486	DIJ[:3] = [HSvals[0],HSvals[0],HSvals[0]]
2487	elif laue in ['6/m','6/mmm','3m1','31m','3']:
2488	DIJ[:4] = [HSvals[0],HSvals[0],HSvals[1],HSvals[0]]
2489	elif laue in ['3R','3mR']:
2490	DIJ = [HSvals[0],HSvals[0],HSvals[0],HSvals[1],HSvals[1],HSvals[1]]
2491	elif laue in ['4/m','4/mmm']:
2492	DIJ[:3] = [HSvals[0],HSvals[0],HSvals[1]]
2493	elif laue in ['mmm']:
2494	DIJ[:3] = [HSvals[0],HSvals[1],HSvals[2]]
2495	elif laue in ['2/m']:
2496	DIJ[:3] = [HSvals[0],HSvals[1],HSvals[2]]
2497	if uniq == 'a':
2498	DIJ[5] = HSvals[3]
2499	elif uniq == 'b':
2500	DIJ[4] = HSvals[3]
2501	elif uniq == 'c':
2502	DIJ[3] = HSvals[3]
2503	else:
2504	DIJ = [HSvals[0],HSvals[1],HSvals[2],HSvals[3],HSvals[4],HSvals[5]]
2505	return DIJ
2506
2507	def HStrainNames(SGData):
2508	'Needs a doc string'
2509	laue = SGData['SGLaue']
2510	uniq = SGData['SGUniq']
2511	if laue in ['m3','m3m']:
2512	return ['D11','eA'] #add cubic strain term
2513	elif laue in ['6/m','6/mmm','3m1','31m','3']:
2514	return ['D11','D33']
2515	elif laue in ['3R','3mR']:
2516	return ['D11','D12']
2517	elif laue in ['4/m','4/mmm']:
2518	return ['D11','D33']
2519	elif laue in ['mmm']:
2520	return ['D11','D22','D33']
2521	elif laue in ['2/m']:
2522	Dij = ['D11','D22','D33']
2523	if uniq == 'a':
2524	Dij += ['D23']
2525	elif uniq == 'b':
2526	Dij += ['D13']
2527	elif uniq == 'c':
2528	Dij += ['D12']
2529	return Dij
2530	else:
2531	Dij = ['D11','D22','D33','D12','D13','D23']
2532	return Dij
2533
2534	def MustrainCoeff(HKL,SGData):
2535	'Needs a doc string'
2536	#NB: order of terms is the same as returned by MustrainNames
2537	laue = SGData['SGLaue']
2538	uniq = SGData['SGUniq']
2539	h,k,l = HKL
2540	Strm = []
2541	if laue in ['m3','m3m']:
2542	Strm.append(h4+k4+l**4)
2543	Strm.append(3.0((hk)*2+(hl)*2+(kl)**2))
2544	elif laue in ['6/m','6/mmm','3m1']:
2545	Strm.append(h4+k4+2.0kh*3+2.0hk3+3.0(hk)*2)
2546	Strm.append(l**4)
2547	Strm.append(3.0((hl)*2+(kl)*2+hkl*2))
2548	elif laue in ['31m','3']:
2549	Strm.append(h4+k4+2.0kh*3+2.0hk3+3.0(hk)*2)
2550	Strm.append(l**4)
2551	Strm.append(3.0((hl)*2+(kl)*2+hkl*2))
2552	Strm.append(4.0hkl(h+k))
2553	elif laue in ['3R','3mR']:
2554	Strm.append(h4+k4+l**4)
2555	Strm.append(3.0((hk)*2+(hl)*2+(kl)**2))
2556	Strm.append(2.0(hl*3+lk*3+kh*3)+2.0(lh3+kl*3+lk**3))
2557	Strm.append(4.0(klh2+hlk2+hkl*2))
2558	elif laue in ['4/m','4/mmm']:
2559	Strm.append(h4+k4)
2560	Strm.append(l**4)
2561	Strm.append(3.0(hk)**2)
2562	Strm.append(3.0((hl)*2+(kl)**2))
2563	elif laue in ['mmm']:
2564	Strm.append(h**4)
2565	Strm.append(k**4)
2566	Strm.append(l**4)
2567	Strm.append(3.0(hk)**2)
2568	Strm.append(3.0(hl)**2)
2569	Strm.append(3.0(kl)**2)
2570	elif laue in ['2/m']:
2571	Strm.append(h**4)
2572	Strm.append(k**4)
2573	Strm.append(l**4)
2574	Strm.append(3.0(hk)**2)
2575	Strm.append(3.0(hl)**2)
2576	Strm.append(3.0(kl)**2)
2577	if uniq == 'a':
2578	Strm.append(2.0kl**3)
2579	Strm.append(2.0lk**3)
2580	Strm.append(4.0klh*2)
2581	elif uniq == 'b':
2582	Strm.append(2.0lh**3)
2583	Strm.append(2.0hl**3)
2584	Strm.append(4.0hlk*2)
2585	elif uniq == 'c':
2586	Strm.append(2.0hk**3)
2587	Strm.append(2.0kh**3)
2588	Strm.append(4.0hkl*2)
2589	else:
2590	Strm.append(h**4)
2591	Strm.append(k**4)
2592	Strm.append(l**4)
2593	Strm.append(3.0(hk)**2)
2594	Strm.append(3.0(hl)**2)
2595	Strm.append(3.0(kl)**2)
2596	Strm.append(2.0kh**3)
2597	Strm.append(2.0hl**3)
2598	Strm.append(2.0lk**3)
2599	Strm.append(2.0hk**3)
2600	Strm.append(2.0lh**3)
2601	Strm.append(2.0kl**3)
2602	Strm.append(4.0klh*2)
2603	Strm.append(4.0hlk*2)
2604	Strm.append(4.0khl*2)
2605	return Strm
2606
2607	def Muiso2Shkl(muiso,SGData,cell):
2608	"this is to convert isotropic mustrain to generalized Shkls"
2609	import GSASIIlattice as G2lat
2610	A = G2lat.cell2AB(cell)[0]
2611
2612	def minMus(Shkl,muiso,H,SGData,A):
2613	U = np.inner(A.T,H)
2614	S = np.array(MustrainCoeff(U,SGData))
2615	Sum = np.sqrt(np.sum(np.multiply(S,Shkl[:,np.newaxis]),axis=0))
2616	rad = np.sqrt(np.sum((Sum[:,np.newaxis]H)*2,axis=1))
2617	return (muiso-rad)**2
2618
2619	laue = SGData['SGLaue']
2620	PHI = np.linspace(0.,360.,60,True)
2621	PSI = np.linspace(0.,180.,60,True)
2622	X = np.outer(npsind(PHI),npsind(PSI))
2623	Y = np.outer(npcosd(PHI),npsind(PSI))
2624	Z = np.outer(np.ones(np.size(PHI)),npcosd(PSI))
2625	HKL = np.dstack((X,Y,Z))
2626	if laue in ['m3','m3m']:
2627	S0 = [1000.,1000.]
2628	elif laue in ['6/m','6/mmm','3m1']:
2629	S0 = [1000.,1000.,1000.]
2630	elif laue in ['31m','3']:
2631	S0 = [1000.,1000.,1000.,1000.]
2632	elif laue in ['3R','3mR']:
2633	S0 = [1000.,1000.,1000.,1000.]
2634	elif laue in ['4/m','4/mmm']:
2635	S0 = [1000.,1000.,1000.,1000.]
2636	elif laue in ['mmm']:
2637	S0 = [1000.,1000.,1000.,1000.,1000.,1000.]
2638	elif laue in ['2/m']:
2639	S0 = [1000.,1000.,1000.,0.,0.,0.,0.,0.,0.]
2640	else:
2641	S0 = [1000.,1000.,1000.,1000.,1000., 1000.,1000.,1000.,1000.,1000.,
2642	1000.,1000.,0.,0.,0.]
2643	S0 = np.array(S0)
2644	HKL = np.reshape(HKL,(-1,3))
2645	result = so.leastsq(minMus,S0,(np.ones(HKL.shape[0])*muiso,HKL,SGData,A))
2646	return result[0]
2647
2648	def PackRot(SGOps):
2649	IRT = []
2650	for ops in SGOps:
2651	M = ops[0]
2652	irt = 0
2653	for j in range(2,-1,-1):
2654	for k in range(2,-1,-1):
2655	irt *= 3
2656	irt += M[k][j]
2657	IRT.append(int(irt))
2658	return IRT
2659
2660	def SytSym(XYZ,SGData):
2661	'''
2662	Generates the number of equivalent positions and a site symmetry code for a specified coordinate and space group
2663
2664	:param XYZ: an array, tuple or list containing 3 elements: x, y & z
2665	:param SGData: from SpcGroup
2666	:Returns: a two element tuple:
2667
2668	* The 1st element is a code for the site symmetry (see GetKNsym)
2669	* The 2nd element is the site multiplicity
2670
2671	'''
2672	Mult = 1
2673	Isym = 0
2674	if SGData['SGLaue'] in ['3','3m1','31m','6/m','6/mmm']:
2675	Isym = 1073741824
2676	Jdup = 0
2677	Ndup = 0
2678	dupDir = {}
2679	Xeqv = list(GenAtom(XYZ,SGData,True))
2680	IRT = PackRot(SGData['SGOps'])
2681	L = -1
2682	for ic,cen in enumerate(SGData['SGCen']):
2683	for invers in range(int(SGData['SGInv']+1)):
2684	for io,ops in enumerate(SGData['SGOps']):
2685	irtx = (1-2invers)IRT[io]
2686	L += 1
2687	if not Xeqv[L][1]:
2688	Ndup = io
2689	Jdup += 1
2690	jx = GetOprPtrName(str(irtx)) #[KN table no,op name,KNsym ptr]
2691	if jx[2] < 39:
2692	px = GetOprName(str(irtx))
2693	if px != '6643': #skip Iden
2694	dupDir[px] = io
2695	Isym += 2**(jx[2]-1)
2696	if Isym == 1073741824: Isym = 0
2697	Mult = len(SGData['SGOps'])len(SGData['SGCen'])(int(SGData['SGInv'])+1)//Jdup
2698
2699	return GetKNsym(str(Isym)),Mult,Ndup,dupDir
2700
2701	def ElemPosition(SGData):
2702	''' Under development.
