source: trunk/GSASIImapvars.py @ 2874

Last change on this file since 2874 was 2874, checked in by toby, 4 years ago

Sequential refinement fixes where # of phases change

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1# -*- coding: utf-8 -*-
2########### SVN repository information ###################
3# $Date: 2017-06-24 14:33:04 +0000 (Sat, 24 Jun 2017) $
4# $Author: toby $
5# $Revision: 2874 $
6# $URL: trunk/GSASIImapvars.py $
7# $Id: GSASIImapvars.py 2874 2017-06-24 14:33:04Z toby $
8########### SVN repository information ###################
9"""
10*GSASIImapvars: Parameter constraints*
11======================================
12
13Module to implements algebraic contraints, parameter redefinition
14and parameter simplification contraints.
15
16Parameter redefinition (new vars) is done by creating one or more relationships
17between a set of parameters
18
19::
20
21   Mx1 * Px + My1 * Py +...
22   Mx2 * Px + Mz2 * Pz + ...
23
24where Pj is a parameter name and Mjk is a constant.
25
26Constant constraint Relations can also be supplied in the form of an equation:
27
28::
29
30  nx1 * Px + ny1 * Py +... = C1
31
32where Cn is a constant. These equations define an algebraic
33constrant.
34
35Parameters can also be "fixed" (held), which prevents them from being refined.
36
37All of the above three cases are input using routines
38GroupConstraints and GenerateConstraints. The input consists of a list of
39relationship dictionaries:
40
41.. code-block:: python
42
43    constrDict = [
44         {'0:12:Scale': 2.0, '0:14:Scale': 4.0, '0:13:Scale': 3.0, '0:0:Scale': 0.5},
45         {'2::C(10,6,1)': 1.0, '1::C(10,6,1)': 1.0},
46         {'0::A0': 0.0}]
47    fixedList = ['5.0', None, '0']
48
49Where the dictionary defines the first part of an expression and the corresponding fixedList
50item is either None (for parameter redefinition) or the constant value, for a constant
51constraint equation. A dictionary that contains a single term defines a variable that
52will be fixed (held). The multiplier and the fixedList value in this case are ignored.
53
54Parameters can also be equivalenced or "slaved" to another parameter, such that one
55(independent) parameter is equated to several (now dependent) parameters. In
56algebraic form this is:
57
58::
59
60   P0 = M1 * P1 = M2 * P2 = ...
61
62Thus parameters P0, P1 and P2,... are linearly equivalent. Routine StoreEquivalence is
63used to specify these equivalences.
64
65Parameter redefinition (new vars) describes a new, independent, parameter, which
66is defined in terms of dependent parameters that are defined in the
67Model, while fixed constrained relations effectively reduce the complexity
68of the Model by removing a degree of freedom. It is possible for a parameter to appear
69in both a parameter redefinition expression and a fixed constraint equation, but a
70parameter cannot be used a parameter equivalance cannot be used elsewhere (not fixed,
71constrained or redefined). Likewise a fixed parameter cannot be used elsewhere (not
72equivalanced, constrained or redefined).
73
74Relationships are grouped so that a set of dependent parameters appear
75in only one group (done in routine GroupConstraints.) Note that if a
76group contains relationships/equations that involve N dependent
77parameters, there must exist N-C new parameters, where C is the number
78of contraint equations in the group. Routine GenerateConstraints takes
79the output from GroupConstraints and generates the
80"missing" relationships and saves that information in the module's
81global variables. Each generated parameter is named sequentially using paramPrefix.
82
83A list of parameters that will be varied is specified as input to GenerateConstraints
84(varyList). A fixed parameter will simply be removed from this list preventing that
85parameter from being varied. Note that all parameters in a constraint relationship
86must specified as varied (appear in varyList) or none can be varied. This is
87checked in GenerateConstraints. Likewise, if all parameters in a constraint are
88not referenced in a refinement, the constraint is ignored, but if some parameters
89in a constraint group are not referenced in a refinement, but others are this
90constitutes and error.
91
92* When a new variable is created, the variable is assigned the name associated
93  in the constraint definition or it is assigned a default name of form
94  ``::constr<n>`` (see paramPrefix). The vary setting for variables used in the
95  constraint are ignored.
96  Note that any generated "missing" relations are not varied. Only
97  the input relations can be are varied.
98 
99* If all parameters in a fixed constraint equation are varied, the generated "missing"
100  relations in the group are all varied. This provides the N-C degrees of freedom.
101
102*External Routines*
103-------------------
104
105To define a set of constrained and unconstrained relations, one
106defines a list of dictionary defining constraint parameters and their
107values, a list of fixed values for each constraint and a list of
108parameters to be varied. In addition, one uses
109:func:`StoreEquivalence` to define parameters that are equivalent. One
110can then use :func:`CheckConstraints` to check that the input is
111internally consistent and finally :func:`GroupConstraints` and
112:func:`GenerateConstraints` to generate the internally used
113tables. Routines :func:`Map2Dict` is used to initialize the parameter
114dictionary and :func:`Dict2Map`, :func:`Dict2Deriv`, and
115:func:`ComputeDepESD` are used to apply constraints. Routine
116:func:`VarRemapShow` is used to print out the constraint information,
117as stored by :func:`GenerateConstraints`.
118
119:func:`InitVars`
120  This is optionally used to clear out all defined previously defined constraint information
121 
122:func:`StoreEquivalence`
123  To implement parameter redefinition, one calls StoreEquivalence. This should be called for every set of
124  equivalence relationships. There is no harm in using StoreEquivalence with the same independent variable:
125
126  .. code-block:: python
127
128       StoreEquivalence('x',('y',))
129       StoreEquivalence('x',('z',))
130
131  or equivalently
132
133  .. code-block:: python
134
135       StoreEquivalence('x',('y','z'))
136
137  The latter will run more efficiently. Note that mixing independent and dependent variables is
138  problematic. This is not allowed:
139
140  .. code-block:: python
141
142        StoreEquivalence('x',('y',))
143        StoreEquivalence('y',('z',))
144       
145  Use StoreEquivalence before calling GenerateConstraints or CheckConstraints
146
147:func:`CheckConstraints`
148   To check that input in internally consistent, use CheckConstraints
149
150:func:`Map2Dict`
151   To determine values for the parameters created in this module, one
152   calls Map2Dict. This will not apply contraints.
