| 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: 2013-10-09 15:27:52 +0000 (Wed, 09 Oct 2013) $ |
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| 8 | # $Author: vondreele $ |
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| 9 | # $Revision: 1092 $ |
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| 10 | # $URL: trunk/GSASIIstrMath.py $ |
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| 11 | # $Id: GSASIIstrMath.py 1092 2013-10-09 15:27:52Z 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: 1092 $") |
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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 | |
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| 30 | sind = lambda x: np.sin(x*np.pi/180.) |
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| 31 | cosd = lambda x: np.cos(x*np.pi/180.) |
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| 32 | tand = lambda x: np.tan(x*np.pi/180.) |
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| 33 | asind = lambda x: 180.*np.arcsin(x)/np.pi |
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| 34 | acosd = lambda x: 180.*np.arccos(x)/np.pi |
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| 35 | atan2d = lambda y,x: 180.*np.arctan2(y,x)/np.pi |
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| 36 | |
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| 37 | ateln2 = 8.0*math.log(2.0) |
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| 38 | |
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| 39 | ################################################################################ |
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| 40 | ##### Rigid Body Models |
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| 41 | ################################################################################ |
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| 42 | |
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| 43 | def ApplyRBModels(parmDict,Phases,rigidbodyDict,Update=False): |
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| 44 | ''' Takes RB info from RBModels in Phase and RB data in rigidbodyDict along with |
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| 45 | current RB values in parmDict & modifies atom contents (xyz & Uij) of parmDict |
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| 46 | ''' |
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| 47 | atxIds = ['Ax:','Ay:','Az:'] |
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| 48 | atuIds = ['AU11:','AU22:','AU33:','AU12:','AU13:','AU23:'] |
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| 49 | RBIds = rigidbodyDict.get('RBIds',{'Vector':[],'Residue':[]}) #these are lists of rbIds |
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| 50 | if not RBIds['Vector'] and not RBIds['Residue']: |
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| 51 | return |
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| 52 | VRBIds = RBIds['Vector'] |
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| 53 | RRBIds = RBIds['Residue'] |
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| 54 | if Update: |
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| 55 | RBData = rigidbodyDict |
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| 56 | else: |
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| 57 | RBData = copy.deepcopy(rigidbodyDict) # don't mess with original! |
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| 58 | if RBIds['Vector']: # first update the vector magnitudes |
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| 59 | VRBData = RBData['Vector'] |
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| 60 | for i,rbId in enumerate(VRBIds): |
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| 61 | if VRBData[rbId]['useCount']: |
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| 62 | for j in range(len(VRBData[rbId]['VectMag'])): |
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| 63 | name = '::RBV;'+str(j)+':'+str(i) |
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| 64 | VRBData[rbId]['VectMag'][j] = parmDict[name] |
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| 65 | for phase in Phases: |
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| 66 | Phase = Phases[phase] |
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| 67 | General = Phase['General'] |
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| 68 | cell = General['Cell'][1:7] |
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| 69 | Amat,Bmat = G2lat.cell2AB(cell) |
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| 70 | AtLookup = G2mth.FillAtomLookUp(Phase['Atoms']) |
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| 71 | pfx = str(Phase['pId'])+'::' |
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| 72 | if Update: |
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| 73 | RBModels = Phase['RBModels'] |
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| 74 | else: |
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| 75 | RBModels = copy.deepcopy(Phase['RBModels']) # again don't mess with original! |
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| 76 | for irb,RBObj in enumerate(RBModels.get('Vector',[])): |
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| 77 | jrb = VRBIds.index(RBObj['RBId']) |
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| 78 | rbsx = str(irb)+':'+str(jrb) |
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| 79 | for i,px in enumerate(['RBVPx:','RBVPy:','RBVPz:']): |
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| 80 | RBObj['Orig'][0][i] = parmDict[pfx+px+rbsx] |
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| 81 | for i,po in enumerate(['RBVOa:','RBVOi:','RBVOj:','RBVOk:']): |
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| 82 | RBObj['Orient'][0][i] = parmDict[pfx+po+rbsx] |
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| 83 | RBObj['Orient'][0] = G2mth.normQ(RBObj['Orient'][0]) |
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| 84 | TLS = RBObj['ThermalMotion'] |
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| 85 | if 'T' in TLS[0]: |
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| 86 | for i,pt in enumerate(['RBVT11:','RBVT22:','RBVT33:','RBVT12:','RBVT13:','RBVT23:']): |
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| 87 | TLS[1][i] = parmDict[pfx+pt+rbsx] |
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| 88 | if 'L' in TLS[0]: |
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| 89 | for i,pt in enumerate(['RBVL11:','RBVL22:','RBVL33:','RBVL12:','RBVL13:','RBVL23:']): |
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| 90 | TLS[1][i+6] = parmDict[pfx+pt+rbsx] |
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| 91 | if 'S' in TLS[0]: |
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| 92 | for i,pt in enumerate(['RBVS12:','RBVS13:','RBVS21:','RBVS23:','RBVS31:','RBVS32:','RBVSAA:','RBVSBB:']): |
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| 93 | TLS[1][i+12] = parmDict[pfx+pt+rbsx] |
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| 94 | if 'U' in TLS[0]: |
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| 95 | TLS[1][0] = parmDict[pfx+'RBVU:'+rbsx] |
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| 96 | XYZ,Cart = G2mth.UpdateRBXYZ(Bmat,RBObj,RBData,'Vector') |
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| 97 | UIJ = G2mth.UpdateRBUIJ(Bmat,Cart,RBObj) |
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| 98 | for i,x in enumerate(XYZ): |
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| 99 | atId = RBObj['Ids'][i] |
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| 100 | for j in [0,1,2]: |
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| 101 | parmDict[pfx+atxIds[j]+str(AtLookup[atId])] = x[j] |
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| 102 | if UIJ[i][0] == 'A': |
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| 103 | for j in range(6): |
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| 104 | parmDict[pfx+atuIds[j]+str(AtLookup[atId])] = UIJ[i][j+2] |
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| 105 | elif UIJ[i][0] == 'I': |
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| 106 | parmDict[pfx+'AUiso:'+str(AtLookup[atId])] = UIJ[i][1] |
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| 107 | |
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| 108 | for irb,RBObj in enumerate(RBModels.get('Residue',[])): |
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| 109 | jrb = RRBIds.index(RBObj['RBId']) |
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| 110 | rbsx = str(irb)+':'+str(jrb) |
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| 111 | for i,px in enumerate(['RBRPx:','RBRPy:','RBRPz:']): |
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| 112 | RBObj['Orig'][0][i] = parmDict[pfx+px+rbsx] |
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| 113 | for i,po in enumerate(['RBROa:','RBROi:','RBROj:','RBROk:']): |
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| 114 | RBObj['Orient'][0][i] = parmDict[pfx+po+rbsx] |
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| 115 | RBObj['Orient'][0] = G2mth.normQ(RBObj['Orient'][0]) |
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| 116 | TLS = RBObj['ThermalMotion'] |
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| 117 | if 'T' in TLS[0]: |
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| 118 | for i,pt in enumerate(['RBRT11:','RBRT22:','RBRT33:','RBRT12:','RBRT13:','RBRT23:']): |
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| 119 | RBObj['ThermalMotion'][1][i] = parmDict[pfx+pt+rbsx] |
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| 120 | if 'L' in TLS[0]: |
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| 121 | for i,pt in enumerate(['RBRL11:','RBRL22:','RBRL33:','RBRL12:','RBRL13:','RBRL23:']): |
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| 122 | RBObj['ThermalMotion'][1][i+6] = parmDict[pfx+pt+rbsx] |
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| 123 | if 'S' in TLS[0]: |
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| 124 | for i,pt in enumerate(['RBRS12:','RBRS13:','RBRS21:','RBRS23:','RBRS31:','RBRS32:','RBRSAA:','RBRSBB:']): |
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| 125 | RBObj['ThermalMotion'][1][i+12] = parmDict[pfx+pt+rbsx] |
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| 126 | if 'U' in TLS[0]: |
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| 127 | RBObj['ThermalMotion'][1][0] = parmDict[pfx+'RBRU:'+rbsx] |
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| 128 | for itors,tors in enumerate(RBObj['Torsions']): |
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| 129 | tors[0] = parmDict[pfx+'RBRTr;'+str(itors)+':'+rbsx] |
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| 130 | XYZ,Cart = G2mth.UpdateRBXYZ(Bmat,RBObj,RBData,'Residue') |
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| 131 | UIJ = G2mth.UpdateRBUIJ(Bmat,Cart,RBObj) |
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| 132 | for i,x in enumerate(XYZ): |
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| 133 | atId = RBObj['Ids'][i] |
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| 134 | for j in [0,1,2]: |
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| 135 | parmDict[pfx+atxIds[j]+str(AtLookup[atId])] = x[j] |
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| 136 | if UIJ[i][0] == 'A': |
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| 137 | for j in range(6): |
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| 138 | parmDict[pfx+atuIds[j]+str(AtLookup[atId])] = UIJ[i][j+2] |
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| 139 | elif UIJ[i][0] == 'I': |
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| 140 | parmDict[pfx+'AUiso:'+str(AtLookup[atId])] = UIJ[i][1] |
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| 141 | |
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| 142 | def ApplyRBModelDervs(dFdvDict,parmDict,rigidbodyDict,Phase): |
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| 143 | 'Needs a doc string' |
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| 144 | atxIds = ['dAx:','dAy:','dAz:'] |
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| 145 | atuIds = ['AU11:','AU22:','AU33:','AU12:','AU13:','AU23:'] |
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| 146 | TIds = ['T11:','T22:','T33:','T12:','T13:','T23:'] |
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| 147 | LIds = ['L11:','L22:','L33:','L12:','L13:','L23:'] |
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| 148 | SIds = ['S12:','S13:','S21:','S23:','S31:','S32:','SAA:','SBB:'] |
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| 149 | PIds = ['Px:','Py:','Pz:'] |
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| 150 | OIds = ['Oa:','Oi:','Oj:','Ok:'] |
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| 151 | RBIds = rigidbodyDict.get('RBIds',{'Vector':[],'Residue':[]}) #these are lists of rbIds |
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| 152 | if not RBIds['Vector'] and not RBIds['Residue']: |
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| 153 | return |
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| 154 | VRBIds = RBIds['Vector'] |
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| 155 | RRBIds = RBIds['Residue'] |
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| 156 | RBData = rigidbodyDict |
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| 157 | for item in parmDict: |
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| 158 | if 'RB' in item: |
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| 159 | dFdvDict[item] = 0. #NB: this is a vector which is no. refl. long & must be filled! |
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| 160 | General = Phase['General'] |
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| 161 | cell = General['Cell'][1:7] |
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| 162 | Amat,Bmat = G2lat.cell2AB(cell) |
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| 163 | rpd = np.pi/180. |
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| 164 | rpd2 = rpd**2 |
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| 165 | g = nl.inv(np.inner(Bmat,Bmat)) |
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| 166 | gvec = np.sqrt(np.array([g[0][0]**2,g[1][1]**2,g[2][2]**2, |
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| 167 | g[0][0]*g[1][1],g[0][0]*g[2][2],g[1][1]*g[2][2]])) |
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| 168 | AtLookup = G2mth.FillAtomLookUp(Phase['Atoms']) |
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| 169 | pfx = str(Phase['pId'])+'::' |
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| 170 | RBModels = Phase['RBModels'] |
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| 171 | for irb,RBObj in enumerate(RBModels.get('Vector',[])): |
