Source code for GSASIImapvars

# TODO: revisit SeqRefine and :meth:`GSASIIdataGUI.GSASII.OnSeqRefine` and :func:`GSASIIseqGUI.UpdateSeqResults`

# -*- coding: utf-8 -*-
########### SVN repository information ###################
# $Date: 2024-02-07 14:07:07 -0600 (Wed, 07 Feb 2024) $
# $Author: toby $
# $Revision: 5723 $
# $URL: https://subversion.xray.aps.anl.gov/pyGSAS/trunk/GSASIImapvars.py $
# $Id: GSASIImapvars.py 5723 2024-02-07 20:07:07Z toby $
########### SVN repository information ###################
"""
Classes and routines defined in :mod:`GSASIImapvars` follow. 

Note that parameter names in GSAS-II are strings of form ``<ph#>:<hst#>:<nam>`` or ``<ph#>::<nam>:<at#>``
where ``<ph#>`` is a phase number, ``<hst#>`` is a histogram number and ``<at#>`` is an atom number. 
``<nam>`` is a name that determines the parameter type (see :func:`GSASIIobj.CompileVarDesc`). When 
stored in the data tree, parameters are saved as :class:`GSASIIobj.G2VarObj` objects 
so that they can be resolved if the phase/histogram order changes.
"""
# Note that documentation for GSASIImapvars.py has been moved
# to file docs/source/GSASIImapvars.rst

from __future__ import division, print_function
import copy
import numpy as np
import GSASIIpath
GSASIIpath.SetVersionNumber("$Revision: 5723 $")
import GSASIIobj as G2obj 
# data used for constraints; 
debug = False # turns on printing as constraint input is processed

#------------------------------------------------------------------------------------
# Global vars used for storing constraints and equivalences after processing
#   note that new var and constraint equations are stored together in groups,
#   where each constraint group contains those parameters that must be handled 
#   together. Equivalences are also stored in these 

dependentParmList = []
'''a list of lists where each item contains a list of parameters in each constraint group. 
note that parameters listed in dependentParmList should not be refined directly.'''
indParmList = [] # a list of names for the new parameters
'''a list of lists where each item contains a list for each constraint group with 
fixed values for constraint equations and names of generated/New Var parameters.
In the case of equivalences, the name of a single independent parameter is stored.
'''
arrayList = []
'''a list of of relationship matrices that map model parameters in each 
constraint group (in :data:`dependentParmList`) to 
generated (New Var) parameters.
'''
invarrayList = []
'''a list of of inverse-relationship matrices that map constrained values and 
generated (New Var) parameters (in :data:`indParmList`) to model parameters
(in :data:`dependentParmList`). 
'''
symGenList = []
'''A list of flags that if True indicates a constraint was generated by symmetry
'''
holdParmList = []
'''List of parameters that should not be refined ("Hold"s).
Set in :func:`StoreHold`. Initialized in :func:`InitVars`.
'''
holdParmType = {}
'''The reason why a parameter has been marked as "Hold". 
Initialized in :func:`InitVars`; set in :func:`StoreHold`.
'''
constrParms = {'indep-equiv':[], 'indep-constr':[], 'dep-equiv':[], 'dep-constr':[]}
'''A dict with parameters in equivalences, compiled from 
(:data:`dependentParmList`) and (:data:`indParmList`).
Used within :func:`GetIndependentVars` and :func:`GetDependentVars`.
'''
saveVaryList = []
'''A list of the varied parameters that was last supplied when constraints were
processed. This is set in :func:`GenerateConstraints` and updated in 
:func:`Map2Dict`. Used in :func:`VarRemapShow`
'''
droppedSym = []
'''A list of symmetry generated equivalences that have been converted to 
constraint equations in :func:`CheckEquivalences`
'''
#------------------------------------------------------------------------------------
# Global vars set in :func:`GenerateConstraints`. Used for intermediate processing of
# constraints.

constrVarList = []
'List of parameters used in "Constr" and "New Var" constraints'
indepVarList = []
'A list of all independent parameters in equivalences'
depVarList = []
'A list of all dependent parameters in equivalences'

#------------------------------------------------------------------------------------
# global variables used in :func:`getConstrError` to store error and warning information.
# set in CheckEquivalences and in GenerateConstraints
convVarList = []
'parameters in equivalences that were converted to "Const" constraints'
multdepVarList = []
'parameters used as dependents multiple times in equivalences'
unvariedParmsList = []
'parameters used in equivalences that are not varied'
undefinedVars = []
'parameters used in equivalences that are not defined in the parameter dict'
groupErrors = []
'parameters in constraints where parameter grouping and matrix inversion fails'

#------------------------------------------------------------------------------------
paramPrefix = "::constr"
'A prefix for generated parameter names'
consNum = 0
'The number to be assigned to the next constraint to be created'

#------------------------------------------------------------------------------------
[docs] class ConstraintException(Exception): '''Defines an Exception that is used when an exception is raised processing constraints. Raised in :func:`GenerateConstraints` during sequential fits. Possible (but highly unlikely) to be raised in :func:`CheckEquivalences` (called by :func:`GenerateConstraints`) if an infinite loop is detected. Also raised in :func:`GramSchmidtOrtho` and :func:`_SwapColumns` but caught within :func:`GenerateConstraints`. ''' pass
[docs] def InitVars(): '''Initializes all constraint information''' global dependentParmList,arrayList,invarrayList,indParmList,consNum,symGenList dependentParmList = [] # contains a list of parameters in each group arrayList = [] # a list of of relationship matrices invarrayList = [] # a list of inverse relationship matrices indParmList = [] # a list of names for the new parameters consNum = 0 # number of the next constraint to be created symGenList = [] # Flag if constraint is generated by symmetry global holdParmList,holdParmType holdParmList = [] holdParmType = {} global droppedSym droppedSym = [] global constrVarList,indepVarList,depVarList constrVarList = [] indepVarList = [] depVarList = []
[docs] def VarKeys(constr): """Finds the keys in a constraint that represent parameters e.g. eliminates any that start with '_' :param dict constr: a single constraint entry of form:: {'var1': mult1, 'var2': mult2,... '_notVar': val,...} (see :func:`GroupConstraints`) :returns: a list of keys where any keys beginning with '_' are removed. """ return [i for i in constr.keys() if not i.startswith('_')]
[docs] def GroupConstraints(constrDict): """Divide the constraints into groups that share no parameters. :param dict constrDict: a list of dicts defining relationships/constraints :: constrDict = [{<constr1>}, {<constr2>}, ...] where {<constr1>} is {'var1': mult1, 'var2': mult2,... } :returns: two lists of lists: * a list of grouped contraints where each constraint grouped containts a list of indices for constraint constrDict entries * a list containing lists of parameter names contained in each group """ assignedlist = [] # relationships that have been used groups = [] # contains a list of grouplists ParmList = [] for i,constrI in enumerate(constrDict): if i in assignedlist: continue # already in a group, skip # starting a new group grouplist = [i,] assignedlist.append(i) groupset = set(VarKeys(constrI)) changes = True # always loop at least once while(changes): # loop until we can't find anything to add to the current group changes = False # but don't loop again unless we find something for j,constrJ in enumerate(constrDict): if j in assignedlist: continue # already in a group, skip if len(set(VarKeys(constrJ)) & groupset) > 0: # true if this needs to be added changes = True grouplist.append(j) assignedlist.append(j) groupset = groupset | set(VarKeys(constrJ)) group = sorted(grouplist) varlist = sorted(list(groupset)) groups.append(group) ParmList.append(varlist) return groups,ParmList