2703	Object here is to return a list of symmetry element types and locations suitable
2704	for say drawing them.
2705	So far I have the element type... getting all possible locations without lookup may be impossible!
2706	'''
2707	Inv = SGData['SGInv']
2708	eleSym = {-3:['','-1'],-2:['',-6],-1:['2','-4'],0:['3','-3'],1:['4','m'],2:['6',''],3:['1','']}
2709	# get operators & expand if centrosymmetric
2710	Ops = SGData['SGOps']
2711	opM = np.array([op[0].T for op in Ops])
2712	opT = np.array([op[1] for op in Ops])
2713	if Inv:
2714	opM = np.concatenate((opM,-opM))
2715	opT = np.concatenate((opT,-opT))
2716	opMT = list(zip(opM,opT))
2717	for M,T in opMT[1:]: #skip I
2718	Dt = int(nl.det(M))
2719	Tr = int(np.trace(M))
2720	Dt = -(Dt-1)//2
2721	Es = eleSym[Tr][Dt]
2722	if Dt: #rotation-inversion
2723	I = np.eye(3)
2724	if Tr == 1: #mirrors/glides
2725	if np.any(T): #glide
2726	M2 = np.inner(M,M)
2727	MT = np.inner(M,T)+T
2728	print ('glide',Es,MT)
2729	print (M2)
2730	else: #mirror
2731	print ('mirror',Es,T)
2732	print (I-M)
2733	X = [-1,-1,-1]
2734	elif Tr == -3: # pure inversion
2735	X = np.inner(nl.inv(I-M),T)
2736	print ('inversion',Es,X)
2737	else: #other rotation-inversion
2738	M2 = np.inner(M,M)
2739	MT = np.inner(M,T)+T
2740	print ('rot-inv',Es,MT)
2741	print (M2)
2742	X = [-1,-1,-1]
2743	else: #rotations
2744	print ('rotation',Es)
2745	X = [-1,-1,-1]
2746	#SymElements.append([Es,X])
2747
2748	return #SymElements
2749
2750	def ApplyStringOps(A,SGData,X,Uij=[]):
2751	'Needs a doc string'
2752	SGOps = SGData['SGOps']
2753	SGCen = SGData['SGCen']
2754	Ax = A.split('+')
2755	Ax[0] = int(Ax[0])
2756	iC = 0
2757	if Ax[0] < 0:
2758	iC = 1
2759	Ax[0] = abs(Ax[0])
2760	nA = Ax[0]%100-1
2761	cA = Ax[0]//100
2762	Cen = SGCen[cA]
2763	M,T = SGOps[nA]
2764	if len(Ax)>1:
2765	cellA = Ax[1].split(',')
2766	cellA = np.array([int(a) for a in cellA])
2767	else:
2768	cellA = np.zeros(3)
2769	newX = Cen+(1-2iC)(np.inner(M,X).T+T)+cellA
2770	if len(Uij):
2771	U = Uij2U(Uij)
2772	U = np.inner(M,np.inner(U,M).T)
2773	newUij = U2Uij(U)
2774	return [newX,newUij]
2775	else:
2776	return newX
2777
2778	def StringOpsProd(A,B,SGData):
2779	"""
2780	Find AB where A & B are in strings '-' + '100c+n' + '+ijk'
2781	where '-' indicates inversion, c(>0) is the cell centering operator,
2782	n is operator number from SgOps and ijk are unit cell translations (each may be <0).
2783	Should return resultant string - C. SGData - dictionary using entries:
2784
2785	* 'SGCen': cell centering vectors [0,0,0] at least
2786	* 'SGOps': symmetry operations as [M,T] so that M*x+T = x'
2787
2788	"""
2789	SGOps = SGData['SGOps']
2790	SGCen = SGData['SGCen']
2791	#1st split out the cell translation part & work on the operator parts
2792	Ax = A.split('+'); Bx = B.split('+')
2793	Ax[0] = int(Ax[0]); Bx[0] = int(Bx[0])
2794	iC = 0
2795	if Ax[0]*Bx[0] < 0:
2796	iC = 1
2797	Ax[0] = abs(Ax[0]); Bx[0] = abs(Bx[0])
2798	nA = Ax[0]%100-1; nB = Bx[0]%100-1
2799	cA = Ax[0]//100; cB = Bx[0]//100
2800	Cen = (SGCen[cA]+SGCen[cB])%1.0
2801	cC = np.nonzero([np.allclose(C,Cen) for C in SGCen])[0][0]
2802	Ma,Ta = SGOps[nA]; Mb,Tb = SGOps[nB]
2803	Mc = np.inner(Ma,Mb.T)
2804	# print Ma,Mb,Mc
2805	Tc = (np.add(np.inner(Mb,Ta)+1.,Tb))%1.0
2806	# print Ta,Tb,Tc
2807	# print [np.allclose(M,Mc)&np.allclose(T,Tc) for M,T in SGOps]
2808	nC = np.nonzero([np.allclose(M,Mc)&np.allclose(T,Tc) for M,T in SGOps])[0][0]
2809	#now the cell translation part
2810	if len(Ax)>1:
2811	cellA = Ax[1].split(',')
2812	cellA = [int(a) for a in cellA]
2813	else:
2814	cellA = [0,0,0]
2815	if len(Bx)>1:
2816	cellB = Bx[1].split(',')
2817	cellB = [int(b) for b in cellB]
2818	else:
2819	cellB = [0,0,0]
2820	cellC = np.add(cellA,cellB)
2821	C = str(((nC+1)+(100cC))(1-2*iC))+'+'+ \
2822	str(int(cellC[0]))+','+str(int(cellC[1]))+','+str(int(cellC[2]))
2823	return C
2824
2825	def U2Uij(U):
2826	#returns the UIJ vector U11,U22,U33,U12,U13,U23 from tensor U
2827	return [U[0][0],U[1][1],U[2][2],U[0][1],U[0][2],U[1][2]]
2828
2829	def Uij2U(Uij):
2830	#returns the thermal motion tensor U from Uij as numpy array
2831	return np.array([[Uij[0],Uij[3],Uij[4]],[Uij[3],Uij[1],Uij[5]],[Uij[4],Uij[5],Uij[2]]])
2832
2833	def StandardizeSpcName(spcgroup):
2834	'''Accept a spacegroup name where spaces may have not been used
2835	in the names according to the GSAS convention (spaces between symmetry
2836	for each axis) and return the space group name as used in GSAS
2837	'''
2838	rspc = spcgroup.replace(' ','').upper()
2839	# deal with rhombohedral and hexagonal setting designations
2840	rhomb = ''
2841	if rspc[-1:] == 'R':
2842	rspc = rspc[:-1]
2843	rhomb = ' R'
2844	elif rspc[-1:] == 'H': # hexagonal is assumed and thus can be ignored
2845	rspc = rspc[:-1]
2846	# look for a match in the spacegroup lists
2847	for i in spglist.values():
2848	for spc in i:
2849	if rspc == spc.replace(' ','').upper():
2850	return spc + rhomb
2851	# how about the post-2002 orthorhombic names?
