source: trunk/GSASIImapvars.py @ 1805

Last change on this file since 1805 was 1805, checked in by toby, 7 years ago

fix bug on with unused constraints and with chained equivalences; improve diagnostics from constraint errors

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1# -*- coding: utf-8 -*-
2########### SVN repository information ###################
3# $Date: 2015-04-24 02:54:49 +0000 (Fri, 24 Apr 2015) $
4# $Author: toby $
5# $Revision: 1805 $
6# $URL: trunk/GSASIImapvars.py $
7# $Id: GSASIImapvars.py 1805 2015-04-24 02:54:49Z 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 GSASIIpath
213GSASIIpath.SetVersionNumber("$Revision: 1805 $")
214# data used for constraints;
215debug = False # turns on printing as constraint input is processed
216# note that constraints are stored listed by contraint groups, where each constraint
217# group contains those parameters that must be handled together
218dependentParmList = [] # contains a list of parameters in each group
219# note that parameters listed in dependentParmList should not be refined
220arrayList = [] # a list of of relationship matrices
221invarrayList = [] # a list of inverse relationship matrices
222indParmList = [] # a list of names for the new parameters
223fixedDict = {} # a dictionary containing the fixed values corresponding to defined parameter equations
224               # key is original ascii string, value is float
225fixedVarList = [] # List of variables that should not be refined
226
227# prefix for parameter names
228paramPrefix = "::constr"
229consNum = 0 # number of the next constraint to be created
230
231def InitVars():
232    '''Initializes all constraint information'''
233    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict,consNum
234    dependentParmList = [] # contains a list of parameters in each group
235    arrayList = [] # a list of of relationship matrices
236    invarrayList = [] # a list of inverse relationship matrices
237    indParmList = [] # a list of names for the new parameters
238    fixedDict = {} # a dictionary containing the fixed values corresponding to defined parameter equations
239    consNum = 0 # number of the next constraint to be created
240    fixedVarList = []
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    indepVarList = []
550    depVarList = []
551    multdepVarList = []
552    translateTable = {} # lookup table for wildcard referenced variables
553    for varlist,mapvars,multarr,invmultarr in zip(       # process equivalences
554        dependentParmList,indParmList,arrayList,invarrayList):
555        if multarr is None: # true only if an equivalence
556            zeromult = False
557            for mv in mapvars:
558                #s = ''
559                varied = 0
560                notvaried = ''
561                if mv in varyList:
562                    varied += 1
563                else:
564                    if notvaried: notvaried += ', '
565                    notvaried += mv
566                if parmDict is not None and mv not in parmDict:
567                    print "Dropping equivalence for variable "+str(mv)+". Not defined in this refinement"
568                    #msg += "\nCannot equivalence to variable "+str(mv)+". Not defined in this refinement"
569                    #continue
570                else: 
571                    if mv not in indepVarList: indepVarList.append(mv)
572                for v,m in zip(varlist,invmultarr):
573                    if parmDict is not None and v not in parmDict:
574                        print "Dropping equivalence for dep. variable "+str(v)+". Not defined in this refinement"
575                        continue
576                    if m == 0: zeromult = True
577                    if v in varyList:
578                        varied += 1
579                    else:
580                        if notvaried: notvaried += ', '
581                        notvaried += v
582                    if v in depVarList:
583                        multdepVarList.append(v)
584                    else:
585                        depVarList.append(v)
586            if varied > 0 and varied != len(varlist)+1:
587                msg += "\nNot all variables refined in equivalence:\n\t"
588                s = ""
589                for v in varlist:
590                    if s != "": s+= " & "
591                    s += str(v)           
592                msg += str(mv) + " => " + s
593                msg += '\nNot refined: ' + notvaried + '\n'
594            if zeromult:
595                msg += "\nZero multiplier is invalid in equivalence:\n\t"
596                s = ""
597                for v in varlist:
598                    if s != "": s+= " & "
599                    s += str(v)           
600                msg += str(mv) + " => " + s + '\n'
601    # save the lists of dep. and indep. vars (after dropping unused)
602    global dependentVars,independentVars
603    dependentVars = depVarList
604    independentVars = indepVarList
605    equivVarList = list(set(indepVarList).union(set(depVarList)))
606
607    # scan through parameters in each relationship. Are all varied? If only some are
608    # varied, create an error message.
