source: trunk/GSASIImapvars.py @ 2519

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1# -*- coding: utf-8 -*-
2########### SVN repository information ###################
3# $Date: 2016-11-09 20:48:37 +0000 (Wed, 09 Nov 2016) $
4# $Author: vondreele $
5# $Revision: 2519 $
6# $URL: trunk/GSASIImapvars.py $
7# $Id: GSASIImapvars.py 2519 2016-11-09 20:48:37Z vondreele $
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: 2519 $")
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    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            if 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:
636        print ' *** ERROR in constraint definitions! ***'
637        print msg
638        raise Exception
639               
640    # now process each group and create the relations that are needed to form
641    # a non-singular square matrix
642    # If all are varied and this is a constraint equation, then set VaryFree flag
643    # so that the newly created relationships will be varied
644    for group,varlist in zip(groups,parmlist):
645        if len(varlist) == 1: continue
646        # for constraints, if all included variables are refined,
647        # set the VaryFree flag, and remaining degrees of freedom will be
648        # varied (since consistency was checked, if any one variable is
649        # refined, then assume that all are)
650        varsList = [] # make a list of all the referenced variables as well
651        VaryFree = False
652        for rel in group:
653            varied = 0
654            unused = 0
655            for var in VarKeys(constrDict[rel]):
656                var = translateTable.get(var,var) # replace wildcards
657                if parmDict is not None and var not in parmDict:
658                    unused += 1                   
659                if var not in varsList: varsList.append(var)
660                if var in varyList: varied += 1
661            if fixedList[rel] is not None and varied > 0:
662                VaryFree = True
663        if len(varlist) < len(group): # too many relationships -- no can do
664            msg = 'too many relationships'
665            break
666        # Since we checked before, if any variables are unused, then all must be.
667        # If so, this set of relationships can be ignored
668        if unused:
669            if debug: print('Constraint ignored (all variables undefined)')
670            if debug: print ('    '+_FormatConstraint(constrDict[rel],fixedList[rel]))
671            continue
672        # fill in additional degrees of freedom
673        try:
674            arr = _FillArray(group,constrDict,varlist)
675            _RowEchelon(len(group),arr,varlist)
676            constrArr = _FillArray(group,constrDict,varlist,FillDiagonals=True)
677            GramSchmidtOrtho(constrArr,len(group))
678        except:
679            msg = 'Singular relationships'
680            break
681        mapvar = []
682        group = group[:]
683        # scan through all generated and input relationships, we need to add to the varied list
684        # all the new parameters where VaryFree has been set or where a New Var is varied.
685        #
686        # If a group does not contain any fixed values (constraint equations)
687        # and nothing in the group is varied, drop this group, so that the
688        # dependent parameters can be refined individually.
689        unused = True
690        for i in range(len(varlist)):
691            if len(group) > 0: # get the original equation reference
692                rel = group.pop(0)
693                fixedval = fixedList[rel]
694                varyflag = constrDict[rel].get('_vary',False)
695                varname = constrDict[rel].get('_name','')
696            else: # this relationship has been generated
697                varyflag = False
698                varname = ''
699                fixedval = None
700            if fixedval is None: # this is a new variable, not a constraint
701                if not varname:
702                    varname = paramPrefix + str(consNum) # no assigned name, create one
703                    consNum += 1
704                mapvar.append(varname)
705                # vary the new relationship if it is a degree of freedom in
706                # a set of contraint equations or if a New Var is flagged to be varied.