153
154:func:`Dict2Map`
155   To take values from the new independent parameters and constraints,
156   one calls Dict2Map. This will apply contraints.
157
158:func:`Dict2Deriv`
159   Use Dict2Deriv to determine derivatives on independent parameters
160   from those on dependent ones
161
162:func:`ComputeDepESD`     
163   Use ComputeDepESD to compute uncertainties on dependent variables
164
165:func:`VarRemapShow`
166   To show a summary of the parameter remapping, one calls VarRemapShow
167
168*Global Variables*
169------------------
170
171dependentParmList:
172   contains a list by group of lists of
173   parameters used in the group. Note that parameters listed in
174   dependentParmList should not be refined as they will not affect
175   the model
176
177indParmList:
178     a list of groups of Independent parameters defined in
179     each group. This contains both parameters used in parameter
180     redefinitions as well as names of generated new parameters.
181
182fixedVarList:
183     a list of variables that have been 'fixed'
184     by defining them as equal to a constant (::var: = 0). Note that
185     the constant value is ignored at present. These variables are
186     later removed from varyList which prevents them from being refined.
187     Unlikely to be used externally.
188
189arrayList:
190     a list by group of relationship matrices to relate
191     parameters in dependentParmList to those in indParmList. Unlikely
192     to be used externally.
193
194invarrayList:
195     a list by group of relationship matrices to relate
196     parameters in indParmList to those in dependentParmList. Unlikely
197     to be used externally.
198
199fixedDict:
200     a dictionary containing the fixed values corresponding
201     to parameter equations.  The dict key is an ascii string, but the
202     dict value is a float.  Unlikely to be used externally.
203
204*Routines*
205----------
206
207Note that parameter names in GSAS-II are strings of form ``<ph>:<hst>:<nam>``
208
209"""
210
211import numpy as np
212import sys
213import GSASIIpath
214GSASIIpath.SetVersionNumber("$Revision: 2874 $")
215# data used for constraints;
216debug = False # turns on printing as constraint input is processed
217# note that constraints are stored listed by contraint groups, where each constraint
218# group contains those parameters that must be handled together
219dependentParmList = [] # contains a list of parameters in each group
220# note that parameters listed in dependentParmList should not be refined
221arrayList = [] # a list of of relationship matrices
222invarrayList = [] # a list of inverse relationship matrices
223indParmList = [] # a list of names for the new parameters
224fixedDict = {} # a dictionary containing the fixed values corresponding to defined parameter equations
225               # key is original ascii string, value is float
226fixedVarList = [] # List of variables that should not be refined
227
228# prefix for parameter names
229paramPrefix = "::constr"
230consNum = 0 # number of the next constraint to be created
231
232def InitVars():
233    '''Initializes all constraint information'''
234    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict,consNum
235    dependentParmList = [] # contains a list of parameters in each group
236    arrayList = [] # a list of of relationship matrices
237    invarrayList = [] # a list of inverse relationship matrices
238    indParmList = [] # a list of names for the new parameters
239    fixedDict = {} # a dictionary containing the fixed values corresponding to defined parameter equations
240    consNum = 0 # number of the next constraint to be created
241
242def VarKeys(constr):
243    """Finds the keys in a constraint that represent variables
244    e.g. eliminates any that start with '_'
245
246    :param dict constr: a single constraint entry of form::
247
248        {'var1': mult1, 'var2': mult2,... '_notVar': val,...}
249
250        (see :func:`GroupConstraints`)
251    :returns: a list of keys where any keys beginning with '_' are
252      removed.
253    """
254    return [i for i in constr.keys() if not i.startswith('_')]
255
256
257def GroupConstraints(constrDict):
258    """divide the constraints into groups that share no parameters.
259
260    :param dict constrDict: a list of dicts defining relationships/constraints
261
262    ::
263   
264       constrDict = [{<constr1>}, {<constr2>}, ...]
265
266    where {<constr1>} is {'var1': mult1, 'var2': mult2,... }
267
268    :returns: two lists of lists:
269   
270      * a list of grouped contraints where each constraint grouped containts a list
271        of indices for constraint constrDict entries
272      * a list containing lists of parameter names contained in each group
273     
274      """
275    assignedlist = [] # relationships that have been used
276    groups = [] # contains a list of grouplists
277    ParmList = []
278    for i,consi in enumerate(constrDict):
279        if i in assignedlist: continue # already in a group, skip
280        # starting a new group
281        grouplist = [i,]
282        assignedlist.append(i)
283        groupset = set(VarKeys(consi))
284        changes = True # always loop at least once
285        while(changes): # loop until we can't find anything to add to the current group
286            changes = False # but don't loop again unless we find something
287            for j,consj in enumerate(constrDict):
288                if j in assignedlist: continue # already in a group, skip
289                if len(set(VarKeys(consj)) & groupset) > 0: # true if this needs to be added
290                    changes = True
291                    grouplist.append(j)
292                    assignedlist.append(j)
293                    groupset = groupset | set(VarKeys(consj))
294        group = sorted(grouplist)
295        varlist = sorted(list(groupset))
296        groups.append(group)
297        ParmList.append(varlist)
298    return groups,ParmList
299
300def CheckConstraints(varyList,constrDict,fixedList):
301    '''Takes a list of relationship entries comprising a group of
302    constraints and checks for inconsistencies such as conflicts in
303    parameter/variable definitions and or inconsistently varied parameters.
304
305    :param list varyList: a list of parameters names that will be varied
306
307    :param dict constrDict: a list of dicts defining relationships/constraints
308      (as created in :func:`GSASIIstrIO.ProcessConstraints` and
309      documented in :func:`GroupConstraints`)
310
311    :param list fixedList: a list of values specifying a fixed value for each
312      dict in constrDict. Values are either strings that can be converted to
313      floats or ``None`` if the constraint defines a new parameter rather
314      than a constant.