609    for group,varlist in zip(groups,parmlist):
610        if len(varlist) == 1: continue
611        for rel in group:
612            varied = 0
613            notvaried = ''
614            unused = 0
615            notused = ''
616            for var in constrDict[rel]:
617                if var.startswith('_'): continue
618                if var.split(':')[1] == '*' and SeqHist is not None:
619                    # convert wildcard var to reference current histogram; save translation in table
620                    sv = var.split(':')
621                    sv[1] = str(SeqHist)
622                    translateTable[var] = ':'.join(sv)
623                    var = translateTable[var]
624                if parmDict is not None and var not in parmDict:
625                    unused += 1
626                    if notvaried: notused += ', '
627                    notused += var
628                if var in varyList:
629                    varied += 1
630                else:
631                    if notvaried: notvaried += ', '
632                    notvaried += var
633                if var in fixedVarList:
634                    msg += '\nError: parameter '+var+" is Fixed and used in a constraint:\n\t"
635                    msg += _FormatConstraint(constrDict[rel],fixedList[rel])+"\n"
636            #if unused > 0:# and unused != len(VarKeys(constrDict[rel])):
637            if unused > 0 and unused != len(VarKeys(constrDict[rel])):
638                msg += "\nSome (but not all) variables in constraint are not defined:\n\t"
639                msg += _FormatConstraint(constrDict[rel],fixedList[rel])
640                msg += '\nNot used: ' + notused + '\n'
641            if varied > 0 and varied != len(VarKeys(constrDict[rel])):
642                msg += "\nNot all variables refined in constraint:\n\t"
643                msg += _FormatConstraint(constrDict[rel],fixedList[rel])
644                msg += '\nNot refined: ' + notvaried + '\n'
645    # if there were errors found, go no farther
646    if msg:
647        print ' *** ERROR in constraint definitions! ***'
648        print msg
649        raise Exception
650               
651    # now process each group and create the relations that are needed to form
652    # a non-singular square matrix
653    # If all are varied and this is a constraint equation, then set VaryFree flag
654    # so that the newly created relationships will be varied
655    for group,varlist in zip(groups,parmlist):
656        if len(varlist) == 1: continue
657        # for constraints, if all included variables are refined,
658        # set the VaryFree flag, and remaining degrees of freedom will be
659        # varied (since consistency was checked, if any one variable is
660        # refined, then assume that all are)
661        varsList = [] # make a list of all the referenced variables as well
662        VaryFree = False
663        for rel in group:
664            varied = 0
665            unused = 0
666            for var in VarKeys(constrDict[rel]):
667                var = translateTable.get(var,var) # replace wildcards
668                if parmDict is not None and var not in parmDict:
669                    unused += 1                   
670                if var not in varsList: varsList.append(var)
671                if var in varyList: varied += 1
672            if fixedList[rel] is not None and varied > 0:
673                VaryFree = True
674        if len(varlist) < len(group): # too many relationships -- no can do
675            msg = 'too many relationships'
676            break
677        # Since we checked before, if any variables are unused, then all must be.
678        # If so, this set of relationships can be ignored
679        if unused:
680            if debug: print('Constraint ignored (all variables undefined)')
681            if debug: print ('    '+_FormatConstraint(constrDict[rel],fixedList[rel]))
682            continue
683        # fill in additional degrees of freedom
684        try:
685            arr = _FillArray(group,constrDict,varlist)
686            _RowEchelon(len(group),arr,varlist)
687            constrArr = _FillArray(group,constrDict,varlist,FillDiagonals=True)
688            GramSchmidtOrtho(constrArr,len(group))
689        except:
690            msg = 'Singular relationships'
691            break
692        mapvar = []
693        group = group[:]
694        # scan through all generated and input relationships, we need to add to the varied list
695        # all the new parameters where VaryFree has been set or where a New Var is varied.
696        #
697        # If a group does not contain any fixed values (constraint equations)
698        # and nothing in the group is varied, drop this group, so that the
699        # dependent parameters can be refined individually.
