| 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: 2015-06-02 20:24:09 +0000 (Tue, 02 Jun 2015) $ |
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| 8 | # $Author: vondreele $ |
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| 9 | # $Revision: 1877 $ |
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| 10 | # $URL: trunk/GSASIIstrMath.py $ |
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| 11 | # $Id: GSASIIstrMath.py 1877 2015-06-02 20:24:09Z vondreele $ |
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| 12 | ########### SVN repository information ################### |
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| 13 | import time |
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| 14 | import math |
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| 15 | import copy |
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| 16 | import numpy as np |
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| 17 | import numpy.ma as ma |
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| 18 | import numpy.linalg as nl |
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| 19 | import scipy.optimize as so |
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| 20 | import scipy.stats as st |
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| 21 | import GSASIIpath |
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| 22 | GSASIIpath.SetVersionNumber("$Revision: 1877 $") |
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| 23 | import GSASIIElem as G2el |
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| 24 | import GSASIIlattice as G2lat |
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| 25 | import GSASIIspc as G2spc |
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| 26 | import GSASIIpwd as G2pwd |
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| 27 | import GSASIImapvars as G2mv |
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| 28 | import GSASIImath as G2mth |
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| 29 | import GSASIIobj as G2obj |
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| 30 | |
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| 31 | sind = lambda x: np.sin(x*np.pi/180.) |
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| 32 | cosd = lambda x: np.cos(x*np.pi/180.) |
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| 33 | tand = lambda x: np.tan(x*np.pi/180.) |
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| 34 | asind = lambda x: 180.*np.arcsin(x)/np.pi |
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| 35 | acosd = lambda x: 180.*np.arccos(x)/np.pi |
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| 36 | atan2d = lambda y,x: 180.*np.arctan2(y,x)/np.pi |
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| 37 | |
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| 38 | ateln2 = 8.0*math.log(2.0) |
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| 39 | twopi = 2.0*np.pi |
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| 40 | twopisq = 2.0*np.pi**2 |
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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 | keys = {'Atype:':Tdata,'Amul:':Mdata,'Afrac:':Fdata,'AI/A:':IAdata, |
|---|
| 596 | 'dAx:':dXdata[0],'dAy:':dXdata[1],'dAz:':dXdata[2], |
|---|
| 597 | 'Ax:':Xdata[0],'Ay:':Xdata[1],'Az:':Xdata[2],'AUiso:':Uisodata, |
|---|
| 598 | 'AU11:':Uijdata[0],'AU22:':Uijdata[1],'AU33:':Uijdata[2], |
|---|
| 599 | 'AU12:':Uijdata[3],'AU13:':Uijdata[4],'AU23:':Uijdata[5]} |
|---|
| 600 | for iatm in range(Natoms): |
|---|
| 601 | for key in keys: |
|---|
| 602 | parm = pfx+key+str(iatm) |
|---|
| 603 | if parm in parmDict: |
|---|
| 604 | keys[key][iatm] = parmDict[parm] |
|---|
| 605 | Fdata = np.where(Fdata,Fdata,1.e-8) #avoid divide by zero in derivative calc.? |
|---|
| 606 | return Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata |
|---|
| 607 | |
|---|
| 608 | def GetAtomSSFXU(pfx,calcControls,parmDict): |
|---|
| 609 | 'Needs a doc string' |
|---|
| 610 | Natoms = calcControls['Natoms'][pfx] |
|---|
| 611 | maxSSwave = calcControls['maxSSwave'][pfx] |
|---|
| 612 | Nwave = {'F':maxSSwave['Sfrac'],'X':maxSSwave['Spos'],'Y':maxSSwave['Spos'],'Z':maxSSwave['Spos'], |
|---|
| 613 | 'U':maxSSwave['Sadp'],'M':maxSSwave['Smag'],'T':maxSSwave['Spos']} |
|---|
| 614 | XSSdata = np.zeros((6,maxSSwave['Spos'],Natoms)) |
|---|
| 615 | FSSdata = np.zeros((2,maxSSwave['Sfrac'],Natoms)) |
|---|
| 616 | USSdata = np.zeros((12,maxSSwave['Sadp'],Natoms)) |
|---|
| 617 | MSSdata = np.zeros((6,maxSSwave['Smag'],Natoms)) |
|---|
| 618 | waveTypes = [] |
|---|
| 619 | keys = {'Fsin:':FSSdata[0],'Fcos:':FSSdata[1],'Fzero:':FSSdata[0],'Fwid:':FSSdata[1], |
|---|
| 620 | 'Tzero:':XSSdata[0],'Xslope:':XSSdata[1],'Yslope:':XSSdata[2],'Zslope:':XSSdata[3], |
|---|
| 621 | 'Xsin:':XSSdata[0],'Ysin:':XSSdata[1],'Zsin:':XSSdata[2],'Xcos:':XSSdata[3],'Ycos:':XSSdata[4],'Zcos:':XSSdata[5], |
|---|
| 622 | 'U11sin:':USSdata[0],'U22sin:':USSdata[1],'U33sin:':USSdata[2],'U12sin:':USSdata[3],'U13sin:':USSdata[4],'U23sin:':USSdata[5], |
|---|
| 623 | 'U11cos:':USSdata[6],'U22cos:':USSdata[7],'U33cos:':USSdata[8],'U12cos:':USSdata[9],'U13cos:':USSdata[10],'U23cos:':USSdata[11], |
|---|
| 624 | 'MXsin:':MSSdata[0],'MYsin:':MSSdata[1],'MZsin:':MSSdata[2],'MXcos:':MSSdata[3],'MYcos:':MSSdata[4],'MZcos:':MSSdata[5]} |
|---|
| 625 | for iatm in range(Natoms): |
|---|
| 626 | waveTypes.append(parmDict[pfx+'waveType:'+str(iatm)]) |
|---|
| 627 | for key in keys: |
|---|
| 628 | for m in range(Nwave[key[0]]): |
|---|
| 629 | parm = pfx+key+str(iatm)+':%d'%(m) |
|---|
| 630 | if parm in parmDict: |
|---|
| 631 | keys[key][m][iatm] = parmDict[parm] |
|---|
| 632 | return waveTypes,FSSdata.squeeze(),XSSdata.squeeze(),USSdata.squeeze(),MSSdata.squeeze() |
|---|
| 633 | |
|---|
| 634 | def StructureFactor(refDict,G,hfx,pfx,SGData,calcControls,parmDict): |
|---|
| 635 | ''' Not Used: here only for comparison the StructureFactor2 - faster version |
|---|
| 636 | Compute structure factors for all h,k,l for phase |
|---|
| 637 | puts the result, F^2, in each ref[8] in refList |
|---|
| 638 | input: |
|---|
| 639 | |
|---|
| 640 | :param dict refDict: where |
|---|
| 641 | 'RefList' list where each ref = h,k,l,m,d,... |
|---|
| 642 | 'FF' dict of form factors - filed in below |
|---|
| 643 | :param np.array G: reciprocal metric tensor |
|---|
| 644 | :param str pfx: phase id string |
|---|
| 645 | :param dict SGData: space group info. dictionary output from SpcGroup |
|---|
| 646 | :param dict calcControls: |
|---|
| 647 | :param dict ParmDict: |
|---|
| 648 | |
|---|
| 649 | ''' |
|---|
| 650 | phfx = pfx.split(':')[0]+hfx |
|---|
| 651 | ast = np.sqrt(np.diag(G)) |
|---|
| 652 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 653 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 654 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 655 | FFtables = calcControls['FFtables'] |
|---|
| 656 | BLtables = calcControls['BLtables'] |
|---|
| 657 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata = GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 658 | FF = np.zeros(len(Tdata)) |
|---|
| 659 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 660 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 661 | else: |
|---|
| 662 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 663 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 664 | Uij = np.array(G2lat.U6toUij(Uijdata)) |
|---|
| 665 | bij = Mast*Uij.T |
|---|
| 666 | if not len(refDict['FF']): |
|---|
| 667 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 668 | dat = G2el.getBLvalues(BLtables) #will need wave here for anom. neutron b's |
|---|
| 669 | else: |
|---|
| 670 | dat = G2el.getFFvalues(FFtables,0.) |
|---|
| 671 | refDict['FF']['El'] = dat.keys() |
|---|
| 672 | refDict['FF']['FF'] = np.zeros((len(refDict['RefList']),len(dat))) |
|---|
| 673 | for iref,refl in enumerate(refDict['RefList']): |
|---|
| 674 | if 'NT' in calcControls[hfx+'histType']: |
|---|
| 675 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,refl[14]) |
|---|
| 676 | fbs = np.array([0,0]) |
|---|
| 677 | H = refl[:3] |
|---|
| 678 | SQ = 1./(2.*refl[4])**2 |
|---|
| 679 | SQfactor = 4.0*SQ*twopisq |
|---|
| 680 | Bab = parmDict[phfx+'BabA']*np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 681 | if not np.any(refDict['FF']['FF'][iref]): #no form factors - 1st time thru StructureFactor |
|---|
| 682 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 683 | dat = G2el.getBLvalues(BLtables) |
|---|
| 684 | refDict['FF']['FF'][iref] = dat.values() |
|---|
| 685 | else: #'X' |
|---|
| 686 | dat = G2el.getFFvalues(FFtables,SQ) |
|---|
| 687 | refDict['FF']['FF'][iref] = dat.values() |
|---|
| 688 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 689 | FF = refDict['FF']['FF'][iref][Tindx] |
|---|
| 690 | Uniq = np.inner(H,SGMT) |
|---|
| 691 | Phi = np.inner(H,SGT) |
|---|
| 692 | phase = twopi*(np.inner(Uniq,(dXdata.T+Xdata.T))+Phi[:,np.newaxis]) |
|---|
| 693 | sinp = np.sin(phase) |
|---|
| 694 | cosp = np.cos(phase) |
|---|
| 695 | biso = -SQfactor*Uisodata |
|---|
| 696 | Tiso = np.where(biso<1.,np.exp(biso),1.0) |
|---|
| 697 | HbH = np.array([-np.inner(h,np.inner(bij,h)) for h in Uniq]) |
|---|
| 698 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0) |
|---|
| 699 | Tcorr = Tiso*Tuij*Mdata*Fdata/len(Uniq) |
|---|
| 700 | fa = np.array([(FF+FP-Bab)*cosp*Tcorr,-FPP*sinp*Tcorr]) |
|---|
| 701 | fas = np.sum(np.sum(fa,axis=1),axis=1) #real |
|---|
| 702 | if not SGData['SGInv']: |
|---|
| 703 | fb = np.array([(FF+FP-Bab)*sinp*Tcorr,FPP*cosp*Tcorr]) |
|---|
| 704 | fbs = np.sum(np.sum(fb,axis=1),axis=1) |
|---|
| 705 | fasq = fas**2 |
|---|
| 706 | fbsq = fbs**2 #imaginary |
|---|
| 707 | refl[9] = np.sum(fasq)+np.sum(fbsq) |
|---|
| 708 | refl[10] = atan2d(fbs[0],fas[0]) |
|---|
| 709 | |
|---|
| 710 | def SStructureFactor(refDict,im,G,hfx,pfx,SGData,SSGData,calcControls,parmDict): |
|---|
| 711 | ''' |
|---|
| 712 | Compute super structure factors for all h,k,l,m for phase |
|---|
| 713 | puts the result, F^2, in each ref[8+im] in refList |
|---|
| 714 | input: |
|---|
| 715 | |
|---|
| 716 | :param dict refDict: where |
|---|
| 717 | 'RefList' list where each ref = h,k,l,m,d,... |
|---|
| 718 | 'FF' dict of form factors - filed in below |
|---|
| 719 | :param np.array G: reciprocal metric tensor |
|---|
| 720 | :param str pfx: phase id string |
|---|
| 721 | :param dict SGData: space group info. dictionary output from SpcGroup |
|---|
| 722 | :param dict calcControls: |
|---|
| 723 | :param dict ParmDict: |
|---|
| 724 | |
|---|
| 725 | ''' |
|---|
| 726 | phfx = pfx.split(':')[0]+hfx |
|---|
| 727 | ast = np.sqrt(np.diag(G)) |
|---|
| 728 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 729 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 730 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 731 | SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']]) |
|---|
| 732 | SSGT = np.array([ops[1] for ops in SSGData['SSGOps']]) |
|---|
| 733 | FFtables = calcControls['FFtables'] |
|---|
| 734 | BLtables = calcControls['BLtables'] |
|---|
| 735 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata = GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 736 | waveTypes,FSSdata,XSSdata,USSdata,MSSdata = GetAtomSSFXU(pfx,calcControls,parmDict) |
|---|
| 737 | FF = np.zeros(len(Tdata)) |
|---|
| 738 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 739 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 740 | else: |
|---|
| 741 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 742 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 743 | Uij = np.array(G2lat.U6toUij(Uijdata)) |
|---|
| 744 | bij = Mast*Uij.T |
|---|
| 745 | if not len(refDict['FF']): |
|---|
| 746 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 747 | dat = G2el.getBLvalues(BLtables) #will need wave here for anom. neutron b's |
|---|
| 748 | else: |
|---|
| 749 | dat = G2el.getFFvalues(FFtables,0.) |
|---|
| 750 | refDict['FF']['El'] = dat.keys() |
|---|
| 751 | refDict['FF']['FF'] = np.zeros((len(refDict['RefList']),len(dat))) |
|---|
| 752 | for iref,refl in enumerate(refDict['RefList']): |
|---|
| 753 | if 'NT' in calcControls[hfx+'histType']: |
|---|
| 754 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,refl[14+im]) |
|---|
| 755 | fbs = np.array([0,0]) |
|---|
| 756 | H = refl[:4] |
|---|
| 757 | SQ = 1./(2.*refl[4+im])**2 |
|---|
| 758 | SQfactor = 4.0*SQ*twopisq |
|---|
| 759 | Bab = parmDict[phfx+'BabA']*np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 760 | if not np.any(refDict['FF']['FF'][iref]): #no form factors - 1st time thru StructureFactor |
|---|
| 761 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 762 | dat = G2el.getBLvalues(BLtables) |
|---|
| 763 | refDict['FF']['FF'][iref] = dat.values() |
|---|
| 764 | else: #'X' |
|---|
| 765 | dat = G2el.getFFvalues(FFtables,SQ) |
|---|
| 766 | refDict['FF']['FF'][iref] = dat.values() |
|---|
| 767 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 768 | FF = refDict['FF']['FF'][iref][Tindx] |
|---|
| 769 | Uniq = np.inner(H[:3],SGMT) |
|---|
| 770 | SSUniq = np.inner(H,SSGMT) |
|---|
| 771 | Phi = np.inner(H[:3],SGT) |
|---|
| 772 | SSPhi = np.inner(H,SSGT) |
|---|
| 773 | GfpuA,GfpuB = G2mth.Modulation(waveTypes,SSUniq,SSPhi,FSSdata,XSSdata,USSdata) |
|---|
| 774 | phase = twopi*(np.inner(Uniq,(dXdata.T+Xdata.T))+Phi[:,np.newaxis]) |
|---|
| 775 | sinp = np.sin(phase) |
|---|
| 776 | cosp = np.cos(phase) |
|---|
| 777 | biso = -SQfactor*Uisodata |
|---|
| 778 | Tiso = np.where(biso<1.,np.exp(biso),1.0) |
|---|
| 779 | HbH = np.array([-np.inner(h,np.inner(bij,h)) for h in Uniq]) |
|---|
| 780 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0) |
|---|
| 781 | Tcorr = Tiso*Tuij*Mdata*Fdata/len(Uniq) |
|---|
| 782 | fa = np.array([(FF+FP-Bab)*cosp*Tcorr,-FPP*sinp*Tcorr]) |
|---|
| 783 | fb = np.zeros_like(fa) |
|---|
| 784 | if not SGData['SGInv']: |
|---|
| 785 | fb = np.array([(FF+FP-Bab)*sinp*Tcorr,FPP*cosp*Tcorr]) |
|---|
| 786 | fa = fa*GfpuA-fb*GfpuB |
|---|
| 787 | fb = fb*GfpuA+fa*GfpuB |
|---|
| 788 | fas = np.real(np.sum(np.sum(fa,axis=1),axis=1)) #real |
|---|
| 789 | fbs = np.real(np.sum(np.sum(fb,axis=1),axis=1)) |
|---|
| 790 | |
|---|
| 791 | fasq = fas**2 |
|---|
| 792 | fbsq = fbs**2 #imaginary |
|---|
| 793 | refl[9+im] = np.sum(fasq)+np.sum(fbsq) |
|---|
| 794 | refl[10+im] = atan2d(fbs[0],fas[0]) |
|---|
| 795 | |
|---|
| 796 | def StructureFactor2(refDict,G,hfx,pfx,SGData,calcControls,parmDict): |
|---|
| 797 | ''' Compute structure factors for all h,k,l for phase |
|---|
| 798 | puts the result, F^2, in each ref[8] in refList |
|---|
| 799 | input: |
|---|
| 800 | |
|---|
| 801 | :param dict refDict: where |
|---|
| 802 | 'RefList' list where each ref = h,k,l,m,d,... |
|---|
| 803 | 'FF' dict of form factors - filed in below |
|---|
| 804 | :param np.array G: reciprocal metric tensor |
|---|
| 805 | :param str pfx: phase id string |
|---|
| 806 | :param dict SGData: space group info. dictionary output from SpcGroup |
|---|
| 807 | :param dict calcControls: |
|---|
| 808 | :param dict ParmDict: |
|---|
| 809 | |
|---|
| 810 | ''' |
|---|
| 811 | phfx = pfx.split(':')[0]+hfx |
|---|
| 812 | ast = np.sqrt(np.diag(G)) |
|---|
| 813 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 814 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 815 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 816 | FFtables = calcControls['FFtables'] |
|---|
| 817 | BLtables = calcControls['BLtables'] |
|---|
| 818 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata = GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 819 | FF = np.zeros(len(Tdata)) |
|---|
| 820 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 821 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 822 | elif 'X' in calcControls[hfx+'histType']: |
|---|
| 823 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 824 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 825 | Uij = np.array(G2lat.U6toUij(Uijdata)) |
|---|
| 826 | bij = Mast*Uij.T |