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| 172 | VModel = RBData['Vector'][RBObj['RBId']] |
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| 173 | Q = RBObj['Orient'][0] |
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| 174 | Pos = RBObj['Orig'][0] |
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| 175 | jrb = VRBIds.index(RBObj['RBId']) |
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| 176 | rbsx = str(irb)+':'+str(jrb) |
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| 177 | dXdv = [] |
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| 178 | for iv in range(len(VModel['VectMag'])): |
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| 179 | dCdv = [] |
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| 180 | for vec in VModel['rbVect'][iv]: |
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| 181 | dCdv.append(G2mth.prodQVQ(Q,vec)) |
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| 182 | dXdv.append(np.inner(Bmat,np.array(dCdv)).T) |
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| 183 | XYZ,Cart = G2mth.UpdateRBXYZ(Bmat,RBObj,RBData,'Vector') |
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| 184 | for ia,atId in enumerate(RBObj['Ids']): |
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| 185 | atNum = AtLookup[atId] |
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| 186 | dx = 0.00001 |
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| 187 | for iv in range(len(VModel['VectMag'])): |
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| 188 | for ix in [0,1,2]: |
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| 189 | dFdvDict['::RBV;'+str(iv)+':'+str(jrb)] += dXdv[iv][ia][ix]*dFdvDict[pfx+atxIds[ix]+str(atNum)] |
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| 190 | for i,name in enumerate(['RBVPx:','RBVPy:','RBVPz:']): |
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| 191 | dFdvDict[pfx+name+rbsx] += dFdvDict[pfx+atxIds[i]+str(atNum)] |
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| 192 | for iv in range(4): |
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| 193 | Q[iv] -= dx |
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| 194 | XYZ1 = G2mth.RotateRBXYZ(Bmat,Cart,G2mth.normQ(Q)) |
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| 195 | Q[iv] += 2.*dx |
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| 196 | XYZ2 = G2mth.RotateRBXYZ(Bmat,Cart,G2mth.normQ(Q)) |
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| 197 | Q[iv] -= dx |
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| 198 | dXdO = (XYZ2[ia]-XYZ1[ia])/(2.*dx) |
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| 199 | for ix in [0,1,2]: |
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| 200 | dFdvDict[pfx+'RBV'+OIds[iv]+rbsx] += dXdO[ix]*dFdvDict[pfx+atxIds[ix]+str(atNum)] |
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| 201 | X = G2mth.prodQVQ(Q,Cart[ia]) |
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| 202 | dFdu = np.array([dFdvDict[pfx+Uid+str(AtLookup[atId])] for Uid in atuIds]).T/gvec |
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| 203 | dFdu = G2lat.U6toUij(dFdu.T) |
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| 204 | dFdu = np.tensordot(Amat,np.tensordot(Amat,dFdu,([1,0])),([0,1])) |
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| 205 | dFdu = G2lat.UijtoU6(dFdu) |
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| 206 | atNum = AtLookup[atId] |
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| 207 | if 'T' in RBObj['ThermalMotion'][0]: |
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| 208 | for i,name in enumerate(['RBVT11:','RBVT22:','RBVT33:','RBVT12:','RBVT13:','RBVT23:']): |
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| 209 | dFdvDict[pfx+name+rbsx] += dFdu[i] |
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| 210 | if 'L' in RBObj['ThermalMotion'][0]: |
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| 211 | 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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| 212 | 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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| 213 | 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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| 214 | dFdvDict[pfx+'RBVL12:'+rbsx] += rpd2*(-dFdu[3]*X[2]**2-2.*dFdu[2]*X[0]*X[1]+ |
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| 215 | dFdu[4]*X[1]*X[2]+dFdu[5]*X[0]*X[2]) |
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| 216 | dFdvDict[pfx+'RBVL13:'+rbsx] += rpd2*(-dFdu[4]*X[1]**2-2.*dFdu[1]*X[0]*X[2]+ |
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| 217 | dFdu[3]*X[1]*X[2]+dFdu[5]*X[0]*X[1]) |
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| 218 | dFdvDict[pfx+'RBVL23:'+rbsx] += rpd2*(-dFdu[5]*X[0]**2-2.*dFdu[0]*X[1]*X[2]+ |
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| 219 | dFdu[3]*X[0]*X[2]+dFdu[4]*X[0]*X[1]) |
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| 220 | if 'S' in RBObj['ThermalMotion'][0]: |
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| 221 | dFdvDict[pfx+'RBVS12:'+rbsx] += rpd*(dFdu[5]*X[1]-2.*dFdu[1]*X[2]) |
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| 222 | dFdvDict[pfx+'RBVS13:'+rbsx] += rpd*(-dFdu[5]*X[2]+2.*dFdu[2]*X[1]) |
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| 223 | dFdvDict[pfx+'RBVS21:'+rbsx] += rpd*(-dFdu[4]*X[0]+2.*dFdu[0]*X[2]) |
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| 224 | dFdvDict[pfx+'RBVS23:'+rbsx] += rpd*(dFdu[4]*X[2]-2.*dFdu[2]*X[0]) |
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| 225 | dFdvDict[pfx+'RBVS31:'+rbsx] += rpd*(dFdu[3]*X[0]-2.*dFdu[0]*X[1]) |
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| 226 | dFdvDict[pfx+'RBVS32:'+rbsx] += rpd*(-dFdu[3]*X[1]+2.*dFdu[1]*X[0]) |
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| 227 | dFdvDict[pfx+'RBVSAA:'+rbsx] += rpd*(dFdu[4]*X[1]-dFdu[3]*X[2]) |
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| 228 | dFdvDict[pfx+'RBVSBB:'+rbsx] += rpd*(dFdu[5]*X[0]-dFdu[3]*X[2]) |
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| 229 | if 'U' in RBObj['ThermalMotion'][0]: |
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| 230 | dFdvDict[pfx+'RBVU:'+rbsx] += dFdvDict[pfx+'AUiso:'+str(AtLookup[atId])] |
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| 231 | |
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| 232 | |
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| 233 | for irb,RBObj in enumerate(RBModels.get('Residue',[])): |
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| 234 | Q = RBObj['Orient'][0] |
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| 235 | Pos = RBObj['Orig'][0] |
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| 236 | jrb = RRBIds.index(RBObj['RBId']) |
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| 237 | torData = RBData['Residue'][RBObj['RBId']]['rbSeq'] |
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| 238 | rbsx = str(irb)+':'+str(jrb) |
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| 239 | XYZ,Cart = G2mth.UpdateRBXYZ(Bmat,RBObj,RBData,'Residue') |
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| 240 | for itors,tors in enumerate(RBObj['Torsions']): #derivative error? |
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| 241 | tname = pfx+'RBRTr;'+str(itors)+':'+rbsx |
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| 242 | orId,pvId = torData[itors][:2] |
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| 243 | pivotVec = Cart[orId]-Cart[pvId] |
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| 244 | QA = G2mth.AVdeg2Q(-0.001,pivotVec) |
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| 245 | QB = G2mth.AVdeg2Q(0.001,pivotVec) |
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| 246 | for ir in torData[itors][3]: |
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| 247 | atNum = AtLookup[RBObj['Ids'][ir]] |
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| 248 | rVec = Cart[ir]-Cart[pvId] |
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| 249 | dR = G2mth.prodQVQ(QB,rVec)-G2mth.prodQVQ(QA,rVec) |
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| 250 | dRdT = np.inner(Bmat,G2mth.prodQVQ(Q,dR))/.002 |
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| 251 | for ix in [0,1,2]: |
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| 252 | dFdvDict[tname] += dRdT[ix]*dFdvDict[pfx+atxIds[ix]+str(atNum)] |
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| 253 | for ia,atId in enumerate(RBObj['Ids']): |
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| 254 | atNum = AtLookup[atId] |
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| 255 | dx = 0.00001 |
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| 256 | for i,name in enumerate(['RBRPx:','RBRPy:','RBRPz:']): |
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| 257 | dFdvDict[pfx+name+rbsx] += dFdvDict[pfx+atxIds[i]+str(atNum)] |
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| 258 | for iv in range(4): |
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| 259 | Q[iv] -= dx |
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| 260 | XYZ1 = G2mth.RotateRBXYZ(Bmat,Cart,G2mth.normQ(Q)) |
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| 261 | Q[iv] += 2.*dx |
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| 262 | XYZ2 = G2mth.RotateRBXYZ(Bmat,Cart,G2mth.normQ(Q)) |
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| 263 | Q[iv] -= dx |
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| 264 | dXdO = (XYZ2[ia]-XYZ1[ia])/(2.*dx) |
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| 265 | for ix in [0,1,2]: |
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| 266 | dFdvDict[pfx+'RBR'+OIds[iv]+rbsx] += dXdO[ix]*dFdvDict[pfx+atxIds[ix]+str(atNum)] |
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| 267 | X = G2mth.prodQVQ(Q,Cart[ia]) |
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| 268 | dFdu = np.array([dFdvDict[pfx+Uid+str(AtLookup[atId])] for Uid in atuIds]).T/gvec |
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| 269 | dFdu = G2lat.U6toUij(dFdu.T) |
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| 270 | dFdu = np.tensordot(Amat.T,np.tensordot(Amat,dFdu,([1,0])),([0,1])) |
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| 271 | dFdu = G2lat.UijtoU6(dFdu) |
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| 272 | atNum = AtLookup[atId] |
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| 273 | if 'T' in RBObj['ThermalMotion'][0]: |
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| 274 | for i,name in enumerate(['RBRT11:','RBRT22:','RBRT33:','RBRT12:','RBRT13:','RBRT23:']): |
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| 275 | dFdvDict[pfx+name+rbsx] += dFdu[i] |
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| 276 | if 'L' in RBObj['ThermalMotion'][0]: |
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| 277 | 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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| 278 | dFdvDict[pfx+'RBRL22:'+rbsx] += rpd2*(dFdu[0]*X[2]**2+dFdu[2]*X[0]**2-dFdu[4]*X[0]*X[2]) |
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| 279 | dFdvDict[pfx+'RBRL33:'+rbsx] += rpd2*(dFdu[0]*X[1]**2+dFdu[1]*X[0]**2-dFdu[3]*X[0]*X[1]) |
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| 280 | dFdvDict[pfx+'RBRL12:'+rbsx] += rpd2*(-dFdu[3]*X[2]**2-2.*dFdu[2]*X[0]*X[1]+ |
|---|
| 281 | dFdu[4]*X[1]*X[2]+dFdu[5]*X[0]*X[2]) |
|---|
| 282 | dFdvDict[pfx+'RBRL13:'+rbsx] += rpd2*(dFdu[4]*X[1]**2-2.*dFdu[1]*X[0]*X[2]+ |
|---|
| 283 | dFdu[3]*X[1]*X[2]+dFdu[5]*X[0]*X[1]) |
|---|
| 284 | dFdvDict[pfx+'RBRL23:'+rbsx] += rpd2*(dFdu[5]*X[0]**2-2.*dFdu[0]*X[1]*X[2]+ |
|---|
| 285 | dFdu[3]*X[0]*X[2]+dFdu[4]*X[0]*X[1]) |
|---|
| 286 | if 'S' in RBObj['ThermalMotion'][0]: |
|---|
| 287 | dFdvDict[pfx+'RBRS12:'+rbsx] += rpd*(dFdu[5]*X[1]-2.*dFdu[1]*X[2]) |
|---|
| 288 | dFdvDict[pfx+'RBRS13:'+rbsx] += rpd*(-dFdu[5]*X[2]+2.*dFdu[2]*X[1]) |
|---|
| 289 | dFdvDict[pfx+'RBRS21:'+rbsx] += rpd*(-dFdu[4]*X[0]+2.*dFdu[0]*X[2]) |
|---|
| 290 | dFdvDict[pfx+'RBRS23:'+rbsx] += rpd*(dFdu[4]*X[2]-2.*dFdu[2]*X[0]) |
|---|
| 291 | dFdvDict[pfx+'RBRS31:'+rbsx] += rpd*(dFdu[3]*X[0]-2.*dFdu[0]*X[1]) |
|---|
| 292 | dFdvDict[pfx+'RBRS32:'+rbsx] += rpd*(-dFdu[3]*X[1]+2.*dFdu[1]*X[0]) |
|---|
| 293 | dFdvDict[pfx+'RBRSAA:'+rbsx] += rpd*(dFdu[4]*X[1]-dFdu[3]*X[2]) |
|---|
| 294 | dFdvDict[pfx+'RBRSBB:'+rbsx] += rpd*(dFdu[5]*X[0]-dFdu[3]*X[2]) |
|---|
| 295 | if 'U' in RBObj['ThermalMotion'][0]: |
|---|
| 296 | dFdvDict[pfx+'RBRU:'+rbsx] += dFdvDict[pfx+'AUiso:'+str(AtLookup[atId])] |
|---|
| 297 | |
|---|
| 298 | ################################################################################ |
|---|
| 299 | ##### Penalty & restraint functions |
|---|
| 300 | ################################################################################ |
|---|
| 301 | |
|---|
| 302 | def penaltyFxn(HistoPhases,parmDict,varyList): |
|---|
| 303 | 'Needs a doc string' |
|---|
| 304 | Histograms,Phases,restraintDict,rigidbodyDict = HistoPhases |
|---|
| 305 | pNames = [] |
|---|
| 306 | pVals = [] |
|---|
| 307 | pWt = [] |
|---|
| 308 | negWt = {} |
|---|
| 309 | pWsum = {} |
|---|
| 310 | for phase in Phases: |
|---|
| 311 | pId = Phases[phase]['pId'] |
|---|
| 312 | negWt[pId] = Phases[phase]['General']['Pawley neg wt'] |
|---|
| 313 | General = Phases[phase]['General'] |
|---|
| 314 | textureData = General['SH Texture'] |
|---|
| 315 | SGData = General['SGData'] |
|---|
| 316 | AtLookup = G2mth.FillAtomLookUp(Phases[phase]['Atoms']) |
|---|
| 317 | cell = General['Cell'][1:7] |
|---|
| 318 | Amat,Bmat = G2lat.cell2AB(cell) |
|---|
| 319 | if phase not in restraintDict: |
|---|
| 320 | continue |
|---|
| 321 | phaseRest = restraintDict[phase] |
|---|
| 322 | names = [['Bond','Bonds'],['Angle','Angles'],['Plane','Planes'], |
|---|
| 323 | ['Chiral','Volumes'],['Torsion','Torsions'],['Rama','Ramas'], |
|---|
| 324 | ['ChemComp','Sites'],['Texture','HKLs']] |
|---|
| 325 | for name,rest in names: |
|---|
| 326 | pWsum[name] = 0. |
|---|
| 327 | itemRest = phaseRest[name] |
|---|
| 328 | if itemRest[rest] and itemRest['Use']: |
|---|
| 329 | wt = itemRest['wtFactor'] |
|---|
| 330 | if name in ['Bond','Angle','Plane','Chiral']: |
|---|
| 331 | for i,[indx,ops,obs,esd] in enumerate(itemRest[rest]): |
|---|
| 332 | pNames.append(str(pId)+':'+name+':'+str(i)) |
|---|
| 333 | XYZ = np.array(G2mth.GetAtomCoordsByID(pId,parmDict,AtLookup,indx)) |
|---|
| 334 | XYZ = G2mth.getSyXYZ(XYZ,ops,SGData) |
|---|
| 335 | if name == 'Bond': |
|---|
| 336 | calc = G2mth.getRestDist(XYZ,Amat) |
|---|
| 337 | elif name == 'Angle': |
|---|
| 338 | calc = G2mth.getRestAngle(XYZ,Amat) |
|---|
| 339 | elif name == 'Plane': |
|---|
| 340 | calc = G2mth.getRestPlane(XYZ,Amat) |
|---|
| 341 | elif name == 'Chiral': |
|---|
| 342 | calc = G2mth.getRestChiral(XYZ,Amat) |
|---|
