source: trunk/GSASIIstruct.py @ 407

#GSASIIstructure - structure computation routines
########### SVN repository information ###################
# $Date: 2011-11-05 22:30:24 +0000 (Sat, 05 Nov 2011) $
# $Author: vondreele $
# $Revision: 407 $
# $URL: trunk/GSASIIstruct.py $
# $Id: GSASIIstruct.py 407 2011-11-05 22:30:24Z vondreele $
########### SVN repository information ###################
import sys
import os
import os.path as ospath
import numpy as np
import numpy.linalg as nl
import cPickle
import time
import math
import GSASIIpath
import GSASIIElem as G2el
import GSASIIlattice as G2lat
import GSASIIspc as G2spc
import GSASIIpwd as G2pwd
import GSASIImapvars as G2mv
import scipy.optimize as so

sind = lambda x: np.sin(x*np.pi/180.)
cosd = lambda x: np.cos(x*np.pi/180.)
tand = lambda x: np.tan(x*np.pi/180.)
asind = lambda x: 180.*np.arcsin(x)/np.pi
atan2d = lambda y,x: 180.*np.arctan2(y,x)/np.pi


def ShowBanner():
    print 80*'*'
    print '   General Structure Analysis System-II Crystal Structure Refinement'
    print '     by Robert B. Von Dreele, Argonne National Laboratory(C), 2010'
    print ' This product includes software developed by the UChicago Argonne, LLC,' 
    print '            as Operator of Argonne National Laboratory.'
    print 80*'*','\n'

def GetControls(GPXfile):
    ''' Returns dictionary of control items found in GSASII gpx file
    input:
        GPXfile = .gpx full file name
    return:
        Controls = dictionary of control items
    '''
    Controls = {'deriv type':'analytical','min dM/M':0.0001,'shift factor':1.}
    file = open(GPXfile,'rb')
    while True:
        try:
            data = cPickle.load(file)
        except EOFError:
            break
        datum = data[0]
        if datum[0] == 'Controls':
            Controls.update(datum[1])
    file.close()
    return Controls
    
def ShowControls(Controls):
    print ' Least squares controls:'
    print ' Derivative type: ',Controls['deriv type']
    print ' Minimum delta-M/M for convergence: ','%.2g'%(Controls['min dM/M'])
    print ' Initial shift factor: ','%.3f'%(Controls['shift factor'])
    
def GetConstraints(GPXfile):
    constrList = []
    file = open(GPXfile,'rb')
    while True:
        try:
            data = cPickle.load(file)
        except EOFError:
            break
        datum = data[0]
        if datum[0] == 'Constraints':
            constDict = datum[1]
            for item in constDict:
                constrList += constDict[item]
    file.close()
    return constrList
    
def GetPhaseNames(GPXfile):
    ''' Returns a list of phase names found under 'Phases' in GSASII gpx file
    input: 
        GPXfile = gpx full file name
    return: 
        PhaseNames = list of phase names
    '''
    file = open(GPXfile,'rb')
    PhaseNames = []
    while True:
        try:
            data = cPickle.load(file)
        except EOFError:
            break
        datum = data[0]
        if 'Phases' == datum[0]:
            for datus in data[1:]:
                PhaseNames.append(datus[0])
    file.close()
    return PhaseNames

def GetAllPhaseData(GPXfile,PhaseName):
    ''' Returns the entire dictionary for PhaseName from GSASII gpx file
    input:
        GPXfile = gpx full file name
        PhaseName = phase name
    return:
        phase dictionary
    '''        
    file = open(GPXfile,'rb')
    General = {}
    Atoms = []
    while True:
        try:
            data = cPickle.load(file)
        except EOFError:
            break
        datum = data[0]
        if 'Phases' == datum[0]:
            for datus in data[1:]:
                if datus[0] == PhaseName:
                    break
    file.close()
    return datus[1]
    
def GetHistograms(GPXfile,hNames):
    """ Returns a dictionary of histograms found in GSASII gpx file
    input: 
        GPXfile = .gpx full file name
        hNames = list of histogram names 
    return: 
        Histograms = dictionary of histograms (types = PWDR & HKLF)
    """
    file = open(GPXfile,'rb')
    Histograms = {}
    while True:
        try:
            data = cPickle.load(file)
        except EOFError:
            break
        datum = data[0]
        hist = datum[0]
        if hist in hNames:
            if 'PWDR' in hist[:4]:
                PWDRdata = {}
                PWDRdata['Data'] = datum[1][1]          #powder data arrays
                PWDRdata[data[2][0]] = data[2][1]       #Limits
                PWDRdata[data[3][0]] = data[3][1]       #Background
                PWDRdata[data[4][0]] = data[4][1]       #Instrument parameters
                PWDRdata[data[5][0]] = data[5][1]       #Sample parameters
                try:
                    PWDRdata[data[9][0]] = data[9][1]       #Reflection lists might be missing
                except IndexError:
                    PWDRdata['Reflection lists'] = {}
    
                Histograms[hist] = PWDRdata
            elif 'HKLF' in hist[:4]:
                HKLFdata = []
                datum = data[0]
                HKLFdata = datum[1:][0]
                Histograms[hist] = HKLFdata           
    file.close()
    return Histograms
    
def GetHistogramNames(GPXfile,hType):
    """ Returns a list of histogram names found in GSASII gpx file
    input: 
        GPXfile = .gpx full file name
        hType = list ['PWDR','HKLF'] 
    return: 
        HistogramNames = list of histogram names (types = PWDR & HKLF)
    """
    file = open(GPXfile,'rb')
    HistogramNames = []
    while True:
        try:
            data = cPickle.load(file)
        except EOFError:
            break
        datum = data[0]
        if datum[0][:4] in hType:
            HistogramNames.append(datum[0])
    file.close()
    return HistogramNames
    
def GetUsedHistogramsAndPhases(GPXfile):
    ''' Returns all histograms that are found in any phase
    and any phase that uses a histogram
    input:
        GPXfile = .gpx full file name
    return:
        Histograms = dictionary of histograms as {name:data,...}
        Phases = dictionary of phases that use histograms
    '''
    phaseNames = GetPhaseNames(GPXfile)
    histoList = GetHistogramNames(GPXfile,['PWDR','HKLF'])
    allHistograms = GetHistograms(GPXfile,histoList)
    phaseData = {}
    for name in phaseNames: 
        phaseData[name] =  GetAllPhaseData(GPXfile,name)
    Histograms = {}
    Phases = {}
    for phase in phaseData:
        Phase = phaseData[phase]
        if Phase['Histograms']:
            if phase not in Phases:
                pId = phaseNames.index(phase)
                Phase['pId'] = pId
                Phases[phase] = Phase
            for hist in Phase['Histograms']:
                if hist not in Histograms:
                    Histograms[hist] = allHistograms[hist]
                    #future restraint, etc. histograms here            
                    hId = histoList.index(hist)
                    Histograms[hist]['hId'] = hId
    return Histograms,Phases
    
def GPXBackup(GPXfile,makeBack=True):
    import distutils.file_util as dfu
    GPXpath,GPXname = ospath.split(GPXfile)
    Name = ospath.splitext(GPXname)[0]
    files = os.listdir(GPXpath)
    last = 0
    for name in files:
        name = name.split('.')
        if len(name) == 3 and name[0] == Name and 'bak' in name[1]:
            if makeBack:
                last = max(last,int(name[1].strip('bak'))+1)
            else:
                last = max(last,int(name[1].strip('bak')))
    GPXback = ospath.join(GPXpath,ospath.splitext(GPXname)[0]+'.bak'+str(last)+'.gpx')
    dfu.copy_file(GPXfile,GPXback)
    return GPXback
        
def SetUsedHistogramsAndPhases(GPXfile,Histograms,Phases,CovData,makeBack=True):
    ''' Updates gpxfile from all histograms that are found in any phase
    and any phase that used a histogram
    input:
        GPXfile = .gpx full file name
        Histograms = dictionary of histograms as {name:data,...}
        Phases = dictionary of phases that use histograms
        CovData = dictionary of refined variables, varyList, & covariance matrix
        makeBack = True if new backup of .gpx file is to be made; else use the last one made
    '''
                        
    GPXback = GPXBackup(GPXfile,makeBack)
    print '\n',135*'-'
    print 'Read from file:',GPXback
    print 'Save to file  :',GPXfile
    infile = open(GPXback,'rb')
    outfile = open(GPXfile,'wb')
    while True:
        try:
            data = cPickle.load(infile)
        except EOFError:
            break
        datum = data[0]
#        print 'read: ',datum[0]
        if datum[0] == 'Phases':
            for iphase in range(len(data)):
                if data[iphase][0] in Phases:
                    phaseName = data[iphase][0]
                    data[iphase][1].update(Phases[phaseName])
        elif datum[0] == 'Covariance':
            data[0][1] = CovData
        try:
            histogram = Histograms[datum[0]]
#            print 'found ',datum[0]
            data[0][1][1] = histogram['Data']
            for datus in data[1:]:
#                print '    read: ',datus[0]
                if datus[0] in ['Background','Instrument Parameters','Sample Parameters','Reflection Lists']:
                    datus[1] = histogram[datus[0]]
        except KeyError:
            pass
                                
        cPickle.dump(data,outfile,1)
    infile.close()
    outfile.close()
    print 'refinement save successful'
    
def SetSeqResult(GPXfile,Histograms,SeqResult):
    GPXback = GPXBackup(GPXfile)
    print '\n',135*'-'
    print 'Read from file:',GPXback
    print 'Save to file  :',GPXfile
    infile = open(GPXback,'rb')
    outfile = open(GPXfile,'wb')
    while True:
        try:
            data = cPickle.load(infile)
        except EOFError:
            break
        datum = data[0]
        if datum[0] == 'Sequental results':
            data[0][1] = SeqResult
        try:
            histogram = Histograms[datum[0]]
            data[0][1][1] = histogram['Data']
            for datus in data[1:]:
                if datus[0] in ['Background','Instrument Parameters','Sample Parameters','Reflection Lists']:
                    datus[1] = histogram[datus[0]]
        except KeyError:
            pass
                                
        cPickle.dump(data,outfile,1)
    infile.close()
    outfile.close()
    print 'refinement save successful'
    
                    
def GetPWDRdata(GPXfile,PWDRname):
    ''' Returns powder data from GSASII gpx file
    input: 
        GPXfile = .gpx full file name
        PWDRname = powder histogram name as obtained from GetHistogramNames
    return: 
        PWDRdata = powder data dictionary with:
            Data - powder data arrays, Limits, Instrument Parameters, Sample Parameters
        
    '''
    file = open(GPXfile,'rb')
    PWDRdata = {}
    while True:
        try:
            data = cPickle.load(file)
        except EOFError:
            break
        datum = data[0]
        if datum[0] == PWDRname:
            PWDRdata['Data'] = datum[1][1]          #powder data arrays
            PWDRdata[data[2][0]] = data[2][1]       #Limits
            PWDRdata[data[3][0]] = data[3][1]       #Background
            PWDRdata[data[4][0]] = data[4][1]       #Instrument parameters
            PWDRdata[data[5][0]] = data[5][1]       #Sample parameters
            try:
                PWDRdata[data[9][0]] = data[9][1]       #Reflection lists might be missing
            except IndexError:
                PWDRdata['Reflection lists'] = {}
    file.close()
    return PWDRdata
    
def GetHKLFdata(GPXfile,HKLFname):
    ''' Returns single crystal data from GSASII gpx file
    input: 
        GPXfile = .gpx full file name
        HKLFname = single crystal histogram name as obtained from GetHistogramNames
    return: 
        HKLFdata = single crystal data list of reflections: for each reflection:
            HKLF = [np.array([h,k,l]),FoSq,sigFoSq,FcSq,Fcp,Fcpp,phase]
    '''
    file = open(GPXfile,'rb')
    HKLFdata = []
    while True:
        try:
            data = cPickle.load(file)
        except EOFError:
            break
        datum = data[0]
        if datum[0] == HKLFname:
            HKLFdata = datum[1:][0]
    file.close()
    return HKLFdata
    
def GetFFtable(General):
    ''' returns a dictionary of form factor data for atom types found in General
    input:
        General = dictionary of phase info.; includes AtomTypes
    return:
        FFtable = dictionary of form factor data; key is atom type
    '''
    atomTypes = General['AtomTypes']
    FFtable = {}
    for El in atomTypes:
        FFs = G2el.GetFormFactorCoeff(El.split('+')[0].split('-')[0])
        for item in FFs:
            if item['Symbol'] == El.upper():
                FFtable[El] = item
    return FFtable
    
def GetPawleyConstr(SGLaue,PawleyRef,pawleyVary):
    if SGLaue in ['-1','2/m','mmm']:
        return                      #no Pawley symmetry required constraints
    for i,varyI in enumerate(pawleyVary):
        refI = int(varyI.split(':')[-1])
        ih,ik,il = PawleyRef[refI][:3]
        for varyJ in pawleyVary[0:i]:
            refJ = int(varyJ.split(':')[-1])
            jh,jk,jl = PawleyRef[refJ][:3]
            if SGLaue in ['4/m','4/mmm']:
                isum = ih**2+ik**2
                jsum = jh**2+jk**2
                if abs(il) == abs(jl) and isum == jsum:
                    G2mv.StoreEquivalence(varyJ,(varyI,))
            elif SGLaue in ['3R','3mR']:
                isum = ih**2+ik**2+il**2
                jsum = jh**2+jk**2*jl**2
                isum2 = ih*ik+ih*il+ik*il
                jsum2 = jh*jk+jh*jl+jk*jl
                if isum == jsum and isum2 == jsum2:
                    G2mv.StoreEquivalence(varyJ,(varyI,))
            elif SGLaue in ['3','3m1','31m','6/m','6/mmm']:
                isum = ih**2+ik**2+ih*ik
                jsum = jh**2+jk**2+jh*jk
                if abs(il) == abs(jl) and isum == jsum:
                    G2mv.StoreEquivalence(varyJ,(varyI,))
            elif SGLaue in ['m3','m3m']:
                isum = ih**2+ik**2+il**2
                jsum = jh**2+jk**2+jl**2
                if isum == jsum:
                    G2mv.StoreEquivalence(varyJ,(varyI,))
                    
def cellVary(pfx,SGData): 
    if SGData['SGLaue'] in ['-1',]:
        return [pfx+'A0',pfx+'A1',pfx+'A2',pfx+'A3',pfx+'A4',pfx+'A5']
    elif SGData['SGLaue'] in ['2/m',]:
        if SGData['SGUniq'] == 'a':
            return [pfx+'A0',pfx+'A1',pfx+'A2',pfx+'A3']
        elif SGData['SGUniq'] == 'b':
            return [pfx+'A0',pfx+'A1',pfx+'A2',pfx+'A4']
        else:
            return [pfx+'A0',pfx+'A1',pfx+'A2',pfx+'A5']
    elif SGData['SGLaue'] in ['mmm',]:
        return [pfx+'A0',pfx+'A1',pfx+'A2']
    elif SGData['SGLaue'] in ['4/m','4/mmm']:
        return [pfx+'A0',pfx+'A2']
    elif SGData['SGLaue'] in ['6/m','6/mmm','3m1', '31m', '3']:
        return [pfx+'A0',pfx+'A2']
    elif SGData['SGLaue'] in ['3R', '3mR']:
        return [pfx+'A0',pfx+'A3']                       
    elif SGData['SGLaue'] in ['m3m','m3']:
        return [pfx+'A0',]
        
            
def GetPhaseData(PhaseData,Print=True):
            
    def PrintFFtable(FFtable):
        print '\n Scattering factors:'
        print '   Symbol     fa                                      fb                                      fc'
        print 99*'-'
        for Ename in FFtable:
            ffdata = FFtable[Ename]
            fa = ffdata['fa']
            fb = ffdata['fb']
            print ' %8s %9.5f %9.5f %9.5f %9.5f %9.5f %9.5f %9.5f %9.5f %9.5f' %  \
                (Ename.ljust(8),fa[0],fa[1],fa[2],fa[3],fb[0],fb[1],fb[2],fb[3],ffdata['fc'])
                