2852	for i,spc in sgequiv_2002_orthorhombic:
2853	if rspc == i.replace(' ','').upper():
2854	return spc
2855	# not found
2856	return ''
2857
2858	spgbyNum = []
2859	'''Space groups indexed by number'''
2860	spgbyNum = [None,
2861	'P 1','P -1', #1-2
2862	'P 2','P 21','C 2','P m','P c','C m','C c','P 2/m','P 21/m',
2863	'C 2/m','P 2/c','P 21/c','C 2/c', #3-15
2864	'P 2 2 2','P 2 2 21','P 21 21 2','P 21 21 21',
2865	'C 2 2 21','C 2 2 2','F 2 2 2','I 2 2 2','I 21 21 21',
2866	'P m m 2','P m c 21','P c c 2','P m a 2','P c a 21',
2867	'P n c 2','P m n 21','P b a 2','P n a 21','P n n 2',
2868	'C m m 2','C m c 21','C c c 2',
2869	'A m m 2','A b m 2','A m a 2','A b a 2',
2870	'F m m 2','F d d 2','I m m 2','I b a 2','I m a 2',
2871	'P m m m','P n n n','P c c m','P b a n',
2872	'P m m a','P n n a','P m n a','P c c a','P b a m','P c c n',
2873	'P b c m','P n n m','P m m n','P b c n','P b c a','P n m a',
2874	'C m c m','C m c a','C m m m','C c c m','C m m a','C c c a',
2875	'F m m m', 'F d d d',
2876	'I m m m','I b a m','I b c a','I m m a', #16-74
2877	'P 4','P 41','P 42','P 43',
2878	'I 4','I 41',
2879	'P -4','I -4','P 4/m','P 42/m','P 4/n','P 42/n',
2880	'I 4/m','I 41/a',
2881	'P 4 2 2','P 4 21 2','P 41 2 2','P 41 21 2','P 42 2 2',
2882	'P 42 21 2','P 43 2 2','P 43 21 2',
2883	'I 4 2 2','I 41 2 2',
2884	'P 4 m m','P 4 b m','P 42 c m','P 42 n m','P 4 c c','P 4 n c',
2885	'P 42 m c','P 42 b c',
2886	'I 4 m m','I 4 c m','I 41 m d','I 41 c d',
2887	'P -4 2 m','P -4 2 c','P -4 21 m','P -4 21 c','P -4 m 2',
2888	'P -4 c 2','P -4 b 2','P -4 n 2',
2889	'I -4 m 2','I -4 c 2','I -4 2 m','I -4 2 d',
2890	'P 4/m m m','P 4/m c c','P 4/n b m','P 4/n n c','P 4/m b m',
2891	'P 4/m n c','P 4/n m m','P 4/n c c','P 42/m m c','P 42/m c m',
2892	'P 42/n b c','P 42/n n m','P 42/m b c','P 42/m n m','P 42/n m c',
2893	'P 42/n c m',
2894	'I 4/m m m','I 4/m c m','I 41/a m d','I 41/a c d',
2895	'P 3','P 31','P 32','R 3','P -3','R -3',
2896	'P 3 1 2','P 3 2 1','P 31 1 2','P 31 2 1','P 32 1 2','P 32 2 1',
2897	'R 3 2',
2898	'P 3 m 1','P 3 1 m','P 3 c 1','P 3 1 c',
2899	'R 3 m','R 3 c',
2900	'P -3 1 m','P -3 1 c','P -3 m 1','P -3 c 1',
2901	'R -3 m','R -3 c', #75-167
2902	'P 6','P 61',
2903	'P 65','P 62','P 64','P 63','P -6','P 6/m','P 63/m','P 6 2 2',
2904	'P 61 2 2','P 65 2 2','P 62 2 2','P 64 2 2','P 63 2 2','P 6 m m',
2905	'P 6 c c','P 63 c m','P 63 m c','P -6 m 2','P -6 c 2','P -6 2 m',
2906	'P -6 2 c','P 6/m m m','P 6/m c c','P 63/m c m','P 63/m m c', #168-194
2907	'P 2 3','F 2 3','I 2 3','P 21 3','I 21 3','P m 3','P n 3',
2908	'F m -3','F d -3','I m -3',
2909	'P a -3','I a -3','P 4 3 2','P 42 3 2','F 4 3 2','F 41 3 2',
2910	'I 4 3 2','P 43 3 2','P 41 3 2','I 41 3 2','P -4 3 m',
2911	'F -4 3 m','I -4 3 m','P -4 3 n','F -4 3 c','I -4 3 d',
2912	'P m -3 m','P n -3 n','P m -3 n','P n -3 m',
2913	'F m -3 m','F m -3 c','F d -3 m','F d -3 c',
2914	'I m -3 m','I a -3 d',] #195-230
2915	spg2origins = {}
2916	''' A dictionary of all spacegroups that have 2nd settings; the value is the
2917	1st --> 2nd setting transformation vector as X(2nd) = X(1st)-V, nonstandard ones are included.
2918	'''
2919	spg2origins = {
2920	'P n n n':[-.25,-.25,-.25],
2921	'P b a n':[-.25,-.25,0],'P n c b':[0,-.25,-.25],'P c n a':[-.25,0,-.25],
2922	'P m m n':[-.25,-.25,0],'P n m m':[0,-.25,-.25],'P m n m':[-.25,0,-.25],
2923	'C c c a':[0,-.25,-.25],'C c c b':[-.25,0,-.25],'A b a a':[-.25,0,-.25],
2924	'A c a a':[-.25,-.25,0],'B b c b':[-.25,-.25,0],'B b a b':[0,-.25,-.25],
2925	'F d d d':[-.125,-.125,-.125],
2926	'P 4/n':[-.25,-.25,0],'P 42/n':[-.25,-.25,-.25],'I 41/a':[0,-.25,-.125],
2927	'P 4/n b m':[-.25,-.25,0],'P 4/n n c':[-.25,-.25,-.25],'P 4/n m m':[-.25,-.25,0],'P 4/n c c':[-.25,-.25,0],
2928	'P 42/n b c':[-.25,-.25,-.25],'P 42/n n m':[-.25,.25,-.25],'P 42/n m c':[-.25,.25,-.25],'P 42/n c m':[-.25,.25,-.25],
2929	'I 41/a m d':[0,.25,-.125],'I 41/a c d':[0,.25,-.125],
2930	'p n -3':[-.25,-.25,-.25],'F d -3':[-.125,-.125,-.125],'P n -3 n':[-.25,-.25,-.25],
2931	'P n -3 m':[-.25,-.25,-.25],'F d -3 m':[-.125,-.125,-.125],'F d -3 c':[-.375,-.375,-.375],
2932	'p n 3':[-.25,-.25,-.25],'F d 3':[-.125,-.125,-.125],'P n 3 n':[-.25,-.25,-.25],
2933	'P n 3 m':[-.25,-.25,-.25],'F d 3 m':[-.125,-.125,-.125],'F d - c':[-.375,-.375,-.375]}
2934	spglist = {}
2935	'''A dictionary of space groups as ordered and named in the pre-2002 International
2936	Tables Volume A, except that spaces are used following the GSAS convention to
2937	separate the different crystallographic directions.
2938	Note that the symmetry codes here will recognize many non-standard space group
2939	symbols with different settings. They are ordered by Laue group
2940	'''
2941	spglist = {
2942	'P1' : ('P 1','P -1',), # 1-2
2943	'C1' : ('C 1','C -1',),
2944	'P2/m': ('P 2','P 21','P m','P a','P c','P n',
2945	'P 2/m','P 21/m','P 2/c','P 2/a','P 2/n','P 21/c','P 21/a','P 21/n',), #3-15
2946	'C2/m':('C 2','C m','C c','C n',
2947	'C 2/m','C 2/c','C 2/n',),
2948	'Pmmm':('P 2 2 2',
2949	'P 2 2 21','P 21 2 2','P 2 21 2',
2950	'P 21 21 2','P 2 21 21','P 21 2 21',
2951	'P 21 21 21',
2952	'P m m 2','P 2 m m','P m 2 m',
2953	'P m c 21','P 21 m a','P b 21 m','P m 21 b','P c m 21','P 21 a m',
2954	'P c c 2','P 2 a a','P b 2 b',
2955	'P m a 2','P 2 m b','P c 2 m','P m 2 a','P b m 2','P 2 c m',
2956	'P c a 21','P 21 a b','P c 21 b','P b 21 a','P b c 21','P 21 c a',