| 343 | pVals.append(obs-calc) |
|---|
| 344 | pWt.append(wt/esd**2) |
|---|
| 345 | pWsum[name] += wt*((obs-calc)/esd)**2 |
|---|
| 346 | elif name in ['Torsion','Rama']: |
|---|
| 347 | coeffDict = itemRest['Coeff'] |
|---|
| 348 | for i,[indx,ops,cofName,esd] in enumerate(itemRest[rest]): |
|---|
| 349 | pNames.append(str(pId)+':'+name+':'+str(i)) |
|---|
| 350 | XYZ = np.array(G2mth.GetAtomCoordsByID(pId,parmDict,AtLookup,indx)) |
|---|
| 351 | XYZ = G2mth.getSyXYZ(XYZ,ops,SGData) |
|---|
| 352 | if name == 'Torsion': |
|---|
| 353 | tor = G2mth.getRestTorsion(XYZ,Amat) |
|---|
| 354 | restr,calc = G2mth.calcTorsionEnergy(tor,coeffDict[cofName]) |
|---|
| 355 | else: |
|---|
| 356 | phi,psi = G2mth.getRestRama(XYZ,Amat) |
|---|
| 357 | restr,calc = G2mth.calcRamaEnergy(phi,psi,coeffDict[cofName]) |
|---|
| 358 | pVals.append(obs-calc) |
|---|
| 359 | pWt.append(wt/esd**2) |
|---|
| 360 | pWsum[name] += wt*((obs-calc)/esd)**2 |
|---|
| 361 | elif name == 'ChemComp': |
|---|
| 362 | for i,[indx,factors,obs,esd] in enumerate(itemRest[rest]): |
|---|
| 363 | pNames.append(str(pId)+':'+name+':'+str(i)) |
|---|
| 364 | mul = np.array(G2mth.GetAtomItemsById(Atoms,AtLookUp,indx,cs+1)) |
|---|
| 365 | frac = np.array(G2mth.GetAtomItemsById(Atoms,AtLookUp,indx,cs-1)) |
|---|
| 366 | calc = np.sum(mul*frac*factors) |
|---|
| 367 | pVals.append(obs-calc) |
|---|
| 368 | pWt.append(wt/esd**2) |
|---|
| 369 | pWsum[name] += wt*((obs-calc)/esd)**2 |
|---|
| 370 | elif name == 'Texture': |
|---|
| 371 | SHkeys = textureData['SH Coeff'][1].keys() |
|---|
| 372 | SHCoef = G2mth.GetSHCoeff(pId,parmDict,SHkeys) |
|---|
| 373 | shModels = ['cylindrical','none','shear - 2/m','rolling - mmm'] |
|---|
| 374 | SamSym = dict(zip(shModels,['0','-1','2/m','mmm'])) |
|---|
| 375 | for i,[hkl,grid,esd1,ifesd2,esd2] in enumerate(itemRest[rest]): |
|---|
| 376 | PH = np.array(hkl) |
|---|
| 377 | phi,beta = G2lat.CrsAng(np.array(hkl),cell,SGData) |
|---|
| 378 | ODFln = G2lat.Flnh(False,SHCoef,phi,beta,SGData) |
|---|
| 379 | R,P,Z = G2mth.getRestPolefig(ODFln,SamSym[textureData['Model']],grid) |
|---|
| 380 | Z1 = -ma.masked_greater(Z,0.0) |
|---|
| 381 | IndZ1 = np.array(ma.nonzero(Z1)) |
|---|
| 382 | for ind in IndZ1.T: |
|---|
| 383 | pNames.append('%d:%s:%d:%.2f:%.2f'%(pId,name,i,R[ind[0],ind[1]],P[ind[0],ind[1]])) |
|---|
| 384 | pVals.append(Z1[ind[0]][ind[1]]) |
|---|
| 385 | pWt.append(wt/esd1**2) |
|---|
| 386 | pWsum[name] += wt*((obs-calc)/esd)**2 |
|---|
| 387 | if ifesd2: |
|---|
| 388 | Z2 = 1.-Z |
|---|
| 389 | for ind in np.ndindex(grid,grid): |
|---|
| 390 | pNames.append('%d:%s:%d:%.2f:%.2f'%(pId,name+'-unit',i,R[ind[0],ind[1]],P[ind[0],ind[1]])) |
|---|
| 391 | pVals.append(Z1[ind[0]][ind[1]]) |
|---|
| 392 | pWt.append(wt/esd2**2) |
|---|
| 393 | pWsum[name] += wt*((obs-calc)/esd)**2 |
|---|
| 394 | |
|---|
| 395 | for item in varyList: |
|---|
| 396 | if 'PWLref' in item and parmDict[item] < 0.: |
|---|
| 397 | pId = int(item.split(':')[0]) |
|---|
| 398 | if negWt[pId]: |
|---|
| 399 | pNames.append(item) |
|---|
| 400 | pVals.append(-parmDict[item]) |
|---|
| 401 | pWt.append(negWt[pId]) |
|---|
| 402 | pWsum[name] += negWt[pId]*(-parmDict[item])**2 |
|---|
| 403 | pVals = np.array(pVals) |
|---|
| 404 | pWt = np.array(pWt) #should this be np.sqrt? |
|---|
| 405 | return pNames,pVals,pWt,pWsum |
|---|
| 406 | |
|---|
| 407 | def penaltyDeriv(pNames,pVal,HistoPhases,parmDict,varyList): |
|---|
| 408 | 'Needs a doc string' |
|---|
| 409 | Histograms,Phases,restraintDict,rigidbodyDict = HistoPhases |
|---|
| 410 | pDerv = np.zeros((len(varyList),len(pVal))) |
|---|
| 411 | for phase in Phases: |
|---|
| 412 | # if phase not in restraintDict: |
|---|
| 413 | # continue |
|---|
| 414 | pId = Phases[phase]['pId'] |
|---|
| 415 | General = Phases[phase]['General'] |
|---|
| 416 | SGData = General['SGData'] |
|---|
| 417 | AtLookup = G2mth.FillAtomLookUp(Phases[phase]['Atoms']) |
|---|
| 418 | cell = General['Cell'][1:7] |
|---|
| 419 | Amat,Bmat = G2lat.cell2AB(cell) |
|---|
| 420 | textureData = General['SH Texture'] |
|---|
| 421 | |
|---|
| 422 | SHkeys = textureData['SH Coeff'][1].keys() |
|---|
| 423 | SHCoef = G2mth.GetSHCoeff(pId,parmDict,SHkeys) |
|---|
| 424 | shModels = ['cylindrical','none','shear - 2/m','rolling - mmm'] |
|---|
| 425 | SamSym = dict(zip(shModels,['0','-1','2/m','mmm'])) |
|---|
| 426 | sam = SamSym[textureData['Model']] |
|---|
| 427 | phaseRest = restraintDict.get(phase,{}) |
|---|
| 428 | names = {'Bond':'Bonds','Angle':'Angles','Plane':'Planes', |
|---|
| 429 | 'Chiral':'Volumes','Torsion':'Torsions','Rama':'Ramas', |
|---|
| 430 | 'ChemComp':'Sites','Texture':'HKLs'} |
|---|
| 431 | lasthkl = np.array([0,0,0]) |
|---|
| 432 | for ip,pName in enumerate(pNames): |
|---|
| 433 | pnames = pName.split(':') |
|---|
| 434 | if pId == int(pnames[0]): |
|---|
| 435 | name = pnames[1] |
|---|
| 436 | if 'PWL' in pName: |
|---|
| 437 | pDerv[varyList.index(pName)][ip] += 1. |
|---|
| 438 | continue |
|---|
| 439 | id = int(pnames[2]) |
|---|
| 440 | itemRest = phaseRest[name] |
|---|
| 441 | if name in ['Bond','Angle','Plane','Chiral']: |
|---|
| 442 | indx,ops,obs,esd = itemRest[names[name]][id] |
|---|
| 443 | dNames = [] |
|---|
| 444 | for ind in indx: |
|---|
| 445 | dNames += [str(pId)+'::dA'+Xname+':'+str(AtLookup[ind]) for Xname in ['x','y','z']] |
|---|
| 446 | XYZ = np.array(G2mth.GetAtomCoordsByID(pId,parmDict,AtLookup,indx)) |
|---|
| 447 | if name == 'Bond': |
|---|
| 448 | deriv = G2mth.getRestDeriv(G2mth.getRestDist,XYZ,Amat,ops,SGData) |
|---|
| 449 | elif name == 'Angle': |
|---|
| 450 | deriv = G2mth.getRestDeriv(G2mth.getRestAngle,XYZ,Amat,ops,SGData) |
|---|
| 451 | elif name == 'Plane': |
|---|
| 452 | deriv = G2mth.getRestDeriv(G2mth.getRestPlane,XYZ,Amat,ops,SGData) |
|---|
| 453 | elif name == 'Chiral': |
|---|
| 454 | deriv = G2mth.getRestDeriv(G2mth.getRestChiral,XYZ,Amat,ops,SGData) |
|---|
| 455 | elif name in ['Torsion','Rama']: |
|---|
| 456 | coffDict = itemRest['Coeff'] |
|---|
| 457 | indx,ops,cofName,esd = itemRest[names[name]][id] |
|---|
| 458 | dNames = [] |
|---|
| 459 | for ind in indx: |
|---|
| 460 | dNames += [str(pId)+'::dA'+Xname+':'+str(AtLookup[ind]) for Xname in ['x','y','z']] |
|---|
| 461 | XYZ = np.array(G2mth.GetAtomCoordsByID(pId,parmDict,AtLookup,indx)) |
|---|
| 462 | if name == 'Torsion': |
|---|
| 463 | deriv = G2mth.getTorsionDeriv(XYZ,Amat,coffDict[cofName]) |
|---|
| 464 | else: |
|---|
| 465 | deriv = G2mth.getRamaDeriv(XYZ,Amat,coffDict[cofName]) |
|---|
| 466 | elif name == 'ChemComp': |
|---|
| 467 | indx,factors,obs,esd = itemRest[names[name]][id] |
|---|
| 468 | dNames = [] |
|---|
| 469 | for ind in indx: |
|---|
| 470 | dNames += [str(pId)+'::Afrac:'+str(AtLookup[ind])] |
|---|
| 471 | mul = np.array(G2mth.GetAtomItemsById(Atoms,AtLookUp,indx,cs+1)) |
|---|
| 472 | deriv = mul*factors |
|---|
| 473 | elif 'Texture' in name: |
|---|
| 474 | deriv = [] |
|---|
| 475 | dNames = [] |
|---|
| 476 | hkl,grid,esd1,ifesd2,esd2 = itemRest[names[name]][id] |
|---|
| 477 | hkl = np.array(hkl) |
|---|
| 478 | if np.any(lasthkl-hkl): |
|---|
| 479 | PH = np.array(hkl) |
|---|
| 480 | phi,beta = G2lat.CrsAng(np.array(hkl),cell,SGData) |
|---|
| 481 | ODFln = G2lat.Flnh(False,SHCoef,phi,beta,SGData) |
|---|
| 482 | lasthkl = copy.copy(hkl) |
|---|
| 483 | if 'unit' in name: |
|---|
| 484 | pass |
|---|
| 485 | else: |
|---|
| 486 | gam = float(pnames[3]) |
|---|
| 487 | psi = float(pnames[4]) |
|---|
| 488 | for SHname in ODFln: |
|---|
| 489 | l,m,n = eval(SHname[1:]) |
|---|
| 490 | Ksl = G2lat.GetKsl(l,m,sam,psi,gam)[0] |
|---|
| 491 | dNames += [str(pId)+'::'+SHname] |
|---|
| 492 | deriv.append(-ODFln[SHname][0]*Ksl/SHCoef[SHname]) |
|---|
| 493 | for dName,drv in zip(dNames,deriv): |
|---|
| 494 | try: |
|---|
| 495 | ind = varyList.index(dName) |
|---|
| 496 | pDerv[ind][ip] += drv |
|---|
| 497 | except ValueError: |
|---|
| 498 | pass |
|---|
| 499 | return pDerv |
|---|
| 500 | |
|---|
| 501 | ################################################################################ |
|---|
| 502 | ##### Function & derivative calculations |
|---|
| 503 | ################################################################################ |
|---|
| 504 | |
|---|
| 505 | def GetAtomFXU(pfx,calcControls,parmDict): |
|---|
| 506 | 'Needs a doc string' |
|---|
| 507 | Natoms = calcControls['Natoms'][pfx] |
|---|
| 508 | Tdata = Natoms*[' ',] |
|---|
| 509 | Mdata = np.zeros(Natoms) |
|---|
| 510 | IAdata = Natoms*[' ',] |
|---|
| 511 | Fdata = np.zeros(Natoms) |
|---|
| 512 | FFdata = [] |
|---|
| 513 | BLdata = [] |
|---|
| 514 | Xdata = np.zeros((3,Natoms)) |
|---|
| 515 | dXdata = np.zeros((3,Natoms)) |
|---|
| 516 | Uisodata = np.zeros(Natoms) |
|---|
| 517 | Uijdata = np.zeros((6,Natoms)) |
|---|
| 518 | keys = {'Atype:':Tdata,'Amul:':Mdata,'Afrac:':Fdata,'AI/A:':IAdata, |
|---|
| 519 | 'dAx:':dXdata[0],'dAy:':dXdata[1],'dAz:':dXdata[2], |
|---|
| 520 | 'Ax:':Xdata[0],'Ay:':Xdata[1],'Az:':Xdata[2],'AUiso:':Uisodata, |
|---|
| 521 | 'AU11:':Uijdata[0],'AU22:':Uijdata[1],'AU33:':Uijdata[2], |
|---|
| 522 | 'AU12:':Uijdata[3],'AU13:':Uijdata[4],'AU23:':Uijdata[5]} |
|---|
| 523 | for iatm in range(Natoms): |
|---|
| 524 | for key in keys: |
|---|
| 525 | parm = pfx+key+str(iatm) |
|---|
| 526 | if parm in parmDict: |
|---|
| 527 | keys[key][iatm] = parmDict[parm] |
|---|
| 528 | return Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata |
|---|
| 529 | |
|---|
| 530 | def StructureFactor(refList,G,hfx,pfx,SGData,calcControls,parmDict): |
|---|
| 531 | ''' Compute structure factors for all h,k,l for phase |
|---|
| 532 | puts the result, F^2, in each ref[8] in refList |
|---|
| 533 | input: |
|---|
| 534 | |
|---|
| 535 | :param list refList: [ref] where each ref = h,k,l,m,d,...,[equiv h,k,l],phase[equiv] |
|---|
| 536 | :param np.array G: reciprocal metric tensor |
|---|
| 537 | :param str pfx: phase id string |
|---|
| 538 | :param dict SGData: space group info. dictionary output from SpcGroup |
|---|
| 539 | :param dict calcControls: |
|---|
| 540 | :param dict ParmDict: |
|---|
| 541 | |
|---|
| 542 | ''' |
|---|
| 543 | twopi = 2.0*np.pi |
|---|
| 544 | twopisq = 2.0*np.pi**2 |
|---|
| 545 | phfx = pfx.split(':')[0]+hfx |
|---|
| 546 | ast = np.sqrt(np.diag(G)) |
|---|
| 547 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 548 | FFtables = calcControls['FFtables'] |
|---|
| 549 | BLtables = calcControls['BLtables'] |
|---|
| 550 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata = GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 551 | FF = np.zeros(len(Tdata)) |
|---|
| 552 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 553 | FP,FPP = G2el.BlenRes(Tdata,BLtables,parmDict[hfx+'Lam']) |
|---|
| 554 | else: |
|---|
| 555 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 556 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 557 | Uij = np.array(G2lat.U6toUij(Uijdata)) |
|---|
| 558 | bij = Mast*Uij.T |
|---|
| 559 | for refl in refList: |
|---|
| 560 | fbs = np.array([0,0]) |
|---|
| 561 | H = refl[:3] |
|---|
| 562 | SQ = 1./(2.*refl[4])**2 |
|---|
| 563 | SQfactor = 4.0*SQ*twopisq |
|---|
| 564 | Bab = parmDict[phfx+'BabA']*np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 565 | if not len(refl[-1]): #no form factors |
|---|
| 566 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 567 | refl[-1] = G2el.getBLvalues(BLtables) |
|---|
| 568 | else: #'X' |
|---|
| 569 | refl[-1] = G2el.getFFvalues(FFtables,SQ) |
|---|
| 570 | for i,El in enumerate(Tdata): |
|---|
| 571 | FF[i] = refl[-1][El] |
|---|
| 572 | Uniq = refl[11] |
|---|
| 573 | phi = refl[12] |
|---|
| 574 | phase = twopi*(np.inner(Uniq,(dXdata.T+Xdata.T))+phi[:,np.newaxis]) |
|---|
| 575 | sinp = np.sin(phase) |
|---|
| 576 | cosp = np.cos(phase) |
|---|
| 577 | occ = Mdata*Fdata/len(Uniq) |
|---|
| 578 | biso = -SQfactor*Uisodata |
|---|
| 579 | Tiso = np.where(biso<1.,np.exp(biso),1.0) |
|---|
| 580 | HbH = np.array([-np.inner(h,np.inner(bij,h)) for h in Uniq]) |
|---|
| 581 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0) |
|---|
| 582 | Tcorr = Tiso*Tuij |
|---|
| 583 | fa = np.array([(FF+FP-Bab)*occ*cosp*Tcorr,-FPP*occ*sinp*Tcorr]) |
|---|
| 584 | fas = np.sum(np.sum(fa,axis=1),axis=1) #real |
|---|
| 585 | if not SGData['SGInv']: |
|---|
| 586 | fb = np.array([(FF+FP-Bab)*occ*sinp*Tcorr,FPP*occ*cosp*Tcorr]) |
|---|
| 587 | fbs = np.sum(np.sum(fb,axis=1),axis=1) |
|---|
| 588 | fasq = fas**2 |
|---|
| 589 | fbsq = fbs**2 #imaginary |
|---|
| 590 | refl[9] = np.sum(fasq)+np.sum(fbsq) |
|---|
| 591 | refl[10] = atan2d(fbs[0],fas[0]) |
|---|
| 592 | |
|---|
| 593 | def StructureFactorDerv(refList,G,hfx,pfx,SGData,calcControls,parmDict): |
|---|
| 594 | 'Needs a doc string' |
|---|
| 595 | twopi = 2.0*np.pi |
|---|
| 596 | twopisq = 2.0*np.pi**2 |
|---|
| 597 | phfx = pfx.split(':')[0]+hfx |
|---|
| 598 | ast = np.sqrt(np.diag(G)) |
|---|
| 599 | Mast = twopisq*np.multiply.outer(ast,ast) |
|---|
| 600 | FFtables = calcControls['FFtables'] |
|---|
| 601 | BLtables = calcControls['BLtables'] |
|---|
| 602 | Tdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata = GetAtomFXU(pfx,calcControls,parmDict) |
|---|
| 603 | FF = np.zeros(len(Tdata)) |
|---|
| 604 | if 'N' in calcControls[hfx+'histType']: |
|---|
| 605 | FP = 0. |
|---|
| 606 | FPP = 0. |
|---|
| 607 | else: |
|---|
| 608 | FP = np.array([FFtables[El][hfx+'FP'] for El in Tdata]) |
|---|
| 609 | FPP = np.array([FFtables[El][hfx+'FPP'] for El in Tdata]) |
|---|
| 610 | Uij = np.array(G2lat.U6toUij(Uijdata)) |
|---|
| 611 | bij = Mast*Uij.T |
|---|
| 612 | dFdvDict = {} |
|---|
| 613 | dFdfr = np.zeros((len(refList),len(Mdata))) |
|---|
| 614 | dFdx = np.zeros((len(refList),len(Mdata),3)) |
|---|
| 615 | dFdui = np.zeros((len(refList),len(Mdata))) |
|---|
| 616 | dFdua = np.zeros((len(refList),len(Mdata),6)) |
|---|
| 617 | dFdbab = np.zeros((len(refList),2)) |
|---|
| 618 | for iref,refl in enumerate(refList): |
|---|
| 619 | H = np.array(refl[:3]) |
|---|
| 620 | SQ = 1./(2.*refl[4])**2 # or (sin(theta)/lambda)**2 |
|---|
| 621 | SQfactor = 8.0*SQ*np.pi**2 |
|---|
| 622 | dBabdA = np.exp(-parmDict[phfx+'BabU']*SQfactor) |
|---|
| 623 | Bab = parmDict[phfx+'BabA']*dBabdA |
|---|
| 624 | for i,El in enumerate(Tdata): |
|---|
| 625 | FF[i] = refl[-1][El] |
|---|
| 626 | Uniq = refl[11] |
|---|
| 627 | phi = refl[12] |
|---|
| 628 | phase = twopi*(np.inner((dXdata.T+Xdata.T),Uniq)+phi[np.newaxis,:]) |
|---|
| 629 | sinp = np.sin(phase) |
|---|
| 630 | cosp = np.cos(phase) |
|---|
| 631 | occ = Mdata*Fdata/len(Uniq) |
|---|
| 632 | biso = -SQfactor*Uisodata |
|---|
| 633 | Tiso = np.where(biso<1.,np.exp(biso),1.0) |
|---|
| 634 | HbH = -np.inner(H,np.inner(bij,H)) |
|---|
| 635 | Hij = np.array([Mast*np.multiply.outer(U,U) for U in Uniq]) |
|---|
| 636 | Hij = np.array([G2lat.UijtoU6(Uij) for Uij in Hij]) |
|---|
| 637 | Tuij = np.where(HbH<1.,np.exp(HbH),1.0) |
|---|
| 638 | Tcorr = Tiso*Tuij |
|---|
| 639 | fot = (FF+FP-Bab)*occ*Tcorr |
|---|
| 640 | fotp = FPP*occ*Tcorr |
|---|