    def PrintAtoms(General,Atoms):
        print '\n Atoms:'
        line = '   name    type  refine?   x         y         z    '+ \
            '  frac site sym  mult I/A   Uiso     U11     U22     U33     U12     U13     U23'
        if General['Type'] == 'magnetic':
            line += '   Mx     My     Mz'
        elif General['Type'] == 'macromolecular':
            line = ' res no  residue  chain '+line
        print line
        if General['Type'] == 'nuclear':
            print 135*'-'
            for i,at in enumerate(Atoms):
                line = '%7s'%(at[0])+'%7s'%(at[1])+'%7s'%(at[2])+'%10.5f'%(at[3])+'%10.5f'%(at[4])+ \
                    '%10.5f'%(at[5])+'%8.3f'%(at[6])+'%7s'%(at[7])+'%5d'%(at[8])+'%5s'%(at[9])
                if at[9] == 'I':
                    line += '%8.4f'%(at[10])+48*' '
                else:
                    line += 8*' '
                    for j in range(6):
                        line += '%8.4f'%(at[11+j])
                print line
        
    def PrintTexture(textureData):
        print '\n Spherical harmonics texture: Order:' + \
            str(textureData['Order'])+' Refine? '+str(textureData['SH Coeff'][0])
        names = ['omega','chi','phi']
        line = '\n'
        for name in names:
            line += ' SH '+name+':'+'%12.4f'%(textureData['Sample '+name][1])+' Refine? '+str(textureData['Sample '+name][0])
        print line
        print '\n Texture coefficients:'
        ptlbls = ' names :'
        ptstr =  ' values:'
        SHcoeff = textureData['SH Coeff'][1]
        for item in SHcoeff:
            ptlbls += '%12s'%(item)
            ptstr += '%12.4f'%(SHcoeff[item]) 
        print ptlbls
        print ptstr    
        
    if Print: print ' Phases:'
    phaseVary = []
    phaseDict = {}
    phaseConstr = {}
    pawleyLookup = {}
    FFtables = {}
    Natoms = {}
    AtMults = {}
    AtIA = {}
    shModels = ['cylindrical','none','shear - 2/m','rolling - mmm']
    SamSym = dict(zip(shModels,['0','-1','2/m','mmm']))
    for name in PhaseData:
        General = PhaseData[name]['General']
        pId = PhaseData[name]['pId']
        pfx = str(pId)+'::'
        FFtable = GetFFtable(General)
        FFtables.update(FFtable)
        Atoms = PhaseData[name]['Atoms']
        try:
            PawleyRef = PhaseData[name]['Pawley ref']
        except KeyError:
            PawleyRef = []
        if Print: print '\n Phase name: ',General['Name']
        SGData = General['SGData']
        SGtext = G2spc.SGPrint(SGData)
        if Print: 
            for line in SGtext: print line
        cell = General['Cell']
        A = G2lat.cell2A(cell[1:7])
        phaseDict.update({pfx+'A0':A[0],pfx+'A1':A[1],pfx+'A2':A[2],pfx+'A3':A[3],pfx+'A4':A[4],pfx+'A5':A[5]})
        if cell[0]:
            phaseVary += cellVary(pfx,SGData)
        if Print: print '\n Unit cell: a =','%.5f'%(cell[1]),' b =','%.5f'%(cell[2]),' c =','%.5f'%(cell[3]), \
            ' alpha =','%.3f'%(cell[4]),' beta =','%.3f'%(cell[5]),' gamma =', \
            '%.3f'%(cell[6]),' volume =','%.3f'%(cell[7]),' Refine?',cell[0]
        if Print and FFtable:
            PrintFFtable(FFtable)
        Natoms[pfx] = 0
        if Atoms:
            if General['Type'] == 'nuclear':
                Natoms[pfx] = len(Atoms)
                for i,at in enumerate(Atoms):
                    phaseDict.update({pfx+'Atype:'+str(i):at[1],pfx+'Afrac:'+str(i):at[6],pfx+'Amul:'+str(i):at[8],
                        pfx+'Ax:'+str(i):at[3],pfx+'Ay:'+str(i):at[4],pfx+'Az:'+str(i):at[5],
                        pfx+'dAx:'+str(i):0.,pfx+'dAy:'+str(i):0.,pfx+'dAz:'+str(i):0.,         #refined shifts for x,y,z
                        pfx+'AI/A:'+str(i):at[9],})
                    if at[9] == 'I':
                        phaseDict[pfx+'AUiso:'+str(i)] = at[10]
                    else:
                        phaseDict.update({pfx+'AU11:'+str(i):at[11],pfx+'AU22:'+str(i):at[12],pfx+'AU33:'+str(i):at[13],
                            pfx+'AU12:'+str(i):at[14],pfx+'AU13:'+str(i):at[15],pfx+'AU23:'+str(i):at[16]})
                    if 'F' in at[2]:
                        phaseVary.append(pfx+'Afrac:'+str(i))
                    if 'X' in at[2]:
                        xId,xCoef = G2spc.GetCSxinel(at[7])
                        delnames = [pfx+'dAx:'+str(i),pfx+'dAy:'+str(i),pfx+'dAz:'+str(i)]
                        for j in range(3):
                            if xId[j] > 0:                               
                                phaseVary.append(delnames[j])
                                for k in range(j):
                                    if xId[j] == xId[k]:
                                        G2mv.StoreEquivalence(delnames[k],((delnames[j],xCoef[j]),)) 
                    if 'U' in at[2]:
                        if at[9] == 'I':
                            phaseVary.append(pfx+'AUiso:'+str(i))
                        else:
                            uId,uCoef = G2spc.GetCSuinel(at[7])[:2]
                            names = [pfx+'AU11:'+str(i),pfx+'AU22:'+str(i),pfx+'AU33:'+str(i),
                                pfx+'AU12:'+str(i),pfx+'AU13:'+str(i),pfx+'AU23:'+str(i)]
                            for j in range(6):
                                if uId[j] > 0:                               
                                    phaseVary.append(names[j])
                                    for k in range(j):
                                        if uId[j] == uId[k]:
                                            G2mv.StoreEquivalence(names[k],((names[j],uCoef[j]),))
#            elif General['Type'] == 'magnetic':
#            elif General['Type'] == 'macromolecular':

            if 'SH Texture' in General:
                textureData = General['SH Texture']
                phaseDict[pfx+'SHmodel'] = SamSym[textureData['Model']]
                phaseDict[pfx+'SHorder'] = textureData['Order']
                for name in ['omega','chi','phi']:
                    phaseDict[pfx+'SH '+name] = textureData['Sample '+name][1]
                    if textureData['Sample '+name][0]:
                        phaseVary.append(pfx+'SH '+name)
                for name in textureData['SH Coeff'][1]:
                    phaseDict[pfx+name] = textureData['SH Coeff'][1][name]
                    if textureData['SH Coeff'][0]:
                        phaseVary.append(pfx+name)
                
            if Print:
                PrintAtoms(General,Atoms)
                if 'SH Texture' in General:
                    PrintTexture(textureData)
                    
        elif PawleyRef:
            pawleyVary = []
            for i,refl in enumerate(PawleyRef):
                phaseDict[pfx+'PWLref:'+str(i)] = refl[6]
                pawleyLookup[pfx+'%d,%d,%d'%(refl[0],refl[1],refl[2])] = i
                if refl[5]:
                    pawleyVary.append(pfx+'PWLref:'+str(i))
            GetPawleyConstr(SGData['SGLaue'],PawleyRef,pawleyVary)      #does G2mv.StoreEquivalence
            phaseVary += pawleyVary
                
    return Natoms,phaseVary,phaseDict,pawleyLookup,FFtables
    
def getVCov(varyNames,varyList,covMatrix):
    vcov = np.zeros((len(varyNames),len(varyNames)))
    for i1,name1 in enumerate(varyNames):
        for i2,name2 in enumerate(varyNames):
            try:
                vcov[i1][i2] = covMatrix[varyList.index(name1)][varyList.index(name2)]
            except ValueError:
                vcov[i1][i2] = 0.0
    return vcov
    
def getCellEsd(pfx,SGData,A,covData):
    dpr = 180./np.pi
    rVsq = G2lat.calc_rVsq(A)
    G,g = G2lat.A2Gmat(A)       #get recip. & real metric tensors
    cell = np.array(G2lat.Gmat2cell(g))   #real cell
    cellst = np.array(G2lat.Gmat2cell(G)) #recip. cell
    scos = cosd(cellst[3:6])
    ssin = sind(cellst[3:6])
    scot = scos/ssin
    rcos = cosd(cell[3:6])
    rsin = sind(cell[3:6])
    rcot = rcos/rsin
    RMnames = [pfx+'A0',pfx+'A1',pfx+'A2',pfx+'A3',pfx+'A4',pfx+'A5']
    varyList = covData['varyList']
    covMatrix = covData['covMatrix']
    vcov = getVCov(RMnames,varyList,covMatrix)
    Ax = np.array(A)
    Ax[3:] /= 2.
    drVdA = np.array([Ax[1]*Ax[2]-Ax[5]**2,Ax[0]*Ax[2]-Ax[4]**2,Ax[0]*Ax[1]-Ax[3]**2,
        Ax[4]*Ax[5]-Ax[2]*Ax[3],Ax[3]*Ax[5]-Ax[1]*Ax[4],Ax[3]*Ax[4]-Ax[0]*Ax[5]])
    srcvlsq = np.inner(drVdA,np.inner(vcov,drVdA.T))
    Vol = 1/np.sqrt(rVsq)
    sigVol = Vol**3*np.sqrt(srcvlsq)/2.
    R123 = Ax[0]*Ax[1]*Ax[2]
    dsasdg = np.zeros((3,6))
    dadg = np.zeros((6,6))
    for i0 in range(3):         #0  1   2
        i1 = (i0+1)%3           #1  2   0
        i2 = (i1+1)%3           #2  0   1
        i3 = 5-i2               #3  5   4
        i4 = 5-i1               #4  3   5
        i5 = 5-i0               #5  4   3
        dsasdg[i0][i1] = 0.5*scot[i0]*scos[i0]/Ax[i1]
        dsasdg[i0][i2] = 0.5*scot[i0]*scos[i0]/Ax[i2]
        dsasdg[i0][i5] = -scot[i0]/np.sqrt(Ax[i1]*Ax[i2])
        denmsq = Ax[i0]*(R123-Ax[i1]*Ax[i4]**2-Ax[i2]*Ax[i3]**2+(Ax[i4]*Ax[i3])**2)
        denom = np.sqrt(denmsq)
        dadg[i5][i0] = -Ax[i5]/denom-rcos[i0]/denmsq*(R123-0.5*Ax[i1]*Ax[i4]**2-0.5*Ax[i2]*Ax[i3]**2)
        dadg[i5][i1] = -0.5*rcos[i0]/denmsq*(Ax[i0]**2*Ax[i2]-Ax[i0]*Ax[i4]**2)
        dadg[i5][i2] = -0.5*rcos[i0]/denmsq*(Ax[i0]**2*Ax[i1]-Ax[i0]*Ax[i3]**2)
        dadg[i5][i3] = Ax[i4]/denom+rcos[i0]/denmsq*(Ax[i0]*Ax[i2]*Ax[i3]-Ax[i3]*Ax[i4]**2)
        dadg[i5][i4] = Ax[i3]/denom+rcos[i0]/denmsq*(Ax[i0]*Ax[i1]*Ax[i4]-Ax[i3]**2*Ax[i4])
        dadg[i5][i5] = -Ax[i0]/denom
    for i0 in range(3):
        i1 = (i0+1)%3
        i2 = (i1+1)%3
        i3 = 5-i2
        for ij in range(6):
            dadg[i0][ij] = cell[i0]*(rcot[i2]*dadg[i3][ij]/rsin[i2]-dsasdg[i1][ij]/ssin[i1])
            if ij == i0:
                dadg[i0][ij] = dadg[i0][ij]-0.5*cell[i0]/Ax[i0]
            dadg[i3][ij] = -dadg[i3][ij]*rsin[2-i0]*dpr
    sigMat = np.inner(dadg,np.inner(vcov,dadg.T))
    var = np.diag(sigMat)
    CS = np.where(var>0.,np.sqrt(var),0.)
    cellSig = [CS[0],CS[1],CS[2],CS[5],CS[4],CS[3],sigVol]  #exchange sig(alp) & sig(gam) to get in right order
    return cellSig            
    
def SetPhaseData(parmDict,sigDict,Phases,covData):
    
    def cellFill(pfx,SGData,parmDict,sigDict): 
        if SGData['SGLaue'] in ['-1',]:
            A = [parmDict[pfx+'A0'],parmDict[pfx+'A1'],parmDict[pfx+'A2'],
                parmDict[pfx+'A3'],parmDict[pfx+'A4'],parmDict[pfx+'A5']]
            sigA = [sigDict[pfx+'A0'],sigDict[pfx+'A1'],sigDict[pfx+'A2'],
                sigDict[pfx+'A3'],sigDict[pfx+'A4'],sigDict[pfx+'A5']]
        elif SGData['SGLaue'] in ['2/m',]:
            if SGData['SGUniq'] == 'a':
                A = [parmDict[pfx+'A0'],parmDict[pfx+'A1'],parmDict[pfx+'A2'],
                    parmDict[pfx+'A3'],0,0]
                sigA = [sigDict[pfx+'A0'],sigDict[pfx+'A1'],sigDict[pfx+'A2'],
                    sigDict[pfx+'A3'],0,0]
            elif SGData['SGUniq'] == 'b':
                A = [parmDict[pfx+'A0'],parmDict[pfx+'A1'],parmDict[pfx+'A2'],
                    0,parmDict[pfx+'A4'],0]
                sigA = [sigDict[pfx+'A0'],sigDict[pfx+'A1'],sigDict[pfx+'A2'],
                    0,sigDict[pfx+'A4'],0]
            else:
                A = [parmDict[pfx+'A0'],parmDict[pfx+'A1'],parmDict[pfx+'A2'],
                    0,0,parmDict[pfx+'A5']]
                sigA = [sigDict[pfx+'A0'],sigDict[pfx+'A1'],sigDict[pfx+'A2'],
                    0,0,sigDict[pfx+'A5']]
        elif SGData['SGLaue'] in ['mmm',]:
            A = [parmDict[pfx+'A0'],parmDict[pfx+'A1'],parmDict[pfx+'A2'],0,0,0]
            sigA = [sigDict[pfx+'A0'],sigDict[pfx+'A1'],sigDict[pfx+'A2'],0,0,0]
        elif SGData['SGLaue'] in ['4/m','4/mmm']:
            A = [parmDict[pfx+'A0'],parmDict[pfx+'A0'],parmDict[pfx+'A2'],0,0,0]
            sigA = [sigDict[pfx+'A0'],0,sigDict[pfx+'A2'],0,0,0]
        elif SGData['SGLaue'] in ['6/m','6/mmm','3m1', '31m', '3']:
            A = [parmDict[pfx+'A0'],parmDict[pfx+'A0'],parmDict[pfx+'A2'],
                parmDict[pfx+'A0'],0,0]
            sigA = [sigDict[pfx+'A0'],0,sigDict[pfx+'A2'],0,0,0]
        elif SGData['SGLaue'] in ['3R', '3mR']:
            A = [parmDict[pfx+'A0'],parmDict[pfx+'A0'],parmDict[pfx+'A0'],
                parmDict[pfx+'A3'],parmDict[pfx+'A3'],parmDict[pfx+'A3']]
            sigA = [sigDict[pfx+'A0'],0,0,sigDict[pfx+'A3'],0,0]
        elif SGData['SGLaue'] in ['m3m','m3']:
            A = [parmDict[pfx+'A0'],parmDict[pfx+'A0'],parmDict[pfx+'A0'],0,0,0]
            sigA = [sigDict[pfx+'A0'],0,0,0,0,0]
        return A,sigA
        