315
316    :returns: two strings:
317
318      * the first lists conflicts internal to the specified constraints
319      * the second lists conflicts where the varyList specifies some
320        parameters in a constraint, but not all
321       
322      If there are no errors, both strings will be empty
323    '''
324    import re
325    global dependentParmList,arrayList,invarrayList,indParmList,consNum
326    errmsg = ''
327    warnmsg = ''
328    fixVlist = []
329    # process fixed variables (holds)
330    for cdict in constrDict:
331        # N.B. No "_" names in holds
332        if len(cdict) == 1:
333            fixVlist.append(cdict.keys()[0])
334   
335    # process equivalences: make a list of dependent and independent vars
336    #    and check for repeated uses (repetition of a parameter as an
337    #    independent var is OK)
338    indepVarList = []
339    depVarList = []
340    multdepVarList = []
341    for varlist,mapvars,multarr,invmultarr in zip(
342        dependentParmList,indParmList,arrayList,invarrayList):
343        if multarr is None: # an equivalence
344            zeromult = False
345            for mv in mapvars:
346                varied = 0
347                notvaried = ''
348                if mv in varyList:
349                    varied += 1
350                else:
351                    if notvaried: notvaried += ', '
352                    notvaried += mv
353                if mv not in indepVarList: indepVarList.append(mv)
354                for v,m in zip(varlist,invmultarr):
355                    if v in indepVarList:
356                        errmsg += '\nVariable '+v+' is used to set values in a constraint before its value is set in another constraint\n'
357                    if m == 0: zeromult = True
358                    if v in varyList:
359                        varied += 1
360                    else:
361                        if notvaried: notvaried += ', '
362                        notvaried += v
363                    if v in depVarList:
364                        multdepVarList.append(v)
365                    else:
366                        depVarList.append(v)
367            if varied > 0 and varied != len(varlist)+1:
368                warnmsg += "\nNot all variables refined in equivalence:\n\t"
369                s = ""
370                for v in varlist:
371                    if s != "": s+= " & "
372                    s += str(v)           
373                warnmsg += str(mv) + " => " + s
374                warnmsg += '\nNot refined: ' + notvaried + '\n'
375            if zeromult:
376                errmsg += "\nZero multiplier is invalid in equivalence:\n\t"
377                s = ""
378                for v in varlist:
379                    if s != "": s+= " & "
380                    s += str(v)           
381                errmsg += str(mv) + " => " + s + '\n'
382
383    # check for errors:
384    if len(multdepVarList) > 0:
385        errmsg += "\nThe following parameters(s) are used in conflicting Equivalence relations as dependent variables:\n"
386        s = ''
387        for var in sorted(set(multdepVarList)):
388            if s != "": s+= ", "
389            s += str(var)           
390        errmsg += '\t'+ s + '\n'
391    equivVarList = list(set(indepVarList).union(set(depVarList)))
392    if debug: print 'equivVarList',equivVarList
393    inboth = set(fixVlist).intersection(set(equivVarList))
394    if len(inboth) > 0:
395        errmsg += "\nThe following parameter(s) are used in both Equivalence and Fixed constraints:\n"
396        s = ''
397        for var in sorted(inboth):
398            if s != "": s+= ", "
399            s += str(var)
400        errmsg += '\t'+ s + '\n'
401
402    groups,parmlist = GroupConstraints(constrDict)
403    # scan through parameters in each relationship. Are all varied? If only some are
404    # varied, create a warning message.
405    for group,varlist in zip(groups,parmlist):
406        if len(varlist) == 1: continue
407        for rel in group:
408            varied = 0
409            notvaried = ''
410            for var in constrDict[rel]:
411                if var.startswith('_'): continue
412                if not re.match('[0-9]*:[0-9\*]*:',var):
413                    warnmsg += "\nVariable "+str(var)+" does not begin with a ':'"
414                if var in varyList:
415                    varied += 1
416                else:
417                    if notvaried: notvaried += ', '
418                    notvaried += var
419                if var in fixVlist:
420                    errmsg += '\nParameter '+var+" is Fixed and used in a constraint:\n\t"
421                    errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])+"\n"
422            if varied > 0 and varied != len(VarKeys(constrDict[rel])):
423                warnmsg += "\nNot all variables refined in constraint:\n\t"
424                warnmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
425                warnmsg += '\nNot refined: ' + notvaried + '\n'
426    if errmsg or warnmsg:
427        return errmsg,warnmsg
428
429    # now look for process each group and create the relations that are needed to form
430    # non-singular square matrix
431    for group,varlist in zip(groups,parmlist):
432        if len(varlist) == 1: continue # a constraint group with a single variable can be ignored
433        if len(varlist) < len(group): # too many relationships -- no can do
434            errmsg += "\nOver-constrained input. "
435            errmsg += "There are more constraints " + str(len(group))
436            errmsg += "\n\tthan variables " + str(len(varlist)) + "\n"
437            for rel in group:
438                errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
439                errmsg += "\n"
440                continue
441        try:
442            multarr = _FillArray(group,constrDict,varlist)
443            _RowEchelon(len(group),multarr,varlist)
444        except:
445            errmsg += "\nSingular input. "
446            errmsg += "There are internal inconsistencies in these constraints\n"
447            for rel in group:
448                errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
449                errmsg += "\n"
450            continue
451        try:
452            multarr = _FillArray(group,constrDict,varlist,FillDiagonals=True)
453            GramSchmidtOrtho(multarr,len(group))
454        except:
455            errmsg += "\nUnexpected singularity with constraints (in Gram-Schmidt)\n"
456            for rel in group:
457                errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
458                errmsg += "\n"
459            continue
460        mapvar = []
461        group = group[:]
462        # scan through all generated and input variables
463        # Check again for inconsistent variable use
464        # for new variables -- where varied and unvaried parameters get grouped
465        # together. I don't think this can happen when not flagged before, but
466        # it does not hurt to check again.