| 641 | fa = np.array([fot[:,np.newaxis]*cosp,fotp[:,np.newaxis]*cosp]) #non positions |
|---|
| 642 | fb = np.array([fot[:,np.newaxis]*sinp,-fotp[:,np.newaxis]*sinp]) |
|---|
| 643 | |
|---|
| 644 | fas = np.sum(np.sum(fa,axis=1),axis=1) |
|---|
| 645 | fbs = np.sum(np.sum(fb,axis=1),axis=1) |
|---|
| 646 | fax = np.array([-fot[:,np.newaxis]*sinp,-fotp[:,np.newaxis]*sinp]) #positions |
|---|
| 647 | fbx = np.array([fot[:,np.newaxis]*cosp,-fot[:,np.newaxis]*cosp]) |
|---|
| 648 | #sum below is over Uniq |
|---|
| 649 | dfadfr = np.sum(fa/occ[:,np.newaxis],axis=2) |
|---|
| 650 | dfadx = np.sum(twopi*Uniq*fax[:,:,:,np.newaxis],axis=2) |
|---|
| 651 | dfadui = np.sum(-SQfactor*fa,axis=2) |
|---|
| 652 | dfadua = np.sum(-Hij*fa[:,:,:,np.newaxis],axis=2) |
|---|
| 653 | dfadba = np.sum(-cosp*(occ*Tcorr)[:,np.newaxis],axis=1) |
|---|
| 654 | #NB: the above have been checked against PA(1:10,1:2) in strfctr.for |
|---|
| 655 | dFdfr[iref] = 2.*(fas[0]*dfadfr[0]+fas[1]*dfadfr[1])*Mdata/len(Uniq) |
|---|
| 656 | dFdx[iref] = 2.*(fas[0]*dfadx[0]+fas[1]*dfadx[1]) |
|---|
| 657 | dFdui[iref] = 2.*(fas[0]*dfadui[0]+fas[1]*dfadui[1]) |
|---|
| 658 | dFdua[iref] = 2.*(fas[0]*dfadua[0]+fas[1]*dfadua[1]) |
|---|
| 659 | dFdbab[iref] = np.array([np.sum(dfadba*dBabdA),np.sum(-dfadba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T |
|---|
| 660 | if not SGData['SGInv']: |
|---|
| 661 | dfbdfr = np.sum(fb/occ[:,np.newaxis],axis=2) #problem here if occ=0 for some atom |
|---|
| 662 | dfbdx = np.sum(twopi*Uniq*fbx[:,:,:,np.newaxis],axis=2) |
|---|
| 663 | dfbdui = np.sum(-SQfactor*fb,axis=2) |
|---|
| 664 | dfbdua = np.sum(-Hij*fb[:,:,:,np.newaxis],axis=2) |
|---|
| 665 | dfbdba = np.sum(-sinp*(occ*Tcorr)[:,np.newaxis],axis=1) |
|---|
| 666 | dFdfr[iref] += 2.*(fbs[0]*dfbdfr[0]-fbs[1]*dfbdfr[1])*Mdata/len(Uniq) |
|---|
| 667 | dFdx[iref] += 2.*(fbs[0]*dfbdx[0]+fbs[1]*dfbdx[1]) |
|---|
| 668 | dFdui[iref] += 2.*(fbs[0]*dfbdui[0]-fbs[1]*dfbdui[1]) |
|---|
| 669 | dFdua[iref] += 2.*(fbs[0]*dfbdua[0]+fbs[1]*dfbdua[1]) |
|---|
| 670 | dFdbab[iref] += np.array([np.sum(dfbdba*dBabdA),np.sum(-dfbdba*parmDict[phfx+'BabA']*SQfactor*dBabdA)]).T |
|---|
| 671 | #loop over atoms - each dict entry is list of derivatives for all the reflections |
|---|
| 672 | for i in range(len(Mdata)): |
|---|
| 673 | dFdvDict[pfx+'Afrac:'+str(i)] = dFdfr.T[i] |
|---|
| 674 | dFdvDict[pfx+'dAx:'+str(i)] = dFdx.T[0][i] |
|---|
| 675 | dFdvDict[pfx+'dAy:'+str(i)] = dFdx.T[1][i] |
|---|
| 676 | dFdvDict[pfx+'dAz:'+str(i)] = dFdx.T[2][i] |
|---|
| 677 | dFdvDict[pfx+'AUiso:'+str(i)] = dFdui.T[i] |
|---|
| 678 | dFdvDict[pfx+'AU11:'+str(i)] = dFdua.T[0][i] |
|---|
| 679 | dFdvDict[pfx+'AU22:'+str(i)] = dFdua.T[1][i] |
|---|
| 680 | dFdvDict[pfx+'AU33:'+str(i)] = dFdua.T[2][i] |
|---|
| 681 | dFdvDict[pfx+'AU12:'+str(i)] = 2.*dFdua.T[3][i] |
|---|
| 682 | dFdvDict[pfx+'AU13:'+str(i)] = 2.*dFdua.T[4][i] |
|---|
| 683 | dFdvDict[pfx+'AU23:'+str(i)] = 2.*dFdua.T[5][i] |
|---|
| 684 | dFdvDict[pfx+'BabA'] = dFdbab.T[0] |
|---|
| 685 | dFdvDict[pfx+'BabU'] = dFdbab.T[1] |
|---|
| 686 | return dFdvDict |
|---|
| 687 | |
|---|
| 688 | def SCExtinction(ref,phfx,hfx,pfx,calcControls,parmDict,varyList): |
|---|
| 689 | ''' Single crystal extinction function; puts correction in ref[13] and returns |
|---|
| 690 | corrections needed for derivatives |
|---|
| 691 | ''' |
|---|
| 692 | ref[13] = 1.0 |
|---|
| 693 | dervCor = 1.0 |
|---|
| 694 | dervDict = {} |
|---|
| 695 | if calcControls[phfx+'EType'] != 'None': |
|---|
| 696 | cos2T = 1.0-0.5*(parmDict[hfx+'Lam']/ref[4])**2 #cos(2theta) |
|---|
| 697 | if 'SXC' in parmDict[hfx+'Type']: |
|---|
| 698 | AV = 7.9406e5/parmDict[pfx+'Vol']**2 |
|---|
| 699 | PL = np.sqrt(1.0-cos2T**2)/parmDict[hfx+'Lam'] |
|---|
| 700 | P12 = (calcControls[phfx+'Cos2TM']+cos2T**4)/(calcControls[phfx+'Cos2TM']+cos2T**2) |
|---|
| 701 | elif 'SNT' in parmDict[hfx+'Type']: |
|---|
| 702 | AV = 1.e7/parmDict[pfx+'Vol']**2 |
|---|
| 703 | PL = 1./(4.*refl[4]**2) |
|---|
| 704 | P12 = 1.0 |
|---|
| 705 | elif 'SNC' in parmDict[hfx+'Type']: |
|---|
| 706 | AV = 1.e7/parmDict[pfx+'Vol']**2 |
|---|
| 707 | PL = np.sqrt(1.0-cos2T**2)/parmDict[hfx+'Lam'] |
|---|
| 708 | P12 = 1.0 |
|---|
| 709 | |
|---|
| 710 | PLZ = AV*P12*parmDict[hfx+'Lam']**2*ref[7] |
|---|
| 711 | if 'Primary' in calcControls[phfx+'EType']: |
|---|
| 712 | PLZ *= 1.5 |
|---|
| 713 | else: |
|---|
| 714 | PLZ *= calcControls[phfx+'Tbar'] |
|---|
| 715 | |
|---|
| 716 | if 'Primary' in calcControls[phfx+'EType']: |
|---|
| 717 | PSIG = parmDict[phfx+'Ep'] |
|---|
| 718 | elif 'I & II' in calcControls[phfx+'EType']: |
|---|
| 719 | PSIG = parmDict[phfx+'Eg']/np.sqrt(1.+(parmDict[phfx+'Es']*PL/parmDict[phfx+'Eg'])**2) |
|---|
| 720 | elif 'Type II' in calcControls[phfx+'EType']: |
|---|
| 721 | PSIG = parmDict[phfx+'Es'] |
|---|
| 722 | else: # 'Secondary Type I' |
|---|
| 723 | PSIG = parmDict[phfx+'Eg']/PL |
|---|
| 724 | |
|---|
| 725 | AG = 0.58+0.48*cos2T+0.24*cos2T**2 |
|---|
| 726 | AL = 0.025+0.285*cos2T |
|---|
| 727 | BG = 0.02-0.025*cos2T |
|---|
| 728 | BL = 0.15-0.2*(0.75-cos2T)**2 |
|---|
| 729 | if cos2T < 0.: |
|---|
| 730 | BL = -0.45*cos2T |
|---|
| 731 | CG = 2. |
|---|
| 732 | CL = 2. |
|---|
| 733 | PF = PLZ*PSIG |
|---|
| 734 | |
|---|
| 735 | if 'Gaussian' in calcControls[phfx+'EApprox']: |
|---|
| 736 | PF4 = 1.+CG*PF+AG*PF**2/(1.+BG*PF) |
|---|
| 737 | extCor = np.sqrt(PF4) |
|---|
| 738 | PF3 = 0.5*(CG+2.*AG*PF/(1.+BG*PF)-AG*PF**2*BG/(1.+BG*PF)**2)/(PF4*extCor) |
|---|
| 739 | else: |
|---|
| 740 | PF4 = 1.+CL*PF+AL*PF**2/(1.+BL*PF) |
|---|
| 741 | extCor = np.sqrt(PF4) |
|---|
| 742 | PF3 = 0.5*(CL+2.*AL*PF/(1.+BL*PF)-AL*PF**2*BL/(1.+BL*PF)**2)/(PF4*extCor) |
|---|
| 743 | |
|---|
| 744 | dervCor = (1.+PF)*PF3 |
|---|
| 745 | if 'Primary' in calcControls[phfx+'EType'] and phfx+'Ep' in varyList: |
|---|
| 746 | dervDict[phfx+'Ep'] = -ref[7]*PLZ*PF3 |
|---|
| 747 | if 'II' in calcControls[phfx+'EType'] and phfx+'Es' in varyList: |
|---|
| 748 | dervDict[phfx+'Es'] = -ref[7]*PLZ*PF3*(PSIG/parmDict[phfx+'Es'])**3 |
|---|
| 749 | if 'I' in calcControls[phfx+'EType'] and phfx+'Eg' in varyList: |
|---|
| 750 | dervDict[phfx+'Eg'] = -ref[7]*PLZ*PF3*(PSIG/parmDict[phfx+'Eg'])**3*PL**2 |
|---|
| 751 | |
|---|
| 752 | ref[13] = 1./extCor |
|---|
| 753 | return dervCor,dervDict |
|---|
| 754 | |
|---|
| 755 | |
|---|
| 756 | def Dict2Values(parmdict, varylist): |
|---|
| 757 | '''Use before call to leastsq to setup list of values for the parameters |
|---|
| 758 | in parmdict, as selected by key in varylist''' |
|---|
| 759 | return [parmdict[key] for key in varylist] |
|---|
| 760 | |
|---|
| 761 | def Values2Dict(parmdict, varylist, values): |
|---|
| 762 | ''' Use after call to leastsq to update the parameter dictionary with |
|---|
| 763 | values corresponding to keys in varylist''' |
|---|
| 764 | parmdict.update(zip(varylist,values)) |
|---|
| 765 | |
|---|
| 766 | def GetNewCellParms(parmDict,varyList): |
|---|
| 767 | 'Needs a doc string' |
|---|
| 768 | newCellDict = {} |
|---|
| 769 | Anames = ['A'+str(i) for i in range(6)] |
|---|
| 770 | Ddict = dict(zip(['D11','D22','D33','D12','D13','D23'],Anames)) |
|---|
| 771 | for item in varyList: |
|---|
| 772 | keys = item.split(':') |
|---|
| 773 | if keys[2] in Ddict: |
|---|
| 774 | key = keys[0]+'::'+Ddict[keys[2]] #key is e.g. '0::A0' |
|---|
| 775 | parm = keys[0]+'::'+keys[2] #parm is e.g. '0::D11' |
|---|
| 776 | newCellDict[parm] = [key,parmDict[key]+parmDict[item]] |
|---|
| 777 | return newCellDict # is e.g. {'0::D11':A0+D11} |
|---|
| 778 | |
|---|
| 779 | def ApplyXYZshifts(parmDict,varyList): |
|---|
| 780 | ''' |
|---|
| 781 | takes atom x,y,z shift and applies it to corresponding atom x,y,z value |
|---|
| 782 | |
|---|
| 783 | :param dict parmDict: parameter dictionary |
|---|
| 784 | :param list varyList: list of variables |
|---|
| 785 | :returns: newAtomDict - dictionary of new atomic coordinate names & values; key is parameter shift name |
|---|
| 786 | |
|---|
| 787 | ''' |
|---|
| 788 | newAtomDict = {} |
|---|
| 789 | for item in parmDict: |
|---|
| 790 | if 'dA' in item: |
|---|
| 791 | parm = ''.join(item.split('d')) |
|---|
| 792 | parmDict[parm] += parmDict[item] |
|---|
| 793 | newAtomDict[item] = [parm,parmDict[parm]] |
|---|
| 794 | return newAtomDict |
|---|
| 795 | |
|---|
| 796 | def SHTXcal(refl,g,pfx,hfx,SGData,calcControls,parmDict): |
|---|
| 797 | 'Spherical harmonics texture' |
|---|
| 798 | IFCoup = 'Bragg' in calcControls[hfx+'instType'] |
|---|
| 799 | odfCor = 1.0 |
|---|
| 800 | H = refl[:3] |
|---|
| 801 | cell = G2lat.Gmat2cell(g) |
|---|
| 802 | Sangls = [parmDict[pfx+'SH omega'],parmDict[pfx+'SH chi'],parmDict[pfx+'SH phi']] |
|---|
| 803 | Gangls = [parmDict[hfx+'Omega'],parmDict[hfx+'Chi'],parmDict[hfx+'Phi'],parmDict[hfx+'Azimuth']] |
|---|
| 804 | phi,beta = G2lat.CrsAng(H,cell,SGData) |
|---|
| 805 | psi,gam,x,x = G2lat.SamAng(refl[5]/2.,Gangls,Sangls,IFCoup) #ignore 2 sets of angle derivs. |
|---|
| 806 | SHnames = G2lat.GenSHCoeff(SGData['SGLaue'],parmDict[pfx+'SHmodel'],parmDict[pfx+'SHorder']) |
|---|
| 807 | for item in SHnames: |
|---|
| 808 | L,M,N = eval(item.strip('C')) |
|---|
| 809 | Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta) |
|---|
| 810 | Ksl,x,x = G2lat.GetKsl(L,M,parmDict[pfx+'SHmodel'],psi,gam) |
|---|
| 811 | Lnorm = G2lat.Lnorm(L) |
|---|
| 812 | odfCor += parmDict[pfx+item]*Lnorm*Kcl*Ksl |
|---|
| 813 | return odfCor |
|---|
| 814 | |
|---|
| 815 | def SHTXcalDerv(refl,g,pfx,hfx,SGData,calcControls,parmDict): |
|---|
| 816 | 'Spherical harmonics texture derivatives' |
|---|
| 817 | FORPI = 4.0*np.pi |
|---|
| 818 | IFCoup = 'Bragg' in calcControls[hfx+'instType'] |
|---|
| 819 | odfCor = 1.0 |
|---|
| 820 | dFdODF = {} |
|---|
| 821 | dFdSA = [0,0,0] |
|---|
| 822 | H = refl[:3] |
|---|
| 823 | cell = G2lat.Gmat2cell(g) |
|---|
| 824 | Sangls = [parmDict[pfx+'SH omega'],parmDict[pfx+'SH chi'],parmDict[pfx+'SH phi']] |
|---|
| 825 | Gangls = [parmDict[hfx+'Omega'],parmDict[hfx+'Chi'],parmDict[hfx+'Phi'],parmDict[hfx+'Azimuth']] |
|---|
| 826 | phi,beta = G2lat.CrsAng(H,cell,SGData) |
|---|
| 827 | psi,gam,dPSdA,dGMdA = G2lat.SamAng(refl[5]/2.,Gangls,Sangls,IFCoup) |
|---|
| 828 | SHnames = G2lat.GenSHCoeff(SGData['SGLaue'],parmDict[pfx+'SHmodel'],parmDict[pfx+'SHorder']) |
|---|
| 829 | for item in SHnames: |
|---|
| 830 | L,M,N = eval(item.strip('C')) |
|---|
| 831 | Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta) |
|---|
| 832 | Ksl,dKsdp,dKsdg = G2lat.GetKsl(L,M,parmDict[pfx+'SHmodel'],psi,gam) |
|---|
| 833 | Lnorm = G2lat.Lnorm(L) |
|---|
| 834 | odfCor += parmDict[pfx+item]*Lnorm*Kcl*Ksl |
|---|
| 835 | dFdODF[pfx+item] = Lnorm*Kcl*Ksl |
|---|
| 836 | for i in range(3): |
|---|
| 837 | dFdSA[i] += parmDict[pfx+item]*Lnorm*Kcl*(dKsdp*dPSdA[i]+dKsdg*dGMdA[i]) |
|---|
| 838 | return odfCor,dFdODF,dFdSA |
|---|
| 839 | |
|---|
| 840 | def SHPOcal(refl,g,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 841 | 'spherical harmonics preferred orientation (cylindrical symmetry only)' |
|---|
| 842 | odfCor = 1.0 |
|---|
| 843 | H = refl[:3] |
|---|
| 844 | cell = G2lat.Gmat2cell(g) |
|---|
| 845 | Sangl = [0.,0.,0.] |
|---|
| 846 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 847 | Gangls = [0.,90.,0.,parmDict[hfx+'Azimuth']] |
|---|
| 848 | IFCoup = True |
|---|
| 849 | else: |
|---|
| 850 | Gangls = [0.,0.,0.,parmDict[hfx+'Azimuth']] |
|---|
| 851 | IFCoup = False |
|---|
| 852 | phi,beta = G2lat.CrsAng(H,cell,SGData) |
|---|
| 853 | psi,gam,x,x = G2lat.SamAng(refl[5]/2.,Gangls,Sangl,IFCoup) #ignore 2 sets of angle derivs. |
|---|
| 854 | SHnames = G2lat.GenSHCoeff(SGData['SGLaue'],'0',calcControls[phfx+'SHord'],False) |
|---|
| 855 | for item in SHnames: |
|---|
| 856 | L,N = eval(item.strip('C')) |
|---|
| 857 | Kcsl,Lnorm = G2lat.GetKclKsl(L,N,SGData['SGLaue'],psi,phi,beta) |
|---|
| 858 | odfCor += parmDict[phfx+item]*Lnorm*Kcsl |
|---|
| 859 | return np.squeeze(odfCor) |
|---|
| 860 | |
|---|
| 861 | def SHPOcalDerv(refl,g,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 862 | 'spherical harmonics preferred orientation derivatives (cylindrical symmetry only)' |
|---|
| 863 | FORPI = 12.5663706143592 |
|---|
| 864 | odfCor = 1.0 |
|---|
| 865 | dFdODF = {} |
|---|
| 866 | H = refl[:3] |
|---|
| 867 | cell = G2lat.Gmat2cell(g) |
|---|
| 868 | Sangl = [0.,0.,0.] |
|---|
| 869 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 870 | Gangls = [0.,90.,0.,parmDict[hfx+'Azimuth']] |
|---|
| 871 | IFCoup = True |
|---|
| 872 | else: |
|---|
| 873 | Gangls = [0.,0.,0.,parmDict[hfx+'Azimuth']] |
|---|
| 874 | IFCoup = False |
|---|
| 875 | phi,beta = G2lat.CrsAng(H,cell,SGData) |
|---|
| 876 | psi,gam,x,x = G2lat.SamAng(refl[5]/2.,Gangls,Sangl,IFCoup) #ignore 2 sets of angle derivs. |
|---|
| 877 | SHnames = G2lat.GenSHCoeff(SGData['SGLaue'],'0',calcControls[phfx+'SHord'],False) |
|---|
| 878 | for item in SHnames: |
|---|
| 879 | L,N = eval(item.strip('C')) |
|---|
| 880 | Kcsl,Lnorm = G2lat.GetKclKsl(L,N,SGData['SGLaue'],psi,phi,beta) |
|---|
| 881 | odfCor += parmDict[phfx+item]*Lnorm*Kcsl |
|---|
| 882 | dFdODF[phfx+item] = Kcsl*Lnorm |
|---|
| 883 | return odfCor,dFdODF |
|---|
| 884 | |
|---|
| 885 | def GetPrefOri(refl,G,g,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 886 | 'Needs a doc string' |
|---|
| 887 | POcorr = 1.0 |
|---|
| 888 | if calcControls[phfx+'poType'] == 'MD': |
|---|
| 889 | MD = parmDict[phfx+'MD'] |
|---|
| 890 | if MD != 1.0: |
|---|
| 891 | MDAxis = calcControls[phfx+'MDAxis'] |
|---|
| 892 | sumMD = 0 |
|---|
| 893 | for H in refl[11]: |
|---|
| 894 | cosP,sinP = G2lat.CosSinAngle(H,MDAxis,G) |
|---|
| 895 | A = 1.0/np.sqrt((MD*cosP)**2+sinP**2/MD) |
|---|
| 896 | sumMD += A**3 |
|---|
| 897 | POcorr = sumMD/len(refl[11]) |
|---|
| 898 | else: #spherical harmonics |
|---|
| 899 | if calcControls[phfx+'SHord']: |
|---|
| 900 | POcorr = SHPOcal(refl,g,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 901 | return POcorr |
|---|
| 902 | |
|---|
| 903 | def GetPrefOriDerv(refl,G,g,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 904 | 'Needs a doc string' |
|---|
| 905 | POcorr = 1.0 |
|---|
| 906 | POderv = {} |
|---|
| 907 | if calcControls[phfx+'poType'] == 'MD': |
|---|
| 908 | MD = parmDict[phfx+'MD'] |
|---|
| 909 | MDAxis = calcControls[phfx+'MDAxis'] |
|---|
| 910 | sumMD = 0 |
|---|
| 911 | sumdMD = 0 |
|---|
| 912 | for H in refl[11]: |
|---|
| 913 | cosP,sinP = G2lat.CosSinAngle(H,MDAxis,G) |
|---|
| 914 | A = 1.0/np.sqrt((MD*cosP)**2+sinP**2/MD) |
|---|
| 915 | sumMD += A**3 |
|---|
| 916 | sumdMD -= (1.5*A**5)*(2.0*MD*cosP**2-(sinP/MD)**2) |
|---|
| 917 | POcorr = sumMD/len(refl[11]) |
|---|
| 918 | POderv[phfx+'MD'] = sumdMD/len(refl[11]) |
|---|
| 919 | else: #spherical harmonics |
|---|
| 920 | if calcControls[phfx+'SHord']: |
|---|
| 921 | POcorr,POderv = SHPOcalDerv(refl,g,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 922 | return POcorr,POderv |
|---|
| 923 | |
|---|
| 924 | def GetAbsorb(refl,hfx,calcControls,parmDict): |
|---|
| 925 | 'Needs a doc string' |
|---|