[docs] def GenerateConstraints(varyList,constrDict,fixedList,parmDict=None, seqHistNum=None,raiseException=False): '''Takes a list of relationship entries that have been stored by :func:`ProcessConstraints` into lists ``constrDict`` and ``fixedList`` This routine then calls :func:`CheckEquivalences` for internal consistency. This includes converting equivalenced variables into constraints when a variable is used in both. Once checked, parameters are grouped so that any parameters that are used in more than one constraint are grouped together. This allows checking for incompatible logic (for example, when four constraints are specified for three variables). If parmDict is not None, the parameter groups are checked for constraints where some parameters are varied, but not others. If so, the value for that unvaried parameter is subtracted from the constant in the constraint. Once all checks are complete, the constraints are then converted to the form used to apply them, saving them as global variables within this module. :param list varyList: a list of parameters names (strings of form ``<ph>:<hst>:<nam>``) that will be varied. Note that this is changed here unless set to None. None is used to indicate that all constraints should be generated. :param dict constrDict: a list of dicts defining relationships/constraints (as described in :func:`GroupConstraints`) :param list fixedList: a list of values specifying a fixed value for each dict in constrDict. Values are either strings that can be converted to floats, float values or None if the constraint defines a new parameter. :param dict parmDict: a dict containing all parameters defined in current refinement. :param int seqHistNum: the hId number of the current histogram in a sequential fit. None (default) otherwise. :param bool raiseException: When True, generation of an error causes an exception to be raised (used in sequential fits) :returns: errmsg,warning,groups,parmlist **errmsg** Is an error message or empty if no errors were found **warning** Is a warning message about constraints that have been ignored or changed **groups** Lists parameter groups **parmlist** Lists parameters in each parameter groups ''' warninfo = {'msg':'', 'shown':{}} def warn(msg,cdict=None,val=None): if cdict is not None and cdict != warninfo['shown']: warninfo['shown'] = cdict if warninfo['msg']: warninfo['msg'] += '\n' if '_vary' in cdict: warninfo['msg'] += '\nProblem with new var expression: ' + _FormatConstraint(cdict,cdict.get('_name','New Var')) else: warninfo['msg'] += '\nProblem with constraint equation: ' + _FormatConstraint(cdict,val) if warninfo['msg']: warninfo['msg'] += '\n' warninfo['msg'] += ' ' + msg global dependentParmList,arrayList,invarrayList,indParmList,consNum # lists of parameters used for error reporting global undefinedVars # parameters that are used in equivalences but are not defined undefinedVars = [] global groupErrors # parameters in constraints that cause grouping errors groupErrors = [] global saveVaryList saveVaryList = copy.copy(varyList) errmsg = '' # save error messages here. If non-blank, constraints cannot be used. warning = '' # save informational text messages here. # find parameters used in constraint equations & new var assignments (all are dependent) global constrVarList constrVarList = [] for cnum,(cdict,fixVal) in enumerate(zip(constrDict,fixedList)): constrVarList += [i for i in cdict if i not in constrVarList and not i.startswith('_')] # Process the equivalences; If there are conflicting parameters, move them into constraints warning = CheckEquivalences(constrDict,varyList,fixedList,parmDict,seqHistNum=seqHistNum) # look through "Constr" and "New Var" constraints looking for zero multipliers and # Hold, Unvaried & Undefined parameters skipList = [] invalidParms = [] for cnum,(cdict,fixVal) in enumerate(zip(constrDict,fixedList)): #constrVarList += [i for i in cdict if i not in constrVarList and not i.startswith('_')] valid = 0 # count of good parameters # error reporting zeroList = [] # parameters with zero multipliers holdList = [] # parameters with "Hold"'s noVaryList = [] # parameters not varied noWildcardList = [] # wildcard parameters in non-sequential fit notDefList = [] # parameters not defined # processing to be done problem = False # constraint must be dropped dropList = [] # parameters to remove for var in VarKeys(cdict): # assemble warning info if cdict[var] == 0: # zero multiplier if var not in zeroList: zeroList.append(var) if var not in dropList: dropList.append(var) elif var in holdParmList: # hold invalid in New Var, drop from constraint eqn holdList.append(var) if fixVal is None: # hold in a newvar is not allowed problem = True else: if var not in dropList: dropList.append(var) elif ':*:' in var : # wildcard still present should be treated as undefined if var not in undefinedVars: undefinedVars.append(var) noWildcardList.append(var) problem = True elif parmDict is not None and var not in parmDict: # not defined, constraint will not be used if var not in undefinedVars: undefinedVars.append(var) notDefList.append(var) if seqHistNum is None: if ':dAx:' in var or ':dAy:' in var or ':dAz:' in var: # coordinates from undefined atoms if fixVal is None: problem = True # invalid in New Var else: if var not in dropList: dropList.append(var) # ignore in constraint eqn else: problem = True elif varyList is None: valid += 1 elif var not in varyList and fixVal is not None: # unvaried, constraint eq. only if var not in unvariedParmsList: unvariedParmsList.append(var) noVaryList.append(var) dropList.append(var) else: valid += 1 if seqHistNum is not None and len(notDefList) > 0 and valid == 0: # for sequential ref can quietly ignore constraints with all undefined vars notDefList = [] for l,m in ((zeroList,"have zero multipliers"), # show warning (holdList,'set as "Hold"'), (noVaryList,"not varied"), (noWildcardList,"wildcard in non-sequential fit"), (notDefList,"not defined")): if l and cdict.get('_vary',True): # true for constr eq & varied New Var msg = "parameter(s) " + m + ': ' for i,v in enumerate(l): if i != 0: msg += ', ' msg += v warn(msg,cdict,fixVal) if valid == 0: # no valid entries if seqHistNum is None: warn('Ignoring constraint, no valid entries',cdict) skipList.append(cnum) elif problem: # mix of valid & refined and undefined items, cannot use this if cdict.get('_vary',True): # true for constr eq & varied New Var warn('New Var constraint will be ignored',cdict) skipList.append(cnum) invalidParms += VarKeys(cdict) elif len(dropList) > 0: # mix of valid and problematic items, drop problem vars, but keep rest if GSASIIpath.GetConfigValue('debug'): msg = '' for v in dropList: if msg: msg += ' ,' msg += v warn('removing: '+msg,cdict) value = fixedList[cnum] for var in dropList: # do cleanup # NB expressions in constraint multipliers have already been evaluated if ':dAx:' in var or ':dAy:' in var or ':dAz:' in var: pass # treat delta coords as 0; no change in total is needed elif cdict[var] != 0: value = float(value) - cdict[var]*parmDict[var] del cdict[var] if float(value) != float(fixedList[cnum]): fixedList[cnum] = float(np.round(value,12)) if GSASIIpath.GetConfigValue('debug'): warn('revised as: '+_FormatConstraint(constrDict[cnum],fixedList[cnum])) for i in list(range(len(constrDict)-1,-1,-1)): # remove the dropped constraints if i in skipList: del constrDict[i] del fixedList[i] for i in invalidParms: StoreHold(i,"Used in invalid constraint") if warning: warning += '\n' warning += warninfo['msg'] groups,parmlist = GroupConstraints(constrDict) # now process each group and create the relations that are needed to form # a non-singular square matrix # Now check that all parameters are varied (probably do not need to do this # any more). For constraint equations, if all are varied, set VaryFree to True # and all newly created relationships will be varied. For NewVar constraints, # vary if the vary flag was set. for group,depPrmList in zip(groups,parmlist): if len(depPrmList) < len(group): # too many relationships -- no can do if errmsg: errmsg += '\n' errmsg += "Over-constrained input. " errmsg += "There are more constraints (" + str(len(group)) errmsg += ") than parameters (" + str(len(depPrmList)) + ")\nin these constraints:" for rel in group: errmsg += '\n\t'+ _FormatConstraint(constrDict[rel],fixedList[rel]) groupErrors += depPrmList continue # go on to next group try: constrArr = _FillArray(group,constrDict,depPrmList) except Exception as err: if errmsg: errmsg += '\n' if 'Initial' in str(err): errmsg += "\nSingular input. " errmsg += "There are internal inconsistencies in these constraints:" else: errmsg += "\nError expanding matrix with these constraints:" for rel in group: errmsg += '\n\t' + _FormatConstraint(constrDict[rel],fixedList[rel]) groupErrors += depPrmList continue try: GramSchmidtOrtho(constrArr,len(group)) except: if errmsg: errmsg += '\n' errmsg += "\nUnexpected singularity with constraints group (in Gram-Schmidt)" for rel in group: errmsg += '\n\t' + _FormatConstraint(constrDict[rel],fixedList[rel]) groupErrors += depPrmList continue try: invConstrArr = np.linalg.inv(constrArr) except: if errmsg: errmsg += '\n' errmsg += "\nSingular input. " errmsg += "The following constraints are not " errmsg += "linearly independent\nor do not " errmsg += "allow for generation of a non-singular set.