    def PrintAtomsAndSig(General,Atoms,atomsSig):
        print '\n Atoms:'
        line = '   name      x         y         z      frac   Uiso     U11     U22     U33     U12     U13     U23'
        if General['Type'] == 'magnetic':
            line += '   Mx     My     Mz'
        elif General['Type'] == 'macromolecular':
            line = ' res no  residue  chain '+line
        print line
        if General['Type'] == 'nuclear':
            print 135*'-'
            fmt = {0:'%7s',1:'%7s',3:'%10.5f',4:'%10.5f',5:'%10.5f',6:'%8.3f',10:'%8.5f',
                11:'%8.5f',12:'%8.5f',13:'%8.5f',14:'%8.5f',15:'%8.5f',16:'%8.5f'}
            noFXsig = {3:[10*' ','%10s'],4:[10*' ','%10s'],5:[10*' ','%10s'],6:[8*' ','%8s']}
            for i,at in enumerate(Atoms):
                name = fmt[0]%(at[0])+fmt[1]%(at[1])+':'
                valstr = ' values:'
                sigstr = ' sig   :'
                for ind in [3,4,5,6]:
                    sigind = str(i)+':'+str(ind)
                    valstr += fmt[ind]%(at[ind])                    
                    if sigind in atomsSig:
                        sigstr += fmt[ind]%(atomsSig[sigind])
                    else:
                        sigstr += noFXsig[ind][1]%(noFXsig[ind][0])
                if at[9] == 'I':
                    valstr += fmt[10]%(at[10])
                    if str(i)+':10' in atomsSig:
                        sigstr += fmt[10]%(atomsSig[str(i)+':10'])
                    else:
                        sigstr += 8*' '
                else:
                    valstr += 8*' '
                    sigstr += 8*' '
                    for ind in [11,12,13,14,15,16]:
                        sigind = str(i)+':'+str(ind)
                        valstr += fmt[ind]%(at[ind])
                        if sigind in atomsSig:                        
                            sigstr += fmt[ind]%(atomsSig[sigind])
                        else:
                            sigstr += 8*' '
                print name
                print valstr
                print sigstr
                
    def PrintSHtextureAndSig(textureData,SHtextureSig):
        print '\n Spherical harmonics texture: Order:' + str(textureData['Order'])
        names = ['omega','chi','phi']
        namstr = '  names :'
        ptstr =  '  values:'
        sigstr = '  esds  :'
        for name in names:
            namstr += '%12s'%(name)
            ptstr += '%12.3f'%(textureData['Sample '+name][1])
            if 'Sample '+name in SHtextureSig:
                sigstr += '%12.3f'%(SHtextureSig['Sample '+name])
            else:
                sigstr += 12*' '
        print namstr
        print ptstr
        print sigstr
        print '\n Texture coefficients:'
        namstr = '  names :'
        ptstr =  '  values:'
        sigstr = '  esds  :'
        SHcoeff = textureData['SH Coeff'][1]
        for name in SHcoeff:
            namstr += '%12s'%(name)
            ptstr += '%12.3f'%(SHcoeff[name])
            if name in SHtextureSig:
                sigstr += '%12.3f'%(SHtextureSig[name])
            else:
                sigstr += 12*' '
        print namstr
        print ptstr
        print sigstr
        
            
    print '\n Phases:'
    for phase in Phases:
        print ' Result for phase: ',phase
        Phase = Phases[phase]
        General = Phase['General']
        SGData = General['SGData']
        Atoms = Phase['Atoms']
        cell = General['Cell']
        textureData = General['SH Texture']
        pId = Phase['pId']
        pfx = str(pId)+'::'
        if cell[0]:
            A,sigA = cellFill(pfx,SGData,parmDict,sigDict)
            cellSig = getCellEsd(pfx,SGData,A,covData)  #includes sigVol
            print ' Reciprocal metric tensor: '
            ptfmt = "%15.9f"
            names = ['A11','A22','A33','A12','A13','A23']
            namstr = '  names :'
            ptstr =  '  values:'
            sigstr = '  esds  :'
            for name,a,siga in zip(names,A,sigA):
                namstr += '%15s'%(name)
                ptstr += ptfmt%(a)
                if siga:
                    sigstr += ptfmt%(siga)
                else:
                    sigstr += 15*' '
            print namstr
            print ptstr
            print sigstr
            cell[1:7] = G2lat.A2cell(A)
            cell[7] = G2lat.calc_V(A)
            print ' New unit cell:'
            ptfmt = ["%12.6f","%12.6f","%12.6f","%12.4f","%12.4f","%12.4f","%12.3f"]
            names = ['a','b','c','alpha','beta','gamma','Volume']
            namstr = '  names :'
            ptstr =  '  values:'
            sigstr = '  esds  :'
            for name,fmt,a,siga in zip(names,ptfmt,cell[1:8],cellSig):
                namstr += '%12s'%(name)
                ptstr += fmt%(a)
                if siga:
                    sigstr += fmt%(siga)
                else:
                    sigstr += 12*' '
            print namstr
            print ptstr
            print sigstr
            
        if 'Pawley' in Phase['General']['Type']:
            pawleyRef = Phase['Pawley ref']
            for i,refl in enumerate(pawleyRef):
                key = pfx+'PWLref:'+str(i)
                refl[6] = abs(parmDict[key])        #suppress negative Fsq
                if key in sigDict:
                    refl[7] = sigDict[key]
                else:
                    refl[7] = 0
        else:
            atomsSig = {}
            if General['Type'] == 'nuclear':
                for i,at in enumerate(Atoms):
                    names = {3:pfx+'Ax:'+str(i),4:pfx+'Ay:'+str(i),5:pfx+'Az:'+str(i),6:pfx+'Afrac:'+str(i),
                        10:pfx+'AUiso:'+str(i),11:pfx+'AU11:'+str(i),12:pfx+'AU22:'+str(i),13:pfx+'AU33:'+str(i),
                        14:pfx+'AU12:'+str(i),15:pfx+'AU13:'+str(i),16:pfx+'AU23:'+str(i)}
                    for ind in [3,4,5,6]:
                        at[ind] = parmDict[names[ind]]
                        if ind in [3,4,5]:
                            name = names[ind].replace('A','dA')
                        else:
                            name = names[ind]
                        if name in sigDict:
                            atomsSig[str(i)+':'+str(ind)] = sigDict[name]
                    if at[9] == 'I':
                        at[10] = parmDict[names[10]]
                        if names[10] in sigDict:
                            atomsSig[str(i)+':10'] = sigDict[names[10]]
                    else:
                        for ind in [11,12,13,14,15,16]:
                            at[ind] = parmDict[names[ind]]
                            if names[ind] in sigDict:
                                atomsSig[str(i)+':'+str(ind)] = sigDict[names[ind]]
            PrintAtomsAndSig(General,Atoms,atomsSig)
            
        if textureData['Order']:
            SHtextureSig = {}
            for name in ['omega','chi','phi']:
                aname = pfx+'SH '+name
                textureData['Sample '+name][1] = parmDict[aname]
                if aname in sigDict:
                    SHtextureSig['Sample '+name] = sigDict[aname]
            for name in textureData['SH Coeff'][1]:
                aname = pfx+name
                textureData['SH Coeff'][1][name] = parmDict[aname]
                if aname in sigDict:
                    SHtextureSig[name] = sigDict[aname]
            PrintSHtextureAndSig(textureData,SHtextureSig)

def GetHistogramPhaseData(Phases,Histograms,Print=True):
    
    def PrintSize(hapData):
        if hapData[0] in ['isotropic','uniaxial']:
            line = '\n Size model    : %9s'%(hapData[0])
            line += ' equatorial:'+'%12.3f'%(hapData[1][0])+' Refine? '+str(hapData[2][0])
            if hapData[0] == 'uniaxial':
                line += ' axial:'+'%12.3f'%(hapData[1][1])+' Refine? '+str(hapData[2][1])
            print line
        else:
            print '\n Size model    : %s'%(hapData[0])
            Snames = ['S11','S22','S33','S12','S13','S23']
            ptlbls = ' names :'
            ptstr =  ' values:'
            varstr = ' refine:'
            for i,name in enumerate(Snames):
                ptlbls += '%12s' % (name)
                ptstr += '%12.6f' % (hapData[4][i])
                varstr += '%12s' % (str(hapData[5][i]))
            print ptlbls
            print ptstr
            print varstr
        
    def PrintMuStrain(hapData,SGData):
        if hapData[0] in ['isotropic','uniaxial']:
            line = '\n Mustrain model: %9s'%(hapData[0])
            line += ' equatorial:'+'%12.1f'%(hapData[1][0])+' Refine? '+str(hapData[2][0])
            if hapData[0] == 'uniaxial':
                line += ' axial:'+'%12.1f'%(hapData[1][1])+' Refine? '+str(hapData[2][1])
            print line
        else:
            print '\n Mustrain model: %s'%(hapData[0])
            Snames = G2spc.MustrainNames(SGData)
            ptlbls = ' names :'
            ptstr =  ' values:'
            varstr = ' refine:'
            for i,name in enumerate(Snames):
                ptlbls += '%12s' % (name)
                ptstr += '%12.6f' % (hapData[4][i])
                varstr += '%12s' % (str(hapData[5][i]))
            print ptlbls
            print ptstr
            print varstr

    def PrintHStrain(hapData,SGData):
        print '\n Hydrostatic/elastic strain: '
        Hsnames = G2spc.HStrainNames(SGData)
        ptlbls = ' names :'
        ptstr =  ' values:'
        varstr = ' refine:'
        for i,name in enumerate(Hsnames):
            ptlbls += '%12s' % (name)
            ptstr += '%12.6f' % (hapData[0][i])
            varstr += '%12s' % (str(hapData[1][i]))
        print ptlbls
        print ptstr
        print varstr

    def PrintSHPO(hapData):
        print '\n Spherical harmonics preferred orientation: Order:' + \
            str(hapData[4])+' Refine? '+str(hapData[2])
        ptlbls = ' names :'
        ptstr =  ' values:'
        for item in hapData[5]:
            ptlbls += '%12s'%(item)
            ptstr += '%12.3f'%(hapData[5][item]) 
        print ptlbls
        print ptstr
    
    hapDict = {}
    hapVary = []
    controlDict = {}
    poType = {}
    poAxes = {}
    spAxes = {}
    spType = {}
    
    for phase in Phases:
        HistoPhase = Phases[phase]['Histograms']
        SGData = Phases[phase]['General']['SGData']
        cell = Phases[phase]['General']['Cell'][1:7]
        A = G2lat.cell2A(cell)
        pId = Phases[phase]['pId']
        for histogram in HistoPhase:
            try:
                Histogram = Histograms[histogram]
            except KeyError:                        
                #skip if histogram not included e.g. in a sequential refinement
                continue
            hapData = HistoPhase[histogram]
            hId = Histogram['hId']
            limits = Histogram['Limits'][1]
            inst = Histogram['Instrument Parameters']
            inst = dict(zip(inst[3],inst[1]))
            Zero = inst['Zero']
            if 'C' in inst['Type']:
                try:
                    wave = inst['Lam']
                except KeyError:
                    wave = inst['Lam1']
                dmin = wave/(2.0*sind(limits[1]/2.0))
            pfx = str(pId)+':'+str(hId)+':'
            for item in ['Scale','Extinction']:
                hapDict[pfx+item] = hapData[item][0]
                if hapData[item][1]:
                    hapVary.append(pfx+item)
            names = G2spc.HStrainNames(SGData)
            for i,name in enumerate(names):
                hapDict[pfx+name] = hapData['HStrain'][0][i]
                if hapData['HStrain'][1][i]:
                    hapVary.append(pfx+name)
            controlDict[pfx+'poType'] = hapData['Pref.Ori.'][0]
            if hapData['Pref.Ori.'][0] == 'MD':
                hapDict[pfx+'MD'] = hapData['Pref.Ori.'][1]
                controlDict[pfx+'MDAxis'] = hapData['Pref.Ori.'][3]
                if hapData['Pref.Ori.'][2]:
                    hapVary.append(pfx+'MD')
            else:                           #'SH' spherical harmonics
                controlDict[pfx+'SHord'] = hapData['Pref.Ori.'][4]
                controlDict[pfx+'SHncof'] = len(hapData['Pref.Ori.'][5])
                for item in hapData['Pref.Ori.'][5]:
                    hapDict[pfx+item] = hapData['Pref.Ori.'][5][item]
                    if hapData['Pref.Ori.'][2]:
                        hapVary.append(pfx+item)
            for item in ['Mustrain','Size']:
                controlDict[pfx+item+'Type'] = hapData[item][0]
                if hapData[item][0] in ['isotropic','uniaxial']:
                    hapDict[pfx+item+':0'] = hapData[item][1][0]
                    if hapData[item][2][0]:
                        hapVary.append(pfx+item+':0')
                    if hapData[item][0] == 'uniaxial':
                        controlDict[pfx+item+'Axis'] = hapData[item][3]
                        hapDict[pfx+item+':1'] = hapData[item][1][1]
                        if hapData[item][2][1]:
                            hapVary.append(pfx+item+':1')
                else:       #generalized for mustrain or ellipsoidal for size
                    if item == 'Mustrain':
                        names = G2spc.MustrainNames(SGData)
                        pwrs = []
                        for name in names:
                            h,k,l = name[1:]
                            pwrs.append([int(h),int(k),int(l)])
                        controlDict[pfx+'MuPwrs'] = pwrs
                    for i in range(len(hapData[item][4])):
                        sfx = ':'+str(i)
                        hapDict[pfx+item+sfx] = hapData[item][4][i]
                        if hapData[item][5][i]:
                            hapVary.append(pfx+item+sfx)
                            
            if Print: 
                print '\n Phase: ',phase,' in histogram: ',histogram
                print 135*'-'
                print ' Phase fraction  : %10.4f'%(hapData['Scale'][0]),' Refine?',hapData['Scale'][1]
                print ' Extinction coeff: %10.4f'%(hapData['Extinction'][0]),' Refine?',hapData['Extinction'][1]
                if hapData['Pref.Ori.'][0] == 'MD':
                    Ax = hapData['Pref.Ori.'][3]
                    print ' March-Dollase PO: %10.4f'%(hapData['Pref.Ori.'][1]),' Refine?',hapData['Pref.Ori.'][2], \
                        ' Axis: %d %d %d'%(Ax[0],Ax[1],Ax[2])
                else: #'SH' for spherical harmonics
                    PrintSHPO(hapData['Pref.Ori.'])
                PrintSize(hapData['Size'])
                PrintMuStrain(hapData['Mustrain'],SGData)
                PrintHStrain(hapData['HStrain'],SGData)
            HKLd = np.array(G2lat.GenHLaue(dmin,SGData,A))
            refList = []
            for h,k,l,d in HKLd:
                ext,mul,Uniq,phi = G2spc.GenHKLf([h,k,l],SGData)
                if ext:
                    continue
                if 'C' in inst['Type']:
                    pos = 2.0*asind(wave/(2.0*d))
                    if limits[0] < pos < limits[1]:
                        refList.append([h,k,l,mul,d,pos,0.0,0.0,0.0,0.0,0.0,Uniq,phi,0.0])
                else:
                    raise ValueError 
            Histogram['Reflection Lists'][phase] = refList
    return hapVary,hapDict,controlDict
    
def SetHistogramPhaseData(parmDict,sigDict,Phases,Histograms,Print=True):
    
    def PrintSizeAndSig(hapData,sizeSig):
        line = '\n Size model:     %9s'%(hapData[0])
        if hapData[0] in ['isotropic','uniaxial']:
            line += ' equatorial:%12.3f'%(hapData[1][0])
            if sizeSig[0][0]:
                line += ', sig: %8.3f'%(sizeSig[0][0])
            if hapData[0] == 'uniaxial':
                line += ' axial:%12.3f'%(hapData[1][1])
                if sizeSig[0][1]:
                    line += ', sig: %8.3f'%(sizeSig[0][1])
            print line
        else:
            print line
            Snames = ['S11','S22','S33','S12','S13','S23']
            ptlbls = ' name  :'
            ptstr =  ' value :'
            sigstr = ' sig   :'
            for i,name in enumerate(Snames):
                ptlbls += '%12s' % (name)
                ptstr += '%12.6f' % (hapData[4][i])
                if sizeSig[1][i]:
                    sigstr += '%12.6f' % (sizeSig[1][i])
                else:
                    sigstr += 12*' '
            print ptlbls
            print ptstr
            print sigstr
        