467        for i in range(len(varlist)):
468            varied = 0
469            notvaried = ''
470            if len(group) > 0:
471                rel = group.pop(0)
472                fixedval = fixedList[rel]
473                for var in VarKeys(constrDict[rel]):
474                    if var in varyList:
475                        varied += 1
476                    else:
477                        if notvaried: notvaried += ', '
478                        notvaried += var
479            else:
480                fixedval = None
481            if fixedval is None:
482                varname = paramPrefix + str(consNum) # assign a name to a variable
483                mapvar.append(varname)
484                consNum += 1
485            else:
486                mapvar.append(fixedval)
487            if varied > 0 and notvaried != '':
488                warnmsg += "\nNot all variables refined in generated constraint"
489                warnmsg += '\nPlease report this unexpected error\n'
490                for rel in group:
491                    warnmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
492                    warnmsg += "\n"
493                warnmsg += '\n\tNot refined: ' + notvaried + '\n'
494        try:
495            np.linalg.inv(multarr)           
496        except:
497            errmsg += "\nSingular input. "
498            errmsg += "The following constraints are not "
499            errmsg += "linearly independent\n\tor do not "
500            errmsg += "allow for generation of a non-singular set\n"
501            errmsg += 'Please report this unexpected error\n'
502            for rel in group:
503                errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
504                errmsg += "\n"
505    return errmsg,warnmsg
506
507def GenerateConstraints(groups,parmlist,varyList,constrDict,fixedList,parmDict=None,SeqHist=None):
508    '''Takes a list of relationship entries comprising a group of
509    constraints and builds the relationship lists and their inverse
510    and stores them in global variables Also checks for internal
511    conflicts or inconsistencies in parameter/variable definitions.
512
513    :param list groups: a list of grouped contraints where each constraint
514      grouped containts a list of indices for constraint constrDict entries,
515      created in :func:`GroupConstraints` (returned as 1st value)
516
517    :param list parmlist: a list containing lists of parameter names
518      contained in each group, created in :func:`GroupConstraints`
519      (returned as 2nd value)
520
521    :param list varyList: a list of parameters names (strings of form
522      ``<ph>:<hst>:<nam>``) that will be varied. Note that this is changed here.
523   
524    :param dict constrDict: a list of dicts defining relationships/constraints
525      (as defined in :func:`GroupConstraints`)
526
527    :param list fixedList: a list of values specifying a fixed value for each
528      dict in constrDict. Values are either strings that can be converted to
529      floats, float values or None if the constraint defines a new parameter.
530     
531    :param dict parmDict: a dict containing all parameters defined in current
532      refinement.
533
534    :param int SeqHist: number of current histogram, when used in a sequential
535      refinement. None (default) otherwise. Wildcard variable names are
536      set to the current histogram, when found if not None.
537    '''
538    global dependentParmList,arrayList,invarrayList,indParmList,consNum
539    msg = ''
540
541    # process fixed (held) variables
542    for cdict in constrDict:
543        if len(cdict) == 1:
544            fixedVarList.append(cdict.keys()[0])
545   
546    # process equivalences: make a list of dependent and independent vars
547    #    and check for repeated uses (repetition of a parameter as an
548    #    independent var is OK [A=B; A=C], but chaining: [A=B; B=C] is not good)
549    dropVarList = []
550    translateTable = {} # lookup table for wildcard referenced variables
551    for varlist,mapvars,multarr,invmultarr in zip(       # process equivalences
552        dependentParmList,indParmList,arrayList,invarrayList):
553        if multarr is None: # true only if an equivalence
554            zeromult = False
555            for mv in mapvars:
556                #s = ''
557                varied = 0
558                notvaried = ''
559                if mv in varyList:
560                    varied += 1
561                else:
562                    if notvaried: notvaried += ', '
563                    notvaried += mv
564                if parmDict is not None and mv not in parmDict:
565                    print "Dropping equivalence for variable "+str(mv)+". Not defined in this refinement"
566                    if mv not in dropVarList: dropVarList.append(mv)
567                    #msg += "\nCannot equivalence to variable "+str(mv)+". Not defined in this refinement"
568                    #continue
569            for v,m in zip(varlist,invmultarr):
570                if parmDict is not None and v not in parmDict:
571                    print "Dropping equivalence for dep. variable "+str(v)+". Not defined in this refinement"
572                    if v not in dropVarList: dropVarList.append(v)
573                    continue
574                if m == 0: zeromult = True
575                if v in varyList:
576                    varied += 1
577                else:
578                    if notvaried: notvaried += ', '
579                    notvaried += v
580            if varied > 0 and varied != len(varlist)+1:
581                msg += "\nNot all variables refined in equivalence:\n\t"
582                s = ""
583                for v in varlist:
584                    if s != "": s+= " & "
585                    s += str(v)           
586                msg += str(mv) + " => " + s
587                msg += '\nNot refined: ' + notvaried + '\n'
588            if zeromult:
589                msg += "\nZero multiplier is invalid in equivalence:\n\t"
590                s = ""
591                for v in varlist:
592                    if s != "": s+= " & "
593                    s += str(v)           
594                msg += str(mv) + " => " + s + '\n'
595
596    # scan through parameters in each relationship. Are all varied? If only some are
597    # varied, create an error message.