700        unused = True
701        for i in range(len(varlist)):
702            if len(group) > 0: # get the original equation reference
703                rel = group.pop(0)
704                fixedval = fixedList[rel]
705                varyflag = constrDict[rel].get('_vary',False)
706                varname = constrDict[rel].get('_name','')
707            else: # this relationship has been generated
708                varyflag = False
709                varname = ''
710                fixedval = None
711            if fixedval is None: # this is a new variable, not a constraint
712                if not varname:
713                    varname = paramPrefix + str(consNum) # no assigned name, create one
714                    consNum += 1
715                mapvar.append(varname)
716                # vary the new relationship if it is a degree of freedom in
717                # a set of contraint equations or if a New Var is flagged to be varied.
718                if VaryFree or varyflag: 
719                    unused = False
720                    varyList.append(varname)
721                    # fix (prevent varying) of all the variables inside the constraint group
722                    # (dependent vars)
723                    for var in varsList:
724                        if var in varyList: varyList.remove(var)
725            else:
726                unused = False
727                mapvar.append(fixedval)
728        if unused: # skip over constraints that don't matter (w/o fixed value or any refined variables)
729            if debug: print('Constraint ignored (all variables unrefined)')
730            if debug: print ('   '+_FormatConstraint(constrDict[rel],fixedList[rel]))
731            continue 
732        dependentParmList.append([translateTable.get(var,var) for var in varlist])
733        arrayList.append(constrArr)
734        invarrayList.append(np.linalg.inv(constrArr))
735        indParmList.append(mapvar)
736    if msg:
737        print ' *** ERROR in constraint definitions! ***'
738        print msg
739        print VarRemapShow(varyList)
740        raise Exception
741    # setup dictionary containing the fixed values
742    global fixedDict
743    # key is original ascii string, value is float
744    for fixedval in fixedList:
745        if fixedval:
746            fixedDict[fixedval] = float(fixedval)
747
748    if debug: # on debug, show what is parsed & generated, semi-readable
749        print 50*'-'
750        print VarRemapShow(varyList)
751        print 'Varied: ',varyList
752        print 'Not Varied: ',fixedVarList
753
754def StoreEquivalence(independentVar,dependentList):
755    '''Takes a list of dependent parameter(s) and stores their
756    relationship to a single independent parameter (independentVar)
757
758    :param str independentVar: name of master parameter that will be used to determine the value
759      to set the dependent variables
760
761    :param list dependentList: a list of parameters that will set from
762         independentVar. Each item in the list can be a string with the parameter
763         name or a tuple containing a name and multiplier:
764         ``['parm1',('parm2',.5),]``
765
766    '''
767   
768    global dependentParmList,arrayList,invarrayList,indParmList
769    mapList = []
770    multlist = []
771    for var in dependentList:
772        if isinstance(var, basestring):
773            mult = 1.0
774        elif len(var) == 2:
775            var,mult = var
776        else:
777            raise Exception("Cannot parse "+repr(var) + " as var or (var,multiplier)")
778        mapList.append(var)
779        multlist.append(tuple((mult,)))
780    # added relationships to stored values
781    arrayList.append(None)
782    invarrayList.append(np.array(multlist))
783    indParmList.append(tuple((independentVar,)))
784    dependentParmList.append(mapList)
785    return
786
787def GetDependentVars():
788    '''Return a list of dependent variables: e.g. variables that are
789    constrained in terms of other variables
790
791    :returns: a list of variable names
792
793    '''
794    return dependentVars
795
796def GetIndependentVars():
797    '''Return a list of independent variables: e.g. variables that are
798    created by constraints of other variables
799
800    :returns: a list of variable names
801
802    '''
803    return independentVars
804
805def PrintIndependentVars(parmDict,varyList,sigDict,PrintAll=False,pFile=None):
806    '''Print the values and uncertainties on the independent variables'''
807    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
808    printlist = []
809    mapvars = GetIndependentVars()
810    for i,name in enumerate(mapvars):
811        if name in fixedDict: continue
812        if PrintAll or name in varyList:
813            sig = sigDict.get(name)
814            printlist.append([name,parmDict[name],sig])
815    if len(printlist) == 0: return
816    s1 = ''
817    print >>pFile,130*'-'
818    print >>pFile,"Variables generated by constraints"