    def PrintMuStrainAndSig(hapData,mustrainSig,SGData):
        line = '\n Mustrain model: %9s'%(hapData[0])
        if hapData[0] in ['isotropic','uniaxial']:
            line += ' equatorial:%12.1f'%(hapData[1][0])
            if mustrainSig[0][0]:
                line += ', sig: %8.1f'%(mustrainSig[0][0])
            if hapData[0] == 'uniaxial':
                line += ' axial:%12.1f'%(hapData[1][1])
                if mustrainSig[0][1]:
                     line += ', sig: %8.1f'%(mustrainSig[0][1])
            print line
        else:
            print line
            Snames = G2spc.MustrainNames(SGData)
            ptlbls = ' name  :'
            ptstr =  ' value :'
            sigstr = ' sig   :'
            for i,name in enumerate(Snames):
                ptlbls += '%12s' % (name)
                ptstr += '%12.6f' % (hapData[4][i])
                if mustrainSig[1][i]:
                    sigstr += '%12.6f' % (mustrainSig[1][i])
                else:
                    sigstr += 12*' '
            print ptlbls
            print ptstr
            print sigstr
            
    def PrintHStrainAndSig(hapData,strainSig,SGData):
        print '\n Hydrostatic/elastic strain: '
        Hsnames = G2spc.HStrainNames(SGData)
        ptlbls = ' name  :'
        ptstr =  ' value :'
        sigstr = ' sig   :'
        for i,name in enumerate(Hsnames):
            ptlbls += '%12s' % (name)
            ptstr += '%12.6g' % (hapData[0][i])
            if name in strainSig:
                sigstr += '%12.6g' % (strainSig[name])
            else:
                sigstr += 12*' '
        print ptlbls
        print ptstr
        print sigstr
        
    def PrintSHPOAndSig(hapData,POsig):
        print '\n Spherical harmonics preferred orientation: Order:'+str(hapData[4])
        ptlbls = ' names :'
        ptstr =  ' values:'
        sigstr = ' sig   :'
        for item in hapData[5]:
            ptlbls += '%12s'%(item)
            ptstr += '%12.3f'%(hapData[5][item])
            if item in POsig:
                sigstr += '%12.3f'%(POsig[item])
            else:
                sigstr += 12*' ' 
        print ptlbls
        print ptstr
        print sigstr
    
    for phase in Phases:
        HistoPhase = Phases[phase]['Histograms']
        SGData = Phases[phase]['General']['SGData']
        pId = Phases[phase]['pId']
        for histogram in HistoPhase:
            try:
                Histogram = Histograms[histogram]
            except KeyError:                        
                #skip if histogram not included e.g. in a sequential refinement
                continue
            print '\n Phase: ',phase,' in histogram: ',histogram
            print 130*'-'
            hapData = HistoPhase[histogram]
            hId = Histogram['hId']
            pfx = str(pId)+':'+str(hId)+':'
            print ' Final refinement RF, RF^2 = %.2f%%, %.2f%% on %d reflections'   \
                %(Histogram[pfx+'Rf'],Histogram[pfx+'Rf^2'],Histogram[pfx+'Nref'])
            
            PhFrExtPOSig = {}
            for item in ['Scale','Extinction']:
                hapData[item][0] = parmDict[pfx+item]
                if pfx+item in sigDict:
                    PhFrExtPOSig[item] = sigDict[pfx+item]
            if hapData['Pref.Ori.'][0] == 'MD':
                hapData['Pref.Ori.'][1] = parmDict[pfx+'MD']
                if pfx+'MD' in sigDict:
                    PhFrExtPOSig['MD'] = sigDict[pfx+'MD']
            else:                           #'SH' spherical harmonics
                for item in hapData['Pref.Ori.'][5]:
                    hapData['Pref.Ori.'][5][item] = parmDict[pfx+item]
                    if pfx+item in sigDict:
                        PhFrExtPOSig[item] = sigDict[pfx+item]
            if Print:
                if 'Scale' in PhFrExtPOSig:
                    print ' Phase fraction  : %10.4f, sig %10.4f'%(hapData['Scale'][0],PhFrExtPOSig['Scale'])
                if 'Extinction' in PhFrExtPOSig:
                    print ' Extinction coeff: %10.4f, sig %10.4f'%(hapData['Extinction'][0],PhFrExtPOSig['Extinction'])
                if hapData['Pref.Ori.'][0] == 'MD':
                    if 'MD' in PhFrExtPOSig:
                        print ' March-Dollase PO: %10.4f, sig %10.4f'%(hapData['Pref.Ori.'][1],PhFrExtPOSig['MD'])
                else:
                    PrintSHPOAndSig(hapData['Pref.Ori.'],PhFrExtPOSig)
            SizeMuStrSig = {'Mustrain':[[0,0],[0 for i in range(len(hapData['Mustrain'][4]))]],
                'Size':[[0,0],[0 for i in range(len(hapData['Size'][4]))]],
                'HStrain':{}}                  
            for item in ['Mustrain','Size']:
                if hapData[item][0] in ['isotropic','uniaxial']:                    
                    hapData[item][1][0] = parmDict[pfx+item+':0']
                    if item == 'Size':
                        hapData[item][1][0] = min(10.,max(0.01,hapData[item][1][0]))
                    if pfx+item+':0' in sigDict: 
                        SizeMuStrSig[item][0][0] = sigDict[pfx+item+':0']
                    if hapData[item][0] == 'uniaxial':
                        hapData[item][1][1] = parmDict[pfx+item+':1']
                        if item == 'Size':
                            hapData[item][1][1] = min(10.,max(0.01,hapData[item][1][1]))                        
                        if pfx+item+':1' in sigDict:
                            SizeMuStrSig[item][0][1] = sigDict[pfx+item+':1']
                else:       #generalized for mustrain or ellipsoidal for size
                    for i in range(len(hapData[item][4])):
                        sfx = ':'+str(i)
                        hapData[item][4][i] = parmDict[pfx+item+sfx]
                        if pfx+item+sfx in sigDict:
                            SizeMuStrSig[item][1][i] = sigDict[pfx+item+sfx]
            names = G2spc.HStrainNames(SGData)
            for i,name in enumerate(names):
                hapData['HStrain'][0][i] = parmDict[pfx+name]
                if pfx+name in sigDict:
                    SizeMuStrSig['HStrain'][name] = sigDict[pfx+name]
            if Print:
                PrintSizeAndSig(hapData['Size'],SizeMuStrSig['Size'])
                PrintMuStrainAndSig(hapData['Mustrain'],SizeMuStrSig['Mustrain'],SGData)
                PrintHStrainAndSig(hapData['HStrain'],SizeMuStrSig['HStrain'],SGData)
    
def GetHistogramData(Histograms,Print=True):
    
    def GetBackgroundParms(hId,Background):
        bakType,bakFlag = Background[:2]
        backVals = Background[3:]
        backNames = [':'+str(hId)+':Back:'+str(i) for i in range(len(backVals))]
        if bakFlag:                                 #returns backNames as varyList = backNames
            return bakType,dict(zip(backNames,backVals)),backNames
        else:                                       #no background varied; varyList = []
            return bakType,dict(zip(backNames,backVals)),[]
        
    def GetInstParms(hId,Inst):
        insVals,insFlags,insNames = Inst[1:4]
        dataType = insVals[0]
        instDict = {}
        insVary = []
        pfx = ':'+str(hId)+':'
        for i,flag in enumerate(insFlags):
            insName = pfx+insNames[i]
            instDict[insName] = insVals[i]
            if flag:
                insVary.append(insName)
        instDict[pfx+'X'] = max(instDict[pfx+'X'],0.01)
        instDict[pfx+'Y'] = max(instDict[pfx+'Y'],0.01)
        instDict[pfx+'SH/L'] = max(instDict[pfx+'SH/L'],0.0005)
        return dataType,instDict,insVary
        
    def GetSampleParms(hId,Sample):
        sampVary = []
        hfx = ':'+str(hId)+':'        
        sampDict = {hfx+'Gonio. radius':Sample['Gonio. radius'],hfx+'Omega':Sample['Omega'],
            hfx+'Chi':Sample['Chi'],hfx+'Phi':Sample['Phi']}
        Type = Sample['Type']
        if 'Bragg' in Type:             #Bragg-Brentano
            for item in ['Scale','Shift','Transparency']:       #surface roughness?, diffuse scattering?
                sampDict[hfx+item] = Sample[item][0]
                if Sample[item][1]:
                    sampVary.append(hfx+item)
        elif 'Debye' in Type:        #Debye-Scherrer
            for item in ['Scale','Absorption','DisplaceX','DisplaceY']:
                sampDict[hfx+item] = Sample[item][0]
                if Sample[item][1]:
                    sampVary.append(hfx+item)
        return Type,sampDict,sampVary
        
    def PrintBackground(Background):
        print '\n Background function: ',Background[0],' Refine?',bool(Background[1])
        line = ' Coefficients: '
        for i,back in enumerate(Background[3:]):
            line += '%10.3f'%(back)
            if i and not i%10:
                line += '\n'+15*' '
        print line 
        
    def PrintInstParms(Inst):
        print '\n Instrument Parameters:'
        ptlbls = ' name  :'
        ptstr =  ' value :'
        varstr = ' refine:'
        instNames = Inst[3][1:]
        for i,name in enumerate(instNames):
            ptlbls += '%12s' % (name)
            ptstr += '%12.6f' % (Inst[1][i+1])
            if name in ['Lam1','Lam2','Azimuth']:
                varstr += 12*' '
            else:
                varstr += '%12s' % (str(bool(Inst[2][i+1])))
        print ptlbls
        print ptstr
        print varstr
        
    def PrintSampleParms(Sample):
        print '\n Sample Parameters:'
        print ' Goniometer omega = %.2f, chi = %.2f, phi = %.2f'% \
            (Sample['Omega'],Sample['Chi'],Sample['Phi'])
        ptlbls = ' name  :'
        ptstr =  ' value :'
        varstr = ' refine:'
        if 'Bragg' in Sample['Type']:
            for item in ['Scale','Shift','Transparency']:
                ptlbls += '%14s'%(item)
                ptstr += '%14.4f'%(Sample[item][0])
                varstr += '%14s'%(str(bool(Sample[item][1])))
            
        elif 'Debye' in Type:        #Debye-Scherrer
            for item in ['Scale','Absorption','DisplaceX','DisplaceY']:
                ptlbls += '%14s'%(item)
                ptstr += '%14.4f'%(Sample[item][0])
                varstr += '%14s'%(str(bool(Sample[item][1])))

        print ptlbls
        print ptstr
        print varstr
        

    histDict = {}
    histVary = []
    controlDict = {}
    for histogram in Histograms:
        Histogram = Histograms[histogram]
        hId = Histogram['hId']
        pfx = ':'+str(hId)+':'
        controlDict[pfx+'Limits'] = Histogram['Limits'][1]
        
        Background = Histogram['Background'][0]
        Type,bakDict,bakVary = GetBackgroundParms(hId,Background)
        controlDict[pfx+'bakType'] = Type
        histDict.update(bakDict)
        histVary += bakVary
        
        Inst = Histogram['Instrument Parameters']
        Type,instDict,insVary = GetInstParms(hId,Inst)
        controlDict[pfx+'histType'] = Type
        if pfx+'Lam1' in instDict:
            controlDict[pfx+'keV'] = 12.397639/instDict[pfx+'Lam1']
        else:
            controlDict[pfx+'keV'] = 12.397639/instDict[pfx+'Lam']            
        histDict.update(instDict)
        histVary += insVary
        
        Sample = Histogram['Sample Parameters']
        Type,sampDict,sampVary = GetSampleParms(hId,Sample)
        controlDict[pfx+'instType'] = Type
        histDict.update(sampDict)
        histVary += sampVary

        if Print: 
            print '\n Histogram: ',histogram,' histogram Id: ',hId
            print 135*'-'
            Units = {'C':' deg','T':' msec'}
            units = Units[controlDict[pfx+'histType'][2]]
            Limits = controlDict[pfx+'Limits']
            print ' Instrument type: ',Sample['Type']
            print ' Histogram limits: %8.2f%s to %8.2f%s'%(Limits[0],units,Limits[1],units)     
            PrintSampleParms(Sample)
            PrintInstParms(Inst)
            PrintBackground(Background)
        
    return histVary,histDict,controlDict
    
def SetHistogramData(parmDict,sigDict,Histograms,Print=True):
    
    def SetBackgroundParms(pfx,Background,parmDict,sigDict):
        lenBack = len(Background[3:])
        backSig = [0 for i in range(lenBack)]
        for i in range(lenBack):
            Background[3+i] = parmDict[pfx+'Back:'+str(i)]
            if pfx+'Back:'+str(i) in sigDict:
                backSig[i] = sigDict[pfx+'Back:'+str(i)]
        return backSig
        
    def SetInstParms(pfx,Inst,parmDict,sigDict):
        insVals,insFlags,insNames = Inst[1:4]
        instSig = [0 for i in range(len(insVals))]
        for i,flag in enumerate(insFlags):
            insName = pfx+insNames[i]
            insVals[i] = parmDict[insName]
            if insName in sigDict:
                instSig[i] = sigDict[insName]
        return instSig
        
    def SetSampleParms(pfx,Sample,parmDict,sigDict):
        if 'Bragg' in Sample['Type']:             #Bragg-Brentano
            sampSig = [0 for i in range(3)]
            for i,item in enumerate(['Scale','Shift','Transparency']):       #surface roughness?, diffuse scattering?
                Sample[item][0] = parmDict[pfx+item]
                if pfx+item in sigDict:
                    sampSig[i] = sigDict[pfx+item]
        elif 'Debye' in Sample['Type']:        #Debye-Scherrer
            sampSig = [0 for i in range(4)]
            for i,item in enumerate(['Scale','Absorption','DisplaceX','DisplaceY']):
                Sample[item][0] = parmDict[pfx+item]
                if pfx+item in sigDict:
                    sampSig[i] = sigDict[pfx+item]
        return sampSig
        
    def PrintBackgroundSig(Background,backSig):
        print '\n Background function: ',Background[0]
        valstr = ' value : '
        sigstr = ' sig   : '
        for i,back in enumerate(Background[3:]):
            valstr += '%10.4f'%(back)
            if Background[1]:
                sigstr += '%10.4f'%(backSig[i])
            else:
                sigstr += 10*' '
        print valstr
        print sigstr 
        
    def PrintInstParmsSig(Inst,instSig):
        print '\n Instrument Parameters:'
        ptlbls = ' names :'
        ptstr =  ' value :'
        sigstr = ' sig   :'
        instNames = Inst[3][1:]
        for i,name in enumerate(instNames):
            ptlbls += '%12s' % (name)
            ptstr += '%12.6f' % (Inst[1][i+1])
            if instSig[i+1]:
                sigstr += '%12.6f' % (instSig[i+1])
            else:
                sigstr += 12*' '
        print ptlbls
        print ptstr
        print sigstr
        
    def PrintSampleParmsSig(Sample,sampleSig):
        print '\n Sample Parameters:'
        ptlbls = ' names :'
        ptstr =  ' values:'
        sigstr = ' sig   :'
        if 'Bragg' in Sample['Type']:
            for i,item in enumerate(['Scale','Shift','Transparency']):
                ptlbls += '%14s'%(item)
                ptstr += '%14.4f'%(Sample[item][0])
                if sampleSig[i]:
                    sigstr += '%14.4f'%(sampleSig[i])
                else:
                    sigstr += 14*' '
            
        elif 'Debye' in Sample['Type']:        #Debye-Scherrer
            for i,item in enumerate(['Scale','Absorption','DisplaceX','DisplaceY']):
                ptlbls += '%14s'%(item)
                ptstr += '%14.4f'%(Sample[item][0])
                if sampleSig[i]:
                    sigstr += '%14.4f'%(sampleSig[i])
                else:
                    sigstr += 14*' '

        print ptlbls
        print ptstr
        print sigstr
        
    for histogram in Histograms:
        if 'PWDR' in histogram:
            Histogram = Histograms[histogram]
            hId = Histogram['hId']
            pfx = ':'+str(hId)+':'
            Background = Histogram['Background'][0]
            backSig = SetBackgroundParms(pfx,Background,parmDict,sigDict)
            
            Inst = Histogram['Instrument Parameters']
            instSig = SetInstParms(pfx,Inst,parmDict,sigDict)
        