|---|
| 827 | blkSize = 100 #no. of reflections in a block |
|---|
| 828 | nRef = refDict['RefList'].shape[0] |
|---|
| 829 | if not len(refDict['FF']): #no form factors - 1st time thru StructureFactor |
|---|
| 830 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 831 | dat = G2el.getBLvalues(BLtables) |
|---|
| 832 | refDict['FF']['El'] = dat.keys() |
|---|
| 833 | refDict['FF']['FF'] = np.ones((nRef,len(dat)))*dat.values() |
|---|
| 834 | else: #'X' |
|---|
| 835 | dat = G2el.getFFvalues(FFtables,0.) |
|---|
| 836 | refDict['FF']['El'] = dat.keys() |
|---|
| 837 | refDict['FF']['FF'] = np.ones((nRef,len(dat))) |
|---|
| 838 | for iref,ref in enumerate(refDict['RefList']): |
|---|
| 839 | SQ = 1./(2.*ref[4])**2 |
|---|
| 840 | dat = G2el.getFFvalues(FFtables,SQ) |
|---|
| 841 | refDict['FF']['FF'][iref] *= dat.values() |
|---|
| 842 | #reflection processing begins here - big arrays! |
|---|
| 843 | iBeg = 0 |
|---|
| 844 | while iBeg < nRef: |
|---|
| 845 | iFin = min(iBeg+blkSize,nRef) |
|---|
| 846 | refl = refDict['RefList'][iBeg:iFin] |
|---|
| 847 | H = refl.T[:3] |
|---|
| 848 | SQ = 1./(2.*refl.T[4])**2 |
|---|
| 849 | SQfactor = 4.0*SQ*twopisq |
|---|
| 850 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 851 | if 'P' in calcControls[hfx+'histType']: |
|---|
| 852 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[14]) |
|---|
| 853 | else: |
|---|
| 854 | FP,FPP = G2el.BlenResTOF(Tdata,BLtables,refl.T[12]) |
|---|
| 855 | FP = np.repeat(FP.T,len(SGT),axis=0) |
|---|
| 856 | FPP = np.repeat(FPP.T,len(SGT),axis=0) |
|---|
| 857 | Bab = np.repeat(parmDict[phfx+'BabA']*np.exp(-parmDict[phfx+'BabU']*SQfactor),len(SGT)) |
|---|
| 858 | Flack = 1.0 |
|---|
| 859 | # Flack = 1.-2.*parmDict[phfx+'Flack'] |
|---|
| 860 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 861 | FF = np.repeat(refDict['FF']['FF'][iBeg:iFin].T[Tindx].T,len(SGT),axis=0) |
|---|
| 862 | Uniq = np.reshape(np.inner(H.T,SGMT),(-1,3)) |
|---|
| 863 | Phi = np.inner(H.T,SGT).flatten() |
|---|
| 864 | phase = twopi*(np.inner(Uniq,(dXdata+Xdata).T)+Phi[:,np.newaxis]) |
|---|
| 865 | sinp = np.sin(phase) |
|---|
| 866 | cosp = np.cos(phase) |
|---|
| 867 | biso = -SQfactor*Uisodata[:,np.newaxis] |
|---|
| 868 | Tiso = np.repeat(np.where(biso<1.,np.exp(biso),1.0),len(SGT),axis=1).T |
|---|
| 869 | HbH = -np.sum(Uniq.T*np.inner(bij,Uniq),axis=1) |
|---|
| 870 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0).T |
|---|
| 871 | Tcorr = Tiso*Tuij*Mdata*Fdata/len(SGMT) |
|---|
| 872 | fa = np.array([((FF+FP).T-Bab).T*cosp*Tcorr,-Flack*FPP*sinp*Tcorr]) |
|---|
| 873 | fa = np.reshape(fa,(2,len(refl),len(SGT),len(Mdata))) #real A,-b |
|---|
| 874 | fas = np.sum(np.sum(fa,axis=2),axis=2) #real sum over atoms & unique hkl |
|---|
| 875 | fb = np.array([((FF+FP).T-Bab).T*sinp*Tcorr,Flack*FPP*cosp*Tcorr]) |
|---|
| 876 | fb = np.reshape(fb,(2,len(refl),len(SGT),len(Mdata))) #imag -B,+a |
|---|
| 877 | fbs = np.sum(np.sum(fb,axis=2),axis=2) #imag sum over atoms & uniq hkl |
|---|
| 878 | if SGData['SGInv']: #centrosymmetric; B=0 |
|---|
| 879 | fbs[0] *= 0. |
|---|
| 880 | if 'P' in calcControls[hfx+'histType']: |
|---|
| 881 | refl.T[9] = np.sum(fas**2,axis=0)+np.sum(fbs**2,axis=0) |
|---|
| 882 | else: |
|---|
| 883 | refl.T[9] = np.sum(fas,axis=0)**2+np.sum(fbs,axis=0)**2 |
|---|
| 884 | refl.T[10] = atan2d(fbs[0],fas[0]) #ignore f' & f"? |
|---|
| 885 | # refl.T[10] = atan2d(np.sum(fbs,axis=0),np.sum(fas,axis=0)) #include f' & f" |
|---|
| 886 | iBeg += blkSize |
|---|
| 887 | |
|---|
| 888 | def StructureFactorDerv(refDict,G,hfx,pfx,SGData,calcControls,parmDict): |
|---|
| 889 | 'Needs a doc string' |
|---|
| 890 | phfx = pfx.split(':')[0]+hfx |
|---|
| 891 | ast = np.sqrt(np.diag(G)) |
|---|
| 892 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 893 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 894 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 895 | FFtables = calcControls['FFtables'] |
|---|
| 896 | BLtables = calcControls['BLtables'] |
|---|
| 897 | nRef = len(refDict['RefList']) |
|---|
| 898 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata = GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 899 | mSize = len(Mdata) |
|---|
| 900 | FF = np.zeros(len(Tdata)) |
|---|
| 901 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 902 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 903 | elif 'X' in calcControls[hfx+'histType']: |
|---|
| 904 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 905 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 906 | Uij = np.array(G2lat.U6toUij(Uijdata)) |
|---|
| 907 | bij = Mast*Uij.T |
|---|
| 908 | dFdvDict = {} |
|---|
| 909 | dFdfr = np.zeros((nRef,mSize)) |
|---|
| 910 | dFdx = np.zeros((nRef,mSize,3)) |
|---|
| 911 | dFdui = np.zeros((nRef,mSize)) |
|---|
| 912 | dFdua = np.zeros((nRef,mSize,6)) |
|---|
| 913 | dFdbab = np.zeros((nRef,2)) |
|---|
| 914 | for iref,refl in enumerate(refDict['RefList']): |
|---|
| 915 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 916 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,refl.T[12]) |
|---|
| 917 | H = np.array(refl[:3]) |
|---|
| 918 | SQ = 1./(2.*refl[4])**2 # or (sin(theta)/lambda)**2 |
|---|
| 919 | SQfactor = 8.0*SQ*np.pi**2 |
|---|
| 920 | dBabdA = np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 921 | Bab = parmDict[phfx+'BabA']*dBabdA |
|---|
| 922 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 923 | FF = refDict['FF']['FF'][iref].T[Tindx] |
|---|
| 924 | Uniq = np.inner(H,SGMT) |
|---|
| 925 | Phi = np.inner(H,SGT) |
|---|
| 926 | phase = twopi*(np.inner((dXdata.T+Xdata.T),Uniq)+Phi[np.newaxis,:]) |
|---|
| 927 | sinp = np.sin(phase) |
|---|
| 928 | cosp = np.cos(phase) |
|---|
| 929 | occ = Mdata*Fdata/len(Uniq) |
|---|
| 930 | biso = -SQfactor*Uisodata |
|---|
| 931 | Tiso = np.where(biso<1.,np.exp(biso),1.0) |
|---|
| 932 | HbH = -np.inner(H,np.inner(bij,H)) |
|---|
| 933 | Hij = np.array([Mast*np.multiply.outer(U,U) for U in Uniq]) |
|---|
| 934 | Hij = np.array([G2lat.UijtoU6(Uij) for Uij in Hij]) |
|---|
| 935 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0) |
|---|
| 936 | Tcorr = Tiso*Tuij |
|---|
| 937 | Flack = 1.0 |
|---|
| 938 | # Flack = (1.-2.*parmDict[phfx+'Flack']) |
|---|
| 939 | fot = (FF+FP-Bab)*occ*Tcorr |
|---|
| 940 | fotp = Flack*FPP*occ*Tcorr |
|---|
| 941 | fa = np.array([fot[:,np.newaxis]*cosp,fotp[:,np.newaxis]*cosp]) #non positions |
|---|
| 942 | fb = np.array([fot[:,np.newaxis]*sinp,-fotp[:,np.newaxis]*sinp]) |
|---|
| 943 | |
|---|
| 944 | fas = np.sum(np.sum(fa,axis=1),axis=1) #real sum over atoms & unique hkl |
|---|
| 945 | fbs = np.sum(np.sum(fb,axis=1),axis=1) #imag sum over atoms & uniq hkl |
|---|
| 946 | fax = np.array([-fot[:,np.newaxis]*sinp,-fotp[:,np.newaxis]*sinp]) #positions |
|---|
| 947 | fbx = np.array([fot[:,np.newaxis]*cosp,-fot[:,np.newaxis]*cosp]) |
|---|
| 948 | #sum below is over Uniq |
|---|
| 949 | dfadfr = np.sum(fa/occ[:,np.newaxis],axis=2) #Fdata != 0 ever avoids /0. problem |
|---|
| 950 | dfadx = np.sum(twopi*Uniq*fax[:,:,:,np.newaxis],axis=2) |
|---|
| 951 | dfadui = np.sum(-SQfactor*fa,axis=2) |
|---|
| 952 | dfadua = np.sum(-Hij*fa[:,:,:,np.newaxis],axis=2) |
|---|
| 953 | dfadba = np.sum(-cosp*(occ*Tcorr)[:,np.newaxis],axis=1) |
|---|
| 954 | if not SGData['SGInv']: |
|---|
| 955 | dfbdfr = np.sum(fb/occ[:,np.newaxis],axis=2) #Fdata != 0 ever avoids /0. problem |
|---|
| 956 | dfbdx = np.sum(twopi*Uniq*fbx[:,:,:,np.newaxis],axis=2) |
|---|
| 957 | dfbdui = np.sum(-SQfactor*fb,axis=2) |
|---|
| 958 | dfbdua = np.sum(-Hij*fb[:,:,:,np.newaxis],axis=2) |
|---|
| 959 | dfbdba = np.sum(-sinp*(occ*Tcorr)[:,np.newaxis],axis=1) |
|---|
| 960 | else: |
|---|
| 961 | dfbdfr = np.zeros_like(dfadfr) |
|---|
| 962 | dfbdx = np.zeros_like(dfadx) |
|---|
| 963 | dfbdui = np.zeros_like(dfadui) |
|---|
| 964 | dfbdua = np.zeros_like(dfadua) |
|---|
| 965 | dfbdba = np.zeros_like(dfadba) |
|---|
| 966 | #NB: the above have been checked against PA(1:10,1:2) in strfctr.for for Al2O3! |
|---|
| 967 | if 'P' in calcControls[hfx+'histType']: #checked perfect for centro & noncentro |
|---|
| 968 | dFdfr[iref] = 2.*(fas[0]*dfadfr[0]+fas[1]*dfadfr[1])*Mdata/len(Uniq)+ \ |
|---|
| 969 | 2.*(fbs[0]*dfbdfr[0]-fbs[1]*dfbdfr[1])*Mdata/len(Uniq) |
|---|
| 970 | dFdx[iref] = 2.*(fas[0]*dfadx[0]+fas[1]*dfadx[1])+ \ |
|---|
| 971 | 2.*(fbs[0]*dfbdx[0]+fbs[1]*dfbdx[1]) |
|---|
| 972 | dFdui[iref] = 2.*(fas[0]*dfadui[0]+fas[1]*dfadui[1])+ \ |
|---|
| 973 | 2.*(fbs[0]*dfbdui[0]-fbs[1]*dfbdui[1]) |
|---|
| 974 | dFdua[iref] = 2.*(fas[0]*dfadua[0]+fas[1]*dfadua[1])+ \ |
|---|
| 975 | 2.*(fbs[0]*dfbdua[0]+fbs[1]*dfbdua[1]) |
|---|
| 976 | else: |
|---|
| 977 | SA = fas[0]-fbs[1] |
|---|
| 978 | SB = fbs[0]+fas[1] |
|---|
| 979 | dFdfr[iref] = 2.*SA*(dfadfr[0]+dfbdfr[1])*Mdata/len(Uniq)+ \ |
|---|
| 980 | 2.*SB*(dfbdfr[0]+dfadfr[1])*Mdata/len(Uniq) |
|---|
| 981 | dFdx[iref] = 2.*SA*(dfadx[0]+dfbdx[1])+2.*SB*(dfbdx[0]+dfadx[1]) |
|---|
| 982 | dFdui[iref] = 2.*SA*(dfadui[0]+dfbdui[1])+2.*SB*(dfbdui[0]+dfadui[1]) |
|---|
| 983 | dFdua[iref] = 2.*SA*(dfadua[0]+dfbdua[1])+2.*SB*(dfbdua[0]+dfadua[1]) |
|---|
| 984 | dFdbab[iref] = 2.*fas[0]*np.array([np.sum(dfadba*dBabdA),np.sum(-dfadba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T+ \ |
|---|
| 985 | 2.*fbs[0]*np.array([np.sum(dfbdba*dBabdA),np.sum(-dfbdba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T |
|---|
| 986 | #loop over atoms - each dict entry is list of derivatives for all the reflections |
|---|
| 987 | for i in range(len(Mdata)): |
|---|
| 988 | dFdvDict[pfx+'Afrac:'+str(i)] = dFdfr.T[i] |
|---|
| 989 | dFdvDict[pfx+'dAx:'+str(i)] = dFdx.T[0][i] |
|---|
| 990 | dFdvDict[pfx+'dAy:'+str(i)] = dFdx.T[1][i] |
|---|
| 991 | dFdvDict[pfx+'dAz:'+str(i)] = dFdx.T[2][i] |
|---|
| 992 | dFdvDict[pfx+'AUiso:'+str(i)] = dFdui.T[i] |
|---|
| 993 | dFdvDict[pfx+'AU11:'+str(i)] = dFdua.T[0][i] |
|---|
| 994 | dFdvDict[pfx+'AU22:'+str(i)] = dFdua.T[1][i] |
|---|
| 995 | dFdvDict[pfx+'AU33:'+str(i)] = dFdua.T[2][i] |
|---|
| 996 | dFdvDict[pfx+'AU12:'+str(i)] = 0.5*dFdua.T[3][i] |
|---|
| 997 | dFdvDict[pfx+'AU13:'+str(i)] = 0.5*dFdua.T[4][i] |
|---|
| 998 | dFdvDict[pfx+'AU23:'+str(i)] = 0.5*dFdua.T[5][i] |
|---|
| 999 | dFdvDict[pfx+'BabA'] = dFdbab.T[0] |
|---|
| 1000 | dFdvDict[pfx+'BabU'] = dFdbab.T[1] |
|---|
| 1001 | return dFdvDict |
|---|
| 1002 | |
|---|
| 1003 | def SStructureFactorDerv(refDict,im,G,hfx,pfx,SGData,SSGData,calcControls,parmDict): |
|---|
| 1004 | 'Needs a doc string' |
|---|
| 1005 | phfx = pfx.split(':')[0]+hfx |
|---|
| 1006 | ast = np.sqrt(np.diag(G)) |
|---|
| 1007 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 1008 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 1009 | SGT = np.array([ops[1] for ops in SGData['SGOps']]) |
|---|
| 1010 | SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']]) |
|---|
| 1011 | SSGT = np.array([ops[1] for ops in SSGData['SSGOps']]) |
|---|
| 1012 | FFtables = calcControls['FFtables'] |
|---|
| 1013 | BLtables = calcControls['BLtables'] |
|---|
| 1014 | nRef = len(refDict['RefList']) |
|---|
| 1015 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata = GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 1016 | waveTypes,FSSdata,XSSdata,USSdata,MSSdata = GetAtomSSFXU(pfx,calcControls,parmDict) |
|---|
| 1017 | mSize = len(Mdata) |
|---|
| 1018 | FF = np.zeros(len(Tdata)) |
|---|
| 1019 | if 'NC' in calcControls[hfx+'histType']: |
|---|
| 1020 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 1021 | elif 'X' in calcControls[hfx+'histType']: |
|---|
| 1022 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 1023 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 1024 | Uij = np.array(G2lat.U6toUij(Uijdata)) |
|---|
| 1025 | bij = Mast*Uij.T |
|---|
| 1026 | dFdvDict = {} |
|---|
| 1027 | dFdfr = np.zeros((nRef,mSize)) |
|---|
| 1028 | dFdx = np.zeros((nRef,mSize,3)) |
|---|
| 1029 | dFdui = np.zeros((nRef,mSize)) |
|---|
| 1030 | dFdua = np.zeros((nRef,mSize,6)) |
|---|
| 1031 | dFdbab = np.zeros((nRef,2)) |
|---|
| 1032 | for iref,refl in enumerate(refDict['RefList']): |
|---|
| 1033 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1034 | FP,FPP = G2el.BlenResCW(Tdata,BLtables,refl.T[12+im]) |
|---|
| 1035 | H = np.array(refl[:4]) |
|---|
| 1036 | SQ = 1./(2.*refl[4+im])**2 # or (sin(theta)/lambda)**2 |
|---|
| 1037 | SQfactor = 8.0*SQ*np.pi**2 |
|---|
| 1038 | dBabdA = np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 1039 | Bab = parmDict[phfx+'BabA']*dBabdA |
|---|
| 1040 | Tindx = np.array([refDict['FF']['El'].index(El) for El in Tdata]) |
|---|
| 1041 | FF = refDict['FF']['FF'][iref].T[Tindx] |
|---|
| 1042 | Uniq = np.inner(H[:3],SGMT) |
|---|
| 1043 | SSUniq = np.inner(H,SSGMT) |
|---|
| 1044 | Phi = np.inner(H[:3],SGT) |
|---|
| 1045 | SSPhi = np.inner(H,SSGT) |
|---|
| 1046 | GfpuA,GfpuB = G2mth.Modulation(waveTypes,SSUniq,SSPhi,FSSdata,XSSdata,USSdata) |
|---|
| 1047 | dGAdk,dGBdk = G2mth.ModulationDerv(waveTypes,SSUniq,SSPhi,FSSdata,XSSdata,USSdata) |
|---|
| 1048 | #need ModulationDerv here dGAdXsin, etc |
|---|
| 1049 | phase = twopi*(np.inner((dXdata.T+Xdata.T),Uniq)+Phi[np.newaxis,:]) |
|---|
| 1050 | sinp = np.sin(phase) |
|---|
| 1051 | cosp = np.cos(phase) |
|---|
| 1052 | occ = Mdata*Fdata/len(Uniq) |
|---|
| 1053 | biso = -SQfactor*Uisodata |
|---|
| 1054 | Tiso = np.where(biso<1.,np.exp(biso),1.0) |
|---|
| 1055 | HbH = -np.inner(H[:3],np.inner(bij,H[:3])) |
|---|
| 1056 | Hij = np.array([Mast*np.multiply.outer(U,U) for U in Uniq]) |
|---|
| 1057 | Hij = np.array([G2lat.UijtoU6(Uij) for Uij in Hij]) |
|---|
| 1058 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0) |
|---|
| 1059 | Tcorr = Tiso*Tuij |
|---|
| 1060 | fot = (FF+FP-Bab)*occ*Tcorr |
|---|
| 1061 | fotp = FPP*occ*Tcorr |
|---|
| 1062 | fa = np.array([fot[:,np.newaxis]*cosp,fotp[:,np.newaxis]*cosp]) #non positions |
|---|
| 1063 | fb = np.array([fot[:,np.newaxis]*sinp,-fotp[:,np.newaxis]*sinp]) |
|---|
| 1064 | GfpuA = np.swapaxes(GfpuA,1,2) |
|---|
| 1065 | GfpuB = np.swapaxes(GfpuB,1,2) |
|---|
| 1066 | fa = fa*GfpuA-fb*GfpuB |
|---|
| 1067 | fb = fb*GfpuA+fa*GfpuB |
|---|
| 1068 | |
|---|
| 1069 | fas = np.sum(np.sum(fa,axis=1),axis=1) |
|---|
| 1070 | fbs = np.sum(np.sum(fb,axis=1),axis=1) |
|---|
| 1071 | fax = np.array([-fot[:,np.newaxis]*sinp,-fotp[:,np.newaxis]*sinp]) #positions |
|---|
| 1072 | fbx = np.array([fot[:,np.newaxis]*cosp,-fot[:,np.newaxis]*cosp]) |
|---|
| 1073 | fax = fax*GfpuA-fbx*GfpuB |
|---|
| 1074 | fbx = fbx*GfpuA+fax*GfpuB |
|---|
| 1075 | #sum below is over Uniq |
|---|
| 1076 | dfadfr = np.sum(fa/occ[:,np.newaxis],axis=2) #Fdata != 0 ever avoids /0. problem |
|---|
| 1077 | dfadx = np.sum(twopi*Uniq*fax[:,:,:,np.newaxis],axis=2) |
|---|
| 1078 | dfadui = np.sum(-SQfactor*fa,axis=2) |
|---|
| 1079 | dfadua = np.sum(-Hij*fa[:,:,:,np.newaxis],axis=2) |
|---|
| 1080 | dfadba = np.sum(-cosp*(occ*Tcorr)[:,np.newaxis],axis=1) |
|---|
| 1081 | #NB: the above have been checked against PA(1:10,1:2) in strfctr.for for al2O3! |
|---|
| 1082 | dFdfr[iref] = 2.*(fas[0]*dfadfr[0]+fas[1]*dfadfr[1])*Mdata/len(Uniq) |
|---|
| 1083 | dFdx[iref] = 2.*(fas[0]*dfadx[0]+fas[1]*dfadx[1]) |
|---|
| 1084 | dFdui[iref] = 2.*(fas[0]*dfadui[0]+fas[1]*dfadui[1]) |
|---|
| 1085 | dFdua[iref] = 2.*(fas[0]*dfadua[0]+fas[1]*dfadua[1]) |
|---|
| 1086 | dFdbab[iref] = 2.*fas[0]*np.array([np.sum(dfadba*dBabdA),np.sum(-dfadba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T |
|---|
| 1087 | #need dFdXsin, etc for modulations... |
|---|
| 1088 | if not SGData['SGInv']: |
|---|
| 1089 | dfbdfr = np.sum(fb/occ[:,np.newaxis],axis=2) #Fdata != 0 ever avoids /0. problem |
|---|
| 1090 | dfbdx = np.sum(twopi*Uniq*fbx[:,:,:,np.newaxis],axis=2) |
|---|
| 1091 | dfbdui = np.sum(-SQfactor*fb,axis=2) |
|---|
| 1092 | dfbdua = np.sum(-Hij*fb[:,:,:,np.newaxis],axis=2) |
|---|
| 1093 | dfbdba = np.sum(-sinp*(occ*Tcorr)[:,np.newaxis],axis=1) |
|---|
| 1094 | dFdfr[iref] += 2.*(fbs[0]*dfbdfr[0]-fbs[1]*dfbdfr[1])*Mdata/len(Uniq) |
|---|
| 1095 | dFdx[iref] += 2.*(fbs[0]*dfbdx[0]+fbs[1]*dfbdx[1]) |
|---|
| 1096 | dFdui[iref] += 2.*(fbs[0]*dfbdui[0]-fbs[1]*dfbdui[1]) |