\n" errmsg += 'This is unexpected. Please report this (toby@anl.gov)' for rel in group: errmsg += '\n\t' + _FormatConstraint(constrDict[rel],fixedList[rel]) groupErrors += depPrmList continue # scan through current group looking for new var assignments hasNewVar = False for rel in group: if fixedList[rel] is None: hasNewVar = True # there a New Var relationship in this group break else: # only constraint equations, check for unvaried parameters in one unvaried = False # this should not happen as they should have been removed for var in depPrmList: if varyList is not None and var not in varyList: unvaried = True break if unvaried: # something is not varied: skip group & remove all parameters from varyList for var in depPrmList: StoreHold(var,'Unexpected: mixed use') if GSASIIpath.GetConfigValue('debug'): print('Unexpected: Constraint group ignored (some parameters unvaried)') for rel in group: print (' '+_FormatConstraint(constrDict[rel],fixedList[rel])) continue maplist = [] # value or param name mapped to each row in expression matrix if not hasNewVar: # constraint equations; all remaining entries varied, vary generated for i in range(len(depPrmList)): if i >= len(group): # tag generated degrees of freedom with names and vary them varname = paramPrefix + str(consNum) # assign a unique name consNum += 1 maplist.append(varname) if varyList is not None: varyList.append(varname) else: rel = group[i] maplist.append(fixedList[rel]) else: # ------------------------- groups with new var assignments, vary only NV's w/flags set for i,rel in enumerate(group): if fixedList[rel] is None: varname = constrDict[rel].get('_name','::?????') maplist.append(varname) if constrDict[rel].get('_vary',False): if varyList is not None: varyList.append(varname) else: maplist.append(fixedList[rel]) # constraint equation for i in range(len(depPrmList)): if i >= len(group): # name generated degrees of freedom varname = paramPrefix + str(consNum) # assign a unique name consNum += 1 maplist.append(varname) for var in depPrmList: StoreHold(var,'New Var use') # keep this group dependentParmList.append(depPrmList) arrayList.append(constrArr) invarrayList.append(invConstrArr) indParmList.append(maplist) symGenList.append(False) if errmsg and raiseException: print (' *** ERROR in constraint definitions! ***') print (errmsg) if warning: print (' also note warnings in constraint processing:') print (warning) raise ConstraintException elif errmsg: return errmsg,warning,None,None # Make list of dependent and independent variables for all constraints constrParms['dep-equiv'] = [] constrParms['dep-constr'] = [] constrParms['indep-equiv'] = [] constrParms['indep-constr'] = [] for varlist,mapvars,multarr in zip(dependentParmList,indParmList,arrayList): # process all constraints for mv in mapvars: if type(mv) is float or type(mv) is int: continue if multarr is None and mv not in constrParms['indep-equiv']: constrParms['indep-equiv'].append(mv) elif mv not in constrParms['indep-constr']: constrParms['indep-constr'].append(mv) for mv in varlist: if multarr is None and mv not in constrParms['dep-equiv']: constrParms['dep-equiv'].append(mv) elif mv not in constrParms['dep-constr']: constrParms['dep-constr'].append(mv) StoreHold(mv,'dependent param') saveVaryList = copy.copy(varyList) # save varyList so it can be used within module if varyList is None: saveVaryList = [] # if equivMoved: # print(60*'=') # print('Constraints were reclassified to avoid conflicts, as below:') # print(mvMsg) # print('New constraints are:') # print (VarRemapShow(varyList,True)) # print(60*'=') return errmsg,warning,groups,parmlist # saved for sequential fits
[docs] def CheckEquivalences(constrDict,varyList,fixedList,parmDict=None,seqHistNum=None): '''Process equivalence constraints, looking for conflicts such as where a parameter is used in both an equivalence and a constraint expression or where chaining is done (A->B and B->C). Removes equivalences or parameters from equivalences or converts equivalences to constraints as described for :ref:`Equivalence Checking and Reorganization <CheckEquivalences>`. :param dict constrDict: a list of dicts defining relationships/constraints :param list varyList: list of varied parameters (defined during refinements only) :param list fixedList: a list of values specifying a fixed value for each dict in constrDict. Values are either strings that can be converted to floats or ``None`` if the constraint defines a new parameter rather than a constant. :param dict parmDict: a dict containing defined parameters and their values. Used to find equivalences where a parameter is has been removed from a refinement. :param int seqHistNum: the hId number of the current histogram in a sequential fit. None (default) otherwise. :returns: warning messages about changes that need to be made to equivalences ''' warninfo = {'msg':'', 'shown':-1} def warnEqv(msg,cnum=None): if cnum is not None and cnum != warninfo['shown']: warninfo['shown'] = cnum if warninfo['msg']: warninfo['msg'] += '\n' warninfo['msg'] += '\nProblem with equivalence: ' + _showEquiv( dependentParmList[cnum],indParmList[cnum],invarrayList[cnum]) if warninfo['msg']: warninfo['msg'] += '\n' warninfo['msg'] += ' ' + msg global depVarList # parameters used in equivalences as dependent parameters global indepVarList # parameters used in equivalences as independent parameters global constrVarList # parameters used in other constraints # lists of parameters used for error reporting global undefinedVars # parameters that are used in equivalences but are not defined global convVarList # parameters in equivalences that will be converted to constraints convVarList = [] # parameters in equivalences to be made into constraints global multdepVarList multdepVarList = [] # list of dependent parameters used in more than one equivalence # local vars dropVarList = [] # parameters that can be removed from equivalences removeList = [] # equivalences that are not needed convertList = [] # equivalences that should be converted to "Const" constraints # tabulate parameters used in equivalences by type depVarList = [] # list of all dependent parameters in equivalences indepVarList = [] # list of all independent parameters in equivalences for cnum,(varlist,mapvars,multarr,invmultarr) in enumerate(zip( dependentParmList,indParmList,arrayList,invarrayList)): #if multarr is not None: continue # equivalence indepVarList += [mv for mv in mapvars if mv not in indepVarList] depVarList += [v for v in varlist if v not in depVarList] # process equivalences: make a list of dependent and independent vars # and check for repeated uses (repetition of a parameter as an # independent var is OK) # look for parameters in equivalences that are used more than once as dependent parameters seenOnce = [] for cnum,(varlist,multarr) in enumerate(zip(dependentParmList,arrayList)): if multarr is not None: continue # equivalences only for v in varlist: if v not in seenOnce: seenOnce.append(v) elif v not in multdepVarList: multdepVarList.append(v) # scan through equivalences looking for other "dual uses". Stop when no new ones are found changed = True count = 0 while changed: changed = False count += 1 if count > 1000: raise ConstraintException("Too many loops in CheckEquivalences") # look for repeated dependent vars convVarList = [] # parameters in equivalences to be made into constraints for cnum,(varlist,mapvars,multarr,invmultarr) in enumerate(zip( dependentParmList,indParmList,arrayList,invarrayList)): if multarr is not None: continue # equivalences only if cnum in convertList: convVarList += [v for v in mapvars+varlist if v not in convVarList and type(v) is not float] continue # identify equivalences that need to be converted to constraints. # Where parameters: # are used both in equivalences & constraints, # are used as dependent multiple times or # where are used as both dependent and independent (chained) msg = False for v in mapvars: if v in constrVarList+convVarList: changed = True msg = True warnEqv("Independent parameter "+str(v)+' used in constraint',cnum) if cnum not in convertList: convertList.append(cnum) for v in varlist: if v in multdepVarList: changed = True msg = True warnEqv("Dependent parameter "+str(v)+' repeated',cnum) if cnum not in convertList: convertList.append(cnum) elif v in indepVarList: changed = True msg = True warnEqv("Dependent parameter "+str(v)+' used elsewhere as independent',cnum) if