| 926 | if 'Debye' in calcControls[hfx+'instType']: |
|---|
| 927 | return G2pwd.Absorb('Cylinder',parmDict[hfx+'Absorption'],refl[5],0,0) |
|---|
| 928 | else: |
|---|
| 929 | return 1.0 |
|---|
| 930 | |
|---|
| 931 | def GetAbsorbDerv(refl,hfx,calcControls,parmDict): |
|---|
| 932 | 'Needs a doc string' |
|---|
| 933 | if 'Debye' in calcControls[hfx+'instType']: |
|---|
| 934 | return G2pwd.AbsorbDerv('Cylinder',parmDict[hfx+'Absorption'],refl[5],0,0) |
|---|
| 935 | else: |
|---|
| 936 | return 0.0 |
|---|
| 937 | |
|---|
| 938 | def GetIntensityCorr(refl,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 939 | 'Needs a doc string' |
|---|
| 940 | Icorr = parmDict[phfx+'Scale']*parmDict[hfx+'Scale']*refl[3] #scale*multiplicity |
|---|
| 941 | if 'X' in parmDict[hfx+'Type']: |
|---|
| 942 | Icorr *= G2pwd.Polarization(parmDict[hfx+'Polariz.'],refl[5],parmDict[hfx+'Azimuth'])[0] |
|---|
| 943 | Icorr *= GetPrefOri(refl,G,g,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 944 | if pfx+'SHorder' in parmDict: |
|---|
| 945 | Icorr *= SHTXcal(refl,g,pfx,hfx,SGData,calcControls,parmDict) |
|---|
| 946 | Icorr *= GetAbsorb(refl,hfx,calcControls,parmDict) |
|---|
| 947 | refl[13] = Icorr |
|---|
| 948 | |
|---|
| 949 | def GetIntensityDerv(refl,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict): |
|---|
| 950 | 'Needs a doc string' |
|---|
| 951 | dIdsh = 1./parmDict[hfx+'Scale'] |
|---|
| 952 | dIdsp = 1./parmDict[phfx+'Scale'] |
|---|
| 953 | if 'X' in parmDict[hfx+'Type']: |
|---|
| 954 | pola,dIdPola = G2pwd.Polarization(parmDict[hfx+'Polariz.'],refl[5],parmDict[hfx+'Azimuth']) |
|---|
| 955 | dIdPola /= pola |
|---|
| 956 | else: #'N' |
|---|
| 957 | dIdPola = 0.0 |
|---|
| 958 | POcorr,dIdPO = GetPrefOriDerv(refl,G,g,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 959 | for iPO in dIdPO: |
|---|
| 960 | dIdPO[iPO] /= POcorr |
|---|
| 961 | dFdODF = {} |
|---|
| 962 | dFdSA = [0,0,0] |
|---|
| 963 | if pfx+'SHorder' in parmDict: |
|---|
| 964 | odfCor,dFdODF,dFdSA = SHTXcalDerv(refl,g,pfx,hfx,SGData,calcControls,parmDict) |
|---|
| 965 | for iSH in dFdODF: |
|---|
| 966 | dFdODF[iSH] /= odfCor |
|---|
| 967 | for i in range(3): |
|---|
| 968 | dFdSA[i] /= odfCor |
|---|
| 969 | dFdAb = GetAbsorbDerv(refl,hfx,calcControls,parmDict) |
|---|
| 970 | return dIdsh,dIdsp,dIdPola,dIdPO,dFdODF,dFdSA,dFdAb |
|---|
| 971 | |
|---|
| 972 | def GetSampleSigGam(refl,wave,G,GB,phfx,calcControls,parmDict): |
|---|
| 973 | 'Needs a doc string' |
|---|
| 974 | costh = cosd(refl[5]/2.) |
|---|
| 975 | #crystallite size |
|---|
| 976 | if calcControls[phfx+'SizeType'] == 'isotropic': |
|---|
| 977 | Sgam = 1.8*wave/(np.pi*parmDict[phfx+'Size;i']*costh) |
|---|
| 978 | elif calcControls[phfx+'SizeType'] == 'uniaxial': |
|---|
| 979 | H = np.array(refl[:3]) |
|---|
| 980 | P = np.array(calcControls[phfx+'SizeAxis']) |
|---|
| 981 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 982 | Sgam = (1.8*wave/np.pi)/(parmDict[phfx+'Size;i']*parmDict[phfx+'Size;a']*costh) |
|---|
| 983 | Sgam *= np.sqrt((sinP*parmDict[phfx+'Size;a'])**2+(cosP*parmDict[phfx+'Size;i'])**2) |
|---|
| 984 | else: #ellipsoidal crystallites |
|---|
| 985 | Sij =[parmDict[phfx+'Size:%d'%(i)] for i in range(6)] |
|---|
| 986 | H = np.array(refl[:3]) |
|---|
| 987 | lenR = G2pwd.ellipseSize(H,Sij,GB) |
|---|
| 988 | Sgam = 1.8*wave/(np.pi*costh*lenR) |
|---|
| 989 | #microstrain |
|---|
| 990 | if calcControls[phfx+'MustrainType'] == 'isotropic': |
|---|
| 991 | Mgam = 0.018*parmDict[phfx+'Mustrain;i']*tand(refl[5]/2.)/np.pi |
|---|
| 992 | elif calcControls[phfx+'MustrainType'] == 'uniaxial': |
|---|
| 993 | H = np.array(refl[:3]) |
|---|
| 994 | P = np.array(calcControls[phfx+'MustrainAxis']) |
|---|
| 995 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 996 | Si = parmDict[phfx+'Mustrain;i'] |
|---|
| 997 | Sa = parmDict[phfx+'Mustrain;a'] |
|---|
| 998 | Mgam = 0.018*Si*Sa*tand(refl[5]/2.)/(np.pi*np.sqrt((Si*cosP)**2+(Sa*sinP)**2)) |
|---|
| 999 | else: #generalized - P.W. Stephens model |
|---|
| 1000 | pwrs = calcControls[phfx+'MuPwrs'] |
|---|
| 1001 | sum = 0 |
|---|
| 1002 | for i,pwr in enumerate(pwrs): |
|---|
| 1003 | sum += parmDict[phfx+'Mustrain:'+str(i)]*refl[0]**pwr[0]*refl[1]**pwr[1]*refl[2]**pwr[2] |
|---|
| 1004 | Mgam = 0.018*refl[4]**2*tand(refl[5]/2.)*sum |
|---|
| 1005 | gam = Sgam*parmDict[phfx+'Size;mx']+Mgam*parmDict[phfx+'Mustrain;mx'] |
|---|
| 1006 | sig = (Sgam*(1.-parmDict[phfx+'Size;mx']))**2+(Mgam*(1.-parmDict[phfx+'Mustrain;mx']))**2 |
|---|
| 1007 | sig /= ateln2 |
|---|
| 1008 | return sig,gam |
|---|
| 1009 | |
|---|
| 1010 | def GetSampleSigGamDerv(refl,wave,G,GB,phfx,calcControls,parmDict): |
|---|
| 1011 | 'Needs a doc string' |
|---|
| 1012 | gamDict = {} |
|---|
| 1013 | sigDict = {} |
|---|
| 1014 | costh = cosd(refl[5]/2.) |
|---|
| 1015 | tanth = tand(refl[5]/2.) |
|---|
| 1016 | #crystallite size derivatives |
|---|
| 1017 | if calcControls[phfx+'SizeType'] == 'isotropic': |
|---|
| 1018 | Sgam = 1.8*wave/(np.pi*parmDict[phfx+'Size;i']*costh) |
|---|
| 1019 | gamDict[phfx+'Size;i'] = -1.8*wave*parmDict[phfx+'Size;mx']/(np.pi*costh) |
|---|
| 1020 | sigDict[phfx+'Size;i'] = -3.6*Sgam*wave*(1.-parmDict[phfx+'Size;mx'])**2/(np.pi*costh*ateln2) |
|---|
| 1021 | elif calcControls[phfx+'SizeType'] == 'uniaxial': |
|---|
| 1022 | H = np.array(refl[:3]) |
|---|
| 1023 | P = np.array(calcControls[phfx+'SizeAxis']) |
|---|
| 1024 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 1025 | Si = parmDict[phfx+'Size;i'] |
|---|
| 1026 | Sa = parmDict[phfx+'Size;a'] |
|---|
| 1027 | gami = (1.8*wave/np.pi)/(Si*Sa) |
|---|
| 1028 | sqtrm = np.sqrt((sinP*Sa)**2+(cosP*Si)**2) |
|---|
| 1029 | Sgam = gami*sqtrm |
|---|
| 1030 | gam = Sgam/costh |
|---|
| 1031 | dsi = (gami*Si*cosP**2/(sqtrm*costh)-gam/Si) |
|---|
| 1032 | dsa = (gami*Sa*sinP**2/(sqtrm*costh)-gam/Sa) |
|---|
| 1033 | gamDict[phfx+'Size;i'] = dsi*parmDict[phfx+'Size;mx'] |
|---|
| 1034 | gamDict[phfx+'Size;a'] = dsa*parmDict[phfx+'Size;mx'] |
|---|
| 1035 | sigDict[phfx+'Size;i'] = 2.*dsi*Sgam*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 1036 | sigDict[phfx+'Size;a'] = 2.*dsa*Sgam*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 1037 | else: #ellipsoidal crystallites |
|---|
| 1038 | const = 1.8*wave/(np.pi*costh) |
|---|
| 1039 | Sij =[parmDict[phfx+'Size:%d'%(i)] for i in range(6)] |
|---|
| 1040 | H = np.array(refl[:3]) |
|---|
| 1041 | lenR,dRdS = G2pwd.ellipseSizeDerv(H,Sij,GB) |
|---|
| 1042 | Sgam = 1.8*wave/(np.pi*costh*lenR) |
|---|
| 1043 | for i,item in enumerate([phfx+'Size:%d'%(j) for j in range(6)]): |
|---|
| 1044 | gamDict[item] = -(const/lenR**2)*dRdS[i]*parmDict[phfx+'Size;mx'] |
|---|
| 1045 | sigDict[item] = -2.*Sgam*(const/lenR**2)*dRdS[i]*(1.-parmDict[phfx+'Size;mx'])**2/ateln2 |
|---|
| 1046 | gamDict[phfx+'Size;mx'] = Sgam |
|---|
| 1047 | sigDict[phfx+'Size;mx'] = -2.*Sgam**2*(1.-parmDict[phfx+'Size;mx'])/ateln2 |
|---|
| 1048 | |
|---|
| 1049 | #microstrain derivatives |
|---|
| 1050 | if calcControls[phfx+'MustrainType'] == 'isotropic': |
|---|
| 1051 | Mgam = 0.018*parmDict[phfx+'Mustrain;i']*tand(refl[5]/2.)/np.pi |
|---|
| 1052 | gamDict[phfx+'Mustrain;i'] = 0.018*tanth*parmDict[phfx+'Mustrain;mx']/np.pi |
|---|
| 1053 | sigDict[phfx+'Mustrain;i'] = 0.036*Mgam*tanth*(1.-parmDict[phfx+'Mustrain;mx'])**2/(np.pi*ateln2) |
|---|
| 1054 | elif calcControls[phfx+'MustrainType'] == 'uniaxial': |
|---|
| 1055 | H = np.array(refl[:3]) |
|---|
| 1056 | P = np.array(calcControls[phfx+'MustrainAxis']) |
|---|
| 1057 | cosP,sinP = G2lat.CosSinAngle(H,P,G) |
|---|
| 1058 | Si = parmDict[phfx+'Mustrain;i'] |
|---|
| 1059 | Sa = parmDict[phfx+'Mustrain;a'] |
|---|
| 1060 | gami = 0.018*Si*Sa*tanth/np.pi |
|---|
| 1061 | sqtrm = np.sqrt((Si*cosP)**2+(Sa*sinP)**2) |
|---|
| 1062 | Mgam = gami/sqtrm |
|---|
| 1063 | dsi = -gami*Si*cosP**2/sqtrm**3 |
|---|
| 1064 | dsa = -gami*Sa*sinP**2/sqtrm**3 |
|---|
| 1065 | gamDict[phfx+'Mustrain;i'] = (Mgam/Si+dsi)*parmDict[phfx+'Mustrain;mx'] |
|---|
| 1066 | gamDict[phfx+'Mustrain;a'] = (Mgam/Sa+dsa)*parmDict[phfx+'Mustrain;mx'] |
|---|
| 1067 | sigDict[phfx+'Mustrain;i'] = 2*(Mgam/Si+dsi)*Mgam*(1.-parmDict[phfx+'Mustrain;mx'])**2/ateln2 |
|---|
| 1068 | sigDict[phfx+'Mustrain;a'] = 2*(Mgam/Sa+dsa)*Mgam*(1.-parmDict[phfx+'Mustrain;mx'])**2/ateln2 |
|---|
| 1069 | else: #generalized - P.W. Stephens model |
|---|
| 1070 | pwrs = calcControls[phfx+'MuPwrs'] |
|---|
| 1071 | const = 0.018*refl[4]**2*tanth |
|---|
| 1072 | sum = 0 |
|---|
| 1073 | for i,pwr in enumerate(pwrs): |
|---|
| 1074 | term = refl[0]**pwr[0]*refl[1]**pwr[1]*refl[2]**pwr[2] |
|---|
| 1075 | sum += parmDict[phfx+'Mustrain:'+str(i)]*term |
|---|
| 1076 | gamDict[phfx+'Mustrain:'+str(i)] = const*term*parmDict[phfx+'Mustrain;mx'] |
|---|
| 1077 | sigDict[phfx+'Mustrain:'+str(i)] = \ |
|---|
| 1078 | 2.*const*term*(1.-parmDict[phfx+'Mustrain;mx'])**2/ateln2 |
|---|
| 1079 | Mgam = 0.018*refl[4]**2*tand(refl[5]/2.)*sum |
|---|
| 1080 | for i in range(len(pwrs)): |
|---|
| 1081 | sigDict[phfx+'Mustrain:'+str(i)] *= Mgam |
|---|
| 1082 | gamDict[phfx+'Mustrain;mx'] = Mgam |
|---|
| 1083 | sigDict[phfx+'Mustrain;mx'] = -2.*Mgam**2*(1.-parmDict[phfx+'Mustrain;mx'])/ateln2 |
|---|
| 1084 | return sigDict,gamDict |
|---|
| 1085 | |
|---|
| 1086 | def GetReflPos(refl,wave,G,hfx,calcControls,parmDict): |
|---|
| 1087 | 'Needs a doc string' |
|---|
| 1088 | h,k,l = refl[:3] |
|---|
| 1089 | dsq = 1./G2lat.calc_rDsq2(np.array([h,k,l]),G) |
|---|
| 1090 | d = np.sqrt(dsq) |
|---|
| 1091 | |
|---|
| 1092 | refl[4] = d |
|---|
| 1093 | pos = 2.0*asind(wave/(2.0*d))+parmDict[hfx+'Zero'] |
|---|
| 1094 | const = 9.e-2/(np.pi*parmDict[hfx+'Gonio. radius']) #shifts in microns |
|---|
| 1095 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 1096 | pos -= const*(4.*parmDict[hfx+'Shift']*cosd(pos/2.0)+ \ |
|---|
| 1097 | parmDict[hfx+'Transparency']*sind(pos)*100.0) #trans(=1/mueff) in cm |
|---|
| 1098 | else: #Debye-Scherrer - simple but maybe not right |
|---|
| 1099 | pos -= const*(parmDict[hfx+'DisplaceX']*cosd(pos)+parmDict[hfx+'DisplaceY']*sind(pos)) |
|---|
| 1100 | return pos |
|---|
| 1101 | |
|---|
| 1102 | def GetReflPosDerv(refl,wave,A,hfx,calcControls,parmDict): |
|---|
| 1103 | 'Needs a doc string' |
|---|
| 1104 | dpr = 180./np.pi |
|---|
| 1105 | h,k,l = refl[:3] |
|---|
| 1106 | dstsq = G2lat.calc_rDsq(np.array([h,k,l]),A) |
|---|
| 1107 | dst = np.sqrt(dstsq) |
|---|
| 1108 | pos = refl[5]-parmDict[hfx+'Zero'] |
|---|
| 1109 | const = dpr/np.sqrt(1.0-wave**2*dstsq/4.0) |
|---|
| 1110 | dpdw = const*dst |
|---|
| 1111 | dpdA = np.array([h**2,k**2,l**2,h*k,h*l,k*l]) |
|---|
| 1112 | dpdA *= const*wave/(2.0*dst) |
|---|
| 1113 | dpdZ = 1.0 |
|---|
| 1114 | const = 9.e-2/(np.pi*parmDict[hfx+'Gonio. radius']) #shifts in microns |
|---|
| 1115 | if 'Bragg' in calcControls[hfx+'instType']: |
|---|
| 1116 | dpdSh = -4.*const*cosd(pos/2.0) |
|---|
| 1117 | dpdTr = -const*sind(pos)*100.0 |
|---|
| 1118 | return dpdA,dpdw,dpdZ,dpdSh,dpdTr,0.,0. |
|---|
| 1119 | else: #Debye-Scherrer - simple but maybe not right |
|---|
| 1120 | dpdXd = -const*cosd(pos) |
|---|
| 1121 | dpdYd = -const*sind(pos) |
|---|
| 1122 | return dpdA,dpdw,dpdZ,0.,0.,dpdXd,dpdYd |
|---|
| 1123 | |
|---|
| 1124 | def GetHStrainShift(refl,SGData,phfx,parmDict): |
|---|
| 1125 | 'Needs a doc string' |
|---|
| 1126 | laue = SGData['SGLaue'] |
|---|
| 1127 | uniq = SGData['SGUniq'] |
|---|
| 1128 | h,k,l = refl[:3] |
|---|
| 1129 | if laue in ['m3','m3m']: |
|---|
| 1130 | Dij = parmDict[phfx+'D11']*(h**2+k**2+l**2)+ \ |
|---|
| 1131 | refl[4]**2*parmDict[phfx+'eA']*((h*k)**2+(h*l)**2+(k*l)**2)/(h**2+k**2+l**2)**2 |
|---|
| 1132 | elif laue in ['6/m','6/mmm','3m1','31m','3']: |
|---|
| 1133 | Dij = parmDict[phfx+'D11']*(h**2+k**2+h*k)+parmDict[phfx+'D33']*l**2 |
|---|
| 1134 | elif laue in ['3R','3mR']: |
|---|
| 1135 | Dij = parmDict[phfx+'D11']*(h**2+k**2+l**2)+parmDict[phfx+'D12']*(h*k+h*l+k*l) |
|---|
| 1136 | elif laue in ['4/m','4/mmm']: |
|---|
| 1137 | Dij = parmDict[phfx+'D11']*(h**2+k**2)+parmDict[phfx+'D33']*l**2 |
|---|
| 1138 | elif laue in ['mmm']: |
|---|
| 1139 | Dij = parmDict[phfx+'D11']*h**2+parmDict[phfx+'D22']*k**2+parmDict[phfx+'D33']*l**2 |
|---|
| 1140 | elif laue in ['2/m']: |
|---|
| 1141 | Dij = parmDict[phfx+'D11']*h**2+parmDict[phfx+'D22']*k**2+parmDict[phfx+'D33']*l**2 |
|---|
| 1142 | if uniq == 'a': |
|---|
| 1143 | Dij += parmDict[phfx+'D23']*k*l |
|---|
| 1144 | elif uniq == 'b': |
|---|
| 1145 | Dij += parmDict[phfx+'D13']*h*l |
|---|
| 1146 | elif uniq == 'c': |
|---|
| 1147 | Dij += parmDict[phfx+'D12']*h*k |
|---|
| 1148 | else: |
|---|
| 1149 | Dij = parmDict[phfx+'D11']*h**2+parmDict[phfx+'D22']*k**2+parmDict[phfx+'D33']*l**2+ \ |
|---|
| 1150 | parmDict[phfx+'D12']*h*k+parmDict[phfx+'D13']*h*l+parmDict[phfx+'D23']*k*l |
|---|
| 1151 | return -Dij*refl[4]**2*tand(refl[5]/2.0) |
|---|
| 1152 | |
|---|
| 1153 | def GetHStrainShiftDerv(refl,SGData,phfx): |
|---|
| 1154 | 'Needs a doc string' |
|---|
| 1155 | laue = SGData['SGLaue'] |
|---|
| 1156 | uniq = SGData['SGUniq'] |
|---|
| 1157 | h,k,l = refl[:3] |
|---|
| 1158 | if laue in ['m3','m3m']: |
|---|
| 1159 | dDijDict = {phfx+'D11':h**2+k**2+l**2, |
|---|
| 1160 | phfx+'eA':refl[4]**2*((h*k)**2+(h*l)**2+(k*l)**2)/(h**2+k**2+l**2)**2} |
|---|
| 1161 | elif laue in ['6/m','6/mmm','3m1','31m','3']: |
|---|
| 1162 | dDijDict = {phfx+'D11':h**2+k**2+h*k,phfx+'D33':l**2} |
|---|
| 1163 | elif laue in ['3R','3mR']: |
|---|
| 1164 | dDijDict = {phfx+'D11':h**2+k**2+l**2,phfx+'D12':h*k+h*l+k*l} |
|---|
| 1165 | elif laue in ['4/m','4/mmm']: |
|---|
| 1166 | dDijDict = {phfx+'D11':h**2+k**2,phfx+'D33':l**2} |
|---|
| 1167 | elif laue in ['mmm']: |
|---|
| 1168 | dDijDict = {phfx+'D11':h**2,phfx+'D22':k**2,phfx+'D33':l**2} |
|---|
| 1169 | elif laue in ['2/m']: |
|---|
| 1170 | dDijDict = {phfx+'D11':h**2,phfx+'D22':k**2,phfx+'D33':l**2} |
|---|
| 1171 | if uniq == 'a': |
|---|
| 1172 | dDijDict[phfx+'D23'] = k*l |
|---|
| 1173 | elif uniq == 'b': |
|---|
| 1174 | dDijDict[phfx+'D13'] = h*l |
|---|
| 1175 | elif uniq == 'c': |
|---|
| 1176 | dDijDict[phfx+'D12'] = h*k |
|---|
| 1177 | names.append() |
|---|
| 1178 | else: |
|---|
| 1179 | dDijDict = {phfx+'D11':h**2,phfx+'D22':k**2,phfx+'D33':l**2, |
|---|
| 1180 | phfx+'D12':h*k,phfx+'D13':h*l,phfx+'D23':k*l} |
|---|
| 1181 | for item in dDijDict: |
|---|
| 1182 | dDijDict[item] *= -refl[4]**2*tand(refl[5]/2.0) |
|---|
| 1183 | return dDijDict |
|---|
| 1184 | |
|---|
| 1185 | def GetFobsSq(Histograms,Phases,parmDict,calcControls): |
|---|
| 1186 | 'Needs a doc string' |
|---|
| 1187 | histoList = Histograms.keys() |
|---|
| 1188 | histoList.sort() |
|---|
| 1189 | for histogram in histoList: |
|---|
| 1190 | if 'PWDR' in histogram[:4]: |
|---|
| 1191 | Histogram = Histograms[histogram] |
|---|
| 1192 | hId = Histogram['hId'] |
|---|
| 1193 | hfx = ':%d:'%(hId) |
|---|
| 1194 | Limits = calcControls[hfx+'Limits'] |
|---|
| 1195 | shl = max(parmDict[hfx+'SH/L'],0.0005) |
|---|
| 1196 | Ka2 = False |
|---|
| 1197 | kRatio = 0.0 |
|---|