|---|
| 1097 | dFdua[iref] += 2.*(fbs[0]*dfbdua[0]+fbs[1]*dfbdua[1]) |
|---|
| 1098 | dFdbab[iref] += 2.*fbs[0]*np.array([np.sum(dfbdba*dBabdA),np.sum(-dfbdba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T |
|---|
| 1099 | #need dFdXsin, etc for modulations... |
|---|
| 1100 | #loop over atoms - each dict entry is list of derivatives for all the reflections |
|---|
| 1101 | for i in range(len(Mdata)): |
|---|
| 1102 | dFdvDict[pfx+'Afrac:'+str(i)] = dFdfr.T[i] |
|---|
| 1103 | dFdvDict[pfx+'dAx:'+str(i)] = dFdx.T[0][i] |
|---|
| 1104 | dFdvDict[pfx+'dAy:'+str(i)] = dFdx.T[1][i] |
|---|
| 1105 | dFdvDict[pfx+'dAz:'+str(i)] = dFdx.T[2][i] |
|---|
| 1106 | dFdvDict[pfx+'AUiso:'+str(i)] = dFdui.T[i] |
|---|
| 1107 | dFdvDict[pfx+'AU11:'+str(i)] = dFdua.T[0][i] |
|---|
| 1108 | dFdvDict[pfx+'AU22:'+str(i)] = dFdua.T[1][i] |
|---|
| 1109 | dFdvDict[pfx+'AU33:'+str(i)] = dFdua.T[2][i] |
|---|
| 1110 | dFdvDict[pfx+'AU12:'+str(i)] = .5*dFdua.T[3][i] |
|---|
| 1111 | dFdvDict[pfx+'AU13:'+str(i)] = .5*dFdua.T[4][i] |
|---|
| 1112 | dFdvDict[pfx+'AU23:'+str(i)] = .5*dFdua.T[5][i] |
|---|
| 1113 | #need dFdvDict[pfx+'Xsin:'+str[i]:str(m)], etc for modulations... |
|---|
| 1114 | dFdvDict[pfx+'BabA'] = dFdbab.T[0] |
|---|
| 1115 | dFdvDict[pfx+'BabU'] = dFdbab.T[1] |
|---|
| 1116 | return dFdvDict |
|---|
| 1117 | |
|---|
| 1118 | def SCExtinction(ref,im,phfx,hfx,pfx,calcControls,parmDict,varyList): |
|---|
| 1119 | ''' Single crystal extinction function; returns extinction & derivative |
|---|
| 1120 | ''' |
|---|
| 1121 | extCor = 1.0 |
|---|
| 1122 | dervDict = {} |
|---|
| 1123 | dervCor = 1.0 |
|---|
| 1124 | if calcControls[phfx+'EType'] != 'None': |
|---|
| 1125 | SQ = 1/(4.*ref[4+im]**2) |
|---|
| 1126 | if 'C' in parmDict[hfx+'Type']: |
|---|
| 1127 | cos2T = 1.0-2.*SQ*parmDict[hfx+'Lam']**2 #cos(2theta) |
|---|
| 1128 | else: #'T' |
|---|
| 1129 | cos2T = 1.0-2.*SQ*ref[12+im]**2 #cos(2theta) |
|---|
| 1130 | if 'SXC' in parmDict[hfx+'Type']: |
|---|
| 1131 | AV = 7.9406e5/parmDict[pfx+'Vol']**2 |
|---|
| 1132 | PL = np.sqrt(1.0-cos2T**2)/parmDict[hfx+'Lam'] |
|---|
| 1133 | P12 = (calcControls[phfx+'Cos2TM']+cos2T**4)/(calcControls[phfx+'Cos2TM']+cos2T**2) |
|---|
| 1134 | PLZ = AV*P12*ref[9+im]*parmDict[hfx+'Lam']**2 |
|---|
| 1135 | elif 'SNT' in parmDict[hfx+'Type']: |
|---|
| 1136 | AV = 1.e7/parmDict[pfx+'Vol']**2 |
|---|
| 1137 | PL = SQ |
|---|
| 1138 | PLZ = AV*ref[9+im]*ref[12+im]**2 |
|---|
| 1139 | elif 'SNC' in parmDict[hfx+'Type']: |
|---|
| 1140 | AV = 1.e7/parmDict[pfx+'Vol']**2 |
|---|
| 1141 | PL = np.sqrt(1.0-cos2T**2)/parmDict[hfx+'Lam'] |
|---|
| 1142 | PLZ = AV*ref[9+im]*parmDict[hfx+'Lam']**2 |
|---|
| 1143 | |
|---|
| 1144 | if 'Primary' in calcControls[phfx+'EType']: |
|---|
| 1145 | PLZ *= 1.5 |
|---|
| 1146 | else: |
|---|
| 1147 | if 'C' in parmDict[hfx+'Type']: |
|---|
| 1148 | PLZ *= calcControls[phfx+'Tbar'] |
|---|
| 1149 | else: #'T' |
|---|
| 1150 | PLZ *= ref[13+im] #t-bar |
|---|
| 1151 | if 'Primary' in calcControls[phfx+'EType']: |
|---|
| 1152 | PLZ *= 1.5 |
|---|
| 1153 | PSIG = parmDict[phfx+'Ep'] |
|---|
| 1154 | elif 'I & II' in calcControls[phfx+'EType']: |
|---|
| 1155 | PSIG = parmDict[phfx+'Eg']/np.sqrt(1.+(parmDict[phfx+'Es']*PL/parmDict[phfx+'Eg'])**2) |
|---|
| 1156 | elif 'Type II' in calcControls[phfx+'EType']: |
|---|
| 1157 | PSIG = parmDict[phfx+'Es'] |
|---|
| 1158 | else: # 'Secondary Type I' |
|---|
| 1159 | PSIG = parmDict[phfx+'Eg']/PL |
|---|
| 1160 | |
|---|
| 1161 | AG = 0.58+0.48*cos2T+0.24*cos2T**2 |
|---|
| 1162 | AL = 0.025+0.285*cos2T |
|---|
| 1163 | BG = 0.02-0.025*cos2T |
|---|
| 1164 | BL = 0.15-0.2*(0.75-cos2T)**2 |
|---|
| 1165 | if cos2T < 0.: |
|---|
| 1166 | BL = -0.45*cos2T |
|---|
| 1167 | CG = 2. |
|---|
| 1168 | CL = 2. |
|---|
| 1169 | PF = PLZ*PSIG |
|---|
| 1170 | |
|---|
| 1171 | if 'Gaussian' in calcControls[phfx+'EApprox']: |
|---|
| 1172 | PF4 = 1.+CG*PF+AG*PF**2/(1.+BG*PF) |
|---|
| 1173 | extCor = np.sqrt(PF4) |
|---|
| 1174 | PF3 = 0.5*(CG+2.*AG*PF/(1.+BG*PF)-AG*PF**2*BG/(1.+BG*PF)**2)/(PF4*extCor) |
|---|
| 1175 | else: |
|---|
| 1176 | PF4 = 1.+CL*PF+AL*PF**2/(1.+BL*PF) |
|---|
| 1177 | extCor = np.sqrt(PF4) |
|---|
| 1178 | PF3 = 0.5*(CL+2.*AL*PF/(1.+BL*PF)-AL*PF**2*BL/(1.+BL*PF)**2)/(PF4*extCor) |
|---|
| 1179 | |
|---|
| 1180 | dervCor = (1.+PF)*PF3 #extinction corr for other derivatives |
|---|
| 1181 | if 'Primary' in calcControls[phfx+'EType'] and phfx+'Ep' in varyList: |
|---|
| 1182 | dervDict[phfx+'Ep'] = -ref[7+im]*PLZ*PF3 |
|---|
| 1183 | if 'II' in calcControls[phfx+'EType'] and phfx+'Es' in varyList: |
|---|
| 1184 | dervDict[phfx+'Es'] = -ref[7+im]*PLZ*PF3*(PSIG/parmDict[phfx+'Es'])**3 |
|---|
| 1185 | if 'I' in calcControls[phfx+'EType'] and phfx+'Eg' in varyList: |
|---|
| 1186 | dervDict[phfx+'Eg'] = -ref[7+im]*PLZ*PF3*(PSIG/parmDict[phfx+'Eg'])**3*PL**2 |
|---|
| 1187 | |
|---|
| 1188 | return 1./extCor,dervDict,dervCor |
|---|
| 1189 | |
|---|
| 1190 | def Dict2Values(parmdict, varylist): |
|---|
| 1191 | '''Use before call to leastsq to setup list of values for the parameters |
|---|
| 1192 | in parmdict, as selected by key in varylist''' |
|---|
| 1193 | return [parmdict[key] for key in varylist] |
|---|
| 1194 | |
|---|
| 1195 | def Values2Dict(parmdict, varylist, values): |
|---|
| 1196 | ''' Use after call to leastsq to update the parameter dictionary with |
|---|
| 1197 | values corresponding to keys in varylist''' |
|---|
| 1198 | parmdict.update(zip(varylist,values)) |
|---|
| 1199 | |
|---|
| 1200 | def GetNewCellParms(parmDict,varyList): |
|---|
| 1201 | 'Needs a doc string' |
|---|
| 1202 | newCellDict = {} |
|---|
| 1203 | Anames = ['A'+str(i) for i in range(6)] |
|---|
| 1204 | Ddict = dict(zip(['D11','D22','D33','D12','D13','D23'],Anames)) |
|---|
| 1205 | for item in varyList: |
|---|
| 1206 | keys = item.split(':') |
|---|
| 1207 | if keys[2] in Ddict: |
|---|
| 1208 | key = keys[0]+'::'+Ddict[keys[2]] #key is e.g. '0::A0' |
|---|
| 1209 | parm = keys[0]+'::'+keys[2] #parm is e.g. '0::D11' |
|---|
| 1210 | newCellDict[parm] = [key,parmDict[key]+parmDict[item]] |
|---|
| 1211 | return newCellDict # is e.g. {'0::D11':A0-D11} |
|---|
| 1212 | |
|---|
| 1213 | def ApplyXYZshifts(parmDict,varyList): |
|---|
| 1214 | ''' |
|---|
| 1215 | takes atom x,y,z shift and applies it to corresponding atom x,y,z value |
|---|
| 1216 | |
|---|
| 1217 | :param dict parmDict: parameter dictionary |
|---|
| 1218 | :param list varyList: list of variables (not used!) |
|---|
| 1219 | :returns: newAtomDict - dictionary of new atomic coordinate names & values; key is parameter shift name |
|---|
| 1220 | |
|---|
| 1221 | ''' |
|---|
| 1222 | newAtomDict = {} |
|---|
| 1223 | for item in parmDict: |
|---|
| 1224 | if 'dA' in item: |
|---|
| 1225 | parm = ''.join(item.split('d')) |
|---|
| 1226 | parmDict[parm] += parmDict[item] |
|---|
| 1227 | newAtomDict[item] = [parm,parmDict[parm]] |
|---|
| 1228 | return newAtomDict |
|---|
| 1229 | |
|---|
| 1230 | def SHTXcal(refl,im,g,pfx,hfx,SGData,calcControls,parmDict): |
|---|
| 1231 | 'Spherical harmonics texture' |
|---|
| 1232 | IFCoup = 'Bragg' in calcControls[hfx+'instType'] |
|---|
| 1233 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1234 | tth = parmDict[hfx+'2-theta'] |
|---|
| 1235 | else: |
|---|
| 1236 | tth = refl[5+im] |
|---|
| 1237 | odfCor = 1.0 |
|---|
| 1238 | H = refl[:3] |
|---|
| 1239 | cell = G2lat.Gmat2cell(g) |
|---|
| 1240 | Sangls = [parmDict[pfx+'SH omega'],parmDict[pfx+'SH chi'],parmDict[pfx+'SH phi']] |
|---|
| 1241 | Gangls = [parmDict[hfx+'Phi'],parmDict[hfx+'Chi'],parmDict[hfx+'Omega'],parmDict[hfx+'Azimuth']] |
|---|
| 1242 | phi,beta = G2lat.CrsAng(H,cell,SGData) |
|---|
| 1243 | psi,gam,x,x = G2lat.SamAng(tth/2.,Gangls,Sangls,IFCoup) #ignore 2 sets of angle derivs. |
|---|
| 1244 | SHnames = G2lat.GenSHCoeff(SGData['SGLaue'],parmDict[pfx+'SHmodel'],parmDict[pfx+'SHorder']) |
|---|
| 1245 | for item in SHnames: |
|---|
| 1246 | L,M,N = eval(item.strip('C')) |
|---|
| 1247 | Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta) |
|---|
| 1248 | Ksl,x,x = G2lat.GetKsl(L,M,parmDict[pfx+'SHmodel'],psi,gam) |
|---|
| 1249 | Lnorm = G2lat.Lnorm(L) |
|---|
| 1250 | odfCor += parmDict[pfx+item]*Lnorm*Kcl*Ksl |
|---|
| 1251 | return odfCor |
|---|
| 1252 | |
|---|
| 1253 | def SHTXcalDerv(refl,im,g,pfx,hfx,SGData,calcControls,parmDict): |
|---|
| 1254 | 'Spherical harmonics texture derivatives' |
|---|
| 1255 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1256 | tth = parmDict[hfx+'2-theta'] |
|---|
| 1257 | else: |
|---|
| 1258 | tth = refl[5+im] |
|---|
| 1259 | IFCoup = 'Bragg' in calcControls[hfx+'instType'] |
|---|
| 1260 | odfCor = 1.0 |
|---|
| 1261 | dFdODF = {} |
|---|
| 1262 | dFdSA = [0,0,0] |
|---|
| 1263 | H = refl[:3] |
|---|
| 1264 | cell = G2lat.Gmat2cell(g) |
|---|
| 1265 | Sangls = [parmDict[pfx+'SH omega'],parmDict[pfx+'SH chi'],parmDict[pfx+'SH phi']] |
|---|
| 1266 | Gangls = [parmDict[hfx+'Phi'],parmDict[hfx+'Chi'],parmDict[hfx+'Omega'],parmDict[hfx+'Azimuth']] |
|---|
| 1267 | phi,beta = G2lat.CrsAng(H,cell,SGData) |
|---|
| 1268 | psi,gam,dPSdA,dGMdA = G2lat.SamAng(tth/2.,Gangls,Sangls,IFCoup) |
|---|
| 1269 | SHnames = G2lat.GenSHCoeff(SGData['SGLaue'],parmDict[pfx+'SHmodel'],parmDict[pfx+'SHorder']) |
|---|
| 1270 | for item in SHnames: |
|---|
| 1271 | L,M,N = eval(item.strip('C')) |
|---|
| 1272 | Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta) |
|---|
| 1273 | Ksl,dKsdp,dKsdg = G2lat.GetKsl(L,M,parmDict[pfx+'SHmodel'],psi,gam) |
|---|
| 1274 | Lnorm = G2lat.Lnorm(L) |
|---|
| 1275 | odfCor += parmDict[pfx+item]*Lnorm*Kcl*Ksl |
|---|
| 1276 | dFdODF[pfx+item] = Lnorm*Kcl*Ksl |
|---|
| 1277 | for i in range(3): |
|---|
| 1278 | dFdSA[i] += parmDict[pfx+item]*Lnorm*Kcl*(dKsdp*dPSdA[i]+dKsdg*dGMdA[i]) |
|---|
| 1279 | return odfCor,dFdODF,dFdSA |
|---|
| 1280 | |
|---|
| 1281 | def SHPOcal(refl,im,g,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 1282 | 'spherical harmonics preferred orientation (cylindrical symmetry only)' |
|---|
| 1283 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1284 | tth = parmDict[hfx+'2-theta'] |
|---|
| 1285 | else: |
|---|
| 1286 | tth = refl[5+im] |
|---|
| 1287 | odfCor = 1.0 |
|---|
| 1288 | H = refl[:3] |
|---|
| 1289 | cell = G2lat.Gmat2cell(g) |
|---|
| 1290 | Sangls = [0.,0.,0.] |
|---|
| 1291 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 1292 | Gangls = [0.,90.,0.,parmDict[hfx+'Azimuth']] |
|---|
| 1293 | IFCoup = True |
|---|
| 1294 | else: |
|---|
| 1295 | Gangls = [parmDict[hfx+'Phi'],parmDict[hfx+'Chi'],parmDict[hfx+'Omega'],parmDict[hfx+'Azimuth']] |
|---|
| 1296 | IFCoup = False |
|---|
| 1297 | phi,beta = G2lat.CrsAng(H,cell,SGData) |
|---|
| 1298 | psi,gam,x,x = G2lat.SamAng(tth/2.,Gangls,Sangls,IFCoup) #ignore 2 sets of angle derivs. |
|---|
| 1299 | SHnames = calcControls[phfx+'SHnames'] |
|---|
| 1300 | for item in SHnames: |
|---|
| 1301 | L,N = eval(item.strip('C')) |
|---|
| 1302 | Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta) |
|---|
| 1303 | Ksl,x,x = G2lat.GetKsl(L,0,'0',psi,gam) |
|---|
| 1304 | Lnorm = G2lat.Lnorm(L) |
|---|
| 1305 | odfCor += parmDict[phfx+item]*Lnorm*Kcl*Ksl |
|---|
| 1306 | return np.squeeze(odfCor) |
|---|
| 1307 | |
|---|
| 1308 | def SHPOcalDerv(refl,im,g,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 1309 | 'spherical harmonics preferred orientation derivatives (cylindrical symmetry only)' |
|---|
| 1310 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1311 | tth = parmDict[hfx+'2-theta'] |
|---|
| 1312 | else: |
|---|
| 1313 | tth = refl[5+im] |
|---|
| 1314 | odfCor = 1.0 |
|---|
| 1315 | dFdODF = {} |
|---|
| 1316 | H = refl[:3] |
|---|
| 1317 | cell = G2lat.Gmat2cell(g) |
|---|
| 1318 | Sangls = [0.,0.,0.] |
|---|
| 1319 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 1320 | Gangls = [0.,90.,0.,parmDict[hfx+'Azimuth']] |
|---|
| 1321 | IFCoup = True |
|---|
| 1322 | else: |
|---|
| 1323 | Gangls = [parmDict[hfx+'Phi'],parmDict[hfx+'Chi'],parmDict[hfx+'Omega'],parmDict[hfx+'Azimuth']] |
|---|
| 1324 | IFCoup = False |
|---|
| 1325 | phi,beta = G2lat.CrsAng(H,cell,SGData) |
|---|
| 1326 | psi,gam,x,x = G2lat.SamAng(tth/2.,Gangls,Sangls,IFCoup) #ignore 2 sets of angle derivs. |
|---|
| 1327 | SHnames = calcControls[phfx+'SHnames'] |
|---|
| 1328 | for item in SHnames: |
|---|
| 1329 | L,N = eval(item.strip('C')) |
|---|
| 1330 | Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta) |
|---|
| 1331 | Ksl,x,x = G2lat.GetKsl(L,0,'0',psi,gam) |
|---|
| 1332 | Lnorm = G2lat.Lnorm(L) |
|---|
| 1333 | odfCor += parmDict[phfx+item]*Lnorm*Kcl*Ksl |
|---|
| 1334 | dFdODF[phfx+item] = Kcl*Ksl*Lnorm |
|---|
| 1335 | return odfCor,dFdODF |
|---|
| 1336 | |
|---|
| 1337 | def GetPrefOri(uniq,G,g,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 1338 | 'March-Dollase preferred orientation correction' |
|---|
| 1339 | POcorr = 1.0 |
|---|
| 1340 | MD = parmDict[phfx+'MD'] |
|---|
| 1341 | if MD != 1.0: |
|---|
| 1342 | MDAxis = calcControls[phfx+'MDAxis'] |
|---|
| 1343 | sumMD = 0 |
|---|
| 1344 | for H in uniq: |
|---|
| 1345 | cosP,sinP = G2lat.CosSinAngle(H,MDAxis,G) |
|---|
| 1346 | A = 1.0/np.sqrt((MD*cosP)**2+sinP**2/MD) |
|---|
| 1347 | sumMD += A**3 |
|---|
| 1348 | POcorr = sumMD/len(uniq) |
|---|
| 1349 | return POcorr |
|---|
| 1350 | |
|---|
| 1351 | def GetPrefOriDerv(refl,im,uniq,G,g,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 1352 | 'Needs a doc string' |
|---|
| 1353 | POcorr = 1.0 |
|---|
| 1354 | POderv = {} |
|---|
| 1355 | if calcControls[phfx+'poType'] == 'MD': |
|---|
| 1356 | MD = parmDict[phfx+'MD'] |
|---|
| 1357 | MDAxis = calcControls[phfx+'MDAxis'] |
|---|
| 1358 | sumMD = 0 |
|---|
| 1359 | sumdMD = 0 |
|---|
| 1360 | for H in uniq: |
|---|
| 1361 | cosP,sinP = G2lat.CosSinAngle(H,MDAxis,G) |
|---|
| 1362 | A = 1.0/np.sqrt((MD*cosP)**2+sinP**2/MD) |
|---|
| 1363 | sumMD += A**3 |
|---|
| 1364 | sumdMD -= (1.5*A**5)*(2.0*MD*cosP**2-(sinP/MD)**2) |
|---|
| 1365 | POcorr = sumMD/len(uniq) |
|---|
| 1366 | POderv[phfx+'MD'] = sumdMD/len(uniq) |
|---|
| 1367 | else: #spherical harmonics |
|---|
| 1368 | if calcControls[phfx+'SHord']: |
|---|
| 1369 | POcorr,POderv = SHPOcalDerv(refl,im,g,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 1370 | return POcorr,POderv |
|---|
| 1371 | |
|---|
| 1372 | def GetAbsorb(refl,im,hfx,calcControls,parmDict): |
|---|
| 1373 | 'Needs a doc string' |
|---|
| 1374 | if 'Debye' in calcControls[hfx+'instType']: |
|---|
| 1375 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1376 | return G2pwd.Absorb('Cylinder',parmDict[hfx+'Absorption']*refl[14+im],abs(parmDict[hfx+'2-theta']),0,0) |
|---|
| 1377 | else: |
|---|
| 1378 | return G2pwd.Absorb('Cylinder',parmDict[hfx+'Absorption'],refl[5+im],0,0) |
|---|
| 1379 | else: |
|---|
| 1380 | return G2pwd.SurfaceRough(parmDict[hfx+'SurfRoughA'],parmDict[hfx+'SurfRoughB'],refl[5+im]) |
|---|
| 1381 | |
|---|
| 1382 | def GetAbsorbDerv(refl,im,hfx,calcControls,parmDict): |
|---|
| 1383 | 'Needs a doc string' |
|---|
| 1384 | if 'Debye' in calcControls[hfx+'instType']: |
|---|
| 1385 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1386 | return G2pwd.AbsorbDerv('Cylinder',parmDict[hfx+'Absorption']*refl[14+im],abs(parmDict[hfx+'2-theta']),0,0) |
|---|
| 1387 | else: |
|---|
| 1388 | return G2pwd.AbsorbDerv('Cylinder',parmDict[hfx+'Absorption'],refl[5+im],0,0) |
|---|
| 1389 | else: |
|---|
| 1390 | return np.array(G2pwd.SurfaceRoughDerv(parmDict[hfx+'SurfRoughA'],parmDict[hfx+'SurfRoughB'],refl[5+im])) |
|---|
| 1391 | |
|---|
| 1392 | def GetPwdrExt(refl,im,pfx,phfx,hfx,calcControls,parmDict): |
|---|
| 1393 | 'Needs a doc string' |
|---|
| 1394 | coef = np.array([-0.5,0.25,-0.10416667,0.036458333,-0.0109375,2.8497409E-3]) |
|---|
| 1395 | pi2 = np.sqrt(2./np.pi) |
|---|
| 1396 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1397 | sth2 = sind(abs(parmDict[hfx+'2-theta'])/2.)**2 |
|---|
| 1398 | wave = refl[14+im] |
|---|
| 1399 | else: #'C'W |
|---|
| 1400 | sth2 = sind(refl[5+im]/2.)**2 |
|---|
| 1401 | wave = parmDict.get(hfx+'Lam',parmDict.get(hfx+'Lam1',1.0)) |
|---|
