| 1 | # -*- coding: utf-8 -*- |
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| 2 | ''' |
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| 3 | *GSASIIstrMath - structure math routines* |
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| 4 | ----------------------------------------- |
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| 5 | ''' |
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| 6 | ########### SVN repository information ################### |
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| 7 | # $Date: 2016-09-30 15:33:12 +0000 (Fri, 30 Sep 2016) $ |
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| 8 | # $Author: vondreele $ |
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| 9 | # $Revision: 2481 $ |
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| 10 | # $URL: trunk/GSASIIstrMath.py $ |
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| 11 | # $Id: GSASIIstrMath.py 2481 2016-09-30 15:33:12Z vondreele $ |
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| 12 | ########### SVN repository information ################### |
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| 13 | import time |
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| 14 | import copy |
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| 15 | import numpy as np |
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| 16 | import numpy.ma as ma |
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| 17 | import numpy.linalg as nl |
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| 18 | import scipy.optimize as so |
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| 19 | import scipy.stats as st |
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| 20 | import GSASIIpath |
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| 21 | GSASIIpath.SetVersionNumber("$Revision: 2481 $") |
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| 22 | import GSASIIElem as G2el |
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| 23 | import GSASIIlattice as G2lat |
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| 24 | import GSASIIspc as G2spc |
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| 25 | import GSASIIpwd as G2pwd |
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| 26 | import GSASIImapvars as G2mv |
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| 27 | import GSASIImath as G2mth |
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| 28 | import GSASIIobj as G2obj |
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| 29 | |
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| 30 | sind = lambda x: np.sin(x*np.pi/180.) |
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| 31 | cosd = lambda x: np.cos(x*np.pi/180.) |
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| 32 | tand = lambda x: np.tan(x*np.pi/180.) |
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| 33 | asind = lambda x: 180.*np.arcsin(x)/np.pi |
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| 34 | acosd = lambda x: 180.*np.arccos(x)/np.pi |
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| 35 | atan2d = lambda y,x: 180.*np.arctan2(y,x)/np.pi |
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| 36 | |
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| 37 | ateln2 = 8.0*np.log(2.0) |
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| 38 | twopi = 2.0*np.pi |
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| 39 | twopisq = 2.0*np.pi**2 |
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| 40 | nxs = np.newaxis |
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| 41 | |
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| 42 | ################################################################################ |
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| 43 | ##### Rigid Body Models |
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| 44 | ################################################################################ |
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| 45 | |
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| 46 | def ApplyRBModels(parmDict,Phases,rigidbodyDict,Update=False): |
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| 47 | ''' Takes RB info from RBModels in Phase and RB data in rigidbodyDict along with |
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| 48 | current RB values in parmDict & modifies atom contents (xyz & Uij) of parmDict |
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| 49 | ''' |
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| 50 | atxIds = ['Ax:','Ay:','Az:'] |
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| 51 | atuIds = ['AU11:','AU22:','AU33:','AU12:','AU13:','AU23:'] |
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| 52 | RBIds = rigidbodyDict.get('RBIds',{'Vector':[],'Residue':[]}) #these are lists of rbIds |
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| 53 | if not RBIds['Vector'] and not RBIds['Residue']: |
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| 54 | return |
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| 55 | VRBIds = RBIds['Vector'] |
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| 56 | RRBIds = RBIds['Residue'] |
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| 57 | if Update: |
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| 58 | RBData = rigidbodyDict |
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| 59 | else: |
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| 60 | RBData = copy.deepcopy(rigidbodyDict) # don't mess with original! |
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| 61 | if RBIds['Vector']: # first update the vector magnitudes |
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| 62 | VRBData = RBData['Vector'] |
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| 63 | for i,rbId in enumerate(VRBIds): |
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| 64 | if VRBData[rbId]['useCount']: |
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| 65 | for j in range(len(VRBData[rbId]['VectMag'])): |
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| 66 | name = '::RBV;'+str(j)+':'+str(i) |
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| 67 | VRBData[rbId]['VectMag'][j] = parmDict[name] |
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| 68 | for phase in Phases: |
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| 69 | Phase = Phases[phase] |
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| 70 | General = Phase['General'] |
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| 71 | cx,ct,cs,cia = General['AtomPtrs'] |
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| 72 | cell = General['Cell'][1:7] |
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| 73 | Amat,Bmat = G2lat.cell2AB(cell) |
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| 74 | AtLookup = G2mth.FillAtomLookUp(Phase['Atoms'],cia+8) |
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| 75 | pfx = str(Phase['pId'])+'::' |
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| 76 | if Update: |
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| 77 | RBModels = Phase['RBModels'] |
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| 78 | else: |
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| 79 | RBModels = copy.deepcopy(Phase['RBModels']) # again don't mess with original! |
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| 80 | for irb,RBObj in enumerate(RBModels.get('Vector',[])): |
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| 81 | jrb = VRBIds.index(RBObj['RBId']) |
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| 82 | rbsx = str(irb)+':'+str(jrb) |
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| 83 | for i,px in enumerate(['RBVPx:','RBVPy:','RBVPz:']): |
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| 84 | RBObj['Orig'][0][i] = parmDict[pfx+px+rbsx] |
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| 85 | for i,po in enumerate(['RBVOa:','RBVOi:','RBVOj:','RBVOk:']): |
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| 86 | RBObj['Orient'][0][i] = parmDict[pfx+po+rbsx] |
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| 87 | RBObj['Orient'][0] = G2mth.normQ(RBObj['Orient'][0]) |
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| 88 | TLS = RBObj['ThermalMotion'] |
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| 89 | if 'T' in TLS[0]: |
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| 90 | for i,pt in enumerate(['RBVT11:','RBVT22:','RBVT33:','RBVT12:','RBVT13:','RBVT23:']): |
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| 91 | TLS[1][i] = parmDict[pfx+pt+rbsx] |
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| 92 | if 'L' in TLS[0]: |
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| 93 | for i,pt in enumerate(['RBVL11:','RBVL22:','RBVL33:','RBVL12:','RBVL13:','RBVL23:']): |
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| 94 | TLS[1][i+6] = parmDict[pfx+pt+rbsx] |
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| 95 | if 'S' in TLS[0]: |
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| 96 | for i,pt in enumerate(['RBVS12:','RBVS13:','RBVS21:','RBVS23:','RBVS31:','RBVS32:','RBVSAA:','RBVSBB:']): |
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| 97 | TLS[1][i+12] = parmDict[pfx+pt+rbsx] |
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| 98 | if 'U' in TLS[0]: |
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| 99 | TLS[1][0] = parmDict[pfx+'RBVU:'+rbsx] |
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| 100 | XYZ,Cart = G2mth.UpdateRBXYZ(Bmat,RBObj,RBData,'Vector') |
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| 101 | UIJ = G2mth.UpdateRBUIJ(Bmat,Cart,RBObj) |
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| 102 | for i,x in enumerate(XYZ): |
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| 103 | atId = RBObj['Ids'][i] |
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| 104 | for j in [0,1,2]: |
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| 105 | parmDict[pfx+atxIds[j]+str(AtLookup[atId])] = x[j] |
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| 106 | if UIJ[i][0] == 'A': |
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| 107 | for j in range(6): |
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| 108 | parmDict[pfx+atuIds[j]+str(AtLookup[atId])] = UIJ[i][j+2] |
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| 109 | elif UIJ[i][0] == 'I': |
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| 110 | parmDict[pfx+'AUiso:'+str(AtLookup[atId])] = UIJ[i][1] |
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| 111 | |
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| 112 | for irb,RBObj in enumerate(RBModels.get('Residue',[])): |
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| 113 | jrb = RRBIds.index(RBObj['RBId']) |
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| 114 | rbsx = str(irb)+':'+str(jrb) |
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| 115 | for i,px in enumerate(['RBRPx:','RBRPy:','RBRPz:']): |
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| 116 | RBObj['Orig'][0][i] = parmDict[pfx+px+rbsx] |
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| 117 | for i,po in enumerate(['RBROa:','RBROi:','RBROj:','RBROk:']): |
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| 118 | RBObj['Orient'][0][i] = parmDict[pfx+po+rbsx] |
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| 119 | RBObj['Orient'][0] = G2mth.normQ(RBObj['Orient'][0]) |
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| 120 | TLS = RBObj['ThermalMotion'] |
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| 121 | if 'T' in TLS[0]: |
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| 122 | for i,pt in enumerate(['RBRT11:','RBRT22:','RBRT33:','RBRT12:','RBRT13:','RBRT23:']): |
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| 123 | RBObj['ThermalMotion'][1][i] = parmDict[pfx+pt+rbsx] |
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| 124 | if 'L' in TLS[0]: |
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| 125 | for i,pt in enumerate(['RBRL11:','RBRL22:','RBRL33:','RBRL12:','RBRL13:','RBRL23:']): |
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| 126 | RBObj['ThermalMotion'][1][i+6] = parmDict[pfx+pt+rbsx] |
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| 127 | if 'S' in TLS[0]: |
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| 128 | for i,pt in enumerate(['RBRS12:','RBRS13:','RBRS21:','RBRS23:','RBRS31:','RBRS32:','RBRSAA:','RBRSBB:']): |
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| 129 | RBObj['ThermalMotion'][1][i+12] = parmDict[pfx+pt+rbsx] |
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| 130 | if 'U' in TLS[0]: |
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| 131 | RBObj['ThermalMotion'][1][0] = parmDict[pfx+'RBRU:'+rbsx] |
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| 132 | for itors,tors in enumerate(RBObj['Torsions']): |
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| 133 | tors[0] = parmDict[pfx+'RBRTr;'+str(itors)+':'+rbsx] |
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| 134 | XYZ,Cart = G2mth.UpdateRBXYZ(Bmat,RBObj,RBData,'Residue') |
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| 135 | UIJ = G2mth.UpdateRBUIJ(Bmat,Cart,RBObj) |
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| 136 | for i,x in enumerate(XYZ): |
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| 137 | atId = RBObj['Ids'][i] |
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| 138 | for j in [0,1,2]: |
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| 139 | parmDict[pfx+atxIds[j]+str(AtLookup[atId])] = x[j] |
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| 140 | if UIJ[i][0] == 'A': |
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| 141 | for j in range(6): |
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| 142 | parmDict[pfx+atuIds[j]+str(AtLookup[atId])] = UIJ[i][j+2] |
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| 143 | elif UIJ[i][0] == 'I': |
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| 144 | parmDict[pfx+'AUiso:'+str(AtLookup[atId])] = UIJ[i][1] |
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| 145 | |
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| 146 | def ApplyRBModelDervs(dFdvDict,parmDict,rigidbodyDict,Phase): |
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| 147 | 'Needs a doc string' |
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| 148 | atxIds = ['dAx:','dAy:','dAz:'] |
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| 149 | atuIds = ['AU11:','AU22:','AU33:','AU12:','AU13:','AU23:'] |
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| 150 | TIds = ['T11:','T22:','T33:','T12:','T13:','T23:'] |
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| 151 | LIds = ['L11:','L22:','L33:','L12:','L13:','L23:'] |
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| 152 | SIds = ['S12:','S13:','S21:','S23:','S31:','S32:','SAA:','SBB:'] |
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| 153 | PIds = ['Px:','Py:','Pz:'] |
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| 154 | OIds = ['Oa:','Oi:','Oj:','Ok:'] |
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| 155 | RBIds = rigidbodyDict.get('RBIds',{'Vector':[],'Residue':[]}) #these are lists of rbIds |
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| 156 | if not RBIds['Vector'] and not RBIds['Residue']: |
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| 157 | return |
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| 158 | VRBIds = RBIds['Vector'] |
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| 159 | RRBIds = RBIds['Residue'] |
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| 160 | RBData = rigidbodyDict |
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| 161 | for item in parmDict: |
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| 162 | if 'RB' in item: |
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| 163 | dFdvDict[item] = 0. #NB: this is a vector which is no. refl. long & must be filled! |
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| 164 | General = Phase['General'] |
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| 165 | cx,ct,cs,cia = General['AtomPtrs'] |
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| 166 | cell = General['Cell'][1:7] |
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| 167 | Amat,Bmat = G2lat.cell2AB(cell) |
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| 168 | rpd = np.pi/180. |
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| 169 | rpd2 = rpd**2 |
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| 170 | g = nl.inv(np.inner(Bmat,Bmat)) |
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| 171 | gvec = np.sqrt(np.array([g[0][0]**2,g[1][1]**2,g[2][2]**2, |
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| 172 | g[0][0]*g[1][1],g[0][0]*g[2][2],g[1][1]*g[2][2]])) |
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| 173 | AtLookup = G2mth.FillAtomLookUp(Phase['Atoms'],cia+8) |
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| 174 | pfx = str(Phase['pId'])+'::' |
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| 175 | RBModels = Phase['RBModels'] |
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| 176 | for irb,RBObj in enumerate(RBModels.get('Vector',[])): |
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| 177 | VModel = RBData['Vector'][RBObj['RBId']] |
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| 178 | Q = RBObj['Orient'][0] |
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| 179 | Pos = RBObj['Orig'][0] |
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| 180 | jrb = VRBIds.index(RBObj['RBId']) |
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| 181 | rbsx = str(irb)+':'+str(jrb) |
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| 182 | dXdv = [] |
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| 183 | for iv in range(len(VModel['VectMag'])): |
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| 184 | dCdv = [] |
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| 185 | for vec in VModel['rbVect'][iv]: |
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| 186 | dCdv.append(G2mth.prodQVQ(Q,vec)) |
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| 187 | dXdv.append(np.inner(Bmat,np.array(dCdv)).T) |
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| 188 | XYZ,Cart = G2mth.UpdateRBXYZ(Bmat,RBObj,RBData,'Vector') |
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| 189 | for ia,atId in enumerate(RBObj['Ids']): |
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| 190 | atNum = AtLookup[atId] |
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| 191 | dx = 0.00001 |
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| 192 | for iv in range(len(VModel['VectMag'])): |
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| 193 | for ix in [0,1,2]: |
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| 194 | dFdvDict['::RBV;'+str(iv)+':'+str(jrb)] += dXdv[iv][ia][ix]*dFdvDict[pfx+atxIds[ix]+str(atNum)] |
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| 195 | for i,name in enumerate(['RBVPx:','RBVPy:','RBVPz:']): |
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| 196 | dFdvDict[pfx+name+rbsx] += dFdvDict[pfx+atxIds[i]+str(atNum)] |
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| 197 | for iv in range(4): |
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| 198 | Q[iv] -= dx |
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| 199 | XYZ1 = G2mth.RotateRBXYZ(Bmat,Cart,G2mth.normQ(Q)) |
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| 200 | Q[iv] += 2.*dx |
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| 201 | XYZ2 = G2mth.RotateRBXYZ(Bmat,Cart,G2mth.normQ(Q)) |
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| 202 | Q[iv] -= dx |
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| 203 | dXdO = (XYZ2[ia]-XYZ1[ia])/(2.*dx) |
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| 204 | for ix in [0,1,2]: |
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| 205 | dFdvDict[pfx+'RBV'+OIds[iv]+rbsx] += dXdO[ix]*dFdvDict[pfx+atxIds[ix]+str(atNum)] |
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| 206 | X = G2mth.prodQVQ(Q,Cart[ia]) |
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| 207 | dFdu = np.array([dFdvDict[pfx+Uid+str(AtLookup[atId])] for Uid in atuIds]).T/gvec |
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| 208 | dFdu = G2lat.U6toUij(dFdu.T) |
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| 209 | dFdu = np.tensordot(Amat,np.tensordot(Amat,dFdu,([1,0])),([0,1])) |
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| 210 | dFdu = G2lat.UijtoU6(dFdu) |
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| 211 | atNum = AtLookup[atId] |
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| 212 | if 'T' in RBObj['ThermalMotion'][0]: |
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| 213 | for i,name in enumerate(['RBVT11:','RBVT22:','RBVT33:','RBVT12:','RBVT13:','RBVT23:']): |
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| 214 | dFdvDict[pfx+name+rbsx] += dFdu[i] |
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| 215 | if 'L' in RBObj['ThermalMotion'][0]: |
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| 216 | dFdvDict[pfx+'RBVL11:'+rbsx] += rpd2*(dFdu[1]*X[2]**2+dFdu[2]*X[1]**2-dFdu[5]*X[1]*X[2]) |
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| 217 | dFdvDict[pfx+'RBVL22:'+rbsx] += rpd2*(dFdu[0]*X[2]**2+dFdu[2]*X[0]**2-dFdu[4]*X[0]*X[2]) |
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| 218 | dFdvDict[pfx+'RBVL33:'+rbsx] += rpd2*(dFdu[0]*X[1]**2+dFdu[1]*X[0]**2-dFdu[3]*X[0]*X[1]) |
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| 219 | dFdvDict[pfx+'RBVL12:'+rbsx] += rpd2*(-dFdu[3]*X[2]**2-2.*dFdu[2]*X[0]*X[1]+ |
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| 220 | dFdu[4]*X[1]*X[2]+dFdu[5]*X[0]*X[2]) |
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| 221 | dFdvDict[pfx+'RBVL13:'+rbsx] += rpd2*(-dFdu[4]*X[1]**2-2.*dFdu[1]*X[0]*X[2]+ |
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| 222 | dFdu[3]*X[1]*X[2]+dFdu[5]*X[0]*X[1]) |
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| 223 | dFdvDict[pfx+'RBVL23:'+rbsx] += rpd2*(-dFdu[5]*X[0]**2-2.*dFdu[0]*X[1]*X[2]+ |
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| 224 | dFdu[3]*X[0]*X[2]+dFdu[4]*X[0]*X[1]) |
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| 225 | if 'S' in RBObj['ThermalMotion'][0]: |
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| 226 | dFdvDict[pfx+'RBVS12:'+rbsx] += rpd*(dFdu[5]*X[1]-2.*dFdu[1]*X[2]) |
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| 227 | dFdvDict[pfx+'RBVS13:'+rbsx] += rpd*(-dFdu[5]*X[2]+2.*dFdu[2]*X[1]) |
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| 228 | dFdvDict[pfx+'RBVS21:'+rbsx] += rpd*(-dFdu[4]*X[0]+2.*dFdu[0]*X[2]) |
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| 229 | dFdvDict[pfx+'RBVS23:'+rbsx] += rpd*(dFdu[4]*X[2]-2.*dFdu[2]*X[0]) |
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| 230 | dFdvDict[pfx+'RBVS31:'+rbsx] += rpd*(dFdu[3]*X[0]-2.*dFdu[0]*X[1]) |
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| 231 | dFdvDict[pfx+'RBVS32:'+rbsx] += rpd*(-dFdu[3]*X[1]+2.*dFdu[1]*X[0]) |
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| 232 | dFdvDict[pfx+'RBVSAA:'+rbsx] += rpd*(dFdu[4]*X[1]-dFdu[3]*X[2]) |
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| 233 | dFdvDict[pfx+'RBVSBB:'+rbsx] += rpd*(dFdu[5]*X[0]-dFdu[3]*X[2]) |
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| 234 | if 'U' in RBObj['ThermalMotion'][0]: |
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| 235 | dFdvDict[pfx+'RBVU:'+rbsx] += dFdvDict[pfx+'AUiso:'+str(AtLookup[atId])] |
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| 236 | |
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| 237 | |
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| 238 | for irb,RBObj in enumerate(RBModels.get('Residue',[])): |
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| 239 | Q = RBObj['Orient'][0] |
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| 240 | Pos = RBObj['Orig'][0] |
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| 241 | jrb = RRBIds.index(RBObj['RBId']) |
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| 242 | torData = RBData['Residue'][RBObj['RBId']]['rbSeq'] |
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| 243 | rbsx = str(irb)+':'+str(jrb) |
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| 244 | XYZ,Cart = G2mth.UpdateRBXYZ(Bmat,RBObj,RBData,'Residue') |
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| 245 | for itors,tors in enumerate(RBObj['Torsions']): #derivative error? |
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| 246 | tname = pfx+'RBRTr;'+str(itors)+':'+rbsx |
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| 247 | orId,pvId = torData[itors][:2] |
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| 248 | pivotVec = Cart[orId]-Cart[pvId] |
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| 249 | QA = G2mth.AVdeg2Q(-0.001,pivotVec) |
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| 250 | QB = G2mth.AVdeg2Q(0.001,pivotVec) |
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| 251 | for ir in torData[itors][3]: |
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| 252 | atNum = AtLookup[RBObj['Ids'][ir]] |
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| 253 | rVec = Cart[ir]-Cart[pvId] |
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| 254 | dR = G2mth.prodQVQ(QB,rVec)-G2mth.prodQVQ(QA,rVec) |
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| 255 | dRdT = np.inner(Bmat,G2mth.prodQVQ(Q,dR))/.002 |
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| 256 | for ix in [0,1,2]: |
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| 257 | dFdvDict[tname] += dRdT[ix]*dFdvDict[pfx+atxIds[ix]+str(atNum)] |
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| 258 | for ia,atId in enumerate(RBObj['Ids']): |
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| 259 | atNum = AtLookup[atId] |
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| 260 | dx = 0.00001 |
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| 261 | for i,name in enumerate(['RBRPx:','RBRPy:','RBRPz:']): |
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| 262 | dFdvDict[pfx+name+rbsx] += dFdvDict[pfx+atxIds[i]+str(atNum)] |
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| 263 | for iv in range(4): |
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| 264 | Q[iv] -= dx |
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| 265 | XYZ1 = G2mth.RotateRBXYZ(Bmat,Cart,G2mth.normQ(Q)) |