598    for group,varlist in zip(groups,parmlist):
599        if len(varlist) == 1: continue
600        for rel in group:
601            varied = 0
602            notvaried = ''
603            unused = 0
604            notused = ''
605            for var in constrDict[rel]:
606                if var.startswith('_'): continue
607                if var.split(':')[1] == '*' and SeqHist is not None:
608                    # convert wildcard var to reference current histogram; save translation in table
609                    sv = var.split(':')
610                    sv[1] = str(SeqHist)
611                    translateTable[var] = ':'.join(sv)
612                    var = translateTable[var]
613                if parmDict is not None and var not in parmDict:
614                    unused += 1
615                    if notvaried: notused += ', '
616                    notused += var
617                if var in varyList:
618                    varied += 1
619                else:
620                    if notvaried: notvaried += ', '
621                    notvaried += var
622                if var in fixedVarList:
623                    msg += '\nError: parameter '+var+" is Fixed and used in a constraint:\n\t"
624                    msg += _FormatConstraint(constrDict[rel],fixedList[rel])+"\n"
625            #if unused > 0:# and unused != len(VarKeys(constrDict[rel])):
626            if unused > 0 and unused != len(VarKeys(constrDict[rel])):
627                msg += "\nSome (but not all) variables in constraint are not defined:\n\t"
628                msg += _FormatConstraint(constrDict[rel],fixedList[rel])
629                msg += '\nNot used: ' + notused + '\n'
630            elif varied > 0 and varied != len(VarKeys(constrDict[rel])):
631                msg += "\nNot all variables refined in constraint:\n\t"
632                msg += _FormatConstraint(constrDict[rel],fixedList[rel])
633                msg += '\nNot refined: ' + notvaried + '\n'
634    # if there were errors found, go no farther
635    if msg and SeqHist is not None:
636        print ' *** Sequential refinement: ignoring constraint definition(s): ***'
637        print msg
638        msg = ''
639    elif msg:
640        print ' *** ERROR in constraint definitions! ***'
641        print msg
642        raise Exception
643               
644    # now process each group and create the relations that are needed to form
645    # a non-singular square matrix
646    # If all are varied and this is a constraint equation, then set VaryFree flag
647    # so that the newly created relationships will be varied
648    for group,varlist in zip(groups,parmlist):
649        if len(varlist) == 1: continue
650        # for constraints, if all included variables are refined,
651        # set the VaryFree flag, and remaining degrees of freedom will be
652        # varied (since consistency was checked, if any one variable is
653        # refined, then assume that all are)
654        varsList = [] # make a list of all the referenced variables as well
655        VaryFree = False
656        for rel in group:
657            varied = 0
658            unused = 0
659            for var in VarKeys(constrDict[rel]):
660                var = translateTable.get(var,var) # replace wildcards
661                if parmDict is not None and var not in parmDict:
662                    unused += 1                   
663                if var not in varsList: varsList.append(var)
664                if var in varyList: varied += 1
665            if fixedList[rel] is not None and varied > 0:
666                VaryFree = True
667        if len(varlist) < len(group): # too many relationships -- no can do
668            msg = 'too many relationships'
669            break
670        # Since we checked before, if any variables are unused, then all must be.
671        # If so, this set of relationships can be ignored
672        if unused:
673            if debug: print('Constraint ignored (all variables undefined)')
674            if debug: print ('    '+_FormatConstraint(constrDict[rel],fixedList[rel]))
675            continue
676        # fill in additional degrees of freedom
677        try:
678            arr = _FillArray(group,constrDict,varlist)
679            _RowEchelon(len(group),arr,varlist)
680            constrArr = _FillArray(group,constrDict,varlist,FillDiagonals=True)
681            GramSchmidtOrtho(constrArr,len(group))
682        except:
683            msg = 'Singular relationships'
684            break
685        mapvar = []
686        group = group[:]
687        # scan through all generated and input relationships, we need to add to the varied list
688        # all the new parameters where VaryFree has been set or where a New Var is varied.
689        #
690        # If a group does not contain any fixed values (constraint equations)
691        # and nothing in the group is varied, drop this group, so that the
692        # dependent parameters can be refined individually.
693        unused = True
694        for i in range(len(varlist)):
695            if len(group) > 0: # get the original equation reference
696                rel = group.pop(0)
697                fixedval = fixedList[rel]
698                varyflag = constrDict[rel].get('_vary',False)
699                varname = constrDict[rel].get('_name','')
700            else: # this relationship has been generated
701                varyflag = False
702                varname = ''
703                fixedval = None
704            if fixedval is None: # this is a new variable, not a constraint
705                if not varname:
706                    varname = paramPrefix + str(consNum) # no assigned name, create one
707                    consNum += 1
708                mapvar.append(varname)
709                # vary the new relationship if it is a degree of freedom in
710                # a set of contraint equations or if a New Var is flagged to be varied.
711                if VaryFree or varyflag: 
712                    unused = False
713                    varyList.append(varname)
714                    # fix (prevent varying) of all the variables inside the constraint group
715                    # (dependent vars)
716                    for var in varsList:
717                        if var in varyList: varyList.remove(var)
718            else:
719                unused = False
720                mapvar.append(fixedval)
721        if unused: # skip over constraints that don't matter (w/o fixed value or any refined variables)
722            if debug: print('Constraint ignored (all variables unrefined)')
723            if debug: print ('   '+_FormatConstraint(constrDict[rel],fixedList[rel]))
724            continue 
725        dependentParmList.append([translateTable.get(var,var) for var in varlist])
726        arrayList.append(constrArr)
727        invarrayList.append(np.linalg.inv(constrArr))
728        indParmList.append(mapvar)
729    if msg:
730        print ' *** ERROR in constraint definitions! ***'
731        print msg
732        print VarRemapShow(varyList)
733        raise Exception
734    # setup dictionary containing the fixed values
735    global fixedDict
736    # key is original ascii string, value is float
737    for fixedval in fixedList:
738        if fixedval:
739            fixedDict[fixedval] = float(fixedval)
740
741    # make list of dependent and independent variables (after dropping unused)
742    global dependentVars
743    global independentVars
744    dependentVars = []
745    independentVars = []
746    for varlist,mapvars in zip(dependentParmList,indParmList):  # process all constraints
747        for mv in mapvars:
748            if mv in dropVarList: continue
749            if mv not in independentVars: independentVars.append(mv)
750        for mv in varlist:
751            if mv in dropVarList: continue
752            if mv not in dependentVars: dependentVars.append(mv)
753    if debug: # on debug, show what is parsed & generated, semi-readable
754        print 50*'-'
755        print VarRemapShow(varyList)
756        print 'Varied: ',varyList
757        print 'Not Varied: ',fixedVarList
758
759def StoreEquivalence(independentVar,dependentList):
760    '''Takes a list of dependent parameter(s) and stores their
761    relationship to a single independent parameter (independentVar)
762
763    :param str independentVar: name of master parameter that will be used to determine the value
764      to set the dependent variables
765
766    :param list dependentList: a list of parameters that will set from
767         independentVar. Each item in the list can be a string with the parameter
768         name or a tuple containing a name and multiplier:
769         ``['parm1',('parm2',.5),]``
770
771    '''
772   
773    global dependentParmList,arrayList,invarrayList,indParmList
774    mapList = []
775    multlist = []
776    for var in dependentList:
777        if isinstance(var, basestring):
778            mult = 1.0
779        elif len(var) == 2:
780            var,mult = var
781        else:
782            raise Exception("Cannot parse "+repr(var) + " as var or (var,multiplier)")
783        mapList.append(var)
784        multlist.append(tuple((mult,)))
785    # added relationships to stored values
786    arrayList.append(None)
787    invarrayList.append(np.array(multlist))
788    indParmList.append(tuple((independentVar,)))
789    dependentParmList.append(mapList)
790    return
791
792def GetDependentVars():
793    '''Return a list of dependent variables: e.g. variables that are
794    constrained in terms of other variables
795
796    :returns: a list of variable names
797
798    '''
799    return dependentVars
800
801def GetIndependentVars():
802    '''Return a list of independent variables: e.g. variables that are
803    created by constraints of other variables
804
805    :returns: a list of variable names
806
807    '''
808    return independentVars
809
810def PrintIndependentVars(parmDict,varyList,sigDict,PrintAll=False,pFile=None):
811    '''Print the values and uncertainties on the independent variables'''
812    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
813    printlist = []
814    mapvars = GetIndependentVars()
815    for i,name in enumerate(mapvars):
816        if name in fixedDict: continue
817        if PrintAll or name in varyList:
818            sig = sigDict.get(name)
819            printlist.append([name,parmDict[name],sig])
820    if len(printlist) == 0: return
821    s1 = ''
822    s2 = ''
823    s3 = ''
824    print >>pFile,130*'-'
825    print >>pFile,"Variables generated by constraints"
826    printlist.append(3*[None])
827    for name,val,esd in printlist:
828        if len(s1) > 120 or name is None:
829            print >>pFile,''
830            print >>pFile,s1
831            print >>pFile,s2
832            print >>pFile,s3
833            s1 = ''
834            if name is None: break
835        if s1 == "":
836            s1 = ' name  :'
837            s2 = ' value :'
838            s3 = ' sig   :'
839        s1 += '%15s' % (name)
840        s2 += '%15.4f' % (val)
841        if esd is None:
842            s3 += '%15s' % ('n/a')
843        else:   
844            s3 += '%15.4f' % (esd)
845
846def ComputeDepESD(covMatrix,varyList,parmDict):
847    '''Compute uncertainties for dependent parameters from independent ones
848    returns a dictionary containing the esd values for dependent parameters
849    '''
850    sigmaDict = {}
851    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
852        #if invmultarr is None: continue # probably not needed
853#        try:
854#            valuelist = [parmDict[var] for var in mapvars]
855#        except KeyError:
856#            continue
857        # get the v-covar matrix for independent parameters
858        vcov = np.zeros((len(mapvars),len(mapvars)))
859        for i1,name1 in enumerate(mapvars):
860            if name1 not in varyList: continue
861            iv1 = varyList.index(name1)
862            for i2,name2 in enumerate(mapvars):
863                if name2 not in varyList: continue
864                iv2 = varyList.index(name2)
865                vcov[i1][i2] = covMatrix[iv1][iv2]
866        # vec is the vector that multiplies each of the independent values
867        for v,vec in zip(varlist,invmultarr):
868            sigmaDict[v] = np.sqrt(np.inner(vec.T,np.inner(vcov,vec)))
869    return sigmaDict
870
871def _FormatConstraint(RelDict,RelVal):
872    '''Formats a Constraint or Function for use in a convenient way'''
873    linelen = 45
874    s = [""]
875    for var,val in RelDict.items():
876        if var.startswith('_'): continue
877        if len(s[-1]) > linelen: s.append(' ')
878        m = val
879        if s[-1] != "" and m >= 0:
880            s[-1] += ' + '
881        elif s[-1] != "":
882            s[-1] += ' - '
883            m = abs(m)
884        s[-1] += '%.3f*%s '%(m,var)
885    if len(s[-1]) > linelen: s.append(' ')
886    if RelVal is None:
887        s[-1] += ' = New variable'
888    else:
889        s[-1] += ' = ' + RelVal
890    s1 = ''
891    for s2 in s:
892        if s1 != '': s1 += '\n\t'
893        s1 += s2
894    return s1
895
896def VarRemapShow(varyList,inputOnly=False):
897    '''List out the saved relationships. This should be done after the constraints have been
898    defined using :func:`StoreEquivalence`, :func:`GroupConstraints` and :func:`GenerateConstraints`.
899
900    :returns: a string containing the details of the contraint relationships
901    '''
902    s = ''
903    if len(fixedVarList) > 0:
904        s += 'Fixed Variables:\n'
905        for v in fixedVarList:
906            s += '    ' + v + '\n'
907    s += 'Variable mapping relations:\n'
908    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
909    for varlist,mapvars,multarr,invmultarr in zip(
910        dependentParmList,indParmList,arrayList,invarrayList):
911        for i,mv in enumerate(mapvars):
912            if multarr is None:
913                s += '  ' + str(mv) + ' is equivalent to parameter(s): '
914                j = 0
915                for v,m in zip(varlist,invmultarr):
916                    if debug: print 'v,m[0]: ',v,m[0]
917                    if j > 0: s += '  & '
918                    j += 1
919                    s += str(v)
920                    if m != 1:
921                        s += " / " + str(m[0])                       
922                s += '\n'
923                continue
924            s += %s = ' % mv
925            j = 0
926            for m,v in zip(multarr[i,:],varlist):
927                if m == 0: continue
928                if j > 0: s += ' + '
929                j += 1
930                s += '(%s * %s)' % (m,v)
931            if mv in varyList: s += ' VARY'
932            s += '\n'
933    if inputOnly: return s
934    s += 'Inverse variable mapping relations:\n'
935    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
936        for i,mv in enumerate(varlist):
937            s += %s = ' % mv
938            j = 0
939            for m,v in zip(invmultarr[i,:],mapvars):
940                if m == 0: continue
941                if j > 0: s += ' + '
942                j += 1
943                s += '(%s * %s)' % (m,v)
944            s += '\n'
945    return s
946
947def Dict2Deriv(varyList,derivDict,dMdv):
948    '''Compute derivatives for Independent Parameters from the
949    derivatives for the original parameters
950
951    :param list varyList: a list of parameters names that will be varied
952
953    :param dict derivDict: a dict containing derivatives for parameter values keyed by the
954      parameter names.