| 1402 | c2th = 1.-2.0*sth2 |
|---|
| 1403 | flv2 = refl[9+im]*(wave/parmDict[pfx+'Vol'])**2 |
|---|
| 1404 | if 'X' in calcControls[hfx+'histType']: |
|---|
| 1405 | flv2 *= 0.079411*(1.0+c2th**2)/2.0 |
|---|
| 1406 | xfac = flv2*parmDict[phfx+'Extinction'] |
|---|
| 1407 | exb = 1.0 |
|---|
| 1408 | if xfac > -1.: |
|---|
| 1409 | exb = 1./np.sqrt(1.+xfac) |
|---|
| 1410 | exl = 1.0 |
|---|
| 1411 | if 0 < xfac <= 1.: |
|---|
| 1412 | xn = np.array([xfac**(i+1) for i in range(6)]) |
|---|
| 1413 | exl += np.sum(xn*coef) |
|---|
| 1414 | elif xfac > 1.: |
|---|
| 1415 | xfac2 = 1./np.sqrt(xfac) |
|---|
| 1416 | exl = pi2*(1.-0.125/xfac)*xfac2 |
|---|
| 1417 | return exb*sth2+exl*(1.-sth2) |
|---|
| 1418 | |
|---|
| 1419 | def GetPwdrExtDerv(refl,im,pfx,phfx,hfx,calcControls,parmDict): |
|---|
| 1420 | 'Needs a doc string' |
|---|
| 1421 | coef = np.array([-0.5,0.25,-0.10416667,0.036458333,-0.0109375,2.8497409E-3]) |
|---|
| 1422 | pi2 = np.sqrt(2./np.pi) |
|---|
| 1423 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 1424 | sth2 = sind(abs(parmDict[hfx+'2-theta'])/2.)**2 |
|---|
| 1425 | wave = refl[14+im] |
|---|
| 1426 | else: #'C'W |
|---|
| 1427 | sth2 = sind(refl[5+im]/2.)**2 |
|---|
| 1428 | wave = parmDict.get(hfx+'Lam',parmDict.get(hfx+'Lam1',1.0)) |
|---|
| 1429 | c2th = 1.-2.0*sth2 |
|---|
| 1430 | flv2 = refl[9+im]*(wave/parmDict[pfx+'Vol'])**2 |
|---|
| 1431 | if 'X' in calcControls[hfx+'histType']: |
|---|
| 1432 | flv2 *= 0.079411*(1.0+c2th**2)/2.0 |
|---|
| 1433 | xfac = flv2*parmDict[phfx+'Extinction'] |
|---|
| 1434 | dbde = -500.*flv2 |
|---|
| 1435 | if xfac > -1.: |
|---|
| 1436 | dbde = -0.5*flv2/np.sqrt(1.+xfac)**3 |
|---|
| 1437 | dlde = 0. |
|---|
| 1438 | if 0 < xfac <= 1.: |
|---|
| 1439 | xn = np.array([i*flv2*xfac**i for i in [1,2,3,4,5,6]]) |
|---|
| 1440 | dlde = np.sum(xn*coef) |
|---|
| 1441 | elif xfac > 1.: |
|---|
| 1442 | xfac2 = 1./np.sqrt(xfac) |
|---|
| 1443 | dlde = flv2*pi2*xfac2*(-1./xfac+0.375/xfac**2) |
|---|
| 1444 | |
|---|
| 1445 | return dbde*sth2+dlde*(1.-sth2) |
|---|
| 1446 | |
|---|
| 1447 | def GetIntensityCorr(refl,im,uniq,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 1448 | 'Needs a doc string' #need powder extinction! |
|---|
| 1449 | Icorr = parmDict[phfx+'Scale']*parmDict[hfx+'Scale']*refl[3+im] #scale*multiplicity |
|---|
| 1450 | if 'X' in parmDict[hfx+'Type']: |
|---|
| 1451 | Icorr *= G2pwd.Polarization(parmDict[hfx+'Polariz.'],refl[5+im],parmDict[hfx+'Azimuth'])[0] |
|---|
| 1452 | POcorr = 1.0 |
|---|
| 1453 | if pfx+'SHorder' in parmDict: #generalized spherical harmonics texture - takes precidence |
|---|
| 1454 | POcorr = SHTXcal(refl,im,g,pfx,hfx,SGData,calcControls,parmDict) |
|---|
| 1455 | elif calcControls[phfx+'poType'] == 'MD': #March-Dollase |
|---|
| 1456 | POcorr = GetPrefOri(uniq,G,g,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 1457 | elif calcControls[phfx+'SHord']: #cylindrical spherical harmonics |
|---|
| 1458 | POcorr = SHPOcal(refl,im,g,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 1459 | Icorr *= POcorr |
|---|
| 1460 | AbsCorr = 1.0 |
|---|
| 1461 | AbsCorr = GetAbsorb(refl,im,hfx,calcControls,parmDict) |
|---|
| 1462 | Icorr *= AbsCorr |
|---|
| 1463 | ExtCorr = GetPwdrExt(refl,im,pfx,phfx,hfx,calcControls,parmDict) |
|---|
| 1464 | Icorr *= ExtCorr |
|---|
| 1465 | return Icorr,POcorr,AbsCorr,ExtCorr |
|---|
| 1466 | |
|---|
| 1467 | def GetIntensityDerv(refl,im,wave,uniq,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 1468 | 'Needs a doc string' #need powder extinction derivs! |
|---|
| 1469 | dIdsh = 1./parmDict[hfx+'Scale'] |
|---|
| 1470 | dIdsp = 1./parmDict[phfx+'Scale'] |
|---|
| 1471 | if 'X' in parmDict[hfx+'Type']: |
|---|
| 1472 | pola,dIdPola = G2pwd.Polarization(parmDict[hfx+'Polariz.'],refl[5+im],parmDict[hfx+'Azimuth']) |
|---|
| 1473 | dIdPola /= pola |
|---|
| 1474 | else: #'N' |
|---|
| 1475 | dIdPola = 0.0 |
|---|
| 1476 | dFdODF = {} |
|---|
| 1477 | dFdSA = [0,0,0] |
|---|
| 1478 | dIdPO = {} |
|---|
| 1479 | if pfx+'SHorder' in parmDict: |
|---|
| 1480 | odfCor,dFdODF,dFdSA = SHTXcalDerv(refl,im,g,pfx,hfx,SGData,calcControls,parmDict) |
|---|
| 1481 | for iSH in dFdODF: |
|---|
| 1482 | dFdODF[iSH] /= odfCor |
|---|
| 1483 | for i in range(3): |
|---|
| 1484 | dFdSA[i] /= odfCor |
|---|
| 1485 | elif calcControls[phfx+'poType'] == 'MD' or calcControls[phfx+'SHord']: |
|---|
| 1486 | POcorr,dIdPO = GetPrefOriDerv(refl,im,uniq,G,g,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 1487 | for iPO in dIdPO: |
|---|
| 1488 | dIdPO[iPO] /= POcorr |
|---|
| 1489 | if 'T' in parmDict[hfx+'Type']: |
|---|
| 1490 | dFdAb = GetAbsorbDerv(refl,im,hfx,calcControls,parmDict)*wave/refl[16+im] #wave/abs corr |
|---|
| 1491 | dFdEx = GetPwdrExtDerv(refl,im,pfx,phfx,hfx,calcControls,parmDict)/refl[17+im] #/ext corr |
|---|
| 1492 | else: |
|---|
| 1493 | dFdAb = GetAbsorbDerv(refl,im,hfx,calcControls,parmDict)*wave/refl[13+im] #wave/abs corr |
|---|
| 1494 | dFdEx = GetPwdrExtDerv(refl,im,pfx,phfx,hfx,calcControls,parmDict)/refl[14+im] #/ext corr |
|---|
| 1495 | return dIdsh,dIdsp,dIdPola,dIdPO,dFdODF,dFdSA,dFdAb,dFdEx |
|---|
| 1496 | |
|---|
| 1497 | def GetSampleSigGam(refl,im,wave,G,GB,SGData,hfx,phfx,calcControls,parmDict): |
|---|
| 1498 | 'Needs a doc string' |
|---|
| 1499 | if 'C' in calcControls[hfx+'histType']: #All checked & OK |
|---|
| 1500 | costh = cosd(refl[5+im]/2.) |
|---|
| 1501 | #crystallite size |
|---|
| 1502 | if calcControls[phfx+'SizeType'] == 'isotropic': |
|---|
| 1503 | Sgam = 1.8*wave/(np.pi*parmDict[phfx+'Size;i']*costh) |
|---|
| 1504 | elif calcControls[phfx+'SizeType'] == 'uniaxial': |
|---|
| 1505 | H = np.array(refl[:3]) |
|---|
| 1506 | P = np.array(calcControls[phfx+'SizeAxis']) |
|---|
| 1507 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 1508 | Sgam = (1.8*wave/np.pi)/(parmDict[phfx+'Size;i']*parmDict[phfx+'Size;a']*costh) |
|---|
| 1509 | Sgam *= np.sqrt((sinP*parmDict[phfx+'Size;a'])**2+(cosP*parmDict[phfx+'Size;i'])**2) |
|---|
| 1510 | else: #ellipsoidal crystallites |
|---|
| 1511 | Sij =[parmDict[phfx+'Size:%d'%(i)] for i in range(6)] |
|---|
| 1512 | H = np.array(refl[:3]) |
|---|
| 1513 | lenR = G2pwd.ellipseSize(H,Sij,GB) |
|---|
| 1514 | Sgam = 1.8*wave/(np.pi*costh*lenR) |
|---|
| 1515 | #microstrain |
|---|
| 1516 | if calcControls[phfx+'MustrainType'] == 'isotropic': |
|---|
| 1517 | Mgam = 0.018*parmDict[phfx+'Mustrain;i']*tand(refl[5+im]/2.)/np.pi |
|---|
| 1518 | elif calcControls[phfx+'MustrainType'] == 'uniaxial': |
|---|
| 1519 | H = np.array(refl[:3]) |
|---|
| 1520 | P = np.array(calcControls[phfx+'MustrainAxis']) |
|---|
| 1521 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 1522 | Si = parmDict[phfx+'Mustrain;i'] |
|---|
| 1523 | Sa = parmDict[phfx+'Mustrain;a'] |
|---|
| 1524 | Mgam = 0.018*Si*Sa*tand(refl[5+im]/2.)/(np.pi*np.sqrt((Si*cosP)**2+(Sa*sinP)**2)) |
|---|
| 1525 | else: #generalized - P.W. Stephens model |
|---|
| 1526 | Strms = G2spc.MustrainCoeff(refl[:3],SGData) |
|---|
| 1527 | Sum = 0 |
|---|
| 1528 | for i,strm in enumerate(Strms): |
|---|
| 1529 | Sum += parmDict[phfx+'Mustrain:'+str(i)]*strm |
|---|
| 1530 | Mgam = 0.018*refl[4+im]**2*tand(refl[5+im]/2.)*np.sqrt(Sum)/np.pi |
|---|
| 1531 | elif 'T' in calcControls[hfx+'histType']: #All checked & OK |
|---|
| 1532 | #crystallite size |
|---|
| 1533 | if calcControls[phfx+'SizeType'] == 'isotropic': #OK |
|---|
| 1534 | Sgam = 1.e-4*parmDict[hfx+'difC']*refl[4+im]**2/parmDict[phfx+'Size;i'] |
|---|
| 1535 | elif calcControls[phfx+'SizeType'] == 'uniaxial': #OK |
|---|
| 1536 | H = np.array(refl[:3]) |
|---|
| 1537 | P = np.array(calcControls[phfx+'SizeAxis']) |
|---|
| 1538 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 1539 | Sgam = 1.e-4*parmDict[hfx+'difC']*refl[4+im]**2/(parmDict[phfx+'Size;i']*parmDict[phfx+'Size;a']) |
|---|
| 1540 | Sgam *= np.sqrt((sinP*parmDict[phfx+'Size;a'])**2+(cosP*parmDict[phfx+'Size;i'])**2) |
|---|
| 1541 | else: #ellipsoidal crystallites #OK |
|---|
| 1542 | Sij =[parmDict[phfx+'Size:%d'%(i)] for i in range(6)] |
|---|
| 1543 | H = np.array(refl[:3]) |
|---|
| 1544 | lenR = G2pwd.ellipseSize(H,Sij,GB) |
|---|
| 1545 | Sgam = 1.e-4*parmDict[hfx+'difC']*refl[4+im]**2/lenR |
|---|
| 1546 | #microstrain |
|---|
| 1547 | if calcControls[phfx+'MustrainType'] == 'isotropic': #OK |
|---|
| 1548 | Mgam = 1.e-6*parmDict[hfx+'difC']*refl[4+im]*parmDict[phfx+'Mustrain;i'] |
|---|
| 1549 | elif calcControls[phfx+'MustrainType'] == 'uniaxial': #OK |
|---|
| 1550 | H = np.array(refl[:3]) |
|---|
| 1551 | P = np.array(calcControls[phfx+'MustrainAxis']) |
|---|
| 1552 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 1553 | Si = parmDict[phfx+'Mustrain;i'] |
|---|
| 1554 | Sa = parmDict[phfx+'Mustrain;a'] |
|---|
| 1555 | Mgam = 1.e-6*parmDict[hfx+'difC']*refl[4+im]*Si*Sa/np.sqrt((Si*cosP)**2+(Sa*sinP)**2) |
|---|
| 1556 | else: #generalized - P.W. Stephens model OK |
|---|
| 1557 | Strms = G2spc.MustrainCoeff(refl[:3],SGData) |
|---|
| 1558 | Sum = 0 |
|---|
| 1559 | for i,strm in enumerate(Strms): |
|---|
| 1560 | Sum += parmDict[phfx+'Mustrain:'+str(i)]*strm |
|---|
| 1561 | Mgam = 1.e-6*parmDict[hfx+'difC']*np.sqrt(Sum)*refl[4+im]**3 |
|---|
| 1562 | |
|---|
| 1563 | gam = Sgam*parmDict[phfx+'Size;mx']+Mgam*parmDict[phfx+'Mustrain;mx'] |
|---|
| 1564 | sig = (Sgam*(1.-parmDict[phfx+'Size;mx']))**2+(Mgam*(1.-parmDict[phfx+'Mustrain;mx']))**2 |
|---|
| 1565 | sig /= ateln2 |
|---|
| 1566 | return sig,gam |
|---|
| 1567 | |
|---|
| 1568 | def GetSampleSigGamDerv(refl,im,wave,G,GB,SGData,hfx,phfx,calcControls,parmDict): |
|---|
| 1569 | 'Needs a doc string' |
|---|
| 1570 | gamDict = {} |
|---|
| 1571 | sigDict = {} |
|---|
| 1572 | if 'C' in calcControls[hfx+'histType']: #All checked & OK |
|---|
| 1573 | costh = cosd(refl[5+im]/2.) |
|---|
| 1574 | tanth = tand(refl[5+im]/2.) |
|---|
| 1575 | #crystallite size derivatives |
|---|
| 1576 | if calcControls[phfx+'SizeType'] == 'isotropic': |
|---|
| 1577 | Sgam = 1.8*wave/(np.pi*parmDict[phfx+'Size;i']*costh) |
|---|
| 1578 | gamDict[phfx+'Size;i'] = -1.8*wave*parmDict[phfx+'Size;mx']/(np.pi*costh) |
|---|
| 1579 | sigDict[phfx+'Size;i'] = -3.6*Sgam*wave*(1.-parmDict[phfx+'Size;mx'])**2/(np.pi*costh*ateln2) |
|---|
| 1580 | elif calcControls[phfx+'SizeType'] == 'uniaxial': |
|---|
| 1581 | H = np.array(refl[:3]) |
|---|
| 1582 | P = np.array(calcControls[phfx+'SizeAxis']) |
|---|
| 1583 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 1584 | Si = parmDict[phfx+'Size;i'] |
|---|
| 1585 | Sa = parmDict[phfx+'Size;a'] |
|---|
| 1586 | gami = 1.8*wave/(costh*np.pi*Si*Sa) |
|---|
| 1587 | sqtrm = np.sqrt((sinP*Sa)**2+(cosP*Si)**2) |
|---|
| 1588 | Sgam = gami*sqtrm |
|---|
| 1589 | dsi = gami*Si*cosP**2/sqtrm-Sgam/Si |
|---|
| 1590 | dsa = gami*Sa*sinP**2/sqtrm-Sgam/Sa |
|---|
| 1591 | gamDict[phfx+'Size;i'] = dsi*parmDict[phfx+'Size;mx'] |
|---|
| 1592 | gamDict[phfx+'Size;a'] = dsa*parmDict[phfx+'Size;mx'] |
|---|
| 1593 | sigDict[phfx+'Size;i'] = 2.*dsi*Sgam*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 1594 | sigDict[phfx+'Size;a'] = 2.*dsa*Sgam*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 1595 | else: #ellipsoidal crystallites |
|---|
| 1596 | const = 1.8*wave/(np.pi*costh) |
|---|
| 1597 | Sij =[parmDict[phfx+'Size:%d'%(i)] for i in range(6)] |
|---|
| 1598 | H = np.array(refl[:3]) |
|---|
| 1599 | lenR,dRdS = G2pwd.ellipseSizeDerv(H,Sij,GB) |
|---|
| 1600 | Sgam = const/lenR |
|---|
| 1601 | for i,item in enumerate([phfx+'Size:%d'%(j) for j in range(6)]): |
|---|
| 1602 | gamDict[item] = -(const/lenR**2)*dRdS[i]*parmDict[phfx+'Size;mx'] |
|---|
| 1603 | sigDict[item] = -2.*Sgam*(const/lenR**2)*dRdS[i]*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 1604 | gamDict[phfx+'Size;mx'] = Sgam |
|---|
| 1605 | sigDict[phfx+'Size;mx'] = -2.*Sgam**2*(1.-parmDict[phfx+'Size;mx'])/ateln2 |
|---|
| 1606 | |
|---|
| 1607 | #microstrain derivatives |
|---|
| 1608 | if calcControls[phfx+'MustrainType'] == 'isotropic': |
|---|
| 1609 | Mgam = 0.018*parmDict[phfx+'Mustrain;i']*tand(refl[5+im]/2.)/np.pi |
|---|
| 1610 | gamDict[phfx+'Mustrain;i'] = 0.018*tanth*parmDict[phfx+'Mustrain;mx']/np.pi |
|---|
| 1611 | sigDict[phfx+'Mustrain;i'] = 0.036*Mgam*tanth*(1.-parmDict[phfx+'Mustrain;mx'])**2/(np.pi*ateln2) |
|---|
| 1612 | elif calcControls[phfx+'MustrainType'] == 'uniaxial': |
|---|
| 1613 | H = np.array(refl[:3]) |
|---|
| 1614 | P = np.array(calcControls[phfx+'MustrainAxis']) |
|---|
| 1615 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 1616 | Si = parmDict[phfx+'Mustrain;i'] |
|---|
| 1617 | Sa = parmDict[phfx+'Mustrain;a'] |
|---|
| 1618 | gami = 0.018*Si*Sa*tanth/np.pi |
|---|
| 1619 | sqtrm = np.sqrt((Si*cosP)**2+(Sa*sinP)**2) |
|---|
| 1620 | Mgam = gami/sqtrm |
|---|
| 1621 | dsi = -gami*Si*cosP**2/sqtrm**3 |
|---|
| 1622 | dsa = -gami*Sa*sinP**2/sqtrm**3 |
|---|
| 1623 | gamDict[phfx+'Mustrain;i'] = (Mgam/Si+dsi)*parmDict[phfx+'Mustrain;mx'] |
|---|
| 1624 | gamDict[phfx+'Mustrain;a'] = (Mgam/Sa+dsa)*parmDict[phfx+'Mustrain;mx'] |
|---|
| 1625 | sigDict[phfx+'Mustrain;i'] = 2*(Mgam/Si+dsi)*Mgam*(1.-parmDict[phfx+'Mustrain;mx'])**2/ateln2 |
|---|
| 1626 | sigDict[phfx+'Mustrain;a'] = 2*(Mgam/Sa+dsa)*Mgam*(1.-parmDict[phfx+'Mustrain;mx'])**2/ateln2 |
|---|
| 1627 | else: #generalized - P.W. Stephens model |
|---|
| 1628 | const = 0.018*refl[4+im]**2*tanth/np.pi |
|---|
| 1629 | Strms = G2spc.MustrainCoeff(refl[:3],SGData) |
|---|
| 1630 | Sum = 0 |
|---|
| 1631 | for i,strm in enumerate(Strms): |
|---|
| 1632 | Sum += parmDict[phfx+'Mustrain:'+str(i)]*strm |
|---|
| 1633 | gamDict[phfx+'Mustrain:'+str(i)] = strm*parmDict[phfx+'Mustrain;mx']/2. |
|---|
| 1634 | sigDict[phfx+'Mustrain:'+str(i)] = strm*(1.-parmDict[phfx+'Mustrain;mx'])**2 |
|---|
| 1635 | Mgam = const*np.sqrt(Sum) |
|---|
| 1636 | for i in range(len(Strms)): |
|---|
| 1637 | gamDict[phfx+'Mustrain:'+str(i)] *= Mgam/Sum |
|---|
| 1638 | sigDict[phfx+'Mustrain:'+str(i)] *= const**2/ateln2 |
|---|
| 1639 | gamDict[phfx+'Mustrain;mx'] = Mgam |
|---|
| 1640 | sigDict[phfx+'Mustrain;mx'] = -2.*Mgam**2*(1.-parmDict[phfx+'Mustrain;mx'])/ateln2 |
|---|
| 1641 | else: #'T'OF - All checked & OK |
|---|
| 1642 | if calcControls[phfx+'SizeType'] == 'isotropic': #OK |
|---|
| 1643 | Sgam = 1.e-4*parmDict[hfx+'difC']*refl[4+im]**2/parmDict[phfx+'Size;i'] |
|---|
| 1644 | gamDict[phfx+'Size;i'] = -Sgam*parmDict[phfx+'Size;mx']/parmDict[phfx+'Size;i'] |
|---|
| 1645 | sigDict[phfx+'Size;i'] = -2.*Sgam**2*(1.-parmDict[phfx+'Size;mx'])**2/(ateln2*parmDict[phfx+'Size;i']) |
|---|
| 1646 | elif calcControls[phfx+'SizeType'] == 'uniaxial': #OK |
|---|
| 1647 | const = 1.e-4*parmDict[hfx+'difC']*refl[4+im]**2 |
|---|
| 1648 | H = np.array(refl[:3]) |
|---|
| 1649 | P = np.array(calcControls[phfx+'SizeAxis']) |
|---|
| 1650 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 1651 | Si = parmDict[phfx+'Size;i'] |
|---|
| 1652 | Sa = parmDict[phfx+'Size;a'] |
|---|
| 1653 | gami = const/(Si*Sa) |
|---|
| 1654 | sqtrm = np.sqrt((sinP*Sa)**2+(cosP*Si)**2) |
|---|
| 1655 | Sgam = gami*sqtrm |
|---|
| 1656 | dsi = gami*Si*cosP**2/sqtrm-Sgam/Si |
|---|
| 1657 | dsa = gami*Sa*sinP**2/sqtrm-Sgam/Sa |
|---|
| 1658 | gamDict[phfx+'Size;i'] = dsi*parmDict[phfx+'Size;mx'] |
|---|
| 1659 | gamDict[phfx+'Size;a'] = dsa*parmDict[phfx+'Size;mx'] |
|---|
| 1660 | sigDict[phfx+'Size;i'] = 2.*dsi*Sgam*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 1661 | sigDict[phfx+'Size;a'] = 2.*dsa*Sgam*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 1662 | else: #OK ellipsoidal crystallites |
|---|
| 1663 | const = 1.e-4*parmDict[hfx+'difC']*refl[4+im]**2 |
|---|
| 1664 | Sij =[parmDict[phfx+'Size:%d'%(i)] for i in range(6)] |
|---|
| 1665 | H = np.array(refl[:3]) |
|---|
| 1666 | lenR,dRdS = G2pwd.ellipseSizeDerv(H,Sij,GB) |
|---|
| 1667 | Sgam = const/lenR |
|---|
| 1668 | for i,item in enumerate([phfx+'Size:%d'%(j) for j in range(6)]): |
|---|
| 1669 | gamDict[item] = -(const/lenR**2)*dRdS[i]*parmDict[phfx+'Size;mx'] |
|---|
| 1670 | sigDict[item] = -2.*Sgam*(const/lenR**2)*dRdS[i]*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 1671 | gamDict[phfx+'Size;mx'] = Sgam #OK |