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| 266 | Q[iv] += 2.*dx |
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| 267 | XYZ2 = G2mth.RotateRBXYZ(Bmat,Cart,G2mth.normQ(Q)) |
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| 268 | Q[iv] -= dx |
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| 269 | dXdO = (XYZ2[ia]-XYZ1[ia])/(2.*dx) |
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| 270 | for ix in [0,1,2]: |
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| 271 | dFdvDict[pfx+'RBR'+OIds[iv]+rbsx] += dXdO[ix]*dFdvDict[pfx+atxIds[ix]+str(atNum)] |
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| 272 | X = G2mth.prodQVQ(Q,Cart[ia]) |
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| 273 | dFdu = np.array([dFdvDict[pfx+Uid+str(AtLookup[atId])] for Uid in atuIds]).T/gvec |
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| 274 | dFdu = G2lat.U6toUij(dFdu.T) |
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| 275 | dFdu = np.tensordot(Amat.T,np.tensordot(Amat,dFdu,([1,0])),([0,1])) |
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| 276 | dFdu = G2lat.UijtoU6(dFdu) |
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| 277 | atNum = AtLookup[atId] |
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| 278 | if 'T' in RBObj['ThermalMotion'][0]: |
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| 279 | for i,name in enumerate(['RBRT11:','RBRT22:','RBRT33:','RBRT12:','RBRT13:','RBRT23:']): |
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| 280 | dFdvDict[pfx+name+rbsx] += dFdu[i] |
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| 281 | if 'L' in RBObj['ThermalMotion'][0]: |
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| 282 | dFdvDict[pfx+'RBRL11:'+rbsx] += rpd2*(dFdu[1]*X[2]**2+dFdu[2]*X[1]**2-dFdu[5]*X[1]*X[2]) |
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| 283 | dFdvDict[pfx+'RBRL22:'+rbsx] += rpd2*(dFdu[0]*X[2]**2+dFdu[2]*X[0]**2-dFdu[4]*X[0]*X[2]) |
|---|
| 284 | dFdvDict[pfx+'RBRL33:'+rbsx] += rpd2*(dFdu[0]*X[1]**2+dFdu[1]*X[0]**2-dFdu[3]*X[0]*X[1]) |
|---|
| 285 | dFdvDict[pfx+'RBRL12:'+rbsx] += rpd2*(-dFdu[3]*X[2]**2-2.*dFdu[2]*X[0]*X[1]+ |
|---|
| 286 | dFdu[4]*X[1]*X[2]+dFdu[5]*X[0]*X[2]) |
|---|
| 287 | dFdvDict[pfx+'RBRL13:'+rbsx] += rpd2*(dFdu[4]*X[1]**2-2.*dFdu[1]*X[0]*X[2]+ |
|---|
| 288 | dFdu[3]*X[1]*X[2]+dFdu[5]*X[0]*X[1]) |
|---|
| 289 | dFdvDict[pfx+'RBRL23:'+rbsx] += rpd2*(dFdu[5]*X[0]**2-2.*dFdu[0]*X[1]*X[2]+ |
|---|
| 290 | dFdu[3]*X[0]*X[2]+dFdu[4]*X[0]*X[1]) |
|---|
| 291 | if 'S' in RBObj['ThermalMotion'][0]: |
|---|
| 292 | dFdvDict[pfx+'RBRS12:'+rbsx] += rpd*(dFdu[5]*X[1]-2.*dFdu[1]*X[2]) |
|---|
| 293 | dFdvDict[pfx+'RBRS13:'+rbsx] += rpd*(-dFdu[5]*X[2]+2.*dFdu[2]*X[1]) |
|---|
| 294 | dFdvDict[pfx+'RBRS21:'+rbsx] += rpd*(-dFdu[4]*X[0]+2.*dFdu[0]*X[2]) |
|---|
| 295 | dFdvDict[pfx+'RBRS23:'+rbsx] += rpd*(dFdu[4]*X[2]-2.*dFdu[2]*X[0]) |
|---|
| 296 | dFdvDict[pfx+'RBRS31:'+rbsx] += rpd*(dFdu[3]*X[0]-2.*dFdu[0]*X[1]) |
|---|
| 297 | dFdvDict[pfx+'RBRS32:'+rbsx] += rpd*(-dFdu[3]*X[1]+2.*dFdu[1]*X[0]) |
|---|
| 298 | dFdvDict[pfx+'RBRSAA:'+rbsx] += rpd*(dFdu[4]*X[1]-dFdu[3]*X[2]) |
|---|
| 299 | dFdvDict[pfx+'RBRSBB:'+rbsx] += rpd*(dFdu[5]*X[0]-dFdu[3]*X[2]) |
|---|
| 300 | if 'U' in RBObj['ThermalMotion'][0]: |
|---|
| 301 | dFdvDict[pfx+'RBRU:'+rbsx] += dFdvDict[pfx+'AUiso:'+str(AtLookup[atId])] |
|---|
| 302 | |
|---|
| 303 | ################################################################################ |
|---|
| 304 | ##### Penalty & restraint functions |
|---|
| 305 | ################################################################################ |
|---|
| 306 | |
|---|
| 307 | def penaltyFxn(HistoPhases,calcControls,parmDict,varyList): |
|---|
| 308 | 'Needs a doc string' |
|---|
| 309 | Histograms,Phases,restraintDict,rigidbodyDict = HistoPhases |
|---|
| 310 | pNames = [] |
|---|
| 311 | pVals = [] |
|---|
| 312 | pWt = [] |
|---|
| 313 | negWt = {} |
|---|
| 314 | pWsum = {} |
|---|
| 315 | for phase in Phases: |
|---|
| 316 | pId = Phases[phase]['pId'] |
|---|
| 317 | negWt[pId] = Phases[phase]['General']['Pawley neg wt'] |
|---|
| 318 | General = Phases[phase]['General'] |
|---|
| 319 | cx,ct,cs,cia = General['AtomPtrs'] |
|---|
| 320 | textureData = General['SH Texture'] |
|---|
| 321 | SGData = General['SGData'] |
|---|
| 322 | AtLookup = G2mth.FillAtomLookUp(Phases[phase]['Atoms'],cia+8) |
|---|
| 323 | cell = General['Cell'][1:7] |
|---|
| 324 | Amat,Bmat = G2lat.cell2AB(cell) |
|---|
| 325 | if phase not in restraintDict: |
|---|
| 326 | continue |
|---|
| 327 | phaseRest = restraintDict[phase] |
|---|
| 328 | names = [['Bond','Bonds'],['Angle','Angles'],['Plane','Planes'], |
|---|
| 329 | ['Chiral','Volumes'],['Torsion','Torsions'],['Rama','Ramas'], |
|---|
| 330 | ['ChemComp','Sites'],['Texture','HKLs'],] |
|---|
| 331 | for name,rest in names: |
|---|
| 332 | pWsum[name] = 0. |
|---|
| 333 | itemRest = phaseRest[name] |
|---|
| 334 | if itemRest[rest] and itemRest['Use']: |
|---|
| 335 | wt = itemRest['wtFactor'] |
|---|
| 336 | if name in ['Bond','Angle','Plane','Chiral']: |
|---|
| 337 | for i,[indx,ops,obs,esd] in enumerate(itemRest[rest]): |
|---|
| 338 | pNames.append(str(pId)+':'+name+':'+str(i)) |
|---|
| 339 | XYZ = np.array(G2mth.GetAtomCoordsByID(pId,parmDict,AtLookup,indx)) |
|---|
| 340 | XYZ = G2mth.getSyXYZ(XYZ,ops,SGData) |
|---|
| 341 | if name == 'Bond': |
|---|
| 342 | calc = G2mth.getRestDist(XYZ,Amat) |
|---|
| 343 | elif name == 'Angle': |
|---|
| 344 | calc = G2mth.getRestAngle(XYZ,Amat) |
|---|
| 345 | elif name == 'Plane': |
|---|
| 346 | calc = G2mth.getRestPlane(XYZ,Amat) |
|---|
| 347 | elif name == 'Chiral': |
|---|
| 348 | calc = G2mth.getRestChiral(XYZ,Amat) |
|---|
| 349 | pVals.append(obs-calc) |
|---|
| 350 | pWt.append(wt/esd**2) |
|---|
| 351 | pWsum[name] += wt*((obs-calc)/esd)**2 |
|---|
| 352 | elif name in ['Torsion','Rama']: |
|---|
| 353 | coeffDict = itemRest['Coeff'] |
|---|
| 354 | for i,[indx,ops,cofName,esd] in enumerate(itemRest[rest]): |
|---|
| 355 | pNames.append(str(pId)+':'+name+':'+str(i)) |
|---|
| 356 | XYZ = np.array(G2mth.GetAtomCoordsByID(pId,parmDict,AtLookup,indx)) |
|---|
| 357 | XYZ = G2mth.getSyXYZ(XYZ,ops,SGData) |
|---|
| 358 | if name == 'Torsion': |
|---|
| 359 | tor = G2mth.getRestTorsion(XYZ,Amat) |
|---|
| 360 | restr,calc = G2mth.calcTorsionEnergy(tor,coeffDict[cofName]) |
|---|
| 361 | else: |
|---|
| 362 | phi,psi = G2mth.getRestRama(XYZ,Amat) |
|---|
| 363 | restr,calc = G2mth.calcRamaEnergy(phi,psi,coeffDict[cofName]) |
|---|
| 364 | pVals.append(restr) |
|---|
| 365 | pWt.append(wt/esd**2) |
|---|
| 366 | pWsum[name] += wt*(restr/esd)**2 |
|---|
| 367 | elif name == 'ChemComp': |
|---|
| 368 | for i,[indx,factors,obs,esd] in enumerate(itemRest[rest]): |
|---|
| 369 | pNames.append(str(pId)+':'+name+':'+str(i)) |
|---|
| 370 | mul = np.array(G2mth.GetAtomItemsById(Atoms,AtLookUp,indx,cs+1)) |
|---|
| 371 | frac = np.array(G2mth.GetAtomItemsById(Atoms,AtLookUp,indx,cs-1)) |
|---|
| 372 | calc = np.sum(mul*frac*factors) |
|---|
| 373 | pVals.append(obs-calc) |
|---|
| 374 | pWt.append(wt/esd**2) |
|---|
| 375 | pWsum[name] += wt*((obs-calc)/esd)**2 |
|---|
| 376 | elif name == 'Texture': |
|---|
| 377 | SHkeys = textureData['SH Coeff'][1].keys() |
|---|
| 378 | SHCoef = G2mth.GetSHCoeff(pId,parmDict,SHkeys) |
|---|
| 379 | shModels = ['cylindrical','none','shear - 2/m','rolling - mmm'] |
|---|
| 380 | SamSym = dict(zip(shModels,['0','-1','2/m','mmm'])) |
|---|
| 381 | for i,[hkl,grid,esd1,ifesd2,esd2] in enumerate(itemRest[rest]): |
|---|
| 382 | PH = np.array(hkl) |
|---|
| 383 | phi,beta = G2lat.CrsAng(np.array(hkl),cell,SGData) |
|---|
| 384 | ODFln = G2lat.Flnh(False,SHCoef,phi,beta,SGData) |
|---|
| 385 | R,P,Z = G2mth.getRestPolefig(ODFln,SamSym[textureData['Model']],grid) |
|---|
| 386 | Z1 = -ma.masked_greater(Z,0.0) |
|---|
| 387 | IndZ1 = np.array(ma.nonzero(Z1)) |
|---|
| 388 | for ind in IndZ1.T: |
|---|
| 389 | pNames.append('%d:%s:%d:%.2f:%.2f'%(pId,name,i,R[ind[0],ind[1]],P[ind[0],ind[1]])) |
|---|
| 390 | pVals.append(Z1[ind[0]][ind[1]]) |
|---|
| 391 | pWt.append(wt/esd1**2) |
|---|
| 392 | pWsum[name] += wt*(-Z1[ind[0]][ind[1]]/esd1)**2 |
|---|
| 393 | if ifesd2: |
|---|
| 394 | Z2 = 1.-Z |
|---|
| 395 | for ind in np.ndindex(grid,grid): |
|---|
| 396 | pNames.append('%d:%s:%d:%.2f:%.2f'%(pId,name+'-unit',i,R[ind[0],ind[1]],P[ind[0],ind[1]])) |
|---|
| 397 | pVals.append(Z1[ind[0]][ind[1]]) |
|---|
| 398 | pWt.append(wt/esd2**2) |
|---|
| 399 | pWsum[name] += wt*(Z2/esd2)**2 |
|---|
| 400 | |
|---|
| 401 | for phase in Phases: |
|---|
| 402 | name = 'SH-Pref.Ori.' |
|---|
| 403 | pId = Phases[phase]['pId'] |
|---|
| 404 | General = Phases[phase]['General'] |
|---|
| 405 | SGData = General['SGData'] |
|---|
| 406 | cell = General['Cell'][1:7] |
|---|
| 407 | pWsum[name] = 0.0 |
|---|
| 408 | for hist in Phases[phase]['Histograms']: |
|---|
| 409 | if hist in Histograms and 'PWDR' in hist: |
|---|
| 410 | hId = Histograms[hist]['hId'] |
|---|
| 411 | phfx = '%d:%d:'%(pId,hId) |
|---|
| 412 | if calcControls[phfx+'poType'] == 'SH': |
|---|
| 413 | toler = calcControls[phfx+'SHtoler'] |
|---|
| 414 | wt = 1./toler**2 |
|---|
| 415 | HKLs = np.array(calcControls[phfx+'SHhkl']) |
|---|
| 416 | SHnames = calcControls[phfx+'SHnames'] |
|---|
| 417 | SHcof = dict(zip(SHnames,[parmDict[phfx+cof] for cof in SHnames])) |
|---|
| 418 | for i,PH in enumerate(HKLs): |
|---|
| 419 | phi,beta = G2lat.CrsAng(PH,cell,SGData) |
|---|
| 420 | SH3Coef = {} |
|---|
| 421 | for item in SHcof: |
|---|
| 422 | L,N = eval(item.strip('C')) |
|---|
| 423 | SH3Coef['C%d,0,%d'%(L,N)] = SHcof[item] |
|---|
| 424 | ODFln = G2lat.Flnh(False,SH3Coef,phi,beta,SGData) |
|---|
| 425 | X = np.linspace(0,90.0,26) |
|---|
| 426 | Y = -ma.masked_greater(G2lat.polfcal(ODFln,'0',X,0.0),0.0) |
|---|
| 427 | IndY = ma.nonzero(Y) |
|---|
| 428 | for ind in IndY[0]: |
|---|
| 429 | pNames.append('%d:%d:%s:%d:%.2f'%(pId,hId,name,i,X[ind])) |
|---|
| 430 | pVals.append(Y[ind]) |
|---|
| 431 | pWt.append(wt) |
|---|
| 432 | pWsum[name] += wt*(Y[ind])**2 |
|---|
| 433 | pWsum['PWLref'] = 0. |
|---|
| 434 | for item in varyList: |
|---|
| 435 | if 'PWLref' in item and parmDict[item] < 0.: |
|---|
| 436 | pId = int(item.split(':')[0]) |
|---|
| 437 | if negWt[pId]: |
|---|
| 438 | pNames.append(item) |
|---|
| 439 | pVals.append(-parmDict[item]) |
|---|
| 440 | pWt.append(negWt[pId]) |
|---|
| 441 | pWsum['PWLref'] += negWt[pId]*(-parmDict[item])**2 |
|---|
| 442 | pVals = np.array(pVals) |
|---|
| 443 | pWt = np.array(pWt) #should this be np.sqrt? |
|---|
| 444 | return pNames,pVals,pWt,pWsum |
|---|
| 445 | |
|---|
| 446 | def penaltyDeriv(pNames,pVal,HistoPhases,calcControls,parmDict,varyList): |
|---|
| 447 | 'Needs a doc string' |
|---|
| 448 | Histograms,Phases,restraintDict,rigidbodyDict = HistoPhases |
|---|
| 449 | pDerv = np.zeros((len(varyList),len(pVal))) |
|---|
| 450 | for phase in Phases: |
|---|
| 451 | # if phase not in restraintDict: |
|---|
| 452 | # continue |
|---|
| 453 | pId = Phases[phase]['pId'] |
|---|
| 454 | General = Phases[phase]['General'] |
|---|
| 455 | cx,ct,cs,cia = General['AtomPtrs'] |
|---|
| 456 | SGData = General['SGData'] |
|---|
| 457 | AtLookup = G2mth.FillAtomLookUp(Phases[phase]['Atoms'],cia+8) |
|---|
| 458 | cell = General['Cell'][1:7] |
|---|
| 459 | Amat,Bmat = G2lat.cell2AB(cell) |
|---|
| 460 | textureData = General['SH Texture'] |
|---|
| 461 | |
|---|
| 462 | SHkeys = textureData['SH Coeff'][1].keys() |
|---|
| 463 | SHCoef = G2mth.GetSHCoeff(pId,parmDict,SHkeys) |
|---|
| 464 | shModels = ['cylindrical','none','shear - 2/m','rolling - mmm'] |
|---|
| 465 | SamSym = dict(zip(shModels,['0','-1','2/m','mmm'])) |
|---|
| 466 | sam = SamSym[textureData['Model']] |
|---|
| 467 | phaseRest = restraintDict.get(phase,{}) |
|---|
| 468 | names = {'Bond':'Bonds','Angle':'Angles','Plane':'Planes', |
|---|
| 469 | 'Chiral':'Volumes','Torsion':'Torsions','Rama':'Ramas', |
|---|
| 470 | 'ChemComp':'Sites','Texture':'HKLs'} |
|---|
| 471 | lasthkl = np.array([0,0,0]) |
|---|
| 472 | for ip,pName in enumerate(pNames): |
|---|
| 473 | pnames = pName.split(':') |
|---|
| 474 | if pId == int(pnames[0]): |
|---|
| 475 | name = pnames[1] |
|---|
| 476 | if 'PWL' in pName: |
|---|
| 477 | pDerv[varyList.index(pName)][ip] += 1. |
|---|
| 478 | continue |
|---|
| 479 | elif 'SH-' in pName: |
|---|
| 480 | continue |
|---|
| 481 | id = int(pnames[2]) |
|---|
| 482 | itemRest = phaseRest[name] |
|---|
| 483 | if name in ['Bond','Angle','Plane','Chiral']: |
|---|
| 484 | indx,ops,obs,esd = itemRest[names[name]][id] |
|---|
| 485 | dNames = [] |
|---|
| 486 | for ind in indx: |
|---|
| 487 | dNames += [str(pId)+'::dA'+Xname+':'+str(AtLookup[ind]) for Xname in ['x','y','z']] |
|---|
| 488 | XYZ = np.array(G2mth.GetAtomCoordsByID(pId,parmDict,AtLookup,indx)) |
|---|
| 489 | if name == 'Bond': |
|---|
| 490 | deriv = G2mth.getRestDeriv(G2mth.getRestDist,XYZ,Amat,ops,SGData) |
|---|
| 491 | elif name == 'Angle': |
|---|
| 492 | deriv = G2mth.getRestDeriv(G2mth.getRestAngle,XYZ,Amat,ops,SGData) |
|---|
| 493 | elif name == 'Plane': |
|---|
| 494 | deriv = G2mth.getRestDeriv(G2mth.getRestPlane,XYZ,Amat,ops,SGData) |
|---|
| 495 | elif name == 'Chiral': |
|---|
| 496 | deriv = G2mth.getRestDeriv(G2mth.getRestChiral,XYZ,Amat,ops,SGData) |
|---|
| 497 | elif name in ['Torsion','Rama']: |
|---|
| 498 | coffDict = itemRest['Coeff'] |
|---|
| 499 | indx,ops,cofName,esd = itemRest[names[name]][id] |
|---|
| 500 | dNames = [] |
|---|
| 501 | for ind in indx: |
|---|
| 502 | dNames += [str(pId)+'::dA'+Xname+':'+str(AtLookup[ind]) for Xname in ['x','y','z']] |
|---|
| 503 | XYZ = np.array(G2mth.GetAtomCoordsByID(pId,parmDict,AtLookup,indx)) |
|---|
| 504 | if name == 'Torsion': |
|---|
| 505 | deriv = G2mth.getTorsionDeriv(XYZ,Amat,coffDict[cofName]) |
|---|
| 506 | else: |
|---|
| 507 | deriv = G2mth.getRamaDeriv(XYZ,Amat,coffDict[cofName]) |
|---|
| 508 | elif name == 'ChemComp': |
|---|
| 509 | indx,factors,obs,esd = itemRest[names[name]][id] |
|---|
| 510 | dNames = [] |
|---|
| 511 | for ind in indx: |
|---|
| 512 | dNames += [str(pId)+'::Afrac:'+str(AtLookup[ind])] |
|---|
| 513 | mul = np.array(G2mth.GetAtomItemsById(Atoms,AtLookUp,indx,cs+1)) |
|---|
| 514 | deriv = mul*factors |
|---|
| 515 | elif 'Texture' in name: |
|---|
| 516 | deriv = [] |
|---|
| 517 | dNames = [] |
|---|
| 518 | hkl,grid,esd1,ifesd2,esd2 = itemRest[names[name]][id] |
|---|
| 519 | hkl = np.array(hkl) |
|---|
| 520 | if np.any(lasthkl-hkl): |
|---|
| 521 | PH = np.array(hkl) |
|---|
| 522 | phi,beta = G2lat.CrsAng(np.array(hkl),cell,SGData) |
|---|
| 523 | ODFln = G2lat.Flnh(False,SHCoef,phi,beta,SGData) |
|---|
| 524 | lasthkl = copy.copy(hkl) |
|---|
| 525 | if 'unit' in name: |
|---|
| 526 | pass |
|---|
| 527 | else: |
|---|
| 528 | gam = float(pnames[3]) |
|---|
| 529 | psi = float(pnames[4]) |
|---|
| 530 | for SHname in ODFln: |
|---|
| 531 | l,m,n = eval(SHname[1:]) |
|---|
| 532 | Ksl = G2lat.GetKsl(l,m,sam,psi,gam)[0] |
|---|
| 533 | dNames += [str(pId)+'::'+SHname] |
|---|
| 534 | deriv.append(-ODFln[SHname][0]*Ksl/SHCoef[SHname]) |
|---|
| 535 | for dName,drv in zip(dNames,deriv): |
|---|
| 536 | try: |
|---|
| 537 | ind = varyList.index(dName) |
|---|
| 538 | pDerv[ind][ip] += drv |
|---|
| 539 | except ValueError: |
|---|
| 540 | pass |
|---|
| 541 | |
|---|
| 542 | lasthkl = np.array([0,0,0]) |
|---|
| 543 | for ip,pName in enumerate(pNames): |
|---|
| 544 | deriv = [] |
|---|
| 545 | dNames = [] |
|---|
| 546 | pnames = pName.split(':') |
|---|
| 547 | if 'SH-' in pName and pId == int(pnames[0]): |
|---|
| 548 | hId = int(pnames[1]) |
|---|
| 549 | phfx = '%d:%d:'%(pId,hId) |
|---|
| 550 | psi = float(pnames[4]) |
|---|
| 551 | HKLs = calcControls[phfx+'SHhkl'] |
|---|
| 552 | SHnames = calcControls[phfx+'SHnames'] |
|---|
| 553 | SHcof = dict(zip(SHnames,[parmDict[phfx+cof] for cof in SHnames])) |
|---|
| 554 | hkl = np.array(HKLs[int(pnames[3])]) |
|---|
| 555 | if np.any(lasthkl-hkl): |
|---|
| 556 | PH = np.array(hkl) |
|---|
| 557 | phi,beta = G2lat.CrsAng(np.array(hkl),cell,SGData) |
|---|
| 558 | SH3Coef = {} |
|---|
| 559 | for item in SHcof: |
|---|
| 560 | L,N = eval(item.strip('C')) |
|---|
| 561 | SH3Coef['C%d,0,%d'%(L,N)] = SHcof[item] |
|---|
| 562 | ODFln = G2lat.Flnh(False,SH3Coef,phi,beta,SGData) |
|---|
| 563 | lasthkl = copy.copy(hkl) |
|---|
| 564 | for SHname in SHnames: |
|---|
| 565 | l,n = eval(SHname[1:]) |
|---|
| 566 | SH3name = 'C%d,0,%d'%(l,n) |
|---|
| 567 | Ksl = G2lat.GetKsl(l,0,'0',psi,0.0)[0] |
|---|
| 568 | dNames += [phfx+SHname] |
|---|
| 569 | deriv.append(ODFln[SH3name][0]*Ksl/SHcof[SHname]) |
|---|
| 570 | for dName,drv in zip(dNames,deriv): |
|---|
| 571 | try: |
|---|
| 572 | ind = varyList.index(dName) |
|---|
| 573 | pDerv[ind][ip] += drv |
|---|
| 574 | except ValueError: |
|---|
| 575 | pass |
|---|
| 576 | return pDerv |
|---|
| 577 | |
|---|
| 578 | ################################################################################ |
|---|
| 579 | ##### Function & derivative calculations |
|---|
| 580 | ################################################################################ |
|---|
| 581 | |
|---|
| 582 | def GetAtomFXU(pfx,calcControls,parmDict): |
|---|
| 583 | 'Needs a doc string' |
|---|
| 584 | Natoms = calcControls['Natoms'][pfx] |
|---|
| 585 | Tdata = Natoms*[' ',] |
|---|
| 586 | Mdata = np.zeros(Natoms) |
|---|
| 587 | IAdata = Natoms*[' ',] |
|---|
| 588 | Fdata = np.zeros(Natoms) |
|---|
| 589 | FFdata = [] |
|---|
| 590 | BLdata = [] |
|---|
| 591 | Xdata = np.zeros((3,Natoms)) |
|---|
| 592 | dXdata = np.zeros((3,Natoms)) |
|---|
| 593 | Uisodata = np.zeros(Natoms) |
|---|
| 594 | Uijdata = np.zeros((6,Natoms)) |
|---|
| 595 | Gdata = np.zeros((3,Natoms)) |
|---|
| 596 | keys = {'Atype:':Tdata,'Amul:':Mdata,'Afrac:':Fdata,'AI/A:':IAdata, |
|---|
| 597 | 'dAx:':dXdata[0],'dAy:':dXdata[1],'dAz:':dXdata[2], |
|---|
| 598 | 'Ax:':Xdata[0],'Ay:':Xdata[1],'Az:':Xdata[2],'AUiso:':Uisodata, |
|---|
| 599 | 'AU11:':Uijdata[0],'AU22:':Uijdata[1],'AU33:':Uijdata[2], |
|---|
| 600 | 'AU12:':Uijdata[3],'AU13:':Uijdata[4],'AU23:':Uijdata[5], |
|---|
| 601 | 'AMx:':Gdata[0],'AMy:':Gdata[1],'AMz:':Gdata[2],} |
|---|
| 602 | for iatm in range(Natoms): |
|---|
| 603 | for key in keys: |
|---|
| 604 | parm = pfx+key+str(iatm) |
|---|
| 605 | if parm in parmDict: |
|---|
| 606 | keys[key][iatm] = parmDict[parm] |
|---|
| 607 | Fdata = np.where(Fdata,Fdata,1.e-8) #avoid divide by zero in derivative calc. |
|---|
| 608 | return Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata,Gdata |
|---|
| 609 | |
|---|
| 610 | def GetAtomSSFXU(pfx,calcControls,parmDict): |
|---|
| 611 | 'Needs a doc string' |
|---|
| 612 | Natoms = calcControls['Natoms'][pfx] |
|---|
| 613 | maxSSwave = calcControls['maxSSwave'][pfx] |
|---|
| 614 | Nwave = {'F':maxSSwave['Sfrac'],'X':maxSSwave['Spos'],'Y':maxSSwave['Spos'],'Z':maxSSwave['Spos'], |
|---|
| 615 | 'U':maxSSwave['Sadp'],'M':maxSSwave['Smag'],'T':maxSSwave['Spos']} |
|---|
| 616 | XSSdata = np.zeros((6,maxSSwave['Spos'],Natoms)) |
|---|
| 617 | FSSdata = np.zeros((2,maxSSwave['Sfrac'],Natoms)) |
|---|
| 618 | USSdata = np.zeros((12,maxSSwave['Sadp'],Natoms)) |
|---|
| 619 | MSSdata = np.zeros((6,maxSSwave['Smag'],Natoms)) |
|---|
| 620 | waveTypes = [] |
|---|
| 621 | keys = {'Fsin:':FSSdata[0],'Fcos:':FSSdata[1],'Fzero:':FSSdata[0],'Fwid:':FSSdata[1], |
|---|
| 622 | 'Tmin:':XSSdata[0],'Tmax:':XSSdata[1],'Xmax:':XSSdata[2],'Ymax:':XSSdata[3],'Zmax:':XSSdata[4], |
|---|
| 623 | 'Xsin:':XSSdata[0],'Ysin:':XSSdata[1],'Zsin:':XSSdata[2],'Xcos:':XSSdata[3],'Ycos:':XSSdata[4],'Zcos:':XSSdata[5], |
|---|
| 624 | 'U11sin:':USSdata[0],'U22sin:':USSdata[1],'U33sin:':USSdata[2],'U12sin:':USSdata[3],'U13sin:':USSdata[4],'U23sin:':USSdata[5], |
|---|
| 625 | 'U11cos:':USSdata[6],'U22cos:':USSdata[7],'U33cos:':USSdata[8],'U12cos:':USSdata[9],'U13cos:':USSdata[10],'U23cos:':USSdata[11], |
|---|
| 626 | 'MXsin:':MSSdata[0],'MYsin:':MSSdata[1],'MZsin:':MSSdata[2],'MXcos:':MSSdata[3],'MYcos:':MSSdata[4],'MZcos:':MSSdata[5]} |
|---|
| 627 | for iatm in range(Natoms): |
|---|
| 628 | waveTypes.append(parmDict[pfx+'waveType:'+str(iatm)]) |
|---|
| 629 | for key in keys: |
|---|
| 630 | for m in range(Nwave[key[0]]): |
|---|
| 631 | parm = pfx+key+str(iatm)+':%d'%(m) |
|---|
| 632 | if parm in parmDict: |
|---|
| 633 | keys[key][m][iatm] = parmDict[parm] |
|---|
| 634 | return np.array(waveTypes),FSSdata,XSSdata,USSdata,MSSdata |
|---|
| 635 | |
|---|
| 636 | #def GetSSTauM(SGOps,SSOps,pfx,calcControls,XData): |
|---|
| 637 | # |
|---|
| 638 | # Natoms = calcControls['Natoms'][pfx] |
|---|
| 639 | # maxSSwave = calcControls['maxSSwave'][pfx] |
|---|
| 640 | # Smult = np.zeros((Natoms,len(SGOps))) |
|---|
| 641 | # TauT = np.zeros((Natoms,len(SGOps))) |
|---|
| 642 | # for ix,xyz in enumerate(XData.T): |
|---|
| 643 | # for isym,(sop,ssop) in enumerate(zip(SGOps,SSOps)): |
|---|
| 644 | # sdet,ssdet,dtau,dT,tauT = G2spc.getTauT(0,sop,ssop,xyz) |
|---|
| 645 | # Smult[ix][isym] = sdet |
|---|
| 646 | # TauT[ix][isym] = tauT |
|---|
| 647 | # return Smult,TauT |
|---|
| 648 | # |
|---|
| 649 | def StructureFactor2(refDict,G,hfx,pfx,SGData,calcControls,parmDict): |
|---|
| 650 | ''' Compute structure factors for all h,k,l for phase |
|---|
| 651 | puts the result, F^2, in each ref[8] in refList |
|---|
| 652 | operates on blocks of 100 reflections for speed |
|---|
| 653 | input: |
|---|
| 654 | |
|---|
| 655 | :param dict refDict: where |
|---|
| 656 | 'RefList' list where each ref = h,k,l,it,d,... |
|---|
| 657 | 'FF' dict of form factors - filed in below |
|---|
| 658 | :param np.array G: reciprocal metric tensor |
|---|
| 659 | :param str pfx: phase id string |
|---|
| 660 | :param dict SGData: space group info. dictionary output from SpcGroup |
|---|
| 661 | :param dict calcControls: |
|---|
| 662 | :param dict ParmDict: |
|---|
| 663 | |
|---|
| 664 | ''' |
|---|
| 665 | phfx = pfx.split(':')[0]+hfx |
|---|
| 666 | ast = np.sqrt(np.diag(G)) |
|---|
| 667 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 668 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 669 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 670 | Ncen = len(SGData['SGCen']) |
|---|
| 671 | FFtables = calcControls['FFtables'] |
|---|
| 672 | BLtables = calcControls['BLtables'] |
|---|
| 673 | MFtables = calcControls['MFtables'] |
|---|
| 674 | Amat,Bmat = G2lat.Gmat2AB(G) |
|---|
| 675 | Flack = 1.0 |
|---|
| 676 | if not SGData['SGInv'] and 'S' in calcControls[hfx+'histType'] and phfx+'Flack' in parmDict: |
|---|
| 677 | Flack = 1.-2.*parmDict[phfx+'Flack'] |
|---|
| 678 | TwinLaw = np.array([[[1,0,0],[0,1,0],[0,0,1]],]) |
|---|
| 679 | TwDict = refDict.get('TwDict',{}) |
|---|
| 680 | if 'S' in calcControls[hfx+'histType']: |
|---|
| 681 | NTL = calcControls[phfx+'NTL'] |
|---|
| 682 | NM = calcControls[phfx+'TwinNMN']+1 |
|---|
| 683 | TwinLaw = calcControls[phfx+'TwinLaw'] |
|---|
| 684 | TwinFr = np.array([parmDict[phfx+'TwinFr:'+str(i)] for i in range(len(TwinLaw))]) |
|---|
| 685 | TwinInv = list(np.where(calcControls[phfx+'TwinInv'],-1,1)) |
|---|
| 686 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata,Gdata = \ |
|---|
| 687 | GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 688 | if parmDict[pfx+'isMag']: |
|---|
| 689 | Mag = np.sqrt(np.sum(Gdata**2,axis=0)) #magnitude of moments for uniq atoms |
|---|
| 690 | Gdata = np.where(Mag>0.,Gdata/Mag,0.) #normalze mag. moments |
|---|
| 691 | Gdata = np.inner(Bmat,Gdata.T) #convert to crystal space |
|---|
| 692 | Gdata = np.inner(Gdata.T,SGMT).T #apply sym. ops. |
|---|
| 693 | if SGData['SGInv']: |
|---|
| 694 | Gdata = np.hstack((Gdata,-Gdata)) #inversion if any |
|---|
| 695 | Gdata = np.repeat(Gdata,Ncen,axis=1) #dup over cell centering |
|---|
| 696 | Gdata = SGData['MagMom'][nxs,:,nxs]*Gdata #flip vectors according to spin flip |
|---|
| 697 | Gdata = np.inner(Amat,Gdata.T) #convert back to cart. space MXYZ, Natoms, NOps*Inv*Ncen |
|---|
| 698 | Gdata = np.swapaxes(Gdata,1,2) # put Natoms last |
|---|
| 699 | # GSASIIpath.IPyBreak() |
|---|
| 700 | Mag = np.tile(Mag[:,nxs],len(SGMT)*Ncen).T |
|---|
| 701 | if SGData['SGInv']: |
|---|
| 702 | Mag = np.repeat(Mag,2,axis=0) #Mag same length as Gdata |
|---|
| 703 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 704 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 705 | elif 'X' in calcControls[hfx+'histType']: |
|---|
| 706 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 707 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 708 | Uij = np.array(G2lat.U6toUij(Uijdata)) |
|---|
| 709 | bij = Mast*Uij.T |
|---|
| 710 | blkSize = 100 #no. of reflections in a block - size seems optimal |
|---|
| 711 | nRef = refDict['RefList'].shape[0] |
|---|
| 712 | if not len(refDict['FF']): #no form factors - 1st time thru StructureFactor |
|---|
| 713 | SQ = 1./(2.*refDict['RefList'].T[4])**2 |
|---|
| 714 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 715 | dat = G2el.getBLvalues(BLtables) |
|---|
| 716 | refDict['FF']['El'] = dat.keys() |
|---|
| 717 | refDict['FF']['FF'] = np.ones((nRef,len(dat)))*dat.values() |
|---|
| 718 | refDict['FF']['MF'] = np.zeros((nRef,len(dat))) |
|---|
| 719 | for iel,El in enumerate(refDict['FF']['El']): |
|---|
| 720 | if El in MFtables: |
|---|
| 721 | refDict['FF']['MF'].T[iel] = G2el.MagScatFac(MFtables[El],SQ) |
|---|
| 722 | else: #'X' |
|---|
| 723 | dat = G2el.getFFvalues(FFtables,0.) |
|---|
| 724 | refDict['FF']['El'] = dat.keys() |
|---|
| 725 | refDict['FF']['FF'] = np.zeros((nRef,len(dat))) |
|---|
| 726 | for iel,El in enumerate(refDict['FF']['El']): |
|---|
| 727 | refDict['FF']['FF'].T[iel] = G2el.ScatFac(FFtables[El],SQ) |
|---|
| 728 | #reflection processing begins here - big arrays! |
|---|
| 729 | iBeg = 0 |
|---|
| 730 | time0 = time.time() |
|---|
| 731 | while iBeg < nRef: |
|---|
| 732 | iFin = min(iBeg+blkSize,nRef) |
|---|
| 733 | refl = refDict['RefList'][iBeg:iFin] #array(blkSize,nItems) |
|---|
| 734 | H = refl.T[:3] #array(blkSize,3) |
|---|
| 735 | H = np.squeeze(np.inner(H.T,TwinLaw)) #maybe array(blkSize,nTwins,3) or (blkSize,3) |
|---|
| 736 | TwMask = np.any(H,axis=-1) |
|---|
| 737 | if TwinLaw.shape[0] > 1 and TwDict: #need np.inner(TwinLaw[?],TwDict[iref][i])*TwinInv[i] |
|---|
| 738 | for ir in range(blkSize): |
|---|
| 739 | iref = ir+iBeg |
|---|
| 740 | if iref in TwDict: |
|---|
| 741 | for i in TwDict[iref]: |
|---|
| 742 | for n in range(NTL): |
|---|
| 743 | H[ir][i+n*NM] = np.inner(TwinLaw[n*NM],np.array(TwDict[iref][i])*TwinInv[i+n*NM]) |
|---|
| 744 | TwMask = np.any(H,axis=-1) |
|---|
| 745 | SQ = 1./(2.*refl.T[4])**2 #array(blkSize) |
|---|
| 746 | SQfactor = 4.0*SQ*twopisq #ditto prev. |
|---|