2957	'P n c 2','P 2 n a','P b 2 n','P n 2 b','P c n 2','P 2 a n',
2958	'P m n 21','P 21 m n','P n 21 m','P m 21 n','P n m 21','P 21 n m',
2959	'P b a 2','P 2 c b','P c 2 a',
2960	'P n a 21','P 21 n b','P c 21 n','P n 21 a','P b n 21','P 21 c n',
2961	'P n n 2','P 2 n n','P n 2 n',
2962	'P m m m','P n n n',
2963	'P c c m','P m a a','P b m b',
2964	'P b a n','P n c b','P c n a',
2965	'P m m a','P b m m','P m c m','P m a m','P m m b','P c m m',
2966	'P n n a','P b n n','P n c n','P n a n','P n n b','P c n n',
2967	'P m n a','P b m n','P n c m','P m a n','P n m b','P c n m',
2968	'P c c a','P b a a','P b c b','P b a b','P c c b','P c a a',
2969	'P b a m','P m c b','P c m a',
2970	'P c c n','P n a a','P b n b',
2971	'P b c m','P m c a','P b m a','P c m b','P c a m','P m a b',
2972	'P n n m','P m n n','P n m n',
2973	'P m m n','P n m m','P m n m',
2974	'P b c n','P n c a','P b n a','P c n b','P c a n','P n a b',
2975	'P b c a','P c a b',
2976	'P n m a','P b n m','P m c n','P n a m','P m n b','P c m n',
2977	),
2978	'Cmmm':('C 2 2 21','C 2 2 2','C m m 2',
2979	'C m c 21','C c m 21','C c c 2','C m 2 m','C 2 m m',
2980	'C m 2 a','C 2 m b','C c 2 m','C 2 c m','C c 2 a','C 2 c b',
2981	'C m c m','C m c a','C c m b',
2982	'C m m m','C c c m','C m m a','C m m b','C c c a','C c c b',),
2983	'Immm':('I 2 2 2','I 21 21 21',
2984	'I m m 2','I m 2 m','I 2 m m',
2985	'I b a 2','I 2 c b','I c 2 a',
2986	'I m a 2','I 2 m b','I c 2 m','I m 2 a','I b m 2','I 2 c m',
2987	'I m m m','I b a m','I m c b','I c m a',
2988	'I b c a','I c a b',
2989	'I m m a','I b m m ','I m c m','I m a m','I m m b','I c m m',),
2990	'Fmmm':('F 2 2 2','F m m m', 'F d d d',
2991	'F m m 2','F m 2 m','F 2 m m',
2992	'F d d 2','F d 2 d','F 2 d d',),
2993	'P4/mmm':('P 4','P 41','P 42','P 43','P -4','P 4/m','P 42/m','P 4/n','P 42/n',
2994	'P 4 2 2','P 4 21 2','P 41 2 2','P 41 21 2','P 42 2 2',
2995	'P 42 21 2','P 43 2 2','P 43 21 2','P 4 m m','P 4 b m','P 42 c m',
2996	'P 42 n m','P 4 c c','P 4 n c','P 42 m c','P 42 b c','P -4 2 m',
2997	'P -4 2 c','P -4 21 m','P -4 21 c','P -4 m 2','P -4 c 2','P -4 b 2',
2998	'P -4 n 2','P 4/m m m','P 4/m c c','P 4/n b m','P 4/n n c','P 4/m b m',
2999	'P 4/m n c','P 4/n m m','P 4/n c c','P 42/m m c','P 42/m c m',
3000	'P 42/n b c','P 42/n n m','P 42/m b c','P 42/m n m','P 42/n m c',
3001	'P 42/n c m',),
3002	'I4/mmm':('I 4','I 41','I -4','I 4/m','I 41/a','I 4 2 2','I 41 2 2','I 4 m m',
3003	'I 4 c m','I 41 m d','I 41 c d',
3004	'I -4 m 2','I -4 c 2','I -4 2 m','I -4 2 d','I 4/m m m','I 4/m c m',
3005	'I 41/a m d','I 41/a c d'),
3006	'R3-H':('R 3','R -3','R 3 2','R 3 m','R 3 c','R -3 m','R -3 c',),
3007	'P6/mmm': ('P 3','P 31','P 32','P -3','P 3 1 2','P 3 2 1','P 31 1 2',
3008	'P 31 2 1','P 32 1 2','P 32 2 1', 'P 3 m 1','P 3 1 m','P 3 c 1',
3009	'P 3 1 c','P -3 1 m','P -3 1 c','P -3 m 1','P -3 c 1','P 6','P 61',
3010	'P 65','P 62','P 64','P 63','P -6','P 6/m','P 63/m','P 6 2 2',
3011	'P 61 2 2','P 65 2 2','P 62 2 2','P 64 2 2','P 63 2 2','P 6 m m',
3012	'P 6 c c','P 63 c m','P 63 m c','P -6 m 2','P -6 c 2','P -6 2 m',
3013	'P -6 2 c','P 6/m m m','P 6/m c c','P 63/m c m','P 63/m m c',),
3014	'Pm3m': ('P 2 3','P 21 3','P m 3','P n 3','P a 3','P 4 3 2','P 42 3 2',
3015	'P 43 3 2','P 41 3 2','P -4 3 m','P -4 3 n','P m 3 m','P n 3 n',
3016	'P m 3 n','P n 3 m',),
3017	'Im3m':('I 2 3','I 21 3','I m -3','I a -3', 'I 4 3 2','I 41 3 2',
3018	'I -4 3 m', 'I -4 3 d','I m -3 m','I m 3 m','I a -3 d',),
3019	'Fm3m':('F 2 3','F m -3','F d -3','F 4 3 2','F 41 3 2','F -4 3 m',
3020	'F -4 3 c','F m -3 m','F m 3 m','F m -3 c','F d -3 m','F d -3 c',),
3021	}
3022
3023	ssdict = {}
3024	'''A dictionary of superspace group symbols allowed for each entry in spglist
3025	(except cubics). Monoclinics are all b-unique setting.
3026	'''
3027	ssdict = {
3028	#1,2
3029	'P 1':['(abg)',],'P -1':['(abg)',],
3030	'C 1':['(abg)',],'C -1':['(abg)',],
3031	#monoclinic - done
3032	#3
3033	'P 2':['(a0g)','(a1/2g)','(0b0)','(0b0)s','(1/2b0)','(0b1/2)',],
3034	#4
3035	'P 21':['(a0g)','(0b0)','(1/2b0)','(0b1/2)',],
3036	#5
3037	'C 2':['(a0g)','(0b0)','(0b0)s','(0b1/2)',],
3038	#6
3039	'P m':['(a0g)','(a0g)s','(a1/2g)','(0b0)','(1/2b0)','(0b1/2)',],
3040	#7
3041	'P a':['(a0g)','(a1/2g)','(0b0)','(0b1/2)',],
3042	'P c':['(a0g)','(a1/2g)','(0b0)','(1/2b0)',],
3043	'P n':['(a0g)','(a1/2g)','(0b0)','(1/2b1/2)',],
3044	#8
3045	'C m':['(a0g)','(a0g)s','(0b0)','(0b1/2)',],
3046	#9
3047	'C c':['(a0g)','(a0g)s','(0b0)',],
3048	'C n':['(a0g)','(a0g)s','(0b0)',],
3049	#10
3050	'P 2/m':['(a0g)','(a0g)0s','(a1/2g)','(0b0)','(0b0)s0','(1/2b0)','(0b1/2)',],
3051	#11
3052	'P 21/m':['(a0g)','(a0g)0s','(0b0)','(0b0)s0','(1/2b0)','(0b1/2)',],
3053	#12
3054	'C 2/m':['(a0g)','(a0g)0s','(0b0)','(0b0)s0','(0b1/2)',],
3055	#13
3056	'P 2/c':['(a0g)','(a0g)0s','(a1/2g)','(0b0)','(0b0)s0','(1/2b0)',],
3057	'P 2/a':['(a0g)','(a0g)0s','(a1/2g)','(0b0)','(0b0)s0','(0b1/2)',],
3058	'P 2/n':['(a0g)','(a0g)0s','(a1/2g)','(0b0)','(0b0)s0','(1/2b1/2)',],
3059	#14
3060	'P 21/c':['(a0g)','(0b0)','(1/2b0)',],
3061	'P 21/a':['(a0g)','(0b0)','(0b1/2)',],
3062	'P 21/n':['(a0g)','(0b0)','(1/2b1/2)',],
3063	#15
3064	'C 2/c':['(a0g)','(0b0)','(0b0)s0',],
3065	'C 2/n':['(a0g)','(0b0)','(0b0)s0',],
3066	#orthorhombic
3067	#16
3068	'P 2 2 2':['(00g)','(00g)00s','(01/2g)','(1/20g)','(1/21/2g)',
3069	'(a00)','(a00)s00','(a01/2)','(a1/20)','(a1/21/2)',
3070	'(0b0)','(0b0)0s0','(1/2b0)','(0b1/2)','(1/2b1/2)',],