|---|
| 1672 | sigDict[phfx+'Size;mx'] = -2.*Sgam**2*(1.-parmDict[phfx+'Size;mx'])/ateln2 #OK |
|---|
| 1673 | |
|---|
| 1674 | #microstrain derivatives |
|---|
| 1675 | if calcControls[phfx+'MustrainType'] == 'isotropic': |
|---|
| 1676 | Mgam = 1.e-6*parmDict[hfx+'difC']*refl[4+im]*parmDict[phfx+'Mustrain;i'] |
|---|
| 1677 | gamDict[phfx+'Mustrain;i'] = 1.e-6*refl[4+im]*parmDict[hfx+'difC']*parmDict[phfx+'Mustrain;mx'] #OK |
|---|
| 1678 | sigDict[phfx+'Mustrain;i'] = 2.*Mgam**2*(1.-parmDict[phfx+'Mustrain;mx'])**2/(ateln2*parmDict[phfx+'Mustrain;i']) |
|---|
| 1679 | elif calcControls[phfx+'MustrainType'] == 'uniaxial': |
|---|
| 1680 | H = np.array(refl[:3]) |
|---|
| 1681 | P = np.array(calcControls[phfx+'MustrainAxis']) |
|---|
| 1682 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 1683 | Si = parmDict[phfx+'Mustrain;i'] |
|---|
| 1684 | Sa = parmDict[phfx+'Mustrain;a'] |
|---|
| 1685 | gami = 1.e-6*parmDict[hfx+'difC']*refl[4+im]*Si*Sa |
|---|
| 1686 | sqtrm = np.sqrt((Si*cosP)**2+(Sa*sinP)**2) |
|---|
| 1687 | Mgam = gami/sqtrm |
|---|
| 1688 | dsi = -gami*Si*cosP**2/sqtrm**3 |
|---|
| 1689 | dsa = -gami*Sa*sinP**2/sqtrm**3 |
|---|
| 1690 | gamDict[phfx+'Mustrain;i'] = (Mgam/Si+dsi)*parmDict[phfx+'Mustrain;mx'] |
|---|
| 1691 | gamDict[phfx+'Mustrain;a'] = (Mgam/Sa+dsa)*parmDict[phfx+'Mustrain;mx'] |
|---|
| 1692 | sigDict[phfx+'Mustrain;i'] = 2*(Mgam/Si+dsi)*Mgam*(1.-parmDict[phfx+'Mustrain;mx'])**2/ateln2 |
|---|
| 1693 | sigDict[phfx+'Mustrain;a'] = 2*(Mgam/Sa+dsa)*Mgam*(1.-parmDict[phfx+'Mustrain;mx'])**2/ateln2 |
|---|
| 1694 | else: #generalized - P.W. Stephens model OK |
|---|
| 1695 | pwrs = calcControls[phfx+'MuPwrs'] |
|---|
| 1696 | Strms = G2spc.MustrainCoeff(refl[:3],SGData) |
|---|
| 1697 | const = 1.e-6*parmDict[hfx+'difC']*refl[4+im]**3 |
|---|
| 1698 | Sum = 0 |
|---|
| 1699 | for i,strm in enumerate(Strms): |
|---|
| 1700 | Sum += parmDict[phfx+'Mustrain:'+str(i)]*strm |
|---|
| 1701 | gamDict[phfx+'Mustrain:'+str(i)] = strm*parmDict[phfx+'Mustrain;mx']/2. |
|---|
| 1702 | sigDict[phfx+'Mustrain:'+str(i)] = strm*(1.-parmDict[phfx+'Mustrain;mx'])**2 |
|---|
| 1703 | Mgam = const*np.sqrt(Sum) |
|---|
| 1704 | for i in range(len(Strms)): |
|---|
| 1705 | gamDict[phfx+'Mustrain:'+str(i)] *= Mgam/Sum |
|---|
| 1706 | sigDict[phfx+'Mustrain:'+str(i)] *= const**2/ateln2 |
|---|
| 1707 | gamDict[phfx+'Mustrain;mx'] = Mgam |
|---|
| 1708 | sigDict[phfx+'Mustrain;mx'] = -2.*Mgam**2*(1.-parmDict[phfx+'Mustrain;mx'])/ateln2 |
|---|
| 1709 | |
|---|
| 1710 | return sigDict,gamDict |
|---|
| 1711 | |
|---|
| 1712 | def GetReflPos(refl,im,wave,A,pfx,hfx,calcControls,parmDict): |
|---|
| 1713 | 'Needs a doc string' |
|---|
| 1714 | if im: |
|---|
| 1715 | h,k,l,m = refl[:4] |
|---|
| 1716 | vec = np.array([parmDict[pfx+'mV0'],parmDict[pfx+'mV1'],parmDict[pfx+'mV2']]) |
|---|
| 1717 | d = 1./np.sqrt(G2lat.calc_rDsqSS(np.array([h,k,l,m]),A,vec)) |
|---|
| 1718 | else: |
|---|
| 1719 | h,k,l = refl[:3] |
|---|
| 1720 | d = 1./np.sqrt(G2lat.calc_rDsq(np.array([h,k,l]),A)) |
|---|
| 1721 | refl[4+im] = d |
|---|
| 1722 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 1723 | pos = 2.0*asind(wave/(2.0*d))+parmDict[hfx+'Zero'] |
|---|
| 1724 | const = 9.e-2/(np.pi*parmDict[hfx+'Gonio. radius']) #shifts in microns |
|---|
| 1725 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 1726 | pos -= const*(4.*parmDict[hfx+'Shift']*cosd(pos/2.0)+ \ |
|---|
| 1727 | parmDict[hfx+'Transparency']*sind(pos)*100.0) #trans(=1/mueff) in cm |
|---|
| 1728 | else: #Debye-Scherrer - simple but maybe not right |
|---|
| 1729 | pos -= const*(parmDict[hfx+'DisplaceX']*cosd(pos)+parmDict[hfx+'DisplaceY']*sind(pos)) |
|---|
| 1730 | elif 'T' in calcControls[hfx+'histType']: |
|---|
| 1731 | pos = parmDict[hfx+'difC']*d+parmDict[hfx+'difA']*d**2+parmDict[hfx+'difB']/d+parmDict[hfx+'Zero'] |
|---|
| 1732 | #do I need sample position effects - maybe? |
|---|
| 1733 | return pos |
|---|
| 1734 | |
|---|
| 1735 | def GetReflPosDerv(refl,im,wave,A,pfx,hfx,calcControls,parmDict): |
|---|
| 1736 | 'Needs a doc string' |
|---|
| 1737 | dpr = 180./np.pi |
|---|
| 1738 | if im: |
|---|
| 1739 | h,k,l,m = refl[:4] |
|---|
| 1740 | vec = np.array([parmDict[pfx+'mV0'],parmDict[pfx+'mV1'],parmDict[pfx+'mV2']]) |
|---|
| 1741 | dstsq = G2lat.calc_rDsqSS(np.array([h,k,l,m]),A,vec) |
|---|
| 1742 | else: |
|---|
| 1743 | m = 0 |
|---|
| 1744 | h,k,l = refl[:3] |
|---|
| 1745 | dstsq = G2lat.calc_rDsq(np.array([h,k,l]),A) |
|---|
| 1746 | dst = np.sqrt(dstsq) |
|---|
| 1747 | dsp = 1./dst |
|---|
| 1748 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 1749 | pos = refl[5+im]-parmDict[hfx+'Zero'] |
|---|
| 1750 | const = dpr/np.sqrt(1.0-wave**2*dstsq/4.0) |
|---|
| 1751 | dpdw = const*dst |
|---|
| 1752 | dpdA = np.array([h**2,k**2,l**2,h*k,h*l,k*l])*const*wave/(2.0*dst) |
|---|
| 1753 | dpdZ = 1.0 |
|---|
| 1754 | dpdV = np.array([2.*h*A[0]+k*A[3]+l*A[4],2*k*A[1]+h*A[3]+l*A[5], |
|---|
| 1755 | 2*l*A[2]+h*A[4]+k*A[5]])*m*const*wave/(2.0*dst) |
|---|
| 1756 | shft = 9.e-2/(np.pi*parmDict[hfx+'Gonio. radius']) #shifts in microns |
|---|
| 1757 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 1758 | dpdSh = -4.*shft*cosd(pos/2.0) |
|---|
| 1759 | dpdTr = -shft*sind(pos)*100.0 |
|---|
| 1760 | return dpdA,dpdw,dpdZ,dpdSh,dpdTr,0.,0.,dpdV |
|---|
| 1761 | else: #Debye-Scherrer - simple but maybe not right |
|---|
| 1762 | dpdXd = -shft*cosd(pos) |
|---|
| 1763 | dpdYd = -shft*sind(pos) |
|---|
| 1764 | return dpdA,dpdw,dpdZ,0.,0.,dpdXd,dpdYd,dpdV |
|---|
| 1765 | elif 'T' in calcControls[hfx+'histType']: |
|---|
| 1766 | dpdA = -np.array([h**2,k**2,l**2,h*k,h*l,k*l])*parmDict[hfx+'difC']*dsp**3/2. |
|---|
| 1767 | dpdZ = 1.0 |
|---|
| 1768 | dpdDC = dsp |
|---|
| 1769 | dpdDA = dsp**2 |
|---|
| 1770 | dpdDB = 1./dsp |
|---|
| 1771 | dpdV = np.array([2.*h*A[0]+k*A[3]+l*A[4],2*k*A[1]+h*A[3]+l*A[5], |
|---|
| 1772 | 2*l*A[2]+h*A[4]+k*A[5]])*m**parmDict[hfx+'difC']*dsp**3/2. |
|---|
| 1773 | return dpdA,dpdZ,dpdDC,dpdDA,dpdDB,dpdV |
|---|
| 1774 | |
|---|
| 1775 | def GetHStrainShift(refl,im,SGData,phfx,hfx,calcControls,parmDict): |
|---|
| 1776 | 'Needs a doc string' |
|---|
| 1777 | laue = SGData['SGLaue'] |
|---|
| 1778 | uniq = SGData['SGUniq'] |
|---|
| 1779 | h,k,l = refl[:3] |
|---|
| 1780 | if laue in ['m3','m3m']: |
|---|
| 1781 | Dij = parmDict[phfx+'D11']*(h**2+k**2+l**2)+ \ |
|---|
| 1782 | refl[4+im]**2*parmDict[phfx+'eA']*((h*k)**2+(h*l)**2+(k*l)**2)/(h**2+k**2+l**2)**2 |
|---|
| 1783 | elif laue in ['6/m','6/mmm','3m1','31m','3']: |
|---|
| 1784 | Dij = parmDict[phfx+'D11']*(h**2+k**2+h*k)+parmDict[phfx+'D33']*l**2 |
|---|
| 1785 | elif laue in ['3R','3mR']: |
|---|
| 1786 | Dij = parmDict[phfx+'D11']*(h**2+k**2+l**2)+parmDict[phfx+'D12']*(h*k+h*l+k*l) |
|---|
| 1787 | elif laue in ['4/m','4/mmm']: |
|---|
| 1788 | Dij = parmDict[phfx+'D11']*(h**2+k**2)+parmDict[phfx+'D33']*l**2 |
|---|
| 1789 | elif laue in ['mmm']: |
|---|
| 1790 | Dij = parmDict[phfx+'D11']*h**2+parmDict[phfx+'D22']*k**2+parmDict[phfx+'D33']*l**2 |
|---|
| 1791 | elif laue in ['2/m']: |
|---|
| 1792 | Dij = parmDict[phfx+'D11']*h**2+parmDict[phfx+'D22']*k**2+parmDict[phfx+'D33']*l**2 |
|---|
| 1793 | if uniq == 'a': |
|---|
| 1794 | Dij += parmDict[phfx+'D23']*k*l |
|---|
| 1795 | elif uniq == 'b': |
|---|
| 1796 | Dij += parmDict[phfx+'D13']*h*l |
|---|
| 1797 | elif uniq == 'c': |
|---|
| 1798 | Dij += parmDict[phfx+'D12']*h*k |
|---|
| 1799 | else: |
|---|
| 1800 | Dij = parmDict[phfx+'D11']*h**2+parmDict[phfx+'D22']*k**2+parmDict[phfx+'D33']*l**2+ \ |
|---|
| 1801 | parmDict[phfx+'D12']*h*k+parmDict[phfx+'D13']*h*l+parmDict[phfx+'D23']*k*l |
|---|
| 1802 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 1803 | return -180.*Dij*refl[4+im]**2*tand(refl[5+im]/2.0)/np.pi |
|---|
| 1804 | else: |
|---|
| 1805 | return -Dij*parmDict[hfx+'difC']*refl[4+im]**2/2. |
|---|
| 1806 | |
|---|
| 1807 | def GetHStrainShiftDerv(refl,im,SGData,phfx,hfx,calcControls,parmDict): |
|---|
| 1808 | 'Needs a doc string' |
|---|
| 1809 | laue = SGData['SGLaue'] |
|---|
| 1810 | uniq = SGData['SGUniq'] |
|---|
| 1811 | h,k,l = refl[:3] |
|---|
| 1812 | if laue in ['m3','m3m']: |
|---|
| 1813 | dDijDict = {phfx+'D11':h**2+k**2+l**2, |
|---|
| 1814 | phfx+'eA':refl[4+im]**2*((h*k)**2+(h*l)**2+(k*l)**2)/(h**2+k**2+l**2)**2} |
|---|
| 1815 | elif laue in ['6/m','6/mmm','3m1','31m','3']: |
|---|
| 1816 | dDijDict = {phfx+'D11':h**2+k**2+h*k,phfx+'D33':l**2} |
|---|
| 1817 | elif laue in ['3R','3mR']: |
|---|
| 1818 | dDijDict = {phfx+'D11':h**2+k**2+l**2,phfx+'D12':h*k+h*l+k*l} |
|---|
| 1819 | elif laue in ['4/m','4/mmm']: |
|---|
| 1820 | dDijDict = {phfx+'D11':h**2+k**2,phfx+'D33':l**2} |
|---|
| 1821 | elif laue in ['mmm']: |
|---|
| 1822 | dDijDict = {phfx+'D11':h**2,phfx+'D22':k**2,phfx+'D33':l**2} |
|---|
| 1823 | elif laue in ['2/m']: |
|---|
| 1824 | dDijDict = {phfx+'D11':h**2,phfx+'D22':k**2,phfx+'D33':l**2} |
|---|
| 1825 | if uniq == 'a': |
|---|
| 1826 | dDijDict[phfx+'D23'] = k*l |
|---|
| 1827 | elif uniq == 'b': |
|---|
| 1828 | dDijDict[phfx+'D13'] = h*l |
|---|
| 1829 | elif uniq == 'c': |
|---|
| 1830 | dDijDict[phfx+'D12'] = h*k |
|---|
| 1831 | else: |
|---|
| 1832 | dDijDict = {phfx+'D11':h**2,phfx+'D22':k**2,phfx+'D33':l**2, |
|---|
| 1833 | phfx+'D12':h*k,phfx+'D13':h*l,phfx+'D23':k*l} |
|---|
| 1834 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 1835 | for item in dDijDict: |
|---|
| 1836 | dDijDict[item] *= 180.0*refl[4+im]**2*tand(refl[5+im]/2.0)/np.pi |
|---|
| 1837 | else: |
|---|
| 1838 | for item in dDijDict: |
|---|
| 1839 | dDijDict[item] *= -parmDict[hfx+'difC']*refl[4+im]**3/2. |
|---|
| 1840 | return dDijDict |
|---|
| 1841 | |
|---|
| 1842 | def GetDij(phfx,SGData,parmDict): |
|---|
| 1843 | HSvals = [parmDict[phfx+name] for name in G2spc.HStrainNames(SGData)] |
|---|
| 1844 | return G2spc.HStrainVals(HSvals,SGData) |
|---|
| 1845 | |
|---|
| 1846 | def GetFobsSq(Histograms,Phases,parmDict,calcControls): |
|---|
| 1847 | 'Needs a doc string' |
|---|
| 1848 | histoList = Histograms.keys() |
|---|
| 1849 | histoList.sort() |
|---|
| 1850 | for histogram in histoList: |
|---|
| 1851 | if 'PWDR' in histogram[:4]: |
|---|
| 1852 | Histogram = Histograms[histogram] |
|---|
| 1853 | hId = Histogram['hId'] |
|---|
| 1854 | hfx = ':%d:'%(hId) |
|---|
| 1855 | Limits = calcControls[hfx+'Limits'] |
|---|
| 1856 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 1857 | shl = max(parmDict[hfx+'SH/L'],0.0005) |
|---|
| 1858 | Ka2 = False |
|---|
| 1859 | kRatio = 0.0 |
|---|
| 1860 | if hfx+'Lam1' in parmDict.keys(): |
|---|
| 1861 | Ka2 = True |
|---|
| 1862 | lamRatio = 360*(parmDict[hfx+'Lam2']-parmDict[hfx+'Lam1'])/(np.pi*parmDict[hfx+'Lam1']) |
|---|
| 1863 | kRatio = parmDict[hfx+'I(L2)/I(L1)'] |
|---|
| 1864 | x,y,w,yc,yb,yd = Histogram['Data'] |
|---|
| 1865 | xB = np.searchsorted(x,Limits[0]) |
|---|
| 1866 | xF = np.searchsorted(x,Limits[1]) |
|---|
| 1867 | ymb = np.array(y-yb) |
|---|
| 1868 | ymb = np.where(ymb,ymb,1.0) |
|---|
| 1869 | ycmb = np.array(yc-yb) |
|---|
| 1870 | ratio = 1./np.where(ycmb,ycmb/ymb,1.e10) |
|---|
| 1871 | refLists = Histogram['Reflection Lists'] |
|---|
| 1872 | for phase in refLists: |
|---|
| 1873 | if phase not in Phases: #skips deleted or renamed phases silently! |
|---|
| 1874 | continue |
|---|
| 1875 | Phase = Phases[phase] |
|---|
| 1876 | im = 0 |
|---|
| 1877 | if Phase['General']['Type'] in ['modulated','magnetic']: |
|---|
| 1878 | im = 1 |
|---|
| 1879 | pId = Phase['pId'] |
|---|
| 1880 | phfx = '%d:%d:'%(pId,hId) |
|---|
| 1881 | refDict = refLists[phase] |
|---|
| 1882 | sumFo = 0.0 |
|---|
| 1883 | sumdF = 0.0 |
|---|
| 1884 | sumFosq = 0.0 |
|---|
| 1885 | sumdFsq = 0.0 |
|---|
| 1886 | sumInt = 0.0 |
|---|
| 1887 | for refl in refDict['RefList']: |
|---|
| 1888 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 1889 | yp = np.zeros_like(yb) |
|---|
| 1890 | Wd,fmin,fmax = G2pwd.getWidthsCW(refl[5+im],refl[6+im],refl[7+im],shl) |
|---|
| 1891 | iBeg = max(xB,np.searchsorted(x,refl[5+im]-fmin)) |
|---|
| 1892 | iFin = max(xB,min(np.searchsorted(x,refl[5+im]+fmax),xF)) |
|---|
| 1893 | iFin2 = iFin |
|---|
| 1894 | if not iBeg+iFin: #peak below low limit - skip peak |
|---|
| 1895 | continue |
|---|
| 1896 | elif not iBeg-iFin: #peak above high limit - done |
|---|
| 1897 | break |
|---|
| 1898 | elif iBeg < iFin: |
|---|
| 1899 | 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 |
|---|
| 1900 | sumInt += refl[11+im]*refl[9+im] |
|---|
| 1901 | if Ka2: |
|---|
| 1902 | pos2 = refl[5+im]+lamRatio*tand(refl[5+im]/2.0) # + 360/pi * Dlam/lam * tan(th) |
|---|
| 1903 | Wd,fmin,fmax = G2pwd.getWidthsCW(pos2,refl[6+im],refl[7+im],shl) |
|---|
| 1904 | iBeg2 = max(xB,np.searchsorted(x,pos2-fmin)) |
|---|
| 1905 | iFin2 = min(np.searchsorted(x,pos2+fmax),xF) |
|---|
| 1906 | if iFin2 > iBeg2: |
|---|
| 1907 | 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 |
|---|
| 1908 | sumInt += refl[11+im]*refl[9+im]*kRatio |
|---|
| 1909 | refl[8+im] = np.sum(np.where(ratio[iBeg:iFin2]>0.,yp[iBeg:iFin2]*ratio[iBeg:iFin2]/(refl[11+im]*(1.+kRatio)),0.0)) |
|---|
| 1910 | |
|---|
| 1911 | elif 'T' in calcControls[hfx+'histType']: |
|---|
| 1912 | yp = np.zeros_like(yb) |
|---|
| 1913 | Wd,fmin,fmax = G2pwd.getWidthsTOF(refl[5+im],refl[12+im],refl[13+im],refl[6+im],refl[7+im]) |
|---|
| 1914 | iBeg = max(xB,np.searchsorted(x,refl[5+im]-fmin)) |
|---|
| 1915 | iFin = max(xB,min(np.searchsorted(x,refl[5+im]+fmax),xF)) |
|---|
| 1916 | if iBeg < iFin: |
|---|
| 1917 | 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 |
|---|
| 1918 | refl[8+im] = np.sum(np.where(ratio[iBeg:iFin]>0.,yp[iBeg:iFin]*ratio[iBeg:iFin]/refl[11+im],0.0)) |
|---|
| 1919 | sumInt += refl[11+im]*refl[9+im] |
|---|
| 1920 | Fo = np.sqrt(np.abs(refl[8+im])) |
|---|
| 1921 | Fc = np.sqrt(np.abs(refl[9]+im)) |
|---|
| 1922 | sumFo += Fo |
|---|
| 1923 | sumFosq += refl[8+im]**2 |
|---|
| 1924 | sumdF += np.abs(Fo-Fc) |
|---|
| 1925 | sumdFsq += (refl[8+im]-refl[9+im])**2 |
|---|
| 1926 | if sumFo: |
|---|
| 1927 | Histogram['Residuals'][phfx+'Rf'] = min(100.,(sumdF/sumFo)*100.) |
|---|
| 1928 | Histogram['Residuals'][phfx+'Rf^2'] = min(100.,np.sqrt(sumdFsq/sumFosq)*100.) |
|---|
| 1929 | else: |
|---|
| 1930 | Histogram['Residuals'][phfx+'Rf'] = 100. |
|---|
| 1931 | Histogram['Residuals'][phfx+'Rf^2'] = 100. |
|---|
| 1932 | Histogram['Residuals'][phfx+'sumInt'] = sumInt |
|---|
| 1933 | Histogram['Residuals'][phfx+'Nref'] = len(refDict['RefList']) |
|---|
| 1934 | Histogram['Residuals']['hId'] = hId |
|---|
| 1935 | elif 'HKLF' in histogram[:4]: |
|---|
| 1936 | Histogram = Histograms[histogram] |
|---|
| 1937 | Histogram['Residuals']['hId'] = Histograms[histogram]['hId'] |
|---|
| 1938 | |
|---|
| 1939 | def getPowderProfile(parmDict,x,varylist,Histogram,Phases,calcControls,pawleyLookup): |
|---|
| 1940 | 'Needs a doc string' |
|---|
| 1941 | |
|---|
| 1942 | def GetReflSigGamCW(refl,im,wave,G,GB,phfx,calcControls,parmDict): |
|---|
| 1943 | U = parmDict[hfx+'U'] |
|---|
| 1944 | V = parmDict[hfx+'V'] |
|---|
| 1945 | W = parmDict[hfx+'W'] |
|---|
| 1946 | X = parmDict[hfx+'X'] |
|---|
| 1947 | Y = parmDict[hfx+'Y'] |
|---|
| 1948 | tanPos = tand(refl[5+im]/2.0) |
|---|
| 1949 | Ssig,Sgam = GetSampleSigGam(refl,im,wave,G,GB,SGData,hfx,phfx,calcControls,parmDict) |
|---|
| 1950 | sig = U*tanPos**2+V*tanPos+W+Ssig #save peak sigma |
|---|
| 1951 | sig = max(0.001,sig) |
|---|
| 1952 | gam = X/cosd(refl[5+im]/2.0)+Y*tanPos+Sgam #save peak gamma |
|---|
| 1953 | gam = max(0.001,gam) |
|---|
| 1954 | return sig,gam |
|---|
| 1955 | |
|---|
| 1956 | def GetReflSigGamTOF(refl,im,G,GB,phfx,calcControls,parmDict): |
|---|
| 1957 | sig = parmDict[hfx+'sig-0']+parmDict[hfx+'sig-1']*refl[4+im]**2+ \ |
|---|
| 1958 | parmDict[hfx+'sig-2']*refl[4+im]**4+parmDict[hfx+'sig-q']/refl[4+im]**2 |
|---|
| 1959 | gam = parmDict[hfx+'X']*refl[4+im]+parmDict[hfx+'Y']*refl[4+im]**2 |
|---|
| 1960 | Ssig,Sgam = GetSampleSigGam(refl,im,0.0,G,GB,SGData,hfx,phfx,calcControls,parmDict) |
|---|
| 1961 | sig += Ssig |
|---|
| 1962 | gam += Sgam |
|---|
| 1963 | return sig,gam |
|---|