cnum not in convertList: convertList.append(cnum) elif v in constrVarList+convVarList: changed = True msg = True warnEqv("Dependent parameter "+str(v)+' used in constraint',cnum) if cnum not in convertList: convertList.append(cnum) if msg: warnEqv('Converting to "Constr"',cnum) if warninfo['msg'] and seqHistNum is not None: # sequential fit -- print the recasts but don't stop with a warning print(warninfo['msg']) warninfo = {'msg':'', 'shown':-1} global unvariedParmsList unvariedParmsList = [] # parameters in equivalences that are not varied # scan equivalences: look for holds for cnum,(varlist,mapvars,multarr,invmultarr) in enumerate(zip( dependentParmList,indParmList,arrayList,invarrayList)): if multarr is not None: continue # not an equivalence if cnum in convertList: continue # look for holds gotHold = False holdList = [] for v in varlist+mapvars: if v in holdParmList: gotHold = True elif type(v) is not float: holdList.append(v) if gotHold: if holdList: msg = ' Some parameters set as "Hold"; setting remainder as "Hold": ' for i,var in enumerate(holdList): if i != 0: msg += ", " msg += var StoreHold(var,'Equiv fixed') else: msg = ' All parameters set as "Hold" ' msg += "\n Will ignore equivalence" warnEqv(msg,cnum) removeList.append(cnum) continue # look for unvaried parameters gotVary = False gotNotVary = False holdList = [] for v in varlist+mapvars: if varyList is None or v in varyList: gotVary = True holdList.append(v) elif type(v) is not float: gotNotVary = True if v not in unvariedParmsList: unvariedParmsList.append(v) if gotNotVary: # at least some unvaried parameters if gotVary: # mix of varied and unvaried parameters msg = '\nSome parameters not varied; setting remainder as "Hold": ' for i,var in enumerate(holdList): if i != 0: msg += ", " msg += var StoreHold(var,'Equiv fixed') elif seqHistNum is not None: # don't need to warn for sequential fit removeList.append(cnum) continue else: msg = 'No parameters varied ' msg += "\n Will ignore equivalence" warnEqv(msg,cnum) removeList.append(cnum) continue # look for undefined or zero multipliers holdList = [] drop = 0 for v,m in zip(varlist,invmultarr): if parmDict is not None and v not in parmDict: if v not in undefinedVars: undefinedVars.append(v) if v not in dropVarList: dropVarList.append(v) drop += 1 elif m == 0: warnEqv("Parameter "+str(v)+" has a zero multiplier, dropping",cnum) if v not in dropVarList: dropVarList.append(v) drop += 1 else: holdList.append(v) if drop == len(varlist): warnEqv("No dependent parameters defined, ignoring equivalence",cnum) removeList.append(cnum) continue for mv in mapvars: if type(mv) is float: continue if parmDict is not None and mv not in parmDict: # independent parameter is undefined, but some dependent parameters are defined # hold them if mv not in undefinedVars: undefinedVars.append(mv) msg = "Parameter(s) "+str(mv) for v in varlist: if v in dropVarList: msg += ', ' + v msg += "not defined in this refinement\n" msg = "Setting holds for: " for i,var in enumerate(holdList): if i != 0: msg += ", " msg += var warnEqv(msg,cnum) drop += 1 if drop: # independent var and at least one dependent variable is defined msg = "Dropping undefined parameter(s) " i = 0 for v in varlist: if v in dropVarList: if i != 0: msg += ', ' i += 1 msg += v warnEqv(msg,cnum) msg = "Some parameters not defined. Setting holds for: " for i,var in enumerate(holdList): if i != 0: msg += ", " msg += var StoreHold(var,'Equiv fixed') warnEqv(msg,cnum) # Convert equivalences where noted for cnum,varlist in enumerate(dependentParmList): if cnum not in convertList: continue indvar = indParmList[cnum][0] # msg = '\nChanging equivalence:\n ' + _showEquiv( # dependentParmList[cnum],indParmList[cnum],invarrayList[cnum]) for dep,mult in zip(dependentParmList[cnum],invarrayList[cnum]): constrDict += [{indvar:-1.,dep:1./mult[0]}] fixedList += ['0.0'] #msg += '\n to constraint(s):' #msg += '\n ' + _FormatConstraint(constrDict[-1],fixedList[-1]) removeList.append(cnum) # Drop equivalences where noted global droppedSym droppedSym = [] if removeList: for i in set(removeList): if symGenList[i]: droppedSym.append((dependentParmList[i],indParmList[i],arrayList[i],invarrayList[i])) for i in sorted(set(removeList),reverse=True): del dependentParmList[i],indParmList[i],arrayList[i],invarrayList[i],symGenList[i] # Drop variables from remaining equivalences for cnum,varlist in enumerate(dependentParmList): for j,v in enumerate(varlist): drop = [] if v in dropVarList: drop.append(j) if drop: for j in sorted(drop,reverse=True): del indParmList[cnum][j] return warninfo['msg']
[docs] def ProcessConstraints(constList,seqmode='use-all',seqhst=None): """Interpret the constraints in the constList input into a dictionary, etc. All :class:`GSASIIobj.G2VarObj` objects are mapped to the appropriate phase/hist/atoms based on the object internals (random Ids). If this can't be done (if a phase has been deleted, etc.), the variable is ignored. If the constraint cannot be used due to too many dropped variables, it is counted as ignored. In the case of sequential refinements, the current histogram number is substituted for a histogram number of "*". NB: this processing does not include symmetry imposed constraints :param list constList: a list of lists where each item in the outer list specifies a constraint of some form, as described in the :mod:`GSASIIobj` :ref:`Constraint definitions <Constraint_definitions_table>`. :param str seqmode: one of 'use-all', 'wildcards-only' or 'auto-wildcard'. When seqmode=='wildcards-only' then any constraint with a numerical histogram number is skipped. With seqmode=='auto-wildcard', any non-null constraint number is set to the selected histogram. :param int seqhst: number for current histogram (used for 'wildcards-only' or 'auto-wildcard' only). Should be None for non-sequential fits. :returns: a tuple of (constrDict,fixedList,ignored) where: * constrDict (list of dicts) contains the constraint relationships * fixedList (list) contains the fixed values for each type of constraint. * ignored (int) counts the number of invalid constraint items (should always be zero!) """ constrDict = [] fixedList = [] ignored = 0 namedVarList = [] for constr in constList: terms = copy.deepcopy(constr[:-3]) # don't change the tree contents # deal with wildcards in sequential fits if seqmode == 'wildcards-only' and seqhst is not None: skip = False for term in terms: if term[1].histogram == '*': term[1] = term[1].varname(seqhst) elif term[1].histogram: skip = True if skip: continue elif seqmode == 'auto-wildcard' and seqhst is not None: for term in terms: term[1] = term[1].varname(seqhst) elif seqhst is not None: for term in terms: if term[1].histogram == '*': term[1] = term[1].varname(seqhst) # else: # term[1] = term[1].varname() # does this change anything??? # separate processing by constraint type if constr[-1] == 'h': # process a hold var = str(terms[0][1]) if '?' not in var: StoreHold(var,'User supplied') else: ignored += 1 elif constr[-1] == 'f': # process a new variable fixedList.append(None) D = {} varyFlag = constr[-2] varname = constr[-3] for term in terms: var = str(term[1]) if '?' not in var: D[var] = term[0] # add extra dict terms for input variable name and vary flag if varname is None: # no assigned name, create one global consNum varname = str(consNum) consNum += 1 else: varname = str(varname) # in case this is a G2VarObj if '::' in varname: D['_name'] = varname.replace('::','::nv-') else: D['_name'] = '::nv-' + varname D['_name'] = G2obj.MakeUniqueLabel(D['_name'],namedVarList) D['_vary'] = varyFlag == True # force to bool constrDict.append(D) elif constr[-1] == 'c': # process a constraint equation D = {} for term in terms: var = str(term[1]) if '?' not in var: D[var] = term[0] if len(D) >= 1: fixedList.append(float(constr[-3])) constrDict.append(D) else: ignored += 1 elif constr[-1] == 'e': # process an equivalence firstmult = None eqlist = [] for term in terms: if term[0] == 0: term[0] = 1.0 var = str(term[1]) if '?' in var: continue if firstmult is None: firstmult = term[0] firstvar = var else: eqlist.append([var,firstmult/term[0]]) if len(eqlist) > 0: StoreEquivalence(firstvar,eqlist,False) else: ignored += 1 else: ignored += 1 return constrDict,fixedList,ignored
[docs] def StoreHold(var,holdType=None): '''Takes a variable name and prepares it to be removed from the refined variables. Called with user-supplied constraints by :func:`ProcessConstraints`. At present symGen is not used, but could be set up to track Holds generated by symmetry. ''' global holdParmList,holdParmType if var not in holdParmList: holdParmList.append(var) if holdType: holdParmType[var] = holdType