707                if VaryFree or varyflag: 
708                    unused = False
709                    varyList.append(varname)
710                    # fix (prevent varying) of all the variables inside the constraint group
711                    # (dependent vars)
712                    for var in varsList:
713                        if var in varyList: varyList.remove(var)
714            else:
715                unused = False
716                mapvar.append(fixedval)
717        if unused: # skip over constraints that don't matter (w/o fixed value or any refined variables)
718            if debug: print('Constraint ignored (all variables unrefined)')
719            if debug: print ('   '+_FormatConstraint(constrDict[rel],fixedList[rel]))
720            continue 
721        dependentParmList.append([translateTable.get(var,var) for var in varlist])
722        arrayList.append(constrArr)
723        invarrayList.append(np.linalg.inv(constrArr))
724        indParmList.append(mapvar)
725    if msg:
726        print ' *** ERROR in constraint definitions! ***'
727        print msg
728        print VarRemapShow(varyList)
729        raise Exception
730    # setup dictionary containing the fixed values
731    global fixedDict
732    # key is original ascii string, value is float
733    for fixedval in fixedList:
734        if fixedval:
735            fixedDict[fixedval] = float(fixedval)
736
737    # make list of dependent and independent variables (after dropping unused)
738    global dependentVars
739    global independentVars
740    dependentVars = []
741    independentVars = []
742    for varlist,mapvars in zip(dependentParmList,indParmList):  # process all constraints
743        for mv in mapvars:
744            if mv in dropVarList: continue
745            if mv not in independentVars: independentVars.append(mv)
746        for mv in varlist:
747            if mv in dropVarList: continue
748            if mv not in dependentVars: dependentVars.append(mv)
749    if debug: # on debug, show what is parsed & generated, semi-readable
750        print 50*'-'
751        print VarRemapShow(varyList)
752        print 'Varied: ',varyList
753        print 'Not Varied: ',fixedVarList
754
755def StoreEquivalence(independentVar,dependentList):
756    '''Takes a list of dependent parameter(s) and stores their
757    relationship to a single independent parameter (independentVar)
758
759    :param str independentVar: name of master parameter that will be used to determine the value
760      to set the dependent variables
761
762    :param list dependentList: a list of parameters that will set from
763         independentVar. Each item in the list can be a string with the parameter
764         name or a tuple containing a name and multiplier:
765         ``['parm1',('parm2',.5),]``
766
767    '''
768   
769    global dependentParmList,arrayList,invarrayList,indParmList
770    mapList = []
771    multlist = []
772    for var in dependentList:
773        if isinstance(var, basestring):
774            mult = 1.0
775        elif len(var) == 2:
776            var,mult = var
777        else:
778            raise Exception("Cannot parse "+repr(var) + " as var or (var,multiplier)")
779        mapList.append(var)
780        multlist.append(tuple((mult,)))
781    # added relationships to stored values
782    arrayList.append(None)
783    invarrayList.append(np.array(multlist))
784    indParmList.append(tuple((independentVar,)))
785    dependentParmList.append(mapList)
786    return
787
788def GetDependentVars():
789    '''Return a list of dependent variables: e.g. variables that are
790    constrained in terms of other variables
791
792    :returns: a list of variable names
793
794    '''
795    return dependentVars
796
797def GetIndependentVars():
798    '''Return a list of independent variables: e.g. variables that are
799    created by constraints of other variables
800
801    :returns: a list of variable names
802
803    '''
804    return independentVars
805
806def PrintIndependentVars(parmDict,varyList,sigDict,PrintAll=False,pFile=None):
807    '''Print the values and uncertainties on the independent variables'''
808    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
809    printlist = []
810    mapvars = GetIndependentVars()
811    for i,name in enumerate(mapvars):
812        if name in fixedDict: continue
813        if PrintAll or name in varyList:
814            sig = sigDict.get(name)
815            printlist.append([name,parmDict[name],sig])
816    if len(printlist) == 0: return
817    s1 = ''
818    print >>pFile,130*'-'
819    print >>pFile,"Variables generated by constraints"
820    printlist.append(3*[None])
821    for name,val,esd in printlist:
822        if len(s1) > 120 or name is None:
823            print >>pFile,''
824            print >>pFile,s1