| 747 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 748 | if 'P' in calcControls[hfx+'histType']: |
|---|
| 749 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[14]) |
|---|
| 750 | else: |
|---|
| 751 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[12]) |
|---|
| 752 | FP = np.repeat(FP.T,len(SGT)*len(TwinLaw),axis=0) |
|---|
| 753 | FPP = np.repeat(FPP.T,len(SGT)*len(TwinLaw),axis=0) |
|---|
| 754 | Bab = np.repeat(parmDict[phfx+'BabA']*np.exp(-parmDict[phfx+'BabU']*SQfactor),len(SGT)*len(TwinLaw)) |
|---|
| 755 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 756 | Uniq = np.inner(H,SGMT) |
|---|
| 757 | Phi = np.inner(H,SGT) |
|---|
| 758 | phase = twopi*(np.inner(Uniq,(dXdata+Xdata).T).T+Phi.T).T |
|---|
| 759 | sinp = np.sin(phase) |
|---|
| 760 | cosp = np.cos(phase) |
|---|
| 761 | biso = -SQfactor*Uisodata[:,nxs] |
|---|
| 762 | Tiso = np.repeat(np.where(biso<1.,np.exp(biso),1.0),len(SGT)*len(TwinLaw),axis=1).T |
|---|
| 763 | HbH = -np.sum(Uniq.T*np.swapaxes(np.inner(bij,Uniq),2,-1),axis=1) |
|---|
| 764 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0).T |
|---|
| 765 | Tcorr = np.reshape(Tiso,Tuij.shape)*Tuij*Mdata*Fdata/len(SGMT) |
|---|
| 766 | FF = np.repeat(refDict['FF']['FF'][iBeg:iFin].T[Tindx].T,len(SGT)*len(TwinLaw),axis=0) |
|---|
| 767 | if 'N' in calcControls[hfx+'histType'] and parmDict[pfx+'isMag']: |
|---|
| 768 | MF = np.repeat(refDict['FF']['MF'][iBeg:iFin].T[Tindx].T,len(TwinLaw),axis=0) #Nref,Natm |
|---|
| 769 | TMcorr = 0.5*0.539*Tcorr[:,0,:]*MF*len(SGMT)/Mdata #Nref,Natm |
|---|
| 770 | if SGData['SGInv']: |
|---|
| 771 | mphase = np.hstack((phase,-phase)) |
|---|
| 772 | else: |
|---|
| 773 | mphase = phase |
|---|
| 774 | mphase = np.array([mphase+twopi*np.inner(cen,H)[:,nxs,nxs] for cen in SGData['SGCen']]) |
|---|
| 775 | mphase = np.concatenate(mphase,axis=1) #Nref,Nop,Natm |
|---|
| 776 | sinm = np.sin(mphase) #ditto - match magstrfc.for |
|---|
| 777 | cosm = np.cos(mphase) #ditto |
|---|
| 778 | HM = np.inner(Bmat.T,H) #put into cartesian space |
|---|
| 779 | HM = HM/np.sqrt(np.sum(HM**2,axis=0)) #Gdata = MAGS & HM = UVEC in magstrfc.for both OK |
|---|
| 780 | eDotK = np.sum(HM[:,:,nxs,nxs]*Gdata[:,nxs,:,:],axis=0) |
|---|
| 781 | Q = -HM[:,:,nxs,nxs]*eDotK[nxs,:,:,:]+Gdata[:,nxs,:,:] #xyz,Nref,Nop,Natm = BPM in magstrfc.for OK |
|---|
| 782 | fam = Q*TMcorr[nxs,:,nxs,:]*SGData['MagMom'][nxs,nxs,:,nxs]*cosm[nxs,:,:,:]*Mag[nxs,nxs,:,:] #ditto |
|---|
| 783 | fbm = Q*TMcorr[nxs,:,nxs,:]*SGData['MagMom'][nxs,nxs,:,nxs]*sinm[nxs,:,:,:]*Mag[nxs,nxs,:,:] #ditto |
|---|
| 784 | fams = np.sum(np.sum(fam,axis=-1),axis=-1) #xyz,Nref |
|---|
| 785 | fbms = np.sum(np.sum(fbm,axis=-1),axis=-1) #ditto |
|---|
| 786 | # GSASIIpath.IPyBreak() |
|---|
| 787 | if 'T' in calcControls[hfx+'histType']: #fa,fb are 2 X blkSize X nTwin X nOps x nAtoms |
|---|
| 788 | fa = np.array([np.reshape(((FF+FP).T-Bab).T,cosp.shape)*cosp*Tcorr,-np.reshape(Flack*FPP,sinp.shape)*sinp*Tcorr]) |
|---|
| 789 | fb = np.array([np.reshape(((FF+FP).T-Bab).T,sinp.shape)*sinp*Tcorr,np.reshape(Flack*FPP,cosp.shape)*cosp*Tcorr]) |
|---|
| 790 | else: |
|---|
| 791 | fa = np.array([np.reshape(((FF+FP).T-Bab).T,cosp.shape)*cosp*Tcorr,-Flack*FPP*sinp*Tcorr]) |
|---|
| 792 | fb = np.array([np.reshape(((FF+FP).T-Bab).T,sinp.shape)*sinp*Tcorr,Flack*FPP*cosp*Tcorr]) |
|---|
| 793 | fas = np.sum(np.sum(fa,axis=-1),axis=-1) #real 2 x blkSize x nTwin; sum over atoms & uniq hkl |
|---|
| 794 | fbs = np.sum(np.sum(fb,axis=-1),axis=-1) #imag |
|---|
| 795 | if SGData['SGInv']: #centrosymmetric; B=0 |
|---|
| 796 | fbs[0] *= 0. |
|---|
| 797 | fas[1] *= 0. |
|---|
| 798 | if 'P' in calcControls[hfx+'histType']: #PXC, PNC & PNT: F^2 = A[0]^2 + A[1]^2 + B[0]^2 + B[1]^2 |
|---|
| 799 | refl.T[9] = np.sum(fas**2,axis=0)+np.sum(fbs**2,axis=0) #add fam**2 & fbm**2 here |
|---|
| 800 | refl.T[10] = atan2d(fbs[0],fas[0]) #ignore f' & f" |
|---|
| 801 | if 'N' in calcControls[hfx+'histType'] and parmDict[pfx+'isMag']: |
|---|
| 802 | refl.T[9] = np.sum(fams**2,axis=0)+np.sum(fbms**2,axis=0) |
|---|
| 803 | else: #HKLF: F^2 = (A[0]+A[1])^2 + (B[0]+B[1])^2 |
|---|
| 804 | if len(TwinLaw) > 1: |
|---|
| 805 | refl.T[9] = np.sum(fas[:,:,0],axis=0)**2+np.sum(fbs[:,:,0],axis=0)**2 #FcT from primary twin element |
|---|
| 806 | refl.T[7] = np.sum(TwinFr*TwMask*np.sum(fas,axis=0)**2,axis=-1)+ \ |
|---|
| 807 | np.sum(TwinFr*TwMask*np.sum(fbs,axis=0)**2,axis=-1) #Fc sum over twins |
|---|
| 808 | refl.T[10] = atan2d(fbs[0].T[0],fas[0].T[0]) #ignore f' & f" & use primary twin |
|---|
| 809 | else: # checked correct!! |
|---|
| 810 | refl.T[9] = np.sum(fas,axis=0)**2+np.sum(fbs,axis=0)**2 |
|---|
| 811 | refl.T[7] = np.copy(refl.T[9]) |
|---|
| 812 | refl.T[10] = atan2d(fbs[0],fas[0]) #ignore f' & f" |
|---|
| 813 | if 'N' in calcControls[hfx+'histType'] and parmDict[pfx+'isMag']: |
|---|
| 814 | refl.T[9] = np.sum(fams**2,axis=0)+np.sum(fbms**2,axis=0) |
|---|
| 815 | # GSASIIpath.IPyBreak() |
|---|
| 816 | # refl.T[10] = atan2d(np.sum(fbs,axis=0),np.sum(fas,axis=0)) #include f' & f" |
|---|
| 817 | iBeg += blkSize |
|---|
| 818 | # print ' %d sf time %.4f\r'%(nRef,time.time()-time0) |
|---|
| 819 | |
|---|
| 820 | #def StructureFactorDerv(refDict,G,hfx,pfx,SGData,calcControls,parmDict): |
|---|
| 821 | # '''Compute structure factor derivatives on single reflections - keep as it works for twins |
|---|
| 822 | # but is slower for powders/nontwins |
|---|
| 823 | # input: |
|---|
| 824 | # |
|---|
| 825 | # :param dict refDict: where |
|---|
| 826 | # 'RefList' list where each ref = h,k,l,it,d,... |
|---|
| 827 | # 'FF' dict of form factors - filled in below |
|---|
| 828 | # :param np.array G: reciprocal metric tensor |
|---|
| 829 | # :param str hfx: histogram id string |
|---|
| 830 | # :param str pfx: phase id string |
|---|
| 831 | # :param dict SGData: space group info. dictionary output from SpcGroup |
|---|
| 832 | # :param dict calcControls: |
|---|
| 833 | # :param dict ParmDict: |
|---|
| 834 | # |
|---|
| 835 | # :returns: dict dFdvDict: dictionary of derivatives |
|---|
| 836 | # ''' |
|---|
| 837 | # phfx = pfx.split(':')[0]+hfx |
|---|
| 838 | # ast = np.sqrt(np.diag(G)) |
|---|
| 839 | # Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 840 | # SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 841 | # SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 842 | # FFtables = calcControls['FFtables'] |
|---|
| 843 | # BLtables = calcControls['BLtables'] |
|---|
| 844 | # TwinLaw = np.array([[[1,0,0],[0,1,0],[0,0,1]],]) |
|---|
| 845 | # TwDict = refDict.get('TwDict',{}) |
|---|
| 846 | # if 'S' in calcControls[hfx+'histType']: |
|---|
| 847 | # NTL = calcControls[phfx+'NTL'] |
|---|
| 848 | # NM = calcControls[phfx+'TwinNMN']+1 |
|---|
| 849 | # TwinLaw = calcControls[phfx+'TwinLaw'] |
|---|
| 850 | # TwinFr = np.array([parmDict[phfx+'TwinFr:'+str(i)] for i in range(len(TwinLaw))]) |
|---|
| 851 | # TwinInv = list(np.where(calcControls[phfx+'TwinInv'],-1,1)) |
|---|
| 852 | # nTwin = len(TwinLaw) |
|---|
| 853 | # nRef = len(refDict['RefList']) |
|---|
| 854 | # Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata,Gdata = \ |
|---|
| 855 | # GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 856 | # mSize = len(Mdata) |
|---|
| 857 | # FF = np.zeros(len(Tdata)) |
|---|
| 858 | # if 'NC' in calcControls[hfx+'histType']: |
|---|
| 859 | # FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 860 | # elif 'X' in calcControls[hfx+'histType']: |
|---|
| 861 | # FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 862 | # FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 863 | # Uij = np.array(G2lat.U6toUij(Uijdata)) |
|---|
| 864 | # bij = Mast*Uij.T |
|---|
| 865 | # dFdvDict = {} |
|---|
| 866 | # if nTwin > 1: |
|---|
| 867 | # dFdfr = np.zeros((nRef,nTwin,mSize)) |
|---|
| 868 | # dFdx = np.zeros((nRef,nTwin,mSize,3)) |
|---|
| 869 | # dFdui = np.zeros((nRef,nTwin,mSize)) |
|---|
| 870 | # dFdua = np.zeros((nRef,nTwin,mSize,6)) |
|---|
| 871 | # dFdbab = np.zeros((nRef,nTwin,2)) |
|---|
| 872 | # dFdfl = np.zeros((nRef,nTwin)) |
|---|
| 873 | # dFdtw = np.zeros((nRef,nTwin)) |
|---|
| 874 | # else: |
|---|
| 875 | # dFdfr = np.zeros((nRef,mSize)) |
|---|
| 876 | # dFdx = np.zeros((nRef,mSize,3)) |
|---|
| 877 | # dFdui = np.zeros((nRef,mSize)) |
|---|
| 878 | # dFdua = np.zeros((nRef,mSize,6)) |
|---|
| 879 | # dFdbab = np.zeros((nRef,2)) |
|---|
| 880 | # dFdfl = np.zeros((nRef)) |
|---|
| 881 | # dFdtw = np.zeros((nRef)) |
|---|
| 882 | # Flack = 1.0 |
|---|
| 883 | # if not SGData['SGInv'] and 'S' in calcControls[hfx+'histType'] and phfx+'Flack' in parmDict: |
|---|
| 884 | # Flack = 1.-2.*parmDict[phfx+'Flack'] |
|---|
| 885 | # time0 = time.time() |
|---|
| 886 | # nref = len(refDict['RefList'])/100 |
|---|
| 887 | # for iref,refl in enumerate(refDict['RefList']): |
|---|
| 888 | # if 'T' in calcControls[hfx+'histType']: |
|---|
| 889 | # FP,FPP = G2el.BlenResCW(Tdata,BLtables,refl.T[12]) |
|---|
| 890 | # H = np.array(refl[:3]) |
|---|
| 891 | # H = np.squeeze(np.inner(H.T,TwinLaw)) #maybe array(3,nTwins) or (3) |
|---|
| 892 | # TwMask = np.any(H,axis=-1) |
|---|
| 893 | # if TwinLaw.shape[0] > 1 and TwDict: |
|---|
| 894 | # if iref in TwDict: |
|---|
| 895 | # for i in TwDict[iref]: |
|---|
| 896 | # for n in range(NTL): |
|---|
| 897 | # H[i+n*NM] = np.inner(TwinLaw[n*NM],np.array(TwDict[iref][i])*TwinInv[i+n*NM]) |
|---|
| 898 | # TwMask = np.any(H,axis=-1) |
|---|
| 899 | # SQ = 1./(2.*refl[4])**2 # or (sin(theta)/lambda)**2 |
|---|
| 900 | # SQfactor = 8.0*SQ*np.pi**2 |
|---|
| 901 | # dBabdA = np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 902 | # Bab = parmDict[phfx+'BabA']*dBabdA |
|---|
| 903 | # Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 904 | # FF = refDict['FF']['FF'][iref].T[Tindx].T |
|---|
| 905 | # Uniq = np.inner(H,SGMT) # array(nSGOp,3) or (nTwin,nSGOp,3) |
|---|
| 906 | # Phi = np.inner(H,SGT) |
|---|
| 907 | # phase = twopi*(np.inner(Uniq,(dXdata+Xdata).T).T+Phi.T).T |
|---|
| 908 | # sinp = np.sin(phase) |
|---|
| 909 | # cosp = np.cos(phase) |
|---|
| 910 | # occ = Mdata*Fdata/len(SGT) |
|---|
| 911 | # biso = -SQfactor*Uisodata[:,nxs] |
|---|
| 912 | # Tiso = np.repeat(np.where(biso<1.,np.exp(biso),1.0),len(SGT)*nTwin,axis=1) |
|---|
| 913 | # HbH = -np.sum(Uniq.T*np.swapaxes(np.inner(bij,Uniq),2,-1),axis=1) |
|---|
| 914 | # Hij = np.array([Mast*np.multiply.outer(U,U) for U in np.reshape(Uniq,(-1,3))]) |
|---|
| 915 | # Hij = np.squeeze(np.reshape(np.array([G2lat.UijtoU6(Uij) for Uij in Hij]),(nTwin,-1,6))) |
|---|
| 916 | # Tuij = np.where(HbH<1.,np.exp(HbH),1.0) |
|---|
| 917 | # Tcorr = (np.reshape(Tiso,Tuij.shape)*Tuij).T*occ |
|---|
| 918 | # fot = (FF+FP-Bab)*Tcorr |
|---|
| 919 | # fotp = FPP*Tcorr |
|---|
| 920 | # fa = np.array([((FF+FP).T-Bab).T*cosp*Tcorr,-Flack*FPP*sinp*Tcorr]) |
|---|
| 921 | # fb = np.array([((FF+FP).T-Bab).T*sinp*Tcorr,Flack*FPP*cosp*Tcorr]) |
|---|
| 922 | ## GSASIIpath.IPyBreak() |
|---|
| 923 | # fas = np.sum(np.sum(fa,axis=-1),axis=-1) #real sum over atoms & unique hkl array(2,nTwins) |
|---|
| 924 | # fbs = np.sum(np.sum(fb,axis=-1),axis=-1) #imag sum over atoms & uniq hkl |
|---|
| 925 | # fax = np.array([-fot*sinp,-fotp*cosp]) #positions array(2,ntwi,nEqv,nAtoms) |
|---|
| 926 | # fbx = np.array([fot*cosp,-fotp*sinp]) |
|---|
| 927 | # #sum below is over Uniq |
|---|
| 928 | # dfadfr = np.sum(fa/occ,axis=-2) #array(2,ntwin,nAtom) Fdata != 0 avoids /0. problem |
|---|
| 929 | # dfadba = np.sum(-cosp*Tcorr[:,nxs],axis=1) |
|---|
| 930 | # dfadui = np.sum(-SQfactor*fa,axis=-2) |
|---|
| 931 | # if nTwin > 1: |
|---|
| 932 | # dfadx = np.array([np.sum(twopi*Uniq[it]*np.swapaxes(fax,-2,-1)[:,it,:,:,nxs],axis=-2) for it in range(nTwin)]) |
|---|
| 933 | # dfadua = np.array([np.sum(-Hij[it]*np.swapaxes(fa,-2,-1)[:,it,:,:,nxs],axis=-2) for it in range(nTwin)]) |
|---|
| 934 | # # array(nTwin,2,nAtom,3) & array(nTwin,2,nAtom,6) |
|---|
| 935 | # else: |
|---|
| 936 | # dfadx = np.sum(twopi*Uniq*np.swapaxes(fax,-2,-1)[:,:,:,nxs],axis=-2) |
|---|
| 937 | # dfadua = np.sum(-Hij*np.swapaxes(fa,-2,-1)[:,:,:,nxs],axis=-2) |
|---|
| 938 | # # array(2,nAtom,3) & array(2,nAtom,6) |
|---|
| 939 | # if not SGData['SGInv']: |
|---|
| 940 | # dfbdfr = np.sum(fb/occ,axis=-2) #Fdata != 0 avoids /0. problem |
|---|
| 941 | # dfadba /= 2. |
|---|
| 942 | # dfbdba = np.sum(-sinp*Tcorr[:,nxs],axis=1)/2. |
|---|
| 943 | # dfbdui = np.sum(-SQfactor*fb,axis=-2) |
|---|
| 944 | # if len(TwinLaw) > 1: |
|---|
| 945 | # dfbdx = np.array([np.sum(twopi*Uniq[it]*np.swapaxes(fbx,-2,-1)[:,it,:,:,nxs],axis=2) for it in range(nTwin)]) |
|---|
| 946 | # dfbdua = np.array([np.sum(-Hij[it]*np.swapaxes(fb,-2,-1)[:,it,:,:,nxs],axis=2) for it in range(nTwin)]) |
|---|
| 947 | # else: |
|---|
| 948 | # dfadfl = np.sum(-FPP*Tcorr*sinp) |
|---|
| 949 | # dfbdfl = np.sum(FPP*Tcorr*cosp) |
|---|
| 950 | # dfbdx = np.sum(twopi*Uniq*np.swapaxes(fbx,-2,-1)[:,:,:,nxs],axis=2) |
|---|
| 951 | # dfbdua = np.sum(-Hij*np.swapaxes(fb,-2,-1)[:,:,:,nxs],axis=2) |
|---|
| 952 | # else: |
|---|
| 953 | # dfbdfr = np.zeros_like(dfadfr) |
|---|
| 954 | # dfbdx = np.zeros_like(dfadx) |
|---|
| 955 | # dfbdui = np.zeros_like(dfadui) |
|---|
| 956 | # dfbdua = np.zeros_like(dfadua) |
|---|
| 957 | # dfbdba = np.zeros_like(dfadba) |
|---|
| 958 | # dfadfl = 0.0 |
|---|
| 959 | # dfbdfl = 0.0 |
|---|
| 960 | # #NB: the above have been checked against PA(1:10,1:2) in strfctr.for for Al2O3! |
|---|
| 961 | # SA = fas[0]+fas[1] |
|---|
| 962 | # SB = fbs[0]+fbs[1] |
|---|
| 963 | # if 'P' in calcControls[hfx+'histType']: #checked perfect for centro & noncentro |
|---|
| 964 | # dFdfr[iref] = 2.*(fas[0]*dfadfr[0]+fas[1]*dfadfr[1])*Mdata/len(Uniq)+ \ |
|---|
| 965 | # 2.*(fbs[0]*dfbdfr[0]-fbs[1]*dfbdfr[1])*Mdata/len(Uniq) |
|---|
| 966 | # dFdx[iref] = 2.*(fas[0]*dfadx[0]+fas[1]*dfadx[1])+ \ |
|---|
| 967 | # 2.*(fbs[0]*dfbdx[0]+fbs[1]*dfbdx[1]) |
|---|
| 968 | # dFdui[iref] = 2.*(fas[0]*dfadui[0]+fas[1]*dfadui[1])+ \ |
|---|
| 969 | # 2.*(fbs[0]*dfbdui[0]-fbs[1]*dfbdui[1]) |
|---|
| 970 | # dFdua[iref] = 2.*(fas[0]*dfadua[0]+fas[1]*dfadua[1])+ \ |
|---|
| 971 | # 2.*(fbs[0]*dfbdua[0]+fbs[1]*dfbdua[1]) |
|---|
| 972 | # else: |
|---|
| 973 | # if nTwin > 1: |
|---|
| 974 | # dFdfr[iref] = [2.*TwMask[it]*(SA[it]*dfadfr[0][it]+SA[it]*dfadfr[1][it]+SB[it]*dfbdfr[0][it]+SB[it]*dfbdfr[1][it])*Mdata/len(Uniq[it]) for it in range(nTwin)] |
|---|
| 975 | # dFdx[iref] = [2.*TwMask[it]*(SA[it]*dfadx[it][0]+SA[it]*dfadx[it][1]+SB[it]*dfbdx[it][0]+SB[it]*dfbdx[it][1]) for it in range(nTwin)] |
|---|
| 976 | # dFdui[iref] = [2.*TwMask[it]*(SA[it]*dfadui[it][0]+SA[it]*dfadui[it][1]+SB[it]*dfbdui[it][0]+SB[it]*dfbdui[it][1]) for it in range(nTwin)] |
|---|
| 977 | # dFdua[iref] = [2.*TwMask[it]*(SA[it]*dfadua[it][0]+SA[it]*dfadua[it][1]+SB[it]*dfbdua[it][0]+SB[it]*dfbdua[it][1]) for it in range(nTwin)] |
|---|
| 978 | # dFdtw[iref] = np.sum(TwMask*fas,axis=0)**2+np.sum(TwMask*fbs,axis=0)**2 |
|---|
| 979 | # else: #these are good for no twin single crystals |
|---|
| 980 | # dFdfr[iref] = (2.*SA*(dfadfr[0]+dfadfr[1])+2.*SB*(dfbdfr[0]+dfbdfr[1]))*Mdata/len(Uniq) |
|---|
| 981 | # dFdx[iref] = 2.*SA*(dfadx[0]+dfadx[1])+2.*SB*(dfbdx[0]+dfbdx[1]) |
|---|
| 982 | # dFdui[iref] = 2.*SA*(dfadui[0]+dfadui[1])+2.*SB*(dfbdui[0]+dfbdui[1]) |
|---|
| 983 | # dFdua[iref] = 2.*SA*(dfadua[0]+dfadua[1])+2.*SB*(dfbdua[0]+dfbdua[1]) |
|---|
| 984 | # dFdfl[iref] = -SA*dfadfl-SB*dfbdfl #array(nRef,) |
|---|
| 985 | # dFdbab[iref] = fas[0]*np.array([np.sum(dfadba*dBabdA),np.sum(-dfadba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T+ \ |
|---|
| 986 | # fbs[0]*np.array([np.sum(dfbdba*dBabdA),np.sum(-dfbdba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T |
|---|
| 987 | ## GSASIIpath.IPyBreak() |
|---|
| 988 | # if not iref%100 : |
|---|
| 989 | # print ' %d derivative time %.4f\r'%(iref,time.time()-time0), |
|---|
| 990 | # print ' %d derivative time %.4f\r'%(len(refDict['RefList']),time.time()-time0) |
|---|
| 991 | # #loop over atoms - each dict entry is list of derivatives for all the reflections |
|---|
| 992 | # if nTwin > 1: |
|---|
| 993 | # for i in range(len(Mdata)): #these all OK? |
|---|
| 994 | # dFdvDict[pfx+'Afrac:'+str(i)] = np.sum(dFdfr.T[i]*TwinFr[:,nxs],axis=0) |
|---|
| 995 | # dFdvDict[pfx+'dAx:'+str(i)] = np.sum(dFdx.T[0][i]*TwinFr[:,nxs],axis=0) |
|---|
| 996 | # dFdvDict[pfx+'dAy:'+str(i)] = np.sum(dFdx.T[1][i]*TwinFr[:,nxs],axis=0) |
|---|
| 997 | # dFdvDict[pfx+'dAz:'+str(i)] = np.sum(dFdx.T[2][i]*TwinFr[:,nxs],axis=0) |
|---|
| 998 | # dFdvDict[pfx+'AUiso:'+str(i)] = np.sum(dFdui.T[i]*TwinFr[:,nxs],axis=0) |
|---|
| 999 | # dFdvDict[pfx+'AU11:'+str(i)] = np.sum(dFdua.T[0][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1000 | # dFdvDict[pfx+'AU22:'+str(i)] = np.sum(dFdua.T[1][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1001 | # dFdvDict[pfx+'AU33:'+str(i)] = np.sum(dFdua.T[2][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1002 | # dFdvDict[pfx+'AU12:'+str(i)] = 2.*np.sum(dFdua.T[3][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1003 | # dFdvDict[pfx+'AU13:'+str(i)] = 2.*np.sum(dFdua.T[4][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1004 | # dFdvDict[pfx+'AU23:'+str(i)] = 2.*np.sum(dFdua.T[5][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1005 | # else: |
|---|
| 1006 | # for i in range(len(Mdata)): |
|---|
| 1007 | # dFdvDict[pfx+'Afrac:'+str(i)] = dFdfr.T[i] |
|---|
| 1008 | # dFdvDict[pfx+'dAx:'+str(i)] = dFdx.T[0][i] |
|---|
| 1009 | # dFdvDict[pfx+'dAy:'+str(i)] = dFdx.T[1][i] |
|---|
| 1010 | # dFdvDict[pfx+'dAz:'+str(i)] = dFdx.T[2][i] |
|---|
| 1011 | # dFdvDict[pfx+'AUiso:'+str(i)] = dFdui.T[i] |
|---|
| 1012 | # dFdvDict[pfx+'AU11:'+str(i)] = dFdua.T[0][i] |
|---|
| 1013 | # dFdvDict[pfx+'AU22:'+str(i)] = dFdua.T[1][i] |
|---|
| 1014 | # dFdvDict[pfx+'AU33:'+str(i)] = dFdua.T[2][i] |
|---|
| 1015 | # dFdvDict[pfx+'AU12:'+str(i)] = 2.*dFdua.T[3][i] |
|---|
| 1016 | # dFdvDict[pfx+'AU13:'+str(i)] = 2.*dFdua.T[4][i] |
|---|
| 1017 | # dFdvDict[pfx+'AU23:'+str(i)] = 2.*dFdua.T[5][i] |
|---|
| 1018 | # dFdvDict[phfx+'Flack'] = 4.*dFdfl.T |
|---|
| 1019 | # dFdvDict[phfx+'BabA'] = dFdbab.T[0] |
|---|
| 1020 | # dFdvDict[phfx+'BabU'] = dFdbab.T[1] |
|---|
| 1021 | # if nTwin > 1: |
|---|
| 1022 | # for i in range(nTwin): |
|---|
| 1023 | # dFdvDict[phfx+'TwinFr:'+str(i)] = dFdtw.T[i] |
|---|
| 1024 | # return dFdvDict |
|---|
| 1025 | |
|---|
| 1026 | def StructureFactorDerv2(refDict,G,hfx,pfx,SGData,calcControls,parmDict): |
|---|
| 1027 | '''Compute structure factor derivatives on blocks of reflections - for powders/nontwins only |
|---|
| 1028 | faster than StructureFactorDerv - correct for powders/nontwins!! |
|---|
| 1029 | input: |
|---|
| 1030 | |
|---|
| 1031 | :param dict refDict: where |
|---|
| 1032 | 'RefList' list where each ref = h,k,l,it,d,... |
|---|
| 1033 | 'FF' dict of form factors - filled in below |
|---|
| 1034 | :param np.array G: reciprocal metric tensor |
|---|
| 1035 | :param str hfx: histogram id string |
|---|
| 1036 | :param str pfx: phase id string |
|---|
| 1037 | :param dict SGData: space group info. dictionary output from SpcGroup |
|---|
| 1038 | :param dict calcControls: |
|---|
| 1039 | :param dict parmDict: |
|---|
| 1040 | |
|---|
| 1041 | :returns: dict dFdvDict: dictionary of derivatives |
|---|
| 1042 | ''' |
|---|
| 1043 | phfx = pfx.split(':')[0]+hfx |
|---|
| 1044 | ast = np.sqrt(np.diag(G)) |
|---|
| 1045 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 1046 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 1047 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 1048 | FFtables = calcControls['FFtables'] |
|---|
| 1049 | BLtables = calcControls['BLtables'] |
|---|
| 1050 | nRef = len(refDict['RefList']) |
|---|
| 1051 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata,Gdata = \ |
|---|
| 1052 | GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 1053 | mSize = len(Mdata) |
|---|
| 1054 | if parmDict[pfx+'isMag']: |
|---|
| 1055 | Mag = np.sqrt(np.sum(Gdata**2,axis=0)) #magnitude of moments for uniq atoms |
|---|
| 1056 | Gdata = np.where(Mag>0.,Gdata/Mag,0.) #normalze mag. moments |
|---|
| 1057 | Gdata = np.inner(Bmat,Gdata.T) #convert to crystal space |
|---|
| 1058 | Gdata = np.inner(Gdata.T,SGMT).T #apply sym. ops. |
|---|
| 1059 | if SGData['SGInv']: |
|---|
| 1060 | Gdata = np.hstack((Gdata,-Gdata)) #inversion if any |
|---|
| 1061 | Gdata = np.repeat(Gdata,Ncen,axis=1) #dup over cell centering |
|---|
| 1062 | Gdata = SGData['MagMom'][nxs,:,nxs]*Gdata #flip vectors according to spin flip |
|---|
| 1063 | Gdata = np.inner(Amat,Gdata.T) #convert back to cart. space MXYZ, Natoms, NOps*Inv*Ncen |
|---|
| 1064 | Gdata = np.swapaxes(Gdata,1,2) # put Natoms last |
|---|
| 1065 | # GSASIIpath.IPyBreak() |
|---|
| 1066 | Mag = np.tile(Mag[:,nxs],len(SGMT)*Ncen).T |
|---|
| 1067 | if SGData['SGInv']: |
|---|
| 1068 | Mag = np.repeat(Mag,2,axis=0) #Mag same length as Gdata |
|---|
| 1069 | dFdMx = np.zeros((nRef,mSize,3)) |
|---|
| 1070 | FF = np.zeros(len(Tdata)) |
|---|
| 1071 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 1072 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 1073 | elif 'X' in calcControls[hfx+'histType']: |
|---|
| 1074 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 1075 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 1076 | Uij = np.array(G2lat.U6toUij(Uijdata)) |
|---|
| 1077 | bij = Mast*Uij.T |
|---|
| 1078 | dFdvDict = {} |
|---|
| 1079 | dFdfr = np.zeros((nRef,mSize)) |
|---|
| 1080 | dFdx = np.zeros((nRef,mSize,3)) |
|---|
| 1081 | dFdui = np.zeros((nRef,mSize)) |
|---|
| 1082 | dFdua = np.zeros((nRef,mSize,6)) |
|---|
| 1083 | dFdbab = np.zeros((nRef,2)) |
|---|
| 1084 | dFdfl = np.zeros((nRef)) |
|---|
| 1085 | Flack = 1.0 |
|---|
| 1086 | if not SGData['SGInv'] and 'S' in calcControls[hfx+'histType'] and phfx+'Flack' in parmDict: |
|---|
| 1087 | Flack = 1.-2.*parmDict[phfx+'Flack'] |
|---|
| 1088 | time0 = time.time() |
|---|
| 1089 | nref = len(refDict['RefList'])/100 |
|---|
| 1090 | #reflection processing begins here - big arrays! |
|---|
| 1091 | iBeg = 0 |
|---|
| 1092 | blkSize = 32 #no. of reflections in a block - optimized for speed |
|---|
| 1093 | while iBeg < nRef: |
|---|
| 1094 | iFin = min(iBeg+blkSize,nRef) |
|---|
| 1095 | refl = refDict['RefList'][iBeg:iFin] #array(blkSize,nItems) |
|---|
| 1096 | H = refl.T[:3] |
|---|
| 1097 | SQ = 1./(2.*refl.T[4])**2 # or (sin(theta)/lambda)**2 |
|---|
| 1098 | SQfactor = 8.0*SQ*np.pi**2 |
|---|
| 1099 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1100 | if 'P' in calcControls[hfx+'histType']: |
|---|
| 1101 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[14]) |
|---|
| 1102 | else: |
|---|
| 1103 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[12]) |
|---|
| 1104 | FP = np.repeat(FP.T,len(SGT),axis=0) |
|---|
| 1105 | FPP = np.repeat(FPP.T,len(SGT),axis=0) |
|---|
| 1106 | dBabdA = np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 1107 | Bab = np.repeat(parmDict[phfx+'BabA']*np.exp(-parmDict[phfx+'BabU']*SQfactor),len(SGT)) |
|---|
| 1108 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 1109 | FF = np.repeat(refDict['FF']['FF'][iBeg:iFin].T[Tindx].T,len(SGT),axis=0) |
|---|
| 1110 | # GSASIIpath.IPyBreak() |
|---|
| 1111 | Uniq = np.inner(H.T,SGMT) # array(nSGOp,3) |
|---|
| 1112 | Phi = np.inner(H.T,SGT) |
|---|
| 1113 | phase = twopi*(np.inner(Uniq,(dXdata+Xdata).T).T+Phi.T).T |
|---|
| 1114 | sinp = np.sin(phase) #refBlk x nOps x nAtoms |
|---|
| 1115 | cosp = np.cos(phase) |
|---|
| 1116 | occ = Mdata*Fdata/len(SGT) |
|---|
| 1117 | biso = -SQfactor*Uisodata[:,nxs] |
|---|
| 1118 | Tiso = np.repeat(np.where(biso<1.,np.exp(biso),1.0),len(SGT),axis=1).T |
|---|
| 1119 | HbH = -np.sum(Uniq.T*np.swapaxes(np.inner(bij,Uniq),2,-1),axis=1) |
|---|
| 1120 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0).T |
|---|
| 1121 | Tcorr = np.reshape(Tiso,Tuij.shape)*Tuij*Mdata*Fdata/len(SGMT) |
|---|
| 1122 | Hij = np.array([Mast*np.multiply.outer(U,U) for U in np.reshape(Uniq,(-1,3))]) |
|---|
| 1123 | Hij = np.reshape(np.array([G2lat.UijtoU6(Uij) for Uij in Hij]),(-1,len(SGT),6)) |
|---|
| 1124 | fot = np.reshape(((FF+FP).T-Bab).T,cosp.shape)*Tcorr |
|---|
| 1125 | if len(FPP.shape) > 1: |
|---|
| 1126 | fotp = np.reshape(FPP,cosp.shape)*Tcorr |
|---|
| 1127 | else: |
|---|
| 1128 | fotp = FPP*Tcorr |
|---|
| 1129 | if 'N' in calcControls[hfx+'histType'] and parmDict[pfx+'isMag']: |
|---|
| 1130 | MF = np.repeat(refDict['FF']['MF'][iBeg:iFin].T[Tindx].T,len(TwinLaw),axis=0) #Nref,Natm |
|---|
| 1131 | TMcorr = 0.5*0.539*Tcorr[:,0,:]*MF*len(SGMT)/Mdata #Nref,Natm |
|---|
| 1132 | if SGData['SGInv']: |
|---|
| 1133 | mphase = np.hstack((phase,-phase)) |
|---|
| 1134 | else: |
|---|
| 1135 | mphase = phase |
|---|
| 1136 | mphase = np.array([mphase+twopi*np.inner(cen,H)[:,nxs,nxs] for cen in SGData['SGCen']]) |
|---|
| 1137 | mphase = np.concatenate(mphase,axis=1) #Nref,Nop,Natm |
|---|
| 1138 | sinm = np.sin(mphase) #ditto - match magstrfc.for |
|---|
| 1139 | cosm = np.cos(mphase) #ditto |
|---|
| 1140 | HM = np.inner(Bmat.T,H) #put into cartesian space |
|---|
| 1141 | HM = HM/np.sqrt(np.sum(HM**2,axis=0)) #Gdata = MAGS & HM = UVEC in magstrfc.for both OK |
|---|
| 1142 | eDotK = np.sum(HM[:,:,nxs,nxs]*Gdata[:,nxs,:,:],axis=0) |
|---|
| 1143 | Q = -HM[:,:,nxs,nxs]*eDotK[nxs,:,:,:]+Gdata[:,nxs,:,:] #xyz,Nref,Nop,Natm = BPM in magstrfc.for OK |
|---|
| 1144 | fam = Q*TMcorr[nxs,:,nxs,:]*SGData['MagMom'][nxs,nxs,:,nxs]*cosm[nxs,:,:,:]*Mag[nxs,nxs,:,:] #ditto |
|---|
| 1145 | fbm = Q*TMcorr[nxs,:,nxs,:]*SGData['MagMom'][nxs,nxs,:,nxs]*sinm[nxs,:,:,:]*Mag[nxs,nxs,:,:] #ditto |
|---|
| 1146 | fams = np.sum(np.sum(fam,axis=-1),axis=-1) #xyz,Nref |
|---|
| 1147 | fbms = np.sum(np.sum(fbm,axis=-1),axis=-1) #ditto |
|---|
| 1148 | # GSASIIpath.IPyBreak() |
|---|
| 1149 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1150 | fa = np.array([fot*cosp,-np.reshape(Flack*FPP,sinp.shape)*sinp*Tcorr]) |
|---|
| 1151 | fb = np.array([fot*sinp,np.reshape(Flack*FPP,cosp.shape)*cosp*Tcorr]) |
|---|
| 1152 | else: |
|---|
| 1153 | fa = np.array([fot*cosp,-Flack*FPP*sinp*Tcorr]) |
|---|
| 1154 | fb = np.array([fot*sinp,Flack*FPP*cosp*Tcorr]) |
|---|
| 1155 | fas = np.sum(np.sum(fa,axis=-1),axis=-1) #real sum over atoms & unique hkl array(2,refBlk,nTwins) |
|---|
| 1156 | fbs = np.sum(np.sum(fb,axis=-1),axis=-1) #imag sum over atoms & uniq hkl |
|---|
| 1157 | fax = np.array([-fot*sinp,-fotp*cosp]) #positions array(2,refBlk,nEqv,nAtoms) |
|---|
| 1158 | fbx = np.array([fot*cosp,-fotp*sinp]) |
|---|
| 1159 | #sum below is over Uniq |
|---|
| 1160 | dfadfr = np.sum(fa/occ,axis=-2) #array(2,refBlk,nAtom) Fdata != 0 avoids /0. problem |
|---|
| 1161 | dfadba = np.sum(-cosp*Tcorr,axis=-2) #array(refBlk,nAtom) |
|---|