            Sample = Histogram['Sample Parameters']
            sampSig = SetSampleParms(pfx,Sample,parmDict,sigDict)

            print '\n Histogram: ',histogram,' histogram Id: ',hId
            print 135*'-'
            print ' Final refinement wRp = %.2f%% on %d observations in this histogram'%(Histogram['wRp'],Histogram['Nobs'])
            if Print:
                print ' Instrument type: ',Sample['Type']
                PrintSampleParmsSig(Sample,sampSig)
                PrintInstParmsSig(Inst,instSig)
                PrintBackgroundSig(Background,backSig)

def GetAtomFXU(pfx,FFtables,calcControls,parmDict):
    Natoms = calcControls['Natoms'][pfx]
    Tdata = Natoms*[' ',]
    Mdata = np.zeros(Natoms)
    IAdata = Natoms*[' ',]
    Fdata = np.zeros(Natoms)
    FFdata = []
    Xdata = np.zeros((3,Natoms))
    dXdata = np.zeros((3,Natoms))
    Uisodata = np.zeros(Natoms)
    Uijdata = np.zeros((6,Natoms))
    keys = {'Atype:':Tdata,'Amul:':Mdata,'Afrac:':Fdata,'AI/A:':IAdata,
        'dAx:':dXdata[0],'dAy:':dXdata[1],'dAz:':dXdata[2],
        'Ax:':Xdata[0],'Ay:':Xdata[1],'Az:':Xdata[2],'AUiso:':Uisodata,
        'AU11:':Uijdata[0],'AU22:':Uijdata[1],'AU33:':Uijdata[2],
        'AU12:':Uijdata[3],'AU13:':Uijdata[4],'AU23:':Uijdata[5]}
    for iatm in range(Natoms):
        for key in keys:
            parm = pfx+key+str(iatm)
            if parm in parmDict:
                keys[key][iatm] = parmDict[parm]
        FFdata.append(FFtables[Tdata[iatm]])
    return FFdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata
    
def StructureFactor(refList,G,hfx,pfx,SGData,calcControls,parmDict):
    ''' Compute structure factors for all h,k,l for phase
    input:
        refList: [ref] where each ref = h,k,l,m,d,...,[equiv h,k,l],phase[equiv] 
        G:      reciprocal metric tensor
        pfx:    phase id string
        SGData: space group info. dictionary output from SpcGroup
        calcControls:
        ParmDict:
    puts result F^2 in each ref[8] in refList
    '''        
    twopi = 2.0*np.pi
    twopisq = 2.0*np.pi**2
    ast = np.sqrt(np.diag(G))
    Mast = twopisq*np.multiply.outer(ast,ast)
    FFtables = calcControls['FFtables']
    FFdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata = GetAtomFXU(pfx,FFtables,calcControls,parmDict)
    FP = np.array([El[hfx+'FP'] for El in FFdata])
    FPP = np.array([El[hfx+'FPP'] for El in FFdata])
    maxPos = len(SGData['SGOps'])
    Uij = np.array(G2lat.U6toUij(Uijdata))
    bij = Mast*Uij.T
    for refl in refList:
        fbs = np.array([0,0])
        H = refl[:3]
        SQ = 1./(2.*refl[4])**2
        FF = np.array([G2el.ScatFac(El,SQ)[0] for El in FFdata])
        SQfactor = 4.0*SQ*twopisq
        Uniq = refl[11]
        phi = refl[12]
        phase = twopi*(np.inner(Uniq,(dXdata.T+Xdata.T))+phi[:,np.newaxis])
        sinp = np.sin(phase)
        cosp = np.cos(phase)
        occ = Mdata*Fdata/len(Uniq)
        biso = -SQfactor*Uisodata
        Tiso = np.where(biso<1.,np.exp(biso),1.0)
        HbH = np.array([-np.inner(h,np.inner(bij,h)) for h in Uniq])
        Tuij = np.where(HbH<1.,np.exp(HbH),1.0)
        Tcorr = Tiso*Tuij
        fa = np.array([(FF+FP)*occ*cosp*Tcorr,-FPP*occ*sinp*Tcorr])
        fas = np.sum(np.sum(fa,axis=1),axis=1)        #real
        if not SGData['SGInv']:
            fb = np.array([(FF+FP)*occ*sinp*Tcorr,FPP*occ*cosp*Tcorr])
            fbs = np.sum(np.sum(fb,axis=1),axis=1)
        fasq = fas**2
        fbsq = fbs**2        #imaginary
        refl[9] = np.sum(fasq)+np.sum(fbsq)
        refl[10] = atan2d(fbs[0],fas[0])
    return refList
    
def StructureFactorDerv(refList,G,hfx,pfx,SGData,calcControls,parmDict):
    twopi = 2.0*np.pi
    twopisq = 2.0*np.pi**2
    ast = np.sqrt(np.diag(G))
    Mast = twopisq*np.multiply.outer(ast,ast)
    FFtables = calcControls['FFtables']
    FFdata,Mdata,Fdata,Xdata,dXdata,IAdata,Uisodata,Uijdata = GetAtomFXU(pfx,FFtables,calcControls,parmDict)
    FP = np.array([El[hfx+'FP'] for El in FFdata])
    FPP = np.array([El[hfx+'FPP'] for El in FFdata])
    maxPos = len(SGData['SGOps'])       
    Uij = np.array(G2lat.U6toUij(Uijdata))
    bij = Mast*Uij.T
    dFdvDict = {}
    dFdfr = np.zeros((len(refList),len(Mdata)))
    dFdx = np.zeros((len(refList),len(Mdata),3))
    dFdui = np.zeros((len(refList),len(Mdata)))
    dFdua = np.zeros((len(refList),len(Mdata),6))
    for iref,refl in enumerate(refList):
        H = np.array(refl[:3])
        SQ = 1./(2.*refl[4])**2          # or (sin(theta)/lambda)**2
        FF = np.array([G2el.ScatFac(El,SQ)[0] for El in FFdata])
        SQfactor = 8.0*SQ*np.pi**2
        Uniq = refl[11]
        phi = refl[12]
        phase = twopi*(np.inner((dXdata.T+Xdata.T),Uniq)+phi[np.newaxis,:])
        sinp = np.sin(phase)
        cosp = np.cos(phase)
        occ = Mdata*Fdata/len(Uniq)
        biso = -SQfactor*Uisodata
        Tiso = np.where(biso<1.,np.exp(biso),1.0)
#        HbH = np.array([-np.inner(h,np.inner(bij,h)) for h in Uniq])
        HbH = -np.inner(H,np.inner(bij,H))
        Hij = np.array([Mast*np.multiply.outer(U,U) for U in Uniq])
        Hij = np.array([G2lat.UijtoU6(Uij) for Uij in Hij])
        Tuij = np.where(HbH<1.,np.exp(HbH),1.0)
        Tcorr = Tiso*Tuij
        fot = (FF+FP)*occ*Tcorr
        fotp = FPP*occ*Tcorr
        fa = np.array([fot[:,np.newaxis]*cosp,fotp[:,np.newaxis]*cosp])       #non positions
        fb = np.array([fot[:,np.newaxis]*sinp,-fotp[:,np.newaxis]*sinp])
        
        fas = np.sum(np.sum(fa,axis=1),axis=1)
        fbs = np.sum(np.sum(fb,axis=1),axis=1)
        fax = np.array([-fot[:,np.newaxis]*sinp,-fotp[:,np.newaxis]*sinp])   #positions
        fbx = np.array([fot[:,np.newaxis]*cosp,-fot[:,np.newaxis]*cosp])
        #sum below is over Uniq
        dfadfr = np.sum(fa/occ[:,np.newaxis],axis=2)
        dfadx = np.sum(twopi*Uniq*fax[:,:,:,np.newaxis],axis=2)
        dfadui = np.sum(-SQfactor*fa,axis=2)
        dfadua = np.sum(-Hij*fa[:,:,:,np.newaxis],axis=2)
        #NB: the above have been checked against PA(1:10,1:2) in strfctr.for      
        dFdfr[iref] = 2.*(fas[0]*dfadfr[0]+fas[1]*dfadfr[1])*Mdata/len(Uniq)
        dFdx[iref] = 2.*(fas[0]*dfadx[0]+fas[1]*dfadx[1])
        dFdui[iref] = 2.*(fas[0]*dfadui[0]+fas[1]*dfadui[1])
        dFdua[iref] = 2.*(fas[0]*dfadua[0]+fas[1]*dfadua[1])
        if not SGData['SGInv']:
            dfbdfr = np.sum(fb/occ[:,np.newaxis],axis=2)
            dfbdx = np.sum(twopi*Uniq*fbx[:,:,:,np.newaxis],axis=2)          
            dfbdui = np.sum(-SQfactor*fb,axis=2)
            dfbdua = np.sum(-Hij*fb[:,:,:,np.newaxis],axis=2)
            dFdfr[iref] += 2.*(fbs[0]*dfbdfr[0]-fbs[1]*dfbdfr[1])*Mdata/len(Uniq)
            dFdx[iref] += 2.*(fbs[0]*dfbdx[0]+fbs[1]*dfbdx[1])
            dFdui[iref] += 2.*(fbs[0]*dfbdui[0]-fbs[1]*dfbdui[1])
            dFdua[iref] += 2.*(fbs[0]*dfbdua[0]+fbs[1]*dfbdua[1])
        #loop over atoms - each dict entry is list of derivatives for all the reflections
    for i in range(len(Mdata)):     
        dFdvDict[pfx+'Afrac:'+str(i)] = dFdfr.T[i]
        dFdvDict[pfx+'dAx:'+str(i)] = dFdx.T[0][i]
        dFdvDict[pfx+'dAy:'+str(i)] = dFdx.T[1][i]
        dFdvDict[pfx+'dAz:'+str(i)] = dFdx.T[2][i]
        dFdvDict[pfx+'AUiso:'+str(i)] = dFdui.T[i]
        dFdvDict[pfx+'AU11:'+str(i)] = dFdua.T[0][i]
        dFdvDict[pfx+'AU22:'+str(i)] = dFdua.T[1][i]
        dFdvDict[pfx+'AU33:'+str(i)] = dFdua.T[2][i]
        dFdvDict[pfx+'AU12:'+str(i)] = 2.*dFdua.T[3][i]
        dFdvDict[pfx+'AU13:'+str(i)] = 2.*dFdua.T[4][i]
        dFdvDict[pfx+'AU23:'+str(i)] = 2.*dFdua.T[5][i]
    return dFdvDict
        
def Dict2Values(parmdict, varylist):
    '''Use before call to leastsq to setup list of values for the parameters 
    in parmdict, as selected by key in varylist'''
    return [parmdict[key] for key in varylist] 
    
def Values2Dict(parmdict, varylist, values):
    ''' Use after call to leastsq to update the parameter dictionary with 
    values corresponding to keys in varylist'''
    parmdict.update(zip(varylist,values))
    
def ApplyXYZshifts(parmDict,varyList):
    ''' takes atom x,y,z shift and applies it to corresponding atom x,y,z value
        input:
            parmDict - parameter dictionary
            varyList - list of variables
        returns:
            newAtomDict - dictionary of new atomic coordinate names & values; 
                key is parameter shift name
    '''
    newAtomDict = {}
    for item in parmDict:
        if 'dA' in item:
            parm = ''.join(item.split('d'))
            parmDict[parm] += parmDict[item]
            newAtomDict[item] = [parm,parmDict[parm]]
    return newAtomDict
    
def SHTXcal(refl,g,pfx,hfx,SGData,calcControls,parmDict):
    IFCoup = 'Bragg' in calcControls[hfx+'instType']
    odfCor = 1.0
    H = refl[:3]
    cell = G2lat.Gmat2cell(g)
    Sangls = [parmDict[pfx+'SH omega'],parmDict[pfx+'SH chi'],parmDict[pfx+'SH phi']]
    Gangls = [parmDict[hfx+'Omega'],parmDict[hfx+'Chi'],parmDict[hfx+'Phi'],parmDict[hfx+'Azimuth']]
    phi,beta = G2lat.CrsAng(H,cell,SGData)
    psi,gam,x,x = G2lat.SamAng(refl[5]/2.,Gangls,Sangls,IFCoup) #ignore 2 sets of angle derivs.
    SHnames = G2lat.GenSHCoeff(SGData['SGLaue'],parmDict[pfx+'SHmodel'],parmDict[pfx+'SHorder'])
    for item in SHnames:
        L,M,N = eval(item.strip('C'))
        Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta)
        Ksl,x,x = G2lat.GetKsl(L,M,parmDict[pfx+'SHmodel'],psi,gam)
        Lnorm = G2lat.Lnorm(L)
        odfCor += parmDict[pfx+item]*Lnorm*Kcl*Ksl
    return odfCor
    
def SHTXcalDerv(refl,g,pfx,hfx,SGData,calcControls,parmDict):
    FORPI = 12.5663706143592
    IFCoup = 'Bragg' in calcControls[hfx+'instType']
    odfCor = 1.0
    dFdODF = {}
    dFdSA = [0,0,0]
    H = refl[:3]
    cell = G2lat.Gmat2cell(g)
    Sangls = [parmDict[pfx+'SH omega'],parmDict[pfx+'SH chi'],parmDict[pfx+'SH phi']]
    Gangls = [parmDict[hfx+'Omega'],parmDict[hfx+'Chi'],parmDict[hfx+'Phi'],parmDict[hfx+'Azimuth']]
    phi,beta = G2lat.CrsAng(H,cell,SGData)
    psi,gam,dPSdA,dGMdA = G2lat.SamAng(refl[5]/2.,Gangls,Sangls,IFCoup)
    SHnames = G2lat.GenSHCoeff(SGData['SGLaue'],parmDict[pfx+'SHmodel'],parmDict[pfx+'SHorder'])
    for item in SHnames:
        L,M,N = eval(item.strip('C'))
        Kcl = G2lat.GetKcl(L,N,SGData['SGLaue'],phi,beta)
        Ksl,dKsdp,dKsdg = G2lat.GetKsl(L,M,parmDict[pfx+'SHmodel'],psi,gam)
        Lnorm = G2lat.Lnorm(L)
        odfCor += parmDict[pfx+item]*Lnorm*Kcl*Ksl
        dFdODF[pfx+item] = Lnorm*Kcl*Ksl
        for i in range(3):
            dFdSA[i] += parmDict[pfx+item]*Lnorm*Kcl*(dKsdp*dPSdA[i]+dKsdg*dGMdA[i])
    return odfCor,dFdODF,dFdSA
    
def SHPOcal(refl,g,phfx,hfx,SGData,calcControls,parmDict):
    odfCor = 1.0
    H = refl[:3]
    cell = G2lat.Gmat2cell(g)
    Sangl = [0.,0.,0.]
    if 'Bragg' in calcControls[hfx+'instType']:
        Gangls = [0.,90.,0.,parmDict[hfx+'Azimuth']]
        IFCoup = True
    else:
        Gangls = [0.,0.,0.,parmDict[hfx+'Azimuth']]
        IFCoup = False
    phi,beta = G2lat.CrsAng(H,cell,SGData)
    psi,gam,x,x = G2lat.SamAng(refl[5]/2.,Gangls,Sangl,IFCoup) #ignore 2 sets of angle derivs.
    SHnames = G2lat.GenSHCoeff(SGData['SGLaue'],'0',calcControls[phfx+'SHord'],False)
    for item in SHnames:
        L,N = eval(item.strip('C'))
        Kcsl,Lnorm = G2lat.GetKclKsl(L,N,SGData['SGLaue'],psi,phi,beta) 
        odfCor += parmDict[phfx+item]*Lnorm*Kcsl
    return odfCor
    
def SHPOcalDerv(refl,g,phfx,hfx,SGData,calcControls,parmDict):
    FORPI = 12.5663706143592
    odfCor = 1.0
    dFdODF = {}
    H = refl[:3]
    cell = G2lat.Gmat2cell(g)
    Sangl = [0.,0.,0.]
    if 'Bragg' in calcControls[hfx+'instType']:
        Gangls = [0.,90.,0.,parmDict[hfx+'Azimuth']]
        IFCoup = True
    else:
        Gangls = [0.,0.,0.,parmDict[hfx+'Azimuth']]
        IFCoup = False
    phi,beta = G2lat.CrsAng(H,cell,SGData)
    psi,gam,x,x = G2lat.SamAng(refl[5]/2.,Gangls,Sangl,IFCoup) #ignore 2 sets of angle derivs.
    SHnames = G2lat.GenSHCoeff(SGData['SGLaue'],'0',calcControls[phfx+'SHord'],False)
    for item in SHnames:
        L,N = eval(item.strip('C'))
        Kcsl,Lnorm = G2lat.GetKclKsl(L,N,SGData['SGLaue'],psi,phi,beta) 
        odfCor += parmDict[phfx+item]*Lnorm*Kcsl
        dFdODF[phfx+item] = Kcsl*Lnorm
    return odfCor,dFdODF
    