3071	#17
3072	'P 2 2 21':['(00g)','(01/2g)','(1/20g)','(1/21/2g)',
3073	'(a00)','(a00)s00','(a1/20)','(0b0)','(0b0)0s0','(1/2b0)',],
3074	'P 21 2 2':['(a00)','(a01/2)','(a1/20)','(a1/21/2)',
3075	'(0b0)','(0b0)0s0','(1/2b0)','(00g)','(00g)00s','(1/20g)',],
3076	'P 2 21 2':['(0b0)','(0b1/2)','(1/2b0)','(1/2b1/2)',
3077	'(00g)','(00g)00s','(1/20g)','(a00)','(a00)s00','(a1/20)',],
3078	#18
3079	'P 21 21 2':['(00g)','(00g)00s','(a00)','(a01/2)','(0b0)','(0b1/2)',],
3080	'P 2 21 21':['(a00)','(a00)s00','(0b0)','(0b1/2)','(00g)','(01/2g)',],
3081	'P 21 2 21':['(0b0)','(0b0)0s0','(00g)','(01/2g)','(a00)','(a01/2)',],
3082	#19
3083	'P 21 21 21':['(00g)','(a00)','(0b0)',],
3084	#20
3085	'C 2 2 21':['(00g)','(10g)','(01g)','(a00)','(a00)s00','(0b0)','(0b0)0s0',],
3086	'A 21 2 2':['(a00)','(a10)','(a01)','(0b0)','(0b0)0s0','(00g)','(00g)00s',],
3087	'B 2 21 2':['(0b0)','(1b0)','(0b1)','(00g)','(00g)00s','(a00)','(a00)s00',],
3088	#21
3089	'C 2 2 2':['(00g)','(00g)00s','(10g)','(10g)00s','(01g)','(01g)00s',
3090	'(a00)','(a00)s00','(a01/2)','(0b0)','(0b0)0s0','(0b1/2)',],
3091	'A 2 2 2':['(a00)','(a00)s00','(a10)','(a10)s00','(a01)','(a01)s00',
3092	'(0b0)','(0b0)0s0','(1/2b0)','(00g)','(00g)00s','(1/20g)',],
3093	'B 2 2 2':['(0b0)','(0b0)0s0','(1b0)','(1b0)0s0','(0b1)','(0b1)0s0',
3094	'(00g)','(00g)00s','(01/2g)','(a00)','(a00)s00','(a1/20)',],
3095	#22
3096	'F 2 2 2':['(00g)','(00g)00s','(10g)','(01g)',
3097	'(a00)','(a00)s00','(a10)','(a01)',
3098	'(0b0)','(0b0)0s0','(1b0)','(0b1)',],
3099	#23
3100	'I 2 2 2':['(00g)','(00g)00s','(a00)','(a00)s00','(0b0)','(0b0)0s0',],
3101	#24
3102	'I 21 21 21':['(00g)','(00g)00s','(a00)','(a00)s00','(0b0)','(0b0)0s0',],
3103	#25
3104	'P m m 2':['(00g)','(00g)s0s','(00g)0ss','(00g)ss0',
3105	'(01/2g)','(01/2g)s0s','(1/20g)','(1/20g)0ss','(1/21/2g)',
3106	'(a00)','(a00)0s0','(a1/20)','(a01/2)','(a01/2)0s0','(a1/21/2)',
3107	'(0b0)','(0b0)s00','(0b1/2)','(0b1/2)s00','(1/2b0)','(1/2b1/2)',],
3108	'P 2 m m':['(a00)','(a00)ss0','(a00)s0s','(a00)0ss',
3109	'(a01/2)','(a01/2)ss0','(a1/20)','(a1/20)s0s','(a1/21/2)',
3110	'(0b0)','(0b0)00s','(1/2b0)','(0b1/2)','(0b1/2)00s','(1/2b1/2)',
3111	'(00g)','(00g)0s0','(01/2g)','(01/2g)0s0','(1/20g)','(1/21/2g)',],
3112	'P m 2 m':['(0b0)','(0b0)ss0','(0b0)0ss','(0b0)s0s',
3113	'(0b1/2)','(0b1/2)ss0','(1/2b0)','(1/2b0)0ss','(1/2b1/2)',
3114	'(00g)','(00g)s00','(1/20g)','(01/2g)','(01/2g)s00','(1/21/2g)',
3115	'(a00)','(a00)0s0','(a01/2)','(a01/2)0s0','(a1/20)','(a1/21/2)',],
3116	#26
3117	'P m c 21':['(00g)','(00g)s0s','(01/2g)','(01/2g)s0s','(1/20g)','(1/21/2g)',
3118	'(a00)','(a00)0s0','(a1/20)','(0b0)','(0b0)s00','(0b1/2)',],
3119	'P 21 m a':['(a00)','(a00)ss0','(a01/2)','(a01/2)ss0','(a1/20)','(a1/21/2)',
3120	'(0b0)','(0b0)00s','(1/2b0)','(00g)','(00g)0s0','(01/2g)',],
3121	'P b 21 m':['(0b0)','(0b0)ss0','(0b1/2)','(0b1/2)ss0','(1/2b0)','(1/2b1/2)',
3122	'(00g)','(00g)s00','(1/20g)','(a00)','(a00)0s0','(a01/2)',],
3123	'P m 21 b':['(a00)','(a00)ss0','(a01/2)','(a01/2)ss0','(a1/20)','(a1/21/2)',
3124	'(00g)','(00g)0s0','(01/2g)','(0b0)','(0b0)s00','(0b1/2)',],
3125	'P c m 21':['(00g)','(00g)0ss','(1/20g)','(1/20g)0ss','(01/2g)','(1/21/2g)',
3126	'(0b0)','(0b0)s00','(1/2b0)','(a00)','(a00)0s0','(a01/2)',],
3127	'P 21 a m':['(0b0)','(0b0)ss0','(0b1/2)','(0b1/2)ss0','(1/2b0)','(1/2b1/2)',
3128	'(a00)','(a00)00s','(a1/20)','(00g)','(00g)s00','(1/20g)',],
3129	#27
3130	'P c c 2':['(00g)','(00g)s0s','(00g)0ss','(01/2g)','(1/20g)','(1/21/2g)',
3131	'(a00)','(a00)0s0','(a1/20)','(0b0)','(0b0)s00','(1/2b0)',],
3132	'P 2 a a':['(a00)','(a00)ss0','(a00)s0s','(a01/2)','(a1/20)','(a1/21/2)',
3133	'(0b0)','(0b0)00s','(0b1/2)','(00g)','(00g)0s0','(01/2g)',],
3134	'P b 2 b':['(0b0)','(0b0)0ss','(0b0)ss0','(1/2b0)','(0b1/2)','(1/2b1/2)',
3135	'(00g)','(00g)s00','(1/20g)','(a00)','(a00)00s','(a01/2)',],
3136	#28
3137	'P m a 2':['(00g)','(00g)s0s','(00g)ss0','(00g)0ss','(01/2g)','(01/2g)s0s',
3138	'(0b1/2)','(0b1/2)s00','(a01/2)','(a00)','(0b0)','(0b0)0s0','(a1/20)','(a1/21/2)'],
3139	'P 2 m b':['(a00)','(a00)s0s','(a00)ss0','(a00)0ss','(a01/2)','(a01/2)s0s',
3140	'(1/20g)','(1/20g)s00','(1/2b0)','(0b0)','(00g)','(00g)0s0','(0b1/2)','(1/2b1/2)'],
3141	'P c 2 m':['(0b0)','(0b0)s0s','(0b0)ss0','(0b0)0ss','(1/2b0)','(1/2b0)s0s',
3142	'(a1/20)','(a1/20)s00','(01/2g)','(00g)','(a00)','(a00)0s0','(1/20g)','(1/21/2g)'],
3143	'P m 2 a':['(0b0)','(0b0)s0s','(0b0)ss0','(0b0)0ss','(0b1/2)','(0b1/2)s0s',
3144	'(01/2g)','(01/2g)s00','(a1/20)','(a00)','(00g)','(00g)0s0','(a01/2)','(a1/21/2)'],
3145	'P b m 2':['(00g)','(00g)s0s','(00g)ss0','(00g)0ss','(1/20g)','(1/20g)s0s',
3146	'(a01/2)','(a01/2)s00','(0b1/2)','(0b0)','(a00)','(a00)0s0','(1/2b0)','(1/2b1/2)'],
3147	'P 2 c m':['(a00)','(a00)s0s','(a00)ss0','(a00)0ss','(a1/20)','(a1/20)s0s',
3148	'(1/2b0)','(1/2b0)s00','(1/20g)','(00g)','(0b0)','(0b0)0s0','(01/2g)','(1/21/2g)'],
3149	#29
3150	'P c a 21':['(00g)','(00g)0ss','(01/2g)','(1/20g)',
3151	'(a00)','(a00)0s0','(a1/20)','(0b0)','(0b0)s00','(1/2b0)',],
3152	'P 21 a b':['(a00)','(a00)s0s','(a01/2)','(a1/20)',
3153	'(0b0)','(0b0)00s','(0b1/2)','(00g)','(00g)0s0','(01/2g)',],
3154	'P c 21 b':['(0b0)','(0b0)ss0','(1/2b0)','(0b1/2)',
3155	'(00g)','(00g)s00','(1/20g)','(a00)','(a00)00s','(a01/2)',],
3156	'P b 21 a':['(0b0)','(0b0)0ss','(0b1/2)','(1/2b0)',
3157	'(a00)','(a00)00s','(a1/20)','(00g)','(00g)s00','(1/20g)',],