819    printlist.append(3*[None])
820    for name,val,esd in printlist:
821        if len(s1) > 120 or name is None:
822            print >>pFile,''
823            print >>pFile,s1
824            print >>pFile,s2
825            print >>pFile,s3
826            s1 = ''
827            if name is None: break
828        if s1 == "":
829            s1 = ' name  :'
830            s2 = ' value :'
831            s3 = ' sig   :'
832        s1 += '%15s' % (name)
833        s2 += '%15.4f' % (val)
834        if esd is None:
835            s3 += '%15s' % ('n/a')
836        else:   
837            s3 += '%15.4f' % (esd)
838
839def ComputeDepESD(covMatrix,varyList,parmDict):
840    '''Compute uncertainties for dependent parameters from independent ones
841    returns a dictionary containing the esd values for dependent parameters
842    '''
843    sigmaDict = {}
844    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
845        #if invmultarr is None: continue # probably not needed
846        try: 
847            valuelist = [parmDict[var] for var in mapvars]
848        except KeyError:
849            continue
850        # get the v-covar matrix for independent parameters
851        vcov = np.zeros((len(mapvars),len(mapvars)))
852        for i1,name1 in enumerate(mapvars):
853            if name1 not in varyList: continue
854            iv1 = varyList.index(name1)
855            for i2,name2 in enumerate(mapvars):
856                if name2 not in varyList: continue
857                iv2 = varyList.index(name2)
858                vcov[i1][i2] = covMatrix[iv1][iv2]
859        # vec is the vector that multiplies each of the independent values
860        for v,vec in zip(varlist,invmultarr):
861            sigmaDict[v] = np.sqrt(np.inner(vec.T,np.inner(vcov,vec)))
862    return sigmaDict
863
864def _FormatConstraint(RelDict,RelVal):
865    '''Formats a Constraint or Function for use in a convenient way'''
866    linelen = 45
867    s = [""]
868    for var,val in RelDict.items():
869        if var.startswith('_'): continue
870        if len(s[-1]) > linelen: s.append(' ')
871        m = val
872        if s[-1] != "" and m >= 0:
873            s[-1] += ' + '
874        elif s[-1] != "":
875            s[-1] += ' - '
876            m = abs(m)
877        s[-1] += '%.3f*%s '%(m,var)
878    if len(s[-1]) > linelen: s.append(' ')
879    if RelVal is None:
880        s[-1] += ' = New variable'
881    else:
882        s[-1] += ' = ' + RelVal
883    s1 = ''
884    for s2 in s:
885        if s1 != '': s1 += '\n\t'
886        s1 += s2
887    return s1
888
889def VarRemapShow(varyList,inputOnly=False):
890    '''List out the saved relationships. This should be done after the constraints have been
891    defined using :func:`StoreEquivalence`, :func:`GroupConstraints` and :func:`GenerateConstraints`.
892
893    :returns: a string containing the details of the contraint relationships
894    '''
895    s = ''
896    if len(fixedVarList) > 0:
897        s += 'Fixed Variables:\n'
898        for v in fixedVarList:
899            s += '    ' + v + '\n'
900    s += 'Variable mapping relations:\n'
901    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
902    for varlist,mapvars,multarr,invmultarr in zip(
903        dependentParmList,indParmList,arrayList,invarrayList):
904        for i,mv in enumerate(mapvars):
905            if multarr is None:
906                s += '  ' + str(mv) + ' is equivalent to parameter(s): '
907                j = 0
908                for v,m in zip(varlist,invmultarr):
909                    if debug: print 'v,m[0]: ',v,m[0]
910                    if j > 0: s += '  & '
911                    j += 1
912                    s += str(v)
913                    if m != 1:
914                        s += " / " + str(m[0])                       
915                s += '\n'
916                continue
917            s += %s = ' % mv
918            j = 0
919            for m,v in zip(multarr[i,:],varlist):
920                if m == 0: continue
921                if j > 0: s += ' + '
922                j += 1
923                s += '(%s * %s)' % (m,v)
924            if mv in varyList: s += ' VARY'
925            s += '\n'
926    if inputOnly: return s
927    s += 'Inverse variable mapping relations:\n'
928    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
929        for i,mv in enumerate(varlist):
930            s += %s = ' % mv
931            j = 0
932            for m,v in zip(invmultarr[i,:],mapvars):
933                if m == 0: continue
934                if j > 0: s += ' + '
935                j += 1
936                s += '(%s * %s)' % (m,v)
937            s += '\n'
938    return s
939
940def Dict2Deriv(varyList,derivDict,dMdv):
941    '''Compute derivatives for Independent Parameters from the
942    derivatives for the original parameters
943
944    :param list varyList: a list of parameters names that will be varied
945
946    :param dict derivDict: a dict containing derivatives for parameter values keyed by the
947      parameter names.