| 1198 | if hfx+'Lam1' in parmDict.keys(): |
|---|
| 1199 | Ka2 = True |
|---|
| 1200 | lamRatio = 360*(parmDict[hfx+'Lam2']-parmDict[hfx+'Lam1'])/(np.pi*parmDict[hfx+'Lam1']) |
|---|
| 1201 | kRatio = parmDict[hfx+'I(L2)/I(L1)'] |
|---|
| 1202 | x,y,w,yc,yb,yd = Histogram['Data'] |
|---|
| 1203 | xB = np.searchsorted(x,Limits[0]) |
|---|
| 1204 | xF = np.searchsorted(x,Limits[1]) |
|---|
| 1205 | ymb = np.array(y-yb) |
|---|
| 1206 | ymb = np.where(ymb,ymb,1.0) |
|---|
| 1207 | ycmb = np.array(yc-yb) |
|---|
| 1208 | ratio = 1./np.where(ycmb,ycmb/ymb,1.e10) |
|---|
| 1209 | refLists = Histogram['Reflection Lists'] |
|---|
| 1210 | for phase in refLists: |
|---|
| 1211 | Phase = Phases[phase] |
|---|
| 1212 | pId = Phase['pId'] |
|---|
| 1213 | phfx = '%d:%d:'%(pId,hId) |
|---|
| 1214 | refList = refLists[phase] |
|---|
| 1215 | sumFo = 0.0 |
|---|
| 1216 | sumdF = 0.0 |
|---|
| 1217 | sumFosq = 0.0 |
|---|
| 1218 | sumdFsq = 0.0 |
|---|
| 1219 | for refl in refList: |
|---|
| 1220 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 1221 | yp = np.zeros_like(yb) |
|---|
| 1222 | Wd,fmin,fmax = G2pwd.getWidthsCW(refl[5],refl[6],refl[7],shl) |
|---|
| 1223 | iBeg = max(xB,np.searchsorted(x,refl[5]-fmin)) |
|---|
| 1224 | iFin = max(xB,min(np.searchsorted(x,refl[5]+fmax),xF)) |
|---|
| 1225 | iFin2 = iFin |
|---|
| 1226 | yp[iBeg:iFin] = refl[13]*refl[9]*G2pwd.getFCJVoigt3(refl[5],refl[6],refl[7],shl,x[iBeg:iFin]) #>90% of time spent here |
|---|
| 1227 | if Ka2: |
|---|
| 1228 | pos2 = refl[5]+lamRatio*tand(refl[5]/2.0) # + 360/pi * Dlam/lam * tan(th) |
|---|
| 1229 | Wd,fmin,fmax = G2pwd.getWidthsCW(pos2,refl[6],refl[7],shl) |
|---|
| 1230 | iBeg2 = max(xB,np.searchsorted(x,pos2-fmin)) |
|---|
| 1231 | iFin2 = min(np.searchsorted(x,pos2+fmax),xF) |
|---|
| 1232 | if not iBeg2+iFin2: #peak below low limit - skip peak |
|---|
| 1233 | continue |
|---|
| 1234 | elif not iBeg2-iFin2: #peak above high limit - done |
|---|
| 1235 | break |
|---|
| 1236 | yp[iBeg2:iFin2] += refl[13]*refl[9]*kRatio*G2pwd.getFCJVoigt3(pos2,refl[6],refl[7],shl,x[iBeg2:iFin2]) #and here |
|---|
| 1237 | refl[8] = np.sum(np.where(ratio[iBeg:iFin2]>0.,yp[iBeg:iFin2]*ratio[iBeg:iFin2]/(refl[13]*(1.+kRatio)),0.0)) |
|---|
| 1238 | elif 'T' in calcControls[hfx+'histType']: |
|---|
| 1239 | print 'TOF Undefined at present' |
|---|
| 1240 | raise Exception #no TOF yet |
|---|
| 1241 | Fo = np.sqrt(np.abs(refl[8])) |
|---|
| 1242 | Fc = np.sqrt(np.abs(refl[9])) |
|---|
| 1243 | sumFo += Fo |
|---|
| 1244 | sumFosq += refl[8]**2 |
|---|
| 1245 | sumdF += np.abs(Fo-Fc) |
|---|
| 1246 | sumdFsq += (refl[8]-refl[9])**2 |
|---|
| 1247 | Histogram['Residuals'][phfx+'Rf'] = min(100.,(sumdF/sumFo)*100.) |
|---|
| 1248 | Histogram['Residuals'][phfx+'Rf^2'] = min(100.,np.sqrt(sumdFsq/sumFosq)*100.) |
|---|
| 1249 | Histogram['Residuals'][phfx+'Nref'] = len(refList) |
|---|
| 1250 | Histogram['Residuals']['hId'] = hId |
|---|
| 1251 | elif 'HKLF' in histogram[:4]: |
|---|
| 1252 | Histogram = Histograms[histogram] |
|---|
| 1253 | Histogram['Residuals']['hId'] = Histograms[histogram]['hId'] |
|---|
| 1254 | |
|---|
| 1255 | def getPowderProfile(parmDict,x,varylist,Histogram,Phases,calcControls,pawleyLookup): |
|---|
| 1256 | 'Needs a doc string' |
|---|
| 1257 | |
|---|
| 1258 | def GetReflSigGam(refl,wave,G,GB,hfx,phfx,calcControls,parmDict): |
|---|
| 1259 | U = parmDict[hfx+'U'] |
|---|
| 1260 | V = parmDict[hfx+'V'] |
|---|
| 1261 | W = parmDict[hfx+'W'] |
|---|
| 1262 | X = parmDict[hfx+'X'] |
|---|
| 1263 | Y = parmDict[hfx+'Y'] |
|---|
| 1264 | tanPos = tand(refl[5]/2.0) |
|---|
| 1265 | Ssig,Sgam = GetSampleSigGam(refl,wave,G,GB,phfx,calcControls,parmDict) |
|---|
| 1266 | sig = U*tanPos**2+V*tanPos+W+Ssig #save peak sigma |
|---|
| 1267 | sig = max(0.001,sig) |
|---|
| 1268 | gam = X/cosd(refl[5]/2.0)+Y*tanPos+Sgam #save peak gamma |
|---|
| 1269 | gam = max(0.001,gam) |
|---|
| 1270 | return sig,gam |
|---|
| 1271 | |
|---|
| 1272 | hId = Histogram['hId'] |
|---|
| 1273 | hfx = ':%d:'%(hId) |
|---|
| 1274 | bakType = calcControls[hfx+'bakType'] |
|---|
| 1275 | yb = G2pwd.getBackground(hfx,parmDict,bakType,x) |
|---|
| 1276 | yc = np.zeros_like(yb) |
|---|
| 1277 | |
|---|
| 1278 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 1279 | shl = max(parmDict[hfx+'SH/L'],0.002) |
|---|
| 1280 | Ka2 = False |
|---|
| 1281 | if hfx+'Lam1' in parmDict.keys(): |
|---|
| 1282 | wave = parmDict[hfx+'Lam1'] |
|---|
| 1283 | Ka2 = True |
|---|
| 1284 | lamRatio = 360*(parmDict[hfx+'Lam2']-parmDict[hfx+'Lam1'])/(np.pi*parmDict[hfx+'Lam1']) |
|---|
| 1285 | kRatio = parmDict[hfx+'I(L2)/I(L1)'] |
|---|
| 1286 | else: |
|---|
| 1287 | wave = parmDict[hfx+'Lam'] |
|---|
| 1288 | else: |
|---|
| 1289 | print 'TOF Undefined at present' |
|---|
| 1290 | raise ValueError |
|---|
| 1291 | for phase in Histogram['Reflection Lists']: |
|---|
| 1292 | refList = Histogram['Reflection Lists'][phase] |
|---|
| 1293 | Phase = Phases[phase] |
|---|
| 1294 | pId = Phase['pId'] |
|---|
| 1295 | pfx = '%d::'%(pId) |
|---|
| 1296 | phfx = '%d:%d:'%(pId,hId) |
|---|
| 1297 | hfx = ':%d:'%(hId) |
|---|
| 1298 | SGData = Phase['General']['SGData'] |
|---|
| 1299 | A = [parmDict[pfx+'A%d'%(i)] for i in range(6)] |
|---|
| 1300 | G,g = G2lat.A2Gmat(A) #recip & real metric tensors |
|---|
| 1301 | GA,GB = G2lat.Gmat2AB(G) #Orthogonalization matricies |
|---|
| 1302 | Vst = np.sqrt(nl.det(G)) #V* |
|---|
| 1303 | if not Phase['General'].get('doPawley'): |
|---|
| 1304 | time0 = time.time() |
|---|
| 1305 | StructureFactor(refList,G,hfx,pfx,SGData,calcControls,parmDict) |
|---|
| 1306 | # print 'sf calc time: %.3fs'%(time.time()-time0) |
|---|
| 1307 | time0 = time.time() |
|---|
| 1308 | for refl in refList: |
|---|
| 1309 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 1310 | h,k,l = refl[:3] |
|---|
| 1311 | refl[5] = GetReflPos(refl,wave,G,hfx,calcControls,parmDict) #corrected reflection position |
|---|
| 1312 | Lorenz = 1./(2.*sind(refl[5]/2.)**2*cosd(refl[5]/2.)) #Lorentz correction |
|---|
| 1313 | refl[5] += GetHStrainShift(refl,SGData,phfx,parmDict) #apply hydrostatic strain shift |
|---|
| 1314 | refl[6:8] = GetReflSigGam(refl,wave,G,GB,hfx,phfx,calcControls,parmDict) #peak sig & gam |
|---|
| 1315 | GetIntensityCorr(refl,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict) #puts corrections in refl[13] |
|---|
| 1316 | refl[13] *= Vst*Lorenz |
|---|
| 1317 | if Phase['General'].get('doPawley'): |
|---|
| 1318 | try: |
|---|
| 1319 | pInd =pfx+'PWLref:%d'%(pawleyLookup[pfx+'%d,%d,%d'%(h,k,l)]) |
|---|
| 1320 | refl[9] = parmDict[pInd] |
|---|
| 1321 | except KeyError: |
|---|
| 1322 | # print ' ***Error %d,%d,%d missing from Pawley reflection list ***'%(h,k,l) |
|---|
| 1323 | continue |
|---|
| 1324 | Wd,fmin,fmax = G2pwd.getWidthsCW(refl[5],refl[6],refl[7],shl) |
|---|
| 1325 | iBeg = np.searchsorted(x,refl[5]-fmin) |
|---|
| 1326 | iFin = np.searchsorted(x,refl[5]+fmax) |
|---|
| 1327 | if not iBeg+iFin: #peak below low limit - skip peak |
|---|
| 1328 | continue |
|---|
| 1329 | elif not iBeg-iFin: #peak above high limit - done |
|---|
| 1330 | break |
|---|
| 1331 | yc[iBeg:iFin] += refl[13]*refl[9]*G2pwd.getFCJVoigt3(refl[5],refl[6],refl[7],shl,ma.getdata(x[iBeg:iFin])) #>90% of time spent here |
|---|
| 1332 | if Ka2: |
|---|
| 1333 | pos2 = refl[5]+lamRatio*tand(refl[5]/2.0) # + 360/pi * Dlam/lam * tan(th) |
|---|
| 1334 | Wd,fmin,fmax = G2pwd.getWidthsCW(pos2,refl[6],refl[7],shl) |
|---|
| 1335 | iBeg = np.searchsorted(x,pos2-fmin) |
|---|
| 1336 | iFin = np.searchsorted(x,pos2+fmax) |
|---|
| 1337 | if not iBeg+iFin: #peak below low limit - skip peak |
|---|
| 1338 | continue |
|---|
| 1339 | elif not iBeg-iFin: #peak above high limit - done |
|---|
| 1340 | return yc,yb |
|---|
| 1341 | yc[iBeg:iFin] += refl[13]*refl[9]*kRatio*G2pwd.getFCJVoigt3(pos2,refl[6],refl[7],shl,ma.getdata(x[iBeg:iFin])) #and here |
|---|
| 1342 | elif 'T' in calcControls[hfx+'histType']: |
|---|
| 1343 | print 'TOF Undefined at present' |
|---|
| 1344 | raise Exception #no TOF yet |
|---|
| 1345 | # print 'profile calc time: %.3fs'%(time.time()-time0) |
|---|
| 1346 | return yc,yb |
|---|
| 1347 | |
|---|
| 1348 | def getPowderProfileDerv(parmDict,x,varylist,Histogram,Phases,rigidbodyDict,calcControls,pawleyLookup): |
|---|
| 1349 | 'Needs a doc string' |
|---|
| 1350 | |
|---|
| 1351 | def cellVaryDerv(pfx,SGData,dpdA): |
|---|
| 1352 | if SGData['SGLaue'] in ['-1',]: |
|---|
| 1353 | return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]], |
|---|
| 1354 | [pfx+'A3',dpdA[3]],[pfx+'A4',dpdA[4]],[pfx+'A5',dpdA[5]]] |
|---|
| 1355 | elif SGData['SGLaue'] in ['2/m',]: |
|---|
| 1356 | if SGData['SGUniq'] == 'a': |
|---|
| 1357 | return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]],[pfx+'A3',dpdA[3]]] |
|---|
| 1358 | elif SGData['SGUniq'] == 'b': |
|---|
| 1359 | return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]],[pfx+'A4',dpdA[4]]] |
|---|
| 1360 | else: |
|---|
| 1361 | return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]],[pfx+'A5',dpdA[5]]] |
|---|
| 1362 | elif SGData['SGLaue'] in ['mmm',]: |
|---|
| 1363 | return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]]] |
|---|
| 1364 | elif SGData['SGLaue'] in ['4/m','4/mmm']: |
|---|
| 1365 | return [[pfx+'A0',dpdA[0]],[pfx+'A2',dpdA[2]]] |
|---|
| 1366 | elif SGData['SGLaue'] in ['6/m','6/mmm','3m1', '31m', '3']: |
|---|
| 1367 | return [[pfx+'A0',dpdA[0]],[pfx+'A2',dpdA[2]]] |
|---|
| 1368 | elif SGData['SGLaue'] in ['3R', '3mR']: |
|---|
| 1369 | return [[pfx+'A0',dpdA[0]+dpdA[1]+dpdA[2]],[pfx+'A3',dpdA[3]+dpdA[4]+dpdA[5]]] |
|---|
| 1370 | elif SGData['SGLaue'] in ['m3m','m3']: |
|---|
| 1371 | return [[pfx+'A0',dpdA[0]]] |
|---|
| 1372 | |
|---|
| 1373 | # create a list of dependent variables and set up a dictionary to hold their derivatives |
|---|
| 1374 | dependentVars = G2mv.GetDependentVars() |
|---|
| 1375 | depDerivDict = {} |
|---|
| 1376 | for j in dependentVars: |
|---|
| 1377 | depDerivDict[j] = np.zeros(shape=(len(x))) |
|---|
| 1378 | #print 'dependent vars',dependentVars |
|---|
| 1379 | lenX = len(x) |
|---|
| 1380 | hId = Histogram['hId'] |
|---|
| 1381 | hfx = ':%d:'%(hId) |
|---|
| 1382 | bakType = calcControls[hfx+'bakType'] |
|---|
| 1383 | dMdv = np.zeros(shape=(len(varylist),len(x))) |
|---|
| 1384 | dMdb,dMddb,dMdpk = G2pwd.getBackgroundDerv(hfx,parmDict,bakType,x) |
|---|
| 1385 | if hfx+'Back:0' in varylist: # for now assume that Back:x vars to not appear in constraints |
|---|
| 1386 | bBpos =varylist.index(hfx+'Back:0') |
|---|
| 1387 | dMdv[bBpos:bBpos+len(dMdb)] = dMdb |
|---|
| 1388 | names = [hfx+'DebyeA',hfx+'DebyeR',hfx+'DebyeU'] |
|---|
| 1389 | for name in varylist: |
|---|
| 1390 | if 'Debye' in name: |
|---|
| 1391 | id = int(name.split(':')[-1]) |
|---|
| 1392 | parm = name[:int(name.rindex(':'))] |
|---|
| 1393 | ip = names.index(parm) |
|---|
| 1394 | dMdv[varylist.index(name)] = dMddb[3*id+ip] |
|---|
| 1395 | names = [hfx+'BkPkpos',hfx+'BkPkint',hfx+'BkPksig',hfx+'BkPkgam'] |
|---|
| 1396 | for name in varylist: |
|---|
| 1397 | if 'BkPk' in name: |
|---|
| 1398 | id = int(name.split(':')[-1]) |
|---|
| 1399 | parm = name[:int(name.rindex(':'))] |
|---|
| 1400 | ip = names.index(parm) |
|---|
| 1401 | dMdv[varylist.index(name)] = dMdpk[4*id+ip] |
|---|
| 1402 | cw = np.diff(x) |
|---|
| 1403 | cw = np.append(cw,cw[-1]) |
|---|
| 1404 | if 'C' in calcControls[hfx+'histType']: |
|---|
| 1405 | shl = max(parmDict[hfx+'SH/L'],0.002) |
|---|
| 1406 | Ka2 = False |
|---|
| 1407 | if hfx+'Lam1' in parmDict.keys(): |
|---|
| 1408 | wave = parmDict[hfx+'Lam1'] |
|---|
| 1409 | Ka2 = True |
|---|
| 1410 | lamRatio = 360*(parmDict[hfx+'Lam2']-parmDict[hfx+'Lam1'])/(np.pi*parmDict[hfx+'Lam1']) |
|---|
| 1411 | kRatio = parmDict[hfx+'I(L2)/I(L1)'] |
|---|
| 1412 | else: |
|---|
| 1413 | wave = parmDict[hfx+'Lam'] |
|---|
| 1414 | else: |
|---|
| 1415 | print 'TOF Undefined at present' |
|---|
| 1416 | raise ValueError |
|---|
| 1417 | for phase in Histogram['Reflection Lists']: |
|---|
| 1418 | refList = Histogram['Reflection Lists'][phase] |
|---|
| 1419 | Phase = Phases[phase] |
|---|
| 1420 | SGData = Phase['General']['SGData'] |
|---|
| 1421 | pId = Phase['pId'] |
|---|
| 1422 | pfx = '%d::'%(pId) |
|---|
| 1423 | phfx = '%d:%d:'%(pId,hId) |
|---|
| 1424 | A = [parmDict[pfx+'A%d'%(i)] for i in range(6)] |
|---|
| 1425 | G,g = G2lat.A2Gmat(A) #recip & real metric tensors |
|---|
| 1426 | GA,GB = G2lat.Gmat2AB(G) #Orthogonalization matricies |
|---|
| 1427 | if not Phase['General'].get('doPawley'): |
|---|
| 1428 | time0 = time.time() |
|---|
| 1429 | dFdvDict = StructureFactorDerv(refList,G,hfx,pfx,SGData,calcControls,parmDict) |
|---|
| 1430 | # print 'sf-derv time %.3fs'%(time.time()-time0) |
|---|
| 1431 | ApplyRBModelDervs(dFdvDict,parmDict,rigidbodyDict,Phase) |
|---|
| 1432 | time0 = time.time() |
|---|
| 1433 | for iref,refl in enumerate(refList): |
|---|
| 1434 | if 'C' in calcControls[hfx+'histType']: #CW powder |
|---|
| 1435 | h,k,l = refl[:3] |
|---|
| 1436 | dIdsh,dIdsp,dIdpola,dIdPO,dFdODF,dFdSA,dFdAb = GetIntensityDerv(refl,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict) |
|---|
| 1437 | Wd,fmin,fmax = G2pwd.getWidthsCW(refl[5],refl[6],refl[7],shl) |
|---|
| 1438 | iBeg = np.searchsorted(x,refl[5]-fmin) |
|---|
| 1439 | iFin = np.searchsorted(x,refl[5]+fmax) |
|---|
| 1440 | if not iBeg+iFin: #peak below low limit - skip peak |
|---|
| 1441 | continue |
|---|
| 1442 | elif not iBeg-iFin: #peak above high limit - done |
|---|
| 1443 | break |
|---|
| 1444 | pos = refl[5] |
|---|
| 1445 | tanth = tand(pos/2.0) |
|---|
| 1446 | costh = cosd(pos/2.0) |
|---|
| 1447 | lenBF = iFin-iBeg |
|---|
| 1448 | dMdpk = np.zeros(shape=(6,lenBF)) |
|---|
| 1449 | dMdipk = G2pwd.getdFCJVoigt3(refl[5],refl[6],refl[7],shl,ma.getdata(x[iBeg:iFin])) |
|---|
| 1450 | for i in range(5): |
|---|
| 1451 | dMdpk[i] += 100.*cw[iBeg:iFin]*refl[13]*refl[9]*dMdipk[i] |
|---|
| 1452 | dervDict = {'int':dMdpk[0],'pos':dMdpk[1],'sig':dMdpk[2],'gam':dMdpk[3],'shl':dMdpk[4],'L1/L2':np.zeros_like(dMdpk[0])} |
|---|
| 1453 | if Ka2: |
|---|
| 1454 | pos2 = refl[5]+lamRatio*tanth # + 360/pi * Dlam/lam * tan(th) |
|---|
| 1455 | iBeg2 = np.searchsorted(x,pos2-fmin) |
|---|
| 1456 | iFin2 = np.searchsorted(x,pos2+fmax) |
|---|
| 1457 | if iBeg2-iFin2: |
|---|
| 1458 | lenBF2 = iFin2-iBeg2 |
|---|
| 1459 | dMdpk2 = np.zeros(shape=(6,lenBF2)) |
|---|
| 1460 | dMdipk2 = G2pwd.getdFCJVoigt3(pos2,refl[6],refl[7],shl,ma.getdata(x[iBeg2:iFin2])) |
|---|
| 1461 | for i in range(5): |
|---|
| 1462 | dMdpk2[i] = 100.*cw[iBeg2:iFin2]*refl[13]*refl[9]*kRatio*dMdipk2[i] |
|---|
| 1463 | dMdpk2[5] = 100.*cw[iBeg2:iFin2]*refl[13]*dMdipk2[0] |
|---|
| 1464 | dervDict2 = {'int':dMdpk2[0],'pos':dMdpk2[1],'sig':dMdpk2[2],'gam':dMdpk2[3],'shl':dMdpk2[4],'L1/L2':dMdpk2[5]*refl[9]} |
|---|
| 1465 | if Phase['General'].get('doPawley'): |
|---|
| 1466 | dMdpw = np.zeros(len(x)) |
|---|
| 1467 | try: |
|---|
| 1468 | pIdx = pfx+'PWLref:'+str(pawleyLookup[pfx+'%d,%d,%d'%(h,k,l)]) |
|---|