3158	'P b c 21':['(00g)','(00g)s0s','(1/20g)','(01/2g)',
3159	'(0b0)','(0b0)s00','(0b1/2)','(a00)','(a00)0s0','(a1/20)',],
3160	'P 21 c a':['(a00)','(a00)ss0','(a1/20)','(a01/2)',
3161	'(00g)','(00g)0s0','(1/20g)','(0b0)','(0b0)00s','(0b1/2)',],
3162	#30
3163	'P c n 2':['(00g)','(00g)s0s','(01/2g)','(a00)','(0b0)','(0b0)s00',
3164	'(a1/20)','(1/2b1/2)q00',],
3165	'P 2 a n':['(a00)','(a00)ss0','(a01/2)','(0b0)','(00g)','(00g)0s0',
3166	'(0b1/2)','(1/21/2g)0q0',],
3167	'P n 2 b':['(0b0)','(0b0)0ss','(1/2b0)','(00g)','(a00)','(a00)00s',
3168	'(1/20g)','(a1/21/2)00q',],
3169	'P b 2 n':['(0b0)','(0b0)ss0','(0b1/2)','(a00)','(00g)','(00g)s00',
3170	'(a01/2)','(1/21/2g)0ss',],
3171	'P n c 2':['(00g)','(00g)0ss','(1/20g)','(0b0)','(a00)','(a00)0s0',
3172	'(1/2b0)','(a1/21/2)s0s',],
3173	'P 2 n a':['(a00)','(a00)s0s','(a1/20)','(00g)','(0b0)','(0b0)00s',
3174	'(01/2g)','(1/2b1/2)ss0',],
3175	#31
3176	'P m n 21':['(00g)','(00g)s0s','(01/2g)','(01/2g)s0s','(a00)','(0b0)',
3177	'(0b0)s00','(a1/20)',],
3178	'P 21 m n':['(a00)','(a00)ss0','(a01/2)','(a01/2)ss0','(0b0)','(00g)',
3179	'(00g)0s0','(0b1/2)',],
3180	'P n 21 m':['(0b0)','(0b0)0ss','(1/2b0)','(1/2b0)0ss','(00g)','(a00)',
3181	'(a00)00s','(1/20g)',],
3182	'P m 21 n':['(0b0)','(0b0)ss0','(0b1/2)','(0b1/2)ss0','(a00)','(00g)',
3183	'(00g)s00','(a01/2)',],
3184	'P n m 21':['(00g)','(00g)0ss','(1/20g)','(1/20g)0ss','(0b0)','(a00)',
3185	'(a00)0s0','(1/2b0)',],
3186	'P 21 n m':['(a00)','(a00)s0s','(a1/20)','(a1/20)s0s','(00g)','(0b0)',
3187	'(0b0)00s','(01/2g)',],
3188	#32
3189	'P b a 2':['(00g)','(00g)s0s','(00g)0ss','(00g)ss0','(1/21/2g)qq0',
3190	'(a00)','(a01/2)','(0b0)','(0b1/2)',],
3191	'P 2 c b':['(a00)','(a00)ss0','(a00)s0s','(a00)0ss','(a1/21/2)0qq',
3192	'(0b0)','(1/2b0)','(00g)','(1/20g)',],
3193	'P c 2 a':['(0b0)','(0b0)ss0','(0b0)0ss','(0b0)s0s','(1/2b1/2)q0q',
3194	'(00g)','01/2g)','(a00)','(a1/20)',],
3195	#33
3196	'P b n 21':['(00g)','(00g)s0s','(1/21/2g)qq0','(a00)','(0b0)',],
3197	'P 21 c n':['(a00)','(a00)ss0','(a1/21/2)0qq','(0b0)','(00g)',],
3198	'P n 21 a':['(0b0)','(0b0)0ss','(1/2b1/2)q0q','(00g)','(a00)',],
3199	'P c 21 n':['(0b0)','(0b0)ss0','(1/2b1/2)q0q','(a00)','(00g)',],
3200	'P n a 21':['(00g)','(00g)0ss','(1/21/2g)qq0','(0b0)','(a00)',],
3201	'P 21 n b':['(a00)','(a00)s0s','(a1/21/2)0qq','(00g)','(0b0)',],
3202	#34
3203	'P n n 2':['(00g)','(00g)s0s','(00g)0ss','(1/21/2g)qq0',
3204	'(a00)','(a1/21/2)0q0','(a1/21/2)00q','(0b0)','(1/2b1/2)q00','(1/2b1/2)00q',],
3205	'P 2 n n':['(a00)','(a00)ss0','(a00)s0s','(a1/21/2)0qq',
3206	'(0b0)','(1/2b1/2)q00','(1/2b1/2)00q','(00g)','(1/21/2g)0q0','(1/21/2g)q00',],
3207	'P n 2 n':['(0b0)','(0b0)ss0','(0b0)0ss','(1/2b1/2)q0q',
3208	'(00g)','(1/21/2g)0q0','(1/21/2g)q00','(a00)','(a1/21/2)00q','(a1/21/2)0q0',],
3209	#35
3210	'C m m 2':['(00g)','(00g)s0s','(00g)ss0','(10g)','(10g)s0s','(10g)ss0',
3211	'(0b0)','(0b0)s00','(0b1/2)','(0b1/2)s00',],
3212	'A 2 m m':['(a00)','(a00)ss0','(a00)0ss','(a10)','(a10)ss0','(a10)0ss',
3213	'(00g)','(00g)0s0','(1/20g)','(1/20g)0s0',],
3214	'B m 2 m':['(0b0)','(0b0)0ss','(0b0)s0s','(0b1)','(0b1)0ss','(0b1)s0s',
3215	'(a00)','(a00)00s','(a1/20)','(a1/20)00s',],
3216	#36
3217	'C m c 21':['(00g)','(00g)s0s','(10g)','(10g)s0s','(a00)','(a00)0s0','(0b0)','(0b0)s00',],
3218	'A 21 m a':['(a00)','(a00)ss0','(a10)','(a10)ss0','(0b0)','(0b0)00s','(00g)','(00g)0s0',],
3219	'B m 21 b':['(0b0)','(0b0)ss0','(1b0)','(1b0)ss0','(a00)','(a00)00s','(00g)','(00g)s00',],
3220	'B b 21 m':['(0b0)','(0b0)0ss','(0b1)','(0b1)ss0','(a00)','(a00)00s','(00g)','(00g)s00',],
3221	'C c m 21':['(00g)','(00g)0ss','(01g)','(01g)0ss','(a00)','(a00)0s0','(0b0)','(0b0)s00',],
3222	'A 21 a m':['(a00)','(a00)s0s','(a01)','(a01)s0s','(0b0)','(0b0)00s','(00g)','(00g)0s0',],
3223	#37
3224	'C c c 2':['(00g)','(00g)s0s','(00g)0ss','(10g)','(10g)s0s','(10g)0ss','(01g)','(01g)s0s','(01g)0ss',
3225	'(a00)','(a00)0s0','(0b0)','(0b0)s00',],
3226	'A 2 a a':['(a00)','(a00)ss0','(a00)s0s','(a10)','(a10)ss0','(a10)ss0','(a01)','(a01)ss0','(a01)ss0',
3227	'(0b0)','(0b0)00s','(00g)','(00g)0s0',],
3228	'B b 2 b':['(0b0)','(0b0)0ss','(0b0)ss0','(0b1)','(0b1)0ss','(0b1)ss0','(1b0)','(1b0)0ss','(1b0)ss0',
3229	'(a00)','(a00)00s','(00g)','(00g)s00',],
3230	#38
3231	'A m m 2':['(a00)','(a00)0s0','(a10)','(a10)0s0','(00g)','(00g)0s0',
3232	'(00g)ss0','(00g)0ss','(1/20g)','(1/20g)0ss','(0b0)','(0b0)s00','(1/2b0)',],
3233	'B 2 m m':['(0b0)','(0b0)00s','(0b1)','(0b1)00s','(a00)','(a00)00s',
3234	'(a00)0ss','(a00)s0s','(a1/20)','(a1/20)s0s','(00g)','(00g)0s0','(01/2g)',],
3235	'C m 2 m':['(00g)','(00g)s00','(10g)','(10g)s00','(0b0)','(0b0)s00',
3236	'(0b0)s0s','(0b0)ss0','(0b1/2)','(0b1/2)ss0','(a00)','(a00)00s','(a01/2)',],
3237	'A m 2 m':['(a00)','(a00)00s','(a01)','(a01)00s','(0b0)','(0b0)00s',
3238	'(0b0)s0s','(0b0)0ss','(1/2b0)','(1/2b0)0ss','(00g)','(00g)s00','(1/20g)',],
3239	'B m m 2':['(0b0)','(0b0)s00','(0b1)','(0b1)s00','(a00)','(a00)0s0',
3240	'(a00)0ss','(a00)ss0','(01/2g)','(01/2g)s0s','(a00)','(a00)0s0','(a1/20)',],
3241	'C 2 m m':['(00g)','(00g)0s0','(10g)','(10g)0s0','(00g)','(00g)s00',
3242	'(0b0)s0s','(0b0)0ss','(a01/2)','(a01/2)ss0','(0b0)','(0b0)00s','(0b1/2)',],
3243	#39
3244	'A b m 2':['(a00)','(a00)0s0','(a01)','(a01)0s0','(00g)','(00g)s0s',
3245	'(00g)ss0','(00g)0ss','(1/20g)','(1/20g)0ss','(0b0)','(0b0)s00','(1/2b0)',],