948
949    :param list dMdv: a Jacobian, as a list of np.array containing derivatives for dependent
950      parameter computed from derivDict
951
952    '''
953    global dependentParmList,arrayList,invarrayList,indParmList,invarrayList
954    for varlist,mapvars,multarr,invmultarr in zip(dependentParmList,indParmList,arrayList,invarrayList):
955        for i,name in enumerate(mapvars):
956            # grouped variables: need to add in the derv. w/r
957            # dependent variables to the independent ones
958            if name not in varyList: continue # skip if independent var not varied
959            if multarr is None:
960                for v,m in zip(varlist,invmultarr):
961                    if debug: print 'start dMdv',dMdv[varyList.index(name)]
962                    if debug: print 'add derv',v,'/',m[0],'to derv',name,'add=',derivDict[v] / m[0]
963                    if m == 0: continue
964                    dMdv[varyList.index(name)] += derivDict[v] / m[0]
965            else:
966                for v,m in zip(varlist,multarr[i,:]):
967                    if debug: print 'start dMdv',dMdv[varyList.index(name)]
968                    if debug: print 'add derv',v,'*',m,'to derv',name,'add=',m * derivDict[v]
969                    if m == 0: continue
970                    dMdv[varyList.index(name)] += m * derivDict[v]
971
972def Map2Dict(parmDict,varyList):
973    '''Create (or update) the Independent Parameters from the original
974    set of Parameters
975
976    Removes dependent variables from the varyList
977
978    This should be done once, after the constraints have been
979    defined using :func:`StoreEquivalence`,
980    :func:`GroupConstraints` and :func:`GenerateConstraints` and
981    before any variable refinement is done. This completes the parameter
982    dictionary by defining independent parameters and it satisfies the
983    constraint equations in the initial parameters
984
985    :param dict parmDict: a dict containing parameter values keyed by the
986      parameter names.
987      This will contain updated values for both dependent and independent
988      parameters after Dict2Map is called. It will also contain some
989      unexpected entries of every constant value {'0':0.0} & {'1.0':1.0},
990      which do not cause any problems.
991
992    :param list varyList: a list of parameters names that will be varied
993   
994
995    '''
996    # process the Independent vars: remove dependent ones from varylist
997    # and then compute values for the Independent ones from their dependents
998    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
999    for varlist,mapvars,multarr in zip(dependentParmList,indParmList,arrayList):
1000        for item in varlist:
1001            try:
1002                varyList.remove(item)
1003            except ValueError:
1004                pass
1005        if multarr is None: continue
1006        valuelist = [parmDict[var] for var in varlist]
1007        parmDict.update(zip(mapvars,
1008                            np.dot(multarr,np.array(valuelist)))
1009                        )
1010    # now remove fixed variables from the varyList
1011    global fixedVarList
1012    for item in fixedVarList:
1013        try:
1014            varyList.remove(item)
1015        except ValueError:
1016            pass
1017    # Set constrained parameters to their fixed values
1018    parmDict.update(fixedDict)
1019
1020def Dict2Map(parmDict,varyList):
1021    '''Applies the constraints defined using :func:`StoreEquivalence`,
1022    :func:`GroupConstraints` and :func:`GenerateConstraints` by changing
1023    values in a dict containing the parameters. This should be
1024    done before the parameters are used for any computations
1025
1026    :param dict parmDict: a dict containing parameter values keyed by the
1027      parameter names.