| 1964 | |
|---|
| 1965 | def GetReflAlpBet(refl,im,hfx,parmDict): |
|---|
| 1966 | alp = parmDict[hfx+'alpha']/refl[4+im] |
|---|
| 1967 | bet = parmDict[hfx+'beta-0']+parmDict[hfx+'beta-1']/refl[4+im]**4+parmDict[hfx+'beta-q']/refl[4+im]**2 |
|---|
| 1968 | return alp,bet |
|---|
| 1969 | |
|---|
| 1970 | hId = Histogram['hId'] |
|---|
| 1971 | hfx = ':%d:'%(hId) |
|---|
| 1972 | bakType = calcControls[hfx+'bakType'] |
|---|
| 1973 | yb,Histogram['sumBk'] = G2pwd.getBackground(hfx,parmDict,bakType,calcControls[hfx+'histType'],x) |
|---|
| 1974 | yc = np.zeros_like(yb) |
|---|
| 1975 | cw = np.diff(x) |
|---|
| 1976 | cw = np.append(cw,cw[-1]) |
|---|
| 1977 | |
|---|
| 1978 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 1979 | shl = max(parmDict[hfx+'SH/L'],0.002) |
|---|
| 1980 | Ka2 = False |
|---|
| 1981 | if hfx+'Lam1' in parmDict.keys(): |
|---|
| 1982 | wave = parmDict[hfx+'Lam1'] |
|---|
| 1983 | Ka2 = True |
|---|
| 1984 | lamRatio = 360*(parmDict[hfx+'Lam2']-parmDict[hfx+'Lam1'])/(np.pi*parmDict[hfx+'Lam1']) |
|---|
| 1985 | kRatio = parmDict[hfx+'I(L2)/I(L1)'] |
|---|
| 1986 | else: |
|---|
| 1987 | wave = parmDict[hfx+'Lam'] |
|---|
| 1988 | for phase in Histogram['Reflection Lists']: |
|---|
| 1989 | refDict = Histogram['Reflection Lists'][phase] |
|---|
| 1990 | if phase not in Phases: #skips deleted or renamed phases silently! |
|---|
| 1991 | continue |
|---|
| 1992 | Phase = Phases[phase] |
|---|
| 1993 | pId = Phase['pId'] |
|---|
| 1994 | pfx = '%d::'%(pId) |
|---|
| 1995 | phfx = '%d:%d:'%(pId,hId) |
|---|
| 1996 | hfx = ':%d:'%(hId) |
|---|
| 1997 | SGData = Phase['General']['SGData'] |
|---|
| 1998 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 1999 | im = 0 |
|---|
| 2000 | if Phase['General']['Type'] in ['modulated','magnetic']: |
|---|
| 2001 | SSGData = Phase['General']['SSGData'] |
|---|
| 2002 | SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']]) |
|---|
| 2003 | im = 1 #offset in SS reflection list |
|---|
| 2004 | #?? |
|---|
| 2005 | Dij = GetDij(phfx,SGData,parmDict) |
|---|
| 2006 | A = [parmDict[pfx+'A%d'%(i)]+Dij[i] for i in range(6)] |
|---|
| 2007 | G,g = G2lat.A2Gmat(A) #recip & real metric tensors |
|---|
| 2008 | if np.any(np.diag(G)<0.): |
|---|
| 2009 | raise G2obj.G2Exception('invalid metric tensor \n cell/Dij refinement not advised') |
|---|
| 2010 | GA,GB = G2lat.Gmat2AB(G) #Orthogonalization matricies |
|---|
| 2011 | Vst = np.sqrt(nl.det(G)) #V* |
|---|
| 2012 | if not Phase['General'].get('doPawley'): |
|---|
| 2013 | time0 = time.time() |
|---|
| 2014 | if im: |
|---|
| 2015 | SStructureFactor(refDict,im,G,hfx,pfx,SGData,SSGData,calcControls,parmDict) |
|---|
| 2016 | else: |
|---|
| 2017 | StructureFactor2(refDict,G,hfx,pfx,SGData,calcControls,parmDict) |
|---|
| 2018 | # print 'sf calc time: %.3fs'%(time.time()-time0) |
|---|
| 2019 | time0 = time.time() |
|---|
| 2020 | badPeak = False |
|---|
| 2021 | for iref,refl in enumerate(refDict['RefList']): |
|---|
| 2022 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 2023 | if im: |
|---|
| 2024 | h,k,l,m = refl[:4] |
|---|
| 2025 | else: |
|---|
| 2026 | h,k,l = refl[:3] |
|---|
| 2027 | Uniq = np.inner(refl[:3],SGMT) |
|---|
| 2028 | refl[5+im] = GetReflPos(refl,im,wave,A,pfx,hfx,calcControls,parmDict) #corrected reflection position |
|---|
| 2029 | Lorenz = 1./(2.*sind(refl[5+im]/2.)**2*cosd(refl[5+im]/2.)) #Lorentz correction |
|---|
| 2030 | refl[6+im:8+im] = GetReflSigGamCW(refl,im,wave,G,GB,phfx,calcControls,parmDict) #peak sig & gam |
|---|
| 2031 | refl[11+im:15+im] = GetIntensityCorr(refl,im,Uniq,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 2032 | refl[11+im] *= Vst*Lorenz |
|---|
| 2033 | |
|---|
| 2034 | if Phase['General'].get('doPawley'): |
|---|
| 2035 | try: |
|---|
| 2036 | if im: |
|---|
| 2037 | pInd = pfx+'PWLref:%d'%(pawleyLookup[pfx+'%d,%d,%d,%d'%(h,k,l,m)]) |
|---|
| 2038 | else: |
|---|
| 2039 | pInd = pfx+'PWLref:%d'%(pawleyLookup[pfx+'%d,%d,%d'%(h,k,l)]) |
|---|
| 2040 | refl[9+im] = parmDict[pInd] |
|---|
| 2041 | except KeyError: |
|---|
| 2042 | # print ' ***Error %d,%d,%d missing from Pawley reflection list ***'%(h,k,l) |
|---|
| 2043 | continue |
|---|
| 2044 | Wd,fmin,fmax = G2pwd.getWidthsCW(refl[5+im],refl[6+im],refl[7+im],shl) |
|---|
| 2045 | iBeg = np.searchsorted(x,refl[5+im]-fmin) |
|---|
| 2046 | iFin = np.searchsorted(x,refl[5+im]+fmax) |
|---|
| 2047 | if not iBeg+iFin: #peak below low limit - skip peak |
|---|
| 2048 | continue |
|---|
| 2049 | elif not iBeg-iFin: #peak above high limit - done |
|---|
| 2050 | break |
|---|
| 2051 | elif iBeg > iFin: #bad peak coeff - skip |
|---|
| 2052 | badPeak = True |
|---|
| 2053 | continue |
|---|
| 2054 | yc[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 |
|---|
| 2055 | if Ka2: |
|---|
| 2056 | pos2 = refl[5+im]+lamRatio*tand(refl[5+im]/2.0) # + 360/pi * Dlam/lam * tan(th) |
|---|
| 2057 | Wd,fmin,fmax = G2pwd.getWidthsCW(pos2,refl[6+im],refl[7+im],shl) |
|---|
| 2058 | iBeg = np.searchsorted(x,pos2-fmin) |
|---|
| 2059 | iFin = np.searchsorted(x,pos2+fmax) |
|---|
| 2060 | if not iBeg+iFin: #peak below low limit - skip peak |
|---|
| 2061 | continue |
|---|
| 2062 | elif not iBeg-iFin: #peak above high limit - done |
|---|
| 2063 | return yc,yb |
|---|
| 2064 | elif iBeg > iFin: #bad peak coeff - skip |
|---|
| 2065 | continue |
|---|
| 2066 | yc[iBeg:iFin] += refl[11+im]*refl[9+im]*kRatio*G2pwd.getFCJVoigt3(pos2,refl[6+im],refl[7+im],shl,ma.getdata(x[iBeg:iFin])) #and here |
|---|
| 2067 | elif 'T' in calcControls[hfx+'histType']: |
|---|
| 2068 | h,k,l = refl[:3] |
|---|
| 2069 | Uniq = np.inner(refl[:3],SGMT) |
|---|
| 2070 | refl[5+im] = GetReflPos(refl,im,0.0,A,pfx,hfx,calcControls,parmDict) #corrected reflection position |
|---|
| 2071 | Lorenz = sind(abs(parmDict[hfx+'2-theta'])/2)*refl[4+im]**4 #TOF Lorentz correction |
|---|
| 2072 | # refl[5+im] += GetHStrainShift(refl,im,SGData,phfx,hfx,calcControls,parmDict) #apply hydrostatic strain shift |
|---|
| 2073 | refl[6+im:8+im] = GetReflSigGamTOF(refl,im,G,GB,phfx,calcControls,parmDict) #peak sig & gam |
|---|
| 2074 | refl[12+im:14+im] = GetReflAlpBet(refl,im,hfx,parmDict) |
|---|
| 2075 | refl[11+im],refl[15+im],refl[16+im],refl[17+im] = GetIntensityCorr(refl,im,Uniq,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 2076 | refl[11+im] *= Vst*Lorenz |
|---|
| 2077 | if Phase['General'].get('doPawley'): |
|---|
| 2078 | try: |
|---|
| 2079 | if im: |
|---|
| 2080 | pInd =pfx+'PWLref:%d'%(pawleyLookup[pfx+'%d,%d,%d,%d'%(h,k,l,m)]) |
|---|
| 2081 | else: |
|---|
| 2082 | pInd =pfx+'PWLref:%d'%(pawleyLookup[pfx+'%d,%d,%d'%(h,k,l)]) |
|---|
| 2083 | refl[9+im] = parmDict[pInd] |
|---|
| 2084 | except KeyError: |
|---|
| 2085 | # print ' ***Error %d,%d,%d missing from Pawley reflection list ***'%(h,k,l) |
|---|
| 2086 | continue |
|---|
| 2087 | Wd,fmin,fmax = G2pwd.getWidthsTOF(refl[5+im],refl[12+im],refl[13+im],refl[6+im],refl[7+im]) |
|---|
| 2088 | iBeg = np.searchsorted(x,refl[5+im]-fmin) |
|---|
| 2089 | iFin = np.searchsorted(x,refl[5+im]+fmax) |
|---|
| 2090 | if not iBeg+iFin: #peak below low limit - skip peak |
|---|
| 2091 | continue |
|---|
| 2092 | elif not iBeg-iFin: #peak above high limit - done |
|---|
| 2093 | break |
|---|
| 2094 | elif iBeg > iFin: #bad peak coeff - skip |
|---|
| 2095 | badPeak = True |
|---|
| 2096 | continue |
|---|
| 2097 | yc[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]))/cw[iBeg:iFin] |
|---|
| 2098 | # print 'profile calc time: %.3fs'%(time.time()-time0) |
|---|
| 2099 | if badPeak: |
|---|
| 2100 | print 'ouch #4 bad profile coefficients yield negative peak width; some reflections skipped' |
|---|
| 2101 | return yc,yb |
|---|
| 2102 | |
|---|
| 2103 | def getPowderProfileDerv(parmDict,x,varylist,Histogram,Phases,rigidbodyDict,calcControls,pawleyLookup): |
|---|
| 2104 | 'Needs a doc string' |
|---|
| 2105 | |
|---|
| 2106 | def cellVaryDerv(pfx,SGData,dpdA): |
|---|
| 2107 | if SGData['SGLaue'] in ['-1',]: |
|---|
| 2108 | return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]], |
|---|
| 2109 | [pfx+'A3',dpdA[3]],[pfx+'A4',dpdA[4]],[pfx+'A5',dpdA[5]]] |
|---|
| 2110 | elif SGData['SGLaue'] in ['2/m',]: |
|---|
| 2111 | if SGData['SGUniq'] == 'a': |
|---|
| 2112 | return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]],[pfx+'A5',dpdA[5]]] |
|---|
| 2113 | elif SGData['SGUniq'] == 'b': |
|---|
| 2114 | return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]],[pfx+'A4',dpdA[4]]] |
|---|
| 2115 | else: |
|---|
| 2116 | return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]],[pfx+'A3',dpdA[3]]] |
|---|
| 2117 | elif SGData['SGLaue'] in ['mmm',]: |
|---|
| 2118 | return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]]] |
|---|
| 2119 | elif SGData['SGLaue'] in ['4/m','4/mmm']: |
|---|
| 2120 | return [[pfx+'A0',dpdA[0]],[pfx+'A2',dpdA[2]]] |
|---|
| 2121 | elif SGData['SGLaue'] in ['6/m','6/mmm','3m1', '31m', '3']: |
|---|
| 2122 | return [[pfx+'A0',dpdA[0]],[pfx+'A2',dpdA[2]]] |
|---|
| 2123 | elif SGData['SGLaue'] in ['3R', '3mR']: |
|---|
| 2124 | return [[pfx+'A0',dpdA[0]+dpdA[1]+dpdA[2]],[pfx+'A3',dpdA[3]+dpdA[4]+dpdA[5]]] |
|---|
| 2125 | elif SGData['SGLaue'] in ['m3m','m3']: |
|---|
| 2126 | return [[pfx+'A0',dpdA[0]]] |
|---|
| 2127 | |
|---|
| 2128 | # create a list of dependent variables and set up a dictionary to hold their derivatives |
|---|
| 2129 | dependentVars = G2mv.GetDependentVars() |
|---|
| 2130 | depDerivDict = {} |
|---|
| 2131 | for j in dependentVars: |
|---|
| 2132 | depDerivDict[j] = np.zeros(shape=(len(x))) |
|---|
| 2133 | #print 'dependent vars',dependentVars |
|---|
| 2134 | lenX = len(x) |
|---|
| 2135 | hId = Histogram['hId'] |
|---|
| 2136 | hfx = ':%d:'%(hId) |
|---|
| 2137 | bakType = calcControls[hfx+'bakType'] |
|---|
| 2138 | dMdv = np.zeros(shape=(len(varylist),len(x))) |
|---|
| 2139 | dMdb,dMddb,dMdpk = G2pwd.getBackgroundDerv(hfx,parmDict,bakType,calcControls[hfx+'histType'],x) |
|---|
| 2140 | if hfx+'Back;0' in varylist: # for now assume that Back;x vars to not appear in constraints |
|---|
| 2141 | bBpos =varylist.index(hfx+'Back;0') |
|---|
| 2142 | dMdv[bBpos:bBpos+len(dMdb)] = dMdb |
|---|
| 2143 | names = [hfx+'DebyeA',hfx+'DebyeR',hfx+'DebyeU'] |
|---|
| 2144 | for name in varylist: |
|---|
| 2145 | if 'Debye' in name: |
|---|
| 2146 | id = int(name.split(';')[-1]) |
|---|
| 2147 | parm = name[:int(name.rindex(';'))] |
|---|
| 2148 | ip = names.index(parm) |
|---|
| 2149 | dMdv[varylist.index(name)] = dMddb[3*id+ip] |
|---|
| 2150 | names = [hfx+'BkPkpos',hfx+'BkPkint',hfx+'BkPksig',hfx+'BkPkgam'] |
|---|
| 2151 | for name in varylist: |
|---|
| 2152 | if 'BkPk' in name: |
|---|
| 2153 | parm,id = name.split(';') |
|---|
| 2154 | id = int(id) |
|---|
| 2155 | if parm in names: |
|---|
| 2156 | ip = names.index(parm) |
|---|
| 2157 | dMdv[varylist.index(name)] = dMdpk[4*id+ip] |
|---|
| 2158 | cw = np.diff(x) |
|---|
| 2159 | cw = np.append(cw,cw[-1]) |
|---|
| 2160 | Ka2 = False #also for TOF! |
|---|
| 2161 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 2162 | shl = max(parmDict[hfx+'SH/L'],0.002) |
|---|
| 2163 | if hfx+'Lam1' in parmDict.keys(): |
|---|
| 2164 | wave = parmDict[hfx+'Lam1'] |
|---|
| 2165 | Ka2 = True |
|---|
| 2166 | lamRatio = 360*(parmDict[hfx+'Lam2']-parmDict[hfx+'Lam1'])/(np.pi*parmDict[hfx+'Lam1']) |
|---|
| 2167 | kRatio = parmDict[hfx+'I(L2)/I(L1)'] |
|---|
| 2168 | else: |
|---|
| 2169 | wave = parmDict[hfx+'Lam'] |
|---|
| 2170 | for phase in Histogram['Reflection Lists']: |
|---|
| 2171 | refDict = Histogram['Reflection Lists'][phase] |
|---|
| 2172 | if phase not in Phases: #skips deleted or renamed phases silently! |
|---|
| 2173 | continue |
|---|
| 2174 | Phase = Phases[phase] |
|---|
| 2175 | SGData = Phase['General']['SGData'] |
|---|
| 2176 | SGMT = np.array([ops[0].T for ops in SGData['SGOps']]) |
|---|
| 2177 | im = 0 |
|---|
| 2178 | if Phase['General']['Type'] in ['modulated','magnetic']: |
|---|
| 2179 | SSGData = Phase['General']['SSGData'] |
|---|
| 2180 | SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']]) |
|---|
| 2181 | im = 1 #offset in SS reflection list |
|---|
| 2182 | #?? |
|---|
| 2183 | pId = Phase['pId'] |
|---|
| 2184 | pfx = '%d::'%(pId) |
|---|
| 2185 | phfx = '%d:%d:'%(pId,hId) |
|---|
| 2186 | Dij = GetDij(phfx,SGData,parmDict) |
|---|
| 2187 | A = [parmDict[pfx+'A%d'%(i)]+Dij[i] for i in range(6)] |
|---|
| 2188 | G,g = G2lat.A2Gmat(A) #recip & real metric tensors |
|---|
| 2189 | GA,GB = G2lat.Gmat2AB(G) #Orthogonalization matricies |
|---|
| 2190 | if not Phase['General'].get('doPawley'): |
|---|
| 2191 | time0 = time.time() |
|---|
| 2192 | if im: |
|---|
| 2193 | dFdvDict = SStructureFactorDerv(refDict,im,G,hfx,pfx,SGData,SSGData,calcControls,parmDict) |
|---|
| 2194 | else: |
|---|
| 2195 | dFdvDict = StructureFactorDerv(refDict,G,hfx,pfx,SGData,calcControls,parmDict) |
|---|
| 2196 | # print 'sf-derv time %.3fs'%(time.time()-time0) |
|---|
| 2197 | ApplyRBModelDervs(dFdvDict,parmDict,rigidbodyDict,Phase) |
|---|
| 2198 | time0 = time.time() |
|---|
| 2199 | for iref,refl in enumerate(refDict['RefList']): |
|---|
| 2200 | if im: |
|---|
| 2201 | h,k,l,m = refl[:4] |
|---|
| 2202 | else: |
|---|
| 2203 | h,k,l = refl[:3] |
|---|
| 2204 | Uniq = np.inner(refl[:3],SGMT) |
|---|
| 2205 | if 'T' in calcControls[hfx+'histType']: |
|---|
| 2206 | wave = refl[14+im] |
|---|
| 2207 | dIdsh,dIdsp,dIdpola,dIdPO,dFdODF,dFdSA,dFdAb,dFdEx = GetIntensityDerv(refl,im,wave,Uniq,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 2208 | if 'C' in calcControls[hfx+'histType']: #CW powder |
|---|
| 2209 | Wd,fmin,fmax = G2pwd.getWidthsCW(refl[5+im],refl[6+im],refl[7+im],shl) |
|---|
| 2210 | else: #'T'OF |
|---|
| 2211 | Wd,fmin,fmax = G2pwd.getWidthsTOF(refl[5+im],refl[12+im],refl[13+im],refl[6+im],refl[7+im]) |
|---|
| 2212 | iBeg = np.searchsorted(x,refl[5+im]-fmin) |
|---|
| 2213 | iFin = np.searchsorted(x,refl[5+im]+fmax) |
|---|
| 2214 | if not iBeg+iFin: #peak below low limit - skip peak |
|---|
| 2215 | continue |
|---|
| 2216 | elif not iBeg-iFin: #peak above high limit - done |
|---|
| 2217 | break |
|---|
| 2218 | pos = refl[5+im] |
|---|
| 2219 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 2220 | tanth = tand(pos/2.0) |
|---|
| 2221 | costh = cosd(pos/2.0) |
|---|
| 2222 | lenBF = iFin-iBeg |
|---|
| 2223 | dMdpk = np.zeros(shape=(6,lenBF)) |
|---|
| 2224 | dMdipk = G2pwd.getdFCJVoigt3(refl[5+im],refl[6+im],refl[7+im],shl,ma.getdata(x[iBeg:iFin])) |
|---|
| 2225 | for i in range(5): |
|---|
| 2226 | dMdpk[i] += 100.*cw[iBeg:iFin]*refl[11+im]*refl[9+im]*dMdipk[i] |
|---|
| 2227 | dervDict = {'int':dMdpk[0],'pos':dMdpk[1],'sig':dMdpk[2],'gam':dMdpk[3],'shl':dMdpk[4],'L1/L2':np.zeros_like(dMdpk[0])} |
|---|
| 2228 | if Ka2: |
|---|
| 2229 | pos2 = refl[5+im]+lamRatio*tanth # + 360/pi * Dlam/lam * tan(th) |
|---|
| 2230 | iBeg2 = np.searchsorted(x,pos2-fmin) |
|---|
| 2231 | iFin2 = np.searchsorted(x,pos2+fmax) |
|---|
| 2232 | if iBeg2-iFin2: |
|---|
| 2233 | lenBF2 = iFin2-iBeg2 |
|---|
| 2234 | dMdpk2 = np.zeros(shape=(6,lenBF2)) |
|---|
| 2235 | dMdipk2 = G2pwd.getdFCJVoigt3(pos2,refl[6+im],refl[7+im],shl,ma.getdata(x[iBeg2:iFin2])) |
|---|
| 2236 | for i in range(5): |
|---|
| 2237 | dMdpk2[i] = 100.*cw[iBeg2:iFin2]*refl[11+im]*refl[9+im]*kRatio*dMdipk2[i] |
|---|
| 2238 | dMdpk2[5] = 100.*cw[iBeg2:iFin2]*refl[11+im]*dMdipk2[0] |
|---|
| 2239 | dervDict2 = {'int':dMdpk2[0],'pos':dMdpk2[1],'sig':dMdpk2[2],'gam':dMdpk2[3],'shl':dMdpk2[4],'L1/L2':dMdpk2[5]*refl[9]} |
|---|
| 2240 | else: #'T'OF |
|---|
| 2241 | lenBF = iFin-iBeg |
|---|
| 2242 | if lenBF < 0: #bad peak coeff |
|---|
| 2243 | break |
|---|
| 2244 | dMdpk = np.zeros(shape=(6,lenBF)) |
|---|
| 2245 | dMdipk = G2pwd.getdEpsVoigt(refl[5+im],refl[12+im],refl[13+im],refl[6+im],refl[7+im],ma.getdata(x[iBeg:iFin])) |
|---|
| 2246 | for i in range(6): |
|---|
| 2247 | dMdpk[i] += refl[11+im]*refl[9+im]*dMdipk[i] #cw[iBeg:iFin]* |
|---|
| 2248 | dervDict = {'int':dMdpk[0],'pos':dMdpk[1],'alp':dMdpk[2],'bet':dMdpk[3],'sig':dMdpk[4],'gam':dMdpk[5]} |
|---|
| 2249 | if Phase['General'].get('doPawley'): |
|---|