| 1469 | idx = varylist.index(pIdx) |
|---|
| 1470 | dMdpw[iBeg:iFin] = dervDict['int']/refl[9] |
|---|
| 1471 | if Ka2: |
|---|
| 1472 | dMdpw[iBeg2:iFin2] += dervDict2['int']/refl[9] |
|---|
| 1473 | dMdv[idx] = dMdpw |
|---|
| 1474 | except: # ValueError: |
|---|
| 1475 | pass |
|---|
| 1476 | dpdA,dpdw,dpdZ,dpdSh,dpdTr,dpdX,dpdY = GetReflPosDerv(refl,wave,A,hfx,calcControls,parmDict) |
|---|
| 1477 | names = {hfx+'Scale':[dIdsh,'int'],hfx+'Polariz.':[dIdpola,'int'],phfx+'Scale':[dIdsp,'int'], |
|---|
| 1478 | hfx+'U':[tanth**2,'sig'],hfx+'V':[tanth,'sig'],hfx+'W':[1.0,'sig'], |
|---|
| 1479 | hfx+'X':[1.0/costh,'gam'],hfx+'Y':[tanth,'gam'],hfx+'SH/L':[1.0,'shl'], |
|---|
| 1480 | hfx+'I(L2)/I(L1)':[1.0,'L1/L2'],hfx+'Zero':[dpdZ,'pos'],hfx+'Lam':[dpdw,'pos'], |
|---|
| 1481 | hfx+'Shift':[dpdSh,'pos'],hfx+'Transparency':[dpdTr,'pos'],hfx+'DisplaceX':[dpdX,'pos'], |
|---|
| 1482 | hfx+'DisplaceY':[dpdY,'pos'],hfx+'Absorption':[dFdAb,'int'],} |
|---|
| 1483 | for name in names: |
|---|
| 1484 | item = names[name] |
|---|
| 1485 | if name in varylist: |
|---|
| 1486 | dMdv[varylist.index(name)][iBeg:iFin] += item[0]*dervDict[item[1]] |
|---|
| 1487 | if Ka2: |
|---|
| 1488 | dMdv[varylist.index(name)][iBeg2:iFin2] += item[0]*dervDict2[item[1]] |
|---|
| 1489 | elif name in dependentVars: |
|---|
| 1490 | depDerivDict[name][iBeg:iFin] += item[0]*dervDict[item[1]] |
|---|
| 1491 | if Ka2: |
|---|
| 1492 | depDerivDict[name][iBeg2:iFin2] += item[0]*dervDict2[item[1]] |
|---|
| 1493 | for iPO in dIdPO: |
|---|
| 1494 | if iPO in varylist: |
|---|
| 1495 | dMdv[varylist.index(iPO)][iBeg:iFin] += dIdPO[iPO]*dervDict['int'] |
|---|
| 1496 | if Ka2: |
|---|
| 1497 | dMdv[varylist.index(iPO)][iBeg2:iFin2] += dIdPO[iPO]*dervDict2['int'] |
|---|
| 1498 | elif iPO in dependentVars: |
|---|
| 1499 | depDerivDict[iPO][iBeg:iFin] += dIdPO[iPO]*dervDict['int'] |
|---|
| 1500 | if Ka2: |
|---|
| 1501 | depDerivDict[iPO][iBeg2:iFin2] += dIdPO[iPO]*dervDict2['int'] |
|---|
| 1502 | for i,name in enumerate(['omega','chi','phi']): |
|---|
| 1503 | aname = pfx+'SH '+name |
|---|
| 1504 | if aname in varylist: |
|---|
| 1505 | dMdv[varylist.index(aname)][iBeg:iFin] += dFdSA[i]*dervDict['int'] |
|---|
| 1506 | if Ka2: |
|---|
| 1507 | dMdv[varylist.index(aname)][iBeg2:iFin2] += dFdSA[i]*dervDict2['int'] |
|---|
| 1508 | elif aname in dependentVars: |
|---|
| 1509 | depDerivDict[aname][iBeg:iFin] += dFdSA[i]*dervDict['int'] |
|---|
| 1510 | if Ka2: |
|---|
| 1511 | depDerivDict[aname][iBeg2:iFin2] += dFdSA[i]*dervDict2['int'] |
|---|
| 1512 | for iSH in dFdODF: |
|---|
| 1513 | if iSH in varylist: |
|---|
| 1514 | dMdv[varylist.index(iSH)][iBeg:iFin] += dFdODF[iSH]*dervDict['int'] |
|---|
| 1515 | if Ka2: |
|---|
| 1516 | dMdv[varylist.index(iSH)][iBeg2:iFin2] += dFdODF[iSH]*dervDict2['int'] |
|---|
| 1517 | elif iSH in dependentVars: |
|---|
| 1518 | depDerivDict[iSH][iBeg:iFin] += dFdODF[iSH]*dervDict['int'] |
|---|
| 1519 | if Ka2: |
|---|
| 1520 | depDerivDict[iSH][iBeg2:iFin2] += dFdODF[iSH]*dervDict2['int'] |
|---|
| 1521 | cellDervNames = cellVaryDerv(pfx,SGData,dpdA) |
|---|
| 1522 | for name,dpdA in cellDervNames: |
|---|
| 1523 | if name in varylist: |
|---|
| 1524 | dMdv[varylist.index(name)][iBeg:iFin] += dpdA*dervDict['pos'] |
|---|
| 1525 | if Ka2: |
|---|
| 1526 | dMdv[varylist.index(name)][iBeg2:iFin2] += dpdA*dervDict2['pos'] |
|---|
| 1527 | elif name in dependentVars: |
|---|
| 1528 | depDerivDict[name][iBeg:iFin] += dpdA*dervDict['pos'] |
|---|
| 1529 | if Ka2: |
|---|
| 1530 | depDerivDict[name][iBeg2:iFin2] += dpdA*dervDict2['pos'] |
|---|
| 1531 | dDijDict = GetHStrainShiftDerv(refl,SGData,phfx) |
|---|
| 1532 | for name in dDijDict: |
|---|
| 1533 | if name in varylist: |
|---|
| 1534 | dMdv[varylist.index(name)][iBeg:iFin] += dDijDict[name]*dervDict['pos'] |
|---|
| 1535 | if Ka2: |
|---|
| 1536 | dMdv[varylist.index(name)][iBeg2:iFin2] += dDijDict[name]*dervDict2['pos'] |
|---|
| 1537 | elif name in dependentVars: |
|---|
| 1538 | depDerivDict[name][iBeg:iFin] += dDijDict[name]*dervDict['pos'] |
|---|
| 1539 | if Ka2: |
|---|
| 1540 | depDerivDict[name][iBeg2:iFin2] += dDijDict[name]*dervDict2['pos'] |
|---|
| 1541 | sigDict,gamDict = GetSampleSigGamDerv(refl,wave,G,GB,phfx,calcControls,parmDict) |
|---|
| 1542 | for name in gamDict: |
|---|
| 1543 | if name in varylist: |
|---|
| 1544 | dMdv[varylist.index(name)][iBeg:iFin] += gamDict[name]*dervDict['gam'] |
|---|
| 1545 | if Ka2: |
|---|
| 1546 | dMdv[varylist.index(name)][iBeg2:iFin2] += gamDict[name]*dervDict2['gam'] |
|---|
| 1547 | elif name in dependentVars: |
|---|
| 1548 | depDerivDict[name][iBeg:iFin] += gamDict[name]*dervDict['gam'] |
|---|
| 1549 | if Ka2: |
|---|
| 1550 | depDerivDict[name][iBeg2:iFin2] += gamDict[name]*dervDict2['gam'] |
|---|
| 1551 | for name in sigDict: |
|---|
| 1552 | if name in varylist: |
|---|
| 1553 | dMdv[varylist.index(name)][iBeg:iFin] += sigDict[name]*dervDict['sig'] |
|---|
| 1554 | if Ka2: |
|---|
| 1555 | dMdv[varylist.index(name)][iBeg2:iFin2] += sigDict[name]*dervDict2['sig'] |
|---|
| 1556 | elif name in dependentVars: |
|---|
| 1557 | depDerivDict[name][iBeg:iFin] += sigDict[name]*dervDict['sig'] |
|---|
| 1558 | if Ka2: |
|---|
| 1559 | depDerivDict[name][iBeg2:iFin2] += sigDict[name]*dervDict2['sig'] |
|---|
| 1560 | for name in ['BabA','BabU']: |
|---|
| 1561 | if phfx+name in varylist: |
|---|
| 1562 | dMdv[varylist.index(phfx+name)][iBeg:iFin] += dFdvDict[pfx+name][iref]*dervDict['int']*cw[iBeg:iFin] |
|---|
| 1563 | if Ka2: |
|---|
| 1564 | dMdv[varylist.index(phfx+name)][iBeg2:iFin2] += dFdvDict[pfx+name][iref]*dervDict2['int']*cw[iBeg2:iFin2] |
|---|
| 1565 | elif phfx+name in dependentVars: |
|---|
| 1566 | depDerivDict[phfx+name][iBeg:iFin] += dFdvDict[pfx+name][iref]*dervDict['int']*cw[iBeg:iFin] |
|---|
| 1567 | if Ka2: |
|---|
| 1568 | depDerivDict[phfx+name][iBeg2:iFin2] += dFdvDict[pfx+name][iref]*dervDict2['int']*cw[iBeg2:iFin2] |
|---|
| 1569 | elif 'T' in calcControls[hfx+'histType']: |
|---|
| 1570 | print 'TOF Undefined at present' |
|---|
| 1571 | raise Exception #no TOF yet |
|---|
| 1572 | if not Phase['General'].get('doPawley'): |
|---|
| 1573 | #do atom derivatives - for RB,F,X & U so far |
|---|
| 1574 | corr = dervDict['int']/refl[9] |
|---|
| 1575 | if Ka2: |
|---|
| 1576 | corr2 = dervDict2['int']/refl[9] |
|---|
| 1577 | for name in varylist+dependentVars: |
|---|
| 1578 | if '::RBV;' in name: |
|---|
| 1579 | pass |
|---|
| 1580 | else: |
|---|
| 1581 | try: |
|---|
| 1582 | aname = name.split(pfx)[1][:2] |
|---|
| 1583 | if aname not in ['Af','dA','AU','RB']: continue # skip anything not an atom or rigid body param |
|---|
| 1584 | except IndexError: |
|---|
| 1585 | continue |
|---|
| 1586 | if name in varylist: |
|---|
| 1587 | dMdv[varylist.index(name)][iBeg:iFin] += dFdvDict[name][iref]*corr |
|---|
| 1588 | if Ka2: |
|---|
| 1589 | dMdv[varylist.index(name)][iBeg2:iFin2] += dFdvDict[name][iref]*corr2 |
|---|
| 1590 | elif name in dependentVars: |
|---|
| 1591 | depDerivDict[name][iBeg:iFin] += dFdvDict[name][iref]*corr |
|---|
| 1592 | if Ka2: |
|---|
| 1593 | depDerivDict[name][iBeg2:iFin2] += dFdvDict[name][iref]*corr2 |
|---|
| 1594 | # print 'profile derv time: %.3fs'%(time.time()-time0) |
|---|
| 1595 | # now process derivatives in constraints |
|---|
| 1596 | G2mv.Dict2Deriv(varylist,depDerivDict,dMdv) |
|---|
| 1597 | return dMdv |
|---|
| 1598 | |
|---|
| 1599 | def dervRefine(values,HistoPhases,parmDict,varylist,calcControls,pawleyLookup,dlg): |
|---|
| 1600 | '''Loop over histograms and compute derivatives of the fitting |
|---|
| 1601 | model (M) with respect to all parameters. Results are returned in |
|---|
| 1602 | a Jacobian matrix (aka design matrix) of dimensions (n by m) where |
|---|
| 1603 | n is the number of parameters and m is the number of data |
|---|
| 1604 | points. This can exceed memory when m gets large. This routine is |
|---|
| 1605 | used when refinement derivatives are selected as "analtytic |
|---|
| 1606 | Jacobian" in Controls. |
|---|
| 1607 | |
|---|
| 1608 | :returns: Jacobian numpy.array dMdv for all histograms concatinated |
|---|
| 1609 | ''' |
|---|
| 1610 | parmDict.update(zip(varylist,values)) |
|---|
| 1611 | G2mv.Dict2Map(parmDict,varylist) |
|---|
| 1612 | Histograms,Phases,restraintDict,rigidbodyDict = HistoPhases |
|---|
| 1613 | nvar = len(varylist) |
|---|
| 1614 | dMdv = np.empty(0) |
|---|
| 1615 | histoList = Histograms.keys() |
|---|
| 1616 | histoList.sort() |
|---|
| 1617 | for histogram in histoList: |
|---|
| 1618 | if 'PWDR' in histogram[:4]: |
|---|
| 1619 | Histogram = Histograms[histogram] |
|---|
| 1620 | hId = Histogram['hId'] |
|---|
| 1621 | hfx = ':%d:'%(hId) |
|---|
| 1622 | wtFactor = calcControls[hfx+'wtFactor'] |
|---|
| 1623 | Limits = calcControls[hfx+'Limits'] |
|---|
| 1624 | x,y,w,yc,yb,yd = Histogram['Data'] |
|---|
| 1625 | W = wtFactor*w |
|---|
| 1626 | xB = np.searchsorted(x,Limits[0]) |
|---|
| 1627 | xF = np.searchsorted(x,Limits[1]) |
|---|
| 1628 | dMdvh = np.sqrt(W[xB:xF])*getPowderProfileDerv(parmDict,x[xB:xF], |
|---|
| 1629 | varylist,Histogram,Phases,rigidbodyDict,calcControls,pawleyLookup) |
|---|
| 1630 | elif 'HKLF' in histogram[:4]: |
|---|
| 1631 | Histogram = Histograms[histogram] |
|---|
| 1632 | nobs = Histogram['Residuals']['Nobs'] |
|---|
| 1633 | phase = Histogram['Reflection Lists'] |
|---|
| 1634 | Phase = Phases[phase] |
|---|
| 1635 | hId = Histogram['hId'] |
|---|
| 1636 | hfx = ':%d:'%(hId) |
|---|
| 1637 | wtFactor = calcControls[hfx+'wtFactor'] |
|---|
| 1638 | pfx = '%d::'%(Phase['pId']) |
|---|
| 1639 | phfx = '%d:%d:'%(Phase['pId'],hId) |
|---|
| 1640 | SGData = Phase['General']['SGData'] |
|---|
| 1641 | A = [parmDict[pfx+'A%d'%(i)] for i in range(6)] |
|---|
| 1642 | G,g = G2lat.A2Gmat(A) #recip & real metric tensors |
|---|
| 1643 | refList = Histogram['Data'] |
|---|
| 1644 | dFdvDict = StructureFactorDerv(refList,G,hfx,pfx,SGData,calcControls,parmDict) |
|---|
| 1645 | ApplyRBModelDervs(dFdvDict,parmDict,rigidbodyDict,Phase) |
|---|
| 1646 | dMdvh = np.zeros((len(varylist),len(refList))) |
|---|
| 1647 | dependentVars = G2mv.GetDependentVars() |
|---|
| 1648 | depDerivDict = {} |
|---|
| 1649 | for j in dependentVars: |
|---|
| 1650 | depDerivDict[j] = np.zeros(shape=(len(refList))) |
|---|
| 1651 | if calcControls['F**2']: |
|---|
| 1652 | for iref,ref in enumerate(refList): |
|---|
| 1653 | if ref[6] > 0: |
|---|
| 1654 | dervCor,dervDict = SCExtinction(ref,phfx,hfx,pfx,calcControls,parmDict,varylist) #puts correction in refl[13] |
|---|
| 1655 | w = 1.0/ref[6] |
|---|
| 1656 | if w*ref[5] >= calcControls['minF/sig']: |
|---|
| 1657 | for j,var in enumerate(varylist): |
|---|
| 1658 | if var in dFdvDict: |
|---|
| 1659 | dMdvh[j][iref] = w*dFdvDict[var][iref]*parmDict[phfx+'Scale']*dervCor |
|---|
| 1660 | for var in dependentVars: |
|---|
| 1661 | if var in dFdvDict: |
|---|
| 1662 | depDerivDict[var][iref] = w*dFdvDict[var][iref]*parmDict[phfx+'Scale']*dervCor |
|---|
| 1663 | if phfx+'Scale' in varylist: |
|---|
| 1664 | dMdvh[varylist.index(phfx+'Scale')][iref] = w*ref[9]*dervCor |
|---|
| 1665 | elif phfx+'Scale' in dependentVars: |
|---|
| 1666 | depDerivDict[phfx+'Scale'][iref] = w*ref[9]*dervCor |
|---|
| 1667 | for item in ['Ep','Es','Eg']: |
|---|
| 1668 | if phfx+item in varylist: |
|---|
| 1669 | dMdvh[varylist.index(phfx+item)][iref] = w*dervDict[phfx+item]*parmDict[phfx+'Scale'] |
|---|
| 1670 | elif phfx+item in dependentVars: |
|---|
| 1671 | depDerivDict[phfx+item][iref] = w*dervDict[phfx+item]*parmDict[phfx+'Scale'] |
|---|
| 1672 | for item in ['BabA','BabU']: |
|---|
| 1673 | if phfx+item in varylist: |
|---|
| 1674 | dMdvh[varylist.index(phfx+item)][iref] = w*dervCor*dFdvDict[pfx+item][iref]*parmDict[phfx+'Scale'] |
|---|
| 1675 | elif phfx+item in dependentVars: |
|---|
| 1676 | depDerivDict[phfx+item][iref] = w*dervCor*dFdvDict[pfx+item][iref]*parmDict[phfx+'Scale'] |
|---|
| 1677 | else: |
|---|
| 1678 | for iref,ref in enumerate(refList): |
|---|
| 1679 | if ref[5] > 0.: |
|---|
| 1680 | dervCor,dervDict = SCExtinction(ref,phfx,hfx,pfx,calcControls,parmDict,varylist) #puts correction in refl[13] |
|---|
| 1681 | Fo = np.sqrt(ref[5]) |
|---|
| 1682 | Fc = np.sqrt(ref[7]) |
|---|
| 1683 | w = 1.0/ref[6] |
|---|
| 1684 | if 2.0*Fo*w*Fo >= calcControls['minF/sig']: |
|---|
| 1685 | for j,var in enumerate(varylist): |
|---|
| 1686 | if var in dFdvDict: |
|---|
| 1687 | dMdvh[j][iref] = w*dFdvDict[var][iref]*dervCor*parmDict[phfx+'Scale'] |
|---|
| 1688 | for var in dependentVars: |
|---|
| 1689 | if var in dFdvDict: |
|---|
| 1690 | depDerivDict[var][iref] = w*dFdvDict[var][iref]*dervCor*parmDict[phfx+'Scale'] |
|---|
| 1691 | if phfx+'Scale' in varylist: |
|---|
| 1692 | dMdvh[varylist.index(phfx+'Scale')][iref] = w*ref[9]*dervCor |
|---|
| 1693 | elif phfx+'Scale' in dependentVars: |
|---|
| 1694 | depDerivDict[phfx+'Scale'][iref] = w*ref[9]*dervCor |
|---|
| 1695 | for item in ['Ep','Es','Eg']: |
|---|
| 1696 | if phfx+item in varylist: |
|---|
| 1697 | dMdvh[varylist.index(phfx+item)][iref] = w*dervDict[phfx+item]*parmDict[phfx+'Scale'] |
|---|
| 1698 | elif phfx+item in dependentVars: |
|---|
| 1699 | depDerivDict[phfx+item][iref] = w*dervDict[phfx+item]*parmDict[phfx+'Scale'] |
|---|
| 1700 | for item in ['BabA','BabU']: |
|---|
| 1701 | if phfx+item in varylist: |
|---|
| 1702 | dMdvh[varylist.index(phfx+item)][iref] = w*dervCor*dFdvDict[pfx+item][iref]*parmDict[phfx+'Scale'] |
|---|
| 1703 | elif phfx+item in dependentVars: |
|---|
| 1704 | depDerivDict[phfx+item][iref] = w*dFdvDict[pfx+item][iref]*parmDict[phfx+'Scale']*dervCor |
|---|
| 1705 | # now process derivatives in constraints |
|---|
| 1706 | G2mv.Dict2Deriv(varylist,depDerivDict,dMdvh) |
|---|
| 1707 | else: |
|---|
| 1708 | continue #skip non-histogram entries |
|---|
| 1709 | if len(dMdv): |
|---|
| 1710 | dMdv = np.concatenate((dMdv.T,np.sqrt(wtFactor)*dMdvh.T)).T |
|---|
| 1711 | else: |
|---|
| 1712 | dMdv = np.sqrt(wtFactor)*dMdvh |
|---|
| 1713 | |
|---|
| 1714 | pNames,pVals,pWt,pWsum = penaltyFxn(HistoPhases,parmDict,varylist) |
|---|
| 1715 | if np.any(pVals): |
|---|
| 1716 | dpdv = penaltyDeriv(pNames,pVals,HistoPhases,parmDict,varylist) |
|---|
| 1717 | dMdv = np.concatenate((dMdv.T,(np.sqrt(pWt)*dpdv).T)).T |
|---|
| 1718 | |
|---|
| 1719 | return dMdv |
|---|
| 1720 | |
|---|
| 1721 | def HessRefine(values,HistoPhases,parmDict,varylist,calcControls,pawleyLookup,dlg): |
|---|
| 1722 | '''Loop over histograms and compute derivatives of the fitting |
|---|
| 1723 | model (M) with respect to all parameters. For each histogram, the |
|---|
| 1724 | Jacobian matrix, dMdv, with dimensions (n by m) where n is the |
|---|
| 1725 | number of parameters and m is the number of data points *in the |
|---|
| 1726 | histogram*. The (n by n) Hessian is computed from each Jacobian |
|---|
| 1727 | and it is returned. This routine is used when refinement |
|---|
| 1728 | derivatives are selected as "analtytic Hessian" in Controls. |
|---|
| 1729 | |
|---|