| 1162 | dfadx = np.sum(twopi*Uniq[nxs,:,nxs,:,:]*np.swapaxes(fax,-2,-1)[:,:,:,:,nxs],axis=-2) |
|---|
| 1163 | dfadui = np.sum(-SQfactor[nxs,:,nxs,nxs]*fa,axis=-2) #array(Ops,refBlk,nAtoms) |
|---|
| 1164 | dfadua = np.sum(-Hij[nxs,:,nxs,:,:]*np.swapaxes(fa,-2,-1)[:,:,:,:,nxs],axis=-2) |
|---|
| 1165 | # array(2,refBlk,nAtom,3) & array(2,refBlk,nAtom,6) |
|---|
| 1166 | if not SGData['SGInv']: |
|---|
| 1167 | dfbdfr = np.sum(fb/occ,axis=-2) #Fdata != 0 avoids /0. problem |
|---|
| 1168 | dfbdba = np.sum(-sinp*Tcorr,axis=-2) |
|---|
| 1169 | dfadfl = np.sum(np.sum(-fotp*sinp,axis=-1),axis=-1) |
|---|
| 1170 | dfbdfl = np.sum(np.sum(fotp*cosp,axis=-1),axis=-1) |
|---|
| 1171 | dfbdx = np.sum(twopi*Uniq[nxs,:,nxs,:,:]*np.swapaxes(fbx,-2,-1)[:,:,:,:,nxs],axis=-2) |
|---|
| 1172 | dfbdui = np.sum(-SQfactor[nxs,:,nxs,nxs]*fb,axis=-2) |
|---|
| 1173 | dfbdua = np.sum(-Hij[nxs,:,nxs,:,:]*np.swapaxes(fb,-2,-1)[:,:,:,:,nxs],axis=-2) |
|---|
| 1174 | else: |
|---|
| 1175 | dfbdfr = np.zeros_like(dfadfr) |
|---|
| 1176 | dfbdx = np.zeros_like(dfadx) |
|---|
| 1177 | dfbdui = np.zeros_like(dfadui) |
|---|
| 1178 | dfbdua = np.zeros_like(dfadua) |
|---|
| 1179 | dfbdba = np.zeros_like(dfadba) |
|---|
| 1180 | dfadfl = 0.0 |
|---|
| 1181 | dfbdfl = 0.0 |
|---|
| 1182 | #NB: the above have been checked against PA(1:10,1:2) in strfctr.for for Al2O3! |
|---|
| 1183 | SA = fas[0]+fas[1] |
|---|
| 1184 | SB = fbs[0]+fbs[1] |
|---|
| 1185 | if 'P' in calcControls[hfx+'histType']: #checked perfect for centro & noncentro |
|---|
| 1186 | dFdfr[iBeg:iFin] = 2.*np.sum(fas[:,:,nxs]*dfadfr+fbs[:,:,nxs]*dfbdfr,axis=0)*Mdata/len(SGMT) |
|---|
| 1187 | dFdx[iBeg:iFin] = 2.*np.sum(fas[:,:,nxs,nxs]*dfadx+fbs[:,:,nxs,nxs]*dfbdx,axis=0) |
|---|
| 1188 | dFdui[iBeg:iFin] = 2.*np.sum(fas[:,:,nxs]*dfadui+fbs[:,:,nxs]*dfbdui,axis=0) |
|---|
| 1189 | dFdua[iBeg:iFin] = 2.*np.sum(fas[:,:,nxs,nxs]*dfadua+fbs[:,:,nxs,nxs]*dfbdua,axis=0) |
|---|
| 1190 | else: |
|---|
| 1191 | dFdfr[iBeg:iFin] = (2.*SA[:,nxs]*(dfadfr[0]+dfadfr[1])+2.*SB[:,nxs]*(dfbdfr[0]+dfbdfr[1]))*Mdata/len(SGMT) |
|---|
| 1192 | dFdx[iBeg:iFin] = 2.*SA[:,nxs,nxs]*(dfadx[0]+dfadx[1])+2.*SB[:,nxs,nxs]*(dfbdx[0]+dfbdx[1]) |
|---|
| 1193 | dFdui[iBeg:iFin] = 2.*SA[:,nxs]*(dfadui[0]+dfadui[1])+2.*SB[:,nxs]*(dfbdui[0]+dfbdui[1]) |
|---|
| 1194 | dFdua[iBeg:iFin] = 2.*SA[:,nxs,nxs]*(dfadua[0]+dfadua[1])+2.*SB[:,nxs,nxs]*(dfbdua[0]+dfbdua[1]) |
|---|
| 1195 | dFdfl[iBeg:iFin] = -SA*dfadfl-SB*dfbdfl #array(nRef,) |
|---|
| 1196 | dFdbab[iBeg:iFin] = 2.*(fas[0,nxs]*np.array([np.sum(dfadba.T*dBabdA,axis=0),np.sum(-dfadba.T*parmDict[phfx+'BabA']*SQfactor*dBabdA,axis=0)])+ \ |
|---|
| 1197 | fbs[0,nxs]*np.array([np.sum(dfbdba.T*dBabdA,axis=0),np.sum(-dfbdba.T*parmDict[phfx+'BabA']*SQfactor*dBabdA,axis=0)])).T |
|---|
| 1198 | # GSASIIpath.IPyBreak() |
|---|
| 1199 | iBeg += blkSize |
|---|
| 1200 | print ' %d derivative time %.4f\r'%(nRef,time.time()-time0) |
|---|
| 1201 | #loop over atoms - each dict entry is list of derivatives for all the reflections |
|---|
| 1202 | for i in range(len(Mdata)): |
|---|
| 1203 | dFdvDict[pfx+'Afrac:'+str(i)] = dFdfr.T[i] |
|---|
| 1204 | dFdvDict[pfx+'dAx:'+str(i)] = dFdx.T[0][i] |
|---|
| 1205 | dFdvDict[pfx+'dAy:'+str(i)] = dFdx.T[1][i] |
|---|
| 1206 | dFdvDict[pfx+'dAz:'+str(i)] = dFdx.T[2][i] |
|---|
| 1207 | dFdvDict[pfx+'AUiso:'+str(i)] = dFdui.T[i] |
|---|
| 1208 | dFdvDict[pfx+'AU11:'+str(i)] = dFdua.T[0][i] |
|---|
| 1209 | dFdvDict[pfx+'AU22:'+str(i)] = dFdua.T[1][i] |
|---|
| 1210 | dFdvDict[pfx+'AU33:'+str(i)] = dFdua.T[2][i] |
|---|
| 1211 | dFdvDict[pfx+'AU12:'+str(i)] = 2.*dFdua.T[3][i] |
|---|
| 1212 | dFdvDict[pfx+'AU13:'+str(i)] = 2.*dFdua.T[4][i] |
|---|
| 1213 | dFdvDict[pfx+'AU23:'+str(i)] = 2.*dFdua.T[5][i] |
|---|
| 1214 | dFdvDict[phfx+'Flack'] = 4.*dFdfl.T |
|---|
| 1215 | dFdvDict[phfx+'BabA'] = dFdbab.T[0] |
|---|
| 1216 | dFdvDict[phfx+'BabU'] = dFdbab.T[1] |
|---|
| 1217 | return dFdvDict |
|---|
| 1218 | |
|---|
| 1219 | #def StructureFactorDervTw(refDict,G,hfx,pfx,SGData,calcControls,parmDict): |
|---|
| 1220 | # '''Compute structure factor derivatives on single reflections - for twins only |
|---|
| 1221 | # input: |
|---|
| 1222 | # |
|---|
| 1223 | # :param dict refDict: where |
|---|
| 1224 | # 'RefList' list where each ref = h,k,l,it,d,... |
|---|
| 1225 | # 'FF' dict of form factors - filled in below |
|---|
| 1226 | # :param np.array G: reciprocal metric tensor |
|---|
| 1227 | # :param str hfx: histogram id string |
|---|
| 1228 | # :param str pfx: phase id string |
|---|
| 1229 | # :param dict SGData: space group info. dictionary output from SpcGroup |
|---|
| 1230 | # :param dict calcControls: |
|---|
| 1231 | # :param dict parmDict: |
|---|
| 1232 | # |
|---|
| 1233 | # :returns: dict dFdvDict: dictionary of derivatives |
|---|
| 1234 | # ''' |
|---|
| 1235 | # phfx = pfx.split(':')[0]+hfx |
|---|
| 1236 | # ast = np.sqrt(np.diag(G)) |
|---|
| 1237 | # Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 1238 | # SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 1239 | # SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 1240 | # FFtables = calcControls['FFtables'] |
|---|
| 1241 | # BLtables = calcControls['BLtables'] |
|---|
| 1242 | # TwDict = refDict.get('TwDict',{}) |
|---|
| 1243 | # NTL = calcControls[phfx+'NTL'] |
|---|
| 1244 | # NM = calcControls[phfx+'TwinNMN']+1 |
|---|
| 1245 | # TwinLaw = calcControls[phfx+'TwinLaw'] |
|---|
| 1246 | # TwinFr = np.array([parmDict[phfx+'TwinFr:'+str(i)] for i in range(len(TwinLaw))]) |
|---|
| 1247 | # TwinInv = list(np.where(calcControls[phfx+'TwinInv'],-1,1)) |
|---|
| 1248 | # nTwin = len(TwinLaw) |
|---|
| 1249 | # nRef = len(refDict['RefList']) |
|---|
| 1250 | # Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata,Gdata = \ |
|---|
| 1251 | # GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 1252 | # mSize = len(Mdata) |
|---|
| 1253 | # FF = np.zeros(len(Tdata)) |
|---|
| 1254 | # if 'NC' in calcControls[hfx+'histType']: |
|---|
| 1255 | # FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 1256 | # elif 'X' in calcControls[hfx+'histType']: |
|---|
| 1257 | # FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 1258 | # FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 1259 | # Uij = np.array(G2lat.U6toUij(Uijdata)) |
|---|
| 1260 | # bij = Mast*Uij.T |
|---|
| 1261 | # dFdvDict = {} |
|---|
| 1262 | # dFdfr = np.zeros((nRef,nTwin,mSize)) |
|---|
| 1263 | # dFdx = np.zeros((nRef,nTwin,mSize,3)) |
|---|
| 1264 | # dFdui = np.zeros((nRef,nTwin,mSize)) |
|---|
| 1265 | # dFdua = np.zeros((nRef,nTwin,mSize,6)) |
|---|
| 1266 | # dFdbab = np.zeros((nRef,nTwin,2)) |
|---|
| 1267 | # dFdtw = np.zeros((nRef,nTwin)) |
|---|
| 1268 | # time0 = time.time() |
|---|
| 1269 | # nref = len(refDict['RefList'])/100 |
|---|
| 1270 | # for iref,refl in enumerate(refDict['RefList']): |
|---|
| 1271 | # if 'T' in calcControls[hfx+'histType']: |
|---|
| 1272 | # FP,FPP = G2el.BlenResCW(Tdata,BLtables,refl.T[12]) |
|---|
| 1273 | # H = np.array(refl[:3]) |
|---|
| 1274 | # H = np.inner(H.T,TwinLaw) #maybe array(3,nTwins) or (3) |
|---|
| 1275 | # TwMask = np.any(H,axis=-1) |
|---|
| 1276 | # if iref in TwDict: |
|---|
| 1277 | # for i in TwDict[iref]: |
|---|
| 1278 | # for n in range(NTL): |
|---|
| 1279 | # H[i+n*NM] = np.inner(TwinLaw[n*NM],np.array(TwDict[iref][i])*TwinInv[i+n*NM]) |
|---|
| 1280 | # TwMask = np.any(H,axis=-1) |
|---|
| 1281 | # SQ = 1./(2.*refl[4])**2 # or (sin(theta)/lambda)**2 |
|---|
| 1282 | # SQfactor = 8.0*SQ*np.pi**2 |
|---|
| 1283 | # dBabdA = np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 1284 | # Bab = parmDict[phfx+'BabA']*dBabdA |
|---|
| 1285 | # Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 1286 | # FF = refDict['FF']['FF'][iref].T[Tindx].T |
|---|
| 1287 | # Uniq = np.inner(H,SGMT) # array(nSGOp,3) or (nTwin,nSGOp,3) |
|---|
| 1288 | # Phi = np.inner(H,SGT) |
|---|
| 1289 | # phase = twopi*(np.inner(Uniq,(dXdata+Xdata).T).T+Phi.T).T |
|---|
| 1290 | # sinp = np.sin(phase) |
|---|
| 1291 | # cosp = np.cos(phase) |
|---|
| 1292 | # occ = Mdata*Fdata/len(SGT) |
|---|
| 1293 | # biso = -SQfactor*Uisodata[:,nxs] |
|---|
| 1294 | # Tiso = np.repeat(np.where(biso<1.,np.exp(biso),1.0),len(SGT)*nTwin,axis=1) |
|---|
| 1295 | # HbH = -np.sum(Uniq.T*np.swapaxes(np.inner(bij,Uniq),2,-1),axis=1) |
|---|
| 1296 | # Hij = np.array([Mast*np.multiply.outer(U,U) for U in np.reshape(Uniq,(-1,3))]) |
|---|
| 1297 | # Hij = np.reshape(np.array([G2lat.UijtoU6(Uij) for Uij in Hij]),(nTwin,-1,6)) |
|---|
| 1298 | # Tuij = np.where(HbH<1.,np.exp(HbH),1.0) |
|---|
| 1299 | # Tcorr = (np.reshape(Tiso,Tuij.shape)*Tuij).T*occ |
|---|
| 1300 | # fot = (FF+FP-Bab)*Tcorr |
|---|
| 1301 | # fotp = FPP*Tcorr |
|---|
| 1302 | # fa = np.array([((FF+FP).T-Bab).T*cosp*Tcorr,-FPP*sinp*Tcorr]) |
|---|
| 1303 | # fb = np.array([((FF+FP).T-Bab).T*sinp*Tcorr,FPP*cosp*Tcorr]) |
|---|
| 1304 | ## GSASIIpath.IPyBreak() |
|---|
| 1305 | # fas = np.sum(np.sum(fa,axis=-1),axis=-1) #real sum over atoms & unique hkl array(2,nTwins) |
|---|
| 1306 | # fbs = np.sum(np.sum(fb,axis=-1),axis=-1) #imag sum over atoms & uniq hkl |
|---|
| 1307 | # if SGData['SGInv']: #centrosymmetric; B=0 |
|---|
| 1308 | # fbs[0] *= 0. |
|---|
| 1309 | # fas[1] *= 0. |
|---|
| 1310 | # fax = np.array([-fot*sinp,-fotp*cosp]) #positions array(2,ntwi,nEqv,nAtoms) |
|---|
| 1311 | # fbx = np.array([fot*cosp,-fotp*sinp]) |
|---|
| 1312 | # #sum below is over Uniq |
|---|
| 1313 | # dfadfr = np.sum(fa/occ,axis=-2) #array(2,ntwin,nAtom) Fdata != 0 avoids /0. problem |
|---|
| 1314 | # dfadba = np.sum(-cosp*Tcorr[:,nxs],axis=1) |
|---|
| 1315 | # dfadui = np.sum(-SQfactor*fa,axis=-2) |
|---|
| 1316 | # dfadx = np.array([np.sum(twopi*Uniq[it]*np.swapaxes(fax,-2,-1)[:,it,:,:,nxs],axis=-2) for it in range(nTwin)]) |
|---|
| 1317 | # dfadua = np.array([np.sum(-Hij[it]*np.swapaxes(fa,-2,-1)[:,it,:,:,nxs],axis=-2) for it in range(nTwin)]) |
|---|
| 1318 | # # array(nTwin,2,nAtom,3) & array(nTwin,2,nAtom,6) |
|---|
| 1319 | # if not SGData['SGInv']: |
|---|
| 1320 | # dfbdfr = np.sum(fb/occ,axis=-2) #Fdata != 0 avoids /0. problem |
|---|
| 1321 | # dfadba /= 2. |
|---|
| 1322 | # dfbdba = np.sum(-sinp*Tcorr[:,nxs],axis=1)/2. |
|---|
| 1323 | # dfbdui = np.sum(-SQfactor*fb,axis=-2) |
|---|
| 1324 | # dfbdx = np.array([np.sum(twopi*Uniq[it]*np.swapaxes(fbx,-2,-1)[:,it,:,:,nxs],axis=2) for it in range(nTwin)]) |
|---|
| 1325 | # dfbdua = np.array([np.sum(-Hij[it]*np.swapaxes(fb,-2,-1)[:,it,:,:,nxs],axis=2) for it in range(nTwin)]) |
|---|
| 1326 | # else: |
|---|
| 1327 | # dfbdfr = np.zeros_like(dfadfr) |
|---|
| 1328 | # dfbdx = np.zeros_like(dfadx) |
|---|
| 1329 | # dfbdui = np.zeros_like(dfadui) |
|---|
| 1330 | # dfbdua = np.zeros_like(dfadua) |
|---|
| 1331 | # dfbdba = np.zeros_like(dfadba) |
|---|
| 1332 | # SA = fas[0]+fas[1] |
|---|
| 1333 | # SB = fbs[0]+fbs[1] |
|---|
| 1334 | # dFdfr[iref] = [2.*TwMask[it]*(SA[it]*dfadfr[0,it]+SA[it]*dfadfr[1,it]+SB[it]*dfbdfr[0,it]+SB[it]*dfbdfr[1,it])*Mdata/len(Uniq[it]) for it in range(nTwin)] |
|---|
| 1335 | # dFdx[iref] = [2.*TwMask[it]*(SA[it]*dfadx[it,0]+SA[it]*dfadx[it,1]+SB[it]*dfbdx[it,0]+SB[it]*dfbdx[it,1]) for it in range(nTwin)] |
|---|
| 1336 | # dFdui[iref] = [2.*TwMask[it]*(SA[it]*dfadui[0,it]+SA[it]*dfadui[1,it]+SB[it]*dfbdui[0,it]+SB[it]*dfbdui[1,it]) for it in range(nTwin)] |
|---|
| 1337 | # dFdua[iref] = [2.*TwMask[it]*(SA[it]*dfadua[it,0]+SA[it]*dfadua[it,1]+SB[it]*dfbdua[it,0]+SB[it]*dfbdua[it,1]) for it in range(nTwin)] |
|---|
| 1338 | # if SGData['SGInv']: #centrosymmetric; B=0 |
|---|
| 1339 | # dFdtw[iref] = np.sum(TwMask[nxs,:]*fas,axis=0)**2 |
|---|
| 1340 | # else: |
|---|
| 1341 | # dFdtw[iref] = np.sum(TwMask[nxs,:]*fas,axis=0)**2+np.sum(TwMask[nxs,:]*fbs,axis=0)**2 |
|---|
| 1342 | # dFdbab[iref] = fas[0,:,nxs]*np.array([np.sum(dfadba*dBabdA),np.sum(-dfadba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T+ \ |
|---|
| 1343 | # fbs[0,:,nxs]*np.array([np.sum(dfbdba*dBabdA),np.sum(-dfbdba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T |
|---|
| 1344 | ## GSASIIpath.IPyBreak() |
|---|
| 1345 | # print ' %d derivative time %.4f\r'%(len(refDict['RefList']),time.time()-time0) |
|---|
| 1346 | # #loop over atoms - each dict entry is list of derivatives for all the reflections |
|---|
| 1347 | # for i in range(len(Mdata)): #these all OK? |
|---|
| 1348 | # dFdvDict[pfx+'Afrac:'+str(i)] = np.sum(dFdfr.T[i]*TwinFr[:,nxs],axis=0) |
|---|
| 1349 | # dFdvDict[pfx+'dAx:'+str(i)] = np.sum(dFdx.T[0][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1350 | # dFdvDict[pfx+'dAy:'+str(i)] = np.sum(dFdx.T[1][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1351 | # dFdvDict[pfx+'dAz:'+str(i)] = np.sum(dFdx.T[2][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1352 | # dFdvDict[pfx+'AUiso:'+str(i)] = np.sum(dFdui.T[i]*TwinFr[:,nxs],axis=0) |
|---|
| 1353 | # dFdvDict[pfx+'AU11:'+str(i)] = np.sum(dFdua.T[0][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1354 | # dFdvDict[pfx+'AU22:'+str(i)] = np.sum(dFdua.T[1][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1355 | # dFdvDict[pfx+'AU33:'+str(i)] = np.sum(dFdua.T[2][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1356 | # dFdvDict[pfx+'AU12:'+str(i)] = 2.*np.sum(dFdua.T[3][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1357 | # dFdvDict[pfx+'AU13:'+str(i)] = 2.*np.sum(dFdua.T[4][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1358 | # dFdvDict[pfx+'AU23:'+str(i)] = 2.*np.sum(dFdua.T[5][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1359 | # dFdvDict[phfx+'BabA'] = dFdbab.T[0] |
|---|
| 1360 | # dFdvDict[phfx+'BabU'] = dFdbab.T[1] |
|---|
| 1361 | # for i in range(nTwin): |
|---|
| 1362 | # dFdvDict[phfx+'TwinFr:'+str(i)] = dFdtw.T[i] |
|---|
| 1363 | # return dFdvDict |
|---|
| 1364 | |
|---|
| 1365 | def StructureFactorDervTw2(refDict,G,hfx,pfx,SGData,calcControls,parmDict): |
|---|
| 1366 | '''Compute structure factor derivatives on blocks of reflections - for twins only |
|---|
| 1367 | faster than StructureFactorDervTw |
|---|
| 1368 | input: |
|---|
| 1369 | |
|---|
| 1370 | :param dict refDict: where |
|---|
| 1371 | 'RefList' list where each ref = h,k,l,it,d,... |
|---|
| 1372 | 'FF' dict of form factors - filled in below |
|---|
| 1373 | :param np.array G: reciprocal metric tensor |
|---|
| 1374 | :param str hfx: histogram id string |
|---|
| 1375 | :param str pfx: phase id string |
|---|
| 1376 | :param dict SGData: space group info. dictionary output from SpcGroup |
|---|
| 1377 | :param dict calcControls: |
|---|
| 1378 | :param dict parmDict: |
|---|
| 1379 | |
|---|
| 1380 | :returns: dict dFdvDict: dictionary of derivatives |
|---|
| 1381 | ''' |
|---|
| 1382 | phfx = pfx.split(':')[0]+hfx |
|---|
| 1383 | ast = np.sqrt(np.diag(G)) |
|---|
| 1384 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 1385 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 1386 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 1387 | FFtables = calcControls['FFtables'] |
|---|
| 1388 | BLtables = calcControls['BLtables'] |
|---|
| 1389 | TwDict = refDict.get('TwDict',{}) |
|---|
| 1390 | NTL = calcControls[phfx+'NTL'] |
|---|
| 1391 | NM = calcControls[phfx+'TwinNMN']+1 |
|---|
| 1392 | TwinLaw = calcControls[phfx+'TwinLaw'] |
|---|
| 1393 | TwinFr = np.array([parmDict[phfx+'TwinFr:'+str(i)] for i in range(len(TwinLaw))]) |
|---|
| 1394 | TwinInv = list(np.where(calcControls[phfx+'TwinInv'],-1,1)) |
|---|
| 1395 | nTwin = len(TwinLaw) |
|---|
| 1396 | nRef = len(refDict['RefList']) |
|---|
| 1397 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata,Gdata = \ |
|---|
| 1398 | GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 1399 | mSize = len(Mdata) |
|---|
| 1400 | FF = np.zeros(len(Tdata)) |
|---|
| 1401 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 1402 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 1403 | elif 'X' in calcControls[hfx+'histType']: |
|---|
| 1404 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 1405 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 1406 | Uij = np.array(G2lat.U6toUij(Uijdata)) |
|---|
| 1407 | bij = Mast*Uij.T |
|---|
| 1408 | dFdvDict = {} |
|---|
| 1409 | dFdfr = np.zeros((nRef,nTwin,mSize)) |
|---|
| 1410 | dFdx = np.zeros((nRef,nTwin,mSize,3)) |
|---|
| 1411 | dFdui = np.zeros((nRef,nTwin,mSize)) |
|---|
| 1412 | dFdua = np.zeros((nRef,nTwin,mSize,6)) |
|---|
| 1413 | dFdbab = np.zeros((nRef,nTwin,2)) |
|---|
| 1414 | dFdtw = np.zeros((nRef,nTwin)) |
|---|
| 1415 | time0 = time.time() |
|---|
| 1416 | #reflection processing begins here - big arrays! |
|---|
| 1417 | iBeg = 0 |
|---|
| 1418 | blkSize = 16 #no. of reflections in a block - optimized for speed |
|---|
| 1419 | while iBeg < nRef: |
|---|
| 1420 | iFin = min(iBeg+blkSize,nRef) |
|---|
| 1421 | refl = refDict['RefList'][iBeg:iFin] #array(blkSize,nItems) |
|---|
| 1422 | H = refl.T[:3] |
|---|
| 1423 | H = np.inner(H.T,TwinLaw) #array(3,nTwins) |
|---|
| 1424 | TwMask = np.any(H,axis=-1) |
|---|
| 1425 | for ir in range(blkSize): |
|---|
| 1426 | iref = ir+iBeg |
|---|
| 1427 | if iref in TwDict: |
|---|
| 1428 | for i in TwDict[iref]: |
|---|
| 1429 | for n in range(NTL): |
|---|
| 1430 | H[ir][i+n*NM] = np.inner(TwinLaw[n*NM],np.array(TwDict[iref][i])*TwinInv[i+n*NM]) |
|---|
| 1431 | TwMask = np.any(H,axis=-1) |
|---|
| 1432 | SQ = 1./(2.*refl.T[4])**2 # or (sin(theta)/lambda)**2 |
|---|
| 1433 | SQfactor = 8.0*SQ*np.pi**2 |
|---|
| 1434 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1435 | if 'P' in calcControls[hfx+'histType']: |
|---|
| 1436 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[14]) |
|---|
| 1437 | else: |
|---|
| 1438 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[12]) |
|---|
| 1439 | FP = np.repeat(FP.T,len(SGT)*len(TwinLaw),axis=0) |
|---|
| 1440 | FPP = np.repeat(FPP.T,len(SGT)*len(TwinLaw),axis=0) |
|---|
| 1441 | dBabdA = np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 1442 | Bab = np.repeat(parmDict[phfx+'BabA']*dBabdA,len(SGT)*nTwin) |
|---|
| 1443 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 1444 | FF = np.repeat(refDict['FF']['FF'][iBeg:iFin].T[Tindx].T,len(SGT)*len(TwinLaw),axis=0) |
|---|
| 1445 | Uniq = np.inner(H,SGMT) # (nTwin,nSGOp,3) |
|---|
| 1446 | Phi = np.inner(H,SGT) |
|---|
| 1447 | phase = twopi*(np.inner(Uniq,(dXdata+Xdata).T).T+Phi.T).T |
|---|
| 1448 | sinp = np.sin(phase) |
|---|
| 1449 | cosp = np.cos(phase) |
|---|
| 1450 | occ = Mdata*Fdata/len(SGT) |
|---|
| 1451 | biso = -SQfactor*Uisodata[:,nxs] |
|---|
| 1452 | Tiso = np.repeat(np.where(biso<1.,np.exp(biso),1.0),len(SGT)*nTwin,axis=1) |
|---|
| 1453 | HbH = -np.sum(Uniq.T*np.swapaxes(np.inner(bij,Uniq),2,-1),axis=1) |
|---|
| 1454 | Hij = np.array([Mast*np.multiply.outer(U,U) for U in np.reshape(Uniq,(-1,3))]) |
|---|
| 1455 | Hij = np.reshape(np.array([G2lat.UijtoU6(Uij) for Uij in Hij]),(-1,nTwin,len(SGT),6)) |
|---|
| 1456 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0) |
|---|
| 1457 | Tcorr = (np.reshape(Tiso,Tuij.shape)*Tuij).T*Mdata*Fdata/len(SGMT) |
|---|
| 1458 | fot = np.reshape(((FF+FP).T-Bab).T,cosp.shape)*Tcorr |
|---|
| 1459 | fotp = FPP*Tcorr |
|---|
| 1460 | if 'T' in calcControls[hfx+'histType']: #fa,fb are 2 X blkSize X nTwin X nOps x nAtoms |
|---|
| 1461 | fa = np.array([np.reshape(((FF+FP).T-Bab).T,cosp.shape)*cosp*Tcorr,-np.reshape(FPP,sinp.shape)*sinp*Tcorr]) |
|---|
| 1462 | fb = np.array([np.reshape(((FF+FP).T-Bab).T,sinp.shape)*sinp*Tcorr,np.reshape(FPP,cosp.shape)*cosp*Tcorr]) |
|---|
| 1463 | else: |
|---|
| 1464 | fa = np.array([np.reshape(((FF+FP).T-Bab).T,cosp.shape)*cosp*Tcorr,-FPP*sinp*Tcorr]) |
|---|
| 1465 | fb = np.array([np.reshape(((FF+FP).T-Bab).T,sinp.shape)*sinp*Tcorr,FPP*cosp*Tcorr]) |
|---|
| 1466 | fas = np.sum(np.sum(fa,axis=-1),axis=-1) #real sum over atoms & unique hkl array(2,nTwins) |
|---|
| 1467 | fbs = np.sum(np.sum(fb,axis=-1),axis=-1) #imag sum over atoms & uniq hkl |
|---|
| 1468 | if SGData['SGInv']: #centrosymmetric; B=0 |
|---|
| 1469 | fbs[0] *= 0. |
|---|
| 1470 | fas[1] *= 0. |
|---|
| 1471 | fax = np.array([-fot*sinp,-fotp*cosp]) #positions array(2,nRef,ntwi,nEqv,nAtoms) |
|---|
| 1472 | fbx = np.array([fot*cosp,-fotp*sinp]) |
|---|
| 1473 | #sum below is over Uniq |
|---|
| 1474 | dfadfr = np.sum(np.sum(fa/occ,axis=-2),axis=0) #array(2,nRef,ntwin,nAtom) Fdata != 0 avoids /0. problem |
|---|
| 1475 | dfadba = np.sum(-cosp*Tcorr[:,nxs],axis=1) |
|---|
| 1476 | dfadui = np.sum(np.sum(-SQfactor[nxs,:,nxs,nxs,nxs]*fa,axis=-2),axis=0) |
|---|
| 1477 | dfadx = np.sum(np.sum(twopi*Uniq[nxs,:,:,:,nxs,:]*fax[:,:,:,:,:,nxs],axis=-3),axis=0) # nRef x nTwin x nAtoms x xyz; sum on ops & A,A' |
|---|
| 1478 | dfadua = np.sum(np.sum(-Hij[nxs,:,:,:,nxs,:]*fa[:,:,:,:,:,nxs],axis=-3),axis=0) |
|---|
| 1479 | if not SGData['SGInv']: |
|---|
| 1480 | dfbdfr = np.sum(np.sum(fb/occ,axis=-2),axis=0) #Fdata != 0 avoids /0. problem |
|---|
| 1481 | dfadba /= 2. |
|---|
| 1482 | dfbdba = np.sum(-sinp*Tcorr[:,nxs],axis=1)/2. |
|---|
| 1483 | dfbdui = np.sum(np.sum(-SQfactor[nxs,:,nxs,nxs,nxs]*fb,axis=-2),axis=0) |
|---|
| 1484 | dfbdx = np.sum(np.sum(twopi*Uniq[nxs,:,:,:,nxs,:]*fbx[:,:,:,:,:,nxs],axis=-3),axis=0) |
|---|
| 1485 | dfbdua = np.sum(np.sum(-Hij[nxs,:,:,:,nxs,:]*fb[:,:,:,:,:,nxs],axis=-3),axis=0) |
|---|
| 1486 | else: |
|---|
| 1487 | dfbdfr = np.zeros_like(dfadfr) |
|---|
| 1488 | dfbdx = np.zeros_like(dfadx) |
|---|
| 1489 | dfbdui = np.zeros_like(dfadui) |
|---|
| 1490 | dfbdua = np.zeros_like(dfadua) |
|---|
| 1491 | dfbdba = np.zeros_like(dfadba) |
|---|
| 1492 | SA = fas[0]+fas[1] |
|---|
| 1493 | SB = fbs[0]+fbs[1] |
|---|
| 1494 | # GSASIIpath.IPyBreak() |
|---|
| 1495 | dFdfr[iBeg:iFin] = ((2.*TwMask*SA)[:,:,nxs]*dfadfr+(2.*TwMask*SB)[:,:,nxs]*dfbdfr)*Mdata[nxs,nxs,:]/len(SGMT) |
|---|
| 1496 | dFdx[iBeg:iFin] = (2.*TwMask*SA)[:,:,nxs,nxs]*dfadx+(2.*TwMask*SB)[:,:,nxs,nxs]*dfbdx |
|---|
| 1497 | dFdui[iBeg:iFin] = (2.*TwMask*SA)[:,:,nxs]*dfadui+(2.*TwMask*SB)[:,:,nxs]*dfbdui |
|---|
| 1498 | dFdua[iBeg:iFin] = (2.*TwMask*SA)[:,:,nxs,nxs]*dfadua+(2.*TwMask*SB)[:,:,nxs,nxs]*dfbdua |
|---|
| 1499 | if SGData['SGInv']: #centrosymmetric; B=0 |
|---|
| 1500 | dFdtw[iBeg:iFin] = np.sum(TwMask[nxs,:]*fas,axis=0)**2 |
|---|
| 1501 | else: |
|---|
| 1502 | dFdtw[iBeg:iFin] = np.sum(TwMask[nxs,:]*fas,axis=0)**2+np.sum(TwMask[nxs,:]*fbs,axis=0)**2 |
|---|
| 1503 | # dFdbab[iBeg:iFin] = fas[0,:,nxs]*np.array([np.sum(dfadba*dBabdA),np.sum(-dfadba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T+ \ |
|---|
| 1504 | # fbs[0,:,nxs]*np.array([np.sum(dfbdba*dBabdA),np.sum(-dfbdba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T |
|---|
| 1505 | iBeg += blkSize |
|---|
| 1506 | # GSASIIpath.IPyBreak() |
|---|
| 1507 | print ' %d derivative time %.4f\r'%(len(refDict['RefList']),time.time()-time0) |
|---|
| 1508 | #loop over atoms - each dict entry is list of derivatives for all the reflections |
|---|
| 1509 | for i in range(len(Mdata)): #these all OK |
|---|
| 1510 | dFdvDict[pfx+'Afrac:'+str(i)] = np.sum(dFdfr.T[i]*TwinFr[:,nxs],axis=0) |
|---|
| 1511 | dFdvDict[pfx+'dAx:'+str(i)] = np.sum(dFdx.T[0][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1512 | dFdvDict[pfx+'dAy:'+str(i)] = np.sum(dFdx.T[1][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1513 | dFdvDict[pfx+'dAz:'+str(i)] = np.sum(dFdx.T[2][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1514 | dFdvDict[pfx+'AUiso:'+str(i)] = np.sum(dFdui.T[i]*TwinFr[:,nxs],axis=0) |
|---|
| 1515 | dFdvDict[pfx+'AU11:'+str(i)] = np.sum(dFdua.T[0][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1516 | dFdvDict[pfx+'AU22:'+str(i)] = np.sum(dFdua.T[1][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1517 | dFdvDict[pfx+'AU33:'+str(i)] = np.sum(dFdua.T[2][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1518 | dFdvDict[pfx+'AU12:'+str(i)] = 2.*np.sum(dFdua.T[3][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1519 | dFdvDict[pfx+'AU13:'+str(i)] = 2.*np.sum(dFdua.T[4][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1520 | dFdvDict[pfx+'AU23:'+str(i)] = 2.*np.sum(dFdua.T[5][i]*TwinFr[:,nxs],axis=0) |
|---|
| 1521 | dFdvDict[phfx+'BabA'] = dFdbab.T[0] |
|---|
| 1522 | dFdvDict[phfx+'BabU'] = dFdbab.T[1] |
|---|
| 1523 | for i in range(nTwin): |
|---|
| 1524 | dFdvDict[phfx+'TwinFr:'+str(i)] = dFdtw.T[i] |
|---|
| 1525 | return dFdvDict |
|---|
| 1526 | |
|---|
| 1527 | def SStructureFactor(refDict,G,hfx,pfx,SGData,SSGData,calcControls,parmDict): |
|---|
| 1528 | ''' |
|---|
| 1529 | Compute super structure factors for all h,k,l,m for phase - no twins |
|---|
| 1530 | puts the result, F^2, in each ref[9] in refList |
|---|
| 1531 | works on blocks of 32 reflections for speed |
|---|
| 1532 | input: |
|---|
| 1533 | |
|---|
| 1534 | :param dict refDict: where |
|---|
| 1535 | 'RefList' list where each ref = h,k,l,m,it,d,... |
|---|
| 1536 | 'FF' dict of form factors - filed in below |
|---|
| 1537 | :param np.array G: reciprocal metric tensor |
|---|
| 1538 | :param str pfx: phase id string |
|---|
| 1539 | :param dict SGData: space group info. dictionary output from SpcGroup |
|---|
| 1540 | :param dict calcControls: |
|---|
| 1541 | :param dict ParmDict: |
|---|
| 1542 | |
|---|
| 1543 | ''' |
|---|
| 1544 | phfx = pfx.split(':')[0]+hfx |
|---|
| 1545 | ast = np.sqrt(np.diag(G)) |
|---|
| 1546 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 1547 | SGInv = SGData['SGInv'] |
|---|
| 1548 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 1549 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 1550 | SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']]) |
|---|
| 1551 | SSGT = np.array([ops[1] for ops in SSGData['SSGOps']]) |
|---|
| 1552 | FFtables = calcControls['FFtables'] |
|---|
| 1553 | BLtables = calcControls['BLtables'] |
|---|
| 1554 | Flack = 1.0 |
|---|
| 1555 | if not SGData['SGInv'] and 'S' in calcControls[hfx+'histType'] and phfx+'Flack' in parmDict: |
|---|
| 1556 | Flack = 1.-2.*parmDict[phfx+'Flack'] |
|---|
| 1557 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata,Gdata = \ |
|---|
| 1558 | GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 1559 | waveTypes,FSSdata,XSSdata,USSdata,MSSdata = GetAtomSSFXU(pfx,calcControls,parmDict) |
|---|
| 1560 | ngl,nWaves,Fmod,Xmod,Umod,glTau,glWt = G2mth.makeWaves(waveTypes,FSSdata,XSSdata,USSdata,Mast) |
|---|
| 1561 | modQ = np.array([parmDict[pfx+'mV0'],parmDict[pfx+'mV1'],parmDict[pfx+'mV2']]) |
|---|
| 1562 | FF = np.zeros(len(Tdata)) |
|---|
| 1563 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 1564 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 1565 | elif 'X' in calcControls[hfx+'histType']: |
|---|
| 1566 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 1567 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 1568 | Uij = np.array(G2lat.U6toUij(Uijdata)).T |
|---|
| 1569 | bij = Mast*Uij |
|---|
| 1570 | blkSize = 32 #no. of reflections in a block |