3246	'B 2 c m':['(0b0)','(0b0)00s','(1b0)','(1b0)00s','(a00)','(a00)ss0',
3247	'(a00)0ss','(a00)s0s','(a1/20)','(a1/20)s0s','(00g)','(00g)0s0','(01/2g)',],
3248	'C m 2 a':['(00g)','(00g)s00','(01g)','(01g)s00','(0b0)','(0b0)0ss',
3249	'(0b0)s0s','(0b0)ss0','(0b1/2)','(0b1/2)ss0','(a00)','(a00)00s','(a01/2)',],
3250	'A c 2 m':['(a00)','(a00)00s','(a10)','(a10)00s','(0b0)','(0b0)ss0',
3251	'(0b0)s0s','(0b0)0ss','(1/2b0)','(1/2b0)0ss','(00g)','(00g)s00','(1/20g)',],
3252	'B m a 2':['(0b0)','(0b0)s00','(0b1)','(0b1)s00','(00g)','(00g)s0s',
3253	'(00g)0ss','(00g)ss0','(01/2g)','(01/2g)ss0','(a00)','(a00)00s','(a1/20)',],
3254	'C 2 m b':['(00g)','(00g)0s0','(10g)','(10g)0s0','(a00)','(a00)0ss',
3255	'(a00)ss0','(a00)s0s','(a01/2)','(a01/2)s0s','(0b0)','(0b0)0s0','(0b1/2)',],
3256	#40
3257	'A m a 2':['(a00)','(a01)','(00g)','(00g)s0s','(00g)ss0','(00g)0ss','(0b0)','(0b0)s00',],
3258	'B 2 m b':['(0b0)','(1b0)','(a00)','(a00)ss0','(a00)0ss','(a00)s0s','(00g)','(00g)0s0',],
3259	'C c 2 m':['(00g)','(01g)','(0b0)','(0b0)0ss','(0b0)s0s','(0b0)ss0','(a00)','(a00)00s',],
3260	'A m 2 a':['(a00)','(a10)','(0b0)','(0b0)ss0','(0b0)s0s','(0b0)0ss','(00g)','(00g)s00',],
3261	'B b m 2':['(0b0)','(0b1)','(00g)','(00g)0ss','(00g)ss0','(00g)s0s','(a00)','(a00)0s0',],
3262	'C 2 c m':['(00g)','(10g)','(a00)','(a00)s0s','(a00)0ss','(a00)ss0','(0b0)','(0b0)00s',],
3263	#41
3264	'A b a 2':['(a00)','(a01)','(00g)','(00g)s0s','(00g)ss0','(00g)0ss','(0b0)','(0b0)s00',],
3265	'B 2 c b':['(0b0)','(1b0)','(a00)','(a00)ss0','(a00)0ss','(a00)s0s','(00g)','(00g)0s0',],
3266	'C c 2 a':['(00g)','(01g)','(0b0)','(0b0)0ss','(0b0)s0s','(0b0)ss0','(a00)','(a00)00s',],
3267	'A c 2 a':['(a00)','(a10)','(0b0)','(0b0)ss0','(0b0)s0s','(0b0)0ss','(00g)','(00g)s00',],
3268	'B b a 2':['(0b0)','(0b1)','(00g)','(00g)0ss','(00g)ss0','(00g)s0s','(a00)','(a00)0s0',],
3269	'C 2 c b':['(00g)','(10g)','(a00)','(a00)s0s','(a00)0ss','(a00)ss0','(0b0)','(0b0)00s',],
3270
3271	#42
3272	'F m m 2':['(00g)','(00g)s0s','(00g)0ss','(00g)ss0','(10g)','(10g)ss0','(10g)s0s',
3273	'(01g)','(01g)ss0','(01g)0ss','(a00)','(a00)0s0','(a01)','(a01)0s0',
3274	'(0b0)','(0b0)s00','(0b1)','(0b1)s00',],
3275	'F 2 m m':['(a00)','(a00)ss0','(a00)s0s','(a00)0ss','(a10)','(a10)0ss','(a10)ss0',
3276	'(a01)','(a01)0ss','(a01)s0s','(0b0)','(0b0)00s','(1b0)','(1b0)00s',
3277	'(00g)','(00g)0s0','(10g)','(10g)0s0',],
3278	'F m 2 m':['(0b0)','(0b0)0ss','(0b0)ss0','(0b0)s0s','(0b1)','(0b1)s0s','(0b1)0ss',
3279	'(1b0)','(1b0)s0s','(1b0)ss0','(00g)','(00g)s00','(01g)','(01g)s00',
3280	'(a00)','(a00)00s','(a10)','(a10)00s',],
3281	#43
3282	'F d d 2':['(00g)','(00g)0ss','(00g)s0s','(a00)','(0b0)',],
3283	'F 2 d d':['(a00)','(a00)s0s','(a00)ss0','(00g)','(0b0)',],
3284	'F d 2 d':['(0b0)','(0b0)0ss','(0b0)ss0','(a00)','(00g)',],
3285	#44
3286	'I m m 2':['(00g)','(00g)ss0','(00g)s0s','(00g)0ss','(a00)','(a00)0s0','(0b0)','(0b0)s00',],
3287	'I 2 m m':['(a00)','(00g)0ss','(00g)ss0','(00g)s0s','(0b0)','(0b0)00s','(00g)','(00g)0s0',],
3288	'I m 2 m':['(0b0)','(0b0)s0s','(0b0)0ss','(0b0)ss0','(00g)','(00g)s00','(a00)','(a00)00s',],
3289	#45
3290	'I b a 2':['(00g)','(00g)ss0','(00g)s0s','(00g)0ss','(a00)','(a00)0s0','(0b0)','(0b0)s00',],
3291	'I 2 c b':['(0b0)','(0b0)s0s','(0b0)0ss','(0b0)ss0','(00g)','(00g)s00','(a00)','(a00)00s',],
3292	'I c 2 a':['(a00)','(00g)0ss','(00g)ss0','(00g)s0s','(0b0)','(0b0)00s','(00g)','(00g)0s0',],
3293	#46
3294	'I m a 2':['(a00)','(00g)0ss','(00g)ss0','(00g)s0s','(0b0)','(0b0)00s','(00g)','(00g)0s0',],
3295	'I 2 m b':['(0b0)','(0b0)s0s','(0b0)0ss','(0b0)ss0','(00g)','(00g)s00','(a00)','(a00)00s',],
3296	'I c 2 m':['(a00)','(00g)0ss','(00g)ss0','(00g)s0s','(0b0)','(0b0)00s','(00g)','(00g)0s0',],
3297	'I m 2 a':['(a00)','(00g)0ss','(00g)ss0','(00g)s0s','(0b0)','(0b0)00s','(00g)','(00g)0s0',],
3298	'I b m 2':['(a00)','(00g)0ss','(00g)ss0','(00g)s0s','(0b0)','(0b0)00s','(00g)','(00g)0s0',],
3299	'I 2 c m':['(0b0)','(0b0)s0s','(0b0)0ss','(0b0)ss0','(00g)','(00g)s00','(a00)','(a00)00s',],
3300	#47
3301	'P m m m':['(00g)','(00g)s00','(00g)0s0','(00g)ss0','(01/2g)','(01/2g)s00','(1/20g)','(1/20g)s00','(1/21/2g)',
3302	'(a00)','(a00)0s0','(a00)00s','(a00)0ss','(a01/2)','(a01/2)0s0','(a1/20)','(a1/20)00s','(a1/21/2)',
3303	'(0b0)','(0b0)s00','(0b0)00s','(0b0)s0s','(1/2b0)','(1/2b0)00s','(0b1/2)','(0b1/2)s00','(1/2b1/2)',],
3304	#48 o@i qq0,0qq,q0q ->000
3305	'P n n n':['(00g)','(00g)s00','(00g)0s0','(1/21/2g)',
3306	'(a00)','(a00)0s0','(a00)00s','(a1/21/2)',
3307	'(0b0)','(0b0)s00','(0b0)00s','(1/2b1/2)',],
3308	#49
3309	'P c c m':['(00g)','(00g)s00','(00g)0s0','(01/2g)','(1/20g)','(1/21/2g)',
3310	'(a00)','(a00)0s0','(a00)00s','(a00)0ss','(a1/20)','(a1/20)00s',
3311	'(0b0)','(0b0)s00','(0b0)00s','(0b0)s0s','(1/2b0)','(1/2b0)00s',],
3312	'P m a a':['(a00)','(a00)0s0','(a00)00s','(a01/2)','(a1/20)','(a1/21/2)',
3313	'(0b0)','(0b0)00s','(0b0)s00','(0b0)s0s','(0b1/2)','(0b1/2)s00',
3314	'(00g)','(00g)0s0','(00g)s00','(00g)ss0','(01/2g)','(01/2g)s00',],
3315	'P b m b':['(0b0)','(0b0)00s','(0b0)s00','(0b1/2)','(1/2b0)','(1/2b1/2)',
3316	'(00g)','(00g)s00','(00g)0s0','(00g)ss0','(1/20g)','(1/20g)0s0',
3317	'(a00)','(a00)00s','(a00)0s0','(a00)0ss','(a01/2)','(a01/2)0s0',],
3318	#50 o@i qq0,0qq,q0q ->000
3319	'P b a n':['(00g)','(00g)s00','(00g)0s0','(00g)ss0','(1/21/2g)',
3320	'(a00)','(a00)0s0','(a01/2)','(0b0)','(0b0)s00','(0b1/2)',],
3321	'P n c b':['(a00)','(a00)0s0','(a00)00s','(a00)0ss','(a1/21/2)',