[docs] def StoreEquivalence(independentVar,dependentList,symGen=True): '''Takes a list of dependent parameter(s) and stores their relationship to a single independent parameter (independentVar). Called with user-supplied constraints by :func:`ProcessConstraints`, with Pawley constraints from :func:`GSASIIstrIO.GetPawleyConstr`, with Unit Cell constraints from :func:`GSASIIstrIO.cellVary` with symmetry-generated atom constraints from :func:`GSASIIstrIO.GetPhaseData` There is no harm in using StoreEquivalence with the same independent variable:: StoreEquivalence('x',('y',)) StoreEquivalence('x',('z',)) but the same outcome can be obtained with a single call:: StoreEquivalence('x',('y','z')) The latter will run more efficiently. Note that mixing independent and dependent variables, such as:: StoreEquivalence('x',('y',)) StoreEquivalence('y',('z',)) is a poor choice. The module will attempt to fix this by transforming the equivalence to a "Const" constraint. :param str independentVar: name of master parameter that will be used to determine the value to set the dependent variables :param list dependentList: a list of parameters that will set from independentVar. Each item in the list can be a string with the parameter name or a tuple containing a name and multiplier: ``['::parm1',('::parm2',.5),]`` ''' global dependentParmList,arrayList,invarrayList,indParmList,symGenList mapList = [] multlist = [] allfloat = True for var in dependentList: if isinstance(var, str): mult = 1.0 elif len(var) == 2: var,mult = var else: raise Exception("Cannot parse "+repr(var) + " as var or (var,multiplier)") mapList.append(var) try: multlist.append(tuple((float(mult),))) except: allfloat = False multlist.append(tuple((mult,))) # added relationships to stored values arrayList.append(None) if allfloat: invarrayList.append(np.array(multlist)) else: invarrayList.append(multlist) indParmList.append(list((independentVar,))) dependentParmList.append(mapList) symGenList.append(symGen) return
[docs] def SubfromParmDict(s,prmDict): '''Process a string as a multiplier and convert it to a float value. This is done by subsituting any GSAS-II parameter names that appear in the string that have associated values in the parameter dict with the value for that parameter. :param str s: a string to be converted to a value :param dict prmDict: a dictionary with keys as GSAS-II parameter names and values the corresponding parameter value. :returns: the evaluated expression as a float. ''' # TODO: perhaps SubfromParmDict should be called to convert the # fixed-val in constraint equations from strings to values. for key in prmDict: if key in s: s = s.replace(key,str(prmDict[key])) return eval(s)
[docs] def EvaluateMultipliers(constList,*dicts): '''Convert multipliers for constraints and equivalences that are specified as strings into values. The strings can specify values in the parameter dicts as well as normal Python functions, such as "2*np.cos(0::Ax:2/2.)" :param list constList: a list of dicts containing constraint expressions :param \\*dicts: one or more dicts containing GSAS-II parameters and their values can be specified :returns: an empty string if there were no errors, or an error message listing the strings that could not be converted. ''' prmDict = {} for d in dicts: prmDict.update(d) # combine all passed parameter dicts problemList = "" # loop through multipliers in contraint expressions for const in constList: for key in const: if key.startswith('_'): continue try: # is this already a float, etc? 1+const[key] continue except: pass try: newval = SubfromParmDict(const[key][:],prmDict) if GSASIIpath.GetConfigValue('debug'): print('Changing ',const[key],'to',newval) const[key] = newval except: if problemList: problemList += ", " problemList += const[key] # loop through multipliers in equivalences global arrayList,invarrayList for i,(a,valList) in enumerate(zip(arrayList,invarrayList)): if a is not None: continue # ignore if not equiv try: valList.shape continue # ignore if already a numpy array except: pass repList = [] for v in valList: try: 1+v[0] repList.append(tuple((v[0],))) continue except: pass try: newval = SubfromParmDict(v[0][:],prmDict) if GSASIIpath.GetConfigValue('debug'): print('Changing ',v[0],'to',newval) repList.append(tuple((newval,))) except: if problemList: problemList += ", " problemList += v[0] repList.append(tuple(('error',))) invarrayList[i] = np.array(repList) return problemList
[docs] def GetDependentVars(opt=None): '''Return a list of dependent variables: e.g. parameters that are constrained in terms of other parameters :param str opt: type of dependent variables. 'equiv': from equivalences, 'constr': from constraints None (default): all :returns: a list of parameter names ''' if opt == 'equiv': return constrParms['dep-equiv'] elif opt == 'constr': return constrParms['dep-constr'] else: return constrParms['dep-equiv']+constrParms['dep-constr']
[docs] def GetIndependentVars(): '''Return a list of independent variables: e.g. parameters that are slaved to other parameters by constraints :returns: a list of parameter names ''' return constrParms['indep-equiv']+constrParms['indep-constr']
[docs] def getConstrError(constrLst,seqmode,seqhst): '''This is used to display error messages for constraints and equivalence relations :parm list constrLst: a single constraint or equivalence as saved in the data tree (see :ref:`constraint definitions <Constraint_definitions_table>`). :param str seqmode: one of 'use-all', 'wildcards-only' or 'auto-wildcard' :param int seqhst: number for current histogram (used for 'wildcards-only' or 'auto-wildcard' only). Should be None for non-sequential fits. :returns: error, msg where error (bool) is True if the constraint/equivalence creates an error, msg (str) can be a warning or an error ''' msg = '' note = '' terms = copy.deepcopy(constrLst[:-3]) if seqmode == 'wildcards-only' and seqhst is not None: if constrLst[-1] == 'e': msg = 'equivalence' else: msg = 'constraint' for term in terms: if term[1].histogram == '*': term[1] = term[1].varname(seqhst) elif term[1].histogram: return False,"Ignoring non-wildcard "+msg, "Ignore" elif seqmode == 'auto-wildcard' and seqhst is not None: for term in terms: term[1] = term[1].varname(seqhst) else: for term in terms: if term[1].histogram == '*': if seqhst is None: msg = "Parameter "+str(terms[0][1])+" contains a wildcard, which are used only sequential refinements. Constraint ignored." return False,msg, "Ignored" else: term[1] = term[1].varname(seqhst) else: term[1] = term[1].varname() if constrLst[-1] == 'e': # conflicting uses if terms[0][1] in constrVarList+convVarList: msg = "Parameter "+str(terms[0][1])+" used in constraint. To be recast as constraint." return False,msg, "Recast as constraint." varList = [] for m,v in terms: if v in constrVarList+convVarList: varList.append(str(v)) if varList: msg = "Parameter(s) used in constraint: " for i,v in enumerate(varList): if i != 0: msg += ', ' msg += v return False,msg,"Recast as constraint." varList = [] for m,v in terms[1:]: if v in indepVarList: varList.append(str(v)) if varList: msg = "Parameter(s) used elsewhere as independent: " for i,v in enumerate(varList): if i != 0: msg += ', ' msg += v return False,msg,"Recast as constraint." varList = [] for m,v in terms[1:]: if v in multdepVarList: varList.append(str(v)) if varList: msg += "Parameter(s) repeated as dependent: " for i,v in enumerate(varList): if i != 0: msg += ', ' msg += v return False,msg,"Recast as constraint." # zero multiplier varList = [] valid = 0 for m,v in terms: if m == 0: varList.append(str(v)) else: valid += 1 if varList and valid > 1: msg += "Parameter(s) with zero multipliers: " for i,v in enumerate(varList): if i != 0: msg += ', ' msg += v msg += " will be ignored" elif varList: msg += "Parameter(s) with zero multipliers:" for i,v in enumerate(varList): if i != 0: msg += ', ' msg += v return False,msg,"Ignored: not varied" # hold parameters s = '' for m,v in terms: if v in holdParmList and ( "User supplied" in holdParmType.get(v,'') or "symmetry" in holdParmType.get(v,'') or "rigid body" in holdParmType.get(v,'')): if s: s += ', ' s += str(v) if s: if msg: msg += '; ' msg += "Parameter(s) set as Hold: "+s msg += "\nThis equivalence will be ignored; all parameters are held." return False,msg,'Has holds: Not varied.' # unrefined parameters gotVary = False gotNotVary = False s = '' for m,v in terms: if v in unvariedParmsList: gotNotVary = True if s: s += ', ' s += str(v) else: gotVary = True if gotNotVary and gotVary: # mix of