|---|
| 1571 | nRef = refDict['RefList'].shape[0] |
|---|
| 1572 | if not len(refDict['FF']): |
|---|
| 1573 | SQ = 1./(2.*refDict['RefList'].T[5])**2 |
|---|
| 1574 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 1575 | dat = G2el.getBLvalues(BLtables) |
|---|
| 1576 | refDict['FF']['El'] = dat.keys() |
|---|
| 1577 | refDict['FF']['FF'] = np.ones((nRef,len(dat)))*dat.values() |
|---|
| 1578 | refDict['FF']['MF'] = np.zeros((nRef,len(dat))) |
|---|
| 1579 | for iel,El in enumerate(refDict['FF']['El']): |
|---|
| 1580 | if El in MFtables: |
|---|
| 1581 | refDict['FF']['MF'].T[iel] = G2el.MagScatFac(MFtables[El],SQ) |
|---|
| 1582 | else: |
|---|
| 1583 | dat = G2el.getFFvalues(FFtables,0.) |
|---|
| 1584 | refDict['FF']['El'] = dat.keys() |
|---|
| 1585 | refDict['FF']['FF'] = np.zeros((nRef,len(dat))) |
|---|
| 1586 | for iel,El in enumerate(refDict['FF']['El']): |
|---|
| 1587 | refDict['FF']['FF'].T[iel] = G2el.ScatFac(FFtables[El],SQ) |
|---|
| 1588 | time0 = time.time() |
|---|
| 1589 | #reflection processing begins here - big arrays! |
|---|
| 1590 | iBeg = 0 |
|---|
| 1591 | while iBeg < nRef: |
|---|
| 1592 | iFin = min(iBeg+blkSize,nRef) |
|---|
| 1593 | refl = refDict['RefList'][iBeg:iFin] #array(blkSize,nItems) |
|---|
| 1594 | H = refl.T[:4] #array(blkSize,4) |
|---|
| 1595 | HP = H[:3]+modQ[:,nxs]*H[3:] #projected hklm to hkl |
|---|
| 1596 | SQ = 1./(2.*refl.T[5])**2 #array(blkSize) |
|---|
| 1597 | SQfactor = 4.0*SQ*twopisq #ditto prev. |
|---|
| 1598 | Uniq = np.inner(H.T,SSGMT) |
|---|
| 1599 | UniqP = np.inner(HP.T,SGMT) |
|---|
| 1600 | Phi = np.inner(H.T,SSGT) |
|---|
| 1601 | if SGInv: #if centro - expand HKL sets |
|---|
| 1602 | Uniq = np.hstack((Uniq,-Uniq)) |
|---|
| 1603 | Phi = np.hstack((Phi,-Phi)) |
|---|
| 1604 | UniqP = np.hstack((UniqP,-UniqP)) |
|---|
| 1605 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1606 | if 'P' in calcControls[hfx+'histType']: |
|---|
| 1607 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[14]) |
|---|
| 1608 | else: |
|---|
| 1609 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[12]) |
|---|
| 1610 | FP = np.repeat(FP.T,Uniq.shape[1],axis=0) |
|---|
| 1611 | FPP = np.repeat(FPP.T,Uniq.shape[1],axis=0) |
|---|
| 1612 | Bab = np.repeat(parmDict[phfx+'BabA']*np.exp(-parmDict[phfx+'BabU']*SQfactor),Uniq.shape[1]) |
|---|
| 1613 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 1614 | FF = np.repeat(refDict['FF']['FF'][iBeg:iFin].T[Tindx].T,Uniq.shape[1],axis=0) |
|---|
| 1615 | phase = twopi*(np.inner(Uniq[:,:,:3],(dXdata.T+Xdata.T))-Phi[:,:,nxs]) |
|---|
| 1616 | sinp = np.sin(phase) |
|---|
| 1617 | cosp = np.cos(phase) |
|---|
| 1618 | biso = -SQfactor*Uisodata[:,nxs] |
|---|
| 1619 | Tiso = np.repeat(np.where(biso<1.,np.exp(biso),1.0),Uniq.shape[1],axis=1).T |
|---|
| 1620 | HbH = -np.sum(UniqP[:,:,nxs,:]*np.inner(UniqP[:,:,:],bij),axis=-1) #use hklt proj to hkl |
|---|
| 1621 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0) |
|---|
| 1622 | Tcorr = np.reshape(Tiso,Tuij.shape)*Tuij*Mdata*Fdata/Uniq.shape[1] #refBlk x ops x atoms |
|---|
| 1623 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1624 | fa = np.array([np.reshape(((FF+FP).T-Bab).T,cosp.shape)*cosp*Tcorr,-np.reshape(Flack*FPP,sinp.shape)*sinp*Tcorr]) |
|---|
| 1625 | fb = np.array([np.reshape(Flack*FPP,cosp.shape)*cosp*Tcorr,np.reshape(((FF+FP).T-Bab).T,sinp.shape)*sinp*Tcorr]) |
|---|
| 1626 | else: |
|---|
| 1627 | fa = np.array([np.reshape(((FF+FP).T-Bab).T,cosp.shape)*cosp*Tcorr,-Flack*FPP*sinp*Tcorr]) |
|---|
| 1628 | fb = np.array([Flack*FPP*cosp*Tcorr,np.reshape(((FF+FP).T-Bab).T,sinp.shape)*sinp*Tcorr]) |
|---|
| 1629 | GfpuA = G2mth.Modulation(Uniq,UniqP,nWaves,Fmod,Xmod,Umod,glTau,glWt) #2 x refBlk x sym X atoms |
|---|
| 1630 | fag = fa*GfpuA[0]-fb*GfpuA[1] #real; 2 x refBlk x sym x atoms |
|---|
| 1631 | fbg = fb*GfpuA[0]+fa*GfpuA[1] |
|---|
| 1632 | fas = np.sum(np.sum(fag,axis=-1),axis=-1) #2 x refBlk; sum sym & atoms |
|---|
| 1633 | fbs = np.sum(np.sum(fbg,axis=-1),axis=-1) |
|---|
| 1634 | # GSASIIpath.IPyBreak() |
|---|
| 1635 | if 'P' in calcControls[hfx+'histType']: |
|---|
| 1636 | refl.T[10] = np.sum(fas,axis=0)**2+np.sum(fbs,axis=0)**2 #square of sums |
|---|
| 1637 | # refl.T[10] = np.sum(fas**2,axis=0)+np.sum(fbs**2,axis=0) |
|---|
| 1638 | refl.T[11] = atan2d(fbs[0],fas[0]) #ignore f' & f" |
|---|
| 1639 | else: |
|---|
| 1640 | refl.T[10] = np.sum(fas,axis=0)**2+np.sum(fbs,axis=0)**2 #square of sums |
|---|
| 1641 | refl.T[8] = np.copy(refl.T[10]) |
|---|
| 1642 | refl.T[11] = atan2d(fbs[0],fas[0]) #ignore f' & f" |
|---|
| 1643 | iBeg += blkSize |
|---|
| 1644 | print 'nRef %d time %.4f\r'%(nRef,time.time()-time0) |
|---|
| 1645 | |
|---|
| 1646 | def SStructureFactorTw(refDict,G,hfx,pfx,SGData,SSGData,calcControls,parmDict): |
|---|
| 1647 | ''' |
|---|
| 1648 | Compute super structure factors for all h,k,l,m for phase - twins only |
|---|
| 1649 | puts the result, F^2, in each ref[8+im] in refList |
|---|
| 1650 | works on blocks of 32 reflections for speed |
|---|
| 1651 | input: |
|---|
| 1652 | |
|---|
| 1653 | :param dict refDict: where |
|---|
| 1654 | 'RefList' list where each ref = h,k,l,m,it,d,... |
|---|
| 1655 | 'FF' dict of form factors - filed in below |
|---|
| 1656 | :param np.array G: reciprocal metric tensor |
|---|
| 1657 | :param str pfx: phase id string |
|---|
| 1658 | :param dict SGData: space group info. dictionary output from SpcGroup |
|---|
| 1659 | :param dict calcControls: |
|---|
| 1660 | :param dict ParmDict: |
|---|
| 1661 | |
|---|
| 1662 | ''' |
|---|
| 1663 | phfx = pfx.split(':')[0]+hfx |
|---|
| 1664 | ast = np.sqrt(np.diag(G)) |
|---|
| 1665 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 1666 | SGInv = SGData['SGInv'] |
|---|
| 1667 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 1668 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 1669 | SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']]) |
|---|
| 1670 | SSGT = np.array([ops[1] for ops in SSGData['SSGOps']]) |
|---|
| 1671 | FFtables = calcControls['FFtables'] |
|---|
| 1672 | BLtables = calcControls['BLtables'] |
|---|
| 1673 | Flack = 1.0 |
|---|
| 1674 | if not SGData['SGInv'] and 'S' in calcControls[hfx+'histType'] and phfx+'Flack' in parmDict: |
|---|
| 1675 | Flack = 1.-2.*parmDict[phfx+'Flack'] |
|---|
| 1676 | TwinLaw = np.array([[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]],]) #4D? |
|---|
| 1677 | TwDict = refDict.get('TwDict',{}) |
|---|
| 1678 | if 'S' in calcControls[hfx+'histType']: |
|---|
| 1679 | NTL = calcControls[phfx+'NTL'] |
|---|
| 1680 | NM = calcControls[phfx+'TwinNMN']+1 |
|---|
| 1681 | TwinLaw = calcControls[phfx+'TwinLaw'] #this'll have to be 4D also... |
|---|
| 1682 | TwinFr = np.array([parmDict[phfx+'TwinFr:'+str(i)] for i in range(len(TwinLaw))]) |
|---|
| 1683 | TwinInv = list(np.where(calcControls[phfx+'TwinInv'],-1,1)) |
|---|
| 1684 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata,Gdata = \ |
|---|
| 1685 | GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 1686 | waveTypes,FSSdata,XSSdata,USSdata,MSSdata = GetAtomSSFXU(pfx,calcControls,parmDict) |
|---|
| 1687 | ngl,nWaves,Fmod,Xmod,Umod,glTau,glWt = G2mth.makeWaves(waveTypes,FSSdata,XSSdata,USSdata,Mast) |
|---|
| 1688 | modQ = np.array([parmDict[pfx+'mV0'],parmDict[pfx+'mV1'],parmDict[pfx+'mV2']]) |
|---|
| 1689 | FF = np.zeros(len(Tdata)) |
|---|
| 1690 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 1691 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 1692 | elif 'X' in calcControls[hfx+'histType']: |
|---|
| 1693 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 1694 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 1695 | Uij = np.array(G2lat.U6toUij(Uijdata)).T |
|---|
| 1696 | bij = Mast*Uij |
|---|
| 1697 | blkSize = 32 #no. of reflections in a block |
|---|
| 1698 | nRef = refDict['RefList'].shape[0] |
|---|
| 1699 | if not len(refDict['FF']): #no form factors - 1st time thru StructureFactor |
|---|
| 1700 | SQ = 1./(2.*refDict['RefList'].T[5])**2 |
|---|
| 1701 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 1702 | dat = G2el.getBLvalues(BLtables) |
|---|
| 1703 | refDict['FF']['El'] = dat.keys() |
|---|
| 1704 | refDict['FF']['FF'] = np.ones((nRef,len(dat)))*dat.values() |
|---|
| 1705 | refDict['FF']['MF'] = np.zeros((nRef,len(dat))) |
|---|
| 1706 | for iel,El in enumerate(refDict['FF']['El']): |
|---|
| 1707 | if El in MFtables: |
|---|
| 1708 | refDict['FF']['MF'].T[iel] = G2el.MagScatFac(MFtables[El],SQ) |
|---|
| 1709 | else: |
|---|
| 1710 | dat = G2el.getFFvalues(FFtables,0.) |
|---|
| 1711 | refDict['FF']['El'] = dat.keys() |
|---|
| 1712 | refDict['FF']['FF'] = np.zeros((nRef,len(dat))) |
|---|
| 1713 | for iel,El in enumerate(refDict['FF']['El']): |
|---|
| 1714 | refDict['FF']['FF'].T[iel] = G2el.ScatFac(FFtables[El],SQ) |
|---|
| 1715 | time0 = time.time() |
|---|
| 1716 | #reflection processing begins here - big arrays! |
|---|
| 1717 | iBeg = 0 |
|---|
| 1718 | while iBeg < nRef: |
|---|
| 1719 | iFin = min(iBeg+blkSize,nRef) |
|---|
| 1720 | refl = refDict['RefList'][iBeg:iFin] #array(blkSize,nItems) |
|---|
| 1721 | H = refl[:,:4] #array(blkSize,4) |
|---|
| 1722 | H3 = refl[:,:3] |
|---|
| 1723 | HP = H[:,:3]+modQ[nxs,:]*H[:,3:] #projected hklm to hkl |
|---|
| 1724 | HP = np.inner(HP,TwinLaw) #array(blkSize,nTwins,4) |
|---|
| 1725 | H3 = np.inner(H3,TwinLaw) |
|---|
| 1726 | TwMask = np.any(HP,axis=-1) |
|---|
| 1727 | if TwinLaw.shape[0] > 1 and TwDict: #need np.inner(TwinLaw[?],TwDict[iref][i])*TwinInv[i] |
|---|
| 1728 | for ir in range(blkSize): |
|---|
| 1729 | iref = ir+iBeg |
|---|
| 1730 | if iref in TwDict: |
|---|
| 1731 | for i in TwDict[iref]: |
|---|
| 1732 | for n in range(NTL): |
|---|
| 1733 | HP[ir][i+n*NM] = np.inner(TwinLaw[n*NM],np.array(TwDict[iref][i])*TwinInv[i+n*NM]) |
|---|
| 1734 | H3[ir][i+n*NM] = np.inner(TwinLaw[n*NM],np.array(TwDict[iref][i])*TwinInv[i+n*NM]) |
|---|
| 1735 | TwMask = np.any(HP,axis=-1) |
|---|
| 1736 | SQ = 1./(2.*refl.T[5])**2 #array(blkSize) |
|---|
| 1737 | SQfactor = 4.0*SQ*twopisq #ditto prev. |
|---|
| 1738 | Uniq = np.inner(H,SSGMT) |
|---|
| 1739 | Uniq3 = np.inner(H3,SGMT) |
|---|
| 1740 | UniqP = np.inner(HP,SGMT) |
|---|
| 1741 | Phi = np.inner(H,SSGT) |
|---|
| 1742 | if SGInv: #if centro - expand HKL sets |
|---|
| 1743 | Uniq = np.hstack((Uniq,-Uniq)) |
|---|
| 1744 | Uniq3 = np.hstack((Uniq3,-Uniq3)) |
|---|
| 1745 | Phi = np.hstack((Phi,-Phi)) |
|---|
| 1746 | UniqP = np.hstack((UniqP,-UniqP)) |
|---|
| 1747 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1748 | if 'P' in calcControls[hfx+'histType']: |
|---|
| 1749 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[14]) |
|---|
| 1750 | else: |
|---|
| 1751 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[12]) |
|---|
| 1752 | FP = np.repeat(FP.T,Uniq.shape[1]*len(TwinLaw),axis=0) |
|---|
| 1753 | FPP = np.repeat(FPP.T,Uniq.shape[1]*len(TwinLaw),axis=0) |
|---|
| 1754 | Bab = np.repeat(parmDict[phfx+'BabA']*np.exp(-parmDict[phfx+'BabU']*SQfactor),Uniq.shape[1]*len(TwinLaw)) |
|---|
| 1755 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 1756 | FF = np.repeat(refDict['FF']['FF'][iBeg:iFin].T[Tindx].T,Uniq.shape[1]*len(TwinLaw),axis=0) |
|---|
| 1757 | phase = twopi*(np.inner(Uniq3,(dXdata.T+Xdata.T))-Phi[:,nxs,:,nxs]) |
|---|
| 1758 | sinp = np.sin(phase) |
|---|
| 1759 | cosp = np.cos(phase) |
|---|
| 1760 | biso = -SQfactor*Uisodata[:,nxs] |
|---|
| 1761 | Tiso = np.repeat(np.where(biso<1.,np.exp(biso),1.0),Uniq.shape[1]*len(TwinLaw),axis=1).T |
|---|
| 1762 | HbH = -np.sum(UniqP[:,:,:,nxs]*np.inner(UniqP[:,:,:],bij),axis=-1) #use hklt proj to hkl |
|---|
| 1763 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0) |
|---|
| 1764 | Tcorr = np.reshape(Tiso,Tuij.shape)*Tuij*Mdata*Fdata/Uniq.shape[1] #refBlk x ops x atoms |
|---|
| 1765 | # GSASIIpath.IPyBreak() |
|---|
| 1766 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1767 | fa = np.array([np.reshape(((FF+FP).T-Bab).T,cosp.shape)*cosp*Tcorr,-np.reshape(Flack*FPP,sinp.shape)*sinp*Tcorr]) |
|---|
| 1768 | fb = np.array([np.reshape(Flack*FPP,cosp.shape)*cosp*Tcorr,np.reshape(((FF+FP).T-Bab).T,sinp.shape)*sinp*Tcorr]) |
|---|
| 1769 | else: |
|---|
| 1770 | fa = np.array([np.reshape(((FF+FP).T-Bab).T,cosp.shape)*cosp*Tcorr,-Flack*FPP*sinp*Tcorr]) |
|---|
| 1771 | fb = np.array([Flack*FPP*cosp*Tcorr,np.reshape(((FF+FP).T-Bab).T,sinp.shape)*sinp*Tcorr]) |
|---|
| 1772 | GfpuA = G2mth.ModulationTw(Uniq,UniqP,nWaves,Fmod,Xmod,Umod,glTau,glWt) #2 x refBlk x sym X atoms |
|---|
| 1773 | fag = fa*GfpuA[0]-fb*GfpuA[1] #real; 2 x refBlk x sym x atoms |
|---|
| 1774 | fbg = fb*GfpuA[0]+fa*GfpuA[1] |
|---|
| 1775 | fas = np.sum(np.sum(fag,axis=-1),axis=-1) #2 x refBlk; sum sym & atoms |
|---|
| 1776 | fbs = np.sum(np.sum(fbg,axis=-1),axis=-1) |
|---|
| 1777 | refl.T[10] = np.sum(fas[:,:,0],axis=0)**2+np.sum(fbs[:,:,0],axis=0)**2 #FcT from primary twin element |
|---|
| 1778 | refl.T[8] = np.sum(TwinFr*np.sum(TwMask[nxs,:,:]*fas,axis=0)**2,axis=-1)+ \ |
|---|
| 1779 | np.sum(TwinFr*np.sum(TwMask[nxs,:,:]*fbs,axis=0)**2,axis=-1) #Fc sum over twins |
|---|
| 1780 | refl.T[11] = atan2d(fbs[0].T[0],fas[0].T[0]) #ignore f' & f" |
|---|
| 1781 | iBeg += blkSize |
|---|
| 1782 | print 'nRef %d time %.4f\r'%(nRef,time.time()-time0) |
|---|
| 1783 | |
|---|
| 1784 | def SStructureFactorDerv(refDict,im,G,hfx,pfx,SGData,SSGData,calcControls,parmDict): |
|---|
| 1785 | ''' |
|---|
| 1786 | Compute super structure factor derivatives for all h,k,l,m for phase - no twins |
|---|
| 1787 | input: |
|---|
| 1788 | |
|---|
| 1789 | :param dict refDict: where |
|---|
| 1790 | 'RefList' list where each ref = h,k,l,m,it,d,... |
|---|
| 1791 | 'FF' dict of form factors - filled in below |
|---|
| 1792 | :param int im: = 1 (could be eliminated) |
|---|
| 1793 | :param np.array G: reciprocal metric tensor |
|---|
| 1794 | :param str hfx: histogram id string |
|---|
| 1795 | :param str pfx: phase id string |
|---|
| 1796 | :param dict SGData: space group info. dictionary output from SpcGroup |
|---|
| 1797 | :param dict SSGData: super space group info. |
|---|
| 1798 | :param dict calcControls: |
|---|
| 1799 | :param dict ParmDict: |
|---|
| 1800 | |
|---|
| 1801 | :returns: dict dFdvDict: dictionary of derivatives |
|---|
| 1802 | ''' |
|---|
| 1803 | phfx = pfx.split(':')[0]+hfx |
|---|
| 1804 | ast = np.sqrt(np.diag(G)) |
|---|
| 1805 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 1806 | SGInv = SGData['SGInv'] |
|---|
| 1807 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 1808 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 1809 | SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']]) |
|---|
| 1810 | SSGT = np.array([ops[1] for ops in SSGData['SSGOps']]) |
|---|
| 1811 | FFtables = calcControls['FFtables'] |
|---|
| 1812 | BLtables = calcControls['BLtables'] |
|---|
| 1813 | nRef = len(refDict['RefList']) |
|---|
| 1814 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata,Gdata = \ |
|---|
| 1815 | GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 1816 | mSize = len(Mdata) #no. atoms |
|---|
| 1817 | waveTypes,FSSdata,XSSdata,USSdata,MSSdata = GetAtomSSFXU(pfx,calcControls,parmDict) |
|---|
| 1818 | ngl,nWaves,Fmod,Xmod,Umod,glTau,glWt = G2mth.makeWaves(waveTypes,FSSdata,XSSdata,USSdata,Mast) |
|---|
| 1819 | waveShapes,SCtauF,SCtauX,SCtauU,UmodAB = G2mth.makeWavesDerv(ngl,waveTypes,FSSdata,XSSdata,USSdata,Mast) |
|---|
| 1820 | modQ = np.array([parmDict[pfx+'mV0'],parmDict[pfx+'mV1'],parmDict[pfx+'mV2']]) |
|---|
| 1821 | FF = np.zeros(len(Tdata)) |
|---|
| 1822 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 1823 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 1824 | elif 'X' in calcControls[hfx+'histType']: |
|---|
| 1825 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 1826 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 1827 | Uij = np.array(G2lat.U6toUij(Uijdata)).T |
|---|
| 1828 | bij = Mast*Uij |
|---|
| 1829 | if not len(refDict['FF']): |
|---|
| 1830 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 1831 | dat = G2el.getBLvalues(BLtables) #will need wave here for anom. neutron b's |
|---|
| 1832 | else: |
|---|
| 1833 | dat = G2el.getFFvalues(FFtables,0.) |
|---|
| 1834 | refDict['FF']['El'] = dat.keys() |
|---|
| 1835 | refDict['FF']['FF'] = np.zeros((len(refDict['RefList']),len(dat))) |
|---|
| 1836 | dFdvDict = {} |
|---|
| 1837 | dFdfr = np.zeros((nRef,mSize)) |
|---|
| 1838 | dFdx = np.zeros((nRef,mSize,3)) |
|---|
| 1839 | dFdui = np.zeros((nRef,mSize)) |
|---|
| 1840 | dFdua = np.zeros((nRef,mSize,6)) |
|---|
| 1841 | dFdbab = np.zeros((nRef,2)) |
|---|
| 1842 | dFdfl = np.zeros((nRef)) |
|---|
| 1843 | dFdtw = np.zeros((nRef)) |
|---|
| 1844 | dFdGf = np.zeros((nRef,mSize,FSSdata.shape[1],2)) |
|---|
| 1845 | dFdGx = np.zeros((nRef,mSize,XSSdata.shape[1],6)) |
|---|
| 1846 | dFdGz = np.zeros((nRef,mSize,5)) |
|---|
| 1847 | dFdGu = np.zeros((nRef,mSize,USSdata.shape[1],12)) |
|---|
| 1848 | Flack = 1.0 |
|---|
| 1849 | if not SGData['SGInv'] and 'S' in calcControls[hfx+'histType'] and phfx+'Flack' in parmDict: |
|---|
| 1850 | Flack = 1.-2.*parmDict[phfx+'Flack'] |
|---|
| 1851 | time0 = time.time() |
|---|
| 1852 | nRef = len(refDict['RefList'])/100 |
|---|
| 1853 | for iref,refl in enumerate(refDict['RefList']): |
|---|
| 1854 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1855 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,refl.T[12+im]) |
|---|
| 1856 | H = np.array(refl[:4]) |
|---|
| 1857 | HP = H[:3]+modQ*H[3:] #projected hklm to hkl |
|---|
| 1858 | SQ = 1./(2.*refl[4+im])**2 # or (sin(theta)/lambda)**2 |
|---|
| 1859 | SQfactor = 8.0*SQ*np.pi**2 |
|---|
| 1860 | dBabdA = np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 1861 | Bab = parmDict[phfx+'BabA']*dBabdA |
|---|
| 1862 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 1863 | FF = refDict['FF']['FF'][iref].T[Tindx] |
|---|
| 1864 | Uniq = np.inner(H,SSGMT) |
|---|
| 1865 | Phi = np.inner(H,SSGT) |
|---|
| 1866 | UniqP = np.inner(HP,SGMT) |
|---|
| 1867 | if SGInv: #if centro - expand HKL sets |
|---|
| 1868 | Uniq = np.vstack((Uniq,-Uniq)) |
|---|
| 1869 | Phi = np.hstack((Phi,-Phi)) |
|---|
| 1870 | UniqP = np.vstack((UniqP,-UniqP)) |
|---|
| 1871 | phase = twopi*(np.inner(Uniq[:,:3],(dXdata+Xdata).T)+Phi[:,nxs]) |
|---|
| 1872 | sinp = np.sin(phase) |
|---|
| 1873 | cosp = np.cos(phase) |
|---|
| 1874 | occ = Mdata*Fdata/Uniq.shape[0] |
|---|
| 1875 | biso = -SQfactor*Uisodata[:,nxs] |
|---|
| 1876 | Tiso = np.repeat(np.where(biso<1.,np.exp(biso),1.0),Uniq.shape[0],axis=1).T #ops x atoms |
|---|
| 1877 | HbH = -np.sum(UniqP[:,nxs,:3]*np.inner(UniqP[:,:3],bij),axis=-1) #ops x atoms |
|---|
| 1878 | Hij = np.array([Mast*np.multiply.outer(U[:3],U[:3]) for U in UniqP]) #atoms x 3x3 |
|---|
| 1879 | Hij = np.array([G2lat.UijtoU6(Uij) for Uij in Hij]) #atoms x 6 |
|---|
| 1880 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0) #ops x atoms |
|---|
| 1881 | Tcorr = np.reshape(Tiso,Tuij.shape)*Tuij*Mdata*Fdata/Uniq.shape[0] #ops x atoms |
|---|
| 1882 | fot = (FF+FP-Bab)*Tcorr #ops x atoms |
|---|
| 1883 | fotp = FPP*Tcorr #ops x atoms |
|---|
| 1884 | GfpuA = G2mth.Modulation(Uniq,UniqP,nWaves,Fmod,Xmod,Umod,glTau,glWt) #2 x sym X atoms |
|---|
| 1885 | dGdf,dGdx,dGdu,dGdz = G2mth.ModulationDerv(Uniq,UniqP,Hij,nWaves,waveShapes,Fmod,Xmod,UmodAB,SCtauF,SCtauX,SCtauU,glTau,glWt) |
|---|
| 1886 | # GfpuA is 2 x ops x atoms |
|---|
| 1887 | # derivs are: ops x atoms x waves x 2,6,12, or 5 parms as [real,imag] parts |
|---|
| 1888 | fa = np.array([((FF+FP).T-Bab).T*cosp*Tcorr,-Flack*FPP*sinp*Tcorr]) # array(2,nEqv,nAtoms) |
|---|
| 1889 | fb = np.array([((FF+FP).T-Bab).T*sinp*Tcorr,Flack*FPP*cosp*Tcorr]) #or array(2,nEqv,nAtoms) |
|---|
| 1890 | fag = fa*GfpuA[0]-fb*GfpuA[1] |
|---|
| 1891 | fbg = fb*GfpuA[0]+fa*GfpuA[1] |
|---|
| 1892 | |
|---|
| 1893 | fas = np.sum(np.sum(fag,axis=1),axis=1) # 2 x twin |
|---|
| 1894 | fbs = np.sum(np.sum(fbg,axis=1),axis=1) |
|---|
| 1895 | fax = np.array([-fot*sinp,-fotp*cosp]) #positions; 2 x ops x atoms |
|---|
| 1896 | fbx = np.array([fot*cosp,-fotp*sinp]) |
|---|
| 1897 | fax = fax*GfpuA[0]-fbx*GfpuA[1] |
|---|
| 1898 | fbx = fbx*GfpuA[0]+fax*GfpuA[1] |
|---|
| 1899 | #sum below is over Uniq |
|---|
| 1900 | dfadfr = np.sum(fag/occ,axis=1) #Fdata != 0 ever avoids /0. problem |
|---|
| 1901 | dfbdfr = np.sum(fbg/occ,axis=1) #Fdata != 0 avoids /0. problem |
|---|
| 1902 | dfadba = np.sum(-cosp*Tcorr[:,nxs],axis=1) |
|---|
| 1903 | dfbdba = np.sum(-sinp*Tcorr[:,nxs],axis=1) |
|---|
| 1904 | dfadui = np.sum(-SQfactor*fag,axis=1) |
|---|
| 1905 | dfbdui = np.sum(-SQfactor*fbg,axis=1) |
|---|
| 1906 | dfadx = np.sum(twopi*Uniq[:,:3]*np.swapaxes(fax,-2,-1)[:,:,:,nxs],axis=-2) #2 x nAtom x 3xyz; sum nOps |
|---|
| 1907 | dfbdx = np.sum(twopi*Uniq[:,:3]*np.swapaxes(fbx,-2,-1)[:,:,:,nxs],axis=-2) |
|---|
| 1908 | dfadua = np.sum(-Hij*np.swapaxes(fag,-2,-1)[:,:,:,nxs],axis=-2) #2 x nAtom x 6Uij; sum nOps |
|---|
| 1909 | dfbdua = np.sum(-Hij*np.swapaxes(fbg,-2,-1)[:,:,:,nxs],axis=-2) #these are correct also for twins above |
|---|
| 1910 | # array(2,nAtom,nWave,2) & array(2,nAtom,nWave,6) & array(2,nAtom,nWave,12); sum on nOps |
|---|
| 1911 | dfadGf = np.sum(fa[:,:,:,nxs,nxs]*dGdf[0][nxs,:,:,:,:]-fb[:,:,:,nxs,nxs]*dGdf[1][nxs,:,:,:,:],axis=1) |
|---|
| 1912 | dfbdGf = np.sum(fb[:,:,:,nxs,nxs]*dGdf[0][nxs,:,:,:,:]+fa[:,:,:,nxs,nxs]*dGdf[1][nxs,:,:,:,:],axis=1) |
|---|
| 1913 | dfadGx = np.sum(fa[:,:,:,nxs,nxs]*dGdx[0][nxs,:,:,:,:]-fb[:,:,:,nxs,nxs]*dGdx[1][nxs,:,:,:,:],axis=1) |
|---|
| 1914 | dfbdGx = np.sum(fb[:,:,:,nxs,nxs]*dGdx[0][nxs,:,:,:,:]+fa[:,:,:,nxs,nxs]*dGdx[1][nxs,:,:,:,:],axis=1) |
|---|
| 1915 | dfadGz = np.sum(fa[:,:,0,nxs,nxs]*dGdz[0][nxs,:,:,:]-fb[:,:,0,nxs,nxs]*dGdz[1][nxs,:,:,:],axis=1) |
|---|
| 1916 | dfbdGz = np.sum(fb[:,:,0,nxs,nxs]*dGdz[0][nxs,:,:,:]+fa[:,:,0,nxs,nxs]*dGdz[1][nxs,:,:,:],axis=1) |
|---|
| 1917 | dfadGu = np.sum(fa[:,:,:,nxs,nxs]*dGdu[0][nxs,:,:,:,:]-fb[:,:,:,nxs,nxs]*dGdu[1][nxs,:,:,:,:],axis=1) |
|---|
| 1918 | dfbdGu = np.sum(fb[:,:,:,nxs,nxs]*dGdu[0][nxs,:,:,:,:]+fa[:,:,:,nxs,nxs]*dGdu[1][nxs,:,:,:,:],axis=1) |
|---|
| 1919 | if not SGData['SGInv']: #Flack derivative |
|---|
| 1920 | dfadfl = np.sum(-FPP*Tcorr*sinp) |
|---|
| 1921 | dfbdfl = np.sum(FPP*Tcorr*cosp) |
|---|
| 1922 | else: |
|---|
| 1923 | dfadfl = 1.0 |
|---|
| 1924 | dfbdfl = 1.0 |
|---|
| 1925 | # GSASIIpath.IPyBreak() |
|---|
| 1926 | #NB: the above have been checked against PA(1:10,1:2) in strfctr.for for Al2O3! |
|---|
| 1927 | SA = fas[0]+fas[1] #float = A+A' |
|---|
| 1928 | SB = fbs[0]+fbs[1] #float = B+B' |
|---|
| 1929 | if 'P' in calcControls[hfx+'histType']: #checked perfect for centro & noncentro? |
|---|
| 1930 | dFdfl[iref] = -SA*dfadfl-SB*dfbdfl #array(nRef,) |
|---|
| 1931 | dFdfr[iref] = 2.*(fas[0]*dfadfr[0]+fas[1]*dfadfr[1])*Mdata/len(Uniq)+ \ |
|---|
| 1932 | 2.*(fbs[0]*dfbdfr[0]-fbs[1]*dfbdfr[1])*Mdata/len(Uniq) |
|---|
| 1933 | dFdx[iref] = 2.*(fas[0]*dfadx[0]+fas[1]*dfadx[1])+ \ |
|---|
| 1934 | 2.*(fbs[0]*dfbdx[0]+fbs[1]*dfbdx[1]) |
|---|
| 1935 | dFdui[iref] = 2.*(fas[0]*dfadui[0]+fas[1]*dfadui[1])+ \ |
|---|
| 1936 | 2.*(fbs[0]*dfbdui[0]-fbs[1]*dfbdui[1]) |
|---|
| 1937 | dFdua[iref] = 2.*(fas[0]*dfadua[0]+fas[1]*dfadua[1])+ \ |
|---|
| 1938 | 2.*(fbs[0]*dfbdua[0]+fbs[1]*dfbdua[1]) |
|---|
| 1939 | dFdGf[iref] = 2.*(fas[0]*dfadGf[0]+fas[1]*dfadGf[1])+ \ |
|---|
| 1940 | 2.*(fbs[0]*dfbdGf[0]+fbs[1]*dfbdGf[1]) |
|---|
| 1941 | dFdGx[iref] = 2.*(fas[0]*dfadGx[0]+fas[1]*dfadGx[1])+ \ |
|---|
| 1942 | 2.*(fbs[0]*dfbdGx[0]-fbs[1]*dfbdGx[1]) |
|---|
| 1943 | dFdGz[iref] = 2.*(fas[0]*dfadGz[0]+fas[1]*dfadGz[1])+ \ |
|---|
| 1944 | 2.*(fbs[0]*dfbdGz[0]+fbs[1]*dfbdGz[1]) |
|---|
| 1945 | dFdGu[iref] = 2.*(fas[0]*dfadGu[0]+fas[1]*dfadGu[1])+ \ |
|---|
| 1946 | 2.*(fbs[0]*dfbdGu[0]+fbs[1]*dfbdGu[1]) |
|---|
| 1947 | else: #OK, I think |
|---|
| 1948 | dFdfr[iref] = 2.*(SA*dfadfr[0]+SA*dfadfr[1]+SB*dfbdfr[0]+SB*dfbdfr[1])*Mdata/len(Uniq) #array(nRef,nAtom) |
|---|
| 1949 | dFdx[iref] = 2.*(SA*dfadx[0]+SA*dfadx[1]+SB*dfbdx[0]+SB*dfbdx[1]) #array(nRef,nAtom,3) |
|---|
| 1950 | dFdui[iref] = 2.*(SA*dfadui[0]+SA*dfadui[1]+SB*dfbdui[0]+SB*dfbdui[1]) #array(nRef,nAtom) |
|---|
| 1951 | dFdua[iref] = 2.*(SA*dfadua[0]+SA*dfadua[1]+SB*dfbdua[0]+SB*dfbdua[1]) #array(nRef,nAtom,6) |
|---|
| 1952 | dFdfl[iref] = -SA*dfadfl-SB*dfbdfl #array(nRef,) |
|---|
| 1953 | |
|---|
| 1954 | dFdGf[iref] = 2.*(SA*dfadGf[0]+SB*dfbdGf[1]) #array(nRef,natom,nwave,2) |
|---|
| 1955 | dFdGx[iref] = 2.*(SA*dfadGx[0]+SB*dfbdGx[1]) #array(nRef,natom,nwave,6) |
|---|
| 1956 | dFdGz[iref] = 2.*(SA*dfadGz[0]+SB*dfbdGz[1]) #array(nRef,natom,5) |
|---|
| 1957 | dFdGu[iref] = 2.*(SA*dfadGu[0]+SB*dfbdGu[1]) #array(nRef,natom,nwave,12) |
|---|
| 1958 | # GSASIIpath.IPyBreak() |
|---|
| 1959 | dFdbab[iref] = 2.*fas[0]*np.array([np.sum(dfadba*dBabdA),np.sum(-dfadba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T+ \ |
|---|
| 1960 | 2.*fbs[0]*np.array([np.sum(dfbdba*dBabdA),np.sum(-dfbdba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T |
|---|
| 1961 | #loop over atoms - each dict entry is list of derivatives for all the reflections |
|---|
| 1962 | if not iref%100 : |
|---|
| 1963 | print ' %d derivative time %.4f\r'%(iref,time.time()-time0), |
|---|
| 1964 | for i in range(len(Mdata)): #loop over atoms |
|---|
| 1965 | dFdvDict[pfx+'Afrac:'+str(i)] = dFdfr.T[i] |
|---|
| 1966 | dFdvDict[pfx+'dAx:'+str(i)] = dFdx.T[0][i] |
|---|
| 1967 | dFdvDict[pfx+'dAy:'+str(i)] = dFdx.T[1][i] |
|---|
| 1968 | dFdvDict[pfx+'dAz:'+str(i)] = dFdx.T[2][i] |
|---|
| 1969 | dFdvDict[pfx+'AUiso:'+str(i)] = dFdui.T[i] |
|---|
| 1970 | dFdvDict[pfx+'AU11:'+str(i)] = dFdua.T[0][i] |
|---|
| 1971 | dFdvDict[pfx+'AU22:'+str(i)] = dFdua.T[1][i] |
|---|
| 1972 | dFdvDict[pfx+'AU33:'+str(i)] = dFdua.T[2][i] |
|---|
| 1973 | dFdvDict[pfx+'AU12:'+str(i)] = 2.*dFdua.T[3][i] |
|---|
| 1974 | dFdvDict[pfx+'AU13:'+str(i)] = 2.*dFdua.T[4][i] |
|---|
| 1975 | dFdvDict[pfx+'AU23:'+str(i)] = 2.*dFdua.T[5][i] |
|---|
| 1976 | for j in range(FSSdata.shape[1]): #loop over waves Fzero & Fwid? |
|---|
| 1977 | dFdvDict[pfx+'Fsin:'+str(i)+':'+str(j)] = dFdGf.T[0][j][i] |
|---|
| 1978 | dFdvDict[pfx+'Fcos:'+str(i)+':'+str(j)] = dFdGf.T[1][j][i] |
|---|
| 1979 | nx = 0 |
|---|
| 1980 | if waveTypes[i] in ['Block','ZigZag']: |
|---|
| 1981 | nx = 1 |
|---|
| 1982 | dFdvDict[pfx+'Tmin:'+str(i)+':0'] = dFdGz.T[0][i] #ZigZag/Block waves (if any) |
|---|
| 1983 | dFdvDict[pfx+'Tmax:'+str(i)+':0'] = dFdGz.T[1][i] |
|---|
| 1984 | dFdvDict[pfx+'Xmax:'+str(i)+':0'] = dFdGz.T[2][i] |
|---|
| 1985 | dFdvDict[pfx+'Ymax:'+str(i)+':0'] = dFdGz.T[3][i] |
|---|
| 1986 | dFdvDict[pfx+'Zmax:'+str(i)+':0'] = dFdGz.T[4][i] |
|---|
| 1987 | for j in range(XSSdata.shape[1]-nx): #loop over waves |
|---|