def GetPrefOri(refl,G,g,phfx,hfx,SGData,calcControls,parmDict):
    if calcControls[phfx+'poType'] == 'MD':
        MD = parmDict[phfx+'MD']
        MDAxis = calcControls[phfx+'MDAxis']
        sumMD = 0
        for H in refl[11]:            
            cosP,sinP = G2lat.CosSinAngle(H,MDAxis,G)
            A = 1.0/np.sqrt((MD*cosP)**2+sinP**2/MD)
            sumMD += A**3
        POcorr = sumMD/len(refl[11])
    else:   #spherical harmonics
        POcorr = SHPOcal(refl,g,phfx,hfx,SGData,calcControls,parmDict)
    return POcorr
    
def GetPrefOriDerv(refl,G,g,phfx,hfx,SGData,calcControls,parmDict):
    POderv = {}
    if calcControls[phfx+'poType'] == 'MD':
        MD = parmDict[phfx+'MD']
        MDAxis = calcControls[phfx+'MDAxis']
        sumMD = 0
        sumdMD = 0
        for H in refl[11]:            
            cosP,sinP = G2lat.CosSinAngle(H,MDAxis,G)
            A = 1.0/np.sqrt((MD*cosP)**2+sinP**2/MD)
            sumMD += A**3
            sumdMD -= (1.5*A**5)*(2.0*MD*cosP**2-(sinP/MD)**2)
        POcorr = sumMD/len(refl[11])
        POderv[phfx+'MD'] = sumdMD/len(refl[11])
    else:   #spherical harmonics
        POcorr,POderv = SHPOcalDerv(refl,g,phfx,hfx,SGData,calcControls,parmDict)
    return POcorr,POderv
    
def GetIntensityCorr(refl,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict):
    Icorr = parmDict[phfx+'Scale']*parmDict[hfx+'Scale']*refl[3]               #scale*multiplicity
    Icorr *= G2pwd.Polarization(parmDict[hfx+'Polariz.'],refl[5],parmDict[hfx+'Azimuth'])[0]
    Icorr *= GetPrefOri(refl,G,g,phfx,hfx,SGData,calcControls,parmDict)
    if pfx+'SHorder' in parmDict:
        Icorr *= SHTXcal(refl,g,pfx,hfx,SGData,calcControls,parmDict)
    refl[13] = Icorr        
    
def GetIntensityDerv(refl,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict):
    dIdsh = 1./parmDict[hfx+'Scale']
    dIdsp = 1./parmDict[phfx+'Scale']
    pola,dIdPola = G2pwd.Polarization(parmDict[hfx+'Polariz.'],refl[5],parmDict[hfx+'Azimuth'])
    dIdPola /= pola
    POcorr,dIdPO = GetPrefOriDerv(refl,G,g,phfx,hfx,SGData,calcControls,parmDict)
    for iPO in dIdPO:
        dIdPO[iPO] /= POcorr
    dFdODF = {}
    dFdSA = [0,0,0]
    if pfx+'SHorder' in parmDict:
        odfCor,dFdODF,dFdSA = SHTXcalDerv(refl,g,pfx,hfx,SGData,calcControls,parmDict)
        for iSH in dFdODF:
            dFdODF[iSH] /= odfCor
        for i in range(3):
            dFdSA[i] /= odfCor
    return dIdsh,dIdsp,dIdPola,dIdPO,dFdODF,dFdSA
        
def GetSampleGam(refl,wave,G,phfx,calcControls,parmDict,sizeEllipse):
    costh = cosd(refl[5]/2.)
    #crystallite size
    if calcControls[phfx+'SizeType'] == 'isotropic':
        gam = 1.8*wave/(np.pi*parmDict[phfx+'Size:0']*costh)
    elif calcControls[phfx+'SizeType'] == 'uniaxial':
        H = np.array(refl[:3])
        P = np.array(calcControls[phfx+'SizeAxis'])
        cosP,sinP = G2lat.CosSinAngle(H,P,G)
        gam = (1.8*wave/np.pi)/(parmDict[phfx+'Size:0']*parmDict[phfx+'Size:1']*costh)
        gam *= np.sqrt((cosP*parmDict[phfx+'Size:1'])**2+(sinP*parmDict[phfx+'Size:0'])**2)
    else:           #ellipsoidal crystallites - wrong not make sense
        H = np.array(refl[:3])
        gam += 1.8*wave/(np.pi*costh*np.inner(H,np.inner(sizeEllipse,H)))
    #microstrain                
    if calcControls[phfx+'MustrainType'] == 'isotropic':
        gam += 0.018*parmDict[phfx+'Mustrain:0']*tand(refl[5]/2.)/np.pi
    elif calcControls[phfx+'MustrainType'] == 'uniaxial':
        H = np.array(refl[:3])
        P = np.array(calcControls[phfx+'MustrainAxis'])
        cosP,sinP = G2lat.CosSinAngle(H,P,G)
        Si = parmDict[phfx+'Mustrain:0']
        Sa = parmDict[phfx+'Mustrain:1']
        gam += 0.018*Si*Sa*tand(refl[5]/2.)/(np.pi*np.sqrt((Si*cosP)**2+(Sa*sinP)**2))
    else:       #generalized - P.W. Stephens model
        pwrs = calcControls[phfx+'MuPwrs']
        sum = 0
        for i,pwr in enumerate(pwrs):
            sum += parmDict[phfx+'Mustrain:'+str(i)]*refl[0]**pwr[0]*refl[1]**pwr[1]*refl[2]**pwr[2]
        gam += 0.018*refl[4]**2*tand(refl[5]/2.)*sum            
    return gam
        
def GetSampleGamDerv(refl,wave,G,phfx,calcControls,parmDict,sizeEllipse):
    gamDict = {}
    costh = cosd(refl[5]/2.)
    tanth = tand(refl[5]/2.)
    #crystallite size derivatives
    if calcControls[phfx+'SizeType'] == 'isotropic':
        gamDict[phfx+'Size:0'] = -1.80*wave/(np.pi*costh)
    elif calcControls[phfx+'SizeType'] == 'uniaxial':
        H = np.array(refl[:3])
        P = np.array(calcControls[phfx+'SizeAxis'])
        cosP,sinP = G2lat.CosSinAngle(H,P,G)
        Si = parmDict[phfx+'Size:0']
        Sa = parmDict[phfx+'Size:1']
        gami = (1.80*wave/np.pi)/(Si*Sa)
        sqtrm = np.sqrt((cosP*Sa)**2+(sinP*Si)**2)
        gam = gami*sqtrm/costh            
        gamDict[phfx+'Size:0'] = gami*Si*sinP**2/(sqtrm*costh)-gam/Si
        gamDict[phfx+'Size:1'] = gami*Sa*cosP**2/(sqtrm*costh)-gam/Sa         
    else:           #ellipsoidal crystallites - do numerically? - not right not make sense
        H = np.array(refl[:3])
        gam = 1.8*wave/(np.pi*costh*np.inner(H,np.inner(sizeEllipse,H)))
    #microstrain derivatives                
    if calcControls[phfx+'MustrainType'] == 'isotropic':
        gamDict[phfx+'Mustrain:0'] =  0.018*tanth/np.pi            
    elif calcControls[phfx+'MustrainType'] == 'uniaxial':
        H = np.array(refl[:3])
        P = np.array(calcControls[phfx+'MustrainAxis'])
        cosP,sinP = G2lat.CosSinAngle(H,P,G)
        Si = parmDict[phfx+'Mustrain:0']
        Sa = parmDict[phfx+'Mustrain:1']
        gami = 0.018*Si*Sa*tanth/np.pi
        sqtrm = np.sqrt((Si*cosP)**2+(Sa*sinP)**2)
        gam = gami/sqtrm
        gamDict[phfx+'Mustrain:0'] = gam/Si-gami*Si*cosP**2/sqtrm**3
        gamDict[phfx+'Mustrain:1'] = gam/Sa-gami*Sa*sinP**2/sqtrm**3
    else:       #generalized - P.W. Stephens model
        pwrs = calcControls[phfx+'MuPwrs']
        const = 0.018*refl[4]**2*tanth
        for i,pwr in enumerate(pwrs):
            gamDict[phfx+'Mustrain:'+str(i)] = const*refl[0]**pwr[0]*refl[1]**pwr[1]*refl[2]**pwr[2]
    return gamDict
        
def GetReflPos(refl,wave,G,hfx,calcControls,parmDict):
    h,k,l = refl[:3]
    dsq = 1./G2lat.calc_rDsq2(np.array([h,k,l]),G)
    d = np.sqrt(dsq)
    refl[4] = d
    pos = 2.0*asind(wave/(2.0*d))+parmDict[hfx+'Zero']
    const = 9.e-2/(np.pi*parmDict[hfx+'Gonio. radius'])                  #shifts in microns
    if 'Bragg' in calcControls[hfx+'instType']:
        pos -= const*(4.*parmDict[hfx+'Shift']*cosd(pos/2.0)+ \
            parmDict[hfx+'Transparency']*sind(pos)*100.0)            #trans(=1/mueff) in cm
    else:               #Debye-Scherrer - simple but maybe not right
        pos -= const*(parmDict[hfx+'DisplaceX']*cosd(pos)+parmDict[hfx+'DisplaceY']*sind(pos))
    return pos

def GetReflPosDerv(refl,wave,A,hfx,calcControls,parmDict):
    dpr = 180./np.pi
    h,k,l = refl[:3]
    dstsq = G2lat.calc_rDsq(np.array([h,k,l]),A)
    dst = np.sqrt(dstsq)
    pos = refl[5]
    const = dpr/np.sqrt(1.0-wave*dst/4.0)
    dpdw = const*dst
    dpdA = np.array([h**2,k**2,l**2,h*k,h*l,k*l])
    dpdA *= const*wave/(2.0*dst)
    dpdZ = 1.0
    const = 9.e-2/(np.pi*parmDict[hfx+'Gonio. radius'])                  #shifts in microns
    if 'Bragg' in calcControls[hfx+'instType']:
        dpdSh = -4.*const*cosd(pos/2.0)
        dpdTr = -const*sind(pos)*100.0
        return dpdA,dpdw,dpdZ,dpdSh,dpdTr,0.,0.
    else:               #Debye-Scherrer - simple but maybe not right
        dpdXd = -const*cosd(pos)
        dpdYd = -const*sind(pos)
        return dpdA,dpdw,dpdZ,0.,0.,dpdXd,dpdYd
            
def GetHStrainShift(refl,SGData,phfx,parmDict):
    laue = SGData['SGLaue']
    uniq = SGData['SGUniq']
    h,k,l = refl[:3]
    if laue in ['m3','m3m']:
        Dij = parmDict[phfx+'D11']*(h**2+k**2+l**2)+ \
            refl[4]**2*parmDict[phfx+'eA']*((h*k)**2+(h*l)**2+(k*l)**2)/(h**2+k**2+l**2)**2
    elif laue in ['6/m','6/mmm','3m1','31m','3']:
        Dij = parmDict[phfx+'D11']*(h**2+k**2+h*k)+parmDict[phfx+'D33']*l**2
    elif laue in ['3R','3mR']:
        Dij = parmDict[phfx+'D11']*(h**2+k**2+l**2)+parmDict[phfx+'D12']*(h*k+h*l+k*l)
    elif laue in ['4/m','4/mmm']:
        Dij = parmDict[phfx+'D11']*(h**2+k**2)+parmDict[phfx+'D33']*l**2
    elif laue in ['mmm']:
        Dij = parmDict[phfx+'D11']*h**2+parmDict[phfx+'D22']*k**2+parmDict[phfx+'D33']*l**2
    elif laue in ['2/m']:
        Dij = parmDict[phfx+'D11']*h**2+parmDict[phfx+'D22']*k**2+parmDict[phfx+'D33']*l**2
        if uniq == 'a':
            Dij += parmDict[phfx+'D23']*k*l
        elif uniq == 'b':
            Dij += parmDict[phfx+'D13']*h*l
        elif uniq == 'c':
            Dij += parmDict[phfx+'D12']*h*k
    else:
        Dij = parmDict[phfx+'D11']*h**2+parmDict[phfx+'D22']*k**2+parmDict[phfx+'D33']*l**2+ \
            parmDict[phfx+'D12']*h*k+parmDict[phfx+'D13']*h*l+parmDict[phfx+'D23']*k*l
    return Dij*refl[4]**2*tand(refl[5]/2.0)
            
def GetHStrainShiftDerv(refl,SGData,phfx):
    laue = SGData['SGLaue']
    uniq = SGData['SGUniq']
    h,k,l = refl[:3]
    if laue in ['m3','m3m']:
        dDijDict = {phfx+'D11':h**2+k**2+l**2,
            phfx+'eA':((h*k)**2+(h*l)**2+(k*l)**2)/(h**2+k**2+l**2)**2}
    elif laue in ['6/m','6/mmm','3m1','31m','3']:
        dDijDict = {phfx+'D11':h**2+k**2+h*k,phfx+'D33':l**2}
    elif laue in ['3R','3mR']:
        dDijDict = {phfx+'D11':h**2+k**2+l**2,phfx+'D12':h*k+h*l+k*l}
    elif laue in ['4/m','4/mmm']:
        dDijDict = {phfx+'D11':h**2+k**2,phfx+'D33':l**2}
    elif laue in ['mmm']:
        dDijDict = {phfx+'D11':h**2,phfx+'D22':k**2,phfx+'D33':l**2}
    elif laue in ['2/m']:
        dDijDict = {phfx+'D11':h**2,phfx+'D22':k**2,phfx+'D33':l**2}
        if uniq == 'a':
            dDijDict[phfx+'D23'] = k*l
        elif uniq == 'b':
            dDijDict[phfx+'D13'] = h*l
        elif uniq == 'c':
            dDijDict[phfx+'D12'] = h*k
            names.append()
    else:
        dDijDict = {phfx+'D11':h**2,phfx+'D22':k**2,phfx+'D33':l**2,
            phfx+'D12':h*k,phfx+'D13':h*l,phfx+'D23':k*l}
    for item in dDijDict:
        dDijDict[item] *= refl[4]**2*tand(refl[5]/2.0)
    return dDijDict
    
def GetFprime(controlDict,Histograms):
    FFtables = controlDict['FFtables']
    if not FFtables:
        return
    for histogram in Histograms:
        if 'PWDR' in histogram[:4]:
            Histogram = Histograms[histogram]
            hId = Histogram['hId']
            hfx = ':%d:'%(hId)
            keV = controlDict[hfx+'keV']
            for El in FFtables:
                Orbs = G2el.GetXsectionCoeff(El.split('+')[0].split('-')[0])
                FP,FPP,Mu = G2el.FPcalc(Orbs, keV)
                FFtables[El][hfx+'FP'] = FP
                FFtables[El][hfx+'FPP'] = FPP                
            
def getPowderProfile(parmDict,x,varylist,Histogram,Phases,calcControls,pawleyLookup):
    
    def GetReflSIgGam(refl,wave,G,hfx,phfx,calcControls,parmDict,sizeEllipse):
        U = parmDict[hfx+'U']
        V = parmDict[hfx+'V']
        W = parmDict[hfx+'W']
        X = parmDict[hfx+'X']
        Y = parmDict[hfx+'Y']
        tanPos = tand(refl[5]/2.0)
        sig = U*tanPos**2+V*tanPos+W        #save peak sigma
        sig = max(0.001,sig)
        gam = X/cosd(refl[5]/2.0)+Y*tanPos+GetSampleGam(refl,wave,G,phfx,calcControls,parmDict,sizeEllipse) #save peak gamma
        gam = max(0.001,gam)
        return sig,gam
                
    hId = Histogram['hId']
    hfx = ':%d:'%(hId)
    bakType = calcControls[hfx+'bakType']
    yb = G2pwd.getBackground(hfx,parmDict,bakType,x)
    yc = np.zeros_like(yb)
        