955
956    :param list dMdv: a Jacobian, as a list of np.array containing derivatives for dependent
957      parameter computed from derivDict
958
959    '''
960    global dependentParmList,arrayList,invarrayList,indParmList,invarrayList
961    for varlist,mapvars,multarr,invmultarr in zip(dependentParmList,indParmList,arrayList,invarrayList):
962        for i,name in enumerate(mapvars):
963            # grouped variables: need to add in the derv. w/r
964            # dependent variables to the independent ones
965            if name not in varyList: continue # skip if independent var not varied
966            if multarr is None:
967                for v,m in zip(varlist,invmultarr):
968                    if debug: print 'start dMdv',dMdv[varyList.index(name)]
969                    if debug: print 'add derv',v,'/',m[0],'to derv',name,'add=',derivDict[v] / m[0]
970                    if m == 0: continue
971                    dMdv[varyList.index(name)] += derivDict[v] / m[0]
972            else:
973                for v,m in zip(varlist,multarr[i,:]):
974                    if debug: print 'start dMdv',dMdv[varyList.index(name)]
975                    if debug: print 'add derv',v,'*',m,'to derv',name,'add=',m * derivDict[v]
976                    if m == 0: continue
977                    dMdv[varyList.index(name)] += m * derivDict[v]
978
979def Map2Dict(parmDict,varyList):
980    '''Create (or update) the Independent Parameters from the original
981    set of Parameters
982
983    Removes dependent variables from the varyList
984
985    This should be done once, after the constraints have been
986    defined using :func:`StoreEquivalence`,
987    :func:`GroupConstraints` and :func:`GenerateConstraints` and
988    before any variable refinement is done. This completes the parameter
989    dictionary by defining independent parameters and it satisfies the
990    constraint equations in the initial parameters
991
992    :param dict parmDict: a dict containing parameter values keyed by the
993      parameter names.
994      This will contain updated values for both dependent and independent
995      parameters after Dict2Map is called. It will also contain some
996      unexpected entries of every constant value {'0':0.0} & {'1.0':1.0},
997      which do not cause any problems.
998
999    :param list varyList: a list of parameters names that will be varied
1000   
1001
1002    '''
1003    # process the Independent vars: remove dependent ones from varylist
1004    # and then compute values for the Independent ones from their dependents
1005    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
1006    for varlist,mapvars,multarr in zip(dependentParmList,indParmList,arrayList):
1007        for item in varlist:
1008            try:
1009                varyList.remove(item)
1010            except ValueError:
1011                pass
1012        if multarr is None: continue
1013        valuelist = [parmDict[var] for var in varlist]
1014        parmDict.update(zip(mapvars,
1015                            np.dot(multarr,np.array(valuelist)))
1016                        )
1017    # now remove fixed variables from the varyList
1018    global fixedVarList
1019    for item in fixedVarList:
1020        try:
1021            varyList.remove(item)
1022        except ValueError:
1023            pass
1024    # Set constrained parameters to their fixed values
1025    parmDict.update(fixedDict)
1026
1027def Dict2Map(parmDict,varyList):
1028    '''Applies the constraints defined using :func:`StoreEquivalence`,
1029    :func:`GroupConstraints` and :func:`GenerateConstraints` by changing
1030    values in a dict containing the parameters. This should be
1031    done before the parameters are used for any computations
1032
1033    :param dict parmDict: a dict containing parameter values keyed by the
1034      parameter names.
1035      This will contain updated values for both dependent and independent
1036      parameters after Dict2Map is called. It will also contain some
1037      unexpected entries of every constant value {'0':0.0} & {'1.0':1.0},
1038      which do not cause any problems.
1039
1040    :param list varyList: a list of parameters names that will be varied
1041   
1042    '''
1043    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
1044    # reset fixed values (should not be needed, but very quick)
1045    # - this seems to update parmDict with {'0':0.0} & {'1.0':1.0} - probably not what was intended
1046    # not needed, but also not a problem - BHT
1047    parmDict.update(fixedDict)
1048    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
1049        #if invmultarr is None: continue
1050        try: 
1051            valuelist = [parmDict[var] for var in mapvars]
1052        except KeyError:
1053            continue
1054        parmDict.update(zip(varlist,np.dot(invmultarr,np.array(valuelist))))
1055
1056#======================================================================
1057# internal routines follow (these routines are unlikely to be called
1058# from outside the module)
1059
1060def GramSchmidtOrtho(a,nkeep=0):
1061    '''Use the Gram-Schmidt process (http://en.wikipedia.org/wiki/Gram-Schmidt) to
1062    find orthonormal unit vectors relative to first row.
1063
1064    If nkeep is non-zero, the first nkeep rows in the array are not changed
1065   
1066    input:
1067       arrayin: a 2-D non-singular square array
1068    returns:
1069       a orthonormal set of unit vectors as a square array
1070    '''
1071    def proj(a,b):
1072        'Projection operator'
1073        return a*(np.dot(a,b)/np.dot(a,a))
1074    for j in range(nkeep,len(a)):
1075        for i in range(j):
1076            a[j] -= proj(a[i],a[j])
1077        if np.allclose(np.linalg.norm(a[j]),0.0):
1078            raise Exception,"Singular input to GramSchmidtOrtho"
1079        a[j] /= np.linalg.norm(a[j])
1080    return a
1081
1082def _FillArray(sel,dict,collist,FillDiagonals=False):
1083    '''Construct a n by n matrix (n = len(collist)
1084    filling in the rows using the relationships defined
1085    in the dictionaries selected by sel
1086
1087    If FillDiagonals is True, diagonal elements in the
1088    array are set to 1.0
1089    '''
1090    n = len(collist)
1091    if FillDiagonals:
1092        arr = np.eye(n)
1093    else:
1094        arr = np.zeros(2*[n,])
1095    # fill the top rows
1096    for i,cnum in enumerate(sel):
1097        for j,var in enumerate(collist):
1098            arr[i,j] = dict[cnum].get(var,0)
1099    return arr
1100
1101def _SwapColumns(i,m,v):
1102    '''Swap columns in matrix m as well as the labels in v
1103    so that element (i,i) is replaced by the first non-zero element in row i after that element
1104
1105    Throws an exception if there are no non-zero elements in that row
1106    '''
1107    for j in range(i+1,len(v)):
1108        if not np.allclose(m[i,j],0):
1109            m[:,(i,j)] = m[:,(j,i)]
1110            v[i],v[j] = v[j],v[i]
1111            return
1112    else:
1113        raise Exception,'Singular input'
1114
1115def _RowEchelon(m,arr,collist):
1116    '''Convert the first m rows in Matrix arr to row-echelon form
1117    exchanging columns in the matrix and collist as needed.