| 1988 | dFdvDict[pfx+'Xsin:'+str(i)+':'+str(j+nx)] = dFdGx.T[0][j][i] |
|---|
| 1989 | dFdvDict[pfx+'Ysin:'+str(i)+':'+str(j+nx)] = dFdGx.T[1][j][i] |
|---|
| 1990 | dFdvDict[pfx+'Zsin:'+str(i)+':'+str(j+nx)] = dFdGx.T[2][j][i] |
|---|
| 1991 | dFdvDict[pfx+'Xcos:'+str(i)+':'+str(j+nx)] = dFdGx.T[3][j][i] |
|---|
| 1992 | dFdvDict[pfx+'Ycos:'+str(i)+':'+str(j+nx)] = dFdGx.T[4][j][i] |
|---|
| 1993 | dFdvDict[pfx+'Zcos:'+str(i)+':'+str(j+nx)] = dFdGx.T[5][j][i] |
|---|
| 1994 | for j in range(USSdata.shape[1]): #loop over waves |
|---|
| 1995 | dFdvDict[pfx+'U11sin:'+str(i)+':'+str(j)] = dFdGu.T[0][j][i] |
|---|
| 1996 | dFdvDict[pfx+'U22sin:'+str(i)+':'+str(j)] = dFdGu.T[1][j][i] |
|---|
| 1997 | dFdvDict[pfx+'U33sin:'+str(i)+':'+str(j)] = dFdGu.T[2][j][i] |
|---|
| 1998 | dFdvDict[pfx+'U12sin:'+str(i)+':'+str(j)] = 2.*dFdGu.T[3][j][i] |
|---|
| 1999 | dFdvDict[pfx+'U13sin:'+str(i)+':'+str(j)] = 2.*dFdGu.T[4][j][i] |
|---|
| 2000 | dFdvDict[pfx+'U23sin:'+str(i)+':'+str(j)] = 2.*dFdGu.T[5][j][i] |
|---|
| 2001 | dFdvDict[pfx+'U11cos:'+str(i)+':'+str(j)] = dFdGu.T[6][j][i] |
|---|
| 2002 | dFdvDict[pfx+'U22cos:'+str(i)+':'+str(j)] = dFdGu.T[7][j][i] |
|---|
| 2003 | dFdvDict[pfx+'U33cos:'+str(i)+':'+str(j)] = dFdGu.T[8][j][i] |
|---|
| 2004 | dFdvDict[pfx+'U12cos:'+str(i)+':'+str(j)] = 2.*dFdGu.T[9][j][i] |
|---|
| 2005 | dFdvDict[pfx+'U13cos:'+str(i)+':'+str(j)] = 2.*dFdGu.T[10][j][i] |
|---|
| 2006 | dFdvDict[pfx+'U23cos:'+str(i)+':'+str(j)] = 2.*dFdGu.T[11][j][i] |
|---|
| 2007 | |
|---|
| 2008 | # GSASIIpath.IPyBreak() |
|---|
| 2009 | dFdvDict[phfx+'Flack'] = 4.*dFdfl.T |
|---|
| 2010 | dFdvDict[phfx+'BabA'] = dFdbab.T[0] |
|---|
| 2011 | dFdvDict[phfx+'BabU'] = dFdbab.T[1] |
|---|
| 2012 | return dFdvDict |
|---|
| 2013 | |
|---|
| 2014 | def SStructureFactorDerv2(refDict,im,G,hfx,pfx,SGData,SSGData,calcControls,parmDict): |
|---|
| 2015 | 'Needs a doc string - no twins' |
|---|
| 2016 | phfx = pfx.split(':')[0]+hfx |
|---|
| 2017 | ast = np.sqrt(np.diag(G)) |
|---|
| 2018 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 2019 | SGInv = SGData['SGInv'] |
|---|
| 2020 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 2021 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 2022 | SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']]) |
|---|
| 2023 | SSGT = np.array([ops[1] for ops in SSGData['SSGOps']]) |
|---|
| 2024 | FFtables = calcControls['FFtables'] |
|---|
| 2025 | BLtables = calcControls['BLtables'] |
|---|
| 2026 | nRef = len(refDict['RefList']) |
|---|
| 2027 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata,Gdata = \ |
|---|
| 2028 | GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 2029 | mSize = len(Mdata) #no. atoms |
|---|
| 2030 | waveTypes,FSSdata,XSSdata,USSdata,MSSdata = GetAtomSSFXU(pfx,calcControls,parmDict) |
|---|
| 2031 | ngl,nWaves,Fmod,Xmod,Umod,glTau,glWt = G2mth.makeWaves(waveTypes,FSSdata,XSSdata,USSdata,Mast) |
|---|
| 2032 | waveShapes,SCtauF,SCtauX,SCtauU,UmodAB = G2mth.makeWavesDerv(ngl,waveTypes,FSSdata,XSSdata,USSdata,Mast) |
|---|
| 2033 | modQ = np.array([parmDict[pfx+'mV0'],parmDict[pfx+'mV1'],parmDict[pfx+'mV2']]) |
|---|
| 2034 | FF = np.zeros(len(Tdata)) |
|---|
| 2035 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 2036 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 2037 | elif 'X' in calcControls[hfx+'histType']: |
|---|
| 2038 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 2039 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 2040 | Uij = np.array(G2lat.U6toUij(Uijdata)).T |
|---|
| 2041 | bij = Mast*Uij |
|---|
| 2042 | if not len(refDict['FF']): |
|---|
| 2043 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 2044 | dat = G2el.getBLvalues(BLtables) #will need wave here for anom. neutron b's |
|---|
| 2045 | else: |
|---|
| 2046 | dat = G2el.getFFvalues(FFtables,0.) |
|---|
| 2047 | refDict['FF']['El'] = dat.keys() |
|---|
| 2048 | refDict['FF']['FF'] = np.zeros((len(refDict['RefList']),len(dat))) |
|---|
| 2049 | dFdvDict = {} |
|---|
| 2050 | dFdfr = np.zeros((nRef,mSize)) |
|---|
| 2051 | dFdx = np.zeros((nRef,mSize,3)) |
|---|
| 2052 | dFdui = np.zeros((nRef,mSize)) |
|---|
| 2053 | dFdua = np.zeros((nRef,mSize,6)) |
|---|
| 2054 | dFdbab = np.zeros((nRef,2)) |
|---|
| 2055 | dFdfl = np.zeros((nRef)) |
|---|
| 2056 | dFdtw = np.zeros((nRef)) |
|---|
| 2057 | dFdGf = np.zeros((nRef,mSize,FSSdata.shape[1],2)) |
|---|
| 2058 | dFdGx = np.zeros((nRef,mSize,XSSdata.shape[1],6)) |
|---|
| 2059 | dFdGz = np.zeros((nRef,mSize,5)) |
|---|
| 2060 | dFdGu = np.zeros((nRef,mSize,USSdata.shape[1],12)) |
|---|
| 2061 | Flack = 1.0 |
|---|
| 2062 | if not SGData['SGInv'] and 'S' in calcControls[hfx+'histType'] and phfx+'Flack' in parmDict: |
|---|
| 2063 | Flack = 1.-2.*parmDict[phfx+'Flack'] |
|---|
| 2064 | time0 = time.time() |
|---|
| 2065 | iBeg = 0 |
|---|
| 2066 | blkSize = 4 #no. of reflections in a block - optimized for speed |
|---|
| 2067 | while iBeg < nRef: |
|---|
| 2068 | iFin = min(iBeg+blkSize,nRef) |
|---|
| 2069 | refl = refDict['RefList'][iBeg:iFin] #array(blkSize,nItems) |
|---|
| 2070 | H = refl.T[:4] |
|---|
| 2071 | HP = H[:3].T+modQ*H.T[:,3:] #projected hklm to hkl |
|---|
| 2072 | SQ = 1./(2.*refl.T[4+im])**2 # or (sin(theta)/lambda)**2 |
|---|
| 2073 | SQfactor = 8.0*SQ*np.pi**2 |
|---|
| 2074 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 2075 | if 'P' in calcControls[hfx+'histType']: |
|---|
| 2076 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[15]) |
|---|
| 2077 | else: |
|---|
| 2078 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[13]) |
|---|
| 2079 | FP = np.repeat(FP.T,len(SGT),axis=0) |
|---|
| 2080 | FPP = np.repeat(FPP.T,len(SGT),axis=0) |
|---|
| 2081 | dBabdA = np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 2082 | Bab = np.repeat(parmDict[phfx+'BabA']*np.exp(-parmDict[phfx+'BabU']*SQfactor),len(SGT)) |
|---|
| 2083 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 2084 | FF = np.repeat(refDict['FF']['FF'][iBeg:iFin].T[Tindx].T,len(SGT),axis=0) |
|---|
| 2085 | Uniq = np.inner(H.T,SSGMT) |
|---|
| 2086 | Phi = np.inner(H.T,SSGT) |
|---|
| 2087 | UniqP = np.inner(HP,SGMT) |
|---|
| 2088 | if SGInv: #if centro - expand HKL sets |
|---|
| 2089 | Uniq = np.hstack((Uniq,-Uniq)) |
|---|
| 2090 | Phi = np.hstack((Phi,-Phi)) |
|---|
| 2091 | UniqP = np.hstack((UniqP,-UniqP)) |
|---|
| 2092 | FF = np.vstack((FF,FF)) |
|---|
| 2093 | Bab = np.concatenate((Bab,Bab)) |
|---|
| 2094 | phase = twopi*(np.inner(Uniq[:,:,:3],(dXdata+Xdata).T)+Phi[:,:,nxs]) |
|---|
| 2095 | sinp = np.sin(phase) |
|---|
| 2096 | cosp = np.cos(phase) |
|---|
| 2097 | occ = Mdata*Fdata/Uniq.shape[1] |
|---|
| 2098 | biso = -SQfactor*Uisodata[:,nxs] |
|---|
| 2099 | Tiso = np.repeat(np.where(biso<1.,np.exp(biso),1.0),Uniq.shape[1],axis=1).T #ops x atoms |
|---|
| 2100 | HbH = -np.sum(UniqP[:,:,nxs,:3]*np.inner(UniqP[:,:,:3],bij),axis=-1) #ops x atoms |
|---|
| 2101 | Hij = np.array([Mast*np.multiply.outer(U[:3],U[:3]) for U in np.reshape(UniqP,(-1,3))]) #atoms x 3x3 |
|---|
| 2102 | Hij = np.reshape(np.array([G2lat.UijtoU6(Uij) for Uij in Hij]),(iFin-iBeg,-1,6)) #atoms x 6 |
|---|
| 2103 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0) #ops x atoms |
|---|
| 2104 | # GSASIIpath.IPyBreak() |
|---|
| 2105 | Tcorr = np.reshape(Tiso,Tuij.shape)*Tuij*Mdata*Fdata/Uniq.shape[0] #ops x atoms |
|---|
| 2106 | fot = np.reshape(FF+FP[nxs,:]-Bab[:,nxs],cosp.shape)*Tcorr #ops x atoms |
|---|
| 2107 | fotp = FPP*Tcorr #ops x atoms |
|---|
| 2108 | GfpuA = G2mth.Modulation(Uniq,UniqP,nWaves,Fmod,Xmod,Umod,glTau,glWt) #2 x sym X atoms |
|---|
| 2109 | dGdf,dGdx,dGdu,dGdz = G2mth.ModulationDerv2(Uniq,UniqP,Hij,nWaves,waveShapes,Fmod,Xmod,UmodAB,SCtauF,SCtauX,SCtauU,glTau,glWt) |
|---|
| 2110 | # GfpuA is 2 x ops x atoms |
|---|
| 2111 | # derivs are: ops x atoms x waves x 2,6,12, or 5 parms as [real,imag] parts |
|---|
| 2112 | fa = np.array([fot*cosp,-Flack*FPP*sinp*Tcorr]) # array(2,nEqv,nAtoms) |
|---|
| 2113 | fb = np.array([fot*sinp,Flack*FPP*cosp*Tcorr]) #or array(2,nEqv,nAtoms) |
|---|
| 2114 | fag = fa*GfpuA[0]-fb*GfpuA[1] |
|---|
| 2115 | fbg = fb*GfpuA[0]+fa*GfpuA[1] |
|---|
| 2116 | |
|---|
| 2117 | fas = np.sum(np.sum(fag,axis=-1),axis=-1) # 2 x refBlk |
|---|
| 2118 | fbs = np.sum(np.sum(fbg,axis=-1),axis=-1) |
|---|
| 2119 | fax = np.array([-fot*sinp,-fotp*cosp]) #positions; 2 x ops x atoms |
|---|
| 2120 | fbx = np.array([fot*cosp,-fotp*sinp]) |
|---|
| 2121 | fax = fax*GfpuA[0]-fbx*GfpuA[1] |
|---|
| 2122 | fbx = fbx*GfpuA[0]+fax*GfpuA[1] |
|---|
| 2123 | #sum below is over Uniq |
|---|
| 2124 | dfadfr = np.sum(fag/occ,axis=-2) #Fdata != 0 ever avoids /0. problem |
|---|
| 2125 | dfbdfr = np.sum(fbg/occ,axis=-2) #Fdata != 0 avoids /0. problem |
|---|
| 2126 | dfadba = np.sum(-cosp*Tcorr,axis=-2) |
|---|
| 2127 | dfbdba = np.sum(-sinp*Tcorr,axis=-2) |
|---|
| 2128 | dfadui = np.sum(-SQfactor[nxs,:,nxs,nxs]*fag,axis=-2) |
|---|
| 2129 | dfbdui = np.sum(-SQfactor[nxs,:,nxs,nxs]*fbg,axis=-2) |
|---|
| 2130 | dfadx = np.sum(twopi*Uniq[nxs,:,:,nxs,:3]*fax[:,:,:,:,nxs],axis=-3) #2 refBlk x x nAtom x 3xyz; sum nOps |
|---|
| 2131 | dfbdx = np.sum(twopi*Uniq[nxs,:,:,nxs,:3]*fbx[:,:,:,:,nxs],axis=-3) #2 refBlk x x nAtom x 3xyz; sum nOps |
|---|
| 2132 | dfadua = np.sum(-Hij[nxs,:,:,nxs,:]*fag[:,:,:,:,nxs],axis=-3) #2 x nAtom x 6Uij; sum nOps |
|---|
| 2133 | dfbdua = np.sum(-Hij[nxs,:,:,nxs,:]*fbg[:,:,:,:,nxs],axis=-3) #2 x nAtom x 6Uij; sum nOps |
|---|
| 2134 | # array(2,nAtom,nWave,2) & array(2,nAtom,nWave,6) & array(2,nAtom,nWave,12); sum on nOps |
|---|
| 2135 | dfadGf = np.sum(fa[:,:,:,:,nxs,nxs]*dGdf[0][nxs,:,nxs,:,:,:]-fb[:,:,:,:,nxs,nxs]*dGdf[1][nxs,:,nxs,:,:,:],axis=2) |
|---|
| 2136 | dfbdGf = np.sum(fb[:,:,:,:,nxs,nxs]*dGdf[0][nxs,:,nxs,:,:,:]+fa[:,:,:,:,nxs,nxs]*dGdf[1][nxs,:,nxs,:,:,:],axis=2) |
|---|
| 2137 | dfadGx = np.sum(fa[:,:,:,:,nxs,nxs]*dGdx[0][nxs,:,:,:,:,:]-fb[:,:,:,:,nxs,nxs]*dGdx[1][nxs,:,:,:,:,:],axis=2) |
|---|
| 2138 | dfbdGx = np.sum(fb[:,:,:,:,nxs,nxs]*dGdx[0][nxs,:,:,:,:,:]+fa[:,:,:,:,nxs,nxs]*dGdx[1][nxs,:,:,:,:,:],axis=2) |
|---|
| 2139 | dfadGz = np.sum(fa[:,:,:,:,nxs]*dGdz[0][nxs,:,:,:,:]-fb[:,:,:,:,nxs]*dGdz[1][nxs,:,:,:,:],axis=2) |
|---|
| 2140 | dfbdGz = np.sum(fb[:,:,:,:,nxs]*dGdz[0][nxs,:,:,:,:]+fa[:,:,:,:,nxs]*dGdz[1][nxs,:,:,:,:],axis=2) |
|---|
| 2141 | dfadGu = np.sum(fa[:,:,:,:,nxs,nxs]*dGdu[0][nxs,:,:,:,:]-fb[:,:,:,:,nxs,nxs]*dGdu[1][nxs,:,:,:,:],axis=2) |
|---|
| 2142 | dfbdGu = np.sum(fb[:,:,:,:,nxs,nxs]*dGdu[0][nxs,:,:,:,:]+fa[:,:,:,:,nxs,nxs]*dGdu[1][nxs,:,:,:,:],axis=2) |
|---|
| 2143 | if not SGData['SGInv']: #Flack derivative |
|---|
| 2144 | dfadfl = np.sum(np.sum(-FPP*Tcorr*sinp,axis=-1),axis=-1) |
|---|
| 2145 | dfbdfl = np.sum(np.sum(FPP*Tcorr*cosp,axis=-1),axis=-1) |
|---|
| 2146 | else: |
|---|
| 2147 | dfadfl = 1.0 |
|---|
| 2148 | dfbdfl = 1.0 |
|---|
| 2149 | #NB: the above have been checked against PA(1:10,1:2) in strfctr.for for Al2O3! |
|---|
| 2150 | SA = fas[0]+fas[1] #float = A+A' (might be array[nTwin]) |
|---|
| 2151 | SB = fbs[0]+fbs[1] #float = B+B' (might be array[nTwin]) |
|---|
| 2152 | if 'P' in calcControls[hfx+'histType']: #checked perfect for centro & noncentro? |
|---|
| 2153 | dFdfl[iBeg:iFin] = -SA*dfadfl-SB*dfbdfl #array(nRef,) |
|---|
| 2154 | dFdfr[iBeg:iFin] = 2.*(fas[0,:,nxs]*dfadfr[0]+fas[1,:,nxs]*dfadfr[1])*Mdata/len(Uniq)+ \ |
|---|
| 2155 | 2.*(fbs[0,:,nxs]*dfbdfr[0]-fbs[1,:,nxs]*dfbdfr[1])*Mdata/len(Uniq) |
|---|
| 2156 | dFdx[iBeg:iFin] = 2.*(fas[0,:,nxs,nxs]*dfadx[0]+fas[1,:,nxs,nxs]*dfadx[1])+ \ |
|---|
| 2157 | 2.*(fbs[0,:,nxs,nxs]*dfbdx[0]+fbs[1,:,nxs,nxs]*dfbdx[1]) |
|---|
| 2158 | dFdui[iBeg:iFin] = 2.*(fas[0,:,nxs]*dfadui[0]+fas[1,:,nxs]*dfadui[1])+ \ |
|---|
| 2159 | 2.*(fbs[0,:,nxs]*dfbdui[0]-fbs[1,:,nxs]*dfbdui[1]) |
|---|
| 2160 | dFdua[iBeg:iFin] = 2.*(fas[0,:,nxs,nxs]*dfadua[0]+fas[1,:,nxs,nxs]*dfadua[1])+ \ |
|---|
| 2161 | 2.*(fbs[0,:,nxs,nxs]*dfbdua[0]+fbs[1,:,nxs,nxs]*dfbdua[1]) |
|---|
| 2162 | dFdGf[iBeg:iFin] = 2.*(fas[0,:,nxs,nxs,nxs]*dfadGf[0]+fas[1,:,nxs,nxs,nxs]*dfadGf[1])+ \ |
|---|
| 2163 | 2.*(fbs[0,:,nxs,nxs,nxs]*dfbdGf[0]+fbs[1,:,nxs,nxs,nxs]*dfbdGf[1]) |
|---|
| 2164 | dFdGx[iBeg:iFin] = 2.*(fas[0,:,nxs,nxs,nxs]*dfadGx[0]+fas[1,:,nxs,nxs,nxs]*dfadGx[1])+ \ |
|---|
| 2165 | 2.*(fbs[0,:,nxs,nxs,nxs]*dfbdGx[0]-fbs[1,:,nxs,nxs,nxs]*dfbdGx[1]) |
|---|
| 2166 | dFdGz[iBeg:iFin] = 2.*(fas[0,:,nxs,nxs]*dfadGz[0]+fas[1,:,nxs,nxs]*dfadGz[1])+ \ |
|---|
| 2167 | 2.*(fbs[0,:,nxs,nxs]*dfbdGz[0]+fbs[1,:,nxs,nxs]*dfbdGz[1]) |
|---|
| 2168 | dFdGu[iBeg:iFin] = 2.*(fas[0,:,nxs,nxs,nxs]*dfadGu[0]+fas[1,:,nxs,nxs,nxs]*dfadGu[1])+ \ |
|---|
| 2169 | 2.*(fbs[0,:,nxs,nxs,nxs]*dfbdGu[0]+fbs[1,:,nxs,nxs,nxs]*dfbdGu[1]) |
|---|
| 2170 | else: #OK, I think |
|---|
| 2171 | dFdfr[iBeg:iFin] = 2.*(SA[:,nxs]*(dfadfr[0]+dfadfr[1])+SB[:,nxs]*(dfbdfr[0]+dfbdfr[1]))*Mdata/len(Uniq) #array(nRef,nAtom) |
|---|
| 2172 | dFdx[iBeg:iFin] = 2.*(SA[:,nxs,nxs]*(dfadx[0]+dfadx[1])+SB[:,nxs,nxs]*(dfbdx[0]+dfbdx[1])) #array(nRef,nAtom,3) |
|---|
| 2173 | dFdui[iBeg:iFin] = 2.*(SA[:,nxs]*(dfadui[0]+dfadui[1])+SB[:,nxs]*(dfbdui[0]+dfbdui[1])) #array(nRef,nAtom) |
|---|
| 2174 | dFdua[iBeg:iFin] = 2.*(SA[:,nxs,nxs]*(dfadua[0]+dfadua[1])+SB[:,nxs,nxs]*(dfbdua[0]+dfbdua[1])) #array(nRef,nAtom,6) |
|---|
| 2175 | dFdfl[iBeg:iFin] = -SA*dfadfl-SB*dfbdfl #array(nRef,) |
|---|
| 2176 | |
|---|
| 2177 | dFdGf[iBeg:iFin] = 2.*(SA[:,nxs,nxs,nxs]*dfadGf[0]+SB[:,nxs,nxs,nxs]*dfbdGf[1]) #array(nRef,natom,nwave,2) |
|---|
| 2178 | dFdGx[iBeg:iFin] = 2.*(SA[:,nxs,nxs,nxs]*dfadGx[0]+SB[:,nxs,nxs,nxs]*dfbdGx[1]) #array(nRef,natom,nwave,6) |
|---|
| 2179 | dFdGz[iBeg:iFin] = 2.*(SA[:,nxs,nxs]*dfadGz[0]+SB[:,nxs,nxs]*dfbdGz[1]) #array(nRef,natom,5) |
|---|
| 2180 | dFdGu[iBeg:iFin] = 2.*(SA[:,nxs,nxs,nxs]*dfadGu[0]+SB[:,nxs,nxs,nxs]*dfbdGu[1]) #array(nRef,natom,nwave,12) |
|---|
| 2181 | # GSASIIpath.IPyBreak() |
|---|
| 2182 | # dFdbab[iBeg:iFin] = 2.*fas[0,:,nxs]*np.array([np.sum(dfadba*dBabdA),np.sum(-dfadba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T+ \ |
|---|
| 2183 | # 2.*fbs[0,:,nxs]*np.array([np.sum(dfbdba*dBabdA),np.sum(-dfbdba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T |
|---|
| 2184 | #loop over atoms - each dict entry is list of derivatives for all the reflections |
|---|
| 2185 | print ' %d derivative time %.4f\r'%(iBeg,time.time()-time0), |
|---|
| 2186 | iBeg += blkSize |
|---|
| 2187 | for i in range(len(Mdata)): #loop over atoms |
|---|
| 2188 | dFdvDict[pfx+'Afrac:'+str(i)] = dFdfr.T[i] |
|---|
| 2189 | dFdvDict[pfx+'dAx:'+str(i)] = dFdx.T[0][i] |
|---|
| 2190 | dFdvDict[pfx+'dAy:'+str(i)] = dFdx.T[1][i] |
|---|
| 2191 | dFdvDict[pfx+'dAz:'+str(i)] = dFdx.T[2][i] |
|---|
| 2192 | dFdvDict[pfx+'AUiso:'+str(i)] = dFdui.T[i] |
|---|
| 2193 | dFdvDict[pfx+'AU11:'+str(i)] = dFdua.T[0][i] |
|---|
| 2194 | dFdvDict[pfx+'AU22:'+str(i)] = dFdua.T[1][i] |
|---|
| 2195 | dFdvDict[pfx+'AU33:'+str(i)] = dFdua.T[2][i] |
|---|
| 2196 | dFdvDict[pfx+'AU12:'+str(i)] = 2.*dFdua.T[3][i] |
|---|
| 2197 | dFdvDict[pfx+'AU13:'+str(i)] = 2.*dFdua.T[4][i] |
|---|
| 2198 | dFdvDict[pfx+'AU23:'+str(i)] = 2.*dFdua.T[5][i] |
|---|
| 2199 | for j in range(FSSdata.shape[1]): #loop over waves Fzero & Fwid? |
|---|
| 2200 | dFdvDict[pfx+'Fsin:'+str(i)+':'+str(j)] = dFdGf.T[0][j][i] |
|---|
| 2201 | dFdvDict[pfx+'Fcos:'+str(i)+':'+str(j)] = dFdGf.T[1][j][i] |
|---|
| 2202 | nx = 0 |
|---|
| 2203 | if waveTypes[i] in ['Block','ZigZag']: |
|---|
| 2204 | nx = 1 |
|---|
| 2205 | dFdvDict[pfx+'Tmin:'+str(i)+':0'] = dFdGz.T[0][i] #ZigZag/Block waves (if any) |
|---|
| 2206 | dFdvDict[pfx+'Tmax:'+str(i)+':0'] = dFdGz.T[1][i] |
|---|
| 2207 | dFdvDict[pfx+'Xmax:'+str(i)+':0'] = dFdGz.T[2][i] |
|---|
| 2208 | dFdvDict[pfx+'Ymax:'+str(i)+':0'] = dFdGz.T[3][i] |
|---|
| 2209 | dFdvDict[pfx+'Zmax:'+str(i)+':0'] = dFdGz.T[4][i] |
|---|
| 2210 | for j in range(XSSdata.shape[1]-nx): #loop over waves |
|---|
| 2211 | dFdvDict[pfx+'Xsin:'+str(i)+':'+str(j+nx)] = dFdGx.T[0][j][i] |
|---|
| 2212 | dFdvDict[pfx+'Ysin:'+str(i)+':'+str(j+nx)] = dFdGx.T[1][j][i] |
|---|
| 2213 | dFdvDict[pfx+'Zsin:'+str(i)+':'+str(j+nx)] = dFdGx.T[2][j][i] |
|---|
| 2214 | dFdvDict[pfx+'Xcos:'+str(i)+':'+str(j+nx)] = dFdGx.T[3][j][i] |
|---|
| 2215 | dFdvDict[pfx+'Ycos:'+str(i)+':'+str(j+nx)] = dFdGx.T[4][j][i] |
|---|
| 2216 | dFdvDict[pfx+'Zcos:'+str(i)+':'+str(j+nx)] = dFdGx.T[5][j][i] |
|---|
| 2217 | for j in range(USSdata.shape[1]): #loop over waves |
|---|
| 2218 | dFdvDict[pfx+'U11sin:'+str(i)+':'+str(j)] = dFdGu.T[0][j][i] |
|---|
| 2219 | dFdvDict[pfx+'U22sin:'+str(i)+':'+str(j)] = dFdGu.T[1][j][i] |
|---|
| 2220 | dFdvDict[pfx+'U33sin:'+str(i)+':'+str(j)] = dFdGu.T[2][j][i] |
|---|
| 2221 | dFdvDict[pfx+'U12sin:'+str(i)+':'+str(j)] = 2.*dFdGu.T[3][j][i] |
|---|
| 2222 | dFdvDict[pfx+'U13sin:'+str(i)+':'+str(j)] = 2.*dFdGu.T[4][j][i] |
|---|
| 2223 | dFdvDict[pfx+'U23sin:'+str(i)+':'+str(j)] = 2.*dFdGu.T[5][j][i] |
|---|
| 2224 | dFdvDict[pfx+'U11cos:'+str(i)+':'+str(j)] = dFdGu.T[6][j][i] |
|---|
| 2225 | dFdvDict[pfx+'U22cos:'+str(i)+':'+str(j)] = dFdGu.T[7][j][i] |
|---|
| 2226 | dFdvDict[pfx+'U33cos:'+str(i)+':'+str(j)] = dFdGu.T[8][j][i] |
|---|
| 2227 | dFdvDict[pfx+'U12cos:'+str(i)+':'+str(j)] = 2.*dFdGu.T[9][j][i] |
|---|
| 2228 | dFdvDict[pfx+'U13cos:'+str(i)+':'+str(j)] = 2.*dFdGu.T[10][j][i] |
|---|
| 2229 | dFdvDict[pfx+'U23cos:'+str(i)+':'+str(j)] = 2.*dFdGu.T[11][j][i] |
|---|
| 2230 | |
|---|
| 2231 | # GSASIIpath.IPyBreak() |
|---|
| 2232 | dFdvDict[phfx+'BabA'] = dFdbab.T[0] |
|---|
| 2233 | dFdvDict[phfx+'BabU'] = dFdbab.T[1] |
|---|
| 2234 | return dFdvDict |
|---|
| 2235 | |
|---|
| 2236 | def SStructureFactorDervTw(refDict,im,G,hfx,pfx,SGData,SSGData,calcControls,parmDict): |
|---|
| 2237 | 'Needs a doc string' |
|---|
| 2238 | phfx = pfx.split(':')[0]+hfx |
|---|
| 2239 | ast = np.sqrt(np.diag(G)) |
|---|
| 2240 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 2241 | SGInv = SGData['SGInv'] |
|---|
| 2242 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 2243 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 2244 | SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']]) |
|---|
| 2245 | SSGT = np.array([ops[1] for ops in SSGData['SSGOps']]) |
|---|
| 2246 | FFtables = calcControls['FFtables'] |
|---|
| 2247 | BLtables = calcControls['BLtables'] |
|---|
| 2248 | TwinLaw = np.array([[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]],]) |
|---|
| 2249 | TwDict = refDict.get('TwDict',{}) |
|---|
| 2250 | if 'S' in calcControls[hfx+'histType']: |
|---|
| 2251 | NTL = calcControls[phfx+'NTL'] |
|---|
| 2252 | NM = calcControls[phfx+'TwinNMN']+1 |
|---|
| 2253 | TwinLaw = calcControls[phfx+'TwinLaw'] |
|---|
| 2254 | TwinFr = np.array([parmDict[phfx+'TwinFr:'+str(i)] for i in range(len(TwinLaw))]) |
|---|
| 2255 | TwinInv = list(np.where(calcControls[phfx+'TwinInv'],-1,1)) |
|---|
| 2256 | nTwin = len(TwinLaw) |
|---|
| 2257 | nRef = len(refDict['RefList']) |
|---|
| 2258 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata,Gdata = \ |
|---|
| 2259 | GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 2260 | mSize = len(Mdata) #no. atoms |
|---|
| 2261 | waveTypes,FSSdata,XSSdata,USSdata,MSSdata = GetAtomSSFXU(pfx,calcControls,parmDict) |
|---|
| 2262 | ngl,nWaves,Fmod,Xmod,Umod,glTau,glWt = G2mth.makeWaves(waveTypes,FSSdata,XSSdata,USSdata,Mast) |
|---|
| 2263 | waveShapes,SCtauF,SCtauX,SCtauU,UmodAB = G2mth.makeWavesDerv(ngl,waveTypes,FSSdata,XSSdata,USSdata,Mast) |
|---|
| 2264 | modQ = np.array([parmDict[pfx+'mV0'],parmDict[pfx+'mV1'],parmDict[pfx+'mV2']]) |
|---|
| 2265 | FF = np.zeros(len(Tdata)) |
|---|
| 2266 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 2267 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 2268 | elif 'X' in calcControls[hfx+'histType']: |
|---|
| 2269 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 2270 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 2271 | Uij = np.array(G2lat.U6toUij(Uijdata)).T |
|---|
| 2272 | bij = Mast*Uij |
|---|
| 2273 | if not len(refDict['FF']): |
|---|
| 2274 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 2275 | dat = G2el.getBLvalues(BLtables) #will need wave here for anom. neutron b's |
|---|
| 2276 | else: |
|---|
| 2277 | dat = G2el.getFFvalues(FFtables,0.) |
|---|
| 2278 | refDict['FF']['El'] = dat.keys() |
|---|
| 2279 | refDict['FF']['FF'] = np.zeros((len(refDict['RefList']),len(dat))) |
|---|
| 2280 | dFdvDict = {} |
|---|
| 2281 | dFdfr = np.zeros((nRef,nTwin,mSize)) |
|---|
| 2282 | dFdx = np.zeros((nRef,nTwin,mSize,3)) |
|---|
| 2283 | dFdui = np.zeros((nRef,nTwin,mSize)) |
|---|
| 2284 | dFdua = np.zeros((nRef,nTwin,mSize,6)) |
|---|
| 2285 | dFdbab = np.zeros((nRef,nTwin,2)) |
|---|
| 2286 | dFdfl = np.zeros((nRef,nTwin)) |
|---|
| 2287 | dFdtw = np.zeros((nRef,nTwin)) |
|---|
| 2288 | dFdGf = np.zeros((nRef,nTwin,mSize,FSSdata.shape[1])) |
|---|
| 2289 | dFdGx = np.zeros((nRef,nTwin,mSize,XSSdata.shape[1],3)) |
|---|
| 2290 | dFdGz = np.zeros((nRef,nTwin,mSize,5)) |
|---|
| 2291 | dFdGu = np.zeros((nRef,nTwin,mSize,USSdata.shape[1],6)) |
|---|
| 2292 | Flack = 1.0 |
|---|
| 2293 | if not SGData['SGInv'] and 'S' in calcControls[hfx+'histType'] and phfx+'Flack' in parmDict: |
|---|
| 2294 | Flack = 1.-2.*parmDict[phfx+'Flack'] |
|---|
| 2295 | time0 = time.time() |
|---|
| 2296 | nRef = len(refDict['RefList'])/100 |
|---|
| 2297 | for iref,refl in enumerate(refDict['RefList']): |
|---|
| 2298 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 2299 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,refl.T[12+im]) |
|---|
| 2300 | H = np.array(refl[:4]) |
|---|
| 2301 | HP = H[:3]+modQ*H[3:] #projected hklm to hkl |
|---|
| 2302 | H = np.inner(H.T,TwinLaw) #maybe array(4,nTwins) or (4) |
|---|
| 2303 | TwMask = np.any(H,axis=-1) |
|---|
| 2304 | if TwinLaw.shape[0] > 1 and TwDict: |
|---|
| 2305 | if iref in TwDict: |
|---|
| 2306 | for i in TwDict[iref]: |
|---|
| 2307 | for n in range(NTL): |
|---|
| 2308 | H[i+n*NM] = np.inner(TwinLaw[n*NM],np.array(TwDict[iref][i])*TwinInv[i+n*NM]) |
|---|
| 2309 | TwMask = np.any(H,axis=-1) |
|---|
| 2310 | SQ = 1./(2.*refl[4+im])**2 # or (sin(theta)/lambda)**2 |
|---|
| 2311 | SQfactor = 8.0*SQ*np.pi**2 |
|---|
| 2312 | dBabdA = np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 2313 | Bab = parmDict[phfx+'BabA']*dBabdA |
|---|
| 2314 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 2315 | FF = refDict['FF']['FF'][iref].T[Tindx] |
|---|
| 2316 | Uniq = np.inner(H,SSGMT) |
|---|
| 2317 | Phi = np.inner(H,SSGT) |
|---|
| 2318 | UniqP = np.inner(HP,SGMT) |
|---|
| 2319 | if SGInv: #if centro - expand HKL sets |
|---|
| 2320 | Uniq = np.vstack((Uniq,-Uniq)) |
|---|
| 2321 | Phi = np.hstack((Phi,-Phi)) |
|---|
| 2322 | UniqP = np.vstack((UniqP,-UniqP)) |
|---|
| 2323 | phase = twopi*(np.inner(Uniq[:,:3],(dXdata+Xdata).T)+Phi[:,nxs]) |
|---|
| 2324 | sinp = np.sin(phase) |
|---|
| 2325 | cosp = np.cos(phase) |
|---|
| 2326 | occ = Mdata*Fdata/Uniq.shape[0] |
|---|
| 2327 | biso = -SQfactor*Uisodata[:,nxs] |
|---|
| 2328 | Tiso = np.repeat(np.where(biso<1.,np.exp(biso),1.0),Uniq.shape[0]*len(TwinLaw),axis=1).T #ops x atoms |
|---|
| 2329 | HbH = -np.sum(UniqP[:,nxs,:3]*np.inner(UniqP[:,:3],bij),axis=-1) #ops x atoms |
|---|
| 2330 | Hij = np.array([Mast*np.multiply.outer(U[:3],U[:3]) for U in UniqP]) #atoms x 3x3 |
|---|
| 2331 | Hij = np.squeeze(np.reshape(np.array([G2lat.UijtoU6(Uij) for Uij in Hij]),(nTwin,-1,6))) |
|---|
| 2332 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0) #ops x atoms |
|---|
| 2333 | Tcorr = np.reshape(Tiso,Tuij.shape)*Tuij*Mdata*Fdata/Uniq.shape[0] #ops x atoms |
|---|
| 2334 | fot = (FF+FP-Bab)*Tcorr #ops x atoms |
|---|
| 2335 | fotp = FPP*Tcorr #ops x atoms |
|---|
| 2336 | GfpuA = G2mth.Modulation(Uniq,UniqP,nWaves,Fmod,Xmod,Umod,glTau,glWt) #2 x sym X atoms |
|---|
| 2337 | dGdf,dGdx,dGdu,dGdz = G2mth.ModulationDerv(Uniq,UniqP,Hij,nWaves,waveShapes,Fmod,Xmod,UmodAB,SCtauF,SCtauX,SCtauU,glTau,glWt) |
|---|
| 2338 | # GfpuA is 2 x ops x atoms |
|---|
| 2339 | # derivs are: ops x atoms x waves x 2,6,12, or 5 parms as [real,imag] parts |
|---|
| 2340 | fa = np.array([((FF+FP).T-Bab).T*cosp*Tcorr,-Flack*FPP*sinp*Tcorr]) # array(2,nTwin,nEqv,nAtoms) |
|---|
| 2341 | fb = np.array([((FF+FP).T-Bab).T*sinp*Tcorr,Flack*FPP*cosp*Tcorr]) #or array(2,nEqv,nAtoms) |
|---|
| 2342 | fag = fa*GfpuA[0]-fb*GfpuA[1] |
|---|
| 2343 | fbg = fb*GfpuA[0]+fa*GfpuA[1] |
|---|
| 2344 | |
|---|
| 2345 | fas = np.sum(np.sum(fag,axis=1),axis=1) # 2 x twin |
|---|
| 2346 | fbs = np.sum(np.sum(fbg,axis=1),axis=1) |
|---|
| 2347 | fax = np.array([-fot*sinp,-fotp*cosp]) #positions; 2 x twin x ops x atoms |
|---|
| 2348 | fbx = np.array([fot*cosp,-fotp*sinp]) |
|---|
| 2349 | fax = fax*GfpuA[0]-fbx*GfpuA[1] |
|---|
| 2350 | fbx = fbx*GfpuA[0]+fax*GfpuA[1] |
|---|
| 2351 | #sum below is over Uniq |
|---|
| 2352 | dfadfr = np.sum(fag/occ,axis=1) #Fdata != 0 ever avoids /0. problem |
|---|
| 2353 | dfbdfr = np.sum(fbg/occ,axis=1) #Fdata != 0 avoids /0. problem |
|---|
| 2354 | dfadba = np.sum(-cosp*Tcorr[:,nxs],axis=1) |
|---|
| 2355 | dfbdba = np.sum(-sinp*Tcorr[:,nxs],axis=1) |
|---|
| 2356 | dfadui = np.sum(-SQfactor*fag,axis=1) |
|---|
| 2357 | dfbdui = np.sum(-SQfactor*fbg,axis=1) |
|---|
| 2358 | dfadx = np.array([np.sum(twopi*Uniq[it,:,:3]*np.swapaxes(fax,-2,-1)[:,it,:,:,nxs],axis=-2) for it in range(nTwin)]) |
|---|
| 2359 | dfbdx = np.array([np.sum(twopi*Uniq[it,:,:3]*np.swapaxes(fbx,-2,-1)[:,it,:,:,nxs],axis=-2) for it in range(nTwin)]) |
|---|
| 2360 | dfadua = np.array([np.sum(-Hij[it]*np.swapaxes(fag,-2,-1)[:,it,:,:,nxs],axis=-2) for it in range(nTwin)]) |
|---|
| 2361 | dfbdua = np.array([np.sum(-Hij[it]*np.swapaxes(fbg,-2,-1)[:,it,:,:,nxs],axis=-2) for it in range(nTwin)]) |
|---|
| 2362 | # array(2,nTwin,nAtom,3) & array(2,nTwin,nAtom,6) & array(2,nTwin,nAtom,12) |
|---|
| 2363 | dfadGf = np.sum(fa[:,it,:,:,nxs,nxs]*dGdf[0][nxs,nxs,:,:,:,:]-fb[:,it,:,:,nxs,nxs]*dGdf[1][nxs,nxs,:,:,:,:],axis=1) |
|---|
| 2364 | dfbdGf = np.sum(fb[:,it,:,:,nxs,nxs]*dGdf[0][nxs,nxs,:,:,:,:]+fa[:,it,:,:,nxs,nxs]*dGdf[1][nxs,nxs,:,:,:,:],axis=1) |
|---|
| 2365 | dfadGx = np.sum(fa[:,it,:,:,nxs,nxs]*dGdx[0][nxs,nxs,:,:,:,:]-fb[:,it,:,:,nxs,nxs]*dGdx[1][nxs,nxs,:,:,:,:],axis=1) |
|---|
| 2366 | dfbdGx = np.sum(fb[:,it,:,:,nxs,nxs]*dGdx[0][nxs,nxs,:,:,:,:]+fa[:,it,:,:,nxs,nxs]*dGdx[1][nxs,nxs,:,:,:,:],axis=1) |
|---|
| 2367 | dfadGz = np.sum(fa[:,it,:,0,nxs,nxs]*dGdz[0][nxs,nxs,:,:,:]-fb[:,it,:,0,nxs,nxs]*dGdz[1][nxs,nxs,:,:,:],axis=1) |
|---|
| 2368 | dfbdGz = np.sum(fb[:,it,:,0,nxs,nxs]*dGdz[0][nxs,nxs,:,:,:]+fa[:,it,:,0,nxs,nxs]*dGdz[1][nxs,nxs,:,:,:],axis=1) |
|---|
| 2369 | dfadGu = np.sum(fa[:,it,:,:,nxs,nxs]*dGdu[0][nxs,nxs,:,:,:,:]-fb[:,it,:,:,nxs,nxs]*dGdu[1][nxs,nxs,:,:,:,:],axis=1) |
|---|
| 2370 | dfbdGu = np.sum(fb[:,it,:,:,nxs,nxs]*dGdu[0][nxs,nxs,:,:,:,:]+fa[:,it,:,:,nxs,nxs]*dGdu[1][nxs,nxs,:,:,:,:],axis=1) |
|---|
| 2371 | # GSASIIpath.IPyBreak() |
|---|