    if 'C' in calcControls[hfx+'histType']:    
        shl = max(parmDict[hfx+'SH/L'],0.002)
        Ka2 = False
        if hfx+'Lam1' in parmDict.keys():
            wave = parmDict[hfx+'Lam1']
            Ka2 = True
            lamRatio = 360*(parmDict[hfx+'Lam2']-parmDict[hfx+'Lam1'])/(np.pi*parmDict[hfx+'Lam1'])
            kRatio = parmDict[hfx+'I(L2)/I(L1)']
        else:
            wave = parmDict[hfx+'Lam']
    else:
        print 'TOF Undefined at present'
        raise ValueError
    for phase in Histogram['Reflection Lists']:
        refList = Histogram['Reflection Lists'][phase]
        Phase = Phases[phase]
        pId = Phase['pId']
        pfx = '%d::'%(pId)
        phfx = '%d:%d:'%(pId,hId)
        hfx = ':%d:'%(hId)
        SGData = Phase['General']['SGData']
        A = [parmDict[pfx+'A%d'%(i)] for i in range(6)]
        G,g = G2lat.A2Gmat(A)       #recip & real metric tensors
        Vst = np.sqrt(nl.det(G))    #V*
        if 'Pawley' not in Phase['General']['Type']:
            refList = StructureFactor(refList,G,hfx,pfx,SGData,calcControls,parmDict)
        sizeEllipse = []
        if calcControls[phfx+'SizeType'] == 'ellipsoidal':
            sizeEllipse = G2lat.U6toUij([parmDIct[phfx+'Size:%d'%(i)] for i in range(6)])
        for refl in refList:
            if 'C' in calcControls[hfx+'histType']:
                h,k,l = refl[:3]
                refl[5] = GetReflPos(refl,wave,G,hfx,calcControls,parmDict)         #corrected reflection position
                Lorenz = 1./(2.*sind(refl[5]/2.)**2*cosd(refl[5]/2.))           #Lorentz correction
                refl[5] += GetHStrainShift(refl,SGData,phfx,parmDict)               #apply hydrostatic strain shift
                refl[6:8] = GetReflSIgGam(refl,wave,G,hfx,phfx,calcControls,parmDict,sizeEllipse)    #peak sig & gam
                GetIntensityCorr(refl,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict)    #puts corrections in refl[13]
                refl[13] *= Vst*Lorenz
                if 'Pawley' in Phase['General']['Type']:
                    try:
                        refl[9] = abs(parmDict[pfx+'PWLref:%d'%(pawleyLookup[pfx+'%d,%d,%d'%(h,k,l)])])
                    except KeyError:
#                        print ' ***Error %d,%d,%d missing from Pawley reflection list ***'%(h,k,l)
                        continue
                Wd,fmin,fmax = G2pwd.getWidths(refl[5],refl[6],refl[7],shl)
                iBeg = np.searchsorted(x,refl[5]-fmin)
                iFin = np.searchsorted(x,refl[5]+fmax)
                if not iBeg+iFin:       #peak below low limit - skip peak
                    continue
                elif not iBeg-iFin:     #peak above high limit - done
                    break
                yc[iBeg:iFin] += refl[13]*refl[9]*G2pwd.getFCJVoigt3(refl[5],refl[6],refl[7],shl,x[iBeg:iFin])    #>90% of time spent here
                if Ka2:
                    pos2 = refl[5]+lamRatio*tand(refl[5]/2.0)       # + 360/pi * Dlam/lam * tan(th)
                    Wd,fmin,fmax = G2pwd.getWidths(pos2,refl[6],refl[7],shl)
                    iBeg = np.searchsorted(x,pos2-fmin)
                    iFin = np.searchsorted(x,pos2+fmax)
                    if not iBeg+iFin:       #peak below low limit - skip peak
                        continue
                    elif not iBeg-iFin:     #peak above high limit - done
                        return yc,yb
                    yc[iBeg:iFin] += refl[13]*refl[9]*kRatio*G2pwd.getFCJVoigt3(pos2,refl[6],refl[7],shl,x[iBeg:iFin])        #and here
            elif 'T' in calcControls[hfx+'histType']:
                print 'TOF Undefined at present'
                raise Exception    #no TOF yet
    return yc,yb
    
def GetFobsSq(Histograms,Phases,parmDict,calcControls):
    for histogram in Histograms:
        if 'PWDR' in histogram[:4]:
            Histogram = Histograms[histogram]
            hId = Histogram['hId']
            hfx = ':%d:'%(hId)
            Limits = calcControls[hfx+'Limits']
            shl = max(parmDict[hfx+'SH/L'],0.002)
            Ka2 = False
            kRatio = 0.0
            if hfx+'Lam1' in parmDict.keys():
                Ka2 = True
                lamRatio = 360*(parmDict[hfx+'Lam2']-parmDict[hfx+'Lam1'])/(np.pi*parmDict[hfx+'Lam1'])
                kRatio = parmDict[hfx+'I(L2)/I(L1)']
            x,y,w,yc,yb,yd = Histogram['Data']
            ymb = np.array(y-yb)
            ycmb = np.array(yc-yb)
            ratio = np.where(ycmb!=0.,ymb/ycmb,0.0)            
            xB = np.searchsorted(x,Limits[0])
            xF = np.searchsorted(x,Limits[1])
            refLists = Histogram['Reflection Lists']
            for phase in refLists:
                Phase = Phases[phase]
                pId = Phase['pId']
                phfx = '%d:%d:'%(pId,hId)
                refList = refLists[phase]
                sumFo = 0.0
                sumdF = 0.0
                sumFosq = 0.0
                sumdFsq = 0.0
                for refl in refList:
                    if 'C' in calcControls[hfx+'histType']:
                        yp = np.zeros_like(yb)
                        Wd,fmin,fmax = G2pwd.getWidths(refl[5],refl[6],refl[7],shl)
                        iBeg = np.searchsorted(x[xB:xF],refl[5]-fmin)
                        iFin = np.searchsorted(x[xB:xF],refl[5]+fmax)
                        iFin2 = iFin
                        yp[iBeg:iFin] = refl[13]*refl[9]*G2pwd.getFCJVoigt3(refl[5],refl[6],refl[7],shl,x[iBeg:iFin])    #>90% of time spent here                            
                        if Ka2:
                            pos2 = refl[5]+lamRatio*tand(refl[5]/2.0)       # + 360/pi * Dlam/lam * tan(th)
                            Wd,fmin,fmax = G2pwd.getWidths(pos2,refl[6],refl[7],shl)
                            iBeg2 = np.searchsorted(x,pos2-fmin)
                            iFin2 = np.searchsorted(x,pos2+fmax)
                            yp[iBeg2:iFin2] += refl[13]*refl[9]*kRatio*G2pwd.getFCJVoigt3(pos2,refl[6],refl[7],shl,x[iBeg2:iFin2])        #and here
                        refl[8] = np.sum(np.where(ratio[iBeg:iFin2]>0.,yp[iBeg:iFin2]*ratio[iBeg:iFin2]/(refl[13]*(1.+kRatio)),0.0))
                    elif 'T' in calcControls[hfx+'histType']:
                        print 'TOF Undefined at present'
                        raise Exception    #no TOF yet
                    Fo = np.sqrt(np.abs(refl[8]))
                    Fc = np.sqrt(np.abs(refl[9]))
                    sumFo += Fo
                    sumFosq += refl[8]**2
                    sumdF += np.abs(Fo-Fc)
                    sumdFsq += (refl[8]-refl[9])**2
                Histogram[phfx+'Rf'] = min(100.,(sumdF/sumFo)*100.)
                Histogram[phfx+'Rf^2'] = min(100.,np.sqrt(sumdFsq/sumFosq)*100.)
                Histogram[phfx+'Nref'] = len(refList)
                
def getPowderProfileDerv(parmDict,x,varylist,Histogram,Phases,calcControls,pawleyLookup):
    
    def cellVaryDerv(pfx,SGData,dpdA): 
        if SGData['SGLaue'] in ['-1',]:
            return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]],
                [pfx+'A3',dpdA[3]],[pfx+'A4',dpdA[4]],[pfx+'A5',dpdA[5]]]
        elif SGData['SGLaue'] in ['2/m',]:
            if SGData['SGUniq'] == 'a':
                return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]],[pfx+'A3',dpdA[3]]]
            elif SGData['SGUniq'] == 'b':
                return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]],[pfx+'A4',dpdA[4]]]
            else:
                return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]],[pfx+'A5',dpdA[5]]]
        elif SGData['SGLaue'] in ['mmm',]:
            return [[pfx+'A0',dpdA[0]],[pfx+'A1',dpdA[1]],[pfx+'A2',dpdA[2]]]
        elif SGData['SGLaue'] in ['4/m','4/mmm']:
            return [[pfx+'A0',dpdA[0]+dpdA[1]],[pfx+'A2',dpdA[2]]]
        elif SGData['SGLaue'] in ['6/m','6/mmm','3m1', '31m', '3']:
            return [[pfx+'A0',dpdA[0]+dpdA[1]+dpdA[3]],[pfx+'A2',dpdA[2]]]
        elif SGData['SGLaue'] in ['3R', '3mR']:
            return [[pfx+'A0',dpdA[0]+dpdA[1]+dpdA[2]],[pfx+'A3',dpdA[3]+dpdA[4]+dpdA[5]]]                       
        elif SGData['SGLaue'] in ['m3m','m3']:
            return [[pfx+'A0',dpdA[0]+dpdA[1]+dpdA[2]]]
    
    lenX = len(x)                
    hId = Histogram['hId']
    hfx = ':%d:'%(hId)
    bakType = calcControls[hfx+'bakType']
    dMdv = np.zeros(shape=(len(varylist),len(x)))
    if hfx+'Back:0' in varylist:
        dMdb = G2pwd.getBackgroundDerv(hfx,parmDict,bakType,x)
        bBpos =varylist.index(hfx+'Back:0')
        dMdv[bBpos:bBpos+len(dMdb)] = dMdb
        
    if 'C' in calcControls[hfx+'histType']:    
        dx = x[1]-x[0]
        shl = max(parmDict[hfx+'SH/L'],0.002)
        Ka2 = False
        if hfx+'Lam1' in parmDict.keys():
            wave = parmDict[hfx+'Lam1']
            Ka2 = True
            lamRatio = 360*(parmDict[hfx+'Lam2']-parmDict[hfx+'Lam1'])/(np.pi*parmDict[hfx+'Lam1'])
            kRatio = parmDict[hfx+'I(L2)/I(L1)']
        else:
            wave = parmDict[hfx+'Lam']
    else:
        print 'TOF Undefined at present'
        raise ValueError
    for phase in Histogram['Reflection Lists']:
        refList = Histogram['Reflection Lists'][phase]
        Phase = Phases[phase]
        SGData = Phase['General']['SGData']
        pId = Phase['pId']
        pfx = '%d::'%(pId)
        phfx = '%d:%d:'%(pId,hId)
        A = [parmDict[pfx+'A%d'%(i)] for i in range(6)]
        G,g = G2lat.A2Gmat(A)       #recip & real metric tensors
        if 'Pawley' not in Phase['General']['Type']:
            dFdvDict = StructureFactorDerv(refList,G,hfx,pfx,SGData,calcControls,parmDict)
        sizeEllipse = []
        if calcControls[phfx+'SizeType'] == 'ellipsoidal':
            sizeEllipse = G2lat.U6toUij([parmDIct[phfx+'Size:%d'%(i)] for i in range(6)])
        for iref,refl in enumerate(refList):
            if 'C' in calcControls[hfx+'histType']:        #CW powder
                h,k,l = refl[:3]
                dIdsh,dIdsp,dIdpola,dIdPO,dFdODF,dFdSA = GetIntensityDerv(refl,G,g,pfx,phfx,hfx,SGData,calcControls,parmDict)
                if 'Pawley' in Phase['General']['Type']:
                    try:
                        refl[9] = abs(parmDict[pfx+'PWLref:%d'%(pawleyLookup[pfx+'%d,%d,%d'%(h,k,l)])])
                    except KeyError:
#                        print ' ***Error %d,%d,%d missing from Pawley reflection list ***'%(h,k,l)
                        continue
                Wd,fmin,fmax = G2pwd.getWidths(refl[5],refl[6],refl[7],shl)
                iBeg = np.searchsorted(x,refl[5]-fmin)
                iFin = np.searchsorted(x,refl[5]+fmax)
                if not iBeg+iFin:       #peak below low limit - skip peak
                    continue
                elif not iBeg-iFin:     #peak above high limit - done
                    break
                pos = refl[5]
                tanth = tand(pos/2.0)
                costh = cosd(pos/2.0)
                dMdpk = np.zeros(shape=(6,len(x)))
                dMdipk = G2pwd.getdFCJVoigt3(refl[5],refl[6],refl[7],shl,x[iBeg:iFin])
                for i in range(1,5):
                    dMdpk[i][iBeg:iFin] += 100.*dx*refl[13]*refl[9]*dMdipk[i]
                dMdpk[0][iBeg:iFin] += 100.*dx*refl[13]*refl[9]*dMdipk[0]
                dervDict = {'int':dMdpk[0],'pos':dMdpk[1],'sig':dMdpk[2],'gam':dMdpk[3],'shl':dMdpk[4]}
                if Ka2:
                    pos2 = refl[5]+lamRatio*tanth       # + 360/pi * Dlam/lam * tan(th)
                    kdelt = int((pos2-refl[5])/dx)               
                    iBeg2 = min(lenX,iBeg+kdelt)
                    iFin2 = min(lenX,iFin+kdelt)
                    if iBeg2-iFin2:
                        dMdipk2 = G2pwd.getdFCJVoigt3(pos2,refl[6],refl[7],shl,x[iBeg2:iFin2])
                        for i in range(1,5):
                            dMdpk[i][iBeg2:iFin2] += 100.*dx*refl[13]*refl[9]*kRatio*dMdipk2[i]
                        dMdpk[0][iBeg2:iFin2] += 100.*dx*refl[13]*refl[9]*kRatio*dMdipk2[0]
                        dMdpk[5][iBeg2:iFin2] += 100.*dx*refl[13]*dMdipk2[0]
                        dervDict = {'int':dMdpk[0],'pos':dMdpk[1],'sig':dMdpk[2],'gam':dMdpk[3],'shl':dMdpk[4],'L1/L2':dMdpk[5]*refl[9]}
                if 'Pawley' in Phase['General']['Type']:
                    try:
                        idx = varylist.index(pfx+'PWLref:'+str(pawleyLookup[pfx+'%d,%d,%d'%(h,k,l)]))
                        dMdv[idx] = dervDict['int']/refl[9]
                    except ValueError:
                        pass
                dpdA,dpdw,dpdZ,dpdSh,dpdTr,dpdX,dpdY = GetReflPosDerv(refl,wave,A,hfx,calcControls,parmDict)
                names = {hfx+'Scale':[dIdsh,'int'],hfx+'Polariz.':[dIdpola,'int'],phfx+'Scale':[dIdsp,'int'],
                    hfx+'U':[tanth**2,'sig'],hfx+'V':[tanth,'sig'],hfx+'W':[1.0,'sig'],
                    hfx+'X':[1.0/costh,'gam'],hfx+'Y':[tanth,'gam'],hfx+'SH/L':[1.0,'shl'],
                    hfx+'I(L2)/I(L1)':[1.0,'L1/L2'],hfx+'Zero':[dpdZ,'pos'],hfx+'Lam':[dpdw,'pos'],
                    hfx+'Shift':[dpdSh,'pos'],hfx+'Transparency':[dpdTr,'pos'],hfx+'DisplaceX':[dpdX,'pos'],
                    hfx+'DisplaceY':[dpdY,'pos'],}
                for name in names:
                    if name in varylist:
                        item = names[name]
                        dMdv[varylist.index(name)] += item[0]*dervDict[item[1]]
                for iPO in dIdPO:
                    if iPO in varylist:
                        dMdv[varylist.index(iPO)] += dIdPO[iPO]*dervDict['int']
                for i,name in enumerate(['omega','chi','phi']):
                    aname = pfx+'SH '+name
                    if aname in varylist:
                        dMdv[varylist.index(aname)] += dFdSA[i]*dervDict['int']
                for iSH in dFdODF:
                    if iSH in varylist:
                        dMdv[varylist.index(iSH)] += dFdODF[iSH]*dervDict['int']
                cellDervNames = cellVaryDerv(pfx,SGData,dpdA)
                for name,dpdA in cellDervNames:
                    if name in varylist:
                        dMdv[varylist.index(name)] += dpdA*dervDict['pos']
                dDijDict = GetHStrainShiftDerv(refl,SGData,phfx)
                for name in dDijDict:
                    if name in varylist:
                        dMdv[varylist.index(name)] += dDijDict[name]*dervDict['pos']
                gamDict = GetSampleGamDerv(refl,wave,G,phfx,calcControls,parmDict,sizeEllipse)
                for name in gamDict:
                    if name in varylist:
                        dMdv[varylist.index(name)] += gamDict[name]*dervDict['gam']
                                               