varied and unvaried parameters if msg: msg += '. ' msg += 'Unvaried parameter(s): '+s+"; remainder set Hold. All parameters fixed." return False,msg, 'Ignored: not all varied' elif gotNotVary: if msg: msg += '. ' msg += 'All parameters not varied. Equivalence Ignored.' return False,msg, 'Ignored: not varied' # undefined parameters undef = 0 s = '' for m,v in terms[1:]: if v in undefinedVars: undef += 1 if s: s += ', ' s += str(v) if undef == len(terms[1:]): msg += 'Ignored: None of the dependent parameters are defined' elif terms[0][1] in undefinedVars: if s: s = terms[0][1] + ', ' + s else: s = terms[0][1] msg += 'Undefined parameter(s): '+s+'. Remainder will be fixed' elif undef: msg += 'Undefined parameter(s): '+s+' will be dropped' elif constrLst[-1] == 'h': v = terms[0][1] if v in undefinedVars: return False,"Parameter is undefined","Ignored" if v in unvariedParmsList: return False,"Parameter is not refined","Ignored" else: # check for post-grouping errors in new var & constr. eq. groups for m,v in terms: if v in groupErrors: return True,'Constraint singularity: see error listing','Singular' zeroList = [] toBeUsed = [] undef = [] unvar = [] hold = [] for m,v in terms: # check for zero multiplier, undefined, unvaried or hold if constrLst[-1] == 'f': # new var expressions; if m == 0: zeroList.append(str(v)) elif v in undefinedVars: undef.append(str(v)) elif (v in holdParmList and constrLst[-2] and "User supplied" in holdParmType.get(v,'') or "symmetry" in holdParmType.get(v,'') or "rigid body" in holdParmType.get(v,'')): hold.append(str(v)) else: # constraint equation if m == 0: zeroList.append(str(v)) elif v in undefinedVars: undef.append(str(v)) elif v in unvariedParmsList: unvar.append(str(v)) elif v in holdParmList and holdParmType.get(v,'') != 'dependent param': hold.append(str(v)) else: toBeUsed.append(str(v)) s = '' for v in zeroList: if s: s += ', ' s += str(v) if s: if msg: msg += '; ' msg += "Parameter(s) with zero multipliers: "+s s = '' for v in undef: if s: s += ', ' s += str(v) if s: if msg: msg += '; ' msg += "Undefined parameter(s): "+s s = '' for v in unvar: if s: s += ', ' s += str(v) if s: if msg: msg += '; ' msg += "Unrefined parameter(s) will be dropped: "+s s = '' for v in hold: if s: s += ', ' s += str(v) if s: if msg: msg += '; ' msg += '"Hold" parameter(s): '+s if hold and constrLst[-1] == 'f': if msg: msg += '; ' msg += "\nNew var with holds cannot be processed; constraint ignored." note = 'Ignored' elif undef and toBeUsed: s = '' for v in toBeUsed: if s: s += ', ' s += str(v) if msg: msg += '; ' msg += "Adding Holds on "+s+"; Constraint Ignored." note = 'Ignored' elif undef or (len(toBeUsed) == 0 and (zeroList or unvar or hold)): if msg: msg += '; ' msg += "No parameters remain. Constraint Ignored." note = 'Ignored' elif len(toBeUsed) == 1 and (zeroList or unvar or hold): if msg: msg += '; ' msg += "One parameter is retained; converted to fixed value." note = 'Converted' elif zeroList or unvar or hold: if msg: msg += ': ' msg += '\nConstraint adjusted for fixed values and retained.' note = 'Parameter(s) removed' return False,msg,note
[docs] def ComputeDepESD(covMatrix,varyList,noSym=False): '''Compute uncertainties for dependent parameters from independent ones returns a dictionary containing the esd values for dependent parameters :param np.array covMatrix: the full covariance matrix :param list varyList: the names of the variables matching the columns and rows in covMatrix :param bool noSym: When True symmetry generated parameters are not included. Do this so that redundant s.u.'s eare not shown. When False (default) s.u. values for all dependent parameters are placed in the returned dict. ''' sigmaDict = {} for varlist,mapvars,multarr,invmultarr,symgen in zip( dependentParmList,indParmList,arrayList,invarrayList,symGenList): if symgen and noSym: continue # skip symmetry generted varied = 0 # get the v-covar matrix for independent parameters vcov = np.zeros((len(mapvars),len(mapvars))) for i1,name1 in enumerate(mapvars): if name1 not in varyList: continue varied += 1 iv1 = varyList.index(name1) for i2,name2 in enumerate(mapvars): if name2 not in varyList: continue iv2 = varyList.index(name2) vcov[i1][i2] = covMatrix[iv1][iv2] # vec is the vector that multiplies each of the independent values for i,(v,vec) in enumerate(zip(varlist,invmultarr)): #if i == varied: break # this limits the number of generated params # to match the number varied. Not sure why I did this. sigmaDict[v] = np.sqrt(np.inner(vec.T,np.inner(vcov,vec))) return sigmaDict
[docs] def _FormatConstraint(RelDict,RelVal): '''Formats a Constraint or Function for use in a convenient way''' linelen = 65 s = [""] for var,val in RelDict.items(): if var.startswith('_'): continue if len(s[-1]) > linelen: s.append(' ') m = val if s[-1] != "" and m >= 0: s[-1] += ' + ' elif s[-1] != "": s[-1] += ' - ' m = abs(m) if m == 1: s[-1] += '%s '%var else: s[-1] += '%.3f*%s '%(m,var) if len(s[-1]) > linelen: s.append(' ') if RelVal is None: s[-1] += ' = New variable' else: s[-1] += ' = ' + str(RelVal) s1 = '' for s2 in s: if s1 != '': s1 += '\n ' s1 += s2 return s1
[docs] def _showEquiv(varlist,mapvars,invmultarr,longmsg=False): '''Format an equivalence relationship, note that varlist, mapvars, invmultarr are elements of dependentParmList, indParmList, invarrayList ''' for i,mv in enumerate(mapvars): s1 = str(mv) if not longmsg: s1 += ' ==> ' elif len(varlist) == 1: s1 += ' is equivalent to ' else: s1 += ' is equivalent to parameters: ' j = 0 for v,m in zip(varlist,invmultarr): if debug: print ('v,m[0]: ',v,m[0]) if len(s1.split('\n')[-1]) > 60: s1 += '\n ' if j > 0: s1 += ' & ' j += 1 s1 += str(v) if m != 1: s1 += " / " + str(m[0]) return s1
[docs] def VarRemapShow(varyList=None,inputOnly=False,linelen=60): '''List out the saved relationships. This should be done after the constraints have been defined using :func:`StoreEquivalence`, :func:`GroupConstraints` and :func:`GenerateConstraints`. :returns: a string containing the details of the contraint relationships ''' if varyList is None: varyList = saveVaryList s = '' depVars = constrParms['dep-equiv']+constrParms['dep-constr'] if len(depVars) > 0: s += '\nDependent parameters from constraints & equivalences:\n' for v in sorted(set(depVars)): s += ' ' + v + '\n' first = True for v in sorted(holdParmList): if v in depVars: continue if v in holdParmType: v += '\t'+holdParmType[v] if first: s += '\nParameters set as Hold:\n' first = False s += ' ' + v + '\n' userOut = '' symOut = '' consOut = '' varOut = '' freeOut = '' global dependentParmList,arrayList,invarrayList,indParmList,symGenList for varlist,mapvars,multarr,invmultarr,symFlag in zip( dependentParmList,indParmList,arrayList,invarrayList,symGenList): for i,mv in enumerate(mapvars): if multarr is None: # s1 = ' ' + str(mv) + ' is equivalent to parameter(s): ' if len(varlist) == 1: s1 = ' ' + str(mv) + ' is equivalent to ' else: s1 = ' ' + str(mv) + ' is equivalent to parameters: ' j = 0 for v,m in zip(varlist,invmultarr): if debug: print ('v,m[0]: ',v,m[0]) if j > 0: s1 += ' & ' j += 1 s1 += str(v) if m != 1: s1 += " / " + '{:.4f}'.format(m[0]) #if len(s1.split('\n')[-1]) > 70: # s1 = ' \n &'.join(s1.rsplit('&',1)) if symFlag: symOut += s1 + '\n' else: userOut += s1 + '\n' continue ln = '' # if mv in varyList: # lineOut = ' (V)* {} = '.format(mv) # else: # lineOut = ' {} = '.format(mv) j = 0 lineOut = ' {} = '.format(mv) for (m,v) in zip(multarr[i,:],varlist): if m == 0: continue if m < 0: lineOut += ' - ' m *= -1 elif j != 0: lineOut += ' + ' j += 1 if len(lineOut) > linelen: ln += lineOut lineOut = '\n ' if m == 1: lineOut += '{}'.format(v) else: lineOut += '({:.4g} * {})'.format(m,v) if mv in varyList: lineOut += '\t *VARIED*' ln += lineOut if type(mv) is float: consOut += ln + '\n' elif '::nv-' in mv: varOut += ln + '\n' else: freeOut += ln + '\n' if userOut: s += '\nUser-supplied equivalences:\n' + userOut if droppedSym: for varlist,mapvars,multarr,invmultarr in droppedSym: for i,mv in enumerate(mapvars): if len(varlist) == 1: s1 = ' ' + str(mv) + ' is equivalent to ' else: s1 = ' ' + str(mv) + ' is equivalent to parameters: ' j = 0 for v,m in zip(varlist,invmultarr): if debug: print ('v,m[0]: ',v,m[0]) if j > 0: s1 += ' & ' j += 1 s1 += str(v) if m != 1: s1 += " / " + '{:.4f}'.format(m[0]) symOut += s1 + '\t *recast as equation*\n' if symOut: s += '\nSymmetry-generated equivalences:\n' + symOut if consOut: s += '\nConstraint Equations:\n' + consOut if varOut: s += '\nNew Variable assignments:\n' + varOut if freeOut: s += '\nGenerated constraint equations:\n' + freeOut if not (userOut or consOut or varOut or symOut): return s + '\nNo constraints or equivalences in use' elif inputOnly: return s s += '\nInverse parameter mapping relations:\n' lineDict = {} # store so we can sort them for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList): varied = False for i,mv in enumerate(varlist): constrVal = 0 # offset to constraint from constant terms lineOut = ' {} = '.format(mv) j = 0 # number of terms shown for m,v in zip(invmultarr[i,:],mapvars): if np.isclose(m,0): continue try: if np.isclose(float(v),0): continue except: pass if v in varyList: varied = True try: constrVal += m*v # v is a constant; add to offset continue except: pass if m < 0: lineOut += ' - ' m *= -1 elif j != 0: lineOut += ' + ' j += 1 if len(lineOut) > linelen: s += lineOut lineOut = '\n ' if m == 1: lineOut += '{}'.format(v) else: lineOut += '({:.4g} * {})'.format(m,v) if constrVal < 0: lineOut += ' - {:.4g}'.format(-constrVal) elif constrVal > 0: lineOut += ' + {:.4g}'.format(constrVal) elif j == 0: lineOut += '0' # no terms, no constants: var fixed at zero if varied: lineOut += '\t *VARIED*' lineDict[mv] = lineOut for key in sorted(lineDict): s += lineDict[key] + '\n' return s