1118
1119    throws an exception if the matrix is singular because
1120    the first m rows are not linearly independent
1121    '''
1122    for i in range(m):
1123        if np.allclose(arr[i,i],0):
1124            _SwapColumns(i,arr,collist)
1125        arr[i,:] /= arr[i,i] # normalize row
1126        # subtract current row from subsequent rows to set values to left of diagonal to 0
1127        for j in range(i+1,m):
1128            arr[j,:] -= arr[i,:] * arr[j,i]
1129
1130if __name__ == "__main__":
1131    parmdict = {}
1132    constrDict = [
1133        {'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},
1134        {'0:0:eA': 0.0},
1135        {'2::C(10,6,1)': 1.0, '1::C(10,6,1)': 1.0},
1136        {'1::C(10,0,1)': 1.0, '2::C(10,0,1)': 1.0},
1137        {'1::AUiso:0': 1.0, '0::AUiso:0': 1.0},
1138        {'0::A0': 0.0}
1139        ]
1140    fixedList = ['5.0', '0', None, None, '1.0', '0']
1141    StoreEquivalence('2::atomx:3',('2::atomy:3', ('2::atomz:3',2,), ))
1142    #StoreEquivalence('1::atomx:3',('2::atomx:3', ('2::atomz:3',2,), )) # error: dependent & independent vars mixed
1143    #StoreEquivalence('1::atomx:3',('2::atomy:3', ('2::atomz:3',2,), )) # error: dependent vars repeated
1144    #StoreEquivalence('0:1:eA',('0:0:eA',)) # error: equiv & fixed
1145    #StoreEquivalence('0:99:Scale',('0:12:Scale',)) # error: equiv & constrained
1146    #StoreEquivalence('0:12:Scale',('0:99:Scale',)) # error: equiv & constrained
1147    varylist = ['2::atomx:3',
1148                '2::C(10,6,1)', '1::C(10,6,1)',
1149                '2::atomy:3', '2::atomz:3',
1150                '0:12:Scale', '0:11:Scale', '0:14:Scale', '0:13:Scale', '0:0:Scale']
1151#    e,w = CheckConstraints([,
1152#                     [{'2:0:Scale': 1.0, '5:0:Scale': 1.0, '10:0:Scale': 1.0, '6:0:Scale': 1.0, '9:0:Scale': 1.0, '8:0:Scale': 1.0,# '3:0:Scale': 1.0, '4:0:Scale': 1.0, '7:0:Scale': 1.0, '1:0:Scale': 1.0, '0:0:Scale': 1.0}],
1153#                     ['1.0'])
1154#    if e: print 'error=',e
1155#    if w: print 'error=',w
1156#    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']
1157#    constrDict = [
1158#        {'0::Afrac:4': 24.0, '0::Afrac:1': 16.0, '0::Afrac:3': 24.0, '0::Afrac:2': 16.0},
1159#        {'0::Afrac:1': 1.0, '0::Afrac:2': 1.0},
1160#        {'0::Afrac:4': 1.0, '0::Afrac:3': 1.0}]
1161#    fixedList = ['40.0', '1.0', '1.0']
1162
1163    errmsg, warnmsg = CheckConstraints(varylist,constrDict,fixedList)
1164    if errmsg:
1165        print "*** Error ********************"
1166        print errmsg
1167    if warnmsg:
1168        print "*** Warning ********************"
1169        print warnmsg
1170    if errmsg or warnmsg:
1171        sys.exit()
1172    groups,parmlist = GroupConstraints(constrDict)
1173    GenerateConstraints(groups,parmlist,varylist,constrDict,fixedList)
1174    print VarRemapShow(varylist)
1175    parmdict.update( {
1176        '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,
1177        '0:0:eA': 0.0,
1178        '2::C(10,6,1)': 0.2, '1::C(10,6,1)': 0.3,
1179        '1::C(10,0,1)': 0.2, '2::C(10,0,1)': 0.3,
1180        '1::AUiso:0': 0.02, '0::AUiso:0': 0.03,
1181        '0::A0': 0.0,
1182        '2::atomx:3':0.23,'2::atomy:3':-.23, '2::atomz:3':-0.11,
1183        })
1184    print 'parmdict start',parmdict
1185    print 'varylist start',varylist
1186    before = parmdict.copy()
1187    Map2Dict(parmdict,varylist)
1188    print 'parmdict before and after Map2Dict'
1189    print '  key / before / after'
1190    for key in sorted(parmdict.keys()):
1191        print '  '+key,'\t',before.get(key),'\t',parmdict[key]
1192    print 'varylist after',varylist
1193    before = parmdict.copy()
1194    Dict2Map(parmdict,varylist)
1195    print 'after Dict2Map'
1196    print '  key / before / after'
1197    for key in sorted(parmdict.keys()):
1198        print '  '+key,'\t',before.get(key),'\t',parmdict[key]
1199#    dMdv = len(varylist)*[0]
1200#    deriv = {}
1201#    for i,v in enumerate(parmdict.keys()): deriv[v]=i
1202#    Dict2Deriv(varylist,deriv,dMdv)
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