825            print >>pFile,s2
826            print >>pFile,s3
827            s1 = ''
828            if name is None: break
829        if s1 == "":
830            s1 = ' name  :'
831            s2 = ' value :'
832            s3 = ' sig   :'
833        s1 += '%15s' % (name)
834        s2 += '%15.4f' % (val)
835        if esd is None:
836            s3 += '%15s' % ('n/a')
837        else:   
838            s3 += '%15.4f' % (esd)
839
840def ComputeDepESD(covMatrix,varyList,parmDict):
841    '''Compute uncertainties for dependent parameters from independent ones
842    returns a dictionary containing the esd values for dependent parameters
843    '''
844    sigmaDict = {}
845    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
846        #if invmultarr is None: continue # probably not needed
847        try: 
848            valuelist = [parmDict[var] for var in mapvars]
849        except KeyError:
850            continue
851        # get the v-covar matrix for independent parameters
852        vcov = np.zeros((len(mapvars),len(mapvars)))
853        for i1,name1 in enumerate(mapvars):
854            if name1 not in varyList: continue
855            iv1 = varyList.index(name1)
856            for i2,name2 in enumerate(mapvars):
857                if name2 not in varyList: continue
858                iv2 = varyList.index(name2)
859                vcov[i1][i2] = covMatrix[iv1][iv2]
860        # vec is the vector that multiplies each of the independent values
861        for v,vec in zip(varlist,invmultarr):
862            sigmaDict[v] = np.sqrt(np.inner(vec.T,np.inner(vcov,vec)))
863    return sigmaDict
864
865def _FormatConstraint(RelDict,RelVal):
866    '''Formats a Constraint or Function for use in a convenient way'''
867    linelen = 45
868    s = [""]
869    for var,val in RelDict.items():
870        if var.startswith('_'): continue
871        if len(s[-1]) > linelen: s.append(' ')
872        m = val
873        if s[-1] != "" and m >= 0:
874            s[-1] += ' + '
875        elif s[-1] != "":
876            s[-1] += ' - '
877            m = abs(m)
878        s[-1] += '%.3f*%s '%(m,var)
879    if len(s[-1]) > linelen: s.append(' ')
880    if RelVal is None:
881        s[-1] += ' = New variable'
882    else:
883        s[-1] += ' = ' + RelVal
884    s1 = ''
885    for s2 in s:
886        if s1 != '': s1 += '\n\t'
887        s1 += s2
888    return s1
889
890def VarRemapShow(varyList,inputOnly=False):
891    '''List out the saved relationships. This should be done after the constraints have been
892    defined using :func:`StoreEquivalence`, :func:`GroupConstraints` and :func:`GenerateConstraints`.
893
894    :returns: a string containing the details of the contraint relationships
895    '''
896    s = ''
897    if len(fixedVarList) > 0:
898        s += 'Fixed Variables:\n'
899        for v in fixedVarList:
900            s += '    ' + v + '\n'
901    s += 'Variable mapping relations:\n'
902    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
903    for varlist,mapvars,multarr,invmultarr in zip(
904        dependentParmList,indParmList,arrayList,invarrayList):
905        for i,mv in enumerate(mapvars):
906            if multarr is None:
907                s += '  ' + str(mv) + ' is equivalent to parameter(s): '
908                j = 0
909                for v,m in zip(varlist,invmultarr):
910                    if debug: print 'v,m[0]: ',v,m[0]
911                    if j > 0: s += '  & '
912                    j += 1
913                    s += str(v)
914                    if m != 1:
915                        s += " / " + str(m[0])                       
916                s += '\n'
917                continue
918            s += %s = ' % mv
919            j = 0
920            for m,v in zip(multarr[i,:],varlist):
921                if m == 0: continue
922                if j > 0: s += ' + '
923                j += 1
924                s += '(%s * %s)' % (m,v)
925            if mv in varyList: s += ' VARY'
926            s += '\n'
927    if inputOnly: return s
928    s += 'Inverse variable mapping relations:\n'
929    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
930        for i,mv in enumerate(varlist):
931            s += %s = ' % mv
932            j = 0
933            for m,v in zip(invmultarr[i,:],mapvars):
934                if m == 0: continue
935                if j > 0: s += ' + '
936                j += 1
937                s += '(%s * %s)' % (m,v)
938            s += '\n'
939    return s
940
941def Dict2Deriv(varyList,derivDict,dMdv):
942    '''Compute derivatives for Independent Parameters from the
943    derivatives for the original parameters
944
945    :param list varyList: a list of parameters names that will be varied
946
947    :param dict derivDict: a dict containing derivatives for parameter values keyed by the
948      parameter names.