            elif 'T' in calcControls[hfx+'histType']:
                print 'TOF Undefined at present'
                raise Exception    #no TOF yet
#do atom derivatives -  for F,X & U so far              
            corr = dervDict['int']/refl[9]
            for name in varylist:
                try:
                    aname = name.split(pfx)[1][:2]
                    if aname in ['Af','dA','AU']:
                         dMdv[varylist.index(name)] += dFdvDict[name][iref]*corr
                except IndexError:
                    pass
    return dMdv

def dervRefine(values,HistoPhases,parmdict,varylist,calcControls,pawleyLookup,dlg):
    parmdict.update(zip(varylist,values))
    G2mv.Dict2Map(parmdict)
    Histograms,Phases = HistoPhases
    dMdv = np.empty(0)
    for histogram in Histograms:
        if 'PWDR' in histogram[:4]:
            Histogram = Histograms[histogram]
            hId = Histogram['hId']
            hfx = ':%d:'%(hId)
            Limits = calcControls[hfx+'Limits']
            x,y,w,yc,yb,yd = Histogram['Data']
            xB = np.searchsorted(x,Limits[0])
            xF = np.searchsorted(x,Limits[1])
            dMdvh = np.sqrt(w[xB:xF])*getPowderProfileDerv(parmdict,x[xB:xF],
                varylist,Histogram,Phases,calcControls,pawleyLookup)
            if len(dMdv):
                dMdv = np.concatenate((dMdv.T,dMdvh.T)).T
            else:
                dMdv = dMdvh
    return dMdv

def errRefine(values,HistoPhases,parmdict,varylist,calcControls,pawleyLookup,dlg):        
    parmdict.update(zip(varylist,values))
    Values2Dict(parmdict, varylist, values)
    G2mv.Dict2Map(parmdict)
    Histograms,Phases = HistoPhases
    M = np.empty(0)
    sumwYo = 0
    Nobs = 0
    for histogram in Histograms:
        if 'PWDR' in histogram[:4]:
            Histogram = Histograms[histogram]
            hId = Histogram['hId']
            hfx = ':%d:'%(hId)
            Limits = calcControls[hfx+'Limits']
            x,y,w,yc,yb,yd = Histogram['Data']
            yc *= 0.0                           #zero full calcd profiles
            yb *= 0.0
            yd *= 0.0
            xB = np.searchsorted(x,Limits[0])
            xF = np.searchsorted(x,Limits[1])
            Histogram['Nobs'] = xF-xB
            Nobs += Histogram['Nobs']
            Histogram['sumwYo'] = np.sum(w[xB:xF]*y[xB:xF]**2)
            sumwYo += Histogram['sumwYo']
            yc[xB:xF],yb[xB:xF] = getPowderProfile(parmdict,x[xB:xF],
                varylist,Histogram,Phases,calcControls,pawleyLookup)
            yc[xB:xF] += yb[xB:xF]
            yd[xB:xF] = yc[xB:xF]-y[xB:xF]          #yc-yo then all dydv have no '-' needed
            Histogram['sumwYd'] = np.sum(np.sqrt(w[xB:xF])*(yd[xB:xF]))
            wdy = np.sqrt(w[xB:xF])*(yd[xB:xF])
            Histogram['wRp'] = min(100.,np.sqrt(np.sum(wdy**2)/Histogram['sumwYo'])*100.)
            M = np.concatenate((M,wdy))
    Histograms['sumwYo'] = sumwYo
    Histograms['Nobs'] = Nobs
    Rwp = min(100.,np.sqrt(np.sum(M**2)/sumwYo)*100.)
    if dlg:
        GoOn = dlg.Update(Rwp,newmsg='%s%8.3f%s'%('Powder profile wRp =',Rwp,'%'))[0]
        if not GoOn:
            parmDict['saved values'] = values
            raise Exception         #Abort!!
    return M
    
                    
def Refine(GPXfile,dlg):
    import cPickle
    import pytexture as ptx
    ptx.pyqlmninit()            #initialize fortran arrays for spherical harmonics
    
    ShowBanner()
    varyList = []
    parmDict = {}
    calcControls = {}
    G2mv.InitVars()    
    Controls = GetControls(GPXfile)
    ShowControls(Controls)            
    constrList = GetConstraints(GPXfile)
    Histograms,Phases = GetUsedHistogramsAndPhases(GPXfile)
    if not Phases:
        print ' *** ERROR - you have no histograms to refine! ***'
        print ' *** Refine aborted ***'
        raise Exception
    if not Histograms:
        print ' *** ERROR - you have no data to refine with! ***'
        print ' *** Refine aborted ***'
        raise Exception
    Natoms,phaseVary,phaseDict,pawleyLookup,FFtables = GetPhaseData(Phases)
    calcControls['Natoms'] = Natoms
    calcControls['FFtables'] = FFtables
    hapVary,hapDict,controlDict = GetHistogramPhaseData(Phases,Histograms)
    calcControls.update(controlDict)
    histVary,histDict,controlDict = GetHistogramData(Histograms)
    calcControls.update(controlDict)
    varyList = phaseVary+hapVary+histVary
    parmDict.update(phaseDict)
    parmDict.update(hapDict)
    parmDict.update(histDict)
    GetFprime(calcControls,Histograms)
    for item in constrList: print item
    constrDict,constrFlag,fixedList = G2mv.InputParse([])        #constraints go here?
    groups,parmlist = G2mv.GroupConstraints(constrDict)
    G2mv.GenerateConstraints(groups,parmlist,constrDict,constrFlag,fixedList)
    G2mv.Map2Dict(parmDict,varyList)

    while True:
        begin = time.time()
        values =  np.array(Dict2Values(parmDict, varyList))
        Ftol = Controls['min dM/M']
        Factor = Controls['shift factor']
        if Controls['deriv type'] == 'analytic':
            result = so.leastsq(errRefine,values,Dfun=dervRefine,full_output=True,
                ftol=Ftol,col_deriv=True,factor=Factor,
                args=([Histograms,Phases],parmDict,varyList,calcControls,pawleyLookup,dlg))
            ncyc = int(result[2]['nfev']/2)                
        else:           #'numeric'
            result = so.leastsq(errRefine,values,full_output=True,ftol=Ftol,epsfcn=1.e-8,factor=Factor,
                args=([Histograms,Phases],parmDict,varyList,calcControls,pawleyLookup,dlg))
            ncyc = int(result[2]['nfev']/len(varyList))
#        table = dict(zip(varyList,zip(values,result[0],(result[0]-values))))
#        for item in table: print item,table[item]               #useful debug - are things shifting?
        runtime = time.time()-begin
        chisq = np.sum(result[2]['fvec']**2)
        Values2Dict(parmDict, varyList, result[0])
        G2mv.Dict2Map(parmDict)
        newAtomDict = ApplyXYZshifts(parmDict,varyList)
        
        Rwp = np.sqrt(chisq/Histograms['sumwYo'])*100.      #to %
        GOF = chisq/(Histograms['Nobs']-len(varyList))
        print '\n Refinement results:'
        print 135*'-'
        print ' Number of function calls:',result[2]['nfev'],' Number of observations: ',Histograms['Nobs'],' Number of parameters: ',len(varyList)
        print ' Refinement time = %8.3fs, %8.3fs/cycle'%(runtime,runtime/ncyc)
        print ' wRp = %7.2f%%, chi**2 = %12.6g, reduced chi**2 = %6.2f'%(Rwp,chisq,GOF)
        try:
            covMatrix = result[1]*GOF
            sig = np.sqrt(np.diag(covMatrix))
            if np.any(np.isnan(sig)):
                print '*** Least squares aborted - some invalid esds possible ***'
#            table = dict(zip(varyList,zip(values,result[0],(result[0]-values)/sig)))
#            for item in table: print item,table[item]               #useful debug - are things shifting?
            break                   #refinement succeeded - finish up!
        except TypeError:          #result[1] is None on singular matrix
            print '**** Refinement failed - singular matrix ****'
            Ipvt = result[2]['ipvt']
            for i,ipvt in enumerate(Ipvt):
                if not np.sum(result[2]['fjac'],axis=1)[i]:
                    print 'Removing parameter: ',varyList[ipvt-1]
                    del(varyList[ipvt-1])
                    break

#    print 'dependentParmList: ',G2mv.dependentParmList
#    print 'arrayList: ',G2mv.arrayList
#    print 'invarrayList: ',G2mv.invarrayList
#    print 'indParmList: ',G2mv.indParmList
#    print 'fixedDict: ',G2mv.fixedDict
    GetFobsSq(Histograms,Phases,parmDict,calcControls)
    sigDict = dict(zip(varyList,sig))
    covData = {'variables':result[0],'varyList':varyList,'sig':sig,
        'covMatrix':covMatrix,'title':GPXfile,'newAtomDict':newAtomDict}
    SetPhaseData(parmDict,sigDict,Phases,covData)
    SetHistogramPhaseData(parmDict,sigDict,Phases,Histograms)
    SetHistogramData(parmDict,sigDict,Histograms)
    SetUsedHistogramsAndPhases(GPXfile,Histograms,Phases,covData)
#for testing purposes!!!
#    file = open('structTestdata.dat','wb')
#    cPickle.dump(parmDict,file,1)
#    cPickle.dump(varyList,file,1)
#    for histogram in Histograms:
#        if 'PWDR' in histogram[:4]:
#            Histogram = Histograms[histogram]
#    cPickle.dump(Histogram,file,1)
#    cPickle.dump(Phases,file,1)
#    cPickle.dump(calcControls,file,1)
#    cPickle.dump(pawleyLookup,file,1)
#    file.close()

def SeqRefine(GPXfile,dlg):
    import cPickle
    import pytexture as ptx
    ptx.pyqlmninit()            #initialize fortran arrays for spherical harmonics
    
    ShowBanner()
    print ' Sequential Refinement'
    G2mv.InitVars()    
    Controls = GetControls(GPXfile)
    ShowControls(Controls)            
    constrList = GetConstraints(GPXfile)
    Histograms,Phases = GetUsedHistogramsAndPhases(GPXfile)
    if not Phases:
        print ' *** ERROR - you have no histograms to refine! ***'
        print ' *** Refine aborted ***'
        raise Exception
    if not Histograms:
        print ' *** ERROR - you have no data to refine with! ***'
        print ' *** Refine aborted ***'
        raise Exception
    Natoms,phaseVary,phaseDict,pawleyLookup,FFtables = GetPhaseData(Phases,False)
    if 'Seq Data' in Controls:
        histNames = Controls['Seq Data']
    else:
        histNames = GetHistogramNames(GPXfile,['PWDR',])
    if 'Reverse Seq' in Controls:
        if Controls['Reverse Seq']:
            histNames.reverse()
    SeqResult = {'histNames':histNames}
    makeBack = True
    for ihst,histogram in enumerate(histNames):
        ifPrint = False
        if dlg:
            dlg.SetTitle('Residual for histogram '+str(ihst))
        calcControls = {}
        calcControls['Natoms'] = Natoms
        calcControls['FFtables'] = FFtables
        varyList = []
        parmDict = {}
        Histo = {histogram:Histograms[histogram],}
        hapVary,hapDict,controlDict = GetHistogramPhaseData(Phases,Histo,False)
        calcControls.update(controlDict)
        histVary,histDict,controlDict = GetHistogramData(Histo,False)
        calcControls.update(controlDict)
        varyList = phaseVary+hapVary+histVary
        if not ihst:
            saveVaryList = varyList[:]
            for i,item in enumerate(saveVaryList):
                items = item.split(':')
                if items[1]:
                    items[1] = ''
                item = ':'.join(items)
                saveVaryList[i] = item
            SeqResult['varyList'] = saveVaryList
        else:
            newVaryList = varyList[:]
            for i,item in enumerate(newVaryList):
                items = item.split(':')
                if items[1]:
                    items[1] = ''
                item = ':'.join(items)
                newVaryList[i] = item
            if newVaryList != SeqResult['varyList']:
                print newVaryList
                print SeqResult['varyList']
                print '**** ERROR - variable list for this histogram does not match previous'
                raise Exception
        parmDict.update(phaseDict)
        parmDict.update(hapDict)
        parmDict.update(histDict)
        GetFprime(calcControls,Histo)
        constrDict,constrFlag,fixedList = G2mv.InputParse([])        #constraints go here?
        groups,parmlist = G2mv.GroupConstraints(constrDict)
        G2mv.GenerateConstraints(groups,parmlist,constrDict,constrFlag,fixedList)
        G2mv.Map2Dict(parmDict,varyList)
    
        while True:
            begin = time.time()
            values =  np.array(Dict2Values(parmDict, varyList))
            Ftol = Controls['min dM/M']
            Factor = Controls['shift factor']
            if Controls['deriv type'] == 'analytic':
                result = so.leastsq(errRefine,values,Dfun=dervRefine,full_output=True,
                    ftol=Ftol,col_deriv=True,factor=Factor,
                    args=([Histo,Phases],parmDict,varyList,calcControls,pawleyLookup,dlg))
                ncyc = int(result[2]['nfev']/2)                
            else:           #'numeric'
                result = so.leastsq(errRefine,values,full_output=True,ftol=Ftol,epsfcn=1.e-8,factor=Factor,
                    args=([Histo,Phases],parmDict,varyList,calcControls,pawleyLookup,dlg))
                ncyc = int(result[2]['nfev']/len(varyList))
            runtime = time.time()-begin
            chisq = np.sum(result[2]['fvec']**2)
            Values2Dict(parmDict, varyList, result[0])
            G2mv.Dict2Map(parmDict)
            newAtomDict = ApplyXYZshifts(parmDict,varyList)
            
            Rwp = np.sqrt(chisq/Histo['sumwYo'])*100.      #to %
            GOF = chisq/(Histo['Nobs']-len(varyList))
            print '\n Refinement results for histogram: v'+histogram
            print 135*'-'
            print ' Number of function calls:',result[2]['nfev'],' Number of observations: ',Histo['Nobs'],' Number of parameters: ',len(varyList)
            print ' Refinement time = %8.3fs, %8.3fs/cycle'%(runtime,runtime/ncyc)
            print ' wRp = %7.2f%%, chi**2 = %12.6g, reduced chi**2 = %6.2f'%(Rwp,chisq,GOF)
            try:
                covMatrix = result[1]*GOF
                sig = np.sqrt(np.diag(covMatrix))
                if np.any(np.isnan(sig)):
                    print '*** Least squares aborted - some invalid esds possible ***'
                    ifPrint = True
                break                   #refinement succeeded - finish up!
            except TypeError:          #result[1] is None on singular matrix
                print '**** Refinement failed - singular matrix ****'
                Ipvt = result[2]['ipvt']
                for i,ipvt in enumerate(Ipvt):
                    if not np.sum(result[2]['fjac'],axis=1)[i]:
                        print 'Removing parameter: ',varyList[ipvt-1]
                        del(varyList[ipvt-1])
                        break
    
        GetFobsSq(Histo,Phases,parmDict,calcControls)
        sigDict = dict(zip(varyList,sig))
        covData = {'variables':result[0],'varyList':varyList,'sig':sig,
            'covMatrix':covMatrix,'title':histogram,'newAtomDict':newAtomDict}
        SetHistogramPhaseData(parmDict,sigDict,Phases,Histo,ifPrint)
        SetHistogramData(parmDict,sigDict,Histo,ifPrint)
        SeqResult[histogram] = covData
        SetUsedHistogramsAndPhases(GPXfile,Histo,Phases,covData,makeBack)
        makeBack = False
    SetSeqResult(GPXfile,Histograms,SeqResult)


def main():
    arg = sys.argv
    if len(arg) > 1:
        GPXfile = arg[1]
        if not ospath.exists(GPXfile):
            print 'ERROR - ',GPXfile," doesn't exist!"
            exit()
        GPXpath = ospath.dirname(arg[1])
        Refine(GPXfile,None)
    else:
        print 'ERROR - missing filename'
        exit()
    print "Done"
         
if __name__ == '__main__':
    main()