1028      This will contain updated values for both dependent and independent
1029      parameters after Dict2Map is called. It will also contain some
1030      unexpected entries of every constant value {'0':0.0} & {'1.0':1.0},
1031      which do not cause any problems.
1032
1033    :param list varyList: a list of parameters names that will be varied
1034   
1035    '''
1036    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
1037    # reset fixed values (should not be needed, but very quick)
1038    # - this seems to update parmDict with {'0':0.0} & {'1.0':1.0} - probably not what was intended
1039    # not needed, but also not a problem - BHT
1040    parmDict.update(fixedDict)
1041    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
1042        #if invmultarr is None: continue
1043        try: 
1044            valuelist = [parmDict[var] for var in mapvars]
1045        except KeyError:
1046            continue
1047        parmDict.update(zip(varlist,
1048                            np.dot(invmultarr,np.array(valuelist)))
1049                        )
1050
1051#======================================================================
1052# internal routines follow (these routines are unlikely to be called
1053# from outside the module)
1054
1055def GramSchmidtOrtho(a,nkeep=0):
1056    '''Use the Gram-Schmidt process (http://en.wikipedia.org/wiki/Gram-Schmidt) to
1057    find orthonormal unit vectors relative to first row.
1058
1059    If nkeep is non-zero, the first nkeep rows in the array are not changed
1060   
1061    input:
1062       arrayin: a 2-D non-singular square array
1063    returns:
1064       a orthonormal set of unit vectors as a square array
1065    '''
1066    def proj(a,b):
1067        'Projection operator'
1068        return a*(np.dot(a,b)/np.dot(a,a))
1069    for j in range(nkeep,len(a)):
1070        for i in range(j):
1071            a[j] -= proj(a[i],a[j])
1072        if np.allclose(np.linalg.norm(a[j]),0.0):
1073            raise Exception,"Singular input to GramSchmidtOrtho"
1074        a[j] /= np.linalg.norm(a[j])
1075    return a
1076
1077def _FillArray(sel,dict,collist,FillDiagonals=False):
1078    '''Construct a n by n matrix (n = len(collist)
1079    filling in the rows using the relationships defined
1080    in the dictionaries selected by sel
1081
1082    If FillDiagonals is True, diagonal elements in the
1083    array are set to 1.0
1084    '''
1085    n = len(collist)
1086    if FillDiagonals:
1087        arr = np.eye(n)
1088    else:
1089        arr = np.zeros(2*[n,])
1090    # fill the top rows
1091    for i,cnum in enumerate(sel):
1092        for j,var in enumerate(collist):
1093            arr[i,j] = dict[cnum].get(var,0)
1094    return arr
1095
1096def _SwapColumns(i,m,v):
1097    '''Swap columns in matrix m as well as the labels in v
1098    so that element (i,i) is replaced by the first non-zero element in row i after that element
1099
1100    Throws an exception if there are no non-zero elements in that row
1101    '''
1102    for j in range(i+1,len(v)):
1103        if not np.allclose(m[i,j],0):
1104            m[:,(i,j)] = m[:,(j,i)]
1105            v[i],v[j] = v[j],v[i]
1106            return
1107    else:
1108        raise Exception,'Singular input'
1109
1110def _RowEchelon(m,arr,collist):
1111    '''Convert the first m rows in Matrix arr to row-echelon form
1112    exchanging columns in the matrix and collist as needed.