949
950    :param list dMdv: a Jacobian, as a list of np.array containing derivatives for dependent
951      parameter computed from derivDict
952
953    '''
954    global dependentParmList,arrayList,invarrayList,indParmList,invarrayList
955    for varlist,mapvars,multarr,invmultarr in zip(dependentParmList,indParmList,arrayList,invarrayList):
956        for i,name in enumerate(mapvars):
957            # grouped variables: need to add in the derv. w/r
958            # dependent variables to the independent ones
959            if name not in varyList: continue # skip if independent var not varied
960            if multarr is None:
961                for v,m in zip(varlist,invmultarr):
962                    if debug: print 'start dMdv',dMdv[varyList.index(name)]
963                    if debug: print 'add derv',v,'/',m[0],'to derv',name,'add=',derivDict[v] / m[0]
964                    if m == 0: continue
965                    dMdv[varyList.index(name)] += derivDict[v] / m[0]
966            else:
967                for v,m in zip(varlist,multarr[i,:]):
968                    if debug: print 'start dMdv',dMdv[varyList.index(name)]
969                    if debug: print 'add derv',v,'*',m,'to derv',name,'add=',m * derivDict[v]
970                    if m == 0: continue
971                    dMdv[varyList.index(name)] += m * derivDict[v]
972
973def Map2Dict(parmDict,varyList):
974    '''Create (or update) the Independent Parameters from the original
975    set of Parameters
976
977    Removes dependent variables from the varyList
978
979    This should be done once, after the constraints have been
980    defined using :func:`StoreEquivalence`,
981    :func:`GroupConstraints` and :func:`GenerateConstraints` and
982    before any variable refinement is done. This completes the parameter
983    dictionary by defining independent parameters and it satisfies the
984    constraint equations in the initial parameters
985
986    :param dict parmDict: a dict containing parameter values keyed by the
987      parameter names.
988      This will contain updated values for both dependent and independent
989      parameters after Dict2Map is called. It will also contain some
990      unexpected entries of every constant value {'0':0.0} & {'1.0':1.0},
991      which do not cause any problems.
992
993    :param list varyList: a list of parameters names that will be varied
994   
995
996    '''
997    # process the Independent vars: remove dependent ones from varylist
998    # and then compute values for the Independent ones from their dependents
999    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
1000    for varlist,mapvars,multarr in zip(dependentParmList,indParmList,arrayList):
1001        for item in varlist:
1002            try:
1003                varyList.remove(item)
1004            except ValueError:
1005                pass
1006        if multarr is None: continue
1007        valuelist = [parmDict[var] for var in varlist]
1008        parmDict.update(zip(mapvars,
1009                            np.dot(multarr,np.array(valuelist)))
1010                        )
1011    # now remove fixed variables from the varyList
1012    global fixedVarList
1013    for item in fixedVarList:
1014        try:
1015            varyList.remove(item)
1016        except ValueError:
1017            pass
1018    # Set constrained parameters to their fixed values
1019    parmDict.update(fixedDict)
1020
1021def Dict2Map(parmDict,varyList):
1022    '''Applies the constraints defined using :func:`StoreEquivalence`,
1023    :func:`GroupConstraints` and :func:`GenerateConstraints` by changing
1024    values in a dict containing the parameters. This should be
1025    done before the parameters are used for any computations
1026
1027    :param dict parmDict: a dict containing parameter values keyed by the
1028      parameter names.
1029      This will contain updated values for both dependent and independent
1030      parameters after Dict2Map is called. It will also contain some
1031      unexpected entries of every constant value {'0':0.0} & {'1.0':1.0},
1032      which do not cause any problems.