3322	'(0b0)','(0b0)00s','(1/2b0)','(00g)','(00g)0s0','(1/20g)',],
3323	'P c n a':['(0b0)','(0b0)s00','(0b0)00s','(0b0)s0s','(1/2b1/2)',
3324	'(00g)','(00g)s00','(01/2g)','(a00)','(a00)00s','(a1/20)',],
3325	#51
3326	'P m m a':['(00g)','(00g)s00','(00g)ss0','(00g)0s0','(0b0)','(0b0)s00',
3327	'(0b0)s0s','(0b0)00s','(a00)','(a00)0s0','(01/2g)','(01/2g)s00',
3328	'(0b1/2)','(0b1/2)s00','(a01/2)','(a01/2)0s0','(1/2b0)','(1/2b1/2)',],
3329	'P b m m':['(a00)','(a00)0s0','(a00)0ss','(a00)00s','(00g)','(00g)0s0',
3330	'(00g)ss0','(00g)s00','(0b0)','(0b0)00s','(a01/2)','(a01/2)0s0',
3331	'(1/20g)','(1/20g)0s0','(1/2b0)','(1/2b0)00s','(01/2g)','(1/21/2g)',],
3332	'P m c m':['(0b0)','(0b0)00s','(0b0)s0s','(0b0)s00','(a00)','(a00)00s',
3333	'(a00)0ss','(a00)0s0','(00g)','(00g)s00','(1/2b0)','(1/2b0)00s',
3334	'(a1/20)','(a1/20)00s','(01/2g)','(01/2g)s00','(a01/2)','(a1/21/2)',],
3335	'P m a m':['(0b0)','(0b0)s00','(0b0)s0s','(0b0)00s','(00g)','(00g)s00',
3336	'(00g)ss0','(00g)0s0','(a00)','(a00)00s','(0b1/2)','(0b1/2)s00',
3337	'(01/2g)','(01/2g)s00','(a1/20)','(a1/20)00s','(1/20g)','(1/21/2g)',],
3338	'P m m b':['(00g)','(00g)0s0','(00g)ss0','(00g)s00','(a00)','(a00)0s0',
3339	'(a00)0ss','(a00)00s','(0b0)','(0b0)s00','(a00)','(a00)0s0',
3340	'(a01/2)','(a01/2)0s0','(0b1/2)','(0b1/2)s00','(a1/20)','(a1/21/2)',],
3341	'P c m m':['(a00)','(a00)00s','(a00)0ss','(a00)0s0','(0b0)','(0b0)00s',
3342	'(0b0)s0s','(0b0)s00','(00g)','(00g)0s0','(0b0)','(0b0)00s',
3343	'(1/2b0)','(1/2b0)00s','(1/20g)','(1/20g)0s0','(0b1/2)','(1/2b1/2)',],
3344	#52 o@i qq0,0qq,q0q ->000
3345	'P n n a':['(00g)','(00g)s00','(00g)0s0','(a00)','(a00)00s',
3346	'(0b0)','(0b0)00s','(a1/21/2)','(1/2b1/2)',],
3347	'P b n n':['(a00)','(a00)0s0','(a00)00s','(0b0)','(0b0)s00',
3348	'(00g)','(00g)s00','(1/2b1/2)','(1/21/2g)',],
3349	'P n c n':['(0b0)','(0b0)s00','(0b0)00s','(00g)','(00g)0s0',
3350	'(a00)','(a00)0s0','(1/21/2g)','(a1/21/2)',],
3351	'P n a n':['(0b0)','(0b0)s00','(0b0)00s','(00g)','(00g)0s0',
3352	'(a00)','(a00)0s0','(1/21/2g)','(a1/21/2)',],
3353	'P n n b':['(00g)','(00g)s00','(00g)0s0','(a00)','(a00)00s',
3354	'(0b0)','(0b0)00s','(a1/21/2)','(1/2b1/2)',],
3355	'P c n n':['(a00)','(a00)0s0','(a00)00s','(0b0)','(0b0)s00',
3356	'(00g)','(00g)s00','(1/2b1/2)','(1/21/2g)',],
3357	#53
3358	'P m n a':['(00g)','(00g)s00','(a00)','(a00)00s','(0b0)','(0b0)00s',
3359	'(0b0)s0s','(0b0)s00','(01/2g)','(01/2g)s00','(a1/20)',],
3360	'P b m n':['(a00)','(a00)0s0','(0b0)','(0b0)s00','(00g)','(00g)s00',
3361	'(00g)ss0','(00g)0s0','(a01/2)','(a01/2)0s0','(0b1/2)',],
3362	'P n c m':['(0b0)','(0b0)00s','(00g)','(00g)0s0','(a00)','(a00)0s0',
3363	'(a00)0ss','(a00)00s','(1/2b0)','(1/2b0)00s','(1/20g)',],
3364	'P m a n':['(0b0)','(0b0)s00','(a00)','(a00)0s0','(00g)','(00g)0s0',
3365	'(00g)ss0','(00g)s00','(0b1/2)','(0b1/2)s00','(a01/2)',],
3366	'P n m b':['(00g)','(00g)0s0','(0b0)','(0b0)00s','(a00)','(a00)00s',
3367	'(a00)0ss','(a00)0s0','(1/20g)','(1/20g)0s0','(1/2b0)',],
3368	'P c n m':['(a00)','(a00)00s','(00g)','(00g)s00','(0b0)','(0b0)s00',
3369	'(0b0)s0s','(0b0)00s','(a1/20)','(a1/20)00s','(01/2g)',],
3370	#54
3371	'P c c a':['(00g)','(00g)s00','(0b0)','(0b0)s00','(a00)','(a00)0s0',
3372	'(a00)0ss','(a00)00s','(01/2g)','(1/2b0)',],
3373	'P b a a':['(a00)','(a00)0s0','(00g)','(00g)0s0','(0b0)','(0b0)00s',
3374	'(0b0)s0s','(0b0)s00','(a01/2)','(01/2g)',],
3375	'P b c b':['(0b0)','(0b0)00s','(a00)','(a00)00s','(00g)','(00g)s00',
3376	'(00g)ss0','(00g)0s0','(1/2b0)','(a01/2)',],
3377	'P b a b':['(0b0)','(0b0)s00','(00g)','(00g)s00','(a00)','(a00)00s',
3378	'(a00)0ss','(a00)0s0','(0b1/2)','(1/20g)',],
3379	'P c c b':['(00g)','(00g)0s0','(a00)','(a00)0s0','(0b0)','(0b0)s00',
3380	'(0b0)s0s','(0b0)00s','(1/20g)','(a1/20)',],
3381	'P c a a':['(a00)','(a00)00s','(0b0)','(0b0)00s','(00g)','(00g)0s0',
3382	'(00g)ss0','(00g)s00','(a1/20)','(0b1/2)',],
3383	#55
3384	'P b a m':['(00g)','(00g)s00','(00g)0s0','(00g)ss0',
3385	'(a00)','(a00)00s','(a01/2)','(0b0)','(0b0)00s','(0b1/2)'],
3386	'P m c b':['(a00)','(a00)0s0','(a00)00s','(a00)0ss',
3387	'(0b0)','(0b0)s00','(1/2b0)','(00g)','(00g)s00','(1/20g)'],
3388	'P c m a':['(0b0)','(0b0)s00','(0b0)00s','(0b0)s0s',
3389	'(a00)','(a00)0s0','(a1/20)','(00g)','(00g)0s0','(01/2g)'],
3390	#56
3391	'P c c n':['(00g)','(00g)s00','(00g)0s0','(a00)','(a00)0s0',
3392	'(0b0)','(0b0)s00'],
3393	'P n a a':['(a00)','(a00)0s0','(a00)00s','(0b0)','(0b0)00s',
3394	'(00g)','(00g)0s0'],
3395	'P b n b':['(0b0)','(0b0)s00','(0b0)00s','(a00)','(a00)00s',
3396	'(00g)','(00g)s00'],
3397	#57
3398	'P c a m':['(00g)','(00g)0s0','(a00)','(a00)00s','(0b0)','(0b0)s00',
3399	'(0b0)ss0','(0b0)00s','(01/2g)','(a1/20)','(a1/20)00s',],
3400	'P m a b':['(a00)','(a00)00s','(0b0)','(0b0)s00','(00g)','(00g)0s0',
3401	'(00g)s0s','(00g)s00','(a01/2)','(0b1/2)','(0b1/2)s00',],
3402	'P c m b':['(0b0)','(0b0)s00','(00g)','(00g)0s0','(a00)','(a00)00s',
3403	'(a00)0ss','(a00)0s0','(1/2b0)','(1/20g)','(1/20g)0s0',],
3404	'P b m a':['(0b0)','(0b0)00s','(a00)','(a00)0s0','(00g)','(00g)s00',
3405	'(00g)ss0','(00g)0s0','(0b1/2)','(a01/2)','(a01/2)0s0',],
3406	'P m c a':['(a00)','(a00)0s0','(00g)','(00g)s00','(0b0)','(0b0)00s',
3407	'(0b0)s0s','(0b0)s00','(a1/20)','(01/2g)','(01/2g)s00'],
3408	'P b c m':['(00g)','(00g)s00','(0b0)','(0b0)00s','(a00)','(a00)0s0',
3409	'(a00)0ss','(a00)00s','(1/20g)','(1/