[docs] def getInvConstraintEq(var,varyList): '''For a dependent variable, find the constraint that defines the dependent variable in terms of varied independent variables. This works for constraint equations (via new var or generated parameters) or equivalences. For equivalences the result will lists of length 1 :param str var: named of refined variable (e.g. 0:0:Scale) :param list varyList: list of refined variables :returns: vList,mList where vList is a list of variables and mList is a list of multipliers for that variable (floats) ''' for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList): if var not in varlist: continue i = varlist.index(var) vList = [] mList = [] for m,v in zip(invmultarr[i,:],mapvars): if v not in varyList: continue if m == 0: continue if v == 0: continue vList.append(v) mList.append(m) return vList,mList if GSASIIpath.GetConfigValue('debug'): print('getInvConstraintEq: not found: ',var) return [],[] # unexpected -- not an independent parameter
[docs] def GetSymEquiv(seqmode,seqhistnum): '''Return the automatically generated (equivalence) relationships. :returns: a list of strings containing the details of the contraint relationships ''' symout = [] symerr = [] symhelp = [] global dependentParmList,arrayList,invarrayList,indParmList,symGenList for varlist,mapvars,multarr,invmultarr,symFlag in zip( dependentParmList,indParmList,arrayList,invarrayList,symGenList): if not symFlag: continue for i,mv in enumerate(mapvars): cnstr = [[1,G2obj.G2VarObj(mv)]] if multarr is None: s1 = '' s2 = ' = ' + str(mv) j = 0 helptext = 'Variable {:} '.format(mv) + " ("+ G2obj.fmtVarDescr(mv) + ")" if len(varlist) == 1: cnstr.append([invmultarr[0][0],G2obj.G2VarObj(varlist[0])]) # format the way Bob prefers if invmultarr[0][0] == 1: s1 = str(varlist[0]) + ' = ' + str(mv) else: s1 = str(varlist[0]) + ' = ' + str( invmultarr[0][0]) + ' * '+ str(mv) s2 = '' m = 1./invmultarr[0][0] var1 = str(varlist[0]) helptext += "\n\nis equivalent to " if m == 1: helptext += '\n {:} '.format(var1) + " ("+ G2obj.fmtVarDescr(var1) + ")" else: helptext += '\n {:3g} * {:} '.format(m,var1) + " ("+ G2obj.fmtVarDescr(var1) + ")" else: helptext += "\n\nis equivalent to the following:" for v,m in zip(varlist,invmultarr): cnstr.append([m,G2obj.G2VarObj(v)]) #if debug: print ('v,m[0]: ',v,m[0]) if len(s1.split('\n')[-1]) > 75: s1 += '\n ' if j > 0: s1 += ' = ' j += 1 s1 += str(v) if m != 1: s1 += " / " + str(m[0]) helptext += '\n {:3g} * {:} '.format(m,v) + " ("+ G2obj.fmtVarDescr(v) + ")" else: helptext += '\n {:} '.format(v) + " ("+ G2obj.fmtVarDescr(v) + ")" err,msg,note = getConstrError(cnstr+[None,None,'e'],seqmode,seqhistnum) symerr.append([msg,note]) symout.append(s1+s2) symhelp.append(helptext) else: s = ' %s = ' % mv j = 0 for m,v in zip(multarr[i,:],varlist): if m == 0: continue if j > 0: s += ' + ' j += 1 s += '(%s * %s)' % (m,v) print ('unexpected sym op='+s) return symout,symerr,symhelp
[docs] def GetDroppedSym(seqmode,seqhistnum): '''Return automatically generated (equivalence) relationships that were converted to constraint equations :returns: a list of strings containing the details of the equivalences ''' symout = [] symerr = [] symhelp = [] global droppedSym for varlist,mapvars,multarr,invmultarr in droppedSym: for i,mv in enumerate(mapvars): cnstr = [[1,G2obj.G2VarObj(mv)]] if multarr is None: s1 = '' s2 = ' = ' + str(mv) j = 0 helptext = 'Variable {:} '.format(mv) + " ("+ G2obj.fmtVarDescr(mv) + ")" if len(varlist) == 1: cnstr.append([invmultarr[0][0],G2obj.G2VarObj(varlist[0])]) # format the way Bob prefers if invmultarr[0][0] == 1: s1 = str(varlist[0]) + ' = ' + str(mv) else: s1 = str(varlist[0]) + ' = ' + str( invmultarr[0][0]) + ' * '+ str(mv) s2 = '' m = 1./invmultarr[0][0] var1 = str(varlist[0]) helptext += "\n\nis equivalent to " if m == 1: helptext += '\n {:} '.format(var1) + " ("+ G2obj.fmtVarDescr(var1) + ")" else: helptext += '\n {:3g} * {:} '.format(m,var1) + " ("+ G2obj.fmtVarDescr(var1) + ")" else: helptext += "\n\nis equivalent to the following:" for v,m in zip(varlist,invmultarr): cnstr.append([m,G2obj.G2VarObj(v)]) #if debug: print ('v,m[0]: ',v,m[0]) if len(s1.split('\n')[-1]) > 75: s1 += '\n ' if j > 0: s1 += ' = ' j += 1 s1 += str(v) if m != 1: s1 += " / " + str(m[0]) helptext += '\n {:3g} * {:} '.format(m,v) + " ("+ G2obj.fmtVarDescr(v) + ")" else: helptext += '\n {:} '.format(v) + " ("+ G2obj.fmtVarDescr(v) + ")" err,msg,note = getConstrError(cnstr+[None,None,'e'],seqmode,seqhistnum) symerr.append([msg,note]) symout.append(s1+s2) symhelp.append(helptext) else: s = ' %s = ' % mv j = 0 for m,v in zip(multarr[i,:],varlist): if m == 0: continue if j > 0: s += ' + ' j += 1 s += '(%s * %s)' % (m,v) print ('unexpected sym op='+s) return symout,symerr,symhelp
[docs] def Dict2Deriv(varyList,derivDict,dMdv): '''Compute derivatives for Independent Parameters from the derivatives for the original parameters :param list varyList: a list of parameters names that will be varied :param dict derivDict: a dict containing derivatives for parameter values keyed by the parameter names. :param list dMdv: a Jacobian, as a list of np.array containing derivatives for dependent parameter computed from derivDict ''' global dependentParmList,arrayList,invarrayList,indParmList,invarrayList for varlist,mapvars,multarr,invmultarr in zip(dependentParmList,indParmList,arrayList,invarrayList): for i,name in enumerate(mapvars): # grouped parameters: need to add in the derv. w/r # dependent variables to the independent ones if name not in varyList: continue # skip if independent var not varied if multarr is None: if debug: print ('start dMdv for',name,dMdv[varyList.index(name)]) for v,m in zip(varlist,invmultarr): if m[0] == 0: continue dMdv[varyList.index(name)] += derivDict[v]/ m[0] else: for v,m in zip(varlist,invmultarr[:,i]): if m == 0: continue dMdv[varyList.index(name)] += m * derivDict[v]
[docs] def Map2Dict(parmDict,varyList): '''Updates the parameter dictionary and the varyList using the equivalence and constraint input. This should be called at least once, after the constraints have been defined using :func:`StoreEquivalence`, :func:`GroupConstraints` and :func:`GenerateConstraints` and before any parameter refinement is done. This completes the parameter dictionary by defining values for parameters created by constraints based on the constraints that define them using the values for the current parameters. It also removes all dependent variables from the varyList :param dict parmDict: a dict containing parameter values keyed by the parameter names. For new variables created by constraints, entries will be added to the dictionary, if not alreay present, or the values will be recomputed. :param list varyList: a list of parameters names. Will be modified. ''' # remove fixed parameters from the varyList for item in holdParmList: if varyList is not None and item in varyList: varyList.remove(item) # process the independent parameters: # * remove dependent ones from varylist # * for equivalences apply the independent parameters onto dependent variables global dependentParmList,arrayList,invarrayList,indParmList for varlist,mapvars,multarr,invmultarr in zip(dependentParmList,indParmList,arrayList,invarrayList): for item in varlist: # TODO: is this still needed? if varyList is not None and item in varyList: varyList.remove(item) if multarr is None: #for v,val in zip( # shows values to be set # varlist, # np.dot(invmultarr,np.array([parmDict[var] for var in mapvars])) # ): print('parmDict set',v,':',val) parmDict.update(zip(varlist,np.dot(invmultarr,np.array([parmDict[var] for var in mapvars])))) # * for the created parameters, compute them from their dependents for varlist,mapvars,multarr in zip(dependentParmList,indParmList,arrayList): if multarr is None: continue # evaluate constraints in the forward direction A = np.array([parmDict[var] for var in varlist]) z = zip(mapvars,np.dot(multarr,A)) # add/replace in parameter dict parmDict.update([i for i in z if type(i[0]) is not float and ':' in i[0]]) # parmDict.update([i for i in zip(mapvars,np.dot(multarr,A)) if ':' in i[0]]) global saveVaryList if varyList is not None: saveVaryList = copy.copy(varyList) else: saveVaryList = []