1033
1034    :param list varyList: a list of parameters names that will be varied
1035   
1036    '''
1037    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
1038    # reset fixed values (should not be needed, but very quick)
1039    # - this seems to update parmDict with {'0':0.0} & {'1.0':1.0} - probably not what was intended
1040    # not needed, but also not a problem - BHT
1041    parmDict.update(fixedDict)
1042    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
1043        #if invmultarr is None: continue
1044        try: 
1045            valuelist = [parmDict[var] for var in mapvars]
1046        except KeyError:
1047            continue
1048        parmDict.update(zip(varlist,np.dot(invmultarr,np.array(valuelist))))
1049
1050#======================================================================
1051# internal routines follow (these routines are unlikely to be called
1052# from outside the module)
1053
1054def GramSchmidtOrtho(a,nkeep=0):
1055    '''Use the Gram-Schmidt process (http://en.wikipedia.org/wiki/Gram-Schmidt) to
1056    find orthonormal unit vectors relative to first row.
1057
1058    If nkeep is non-zero, the first nkeep rows in the array are not changed
1059   
1060    input:
1061       arrayin: a 2-D non-singular square array
1062    returns:
1063       a orthonormal set of unit vectors as a square array
1064    '''
1065    def proj(a,b):
1066        'Projection operator'
1067        return a*(np.dot(a,b)/np.dot(a,a))
1068    for j in range(nkeep,len(a)):
1069        for i in range(j):
1070            a[j] -= proj(a[i],a[j])
1071        if np.allclose(np.linalg.norm(a[j]),0.0):
1072            raise Exception,"Singular input to GramSchmidtOrtho"
1073        a[j] /= np.linalg.norm(a[j])
1074    return a
1075
1076def _FillArray(sel,dict,collist,FillDiagonals=False):
1077    '''Construct a n by n matrix (n = len(collist)
1078    filling in the rows using the relationships defined
1079    in the dictionaries selected by sel
1080
1081    If FillDiagonals is True, diagonal elements in the
1082    array are set to 1.0
1083    '''
1084    n = len(collist)
1085    if FillDiagonals:
1086        arr = np.eye(n)
1087    else:
1088        arr = np.zeros(2*[n,])
1089    # fill the top rows
1090    for i,cnum in enumerate(sel):
1091        for j,var in enumerate(collist):
1092            arr[i,j] = dict[cnum].get(var,0)
1093    return arr
1094
1095def _SwapColumns(i,m,v):
1096    '''Swap columns in matrix m as well as the labels in v
1097    so that element (i,i) is replaced by the first non-zero element in row i after that element
1098
1099    Throws an exception if there are no non-zero elements in that row
1100    '''
1101    for j in range(i+1,len(v)):
1102        if not np.allclose(m[i,j],0):
1103            m[:,(i,j)] = m[:,(j,i)]
1104            v[i],v[j] = v[j],v[i]
1105            return
1106    else:
1107        raise Exception,'Singular input'
1108
1109def _RowEchelon(m,arr,collist):
1110    '''Convert the first m rows in Matrix arr to row-echelon form
1111    exchanging columns in the matrix and collist as needed.