| 2250 | dMdpw = np.zeros(len(x)) |
|---|
| 2251 | try: |
|---|
| 2252 | if im: |
|---|
| 2253 | pIdx = pfx+'PWLref:'+str(pawleyLookup[pfx+'%d,%d,%d,%d'%(h,k,l,m)]) |
|---|
| 2254 | else: |
|---|
| 2255 | pIdx = pfx+'PWLref:'+str(pawleyLookup[pfx+'%d,%d,%d'%(h,k,l)]) |
|---|
| 2256 | idx = varylist.index(pIdx) |
|---|
| 2257 | dMdpw[iBeg:iFin] = dervDict['int']/refl[9+im] |
|---|
| 2258 | if Ka2: #not for TOF either |
|---|
| 2259 | dMdpw[iBeg2:iFin2] += dervDict2['int']/refl[9+im] |
|---|
| 2260 | dMdv[idx] = dMdpw |
|---|
| 2261 | except: # ValueError: |
|---|
| 2262 | pass |
|---|
| 2263 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 2264 | dpdA,dpdw,dpdZ,dpdSh,dpdTr,dpdX,dpdY,dpdV = GetReflPosDerv(refl,im,wave,A,pfx,hfx,calcControls,parmDict) |
|---|
| 2265 | names = {hfx+'Scale':[dIdsh,'int'],hfx+'Polariz.':[dIdpola,'int'],phfx+'Scale':[dIdsp,'int'], |
|---|
| 2266 | hfx+'U':[tanth**2,'sig'],hfx+'V':[tanth,'sig'],hfx+'W':[1.0,'sig'], |
|---|
| 2267 | hfx+'X':[1.0/costh,'gam'],hfx+'Y':[tanth,'gam'],hfx+'SH/L':[1.0,'shl'], |
|---|
| 2268 | hfx+'I(L2)/I(L1)':[1.0,'L1/L2'],hfx+'Zero':[dpdZ,'pos'],hfx+'Lam':[dpdw,'pos'], |
|---|
| 2269 | hfx+'Shift':[dpdSh,'pos'],hfx+'Transparency':[dpdTr,'pos'],hfx+'DisplaceX':[dpdX,'pos'], |
|---|
| 2270 | hfx+'DisplaceY':[dpdY,'pos'],} |
|---|
| 2271 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 2272 | names.update({hfx+'SurfRoughA':[dFdAb[0],'int'], |
|---|
| 2273 | hfx+'SurfRoughB':[dFdAb[1],'int'],}) |
|---|
| 2274 | else: |
|---|
| 2275 | names.update({hfx+'Absorption':[dFdAb,'int'],}) |
|---|
| 2276 | else: #'T'OF |
|---|
| 2277 | dpdA,dpdZ,dpdDC,dpdDA,dpdDB,dpdV = GetReflPosDerv(refl,im,0.0,A,pfx,hfx,calcControls,parmDict) |
|---|
| 2278 | names = {hfx+'Scale':[dIdsh,'int'],phfx+'Scale':[dIdsp,'int'], |
|---|
| 2279 | hfx+'difC':[dpdDC,'pos'],hfx+'difA':[dpdDA,'pos'],hfx+'difB':[dpdDB,'pos'], |
|---|
| 2280 | hfx+'Zero':[dpdZ,'pos'],hfx+'X':[refl[4+im],'gam'],hfx+'Y':[refl[4+im]**2,'gam'], |
|---|
| 2281 | hfx+'alpha':[1./refl[4+im],'alp'],hfx+'beta-0':[1.0,'bet'],hfx+'beta-1':[1./refl[4+im]**4,'bet'], |
|---|
| 2282 | hfx+'beta-q':[1./refl[4+im]**2,'bet'],hfx+'sig-0':[1.0,'sig'],hfx+'sig-1':[refl[4+im]**2,'sig'], |
|---|
| 2283 | hfx+'sig-2':[refl[4+im]**4,'sig'],hfx+'sig-q':[1./refl[4+im]**2,'sig'], |
|---|
| 2284 | hfx+'Absorption':[dFdAb,'int'],phfx+'Extinction':[dFdEx,'int'],} |
|---|
| 2285 | for name in names: |
|---|
| 2286 | item = names[name] |
|---|
| 2287 | if name in varylist: |
|---|
| 2288 | dMdv[varylist.index(name)][iBeg:iFin] += item[0]*dervDict[item[1]] |
|---|
| 2289 | if Ka2 and iFin2-iBeg2: |
|---|
| 2290 | dMdv[varylist.index(name)][iBeg2:iFin2] += item[0]*dervDict2[item[1]] |
|---|
| 2291 | elif name in dependentVars: |
|---|
| 2292 | depDerivDict[name][iBeg:iFin] += item[0]*dervDict[item[1]] |
|---|
| 2293 | if Ka2 and iFin2-iBeg2: |
|---|
| 2294 | depDerivDict[name][iBeg2:iFin2] += item[0]*dervDict2[item[1]] |
|---|
| 2295 | for iPO in dIdPO: |
|---|
| 2296 | if iPO in varylist: |
|---|
| 2297 | dMdv[varylist.index(iPO)][iBeg:iFin] += dIdPO[iPO]*dervDict['int'] |
|---|
| 2298 | if Ka2 and iFin2-iBeg2: |
|---|
| 2299 | dMdv[varylist.index(iPO)][iBeg2:iFin2] += dIdPO[iPO]*dervDict2['int'] |
|---|
| 2300 | elif iPO in dependentVars: |
|---|
| 2301 | depDerivDict[iPO][iBeg:iFin] += dIdPO[iPO]*dervDict['int'] |
|---|
| 2302 | if Ka2 and iFin2-iBeg2: |
|---|
| 2303 | depDerivDict[iPO][iBeg2:iFin2] += dIdPO[iPO]*dervDict2['int'] |
|---|
| 2304 | for i,name in enumerate(['omega','chi','phi']): |
|---|
| 2305 | aname = pfx+'SH '+name |
|---|
| 2306 | if aname in varylist: |
|---|
| 2307 | dMdv[varylist.index(aname)][iBeg:iFin] += dFdSA[i]*dervDict['int'] |
|---|
| 2308 | if Ka2 and iFin2-iBeg2: |
|---|
| 2309 | dMdv[varylist.index(aname)][iBeg2:iFin2] += dFdSA[i]*dervDict2['int'] |
|---|
| 2310 | elif aname in dependentVars: |
|---|
| 2311 | depDerivDict[aname][iBeg:iFin] += dFdSA[i]*dervDict['int'] |
|---|
| 2312 | if Ka2 and iFin2-iBeg2: |
|---|
| 2313 | depDerivDict[aname][iBeg2:iFin2] += dFdSA[i]*dervDict2['int'] |
|---|
| 2314 | for iSH in dFdODF: |
|---|
| 2315 | if iSH in varylist: |
|---|
| 2316 | dMdv[varylist.index(iSH)][iBeg:iFin] += dFdODF[iSH]*dervDict['int'] |
|---|
| 2317 | if Ka2 and iFin2-iBeg2: |
|---|
| 2318 | dMdv[varylist.index(iSH)][iBeg2:iFin2] += dFdODF[iSH]*dervDict2['int'] |
|---|
| 2319 | elif iSH in dependentVars: |
|---|
| 2320 | depDerivDict[iSH][iBeg:iFin] += dFdODF[iSH]*dervDict['int'] |
|---|
| 2321 | if Ka2 and iFin2-iBeg2: |
|---|
| 2322 | depDerivDict[iSH][iBeg2:iFin2] += dFdODF[iSH]*dervDict2['int'] |
|---|
| 2323 | cellDervNames = cellVaryDerv(pfx,SGData,dpdA) |
|---|
| 2324 | for name,dpdA in cellDervNames: |
|---|
| 2325 | if name in varylist: |
|---|
| 2326 | dMdv[varylist.index(name)][iBeg:iFin] += dpdA*dervDict['pos'] |
|---|
| 2327 | if Ka2 and iFin2-iBeg2: |
|---|
| 2328 | dMdv[varylist.index(name)][iBeg2:iFin2] += dpdA*dervDict2['pos'] |
|---|
| 2329 | elif name in dependentVars: |
|---|
| 2330 | depDerivDict[name][iBeg:iFin] += dpdA*dervDict['pos'] |
|---|
| 2331 | if Ka2 and iFin2-iBeg2: |
|---|
| 2332 | depDerivDict[name][iBeg2:iFin2] += dpdA*dervDict2['pos'] |
|---|
| 2333 | dDijDict = GetHStrainShiftDerv(refl,im,SGData,phfx,hfx,calcControls,parmDict) |
|---|
| 2334 | for name in dDijDict: |
|---|
| 2335 | if name in varylist: |
|---|
| 2336 | dMdv[varylist.index(name)][iBeg:iFin] += dDijDict[name]*dervDict['pos'] |
|---|
| 2337 | if Ka2 and iFin2-iBeg2: |
|---|
| 2338 | dMdv[varylist.index(name)][iBeg2:iFin2] += dDijDict[name]*dervDict2['pos'] |
|---|
| 2339 | elif name in dependentVars: |
|---|
| 2340 | depDerivDict[name][iBeg:iFin] += dDijDict[name]*dervDict['pos'] |
|---|
| 2341 | if Ka2 and iFin2-iBeg2: |
|---|
| 2342 | depDerivDict[name][iBeg2:iFin2] += dDijDict[name]*dervDict2['pos'] |
|---|
| 2343 | for i,name in enumerate([pfx+'mV0',pfx+'mV1',pfx+'mV2']): |
|---|
| 2344 | if name in varylist: |
|---|
| 2345 | dMdv[varylist.index(name)][iBeg:iFin] += dpdV[i]*dervDict['pos'] |
|---|
| 2346 | if Ka2 and iFin2-iBeg2: |
|---|
| 2347 | dMdv[varylist.index(name)][iBeg2:iFin2] += dpdV[i]*dervDict2['pos'] |
|---|
| 2348 | elif name in dependentVars: |
|---|
| 2349 | depDerivDict[name][iBeg:iFin] += dpdV[i]*dervDict['pos'] |
|---|
| 2350 | if Ka2 and iFin2-iBeg2: |
|---|
| 2351 | depDerivDict[name][iBeg2:iFin2] += dpdV[i]*dervDict2['pos'] |
|---|
| 2352 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 2353 | sigDict,gamDict = GetSampleSigGamDerv(refl,im,wave,G,GB,SGData,hfx,phfx,calcControls,parmDict) |
|---|
| 2354 | else: #'T'OF |
|---|
| 2355 | sigDict,gamDict = GetSampleSigGamDerv(refl,im,0.0,G,GB,SGData,hfx,phfx,calcControls,parmDict) |
|---|
| 2356 | for name in gamDict: |
|---|
| 2357 | if name in varylist: |
|---|
| 2358 | dMdv[varylist.index(name)][iBeg:iFin] += gamDict[name]*dervDict['gam'] |
|---|
| 2359 | if Ka2 and iFin2-iBeg2: |
|---|
| 2360 | dMdv[varylist.index(name)][iBeg2:iFin2] += gamDict[name]*dervDict2['gam'] |
|---|
| 2361 | elif name in dependentVars: |
|---|
| 2362 | depDerivDict[name][iBeg:iFin] += gamDict[name]*dervDict['gam'] |
|---|
| 2363 | if Ka2 and iFin2-iBeg2: |
|---|
| 2364 | depDerivDict[name][iBeg2:iFin2] += gamDict[name]*dervDict2['gam'] |
|---|
| 2365 | for name in sigDict: |
|---|
| 2366 | if name in varylist: |
|---|
| 2367 | dMdv[varylist.index(name)][iBeg:iFin] += sigDict[name]*dervDict['sig'] |
|---|
| 2368 | if Ka2 and iFin2-iBeg2: |
|---|
| 2369 | dMdv[varylist.index(name)][iBeg2:iFin2] += sigDict[name]*dervDict2['sig'] |
|---|
| 2370 | elif name in dependentVars: |
|---|
| 2371 | depDerivDict[name][iBeg:iFin] += sigDict[name]*dervDict['sig'] |
|---|
| 2372 | if Ka2 and iFin2-iBeg2: |
|---|
| 2373 | depDerivDict[name][iBeg2:iFin2] += sigDict[name]*dervDict2['sig'] |
|---|
| 2374 | for name in ['BabA','BabU']: |
|---|
| 2375 | if refl[9+im]: |
|---|
| 2376 | if phfx+name in varylist: |
|---|
| 2377 | dMdv[varylist.index(phfx+name)][iBeg:iFin] += dFdvDict[pfx+name][iref]*dervDict['int']/refl[9+im] |
|---|
| 2378 | if Ka2 and iFin2-iBeg2: |
|---|
| 2379 | dMdv[varylist.index(phfx+name)][iBeg2:iFin2] += dFdvDict[pfx+name][iref]*dervDict2['int']/refl[9+im] |
|---|
| 2380 | elif phfx+name in dependentVars: |
|---|
| 2381 | depDerivDict[phfx+name][iBeg:iFin] += dFdvDict[pfx+name][iref]*dervDict['int']/refl[9+im] |
|---|
| 2382 | if Ka2 and iFin2-iBeg2: |
|---|
| 2383 | depDerivDict[phfx+name][iBeg2:iFin2] += dFdvDict[pfx+name][iref]*dervDict2['int']/refl[9+im] |
|---|
| 2384 | if not Phase['General'].get('doPawley'): |
|---|
| 2385 | #do atom derivatives - for RB,F,X & U so far |
|---|
| 2386 | corr = dervDict['int']/refl[9+im] |
|---|
| 2387 | if Ka2 and iFin2-iBeg2: |
|---|
| 2388 | corr2 = dervDict2['int']/refl[9+im] |
|---|
| 2389 | for name in varylist+dependentVars: |
|---|
| 2390 | if '::RBV;' in name: |
|---|
| 2391 | pass |
|---|
| 2392 | else: |
|---|
| 2393 | try: |
|---|
| 2394 | aname = name.split(pfx)[1][:2] |
|---|
| 2395 | if aname not in ['Af','dA','AU','RB']: continue # skip anything not an atom or rigid body param |
|---|
| 2396 | except IndexError: |
|---|
| 2397 | continue |
|---|
| 2398 | if name in varylist: |
|---|
| 2399 | dMdv[varylist.index(name)][iBeg:iFin] += dFdvDict[name][iref]*corr |
|---|
| 2400 | if Ka2 and iFin2-iBeg2: |
|---|
| 2401 | dMdv[varylist.index(name)][iBeg2:iFin2] += dFdvDict[name][iref]*corr2 |
|---|
| 2402 | elif name in dependentVars: |
|---|
| 2403 | depDerivDict[name][iBeg:iFin] += dFdvDict[name][iref]*corr |
|---|
| 2404 | if Ka2 and iFin2-iBeg2: |
|---|
| 2405 | depDerivDict[name][iBeg2:iFin2] += dFdvDict[name][iref]*corr2 |
|---|
| 2406 | # print 'profile derv time: %.3fs'%(time.time()-time0) |
|---|
| 2407 | # now process derivatives in constraints |
|---|
| 2408 | G2mv.Dict2Deriv(varylist,depDerivDict,dMdv) |
|---|
| 2409 | return dMdv |
|---|
| 2410 | |
|---|
| 2411 | def UserRejectHKL(ref,im,userReject): |
|---|
| 2412 | if ref[5+im]/ref[6+im] < userReject['minF/sig']: |
|---|
| 2413 | return False |
|---|
| 2414 | elif userReject['MaxD'] < ref[4+im] > userReject['MinD']: |
|---|
| 2415 | return False |
|---|
| 2416 | elif ref[11+im] < userReject['MinExt']: |
|---|
| 2417 | return False |
|---|
| 2418 | elif abs(ref[5+im]-ref[7+im])/ref[6+im] > userReject['MaxDF/F']: |
|---|
| 2419 | return False |
|---|
| 2420 | return True |
|---|
| 2421 | |
|---|
| 2422 | def dervHKLF(Histogram,Phase,calcControls,varylist,parmDict,rigidbodyDict): |
|---|
| 2423 | '''Loop over reflections in a HKLF histogram and compute derivatives of the fitting |
|---|
| 2424 | model (M) with respect to all parameters. Independent and dependant dM/dp arrays |
|---|
| 2425 | are returned to either dervRefine or HessRefine. |
|---|
| 2426 | |
|---|
| 2427 | :returns: |
|---|
| 2428 | ''' |
|---|
| 2429 | nobs = Histogram['Residuals']['Nobs'] |
|---|
| 2430 | hId = Histogram['hId'] |
|---|
| 2431 | hfx = ':%d:'%(hId) |
|---|
| 2432 | pfx = '%d::'%(Phase['pId']) |
|---|
| 2433 | phfx = '%d:%d:'%(Phase['pId'],hId) |
|---|
| 2434 | SGData = Phase['General']['SGData'] |
|---|
| 2435 | im = 0 |
|---|
| 2436 | if Phase['General']['Type'] in ['modulated','magnetic']: |
|---|
| 2437 | SSGData = Phase['General']['SSGData'] |
|---|
| 2438 | SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']]) |
|---|
| 2439 | im = 1 #offset in SS reflection list |
|---|
| 2440 | A = [parmDict[pfx+'A%d'%(i)] for i in range(6)] |
|---|
| 2441 | G,g = G2lat.A2Gmat(A) #recip & real metric tensors |
|---|
| 2442 | refDict = Histogram['Data'] |
|---|
| 2443 | if im: |
|---|
| 2444 | dFdvDict = SStructureFactorDerv(refDict,im,G,hfx,pfx,SGData,SSGData,calcControls,parmDict) |
|---|
| 2445 | else: |
|---|
| 2446 | dFdvDict = StructureFactorDerv(refDict,G,hfx,pfx,SGData,calcControls,parmDict) |
|---|
| 2447 | ApplyRBModelDervs(dFdvDict,parmDict,rigidbodyDict,Phase) |
|---|
| 2448 | dMdvh = np.zeros((len(varylist),len(refDict['RefList']))) |
|---|
| 2449 | dependentVars = G2mv.GetDependentVars() |
|---|
| 2450 | depDerivDict = {} |
|---|
| 2451 | for j in dependentVars: |
|---|
| 2452 | depDerivDict[j] = np.zeros(shape=(len(refDict['RefList']))) |
|---|
| 2453 | wdf = np.zeros(len(refDict['RefList'])) |
|---|
| 2454 | if calcControls['F**2']: |
|---|
| 2455 | for iref,ref in enumerate(refDict['RefList']): |
|---|
| 2456 | if ref[6+im] > 0: |
|---|
| 2457 | dervDict,dervCor = SCExtinction(ref,im,phfx,hfx,pfx,calcControls,parmDict,varylist+dependentVars)[1:] |
|---|
| 2458 | w = 1.0/ref[6+im] |
|---|
| 2459 | if ref[3+im] > 0: |
|---|
| 2460 | wdf[iref] = w*(ref[5+im]-ref[7+im]) |
|---|
| 2461 | for j,var in enumerate(varylist): |
|---|
| 2462 | if var in dFdvDict: |
|---|
| 2463 | dMdvh[j][iref] = w*dFdvDict[var][iref]*parmDict[phfx+'Scale']*ref[11+im] |
|---|
| 2464 | for var in dependentVars: |
|---|
| 2465 | if var in dFdvDict: |
|---|
| 2466 | depDerivDict[var][iref] = w*dFdvDict[var][iref]*parmDict[phfx+'Scale']*ref[11+im] |
|---|
| 2467 | if phfx+'Scale' in varylist: |
|---|
| 2468 | dMdvh[varylist.index(phfx+'Scale')][iref] = w*ref[9+im]*ref[11+im] #OK |
|---|
| 2469 | elif phfx+'Scale' in dependentVars: |
|---|
| 2470 | depDerivDict[phfx+'Scale'][iref] = w*ref[9+im]*ref[11+im] #OK |
|---|
| 2471 | for item in ['Ep','Es','Eg']: |
|---|
| 2472 | if phfx+item in varylist and phfx+item in dervDict: |
|---|
| 2473 | dMdvh[varylist.index(phfx+item)][iref] = w*dervDict[phfx+item]/ref[11+im] #OK |
|---|
| 2474 | elif phfx+item in dependentVars and phfx+item in dervDict: |
|---|
| 2475 | depDerivDict[phfx+item][iref] = w*dervDict[phfx+item]/ref[11+im] #OK |
|---|
| 2476 | for item in ['BabA','BabU']: |
|---|
| 2477 | if phfx+item in varylist: |
|---|
| 2478 | dMdvh[varylist.index(phfx+item)][iref] = w*dFdvDict[pfx+item][iref]*parmDict[phfx+'Scale']*ref[11+im] |
|---|
| 2479 | elif phfx+item in dependentVars: |
|---|
| 2480 | depDerivDict[phfx+item][iref] = w*dFdvDict[pfx+item][iref]*parmDict[phfx+'Scale']*ref[11+im] |
|---|
| 2481 | else: #F refinement |
|---|
| 2482 | for iref,ref in enumerate(refDict['RefList']): |
|---|
| 2483 | if ref[5+im] > 0.: |
|---|
| 2484 | dervDict,dervCor = SCExtinction(ref,im,phfx,hfx,pfx,calcControls,parmDict,varylist+dependentVars)[1:] |
|---|
| 2485 | Fo = np.sqrt(ref[5+im]) |
|---|
| 2486 | Fc = np.sqrt(ref[7+im]) |
|---|
| 2487 | w = 1.0/ref[6+im] |
|---|
| 2488 | if ref[3+im] > 0: |
|---|
| 2489 | wdf[iref] = 2.0*Fc*w*(Fo-Fc) |
|---|
| 2490 | for j,var in enumerate(varylist): |
|---|
| 2491 | if var in dFdvDict: |
|---|
| 2492 | dMdvh[j][iref] = w*dFdvDict[var][iref]*parmDict[phfx+'Scale']*ref[11+im] |
|---|
| 2493 | for var in dependentVars: |
|---|
| 2494 | if var in dFdvDict: |
|---|
| 2495 | depDerivDict[var][iref] = w*dFdvDict[var][iref]*parmDict[phfx+'Scale']*ref[11+im] |
|---|
| 2496 | if phfx+'Scale' in varylist: |
|---|
| 2497 | dMdvh[varylist.index(phfx+'Scale')][iref] = w*ref[9+im]*ref[11+im] #OK |
|---|
| 2498 | elif phfx+'Scale' in dependentVars: |
|---|
| 2499 | depDerivDict[phfx+'Scale'][iref] = w*ref[9+im]*ref[11+im] #OK |
|---|
| 2500 | for item in ['Ep','Es','Eg']: #OK! |
|---|
| 2501 | if phfx+item in varylist and phfx+item in dervDict: |
|---|
| 2502 | dMdvh[varylist.index(phfx+item)][iref] = w*dervDict[phfx+item]/ref[11+im] |
|---|
| 2503 | elif phfx+item in dependentVars and phfx+item in dervDict: |
|---|
| 2504 | depDerivDict[phfx+item][iref] = w*dervDict[phfx+item]/ref[11+im] |
|---|
| 2505 | for item in ['BabA','BabU']: |
|---|
| 2506 | if phfx+item in varylist: |
|---|
| 2507 | dMdvh[varylist.index(phfx+item)][iref] = w*dFdvDict[pfx+item][iref]*parmDict[phfx+'Scale']*ref[11+im] |
|---|
| 2508 | elif phfx+item in dependentVars: |
|---|
| 2509 | depDerivDict[phfx+item][iref] = w*dFdvDict[pfx+item][iref]*parmDict[phfx+'Scale']*ref[11+im] |
|---|
| 2510 | return dMdvh,depDerivDict,wdf |
|---|
| 2511 | |
|---|
| 2512 | |
|---|
| 2513 | def dervRefine(values,HistoPhases,parmDict,varylist,calcControls,pawleyLookup,dlg): |
|---|
| 2514 | '''Loop over histograms and compute derivatives of the fitting |
|---|
| 2515 | model (M) with respect to all parameters. Results are returned in |
|---|
| 2516 | a Jacobian matrix (aka design matrix) of dimensions (n by m) where |