[docs] def normParms(parmDict): '''Attempt to put parameters into the right ballpark by scaling to enforce constraint equations ''' for varlist,mapvars,multarr,invmultarr in zip( dependentParmList,indParmList,arrayList,invarrayList): if multarr is None or invmultarr is None: continue # unexpected for i,s in enumerate(mapvars): try: s = float(s) except: continue sumcons = 0. for var,m in zip(varlist,multarr[i]): if var not in parmDict: print('normParms error: Parameter',var,'not in parmDict') break sumcons += parmDict[var] * m if sumcons != s and sumcons != 0 and s != 0: for var in varlist: parmDict[var] *= s/sumcons
[docs] def Dict2Map(parmDict): '''Applies the constraints defined using :func:`StoreEquivalence`, :func:`GroupConstraints` and :func:`GenerateConstraints` by changing values in a dict containing the parameters. This should be done after refinement and before the parameters are used for any computations :param dict parmDict: a dict containing parameter values keyed by the parameter names. After this is called, all the dependent variables will be updated based on constraints and equivalences. ''' global dependentParmList,arrayList,invarrayList,indParmList for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList): if invmultarr is None: # is this needed? if GSASIIpath.GetConfigValue('debug'): print('Why does this constraint have None for invmultarr?',varlist,mapvars) continue valslist = np.array([float(parmDict.get(var,var)) for var in mapvars]) #for v,val in zip(varlist,np.dot(invmultarr,np.array(valslist))): print(v,val) # shows what is being set parmDict.update(zip(varlist,np.dot(invmultarr,valslist)))
#====================================================================== # internal routines follow (these routines are unlikely to be called # from outside the module)
[docs] def GramSchmidtOrtho(a,nkeep=0): '''Use the Gram-Schmidt process (http://en.wikipedia.org/wiki/Gram-Schmidt) to find orthonormal unit vectors relative to first row. If nkeep is non-zero, the first nkeep rows in the array are not changed input: arrayin: a 2-D non-singular square array returns: a orthonormal set of unit vectors as a square array ''' def proj(a,b): 'Projection operator' return a*(np.dot(a,b)/np.dot(a,a)) for j in range(nkeep,len(a)): for i in range(j): a[j] -= proj(a[i],a[j]) if np.allclose(np.linalg.norm(a[j]),0.0): raise ConstraintException("Singular input to GramSchmidtOrtho") a[j] /= np.linalg.norm(a[j]) return a
[docs] def _FillArray(sel,d,collist): '''Construct a n by n matrix [n = len(collist)] with the initial m rows [m = len(sel)] using the relationships defined in the expressions dict, d. Since m may be smaller than n, the remaining rows are filled with rows that are tested to not create a singular matrix. :param list sel: a list of indices in dict d :param list d: a list of dict's where each dict describes an expression from a constraint equation or a new var :param list collist: a list parameter names. :returns: an n by n numpy.array matrix ''' n = len(collist) m = len(sel) arr = np.zeros(2*[n,]) # fill the top rows for i,cnum in enumerate(sel): for j,var in enumerate(collist): arr[i,j] = d[cnum].get(var,0) try: _RowEchelon(m,copy.copy(arr),collist[:]) except: raise Exception('Initial constraints singular') for i in range(m,n): arr[i][i] = 1 # add a diagonal element try: _RowEchelon(i+1,copy.copy(arr),collist[:]) continue except: pass for j in range(n): if j == i: continue arr[i][j] = 1 # add another element try: _RowEchelon(i+1,copy.copy(arr),collist[:]) break except: pass arr[i][j] = -1 # try a different valuefor this element try: _RowEchelon(i+1,copy.copy(arr),collist[:]) break except: arr[i][j] = 0 # reset to add another element else: raise Exception('Unable to create non-singular matrix') return arr
[docs] def _SwapColumns(i,m,v): '''Swap columns in matrix m as well as the labels in v so that element (i,i) is replaced by the first non-zero element in row i after that element Throws an exception if there are no non-zero elements in that row ''' for j in range(i+1,len(v)): if not np.allclose(m[i,j],0): m[:,(i,j)] = m[:,(j,i)] v[i],v[j] = v[j],v[i] return else: raise ConstraintException('Singular input')
[docs] def _RowEchelon(m,arr,collist): '''Convert the first m rows in Matrix arr to row-echelon form exchanging columns in the matrix and collist as needed. throws an exception if the matrix is singular because the first m rows are not linearly independent ''' for i in range(m): if np.allclose(arr[i,i],0): _SwapColumns(i,arr,collist) arr[i,:] /= arr[i,i] # normalize row # subtract current row from subsequent rows to set values to left of diagonal to 0 for j in range(i+1,m): arr[j,:] -= arr[i,:] * arr[j,i]
if __name__ == "__main__": d = [{'a': 0, 'b': 1.5,'d':0}, {'d': -1}] lbls = ['a','c','b','d'] sel = (0,1) try: arr2 = _FillArray(sel,d,lbls) except Exception as err: if 'Initial' in str(err): print('initial error') else: print('unable to extend matrix error') import sys; sys.exit() print(arr2) d = [{'a': 1, 'b': 1,}] lbls = ['a','b'] sel = (0,) arr1 = _FillArray(sel,d,lbls) print(arr1) print(GramSchmidtOrtho(arr1,1)) import sys; sys.exit() parmdict = {} constrDict = [ {'0:12:Scale': 2.0, '0:11:Scale': 1.0, '0:14:Scale': 4.0, '0:13:Scale': 3.0, '0:0:Scale': 0.5}, {'0:0:eA': 0.0}, {'2::C(10,6,1)': 1.0, '1::C(10,6,1)': 1.0}, {'1::C(10,0,1)': 1.0, '2::C(10,0,1)': 1.0}, {'1::AUiso:0': 1.0, '0::AUiso:0': 1.0}, {'0::A0': 0.0} ] fixedList = ['5.0', '0', None, None, '1.0', '0'] StoreEquivalence('2::atomx:3',('2::atomy:3', ('2::atomz:3',2,), )) #StoreEquivalence('1::atomx:3',('2::atomx:3', ('2::atomz:3',2,), )) # error: dependent & independent vars mixed #StoreEquivalence('1::atomx:3',('2::atomy:3', ('2::atomz:3',2,), )) # error: dependent vars repeated #StoreEquivalence('0:1:eA',('0:0:eA',)) # error: equiv & fixed #StoreEquivalence('0:99:Scale',('0:12:Scale',)) # error: equiv & constrained #StoreEquivalence('0:12:Scale',('0:99:Scale',)) # error: equiv & constrained varyList = ['2::atomx:3', '2::C(10,6,1)', '1::C(10,6,1)', '2::atomy:3', '2::atomz:3', '0:12:Scale', '0:11:Scale', '0:14:Scale', '0:13:Scale', '0:0:Scale'] # varyList = ['0::A0', '0::AUiso:0', '0::Afrac:1', '0::Afrac:2', '0::Afrac:3', '0::Afrac:4', # '0::dAx:5', '0::dAy:5', '0::dAz:5', '0::AUiso:5', ':0:Back;0', ':0:Back;1', ':0:Back;2', ':0:Back;3', # ':0:Back;4', ':0:Back;5', ':0:Back;6', ':0:Back;7', ':0:Back;8', ':0:Back;9', ':0:Back;10', ':0:Back;11' # :0:U', ':0:V', ':0:W', ':0:X', ':0:Y', ':0:Scale', ':0:DisplaceX', ':0:DisplaceY'] # constrDict = [ # {'0::Afrac:4': 24.0, '0::Afrac:1': 16.0, '0::Afrac:3': 24.0, '0::Afrac:2': 16.0}, # {'0::Afrac:1': 1.0, '0::Afrac:2': 1.0}, # {'0::Afrac:4': 1.0, '0::Afrac:3': 1.0}] # fixedList = ['40.0', '1.0', '1.0'] msg,warning,groups,parmlist = GenerateConstraints(varyList,constrDict,fixedList,parmdict) print (VarRemapShow(varyList)) parmdict.update( { '0:12:Scale': 1.0, '0:11:Scale': 1.0, '0:14:Scale': 1.0, '0:13:Scale': 1.0, '0:0:Scale': 2.0, '0:0:eA': 0.0, '2::C(10,6,1)': 0.2, '1::C(10,6,1)': 0.3, '1::C(10,0,1)': 0.2, '2::C(10,0,1)': 0.3, '1::AUiso:0': 0.02, '0::AUiso:0': 0.03, '0::A0': 0.0, '2::atomx:3':0.23,'2::atomy:3':-.23, '2::atomz:3':-0.11, }) print ('parmdict start',parmdict) print ('varylist start',varyList) before = parmdict.copy() Map2Dict(parmdict,varyList) print ('parmdict before and after Map2Dict') print (' key / before / after') for key in sorted(list(parmdict.keys())): print (' '+key,'\t',before.get(key),'\t',parmdict[key]) print ('varylist after',varyList) before = parmdict.copy() Dict2Map(parmdict) print ('after Dict2Map') print (' key / before / after') for key in sorted(list(parmdict.keys())): print (' '+key,'\t',before.get(key),'\t',parmdict[key]) # dMdv = len(varylist)*[0] # deriv = {} # for i,v in enumerate(parmdict.keys()): deriv[v]=i # Dict2Deriv(varylist,deriv,dMdv)