| 2372 | if not SGData['SGInv'] and len(TwinLaw) == 1: #Flack derivative |
|---|
| 2373 | dfadfl = np.sum(-FPP*Tcorr*sinp) |
|---|
| 2374 | dfbdfl = np.sum(FPP*Tcorr*cosp) |
|---|
| 2375 | else: |
|---|
| 2376 | dfadfl = 1.0 |
|---|
| 2377 | dfbdfl = 1.0 |
|---|
| 2378 | #NB: the above have been checked against PA(1:10,1:2) in strfctr.for for Al2O3! |
|---|
| 2379 | SA = fas[0]+fas[1] #float = A+A' (might be array[nTwin]) |
|---|
| 2380 | SB = fbs[0]+fbs[1] #float = B+B' (might be array[nTwin]) |
|---|
| 2381 | dFdfr[iref] = [2.*TwMask[it]*(SA[it]*dfadfr[0][it]+SA[it]*dfadfr[1][it]+SB[it]*dfbdfr[0][it]+SB[it]*dfbdfr[1][it])*Mdata/len(Uniq[it]) for it in range(nTwin)] |
|---|
| 2382 | dFdx[iref] = [2.*TwMask[it]*(SA[it]*dfadx[it][0]+SA[it]*dfadx[it][1]+SB[it]*dfbdx[it][0]+SB[it]*dfbdx[it][1]) for it in range(nTwin)] |
|---|
| 2383 | dFdui[iref] = [2.*TwMask[it]*(SA[it]*dfadui[it][0]+SA[it]*dfadui[it][1]+SB[it]*dfbdui[it][0]+SB[it]*dfbdui[it][1]) for it in range(nTwin)] |
|---|
| 2384 | dFdua[iref] = [2.*TwMask[it]*(SA[it]*dfadua[it][0]+SA[it]*dfadua[it][1]+SB[it]*dfbdua[it][0]+SB[it]*dfbdua[it][1]) for it in range(nTwin)] |
|---|
| 2385 | dFdtw[iref] = np.sum(TwMask*fas,axis=0)**2+np.sum(TwMask*fbs,axis=0)**2 |
|---|
| 2386 | |
|---|
| 2387 | dFdGf[iref] = [2.*TwMask[it]*(SA[it]*dfadGf[1]+SB[it]*dfbdGf[1]) for it in range(nTwin)] |
|---|
| 2388 | dFdGx[iref] = [2.*TwMask[it]*(SA[it]*dfadGx[1]+SB[it]*dfbdGx[1]) for it in range(nTwin)] |
|---|
| 2389 | dFdGz[iref] = [2.*TwMask[it]*(SA[it]*dfadGz[1]+SB[it]*dfbdGz[1]) for it in range(nTwin)] |
|---|
| 2390 | dFdGu[iref] = [2.*TwMask[it]*(SA[it]*dfadGu[1]+SB[it]*dfbdGu[1]) for it in range(nTwin)] |
|---|
| 2391 | # GSASIIpath.IPyBreak() |
|---|
| 2392 | dFdbab[iref] = 2.*fas[0]*np.array([np.sum(dfadba*dBabdA),np.sum(-dfadba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T+ \ |
|---|
| 2393 | 2.*fbs[0]*np.array([np.sum(dfbdba*dBabdA),np.sum(-dfbdba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T |
|---|
| 2394 | #loop over atoms - each dict entry is list of derivatives for all the reflections |
|---|
| 2395 | if not iref%100 : |
|---|
| 2396 | print ' %d derivative time %.4f\r'%(iref,time.time()-time0), |
|---|
| 2397 | for i in range(len(Mdata)): #loop over atoms |
|---|
| 2398 | dFdvDict[pfx+'Afrac:'+str(i)] = dFdfr.T[i] |
|---|
| 2399 | dFdvDict[pfx+'dAx:'+str(i)] = dFdx.T[0][i] |
|---|
| 2400 | dFdvDict[pfx+'dAy:'+str(i)] = dFdx.T[1][i] |
|---|
| 2401 | dFdvDict[pfx+'dAz:'+str(i)] = dFdx.T[2][i] |
|---|
| 2402 | dFdvDict[pfx+'AUiso:'+str(i)] = dFdui.T[i] |
|---|
| 2403 | dFdvDict[pfx+'AU11:'+str(i)] = dFdua.T[0][i] |
|---|
| 2404 | dFdvDict[pfx+'AU22:'+str(i)] = dFdua.T[1][i] |
|---|
| 2405 | dFdvDict[pfx+'AU33:'+str(i)] = dFdua.T[2][i] |
|---|
| 2406 | dFdvDict[pfx+'AU12:'+str(i)] = 2.*dFdua.T[3][i] |
|---|
| 2407 | dFdvDict[pfx+'AU13:'+str(i)] = 2.*dFdua.T[4][i] |
|---|
| 2408 | dFdvDict[pfx+'AU23:'+str(i)] = 2.*dFdua.T[5][i] |
|---|
| 2409 | for j in range(FSSdata.shape[1]): #loop over waves Fzero & Fwid? |
|---|
| 2410 | dFdvDict[pfx+'Fsin:'+str(i)+':'+str(j)] = dFdGf.T[0][j][i] |
|---|
| 2411 | dFdvDict[pfx+'Fcos:'+str(i)+':'+str(j)] = dFdGf.T[1][j][i] |
|---|
| 2412 | nx = 0 |
|---|
| 2413 | if waveTypes[i] in ['Block','ZigZag']: |
|---|
| 2414 | nx = 1 |
|---|
| 2415 | dFdvDict[pfx+'Tmin:'+str(i)+':0'] = dFdGz.T[0][i] #ZigZag/Block waves (if any) |
|---|
| 2416 | dFdvDict[pfx+'Tmax:'+str(i)+':0'] = dFdGz.T[1][i] |
|---|
| 2417 | dFdvDict[pfx+'Xmax:'+str(i)+':0'] = dFdGz.T[2][i] |
|---|
| 2418 | dFdvDict[pfx+'Ymax:'+str(i)+':0'] = dFdGz.T[3][i] |
|---|
| 2419 | dFdvDict[pfx+'Zmax:'+str(i)+':0'] = dFdGz.T[4][i] |
|---|
| 2420 | for j in range(XSSdata.shape[1]-nx): #loop over waves |
|---|
| 2421 | dFdvDict[pfx+'Xsin:'+str(i)+':'+str(j+nx)] = dFdGx.T[0][j][i] |
|---|
| 2422 | dFdvDict[pfx+'Ysin:'+str(i)+':'+str(j+nx)] = dFdGx.T[1][j][i] |
|---|
| 2423 | dFdvDict[pfx+'Zsin:'+str(i)+':'+str(j+nx)] = dFdGx.T[2][j][i] |
|---|
| 2424 | dFdvDict[pfx+'Xcos:'+str(i)+':'+str(j+nx)] = dFdGx.T[3][j][i] |
|---|
| 2425 | dFdvDict[pfx+'Ycos:'+str(i)+':'+str(j+nx)] = dFdGx.T[4][j][i] |
|---|
| 2426 | dFdvDict[pfx+'Zcos:'+str(i)+':'+str(j+nx)] = dFdGx.T[5][j][i] |
|---|
| 2427 | for j in range(USSdata.shape[1]): #loop over waves |
|---|
| 2428 | dFdvDict[pfx+'U11sin:'+str(i)+':'+str(j)] = dFdGu.T[0][j][i] |
|---|
| 2429 | dFdvDict[pfx+'U22sin:'+str(i)+':'+str(j)] = dFdGu.T[1][j][i] |
|---|
| 2430 | dFdvDict[pfx+'U33sin:'+str(i)+':'+str(j)] = dFdGu.T[2][j][i] |
|---|
| 2431 | dFdvDict[pfx+'U12sin:'+str(i)+':'+str(j)] = 2.*dFdGu.T[3][j][i] |
|---|
| 2432 | dFdvDict[pfx+'U13sin:'+str(i)+':'+str(j)] = 2.*dFdGu.T[4][j][i] |
|---|
| 2433 | dFdvDict[pfx+'U23sin:'+str(i)+':'+str(j)] = 2.*dFdGu.T[5][j][i] |
|---|
| 2434 | dFdvDict[pfx+'U11cos:'+str(i)+':'+str(j)] = dFdGu.T[6][j][i] |
|---|
| 2435 | dFdvDict[pfx+'U22cos:'+str(i)+':'+str(j)] = dFdGu.T[7][j][i] |
|---|
| 2436 | dFdvDict[pfx+'U33cos:'+str(i)+':'+str(j)] = dFdGu.T[8][j][i] |
|---|
| 2437 | dFdvDict[pfx+'U12cos:'+str(i)+':'+str(j)] = 2.*dFdGu.T[9][j][i] |
|---|
| 2438 | dFdvDict[pfx+'U13cos:'+str(i)+':'+str(j)] = 2.*dFdGu.T[10][j][i] |
|---|
| 2439 | dFdvDict[pfx+'U23cos:'+str(i)+':'+str(j)] = 2.*dFdGu.T[11][j][i] |
|---|
| 2440 | |
|---|
| 2441 | # GSASIIpath.IPyBreak() |
|---|
| 2442 | dFdvDict[phfx+'BabA'] = dFdbab.T[0] |
|---|
| 2443 | dFdvDict[phfx+'BabU'] = dFdbab.T[1] |
|---|
| 2444 | return dFdvDict |
|---|
| 2445 | |
|---|
| 2446 | def SCExtinction(ref,im,phfx,hfx,pfx,calcControls,parmDict,varyList): |
|---|
| 2447 | ''' Single crystal extinction function; returns extinction & derivative |
|---|
| 2448 | ''' |
|---|
| 2449 | extCor = 1.0 |
|---|
| 2450 | dervDict = {} |
|---|
| 2451 | dervCor = 1.0 |
|---|
| 2452 | if calcControls[phfx+'EType'] != 'None': |
|---|
| 2453 | SQ = 1/(4.*ref[4+im]**2) |
|---|
| 2454 | if 'C' in parmDict[hfx+'Type']: |
|---|
| 2455 | cos2T = 1.0-2.*SQ*parmDict[hfx+'Lam']**2 #cos(2theta) |
|---|
| 2456 | else: #'T' |
|---|
| 2457 | cos2T = 1.0-2.*SQ*ref[12+im]**2 #cos(2theta) |
|---|
| 2458 | if 'SXC' in parmDict[hfx+'Type']: |
|---|
| 2459 | AV = 7.9406e5/parmDict[pfx+'Vol']**2 |
|---|
| 2460 | PL = np.sqrt(1.0-cos2T**2)/parmDict[hfx+'Lam'] |
|---|
| 2461 | P12 = (calcControls[phfx+'Cos2TM']+cos2T**4)/(calcControls[phfx+'Cos2TM']+cos2T**2) |
|---|
| 2462 | PLZ = AV*P12*ref[9+im]*parmDict[hfx+'Lam']**2 |
|---|
| 2463 | elif 'SNT' in parmDict[hfx+'Type']: |
|---|
| 2464 | AV = 1.e7/parmDict[pfx+'Vol']**2 |
|---|
| 2465 | PL = SQ |
|---|
| 2466 | PLZ = AV*ref[9+im]*ref[12+im]**2 |
|---|
| 2467 | elif 'SNC' in parmDict[hfx+'Type']: |
|---|
| 2468 | AV = 1.e7/parmDict[pfx+'Vol']**2 |
|---|
| 2469 | PL = np.sqrt(1.0-cos2T**2)/parmDict[hfx+'Lam'] |
|---|
| 2470 | PLZ = AV*ref[9+im]*parmDict[hfx+'Lam']**2 |
|---|
| 2471 | |
|---|
| 2472 | if 'Primary' in calcControls[phfx+'EType']: |
|---|
| 2473 | PLZ *= 1.5 |
|---|
| 2474 | else: |
|---|
| 2475 | if 'C' in parmDict[hfx+'Type']: |
|---|
| 2476 | PLZ *= calcControls[phfx+'Tbar'] |
|---|
| 2477 | else: #'T' |
|---|
| 2478 | PLZ *= ref[13+im] #t-bar |
|---|
| 2479 | if 'Primary' in calcControls[phfx+'EType']: |
|---|
| 2480 | PLZ *= 1.5 |
|---|
| 2481 | PSIG = parmDict[phfx+'Ep'] |
|---|
| 2482 | elif 'I & II' in calcControls[phfx+'EType']: |
|---|
| 2483 | PSIG = parmDict[phfx+'Eg']/np.sqrt(1.+(parmDict[phfx+'Es']*PL/parmDict[phfx+'Eg'])**2) |
|---|
| 2484 | elif 'Type II' in calcControls[phfx+'EType']: |
|---|
| 2485 | PSIG = parmDict[phfx+'Es'] |
|---|
| 2486 | else: # 'Secondary Type I' |
|---|
| 2487 | PSIG = parmDict[phfx+'Eg']/PL |
|---|
| 2488 | |
|---|
| 2489 | AG = 0.58+0.48*cos2T+0.24*cos2T**2 |
|---|
| 2490 | AL = 0.025+0.285*cos2T |
|---|
| 2491 | BG = 0.02-0.025*cos2T |
|---|
| 2492 | BL = 0.15-0.2*(0.75-cos2T)**2 |
|---|
| 2493 | if cos2T < 0.: |
|---|
| 2494 | BL = -0.45*cos2T |
|---|
| 2495 | CG = 2. |
|---|
| 2496 | CL = 2. |
|---|
| 2497 | PF = PLZ*PSIG |
|---|
| 2498 | |
|---|
| 2499 | if 'Gaussian' in calcControls[phfx+'EApprox']: |
|---|
| 2500 | PF4 = 1.+CG*PF+AG*PF**2/(1.+BG*PF) |
|---|
| 2501 | extCor = np.sqrt(PF4) |
|---|
| 2502 | PF3 = 0.5*(CG+2.*AG*PF/(1.+BG*PF)-AG*PF**2*BG/(1.+BG*PF)**2)/(PF4*extCor) |
|---|
| 2503 | else: |
|---|
| 2504 | PF4 = 1.+CL*PF+AL*PF**2/(1.+BL*PF) |
|---|
| 2505 | extCor = np.sqrt(PF4) |
|---|
| 2506 | PF3 = 0.5*(CL+2.*AL*PF/(1.+BL*PF)-AL*PF**2*BL/(1.+BL*PF)**2)/(PF4*extCor) |
|---|
| 2507 | |
|---|
| 2508 | dervCor = (1.+PF)*PF3 #extinction corr for other derivatives |
|---|
| 2509 | if 'Primary' in calcControls[phfx+'EType'] and phfx+'Ep' in varyList: |
|---|
| 2510 | dervDict[phfx+'Ep'] = -ref[7+im]*PLZ*PF3 |
|---|
| 2511 | if 'II' in calcControls[phfx+'EType'] and phfx+'Es' in varyList: |
|---|
| 2512 | dervDict[phfx+'Es'] = -ref[7+im]*PLZ*PF3*(PSIG/parmDict[phfx+'Es'])**3 |
|---|
| 2513 | if 'I' in calcControls[phfx+'EType'] and phfx+'Eg' in varyList: |
|---|
| 2514 | dervDict[phfx+'Eg'] = -ref[7+im]*PLZ*PF3*(PSIG/parmDict[phfx+'Eg'])**3*PL**2 |
|---|
| 2515 | |
|---|
| 2516 | return 1./extCor,dervDict,dervCor |
|---|
| 2517 | |
|---|
| 2518 | def Dict2Values(parmdict, varylist): |
|---|
| 2519 | '''Use before call to leastsq to setup list of values for the parameters |
|---|
| 2520 | in parmdict, as selected by key in varylist''' |
|---|
| 2521 | return [parmdict[key] for key in varylist] |
|---|
| 2522 | |
|---|
| 2523 | def Values2Dict(parmdict, varylist, values): |
|---|
| 2524 | ''' Use after call to leastsq to update the parameter dictionary with |
|---|
| 2525 | values corresponding to keys in varylist''' |
|---|
| 2526 | parmdict.update(zip(varylist,values)) |
|---|
| 2527 | |
|---|
| 2528 | def GetNewCellParms(parmDict,varyList): |
|---|
| 2529 | 'Needs a doc string' |
|---|
| 2530 | newCellDict = {} |
|---|
| 2531 | Anames = ['A'+str(i) for i in range(6)] |
|---|
| 2532 | Ddict = dict(zip(['D11','D22','D33','D12','D13','D23'],Anames)) |
|---|
| 2533 | for item in varyList: |
|---|
| 2534 | keys = item.split(':') |
|---|
| 2535 | if keys[2] in Ddict: |
|---|
| 2536 | key = keys[0]+'::'+Ddict[keys[2]] #key is e.g. '0::A0' |
|---|
| 2537 | parm = keys[0]+'::'+keys[2] #parm is e.g. '0::D11' |
|---|
| 2538 | newCellDict[parm] = [key,parmDict[key]+parmDict[item]] |
|---|
| 2539 | return newCellDict # is e.g. {'0::D11':A0-D11} |
|---|
| 2540 | |
|---|
| 2541 | def ApplyXYZshifts(parmDict,varyList): |
|---|
| 2542 | ''' |
|---|
| 2543 | takes atom x,y,z shift and applies it to corresponding atom x,y,z value |
|---|
| 2544 | |
|---|
| 2545 | :param dict parmDict: parameter dictionary |
|---|
| 2546 | :param list varyList: list of variables (not used!) |
|---|
| 2547 | :returns: newAtomDict - dictionary of new atomic coordinate names & values; key is parameter shift name |
|---|
| 2548 | |
|---|
| 2549 | ''' |
|---|
| 2550 | newAtomDict = {} |
|---|
| 2551 | for item in parmDict: |
|---|
| 2552 | if 'dA' in item: |
|---|
| 2553 | parm = ''.join(item.split('d')) |
|---|
| 2554 | parmDict[parm] += parmDict[item] |
|---|
| 2555 | newAtomDict[item] = [parm,parmDict[parm]] |
|---|
| 2556 | return newAtomDict |
|---|
| 2557 | |
|---|
| 2558 | def SHTXcal(refl,im,g,pfx,hfx,SGData,calcControls,parmDict): |
|---|
| 2559 | 'Spherical harmonics texture' |
|---|
| 2560 | IFCoup = 'Bragg' in calcControls[hfx+'instType'] |
|---|
| 2561 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 2562 | tth = parmDict[hfx+'2-theta'] |
|---|
| 2563 | else: |
|---|
| 2564 | tth = refl[5+im] |
|---|
| 2565 | odfCor = 1.0 |
|---|
| 2566 | H = refl[:3] |
|---|
| 2567 | cell = G2lat.Gmat2cell(g) |
|---|
| 2568 | Sangls = [parmDict[pfx+'SH omega'],parmDict[pfx+'SH chi'],parmDict[pfx+'SH phi']] |
|---|
| 2569 | Gangls = [parmDict[hfx+'Phi'],parmDict[hfx+'Chi'],parmDict[hfx+'Omega'],parmDict[hfx+'Azimuth']] |
|---|
| 2570 | phi,beta = G2lat.CrsAng(H,cell,SGData) |
|---|
| 2571 | psi,gam,x,x = G2lat.SamAng(tth/2.,Gangls,Sangls,IFCoup) #ignore 2 sets of angle derivs. |
|---|
| 2572 | SHnames = G2lat.GenSHCoeff(SGData['SGLaue'],parmDict[pfx+'SHmodel'],parmDict[pfx+'SHorder']) |
|---|
| 2573 | for item in SHnames: |
|---|
| 2574 | L,M,N = eval(item.strip('C')) |
|---|
| 2575 | Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta) |
|---|
| 2576 | Ksl,x,x = G2lat.GetKsl(L,M,parmDict[pfx+'SHmodel'],psi,gam) |
|---|
| 2577 | Lnorm = G2lat.Lnorm(L) |
|---|
| 2578 | odfCor += parmDict[pfx+item]*Lnorm*Kcl*Ksl |
|---|
| 2579 | return odfCor |
|---|
| 2580 | |
|---|
| 2581 | def SHTXcalDerv(refl,im,g,pfx,hfx,SGData,calcControls,parmDict): |
|---|
| 2582 | 'Spherical harmonics texture derivatives' |
|---|
| 2583 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 2584 | tth = parmDict[hfx+'2-theta'] |
|---|
| 2585 | else: |
|---|
| 2586 | tth = refl[5+im] |
|---|
| 2587 | IFCoup = 'Bragg' in calcControls[hfx+'instType'] |
|---|
| 2588 | odfCor = 1.0 |
|---|
| 2589 | dFdODF = {} |
|---|
| 2590 | dFdSA = [0,0,0] |
|---|
| 2591 | H = refl[:3] |
|---|
| 2592 | cell = G2lat.Gmat2cell(g) |
|---|
| 2593 | Sangls = [parmDict[pfx+'SH omega'],parmDict[pfx+'SH chi'],parmDict[pfx+'SH phi']] |
|---|
| 2594 | Gangls = [parmDict[hfx+'Phi'],parmDict[hfx+'Chi'],parmDict[hfx+'Omega'],parmDict[hfx+'Azimuth']] |
|---|
| 2595 | phi,beta = G2lat.CrsAng(H,cell,SGData) |
|---|
| 2596 | psi,gam,dPSdA,dGMdA = G2lat.SamAng(tth/2.,Gangls,Sangls,IFCoup) |
|---|
| 2597 | SHnames = G2lat.GenSHCoeff(SGData['SGLaue'],parmDict[pfx+'SHmodel'],parmDict[pfx+'SHorder']) |
|---|
| 2598 | for item in SHnames: |
|---|
| 2599 | L,M,N = eval(item.strip('C')) |
|---|
| 2600 | Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta) |
|---|
| 2601 | Ksl,dKsdp,dKsdg = G2lat.GetKsl(L,M,parmDict[pfx+'SHmodel'],psi,gam) |
|---|
| 2602 | Lnorm = G2lat.Lnorm(L) |
|---|
| 2603 | odfCor += parmDict[pfx+item]*Lnorm*Kcl*Ksl |
|---|
| 2604 | dFdODF[pfx+item] = Lnorm*Kcl*Ksl |
|---|
| 2605 | for i in range(3): |
|---|
| 2606 | dFdSA[i] += parmDict[pfx+item]*Lnorm*Kcl*(dKsdp*dPSdA[i]+dKsdg*dGMdA[i]) |
|---|
| 2607 | return odfCor,dFdODF,dFdSA |
|---|
| 2608 | |
|---|
| 2609 | def SHPOcal(refl,im,g,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 2610 | 'spherical harmonics preferred orientation (cylindrical symmetry only)' |
|---|
| 2611 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 2612 | tth = parmDict[hfx+'2-theta'] |
|---|
| 2613 | else: |
|---|
| 2614 | tth = refl[5+im] |
|---|
| 2615 | odfCor = 1.0 |
|---|
| 2616 | H = refl[:3] |
|---|
| 2617 | cell = G2lat.Gmat2cell(g) |
|---|
| 2618 | Sangls = [0.,0.,0.] |
|---|
| 2619 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 2620 | Gangls = [0.,90.,0.,parmDict[hfx+'Azimuth']] |
|---|
| 2621 | IFCoup = True |
|---|
| 2622 | else: |
|---|
| 2623 | Gangls = [parmDict[hfx+'Phi'],parmDict[hfx+'Chi'],parmDict[hfx+'Omega'],parmDict[hfx+'Azimuth']] |
|---|
| 2624 | IFCoup = False |
|---|
| 2625 | phi,beta = G2lat.CrsAng(H,cell,SGData) |
|---|
| 2626 | psi,gam,x,x = G2lat.SamAng(tth/2.,Gangls,Sangls,IFCoup) #ignore 2 sets of angle derivs. |
|---|
| 2627 | SHnames = calcControls[phfx+'SHnames'] |
|---|
| 2628 | for item in SHnames: |
|---|
| 2629 | L,N = eval(item.strip('C')) |
|---|
| 2630 | Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta) |
|---|
| 2631 | Ksl,x,x = G2lat.GetKsl(L,0,'0',psi,gam) |
|---|
| 2632 | Lnorm = G2lat.Lnorm(L) |
|---|
| 2633 | odfCor += parmDict[phfx+item]*Lnorm*Kcl*Ksl |
|---|
| 2634 | return np.squeeze(odfCor) |
|---|
| 2635 | |
|---|
| 2636 | def SHPOcalDerv(refl,im,g,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 2637 | 'spherical harmonics preferred orientation derivatives (cylindrical symmetry only)' |
|---|
| 2638 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 2639 | tth = parmDict[hfx+'2-theta'] |
|---|
| 2640 | else: |
|---|
| 2641 | tth = refl[5+im] |
|---|
| 2642 | odfCor = 1.0 |
|---|
| 2643 | dFdODF = {} |
|---|
| 2644 | H = refl[:3] |
|---|
| 2645 | cell = G2lat.Gmat2cell(g) |
|---|
| 2646 | Sangls = [0.,0.,0.] |
|---|
| 2647 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 2648 | Gangls = [0.,90.,0.,parmDict[hfx+'Azimuth']] |
|---|
| 2649 | IFCoup = True |
|---|
| 2650 | else: |
|---|
| 2651 | Gangls = [parmDict[hfx+'Phi'],parmDict[hfx+'Chi'],parmDict[hfx+'Omega'],parmDict[hfx+'Azimuth']] |
|---|
| 2652 | IFCoup = False |
|---|
| 2653 | phi,beta = G2lat.CrsAng(H,cell,SGData) |
|---|
| 2654 | psi,gam,x,x = G2lat.SamAng(tth/2.,Gangls,Sangls,IFCoup) #ignore 2 sets of angle derivs. |
|---|
| 2655 | SHnames = calcControls[phfx+'SHnames'] |
|---|
| 2656 | for item in SHnames: |
|---|
| 2657 | L,N = eval(item.strip('C')) |
|---|
| 2658 | Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta) |
|---|
| 2659 | Ksl,x,x = G2lat.GetKsl(L,0,'0',psi,gam) |
|---|
| 2660 | Lnorm = G2lat.Lnorm(L) |
|---|
| 2661 | odfCor += parmDict[phfx+item]*Lnorm*Kcl*Ksl |
|---|
| 2662 | dFdODF[phfx+item] = Kcl*Ksl*Lnorm |
|---|
| 2663 | return odfCor,dFdODF |
|---|
| 2664 | |
|---|
| 2665 | def GetPrefOri(uniq,G,g,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 2666 | 'March-Dollase preferred orientation correction' |
|---|
| 2667 | POcorr = 1.0 |
|---|
| 2668 | MD = parmDict[phfx+'MD'] |
|---|
| 2669 | if MD != 1.0: |
|---|
| 2670 | MDAxis = calcControls[phfx+'MDAxis'] |
|---|
| 2671 | sumMD = 0 |
|---|
| 2672 | for H in uniq: |
|---|
| 2673 | cosP,sinP = G2lat.CosSinAngle(H,MDAxis,G) |
|---|
| 2674 | A = 1.0/np.sqrt((MD*cosP)**2+sinP**2/MD) |
|---|
| 2675 | sumMD += A**3 |
|---|
| 2676 | POcorr = sumMD/len(uniq) |
|---|
| 2677 | return POcorr |
|---|
| 2678 | |
|---|
| 2679 | def GetPrefOriDerv(refl,im,uniq,G,g,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 2680 | 'Needs a doc string' |
|---|
| 2681 | POcorr = 1.0 |
|---|
| 2682 | POderv = {} |
|---|
| 2683 | if calcControls[phfx+'poType'] == 'MD': |
|---|
| 2684 | MD = parmDict[phfx+'MD'] |
|---|
| 2685 | MDAxis = calcControls[phfx+'MDAxis'] |
|---|
| 2686 | sumMD = 0 |
|---|
| 2687 | sumdMD = 0 |
|---|
| 2688 | for H in uniq: |
|---|
| 2689 | cosP,sinP = G2lat.CosSinAngle(H,MDAxis,G) |
|---|
| 2690 | A = 1.0/np.sqrt((MD*cosP)**2+sinP**2/MD) |
|---|
| 2691 | sumMD += A**3 |
|---|
| 2692 | sumdMD -= (1.5*A**5)*(2.0*MD*cosP**2-(sinP/MD)**2) |
|---|
| 2693 | POcorr = sumMD/len(uniq) |
|---|
| 2694 | POderv[phfx+'MD'] = sumdMD/len(uniq) |
|---|
| 2695 | else: #spherical harmonics |
|---|
| 2696 | if calcControls[phfx+'SHord']: |
|---|
| 2697 | POcorr,POderv = SHPOcalDerv(refl,im,g,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 2698 | return POcorr,POderv |
|---|
| 2699 | |
|---|
| 2700 | def GetAbsorb(refl,im,hfx,calcControls,parmDict): |
|---|
| 2701 | 'Needs a doc string' |
|---|
| 2702 | if 'Debye' in calcControls[hfx+'instType']: |
|---|
| 2703 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 2704 | return G2pwd.Absorb('Cylinder',parmDict[hfx+'Absorption']*refl[14+im],abs(parmDict[hfx+'2-theta']),0,0) |
|---|
| 2705 | else: |
|---|
| 2706 | return G2pwd.Absorb('Cylinder',parmDict[hfx+'Absorption'],refl[5+im],0,0) |
|---|
| 2707 | else: |
|---|
| 2708 | return G2pwd.SurfaceRough(parmDict[hfx+'SurfRoughA'],parmDict[hfx+'SurfRoughB'],refl[5+im]) |
|---|
| 2709 | |
|---|
| 2710 | def GetAbsorbDerv(refl,im,hfx,calcControls,parmDict): |
|---|
| 2711 | 'Needs a doc string' |
|---|
| 2712 | if 'Debye' in calcControls[hfx+'instType']: |
|---|
| 2713 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 2714 | return G2pwd.AbsorbDerv('Cylinder',parmDict[hfx+'Absorption']*refl[14+im],abs(parmDict[hfx+'2-theta']),0,0) |
|---|
| 2715 | else: |
|---|
| 2716 | return G2pwd.AbsorbDerv('Cylinder',parmDict[hfx+'Absorption'],refl[5+im],0,0) |
|---|
| 2717 | else: |
|---|
| 2718 | return np.array(G2pwd.SurfaceRoughDerv(parmDict[hfx+'SurfRoughA'],parmDict[hfx+'SurfRoughB'],refl[5+im])) |
|---|
| 2719 | |
|---|
| 2720 | def GetPwdrExt(refl,im,pfx,phfx,hfx,calcControls,parmDict): |
|---|
| 2721 | 'Needs a doc string' |
|---|
| 2722 | coef = np.array([-0.5,0.25,-0.10416667,0.036458333,-0.0109375,2.8497409E-3]) |
|---|
| 2723 | pi2 = np.sqrt(2./np.pi) |
|---|
| 2724 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 2725 | sth2 = sind(abs(parmDict[hfx+'2-theta'])/2.)**2 |
|---|
| 2726 | wave = refl[14+im] |
|---|
| 2727 | else: #'C'W |
|---|
| 2728 | sth2 = sind(refl[5+im]/2.)**2 |
|---|
| 2729 | wave = parmDict.get(hfx+'Lam',parmDict.get(hfx+'Lam1',1.0)) |
|---|
| 2730 | c2th = 1.-2.0*sth2 |
|---|
| 2731 | flv2 = refl[9+im]*(wave/parmDict[pfx+'Vol'])**2 |
|---|
| 2732 | if 'X' in calcControls[hfx+'histType']: |
|---|
| 2733 | flv2 *= 0.079411*(1.0+c2th**2)/2.0 |
|---|
| 2734 | xfac = flv2*parmDict[phfx+'Extinction'] |
|---|
| 2735 | exb = 1.0 |
|---|
| 2736 | if xfac > -1.: |
|---|
| 2737 | exb = 1./np.sqrt(1.+xfac) |
|---|
| 2738 | exl = 1.0 |
|---|
| 2739 | if 0 < xfac <= 1.: |
|---|
| 2740 | xn = np.array([xfac**(i+1) for i in range(6)]) |
|---|
| 2741 | exl += np.sum(xn*coef) |
|---|
| 2742 | elif xfac > 1.: |
|---|
| 2743 | xfac2 = 1./np.sqrt(xfac) |
|---|
| 2744 | exl = pi2*(1.-0.125/xfac)*xfac2 |
|---|
| 2745 | return exb*sth2+exl*(1.-sth2) |
|---|
| 2746 | |
|---|
| 2747 | def GetPwdrExtDerv(refl,im,pfx,phfx,hfx,calcControls,parmDict): |
|---|
| 2748 | 'Needs a doc string' |
|---|
| 2749 | coef = np.array([-0.5,0.25,-0.10416667,0.036458333,-0.0109375,2.8497409E-3]) |
|---|
| 2750 | pi2 = np.sqrt(2./np.pi) |
|---|
| 2751 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 2752 | sth2 = sind(abs(parmDict[hfx+'2-theta'])/2.)**2 |
|---|
| 2753 | wave = refl[14+im] |
|---|
| 2754 | else: #'C'W |
|---|
| 2755 | sth2 = sind(refl[5+im]/2.)**2 |
|---|
| 2756 | wave = parmDict.get(hfx+'Lam',parmDict.get(hfx+'Lam1',1.0)) |
|---|
| 2757 | c2th = 1.-2.0*sth2 |
|---|
| 2758 | flv2 = refl[9+im]*(wave/parmDict[pfx+'Vol'])**2 |
|---|
| 2759 | if 'X' in calcControls[hfx+'histType']: |
|---|
| 2760 | flv2 *= 0.079411*(1.0+c2th**2)/2.0 |
|---|
| 2761 | xfac = flv2*parmDict[phfx+'Extinction'] |
|---|
| 2762 | dbde = -500.*flv2 |
|---|
| 2763 | if xfac > -1.: |
|---|
| 2764 | dbde = -0.5*flv2/np.sqrt(1.+xfac)**3 |
|---|
| 2765 | dlde = 0. |
|---|
| 2766 | if 0 < xfac <= 1.: |
|---|
| 2767 | xn = np.array([i*flv2*xfac**i for i in [1,2,3,4,5,6]]) |
|---|
| 2768 | dlde = np.sum(xn*coef) |
|---|
| 2769 | elif xfac > 1.: |
|---|
| 2770 | xfac2 = 1./np.sqrt(xfac) |
|---|
| 2771 | dlde = flv2*pi2*xfac2*(-1./xfac+0.375/xfac**2) |
|---|
| 2772 | |
|---|
| 2773 | return dbde*sth2+dlde*(1.-sth2) |
|---|
| 2774 | |
|---|
| 2775 | def GetIntensityCorr(refl,im,uniq,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 2776 | 'Needs a doc string' #need powder extinction! |
|---|
| 2777 | Icorr = parmDict[phfx+'Scale']*parmDict[hfx+'Scale']*refl[3+im] #scale*multiplicity |
|---|
| 2778 | if 'X' in parmDict[hfx+'Type']: |
|---|
| 2779 | Icorr *= G2pwd.Polarization(parmDict[hfx+'Polariz.'],refl[5+im],parmDict[hfx+'Azimuth'])[0] |
|---|
| 2780 | POcorr = 1.0 |
|---|
| 2781 | if pfx+'SHorder' in parmDict: #generalized spherical harmonics texture - takes precidence |
|---|
| 2782 | POcorr = SHTXcal(refl,im,g,pfx,hfx,SGData,calcControls,parmDict) |
|---|
| 2783 | elif calcControls[phfx+'poType'] == 'MD': #March-Dollase |
|---|
| 2784 | POcorr = GetPrefOri(uniq,G,g,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 2785 | elif calcControls[phfx+'SHord']: #cylindrical spherical harmonics |
|---|
| 2786 | POcorr = SHPOcal(refl,im,g,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 2787 | Icorr *= POcorr |
|---|
| 2788 | AbsCorr = 1.0 |
|---|
| 2789 | AbsCorr = GetAbsorb(refl,im,hfx,calcControls,parmDict) |
|---|
| 2790 | Icorr *= AbsCorr |
|---|
| 2791 | ExtCorr = GetPwdrExt(refl,im,pfx,phfx,hfx,calcControls,parmDict) |
|---|
| 2792 | Icorr *= ExtCorr |
|---|
| 2793 | return Icorr,POcorr,AbsCorr,ExtCorr |
|---|
| 2794 | |
|---|
| 2795 | def GetIntensityDerv(refl,im,wave,uniq,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 2796 | 'Needs a doc string' #need powder extinction derivs! |
|---|
| 2797 | dIdsh = 1./parmDict[hfx+'Scale'] |
|---|
| 2798 | dIdsp = 1./parmDict[phfx+'Scale'] |
|---|
| 2799 | if 'X' in parmDict[hfx+'Type']: |
|---|
| 2800 | pola,dIdPola = G2pwd.Polarization(parmDict[hfx+'Polariz.'],refl[5+im],parmDict[hfx+'Azimuth']) |
|---|
| 2801 | dIdPola /= pola |
|---|
| 2802 | else: #'N' |
|---|
| 2803 | dIdPola = 0.0 |
|---|
| 2804 | dFdODF = {} |
|---|
| 2805 | dFdSA = [0,0,0] |
|---|
| 2806 | dIdPO = {} |
|---|
| 2807 | if pfx+'SHorder' in parmDict: |
|---|
| 2808 | odfCor,dFdODF,dFdSA = SHTXcalDerv(refl,im,g,pfx,hfx,SGData,calcControls,parmDict) |
|---|
| 2809 | for iSH in dFdODF: |
|---|
| 2810 | dFdODF[iSH] /= odfCor |
|---|
| 2811 | for i in range(3): |
|---|
| 2812 | dFdSA[i] /= odfCor |
|---|
| 2813 | elif calcControls[phfx+'poType'] == 'MD' or calcControls[phfx+'SHord']: |
|---|
| 2814 | POcorr,dIdPO = GetPrefOriDerv(refl,im,uniq,G,g,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 2815 | for iPO in dIdPO: |
|---|
| 2816 | dIdPO[iPO] /= POcorr |
|---|
| 2817 | if 'T' in parmDict[hfx+'Type']: |
|---|
| 2818 | dFdAb = GetAbsorbDerv(refl,im,hfx,calcControls,parmDict)*wave/refl[16+im] #wave/abs corr |
|---|
| 2819 | dFdEx = GetPwdrExtDerv(refl,im,pfx,phfx,hfx,calcControls,parmDict)/refl[17+im] #/ext corr |
|---|
| 2820 | else: |
|---|
| 2821 | dFdAb = GetAbsorbDerv(refl,im,hfx,calcControls,parmDict)*wave/refl[13+im] #wave/abs corr |
|---|
| 2822 | dFdEx = GetPwdrExtDerv(refl,im,pfx,phfx,hfx,calcControls,parmDict)/refl[14+im] #/ext corr |
|---|
| 2823 | return dIdsh,dIdsp,dIdPola,dIdPO,dFdODF,dFdSA,dFdAb,dFdEx |
|---|
| 2824 | |
|---|
| 2825 | def GetSampleSigGam(refl,im,wave,G,GB,SGData,hfx,phfx,calcControls,parmDict): |
|---|
| 2826 | 'Needs a doc string' |
|---|
| 2827 | if 'C' in calcControls[hfx+'histType']: #All checked & OK |
|---|
| 2828 | costh = cosd(refl[5+im]/2.) |
|---|
| 2829 | #crystallite size |
|---|
| 2830 | if calcControls[phfx+'SizeType'] == 'isotropic': |
|---|
| 2831 | Sgam = 1.8*wave/(np.pi*parmDict[phfx+'Size;i']*costh) |
|---|
| 2832 | elif calcControls[phfx+'SizeType'] == 'uniaxial': |
|---|
| 2833 | H = np.array(refl[:3]) |
|---|
| 2834 | P = np.array(calcControls[phfx+'SizeAxis']) |
|---|
| 2835 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 2836 | Sgam = (1.8*wave/np.pi)/(parmDict[phfx+'Size;i']*parmDict[phfx+'Size;a']*costh) |
|---|
| 2837 | Sgam *= np.sqrt((sinP*parmDict[phfx+'Size;a'])**2+(cosP*parmDict[phfx+'Size;i'])**2) |
|---|
| 2838 | else: #ellipsoidal crystallites |
|---|
| 2839 | Sij =[parmDict[phfx+'Size:%d'%(i)] for i in range(6)] |
|---|
| 2840 | H = np.array(refl[:3]) |
|---|
| 2841 | lenR = G2pwd.ellipseSize(H,Sij,GB) |
|---|
| 2842 | Sgam = 1.8*wave/(np.pi*costh*lenR) |
|---|
| 2843 | #microstrain |
|---|
| 2844 | if calcControls[phfx+'MustrainType'] == 'isotropic': |
|---|
| 2845 | Mgam = 0.018*parmDict[phfx+'Mustrain;i']*tand(refl[5+im]/2.)/np.pi |
|---|
| 2846 | elif calcControls[phfx+'MustrainType'] == 'uniaxial': |
|---|
| 2847 | H = np.array(refl[:3]) |
|---|
| 2848 | P = np.array(calcControls[phfx+'MustrainAxis']) |
|---|