1112
1113    throws an exception if the matrix is singular because
1114    the first m rows are not linearly independent
1115    '''
1116    n = len(collist)
1117    for i in range(m):
1118        if np.allclose(arr[i,i],0):
1119            _SwapColumns(i,arr,collist)
1120        arr[i,:] /= arr[i,i] # normalize row
1121        # subtract current row from subsequent rows to set values to left of diagonal to 0
1122        for j in range(i+1,m):
1123            arr[j,:] -= arr[i,:] * arr[j,i]
1124
1125if __name__ == "__main__":
1126    parmdict = {}
1127    constrDict = [
1128        {'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},
1129        {'0:0:eA': 0.0},
1130        {'2::C(10,6,1)': 1.0, '1::C(10,6,1)': 1.0},
1131        {'1::C(10,0,1)': 1.0, '2::C(10,0,1)': 1.0},
1132        {'1::AUiso:0': 1.0, '0::AUiso:0': 1.0},
1133        {'0::A0': 0.0}
1134        ]
1135    fixedList = ['5.0', '0', None, None, '1.0', '0']
1136    StoreEquivalence('2::atomx:3',('2::atomy:3', ('2::atomz:3',2,), ))
1137    #StoreEquivalence('1::atomx:3',('2::atomx:3', ('2::atomz:3',2,), )) # error: dependent & independent vars mixed
1138    #StoreEquivalence('1::atomx:3',('2::atomy:3', ('2::atomz:3',2,), )) # error: dependent vars repeated
1139    #StoreEquivalence('0:1:eA',('0:0:eA',)) # error: equiv & fixed
1140    #StoreEquivalence('0:99:Scale',('0:12:Scale',)) # error: equiv & constrained
1141    #StoreEquivalence('0:12:Scale',('0:99:Scale',)) # error: equiv & constrained
1142    varylist = ['2::atomx:3',
1143                '2::C(10,6,1)', '1::C(10,6,1)',
1144                '2::atomy:3', '2::atomz:3',
1145                '0:12:Scale', '0:11:Scale', '0:14:Scale', '0:13:Scale', '0:0:Scale']
1146#    e,w = CheckConstraints([,
1147#                     [{'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}],
1148#                     ['1.0'])
1149#    if e: print 'error=',e
1150#    if w: print 'error=',w
1151#    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']
1152#    constrDict = [
1153#        {'0::Afrac:4': 24.0, '0::Afrac:1': 16.0, '0::Afrac:3': 24.0, '0::Afrac:2': 16.0},
1154#        {'0::Afrac:1': 1.0, '0::Afrac:2': 1.0},
1155#        {'0::Afrac:4': 1.0, '0::Afrac:3': 1.0}]
1156#    fixedList = ['40.0', '1.0', '1.0']
1157
1158    errmsg, warnmsg = CheckConstraints(varylist,constrDict,fixedList)
1159    if errmsg:
1160        print "*** Error ********************"
1161        print errmsg
1162    if warnmsg:
1163        print "*** Warning ********************"
1164        print warnmsg
1165    if errmsg or warnmsg:
1166        sys.exit()
1167    groups,parmlist = GroupConstraints(constrDict)
1168    GenerateConstraints(groups,parmlist,varylist,constrDict,fixedList)
1169    print VarRemapShow(varylist)
1170    parmdict.update( {
1171        '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,
1172        '0:0:eA': 0.0,
1173        '2::C(10,6,1)': 0.2, '1::C(10,6,1)': 0.3,
1174        '1::C(10,0,1)': 0.2, '2::C(10,0,1)': 0.3,
1175        '1::AUiso:0': 0.02, '0::AUiso:0': 0.03,
1176        '0::A0': 0.0,
1177        '2::atomx:3':0.23,'2::atomy:3':-.23, '2::atomz:3':-0.11,
1178        })
1179    print 'parmdict start',parmdict
1180    print 'varylist start',varylist
1181    before = parmdict.copy()
1182    Map2Dict(parmdict,varylist)
1183    print 'parmdict before and after Map2Dict'
1184    print '  key / before / after'
1185    for key in sorted(parmdict.keys()):
1186        print '  '+key,'\t',before.get(key),'\t',parmdict[key]
1187    print 'varylist after',varylist
1188    before = parmdict.copy()
1189    Dict2Map(parmdict,varylist)
1190    print 'after Dict2Map'
1191    print '  key / before / after'
1192    for key in sorted(parmdict.keys()):
1193        print '  '+key,'\t',before.get(key),'\t',parmdict[key]
1194#    dMdv = len(varylist)*[0]
1195#    deriv = {}
1196#    for i,v in enumerate(parmdict.keys()): deriv[v]=i
1197#    Dict2Deriv(varylist,deriv,dMdv)
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