|---|
| 2517 | n is the number of parameters and m is the number of data |
|---|
| 2518 | points. This can exceed memory when m gets large. This routine is |
|---|
| 2519 | used when refinement derivatives are selected as "analtytic |
|---|
| 2520 | Jacobian" in Controls. |
|---|
| 2521 | |
|---|
| 2522 | :returns: Jacobian numpy.array dMdv for all histograms concatinated |
|---|
| 2523 | ''' |
|---|
| 2524 | parmDict.update(zip(varylist,values)) |
|---|
| 2525 | G2mv.Dict2Map(parmDict,varylist) |
|---|
| 2526 | Histograms,Phases,restraintDict,rigidbodyDict = HistoPhases |
|---|
| 2527 | nvar = len(varylist) |
|---|
| 2528 | dMdv = np.empty(0) |
|---|
| 2529 | histoList = Histograms.keys() |
|---|
| 2530 | histoList.sort() |
|---|
| 2531 | for histogram in histoList: |
|---|
| 2532 | if 'PWDR' in histogram[:4]: |
|---|
| 2533 | Histogram = Histograms[histogram] |
|---|
| 2534 | hId = Histogram['hId'] |
|---|
| 2535 | hfx = ':%d:'%(hId) |
|---|
| 2536 | wtFactor = calcControls[hfx+'wtFactor'] |
|---|
| 2537 | Limits = calcControls[hfx+'Limits'] |
|---|
| 2538 | x,y,w,yc,yb,yd = Histogram['Data'] |
|---|
| 2539 | xB = np.searchsorted(x,Limits[0]) |
|---|
| 2540 | xF = np.searchsorted(x,Limits[1]) |
|---|
| 2541 | dMdvh = np.sqrt(w[xB:xF])*getPowderProfileDerv(parmDict,x[xB:xF], |
|---|
| 2542 | varylist,Histogram,Phases,rigidbodyDict,calcControls,pawleyLookup) |
|---|
| 2543 | elif 'HKLF' in histogram[:4]: |
|---|
| 2544 | Histogram = Histograms[histogram] |
|---|
| 2545 | phase = Histogram['Reflection Lists'] |
|---|
| 2546 | Phase = Phases[phase] |
|---|
| 2547 | dMdvh,depDerivDict,wdf = dervHKLF(Histogram,Phase,calcControls,varylist,parmDict,rigidbodyDict) |
|---|
| 2548 | hfx = ':%d:'%(Histogram['hId']) |
|---|
| 2549 | wtFactor = calcControls[hfx+'wtFactor'] |
|---|
| 2550 | # now process derivatives in constraints |
|---|
| 2551 | G2mv.Dict2Deriv(varylist,depDerivDict,dMdvh) |
|---|
| 2552 | else: |
|---|
| 2553 | continue #skip non-histogram entries |
|---|
| 2554 | if len(dMdv): |
|---|
| 2555 | dMdv = np.concatenate((dMdv.T,np.sqrt(wtFactor)*dMdvh.T)).T |
|---|
| 2556 | else: |
|---|
| 2557 | dMdv = np.sqrt(wtFactor)*dMdvh |
|---|
| 2558 | |
|---|
| 2559 | pNames,pVals,pWt,pWsum = penaltyFxn(HistoPhases,calcControls,parmDict,varylist) |
|---|
| 2560 | if np.any(pVals): |
|---|
| 2561 | dpdv = penaltyDeriv(pNames,pVals,HistoPhases,calcControls,parmDict,varylist) |
|---|
| 2562 | dMdv = np.concatenate((dMdv.T,(np.sqrt(pWt)*dpdv).T)).T |
|---|
| 2563 | |
|---|
| 2564 | return dMdv |
|---|
| 2565 | |
|---|
| 2566 | def HessRefine(values,HistoPhases,parmDict,varylist,calcControls,pawleyLookup,dlg): |
|---|
| 2567 | '''Loop over histograms and compute derivatives of the fitting |
|---|
| 2568 | model (M) with respect to all parameters. For each histogram, the |
|---|
| 2569 | Jacobian matrix, dMdv, with dimensions (n by m) where n is the |
|---|
| 2570 | number of parameters and m is the number of data points *in the |
|---|
| 2571 | histogram*. The (n by n) Hessian is computed from each Jacobian |
|---|
| 2572 | and it is returned. This routine is used when refinement |
|---|
| 2573 | derivatives are selected as "analtytic Hessian" in Controls. |
|---|
| 2574 | |
|---|
| 2575 | :returns: Vec,Hess where Vec is the least-squares vector and Hess is the Hessian |
|---|
| 2576 | ''' |
|---|
| 2577 | parmDict.update(zip(varylist,values)) |
|---|
| 2578 | G2mv.Dict2Map(parmDict,varylist) |
|---|
| 2579 | Histograms,Phases,restraintDict,rigidbodyDict = HistoPhases |
|---|
| 2580 | ApplyRBModels(parmDict,Phases,rigidbodyDict) #,Update=True?? |
|---|
| 2581 | nvar = len(varylist) |
|---|
| 2582 | Hess = np.empty(0) |
|---|
| 2583 | histoList = Histograms.keys() |
|---|
| 2584 | histoList.sort() |
|---|
| 2585 | for histogram in histoList: |
|---|
| 2586 | if 'PWDR' in histogram[:4]: |
|---|
| 2587 | Histogram = Histograms[histogram] |
|---|
| 2588 | hId = Histogram['hId'] |
|---|
| 2589 | hfx = ':%d:'%(hId) |
|---|
| 2590 | wtFactor = calcControls[hfx+'wtFactor'] |
|---|
| 2591 | Limits = calcControls[hfx+'Limits'] |
|---|
| 2592 | x,y,w,yc,yb,yd = Histogram['Data'] |
|---|
| 2593 | W = wtFactor*w |
|---|
| 2594 | dy = y-yc |
|---|
| 2595 | xB = np.searchsorted(x,Limits[0]) |
|---|
| 2596 | xF = np.searchsorted(x,Limits[1]) |
|---|
| 2597 | dMdvh = getPowderProfileDerv(parmDict,x[xB:xF], |
|---|
| 2598 | varylist,Histogram,Phases,rigidbodyDict,calcControls,pawleyLookup) |
|---|
| 2599 | Wt = ma.sqrt(W[xB:xF])[np.newaxis,:] |
|---|
| 2600 | Dy = dy[xB:xF][np.newaxis,:] |
|---|
| 2601 | dMdvh *= Wt |
|---|
| 2602 | if dlg: |
|---|
| 2603 | dlg.Update(Histogram['Residuals']['wR'],newmsg='Hessian for histogram %d\nAll data Rw=%8.3f%s'%(hId,Histogram['Residuals']['wR'],'%')) |
|---|
| 2604 | if len(Hess): |
|---|
| 2605 | Hess += np.inner(dMdvh,dMdvh) |
|---|
| 2606 | dMdvh *= Wt*Dy |
|---|
| 2607 | Vec += np.sum(dMdvh,axis=1) |
|---|
| 2608 | else: |
|---|
| 2609 | Hess = np.inner(dMdvh,dMdvh) |
|---|
| 2610 | dMdvh *= Wt*Dy |
|---|
| 2611 | Vec = np.sum(dMdvh,axis=1) |
|---|
| 2612 | elif 'HKLF' in histogram[:4]: |
|---|
| 2613 | Histogram = Histograms[histogram] |
|---|
| 2614 | phase = Histogram['Reflection Lists'] |
|---|
| 2615 | Phase = Phases[phase] |
|---|
| 2616 | dMdvh,depDerivDict,wdf = dervHKLF(Histogram,Phase,calcControls,varylist,parmDict,rigidbodyDict) |
|---|
| 2617 | hId = Histogram['hId'] |
|---|
| 2618 | hfx = ':%d:'%(Histogram['hId']) |
|---|
| 2619 | wtFactor = calcControls[hfx+'wtFactor'] |
|---|
| 2620 | # now process derivatives in constraints |
|---|
| 2621 | G2mv.Dict2Deriv(varylist,depDerivDict,dMdvh) |
|---|
| 2622 | # print 'matrix build time: %.3f'%(time.time()-time0) |
|---|
| 2623 | |
|---|
| 2624 | if dlg: |
|---|
| 2625 | dlg.Update(Histogram['Residuals']['wR'],newmsg='Hessian for histogram %d Rw=%8.3f%s'%(hId,Histogram['Residuals']['wR'],'%'))[0] |
|---|
| 2626 | if len(Hess): |
|---|
| 2627 | Vec += wtFactor*np.sum(dMdvh*wdf,axis=1) |
|---|
| 2628 | Hess += wtFactor*np.inner(dMdvh,dMdvh) |
|---|
| 2629 | else: |
|---|
| 2630 | Vec = wtFactor*np.sum(dMdvh*wdf,axis=1) |
|---|
| 2631 | Hess = wtFactor*np.inner(dMdvh,dMdvh) |
|---|
| 2632 | else: |
|---|
| 2633 | continue #skip non-histogram entries |
|---|
| 2634 | pNames,pVals,pWt,pWsum = penaltyFxn(HistoPhases,calcControls,parmDict,varylist) |
|---|
| 2635 | if np.any(pVals): |
|---|
| 2636 | dpdv = penaltyDeriv(pNames,pVals,HistoPhases,calcControls,parmDict,varylist) |
|---|
| 2637 | Vec += np.sum(dpdv*pWt*pVals,axis=1) |
|---|
| 2638 | Hess += np.inner(dpdv*pWt,dpdv) |
|---|
| 2639 | return Vec,Hess |
|---|
| 2640 | |
|---|
| 2641 | def errRefine(values,HistoPhases,parmDict,varylist,calcControls,pawleyLookup,dlg=None): |
|---|
| 2642 | '''Computes the point-by-point discrepancies between every data point in every histogram |
|---|
| 2643 | and the observed value |
|---|
| 2644 | |
|---|
| 2645 | :returns: an np array of differences between observed and computed diffraction values. |
|---|
| 2646 | ''' |
|---|
| 2647 | Values2Dict(parmDict, varylist, values) |
|---|
| 2648 | G2mv.Dict2Map(parmDict,varylist) |
|---|
| 2649 | Histograms,Phases,restraintDict,rigidbodyDict = HistoPhases |
|---|
| 2650 | M = np.empty(0) |
|---|
| 2651 | SumwYo = 0 |
|---|
| 2652 | Nobs = 0 |
|---|
| 2653 | Nrej = 0 |
|---|
| 2654 | Next = 0 |
|---|
| 2655 | ApplyRBModels(parmDict,Phases,rigidbodyDict) |
|---|
| 2656 | histoList = Histograms.keys() |
|---|
| 2657 | histoList.sort() |
|---|
| 2658 | for histogram in histoList: |
|---|
| 2659 | if 'PWDR' in histogram[:4]: |
|---|
| 2660 | Histogram = Histograms[histogram] |
|---|
| 2661 | hId = Histogram['hId'] |
|---|
| 2662 | hfx = ':%d:'%(hId) |
|---|
| 2663 | wtFactor = calcControls[hfx+'wtFactor'] |
|---|
| 2664 | Limits = calcControls[hfx+'Limits'] |
|---|
| 2665 | x,y,w,yc,yb,yd = Histogram['Data'] |
|---|
| 2666 | yc *= 0.0 #zero full calcd profiles |
|---|
| 2667 | yb *= 0.0 |
|---|
| 2668 | yd *= 0.0 |
|---|
| 2669 | xB = np.searchsorted(x,Limits[0]) |
|---|
| 2670 | xF = np.searchsorted(x,Limits[1]) |
|---|
| 2671 | yc[xB:xF],yb[xB:xF] = getPowderProfile(parmDict,x[xB:xF], |
|---|
| 2672 | varylist,Histogram,Phases,calcControls,pawleyLookup) |
|---|
| 2673 | yc[xB:xF] += yb[xB:xF] |
|---|
| 2674 | if not np.any(y): #fill dummy data |
|---|
| 2675 | rv = st.poisson(yc[xB:xF]) |
|---|
| 2676 | y[xB:xF] = rv.rvs() |
|---|
| 2677 | Z = np.ones_like(yc[xB:xF]) |
|---|
| 2678 | Z[1::2] *= -1 |
|---|
| 2679 | y[xB:xF] = yc[xB:xF]+np.abs(y[xB:xF]-yc[xB:xF])*Z |
|---|
| 2680 | w[xB:xF] = np.where(y[xB:xF]>0.,1./y[xB:xF],1.0) |
|---|
| 2681 | yd[xB:xF] = y[xB:xF]-yc[xB:xF] |
|---|
| 2682 | W = wtFactor*w |
|---|
| 2683 | wdy = -ma.sqrt(W[xB:xF])*(yd[xB:xF]) |
|---|
| 2684 | Histogram['Residuals']['Nobs'] = ma.count(x[xB:xF]) |
|---|
| 2685 | Nobs += Histogram['Residuals']['Nobs'] |
|---|
| 2686 | Histogram['Residuals']['sumwYo'] = ma.sum(W[xB:xF]*y[xB:xF]**2) |
|---|
| 2687 | SumwYo += Histogram['Residuals']['sumwYo'] |
|---|
| 2688 | Histogram['Residuals']['R'] = min(100.,ma.sum(ma.abs(yd[xB:xF]))/ma.sum(y[xB:xF])*100.) |
|---|
| 2689 | Histogram['Residuals']['wR'] = min(100.,ma.sqrt(ma.sum(wdy**2)/Histogram['Residuals']['sumwYo'])*100.) |
|---|
| 2690 | sumYmB = ma.sum(ma.where(yc[xB:xF]!=yb[xB:xF],ma.abs(y[xB:xF]-yb[xB:xF]),0.)) |
|---|
| 2691 | sumwYmB2 = ma.sum(ma.where(yc[xB:xF]!=yb[xB:xF],W[xB:xF]*(y[xB:xF]-yb[xB:xF])**2,0.)) |
|---|
| 2692 | sumYB = ma.sum(ma.where(yc[xB:xF]!=yb[xB:xF],ma.abs(y[xB:xF]-yc[xB:xF])*ma.abs(y[xB:xF]-yb[xB:xF])/y[xB:xF],0.)) |
|---|
| 2693 | sumwYB2 = ma.sum(ma.where(yc[xB:xF]!=yb[xB:xF],W[xB:xF]*(ma.abs(y[xB:xF]-yc[xB:xF])*ma.abs(y[xB:xF]-yb[xB:xF])/y[xB:xF])**2,0.)) |
|---|
| 2694 | Histogram['Residuals']['Rb'] = min(100.,100.*sumYB/sumYmB) |
|---|
| 2695 | Histogram['Residuals']['wRb'] = min(100.,100.*ma.sqrt(sumwYB2/sumwYmB2)) |
|---|
| 2696 | Histogram['Residuals']['wRmin'] = min(100.,100.*ma.sqrt(Histogram['Residuals']['Nobs']/Histogram['Residuals']['sumwYo'])) |
|---|
| 2697 | if dlg: |
|---|
| 2698 | dlg.Update(Histogram['Residuals']['wR'],newmsg='For histogram %d Rw=%8.3f%s'%(hId,Histogram['Residuals']['wR'],'%'))[0] |
|---|
| 2699 | M = np.concatenate((M,wdy)) |
|---|
| 2700 | #end of PWDR processing |
|---|
| 2701 | elif 'HKLF' in histogram[:4]: |
|---|
| 2702 | Histogram = Histograms[histogram] |
|---|
| 2703 | Histogram['Residuals'] = {} |
|---|
| 2704 | phase = Histogram['Reflection Lists'] |
|---|
| 2705 | Phase = Phases[phase] |
|---|
| 2706 | hId = Histogram['hId'] |
|---|
| 2707 | hfx = ':%d:'%(hId) |
|---|
| 2708 | wtFactor = calcControls[hfx+'wtFactor'] |
|---|
| 2709 | pfx = '%d::'%(Phase['pId']) |
|---|
| 2710 | phfx = '%d:%d:'%(Phase['pId'],hId) |
|---|
| 2711 | SGData = Phase['General']['SGData'] |
|---|
| 2712 | im = 0 |
|---|
| 2713 | if Phase['General']['Type'] in ['modulated','magnetic']: |
|---|
| 2714 | SSGData = Phase['General']['SSGData'] |
|---|
| 2715 | SSGMT = np.array([ops[0].T for ops in SSGData['SSGOps']]) |
|---|
| 2716 | im = 1 #offset in SS reflection list |
|---|
| 2717 | A = [parmDict[pfx+'A%d'%(i)] for i in range(6)] |
|---|
| 2718 | G,g = G2lat.A2Gmat(A) #recip & real metric tensors |
|---|
| 2719 | refDict = Histogram['Data'] |
|---|
| 2720 | time0 = time.time() |
|---|
| 2721 | if im: |
|---|
| 2722 | SStructureFactor(refDict,im,G,hfx,pfx,SGData,SSGData,calcControls,parmDict) |
|---|
| 2723 | else: |
|---|
| 2724 | StructureFactor2(refDict,G,hfx,pfx,SGData,calcControls,parmDict) |
|---|
| 2725 | # print 'sf-calc time: %.3f'%(time.time()-time0) |
|---|
| 2726 | df = np.zeros(len(refDict['RefList'])) |
|---|
| 2727 | sumwYo = 0 |
|---|
| 2728 | sumFo = 0 |
|---|
| 2729 | sumFo2 = 0 |
|---|
| 2730 | sumdF = 0 |
|---|
| 2731 | sumdF2 = 0 |
|---|
| 2732 | nobs = 0 |
|---|
| 2733 | nrej = 0 |
|---|
| 2734 | next = 0 |
|---|
| 2735 | if calcControls['F**2']: |
|---|
| 2736 | for i,ref in enumerate(refDict['RefList']): |
|---|
| 2737 | if ref[6+im] > 0: |
|---|
| 2738 | ref[11+im] = SCExtinction(ref,im,phfx,hfx,pfx,calcControls,parmDict,varylist)[0] |
|---|
| 2739 | w = 1.0/ref[6+im] # 1/sig(F^2) |
|---|
| 2740 | ref[7+im] = parmDict[phfx+'Scale']*ref[9+im]*ref[11+im] #correct Fc^2 for extinction |
|---|
| 2741 | ref[8+im] = ref[5+im]/(parmDict[phfx+'Scale']*ref[11+im]) |
|---|
| 2742 | if UserRejectHKL(ref,im,calcControls['UsrReject']) and ref[3+im]: #skip sp.gp. absences (mul=0) |
|---|
| 2743 | ref[3+im] = abs(ref[3+im]) #mark as allowed |
|---|
| 2744 | Fo = np.sqrt(ref[5+im]) |
|---|
| 2745 | sumFo += Fo |
|---|
| 2746 | sumFo2 += ref[5+im] |
|---|
| 2747 | sumdF += abs(Fo-np.sqrt(ref[7+im])) |
|---|
| 2748 | sumdF2 += abs(ref[5+im]-ref[7+im]) |
|---|
| 2749 | nobs += 1 |
|---|
| 2750 | df[i] = -w*(ref[5+im]-ref[7+im]) |
|---|
| 2751 | sumwYo += (w*ref[5+im])**2 #w*Fo^2 |
|---|
| 2752 | else: |
|---|
| 2753 | if ref[3+im]: |
|---|
| 2754 | ref[3+im] = -abs(ref[3+im]) #mark as rejected |
|---|
| 2755 | nrej += 1 |
|---|
| 2756 | else: #sp.gp.extinct |
|---|
| 2757 | next += 1 |
|---|
| 2758 | else: |
|---|
| 2759 | for i,ref in enumerate(refDict['RefList']): |
|---|
| 2760 | if ref[5+im] > 0.: |
|---|
| 2761 | ref[11+im] = SCExtinction(ref,im,phfx,hfx,pfx,calcControls,parmDict,varylist)[0] |
|---|
| 2762 | ref[7+im] = parmDict[phfx+'Scale']*ref[9+im]*ref[11+im] #correct Fc^2 for extinction |
|---|
| 2763 | ref[8+im] = ref[5+im]/(parmDict[phfx+'Scale']*ref[11+im]) |
|---|
| 2764 | Fo = np.sqrt(ref[5+im]) |
|---|
| 2765 | Fc = np.sqrt(ref[7+im]) |
|---|
| 2766 | w = 2.0*Fo/ref[6+im] # 1/sig(F)? |
|---|
| 2767 | if UserRejectHKL(ref,im,calcControls['UsrReject']) and ref[3+im]: #skip sp.gp. absences (mul=0) |
|---|
| 2768 | ref[3+im] = abs(ref[3+im]) #mark as allowed |
|---|
| 2769 | sumFo += Fo |
|---|
| 2770 | sumFo2 += ref[5+im] |
|---|
| 2771 | sumdF += abs(Fo-Fc) |
|---|
| 2772 | sumdF2 += abs(ref[5+im]-ref[7+im]) |
|---|
| 2773 | nobs += 1 |
|---|
| 2774 | df[i] = -w*(Fo-Fc) |
|---|
| 2775 | sumwYo += (w*Fo)**2 |
|---|
| 2776 | else: |
|---|
| 2777 | if ref[3+im]: |
|---|
| 2778 | ref[3+im] = -abs(ref[3+im]) #mark as rejected |
|---|
| 2779 | nrej += 1 |
|---|
| 2780 | else: #sp.gp.extinct |
|---|
| 2781 | next += 1 |
|---|
| 2782 | Histogram['Residuals']['Nobs'] = nobs |
|---|
| 2783 | Histogram['Residuals']['sumwYo'] = sumwYo |
|---|
| 2784 | SumwYo += sumwYo |
|---|
| 2785 | Histogram['Residuals']['wR'] = min(100.,np.sqrt(np.sum(df**2)/sumwYo)*100.) |
|---|
| 2786 | Histogram['Residuals'][phfx+'Rf'] = 100.*sumdF/sumFo |
|---|
| 2787 | Histogram['Residuals'][phfx+'Rf^2'] = 100.*sumdF2/sumFo2 |
|---|
| 2788 | Histogram['Residuals'][phfx+'Nref'] = nobs |
|---|
| 2789 | Histogram['Residuals'][phfx+'Nrej'] = nrej |
|---|
| 2790 | Histogram['Residuals'][phfx+'Next'] = next |
|---|
| 2791 | Nobs += nobs |
|---|
| 2792 | Nrej += nrej |
|---|
| 2793 | Next += next |
|---|
| 2794 | if dlg: |
|---|
| 2795 | dlg.Update(Histogram['Residuals']['wR'],newmsg='For histogram %d Rw=%8.3f%s'%(hId,Histogram['Residuals']['wR'],'%'))[0] |
|---|
| 2796 | M = np.concatenate((M,wtFactor*df)) |
|---|
| 2797 | # end of HKLF processing |
|---|
| 2798 | Histograms['sumwYo'] = SumwYo |
|---|
| 2799 | Histograms['Nobs'] = Nobs |
|---|
| 2800 | Histograms['Nrej'] = Nrej |
|---|
| 2801 | Histograms['Next'] = Next |
|---|
| 2802 | Rw = min(100.,np.sqrt(np.sum(M**2)/SumwYo)*100.) |
|---|
| 2803 | if dlg: |
|---|
| 2804 | GoOn = dlg.Update(Rw,newmsg='%s%8.3f%s'%('All data Rw =',Rw,'%'))[0] |
|---|
| 2805 | if not GoOn: |
|---|
| 2806 | parmDict['saved values'] = values |
|---|
| 2807 | dlg.Destroy() |
|---|
| 2808 | raise G2obj.G2Exception('User abort') #Abort!! |
|---|
| 2809 | pDict,pVals,pWt,pWsum = penaltyFxn(HistoPhases,calcControls,parmDict,varylist) |
|---|
| 2810 | if len(pVals): |
|---|
| 2811 | pSum = np.sum(pWt*pVals**2) |
|---|
| 2812 | for name in pWsum: |
|---|
| 2813 | if pWsum[name]: |
|---|
| 2814 | print ' Penalty function for %8s = %12.5g'%(name,pWsum[name]) |
|---|
| 2815 | print 'Total penalty function: %12.5g on %d terms'%(pSum,len(pVals)) |
|---|
| 2816 | Nobs += len(pVals) |
|---|
| 2817 | M = np.concatenate((M,np.sqrt(pWt)*pVals)) |
|---|
| 2818 | return M |
|---|
| 2819 | |
|---|