| 1730 | :returns: Vec,Hess where Vec is the least-squares vector and Hess is the Hessian |
|---|
| 1731 | ''' |
|---|
| 1732 | parmDict.update(zip(varylist,values)) |
|---|
| 1733 | G2mv.Dict2Map(parmDict,varylist) |
|---|
| 1734 | Histograms,Phases,restraintDict,rigidbodyDict = HistoPhases |
|---|
| 1735 | ApplyRBModels(parmDict,Phases,rigidbodyDict) #,Update=True?? |
|---|
| 1736 | nvar = len(varylist) |
|---|
| 1737 | Hess = np.empty(0) |
|---|
| 1738 | histoList = Histograms.keys() |
|---|
| 1739 | histoList.sort() |
|---|
| 1740 | for histogram in histoList: |
|---|
| 1741 | if 'PWDR' in histogram[:4]: |
|---|
| 1742 | Histogram = Histograms[histogram] |
|---|
| 1743 | hId = Histogram['hId'] |
|---|
| 1744 | hfx = ':%d:'%(hId) |
|---|
| 1745 | wtFactor = calcControls[hfx+'wtFactor'] |
|---|
| 1746 | Limits = calcControls[hfx+'Limits'] |
|---|
| 1747 | x,y,w,yc,yb,yd = Histogram['Data'] |
|---|
| 1748 | W = wtFactor*w |
|---|
| 1749 | dy = y-yc |
|---|
| 1750 | xB = np.searchsorted(x,Limits[0]) |
|---|
| 1751 | xF = np.searchsorted(x,Limits[1]) |
|---|
| 1752 | dMdvh = getPowderProfileDerv(parmDict,x[xB:xF], |
|---|
| 1753 | varylist,Histogram,Phases,rigidbodyDict,calcControls,pawleyLookup) |
|---|
| 1754 | Wt = ma.sqrt(W[xB:xF])[np.newaxis,:] |
|---|
| 1755 | Dy = dy[xB:xF][np.newaxis,:] |
|---|
| 1756 | dMdvh *= Wt |
|---|
| 1757 | if dlg: |
|---|
| 1758 | dlg.Update(Histogram['Residuals']['wR'],newmsg='Hessian for histogram %d\nAll data Rw=%8.3f%s'%(hId,Histogram['Residuals']['wR'],'%'))[0] |
|---|
| 1759 | if len(Hess): |
|---|
| 1760 | Hess += np.inner(dMdvh,dMdvh) |
|---|
| 1761 | dMdvh *= Wt*Dy |
|---|
| 1762 | Vec += np.sum(dMdvh,axis=1) |
|---|
| 1763 | else: |
|---|
| 1764 | Hess = np.inner(dMdvh,dMdvh) |
|---|
| 1765 | dMdvh *= Wt*Dy |
|---|
| 1766 | Vec = np.sum(dMdvh,axis=1) |
|---|
| 1767 | elif 'HKLF' in histogram[:4]: |
|---|
| 1768 | Histogram = Histograms[histogram] |
|---|
| 1769 | nobs = Histogram['Residuals']['Nobs'] |
|---|
| 1770 | phase = Histogram['Reflection Lists'] |
|---|
| 1771 | Phase = Phases[phase] |
|---|
| 1772 | hId = Histogram['hId'] |
|---|
| 1773 | hfx = ':%d:'%(hId) |
|---|
| 1774 | wtFactor = calcControls[hfx+'wtFactor'] |
|---|
| 1775 | pfx = '%d::'%(Phase['pId']) |
|---|
| 1776 | phfx = '%d:%d:'%(Phase['pId'],hId) |
|---|
| 1777 | SGData = Phase['General']['SGData'] |
|---|
| 1778 | A = [parmDict[pfx+'A%d'%(i)] for i in range(6)] |
|---|
| 1779 | G,g = G2lat.A2Gmat(A) #recip & real metric tensors |
|---|
| 1780 | refList = Histogram['Data'] |
|---|
| 1781 | time0 = time.time() |
|---|
| 1782 | dFdvDict = StructureFactorDerv(refList,G,hfx,pfx,SGData,calcControls,parmDict) #accurate for powders! |
|---|
| 1783 | ApplyRBModelDervs(dFdvDict,parmDict,rigidbodyDict,Phase) |
|---|
| 1784 | dMdvh = np.zeros((len(varylist),len(refList))) |
|---|
| 1785 | dependentVars = G2mv.GetDependentVars() |
|---|
| 1786 | depDerivDict = {} |
|---|
| 1787 | for j in dependentVars: |
|---|
| 1788 | depDerivDict[j] = np.zeros(shape=(len(refList))) |
|---|
| 1789 | wdf = np.zeros(len(refList)) |
|---|
| 1790 | if calcControls['F**2']: |
|---|
| 1791 | for iref,ref in enumerate(refList): |
|---|
| 1792 | if ref[6] > 0: |
|---|
| 1793 | dervCor,dervDict = SCExtinction(ref,phfx,hfx,pfx,calcControls,parmDict,varylist) #puts correction in refl[13] |
|---|
| 1794 | w = 1.0/ref[6] |
|---|
| 1795 | if w*ref[5] >= calcControls['minF/sig']: |
|---|
| 1796 | wdf[iref] = w*(ref[5]-ref[7]) |
|---|
| 1797 | for j,var in enumerate(varylist): |
|---|
| 1798 | if var in dFdvDict: |
|---|
| 1799 | dMdvh[j][iref] = w*dFdvDict[var][iref]*dervCor*parmDict[phfx+'Scale'] |
|---|
| 1800 | for var in dependentVars: |
|---|
| 1801 | if var in dFdvDict: |
|---|
| 1802 | depDerivDict[var][iref] = w*dFdvDict[var][iref]*dervCor*parmDict[phfx+'Scale'] |
|---|
| 1803 | if phfx+'Scale' in varylist: |
|---|
| 1804 | dMdvh[varylist.index(phfx+'Scale')][iref] = w*ref[9]*dervCor |
|---|
| 1805 | elif phfx+'Scale' in dependentVars: |
|---|
| 1806 | depDerivDict[phfx+'Scale'][iref] = w*ref[9]*dervCor |
|---|
| 1807 | for item in ['Ep','Es','Eg']: |
|---|
| 1808 | if phfx+item in varylist: |
|---|
| 1809 | dMdvh[varylist.index(phfx+item)][iref] = w*dervDict[phfx+item]*parmDict[phfx+'Scale'] |
|---|
| 1810 | elif phfx+item in dependentVars: |
|---|
| 1811 | depDerivDict[phfx+item][iref] = w*dervDict[phfx+item]*parmDict[phfx+'Scale'] |
|---|
| 1812 | for item in ['BabA','BabU']: |
|---|
| 1813 | if phfx+item in varylist: |
|---|
| 1814 | dMdvh[varylist.index(phfx+item)][iref] = w*dFdvDict[pfx+item][iref]*parmDict[phfx+'Scale']*dervCor |
|---|
| 1815 | elif phfx+item in dependentVars: |
|---|
| 1816 | depDerivDict[phfx+item][iref] = w*dFdvDict[pfx+item][iref]*parmDict[phfx+'Scale']*dervCor |
|---|
| 1817 | else: |
|---|
| 1818 | for iref,ref in enumerate(refList): |
|---|
| 1819 | if ref[5] > 0.: |
|---|
| 1820 | dervCor,dervDict = SCExtinction(ref,phfx,hfx,pfx,calcControls,parmDict,varylist) #puts correction in refl[13] |
|---|
| 1821 | Fo = np.sqrt(ref[5]) |
|---|
| 1822 | Fc = np.sqrt(ref[7]) |
|---|
| 1823 | w = 1.0/ref[6] |
|---|
| 1824 | if 2.0*Fo*w*Fo >= calcControls['minF/sig']: |
|---|
| 1825 | wdf[iref] = 2.0*Fo*w*(Fo-Fc) |
|---|
| 1826 | for j,var in enumerate(varylist): |
|---|
| 1827 | if var in dFdvDict: |
|---|
| 1828 | dMdvh[j][iref] = w*dFdvDict[var][iref]*dervCor*parmDict[phfx+'Scale'] |
|---|
| 1829 | for var in dependentVars: |
|---|
| 1830 | if var in dFdvDict: |
|---|
| 1831 | depDerivDict[var][iref] = w*dFdvDict[var][iref]*dervCor*parmDict[phfx+'Scale'] |
|---|
| 1832 | if phfx+'Scale' in varylist: |
|---|
| 1833 | dMdvh[varylist.index(phfx+'Scale')][iref] = w*ref[9]*dervCor |
|---|
| 1834 | elif phfx+'Scale' in dependentVars: |
|---|
| 1835 | depDerivDict[phfx+'Scale'][iref] = w*ref[9]*dervCor |
|---|
| 1836 | for item in ['Ep','Es','Eg']: |
|---|
| 1837 | if phfx+item in varylist: |
|---|
| 1838 | dMdvh[varylist.index(phfx+item)][iref] = w*dervDict[phfx+item]*parmDict[phfx+'Scale'] |
|---|
| 1839 | elif phfx+item in dependentVars: |
|---|
| 1840 | depDerivDict[phfx+item][iref] = w*dervDict[phfx+item]*parmDict[phfx+'Scale'] |
|---|
| 1841 | for item in ['BabA','BabU']: |
|---|
| 1842 | if phfx+item in varylist: |
|---|
| 1843 | dMdvh[varylist.index(phfx+item)][iref] = w*dFdvDict[pfx+item][iref]*parmDict[phfx+'Scale']*dervCor |
|---|
| 1844 | elif phfx+item in dependentVars: |
|---|
| 1845 | depDerivDict[phfx+item][iref] = w*dFdvDict[pfx+item][iref]*parmDict[phfx+'Scale']*dervCor |
|---|
| 1846 | # now process derivatives in constraints |
|---|
| 1847 | G2mv.Dict2Deriv(varylist,depDerivDict,dMdvh) |
|---|
| 1848 | |
|---|
| 1849 | if dlg: |
|---|
| 1850 | dlg.Update(Histogram['Residuals']['wR'],newmsg='Hessian for histogram %d Rw=%8.3f%s'%(hId,Histogram['Residuals']['wR'],'%'))[0] |
|---|
| 1851 | if len(Hess): |
|---|
| 1852 | Vec += wtFactor*np.sum(dMdvh*wdf,axis=1) |
|---|
| 1853 | Hess += wtFactor*np.inner(dMdvh,dMdvh) |
|---|
| 1854 | else: |
|---|
| 1855 | Vec = wtFactor*np.sum(dMdvh*wdf,axis=1) |
|---|
| 1856 | Hess = wtFactor*np.inner(dMdvh,dMdvh) |
|---|
| 1857 | else: |
|---|
| 1858 | continue #skip non-histogram entries |
|---|
| 1859 | pNames,pVals,pWt,pWsum = penaltyFxn(HistoPhases,parmDict,varylist) |
|---|
| 1860 | if np.any(pVals): |
|---|
| 1861 | dpdv = penaltyDeriv(pNames,pVals,HistoPhases,parmDict,varylist) |
|---|
| 1862 | Vec += np.sum(dpdv*pWt*pVals,axis=1) |
|---|
| 1863 | Hess += np.inner(dpdv*pWt,dpdv) |
|---|
| 1864 | return Vec,Hess |
|---|
| 1865 | |
|---|
| 1866 | def errRefine(values,HistoPhases,parmDict,varylist,calcControls,pawleyLookup,dlg): |
|---|
| 1867 | 'Needs a doc string' |
|---|
| 1868 | parmDict.update(zip(varylist,values)) |
|---|
| 1869 | Values2Dict(parmDict, varylist, values) |
|---|
| 1870 | G2mv.Dict2Map(parmDict,varylist) |
|---|
| 1871 | Histograms,Phases,restraintDict,rigidbodyDict = HistoPhases |
|---|
| 1872 | M = np.empty(0) |
|---|
| 1873 | SumwYo = 0 |
|---|
| 1874 | Nobs = 0 |
|---|
| 1875 | ApplyRBModels(parmDict,Phases,rigidbodyDict) |
|---|
| 1876 | histoList = Histograms.keys() |
|---|
| 1877 | histoList.sort() |
|---|
| 1878 | for histogram in histoList: |
|---|
| 1879 | if 'PWDR' in histogram[:4]: |
|---|
| 1880 | Histogram = Histograms[histogram] |
|---|
| 1881 | hId = Histogram['hId'] |
|---|
| 1882 | hfx = ':%d:'%(hId) |
|---|
| 1883 | wtFactor = calcControls[hfx+'wtFactor'] |
|---|
| 1884 | Limits = calcControls[hfx+'Limits'] |
|---|
| 1885 | x,y,w,yc,yb,yd = Histogram['Data'] |
|---|
| 1886 | yc *= 0.0 #zero full calcd profiles |
|---|
| 1887 | yb *= 0.0 |
|---|
| 1888 | yd *= 0.0 |
|---|
| 1889 | xB = np.searchsorted(x,Limits[0]) |
|---|
| 1890 | xF = np.searchsorted(x,Limits[1]) |
|---|
| 1891 | yc[xB:xF],yb[xB:xF] = getPowderProfile(parmDict,x[xB:xF], |
|---|
| 1892 | varylist,Histogram,Phases,calcControls,pawleyLookup) |
|---|
| 1893 | yc[xB:xF] += yb[xB:xF] |
|---|
| 1894 | if not np.any(y): #fill dummy data |
|---|
| 1895 | rv = st.poisson(yc[xB:xF]) |
|---|
| 1896 | y[xB:xF] = rv.rvs() |
|---|
| 1897 | Z = np.ones_like(yc[xB:xF]) |
|---|
| 1898 | Z[1::2] *= -1 |
|---|
| 1899 | y[xB:xF] = yc[xB:xF]+np.abs(y[xB:xF]-yc[xB:xF])*Z |
|---|
| 1900 | w[xB:xF] = np.where(y[xB:xF]>0.,1./y[xB:xF],1.0) |
|---|
| 1901 | yd[xB:xF] = y[xB:xF]-yc[xB:xF] |
|---|
| 1902 | W = wtFactor*w |
|---|
| 1903 | wdy = -ma.sqrt(W[xB:xF])*(yd[xB:xF]) |
|---|
| 1904 | Histogram['Residuals']['Nobs'] = ma.count(x[xB:xF]) |
|---|
| 1905 | Nobs += Histogram['Residuals']['Nobs'] |
|---|
| 1906 | Histogram['Residuals']['sumwYo'] = ma.sum(W[xB:xF]*y[xB:xF]**2) |
|---|
| 1907 | SumwYo += Histogram['Residuals']['sumwYo'] |
|---|
| 1908 | Histogram['Residuals']['R'] = min(100.,ma.sum(ma.abs(yd[xB:xF]))/ma.sum(y[xB:xF])*100.) |
|---|
| 1909 | Histogram['Residuals']['wR'] = min(100.,ma.sqrt(ma.sum(wdy**2)/Histogram['Residuals']['sumwYo'])*100.) |
|---|
| 1910 | sumYmB = ma.sum(ma.where(yc[xB:xF]!=yb[xB:xF],ma.abs(y[xB:xF]-yb[xB:xF]),0.)) |
|---|
| 1911 | sumwYmB2 = ma.sum(ma.where(yc[xB:xF]!=yb[xB:xF],W[xB:xF]*(y[xB:xF]-yb[xB:xF])**2,0.)) |
|---|
| 1912 | 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.)) |
|---|
| 1913 | 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.)) |
|---|
| 1914 | Histogram['Residuals']['Rb'] = min(100.,100.*sumYB/sumYmB) |
|---|
| 1915 | Histogram['Residuals']['wRb'] = min(100.,100.*ma.sqrt(sumwYB2/sumwYmB2)) |
|---|
| 1916 | Histogram['Residuals']['wRmin'] = min(100.,100.*ma.sqrt(Histogram['Residuals']['Nobs']/Histogram['Residuals']['sumwYo'])) |
|---|
| 1917 | if dlg: |
|---|
| 1918 | dlg.Update(Histogram['Residuals']['wR'],newmsg='For histogram %d Rw=%8.3f%s'%(hId,Histogram['Residuals']['wR'],'%'))[0] |
|---|
| 1919 | M = np.concatenate((M,wdy)) |
|---|
| 1920 | #end of PWDR processing |
|---|
| 1921 | elif 'HKLF' in histogram[:4]: |
|---|
| 1922 | Histogram = Histograms[histogram] |
|---|
| 1923 | Histogram['Residuals'] = {} |
|---|
| 1924 | phase = Histogram['Reflection Lists'] |
|---|
| 1925 | Phase = Phases[phase] |
|---|
| 1926 | hId = Histogram['hId'] |
|---|
| 1927 | hfx = ':%d:'%(hId) |
|---|
| 1928 | wtFactor = calcControls[hfx+'wtFactor'] |
|---|
| 1929 | pfx = '%d::'%(Phase['pId']) |
|---|
| 1930 | phfx = '%d:%d:'%(Phase['pId'],hId) |
|---|
| 1931 | SGData = Phase['General']['SGData'] |
|---|
| 1932 | A = [parmDict[pfx+'A%d'%(i)] for i in range(6)] |
|---|
| 1933 | G,g = G2lat.A2Gmat(A) #recip & real metric tensors |
|---|
| 1934 | refList = Histogram['Data'] |
|---|
| 1935 | time0 = time.time() |
|---|
| 1936 | StructureFactor(refList,G,hfx,pfx,SGData,calcControls,parmDict) |
|---|
| 1937 | # print 'sf-calc time: %.3f'%(time.time()-time0) |
|---|
| 1938 | df = np.zeros(len(refList)) |
|---|
| 1939 | sumwYo = 0 |
|---|
| 1940 | sumFo = 0 |
|---|
| 1941 | sumFo2 = 0 |
|---|
| 1942 | sumdF = 0 |
|---|
| 1943 | sumdF2 = 0 |
|---|
| 1944 | nobs = 0 |
|---|
| 1945 | if calcControls['F**2']: |
|---|
| 1946 | for i,ref in enumerate(refList): |
|---|
| 1947 | if ref[6] > 0: |
|---|
| 1948 | SCExtinction(ref,phfx,hfx,pfx,calcControls,parmDict,varylist) #puts correction in refl[13] |
|---|
| 1949 | w = 1.0/ref[6] |
|---|
| 1950 | ref[7] = parmDict[phfx+'Scale']*ref[9] |
|---|
| 1951 | ref[7] *= ref[13] #correct Fc^2 for extinction |
|---|
| 1952 | ref[8] = ref[5]/parmDict[phfx+'Scale'] |
|---|
| 1953 | if w*ref[5] >= calcControls['minF/sig']: |
|---|
| 1954 | sumFo2 += ref[5] |
|---|
| 1955 | Fo = np.sqrt(ref[5]) |
|---|
| 1956 | sumFo += Fo |
|---|
| 1957 | sumFo2 += ref[5] |
|---|
| 1958 | sumdF += abs(Fo-np.sqrt(ref[7])) |
|---|
| 1959 | sumdF2 += abs(ref[5]-ref[7]) |
|---|
| 1960 | nobs += 1 |
|---|
| 1961 | df[i] = -w*(ref[5]-ref[7]) |
|---|
| 1962 | sumwYo += (w*ref[5])**2 |
|---|
| 1963 | else: |
|---|
| 1964 | for i,ref in enumerate(refList): |
|---|
| 1965 | if ref[5] > 0.: |
|---|
| 1966 | SCExtinction(ref,phfx,hfx,pfx,calcControls,parmDict,varylist) #puts correction in refl[13] |
|---|
| 1967 | ref[7] = parmDict[phfx+'Scale']*ref[9] |
|---|
| 1968 | ref[7] *= ref[13] #correct Fc^2 for extinction |
|---|
| 1969 | Fo = np.sqrt(ref[5]) |
|---|
| 1970 | Fc = np.sqrt(ref[7]) |
|---|
| 1971 | w = 2.0*Fo/ref[6] |
|---|
| 1972 | if w*Fo >= calcControls['minF/sig']: |
|---|
| 1973 | sumFo += Fo |
|---|
| 1974 | sumFo2 += ref[5] |
|---|
| 1975 | sumdF += abs(Fo-Fc) |
|---|
| 1976 | sumdF2 += abs(ref[5]-ref[7]) |
|---|
| 1977 | nobs += 1 |
|---|
| 1978 | df[i] = -w*(Fo-Fc) |
|---|
| 1979 | sumwYo += (w*Fo)**2 |
|---|
| 1980 | Histogram['Residuals']['Nobs'] = nobs |
|---|
| 1981 | Histogram['Residuals']['sumwYo'] = sumwYo |
|---|
| 1982 | SumwYo += sumwYo |
|---|
| 1983 | Histogram['Residuals']['wR'] = min(100.,np.sqrt(np.sum(df**2)/Histogram['Residuals']['sumwYo'])*100.) |
|---|
| 1984 | Histogram['Residuals'][phfx+'Rf'] = 100.*sumdF/sumFo |
|---|
| 1985 | Histogram['Residuals'][phfx+'Rf^2'] = 100.*sumdF2/sumFo2 |
|---|
| 1986 | Histogram['Residuals'][phfx+'Nref'] = nobs |
|---|
| 1987 | Nobs += nobs |
|---|
| 1988 | if dlg: |
|---|
| 1989 | dlg.Update(Histogram['Residuals']['wR'],newmsg='For histogram %d Rw=%8.3f%s'%(hId,Histogram['Residuals']['wR'],'%'))[0] |
|---|
| 1990 | M = np.concatenate((M,wtFactor*df)) |
|---|
| 1991 | # end of HKLF processing |
|---|
| 1992 | Histograms['sumwYo'] = SumwYo |
|---|
| 1993 | Histograms['Nobs'] = Nobs |
|---|
| 1994 | Rw = min(100.,np.sqrt(np.sum(M**2)/SumwYo)*100.) |
|---|
| 1995 | if dlg: |
|---|
| 1996 | GoOn = dlg.Update(Rw,newmsg='%s%8.3f%s'%('All data Rw =',Rw,'%'))[0] |
|---|
| 1997 | if not GoOn: |
|---|
| 1998 | parmDict['saved values'] = values |
|---|
| 1999 | dlg.Destroy() |
|---|
| 2000 | raise Exception #Abort!! |
|---|
| 2001 | pDict,pVals,pWt,pWsum = penaltyFxn(HistoPhases,parmDict,varylist) |
|---|
| 2002 | if np.any(pVals): |
|---|
| 2003 | pSum = np.sum(pWt*pVals**2) |
|---|
| 2004 | for name in pWsum: |
|---|
| 2005 | print ' Penalty function for %s = %.3f'%(name,pWsum[name]) |
|---|
| 2006 | print 'Total penalty function: %.3f on %d terms'%(pSum,len(pVals)) |
|---|
| 2007 | Nobs += len(pVals) |
|---|
| 2008 | M = np.concatenate((M,np.sqrt(pWt)*pVals)) |
|---|
| 2009 | return M |
|---|
| 2010 | |
|---|