| 2849 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 2850 | Si = parmDict[phfx+'Mustrain;i'] |
|---|
| 2851 | Sa = parmDict[phfx+'Mustrain;a'] |
|---|
| 2852 | Mgam = 0.018*Si*Sa*tand(refl[5+im]/2.)/(np.pi*np.sqrt((Si*cosP)**2+(Sa*sinP)**2)) |
|---|
| 2853 | else: #generalized - P.W. Stephens model |
|---|
| 2854 | Strms = G2spc.MustrainCoeff(refl[:3],SGData) |
|---|
| 2855 | Sum = 0 |
|---|
| 2856 | for i,strm in enumerate(Strms): |
|---|
| 2857 | Sum += parmDict[phfx+'Mustrain;'+str(i)]*strm |
|---|
| 2858 | Mgam = 0.018*refl[4+im]**2*tand(refl[5+im]/2.)*np.sqrt(Sum)/np.pi |
|---|
| 2859 | elif 'T' in calcControls[hfx+'histType']: #All checked & OK |
|---|
| 2860 | #crystallite size |
|---|
| 2861 | if calcControls[phfx+'SizeType'] == 'isotropic': #OK |
|---|
| 2862 | Sgam = 1.e-4*parmDict[hfx+'difC']*refl[4+im]**2/parmDict[phfx+'Size;i'] |
|---|
| 2863 | elif calcControls[phfx+'SizeType'] == 'uniaxial': #OK |
|---|
| 2864 | H = np.array(refl[:3]) |
|---|
| 2865 | P = np.array(calcControls[phfx+'SizeAxis']) |
|---|
| 2866 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 2867 | Sgam = 1.e-4*parmDict[hfx+'difC']*refl[4+im]**2/(parmDict[phfx+'Size;i']*parmDict[phfx+'Size;a']) |
|---|
| 2868 | Sgam *= np.sqrt((sinP*parmDict[phfx+'Size;a'])**2+(cosP*parmDict[phfx+'Size;i'])**2) |
|---|
| 2869 | else: #ellipsoidal crystallites #OK |
|---|
| 2870 | Sij =[parmDict[phfx+'Size:%d'%(i)] for i in range(6)] |
|---|
| 2871 | H = np.array(refl[:3]) |
|---|
| 2872 | lenR = G2pwd.ellipseSize(H,Sij,GB) |
|---|
| 2873 | Sgam = 1.e-4*parmDict[hfx+'difC']*refl[4+im]**2/lenR |
|---|
| 2874 | #microstrain |
|---|
| 2875 | if calcControls[phfx+'MustrainType'] == 'isotropic': #OK |
|---|
| 2876 | Mgam = 1.e-6*parmDict[hfx+'difC']*refl[4+im]*parmDict[phfx+'Mustrain;i'] |
|---|
| 2877 | elif calcControls[phfx+'MustrainType'] == 'uniaxial': #OK |
|---|
| 2878 | H = np.array(refl[:3]) |
|---|
| 2879 | P = np.array(calcControls[phfx+'MustrainAxis']) |
|---|
| 2880 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 2881 | Si = parmDict[phfx+'Mustrain;i'] |
|---|
| 2882 | Sa = parmDict[phfx+'Mustrain;a'] |
|---|
| 2883 | Mgam = 1.e-6*parmDict[hfx+'difC']*refl[4+im]*Si*Sa/np.sqrt((Si*cosP)**2+(Sa*sinP)**2) |
|---|
| 2884 | else: #generalized - P.W. Stephens model OK |
|---|
| 2885 | Strms = G2spc.MustrainCoeff(refl[:3],SGData) |
|---|
| 2886 | Sum = 0 |
|---|
| 2887 | for i,strm in enumerate(Strms): |
|---|
| 2888 | Sum += parmDict[phfx+'Mustrain;'+str(i)]*strm |
|---|
| 2889 | Mgam = 1.e-6*parmDict[hfx+'difC']*np.sqrt(Sum)*refl[4+im]**3 |
|---|
| 2890 | |
|---|
| 2891 | gam = Sgam*parmDict[phfx+'Size;mx']+Mgam*parmDict[phfx+'Mustrain;mx'] |
|---|
| 2892 | sig = (Sgam*(1.-parmDict[phfx+'Size;mx']))**2+(Mgam*(1.-parmDict[phfx+'Mustrain;mx']))**2 |
|---|
| 2893 | sig /= ateln2 |
|---|
| 2894 | return sig,gam |
|---|
| 2895 | |
|---|
| 2896 | def GetSampleSigGamDerv(refl,im,wave,G,GB,SGData,hfx,phfx,calcControls,parmDict): |
|---|
| 2897 | 'Needs a doc string' |
|---|
| 2898 | gamDict = {} |
|---|
| 2899 | sigDict = {} |
|---|
| 2900 | if 'C' in calcControls[hfx+'histType']: #All checked & OK |
|---|
| 2901 | costh = cosd(refl[5+im]/2.) |
|---|
| 2902 | tanth = tand(refl[5+im]/2.) |
|---|
| 2903 | #crystallite size derivatives |
|---|
| 2904 | if calcControls[phfx+'SizeType'] == 'isotropic': |
|---|
| 2905 | Sgam = 1.8*wave/(np.pi*parmDict[phfx+'Size;i']*costh) |
|---|
| 2906 | gamDict[phfx+'Size;i'] = -1.8*wave*parmDict[phfx+'Size;mx']/(np.pi*costh) |
|---|
| 2907 | sigDict[phfx+'Size;i'] = -3.6*Sgam*wave*(1.-parmDict[phfx+'Size;mx'])**2/(np.pi*costh*ateln2) |
|---|
| 2908 | elif calcControls[phfx+'SizeType'] == 'uniaxial': |
|---|
| 2909 | H = np.array(refl[:3]) |
|---|
| 2910 | P = np.array(calcControls[phfx+'SizeAxis']) |
|---|
| 2911 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 2912 | Si = parmDict[phfx+'Size;i'] |
|---|
| 2913 | Sa = parmDict[phfx+'Size;a'] |
|---|
| 2914 | gami = 1.8*wave/(costh*np.pi*Si*Sa) |
|---|
| 2915 | sqtrm = np.sqrt((sinP*Sa)**2+(cosP*Si)**2) |
|---|
| 2916 | Sgam = gami*sqtrm |
|---|
| 2917 | dsi = gami*Si*cosP**2/sqtrm-Sgam/Si |
|---|
| 2918 | dsa = gami*Sa*sinP**2/sqtrm-Sgam/Sa |
|---|
| 2919 | gamDict[phfx+'Size;i'] = dsi*parmDict[phfx+'Size;mx'] |
|---|
| 2920 | gamDict[phfx+'Size;a'] = dsa*parmDict[phfx+'Size;mx'] |
|---|
| 2921 | sigDict[phfx+'Size;i'] = 2.*dsi*Sgam*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 2922 | sigDict[phfx+'Size;a'] = 2.*dsa*Sgam*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 2923 | else: #ellipsoidal crystallites |
|---|
| 2924 | const = 1.8*wave/(np.pi*costh) |
|---|
| 2925 | Sij =[parmDict[phfx+'Size:%d'%(i)] for i in range(6)] |
|---|
| 2926 | H = np.array(refl[:3]) |
|---|
| 2927 | lenR,dRdS = G2pwd.ellipseSizeDerv(H,Sij,GB) |
|---|
| 2928 | Sgam = const/lenR |
|---|
| 2929 | for i,item in enumerate([phfx+'Size:%d'%(j) for j in range(6)]): |
|---|
| 2930 | gamDict[item] = -(const/lenR**2)*dRdS[i]*parmDict[phfx+'Size;mx'] |
|---|
| 2931 | sigDict[item] = -2.*Sgam*(const/lenR**2)*dRdS[i]*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 2932 | gamDict[phfx+'Size;mx'] = Sgam |
|---|
| 2933 | sigDict[phfx+'Size;mx'] = -2.*Sgam**2*(1.-parmDict[phfx+'Size;mx'])/ateln2 |
|---|
| 2934 | |
|---|
| 2935 | #microstrain derivatives |
|---|
| 2936 | if calcControls[phfx+'MustrainType'] == 'isotropic': |
|---|
| 2937 | Mgam = 0.018*parmDict[phfx+'Mustrain;i']*tand(refl[5+im]/2.)/np.pi |
|---|
| 2938 | gamDict[phfx+'Mustrain;i'] = 0.018*tanth*parmDict[phfx+'Mustrain;mx']/np.pi |
|---|
| 2939 | sigDict[phfx+'Mustrain;i'] = 0.036*Mgam*tanth*(1.-parmDict[phfx+'Mustrain;mx'])**2/(np.pi*ateln2) |
|---|
| 2940 | elif calcControls[phfx+'MustrainType'] == 'uniaxial': |
|---|
| 2941 | H = np.array(refl[:3]) |
|---|
| 2942 | P = np.array(calcControls[phfx+'MustrainAxis']) |
|---|
| 2943 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 2944 | Si = parmDict[phfx+'Mustrain;i'] |
|---|
| 2945 | Sa = parmDict[phfx+'Mustrain;a'] |
|---|
| 2946 | gami = 0.018*Si*Sa*tanth/np.pi |
|---|
| 2947 | sqtrm = np.sqrt((Si*cosP)**2+(Sa*sinP)**2) |
|---|
| 2948 | Mgam = gami/sqtrm |
|---|
| 2949 | dsi = -gami*Si*cosP**2/sqtrm**3 |
|---|
| 2950 | dsa = -gami*Sa*sinP**2/sqtrm**3 |
|---|
| 2951 | gamDict[phfx+'Mustrain;i'] = (Mgam/Si+dsi)*parmDict[phfx+'Mustrain;mx'] |
|---|
| 2952 | gamDict[phfx+'Mustrain;a'] = (Mgam/Sa+dsa)*parmDict[phfx+'Mustrain;mx'] |
|---|
| 2953 | sigDict[phfx+'Mustrain;i'] = 2*(Mgam/Si+dsi)*Mgam*(1.-parmDict[phfx+'Mustrain;mx'])**2/ateln2 |
|---|
| 2954 | sigDict[phfx+'Mustrain;a'] = 2*(Mgam/Sa+dsa)*Mgam*(1.-parmDict[phfx+'Mustrain;mx'])**2/ateln2 |
|---|
| 2955 | else: #generalized - P.W. Stephens model |
|---|
| 2956 | const = 0.018*refl[4+im]**2*tanth/np.pi |
|---|
| 2957 | Strms = G2spc.MustrainCoeff(refl[:3],SGData) |
|---|
| 2958 | Sum = 0 |
|---|
| 2959 | for i,strm in enumerate(Strms): |
|---|
| 2960 | Sum += parmDict[phfx+'Mustrain;'+str(i)]*strm |
|---|
| 2961 | gamDict[phfx+'Mustrain;'+str(i)] = strm*parmDict[phfx+'Mustrain;mx']/2. |
|---|
| 2962 | sigDict[phfx+'Mustrain;'+str(i)] = strm*(1.-parmDict[phfx+'Mustrain;mx'])**2 |
|---|
| 2963 | Mgam = const*np.sqrt(Sum) |
|---|
| 2964 | for i in range(len(Strms)): |
|---|
| 2965 | gamDict[phfx+'Mustrain;'+str(i)] *= Mgam/Sum |
|---|
| 2966 | sigDict[phfx+'Mustrain;'+str(i)] *= const**2/ateln2 |
|---|
| 2967 | gamDict[phfx+'Mustrain;mx'] = Mgam |
|---|
| 2968 | sigDict[phfx+'Mustrain;mx'] = -2.*Mgam**2*(1.-parmDict[phfx+'Mustrain;mx'])/ateln2 |
|---|
| 2969 | else: #'T'OF - All checked & OK |
|---|
| 2970 | if calcControls[phfx+'SizeType'] == 'isotropic': #OK |
|---|
| 2971 | Sgam = 1.e-4*parmDict[hfx+'difC']*refl[4+im]**2/parmDict[phfx+'Size;i'] |
|---|
| 2972 | gamDict[phfx+'Size;i'] = -Sgam*parmDict[phfx+'Size;mx']/parmDict[phfx+'Size;i'] |
|---|
| 2973 | sigDict[phfx+'Size;i'] = -2.*Sgam**2*(1.-parmDict[phfx+'Size;mx'])**2/(ateln2*parmDict[phfx+'Size;i']) |
|---|
| 2974 | elif calcControls[phfx+'SizeType'] == 'uniaxial': #OK |
|---|
| 2975 | const = 1.e-4*parmDict[hfx+'difC']*refl[4+im]**2 |
|---|
| 2976 | H = np.array(refl[:3]) |
|---|
| 2977 | P = np.array(calcControls[phfx+'SizeAxis']) |
|---|
| 2978 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 2979 | Si = parmDict[phfx+'Size;i'] |
|---|
| 2980 | Sa = parmDict[phfx+'Size;a'] |
|---|
| 2981 | gami = const/(Si*Sa) |
|---|
| 2982 | sqtrm = np.sqrt((sinP*Sa)**2+(cosP*Si)**2) |
|---|
| 2983 | Sgam = gami*sqtrm |
|---|
| 2984 | dsi = gami*Si*cosP**2/sqtrm-Sgam/Si |
|---|
| 2985 | dsa = gami*Sa*sinP**2/sqtrm-Sgam/Sa |
|---|
| 2986 | gamDict[phfx+'Size;i'] = dsi*parmDict[phfx+'Size;mx'] |
|---|
| 2987 | gamDict[phfx+'Size;a'] = dsa*parmDict[phfx+'Size;mx'] |
|---|
| 2988 | sigDict[phfx+'Size;i'] = 2.*dsi*Sgam*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 2989 | sigDict[phfx+'Size;a'] = 2.*dsa*Sgam*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 2990 | else: #OK ellipsoidal crystallites |
|---|
| 2991 | const = 1.e-4*parmDict[hfx+'difC']*refl[4+im]**2 |
|---|
| 2992 | Sij =[parmDict[phfx+'Size:%d'%(i)] for i in range(6)] |
|---|
| 2993 | H = np.array(refl[:3]) |
|---|
| 2994 | lenR,dRdS = G2pwd.ellipseSizeDerv(H,Sij,GB) |
|---|
| 2995 | Sgam = const/lenR |
|---|
| 2996 | for i,item in enumerate([phfx+'Size:%d'%(j) for j in range(6)]): |
|---|
| 2997 | gamDict[item] = -(const/lenR**2)*dRdS[i]*parmDict[phfx+'Size;mx'] |
|---|
| 2998 | sigDict[item] = -2.*Sgam*(const/lenR**2)*dRdS[i]*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 2999 | gamDict[phfx+'Size;mx'] = Sgam #OK |
|---|
| 3000 | sigDict[phfx+'Size;mx'] = -2.*Sgam**2*(1.-parmDict[phfx+'Size;mx'])/ateln2 #OK |
|---|
| 3001 | |
|---|
| 3002 | #microstrain derivatives |
|---|
| 3003 | if calcControls[phfx+'MustrainType'] == 'isotropic': |
|---|
| 3004 | Mgam = 1.e-6*parmDict[hfx+'difC']*refl[4+im]*parmDict[phfx+'Mustrain;i'] |
|---|
| 3005 | gamDict[phfx+'Mustrain;i'] = 1.e-6*refl[4+im]*parmDict[hfx+'difC']*parmDict[phfx+'Mustrain;mx'] #OK |
|---|
| 3006 | sigDict[phfx+'Mustrain;i'] = 2.*Mgam**2*(1.-parmDict[phfx+'Mustrain;mx'])**2/(ateln2*parmDict[phfx+'Mustrain;i']) |
|---|
| 3007 | elif calcControls[phfx+'MustrainType'] == 'uniaxial': |
|---|
| 3008 | H = np.array(refl[:3]) |
|---|
| 3009 | P = np.array(calcControls[phfx+'MustrainAxis']) |
|---|
| 3010 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 3011 | Si = parmDict[phfx+'Mustrain;i'] |
|---|
| 3012 | Sa = parmDict[phfx+'Mustrain;a'] |
|---|
| 3013 | gami = 1.e-6*parmDict[hfx+'difC']*refl[4+im]*Si*Sa |
|---|
| 3014 | sqtrm = np.sqrt((Si*cosP)**2+(Sa*sinP)**2) |
|---|
| 3015 | Mgam = gami/sqtrm |
|---|
| 3016 | dsi = -gami*Si*cosP**2/sqtrm**3 |
|---|
| 3017 | dsa = -gami*Sa*sinP**2/sqtrm**3 |
|---|
| 3018 | gamDict[phfx+'Mustrain;i'] = (Mgam/Si+dsi)*parmDict[phfx+'Mustrain;mx'] |
|---|
| 3019 | gamDict[phfx+'Mustrain;a'] = (Mgam/Sa+dsa)*parmDict[phfx+'Mustrain;mx'] |
|---|
| 3020 | sigDict[phfx+'Mustrain;i'] = 2*(Mgam/Si+dsi)*Mgam*(1.-parmDict[phfx+'Mustrain;mx'])**2/ateln2 |
|---|
| 3021 | sigDict[phfx+'Mustrain;a'] = 2*(Mgam/Sa+dsa)*Mgam*(1.-parmDict[phfx+'Mustrain;mx'])**2/ateln2 |
|---|
| 3022 | else: #generalized - P.W. Stephens model OK |
|---|
| 3023 | pwrs = calcControls[phfx+'MuPwrs'] |
|---|
| 3024 | Strms = G2spc.MustrainCoeff(refl[:3],SGData) |
|---|
| 3025 | const = 1.e-6*parmDict[hfx+'difC']*refl[4+im]**3 |
|---|
| 3026 | Sum = 0 |
|---|
| 3027 | for i,strm in enumerate(Strms): |
|---|
| 3028 | Sum += parmDict[phfx+'Mustrain;'+str(i)]*strm |
|---|
| 3029 | gamDict[phfx+'Mustrain;'+str(i)] = strm*parmDict[phfx+'Mustrain;mx']/2. |
|---|
| 3030 | sigDict[phfx+'Mustrain;'+str(i)] = strm*(1.-parmDict[phfx+'Mustrain;mx'])**2 |
|---|
| 3031 | Mgam = const*np.sqrt(Sum) |
|---|
| 3032 | for i in range(len(Strms)): |
|---|
| 3033 | gamDict[phfx+'Mustrain;'+str(i)] *= Mgam/Sum |
|---|
| 3034 | sigDict[phfx+'Mustrain;'+str(i)] *= const**2/ateln2 |
|---|
| 3035 | gamDict[phfx+'Mustrain;mx'] = Mgam |
|---|
| 3036 | sigDict[phfx+'Mustrain;mx'] = -2.*Mgam**2*(1.-parmDict[phfx+'Mustrain;mx'])/ateln2 |
|---|
| 3037 | |
|---|
| 3038 | return sigDict,gamDict |
|---|
| 3039 | |
|---|
| 3040 | def GetReflPos(refl,im,wave,A,pfx,hfx,calcControls,parmDict): |
|---|
| 3041 | 'Needs a doc string' |
|---|
| 3042 | if im: |
|---|
| 3043 | h,k,l,m = refl[:4] |
|---|
| 3044 | vec = np.array([parmDict[pfx+'mV0'],parmDict[pfx+'mV1'],parmDict[pfx+'mV2']]) |
|---|
| 3045 | d = 1./np.sqrt(G2lat.calc_rDsqSS(np.array([h,k,l,m]),A,vec)) |
|---|
| 3046 | else: |
|---|
| 3047 | h,k,l = refl[:3] |
|---|
| 3048 | d = 1./np.sqrt(G2lat.calc_rDsq(np.array([h,k,l]),A)) |
|---|
| 3049 | refl[4+im] = d |
|---|
| 3050 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 3051 | pos = 2.0*asind(wave/(2.0*d))+parmDict[hfx+'Zero'] |
|---|
| 3052 | const = 9.e-2/(np.pi*parmDict[hfx+'Gonio. radius']) #shifts in microns |
|---|
| 3053 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 3054 | pos -= const*(4.*parmDict[hfx+'Shift']*cosd(pos/2.0)+ \ |
|---|
| 3055 | parmDict[hfx+'Transparency']*sind(pos)*100.0) #trans(=1/mueff) in cm |
|---|
| 3056 | else: #Debye-Scherrer - simple but maybe not right |
|---|
| 3057 | pos -= const*(parmDict[hfx+'DisplaceX']*cosd(pos)+parmDict[hfx+'DisplaceY']*sind(pos)) |
|---|
| 3058 | elif 'T' in calcControls[hfx+'histType']: |
|---|
| 3059 | pos = parmDict[hfx+'difC']*d+parmDict[hfx+'difA']*d**2+parmDict[hfx+'difB']/d+parmDict[hfx+'Zero'] |
|---|
| 3060 | #do I need sample position effects - maybe? |
|---|
| 3061 | return pos |
|---|
| 3062 | |
|---|
| 3063 | def GetReflPosDerv(refl,im,wave,A,pfx,hfx,calcControls,parmDict): |
|---|
| 3064 | 'Needs a doc string' |
|---|
| 3065 | dpr = 180./np.pi |
|---|
| 3066 | if im: |
|---|
| 3067 | h,k,l,m = refl[:4] |
|---|
| 3068 | vec = np.array([parmDict[pfx+'mV0'],parmDict[pfx+'mV1'],parmDict[pfx+'mV2']]) |
|---|
| 3069 | dstsq = G2lat.calc_rDsqSS(np.array([h,k,l,m]),A,vec) |
|---|
| 3070 | h,k,l = [h+m*vec[0],k+m*vec[1],l+m*vec[2]] #do proj of hklm to hkl so dPdA & dPdV come out right |
|---|
| 3071 | else: |
|---|
| 3072 | m = 0 |
|---|
| 3073 | h,k,l = refl[:3] |
|---|
| 3074 | dstsq = G2lat.calc_rDsq(np.array([h,k,l]),A) |
|---|
| 3075 | dst = np.sqrt(dstsq) |
|---|
| 3076 | dsp = 1./dst |
|---|
| 3077 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 3078 | pos = refl[5+im]-parmDict[hfx+'Zero'] |
|---|
| 3079 | const = dpr/np.sqrt(1.0-wave**2*dstsq/4.0) |
|---|
| 3080 | dpdw = const*dst |
|---|
| 3081 | dpdA = np.array([h**2,k**2,l**2,h*k,h*l,k*l])*const*wave/(2.0*dst) |
|---|
| 3082 | dpdZ = 1.0 |
|---|
| 3083 | dpdV = np.array([2.*h*A[0]+k*A[3]+l*A[4],2*k*A[1]+h*A[3]+l*A[5], |
|---|
| 3084 | 2*l*A[2]+h*A[4]+k*A[5]])*m*const*wave/(2.0*dst) |
|---|
| 3085 | shft = 9.e-2/(np.pi*parmDict[hfx+'Gonio. radius']) #shifts in microns |
|---|
| 3086 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 3087 | dpdSh = -4.*shft*cosd(pos/2.0) |
|---|
| 3088 | dpdTr = -shft*sind(pos)*100.0 |
|---|
| 3089 | return dpdA,dpdw,dpdZ,dpdSh,dpdTr,0.,0.,dpdV |
|---|
| 3090 | else: #Debye-Scherrer - simple but maybe not right |
|---|
| 3091 | dpdXd = -shft*cosd(pos) |
|---|
| 3092 | dpdYd = -shft*sind(pos) |
|---|
| 3093 | return dpdA,dpdw,dpdZ,0.,0.,dpdXd,dpdYd,dpdV |
|---|
| 3094 | elif 'T' in calcControls[hfx+'histType']: |
|---|
| 3095 | dpdA = -np.array([h**2,k**2,l**2,h*k,h*l,k*l])*parmDict[hfx+'difC']*dsp**3/2. |
|---|
| 3096 | dpdZ = 1.0 |
|---|
| 3097 | dpdDC = dsp |
|---|
| 3098 | dpdDA = dsp**2 |
|---|
| 3099 | dpdDB = 1./dsp |
|---|
| 3100 | dpdV = np.array([2.*h*A[0]+k*A[3]+l*A[4],2*k*A[1]+h*A[3]+l*A[5], |
|---|
| 3101 | 2*l*A[2]+h*A[4]+k*A[5]])*m*parmDict[hfx+'difC']*dsp**3/2. |
|---|
| 3102 | return dpdA,dpdZ,dpdDC,dpdDA,dpdDB,dpdV |
|---|
| 3103 | |
|---|
| 3104 | def GetHStrainShift(refl,im,SGData,phfx,hfx,calcControls,parmDict): |
|---|
| 3105 | 'Needs a doc string' |
|---|
| 3106 | laue = SGData['SGLaue'] |
|---|
| 3107 | uniq = SGData['SGUniq'] |
|---|
| 3108 | h,k,l = refl[:3] |
|---|
| 3109 | if laue in ['m3','m3m']: |
|---|
| 3110 | Dij = parmDict[phfx+'D11']*(h**2+k**2+l**2)+ \ |
|---|
| 3111 | refl[4+im]**2*parmDict[phfx+'eA']*((h*k)**2+(h*l)**2+(k*l)**2)/(h**2+k**2+l**2)**2 |
|---|
| 3112 | elif laue in ['6/m','6/mmm','3m1','31m','3']: |
|---|
| 3113 | Dij = parmDict[phfx+'D11']*(h**2+k**2+h*k)+parmDict[phfx+'D33']*l**2 |
|---|
| 3114 | elif laue in ['3R','3mR']: |
|---|
| 3115 | Dij = parmDict[phfx+'D11']*(h**2+k**2+l**2)+parmDict[phfx+'D12']*(h*k+h*l+k*l) |
|---|
| 3116 | elif laue in ['4/m','4/mmm']: |
|---|
| 3117 | Dij = parmDict[phfx+'D11']*(h**2+k**2)+parmDict[phfx+'D33']*l**2 |
|---|
| 3118 | elif laue in ['mmm']: |
|---|
| 3119 | Dij = parmDict[phfx+'D11']*h**2+parmDict[phfx+'D22']*k**2+parmDict[phfx+'D33']*l**2 |
|---|
| 3120 | elif laue in ['2/m']: |
|---|
| 3121 | Dij = parmDict[phfx+'D11']*h**2+parmDict[phfx+'D22']*k**2+parmDict[phfx+'D33']*l**2 |
|---|
| 3122 | if uniq == 'a': |
|---|
| 3123 | Dij += parmDict[phfx+'D23']*k*l |
|---|
| 3124 | elif uniq == 'b': |
|---|
| 3125 | Dij += parmDict[phfx+'D13']*h*l |
|---|
| 3126 | elif uniq == 'c': |
|---|
| 3127 | Dij += parmDict[phfx+'D12']*h*k |
|---|
| 3128 | else: |
|---|
| 3129 | Dij = parmDict[phfx+'D11']*h**2+parmDict[phfx+'D22']*k**2+parmDict[phfx+'D33']*l**2+ \ |
|---|
| 3130 | parmDict[phfx+'D12']*h*k+parmDict[phfx+'D13']*h*l+parmDict[phfx+'D23']*k*l |
|---|
| 3131 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 3132 | return -180.*Dij*refl[4+im]**2*tand(refl[5+im]/2.0)/np.pi |
|---|
| 3133 | else: |
|---|
| 3134 | return -Dij*parmDict[hfx+'difC']*refl[4+im]**2/2. |
|---|
| 3135 | |
|---|
| 3136 | def GetHStrainShiftDerv(refl,im,SGData,phfx,hfx,calcControls,parmDict): |
|---|
| 3137 | 'Needs a doc string' |
|---|
| 3138 | laue = SGData['SGLaue'] |
|---|
| 3139 | uniq = SGData['SGUniq'] |
|---|
| 3140 | h,k,l = refl[:3] |
|---|
| 3141 | if laue in ['m3','m3m']: |
|---|
| 3142 | dDijDict = {phfx+'D11':h**2+k**2+l**2, |
|---|
| 3143 | phfx+'eA':refl[4+im]**2*((h*k)**2+(h*l)**2+(k*l)**2)/(h**2+k**2+l**2)**2} |
|---|
| 3144 | elif laue in ['6/m','6/mmm','3m1','31m','3']: |
|---|
| 3145 | dDijDict = {phfx+'D11':h**2+k**2+h*k,phfx+'D33':l**2} |
|---|
| 3146 | elif laue in ['3R','3mR']: |
|---|
| 3147 | dDijDict = {phfx+'D11':h**2+k**2+l**2,phfx+'D12':h*k+h*l+k*l} |
|---|
| 3148 | elif laue in ['4/m','4/mmm']: |
|---|
| 3149 | dDijDict = {phfx+'D11':h**2+k**2,phfx+'D33':l**2} |
|---|
| 3150 | elif laue in ['mmm']: |
|---|
| 3151 | dDijDict = {phfx+'D11':h**2,phfx+'D22':k**2,phfx+'D33':l**2} |
|---|
| 3152 | elif laue in ['2/m']: |
|---|
| 3153 | dDijDict = {phfx+'D11':h**2,phfx+'D22':k**2,phfx+'D33':l**2} |
|---|
| 3154 | if uniq == 'a': |
|---|
| 3155 | dDijDict[phfx+'D23'] = k*l |
|---|
| 3156 | elif uniq == 'b': |
|---|
| 3157 | dDijDict[phfx+'D13'] = h*l |
|---|
| 3158 | elif uniq == 'c': |
|---|
| 3159 | dDijDict[phfx+'D12'] = h*k |
|---|
| 3160 | else: |
|---|
| 3161 | dDijDict = {phfx+'D11':h**2,phfx+'D22':k**2,phfx+'D33':l**2, |
|---|
| 3162 | phfx+'D12':h*k,phfx+'D13':h*l,phfx+'D23':k*l} |
|---|
| 3163 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 3164 | for item in dDijDict: |
|---|
| 3165 | dDijDict[item] *= 180.0*refl[4+im]**2*tand(refl[5+im]/2.0)/np.pi |
|---|
| 3166 | else: |
|---|
| 3167 | for item in dDijDict: |
|---|
| 3168 | dDijDict[item] *= -parmDict[hfx+'difC']*refl[4+im]**3/2. |
|---|
| 3169 | return dDijDict |
|---|
| 3170 | |
|---|
| 3171 | def GetDij(phfx,SGData,parmDict): |
|---|
| 3172 | HSvals = [parmDict[phfx+name] for name in G2spc.HStrainNames(SGData)] |
|---|
| 3173 | return G2spc.HStrainVals(HSvals,SGData) |
|---|
| 3174 | |
|---|
| 3175 | def GetFobsSq(Histograms,Phases,parmDict,calcControls): |
|---|
| 3176 | 'Needs a doc string' |
|---|
| 3177 | histoList = Histograms.keys() |
|---|
| 3178 | histoList.sort() |
|---|
| 3179 | for histogram in histoList: |
|---|
| 3180 | if 'PWDR' in histogram[:4]: |
|---|
| 3181 | Histogram = Histograms[histogram] |
|---|
| 3182 | hId = Histogram['hId'] |
|---|
| 3183 | hfx = ':%d:'%(hId) |
|---|
| 3184 | Limits = calcControls[hfx+'Limits'] |
|---|
| 3185 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 3186 | shl = max(parmDict[hfx+'SH/L'],0.0005) |
|---|
| 3187 | Ka2 = False |
|---|
| 3188 | kRatio = 0.0 |
|---|
| 3189 | if hfx+'Lam1' in parmDict.keys(): |
|---|
| 3190 | Ka2 = True |
|---|
| 3191 | lamRatio = 360*(parmDict[hfx+'Lam2']-parmDict[hfx+'Lam1'])/(np.pi*parmDict[hfx+'Lam1']) |
|---|
| 3192 | kRatio = parmDict[hfx+'I(L2)/I(L1)'] |
|---|
| 3193 | x,y,w,yc,yb,yd = Histogram['Data'] |
|---|
| 3194 | xMask = ma.getmaskarray(x) |
|---|
| 3195 | xB = np.searchsorted(x,Limits[0]) |
|---|
| 3196 | xF = np.searchsorted(x,Limits[1]) |
|---|
| 3197 | ymb = np.array(y-yb) |
|---|
| 3198 | ymb = np.where(ymb,ymb,1.0) |
|---|
| 3199 | ycmb = np.array(yc-yb) |
|---|
| 3200 | ratio = 1./np.where(ycmb,ycmb/ymb,1.e10) |
|---|
| 3201 | refLists = Histogram['Reflection Lists'] |
|---|
| 3202 | for phase in refLists: |
|---|
| 3203 | if phase not in Phases: #skips deleted or renamed phases silently! |
|---|
| 3204 | continue |
|---|
| 3205 | Phase = Phases[phase] |
|---|
| 3206 | im = 0 |
|---|
| 3207 | if Phase['General'].get('Modulated',False): |
|---|
| 3208 | im = 1 |
|---|
| 3209 | pId = Phase['pId'] |
|---|
| 3210 | phfx = '%d:%d:'%(pId,hId) |
|---|
| 3211 | refDict = refLists[phase] |
|---|
| 3212 | sumFo = 0.0 |
|---|
| 3213 | sumdF = 0.0 |
|---|
| 3214 | sumFosq = 0.0 |
|---|
| 3215 | sumdFsq = 0.0 |
|---|
| 3216 | sumInt = 0.0 |
|---|
| 3217 | nExcl = 0 |
|---|
| 3218 | for refl in refDict['RefList']: |
|---|
| 3219 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 3220 | yp = np.zeros_like(yb) |
|---|
| 3221 | Wd,fmin,fmax = G2pwd.getWidthsCW(refl[5+im],refl[6+im],refl[7+im],shl) |
|---|
| 3222 | iBeg = max(xB,np.searchsorted(x,refl[5+im]-fmin)) |
|---|
| 3223 | iFin = max(xB,min(np.searchsorted(x,refl[5+im]+fmax),xF)) |
|---|
| 3224 | iFin2 = iFin |
|---|
| 3225 | if not iBeg+iFin: #peak below low limit - skip peak |
|---|
| 3226 | continue |
|---|
| 3227 | if ma.all(xMask[iBeg:iFin]): #peak entirely masked - skip peak |
|---|
| 3228 | refl[3+im] *= -1 |
|---|
| 3229 | nExcl += 1 |
|---|
| 3230 | continue |
|---|
| 3231 | elif not iBeg-iFin: #peak above high limit - done |
|---|
| 3232 | break |
|---|
| 3233 | elif iBeg < iFin: |
|---|
| 3234 | yp[iBeg:iFin] = refl[11+im]*refl[9+im]*G2pwd.getFCJVoigt3(refl[5+im],refl[6+im],refl[7+im],shl,ma.getdata(x[iBeg:iFin])) #>90% of time spent here |
|---|
| 3235 | sumInt += refl[11+im]*refl[9+im] |
|---|
| 3236 | if Ka2: |
|---|
| 3237 | pos2 = refl[5+im]+lamRatio*tand(refl[5+im]/2.0) # + 360/pi * Dlam/lam * tan(th) |
|---|
| 3238 | Wd,fmin,fmax = G2pwd.getWidthsCW(pos2,refl[6+im],refl[7+im],shl) |
|---|
| 3239 | iBeg2 = max(xB,np.searchsorted(x,pos2-fmin)) |
|---|
| 3240 | iFin2 = min(np.searchsorted(x,pos2+fmax),xF) |
|---|
| 3241 | if iFin2 > iBeg2: |
|---|
| 3242 | yp[iBeg2:iFin2] += refl[11+im]*refl[9+im]*kRatio*G2pwd.getFCJVoigt3(pos2,refl[6+im],refl[7+im],shl,ma.getdata(x[iBeg2:iFin2])) #and here |
|---|
| 3243 | sumInt += refl[11+im]*refl[9+im]*kRatio |
|---|
| 3244 | refl[8+im] = np.sum(np.where(ratio[iBeg:iFin2]>0.,yp[iBeg:iFin2]*ratio[iBeg:iFin2]/(refl[11+im]*(1.+kRatio)),0.0)) |
|---|
| 3245 | |
|---|
| 3246 | elif 'T' in calcControls[hfx+'histType']: |
|---|
| 3247 | yp = np.zeros_like(yb) |
|---|
| 3248 | Wd,fmin,fmax = G2pwd.getWidthsTOF(refl[5+im],refl[12+im],refl[13+im],refl[6+im],refl[7+im]) |
|---|
| 3249 | iBeg = max(xB,np.searchsorted(x,refl[5+im]-fmin)) |
|---|
| 3250 | iFin = max(xB,min(np.searchsorted(x,refl[5+im]+fmax),xF)) |
|---|
| 3251 | if not iBeg+iFin: #peak below low limit - skip peak |
|---|
| 3252 | continue |
|---|
| 3253 | if ma.all(xMask[iBeg:iFin]): #peak entirely masked - skip peak |
|---|
| 3254 | refl[3+im] *= -1 |
|---|
| 3255 | nExcl += 1 |
|---|
| 3256 | continue |
|---|
| 3257 | elif not iBeg-iFin: #peak above high limit - done |
|---|
| 3258 | break |
|---|
| 3259 | if iBeg < iFin: |
|---|
| 3260 | yp[iBeg:iFin] = refl[11+im]*refl[9+im]*G2pwd.getEpsVoigt(refl[5+im],refl[12+im],refl[13+im],refl[6+im],refl[7+im],ma.getdata(x[iBeg:iFin])) #>90% of time spent here |
|---|
| 3261 | refl[8+im] = np.sum(np.where(ratio[iBeg:iFin]>0.,yp[iBeg:iFin]*ratio[iBeg:iFin]/refl[11+im],0.0)) |
|---|
| 3262 | sumInt += refl[11+im]*refl[9+im] |
|---|
| 3263 | Fo = np.sqrt(np.abs(refl[8+im])) |
|---|
| 3264 | Fc = np.sqrt(np.abs(refl[9]+im)) |
|---|
| 3265 | sumFo += Fo |
|---|
| 3266 | sumFosq += refl[8+im]**2 |
|---|
| 3267 | sumdF += np.abs(Fo-Fc) |
|---|
| 3268 | sumdFsq += (refl[8+im]-refl[9+im])**2 |
|---|
| 3269 | if sumFo: |
|---|
| 3270 | Histogram['Residuals'][phfx+'Rf'] = min(100.,(sumdF/sumFo)*100.) |
|---|
| 3271 | Histogram['Residuals'][phfx+'Rf^2'] = min(100.,np.sqrt(sumdFsq/sumFosq)*100.) |
|---|
| 3272 | else: |
|---|
| 3273 | Histogram['Residuals'][phfx+'Rf'] = 100. |
|---|
| 3274 | Histogram['Residuals'][phfx+'Rf^2'] = 100. |
|---|
| 3275 | Histogram['Residuals'][phfx+'sumInt'] = sumInt |
|---|
| 3276 | Histogram['Residuals'][phfx+'Nref'] = len(refDict['RefList'])-nExcl |
|---|
| 3277 | Histogram['Residuals']['hId'] = hId |
|---|
| 3278 | elif 'HKLF' in histogram[:4]: |
|---|
| 3279 | Histogram = Histograms[histogram] |
|---|
| 3280 | Histogram['Residuals']['hId'] = Histograms[histogram]['hId'] |
|---|
| 3281 | |
|---|
| 3282 | def getPowderProfile(parmDict,x,varylist,Histogram,Phases,calcControls,pawleyLookup): |
|---|
| 3283 | 'Needs a doc string' |
|---|
| 3284 | |
|---|
| 3285 | def GetReflSigGamCW(refl,im,wave,G,GB,phfx,calcControls,parmDict): |
|---|
| 3286 | U = parmDict[hfx+'U'] |
|---|
| 3287 | V = parmDict[hfx+'V'] |
|---|
| 3288 | W = parmDict[hfx+'W'] |
|---|
| 3289 | X = parmDict[hfx+'X'] |
|---|
| 3290 | Y = parmDict[hfx+'Y'] |
|---|
| 3291 | tanPos = tand(refl[5+im]/2.0) |
|---|
| 3292 | Ssig,Sgam = GetSampleSigGam(refl,im,wave,G,GB,SGData,hfx,phfx,calcControls,parmDict) |
|---|
| 3293 | sig = U*tanPos**2+V*tanPos+W+Ssig #save peak sigma |
|---|
| 3294 | sig = max(0.001,sig) |
|---|
| 3295 | gam = X/cosd(refl[5+im]/2.0)+Y*tanPos+Sgam #save peak gamma |
|---|
| 3296 | gam = max(0.001,gam) |
|---|
| 3297 | return sig,gam |
|---|
| 3298 | |
|---|
| 3299 | def GetReflSigGamTOF(refl,im,G,GB,phfx,calcControls,parmDict): |
|---|
| 3300 | sig = parmDict[hfx+'sig-0']+parmDict[hfx+'sig-1']*refl[4+im]**2+ \ |
|---|
| 3301 | parmDict[hfx+'sig-2']*refl[4+im]**4+parmDict[hfx+'sig-q']/refl[4+im]**2 |
|---|
| 3302 | gam = parmDict[hfx+'X']*refl[4+im]+parmDict[hfx+'Y']*refl[4+im]**2 |
|---|
| 3303 | Ssig,Sgam = GetSampleSigGam(refl,im,0.0,G,GB,SGData,hfx,phfx,calcControls,parmDict) |
|---|
| 3304 | sig += Ssig |
|---|
| 3305 | gam += Sgam |
|---|
| 3306 | return sig,gam |
|---|
| 3307 | |
|---|
| 3308 | def GetReflAlpBet(refl,im,hfx,parmDict): |
|---|
| 3309 | alp = parmDict[hfx+'alpha']/refl[4+im] |
|---|
| 3310 | bet = parmDict[hfx+'beta-0']+parmDict[hfx+'beta-1']/refl[4+im]**4+parmDict[hfx+'beta-q']/refl[4+im]** |
|---|