1113
1114    throws an exception if the matrix is singular because
1115    the first m rows are not linearly independent
1116    '''
1117    n = len(collist)
1118    for i in range(m):
1119        if np.allclose(arr[i,i],0):
1120            _SwapColumns(i,arr,collist)
1121        arr[i,:] /= arr[i,i] # normalize row
1122        # subtract current row from subsequent rows to set values to left of diagonal to 0
1123        for j in range(i+1,m):
1124            arr[j,:] -= arr[i,:] * arr[j,i]
1125
1126if __name__ == "__main__":
1127    parmdict = {}
1128    constrDict = [
1129        {'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},
1130        {'0:0:eA': 0.0},
1131        {'2::C(10,6,1)': 1.0, '1::C(10,6,1)': 1.0},
1132        {'1::C(10,0,1)': 1.0, '2::C(10,0,1)': 1.0},
1133        {'1::AUiso:0': 1.0, '0::AUiso:0': 1.0},
1134        {'0::A0': 0.0}
1135        ]
1136    fixedList = ['5.0', '0', None, None, '1.0', '0']
1137    StoreEquivalence('2::atomx:3',('2::atomy:3', ('2::atomz:3',2,), ))
1138    #StoreEquivalence('1::atomx:3',('2::atomx:3', ('2::atomz:3',2,), )) # error: dependent & independent vars mixed
1139    #StoreEquivalence('1::atomx:3',('2::atomy:3', ('2::atomz:3',2,), )) # error: dependent vars repeated
1140    #StoreEquivalence('0:1:eA',('0:0:eA',)) # error: equiv & fixed
1141    #StoreEquivalence('0:99:Scale',('0:12:Scale',)) # error: equiv & constrained
1142    #StoreEquivalence('0:12:Scale',('0:99:Scale',)) # error: equiv & constrained
1143    varylist = ['2::atomx:3',
1144                '2::C(10,6,1)', '1::C(10,6,1)',
1145                '2::atomy:3', '2::atomz:3',
1146                '0:12:Scale', '0:11:Scale', '0:14:Scale', '0:13:Scale', '0:0:Scale']
1147#    e,w = CheckConstraints([,
1148#                     [{'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}],
1149#                     ['1.0'])
1150#    if e: print 'error=',e
1151#    if w: print 'error=',w
1152#    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']
1153#    constrDict = [
1154#        {'0::Afrac:4': 24.0, '0::Afrac:1': 16.0, '0::Afrac:3': 24.0, '0::Afrac:2': 16.0},
1155#        {'0::Afrac:1': 1.0, '0::Afrac:2': 1.0},
1156#        {'0::Afrac:4': 1.0, '0::Afrac:3': 1.0}]
1157#    fixedList = ['40.0', '1.0', '1.0']
1158
1159    errmsg, warnmsg = CheckConstraints(varylist,constrDict,fixedList)
1160    if errmsg:
1161        print "*** Error ********************"
1162        print errmsg
1163    if warnmsg:
1164        print "*** Warning ********************"
1165        print warnmsg
1166    if errmsg or warnmsg:
1167        sys.exit()
1168    groups,parmlist = GroupConstraints(constrDict)
1169    GenerateConstraints(groups,parmlist,varylist,constrDict,fixedList)
1170    print VarRemapShow(varylist)
1171    parmdict.update( {
1172        '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,
1173        '0:0:eA': 0.0,
1174        '2::C(10,6,1)': 0.2, '1::C(10,6,1)': 0.3,
1175        '1::C(10,0,1)': 0.2, '2::C(10,0,1)': 0.3,
1176        '1::AUiso:0': 0.02, '0::AUiso:0': 0.03,
1177        '0::A0': 0.0,
1178        '2::atomx:3':0.23,'2::atomy:3':-.23, '2::atomz:3':-0.11,
1179        })
1180    print 'parmdict start',parmdict
1181    print 'varylist start',varylist
1182    before = parmdict.copy()
1183    Map2Dict(parmdict,varylist)
1184    print 'parmdict before and after Map2Dict'
1185    print '  key / before / after'
1186    for key in sorted(parmdict.keys()):
1187        print '  '+key,'\t',before.get(key),'\t',parmdict[key]
1188    print 'varylist after',varylist
1189    before = parmdict.copy()
1190    Dict2Map(parmdict,varylist)
1191    print 'after Dict2Map'
1192    print '  key / before / after'
1193    for key in sorted(parmdict.keys()):
1194        print '  '+key,'\t',before.get(key),'\t',parmdict[key]
1195#    dMdv = len(varylist)*[0]
1196#    deriv = {}
1197#    for i,v in enumerate(parmdict.keys()): deriv[v]=i
1198#    Dict2Deriv(varylist,deriv,dMdv)
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