source: trunk/GSASIImapvars.py @ 2546

Last change on this file since 2546 was 2546, checked in by vondreele, 5 years ago

cleanup of all GSASII main routines - remove unused variables, dead code, etc.

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1# -*- coding: utf-8 -*-
2########### SVN repository information ###################
3# $Date: 2016-11-22 19:08:48 +0000 (Tue, 22 Nov 2016) $
4# $Author: vondreele $
5# $Revision: 2546 $
6# $URL: trunk/GSASIImapvars.py $
7# $Id: GSASIImapvars.py 2546 2016-11-22 19:08:48Z 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 sys
213import GSASIIpath
214GSASIIpath.SetVersionNumber("$Revision: 2546 $")
215# data used for constraints;
216debug = False # turns on printing as constraint input is processed
217# note that constraints are stored listed by contraint groups, where each constraint
218# group contains those parameters that must be handled together
219dependentParmList = [] # contains a list of parameters in each group
220# note that parameters listed in dependentParmList should not be refined
221arrayList = [] # a list of of relationship matrices
222invarrayList = [] # a list of inverse relationship matrices
223indParmList = [] # a list of names for the new parameters
224fixedDict = {} # a dictionary containing the fixed values corresponding to defined parameter equations
225               # key is original ascii string, value is float
226fixedVarList = [] # List of variables that should not be refined
227
228# prefix for parameter names
229paramPrefix = "::constr"
230consNum = 0 # number of the next constraint to be created
231
232def InitVars():
233    '''Initializes all constraint information'''
234    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict,consNum
235    dependentParmList = [] # contains a list of parameters in each group
236    arrayList = [] # a list of of relationship matrices
237    invarrayList = [] # a list of inverse relationship matrices
238    indParmList = [] # a list of names for the new parameters
239    fixedDict = {} # a dictionary containing the fixed values corresponding to defined parameter equations
240    consNum = 0 # number of the next constraint to be created
241
242def VarKeys(constr):
243    """Finds the keys in a constraint that represent variables
244    e.g. eliminates any that start with '_'
245
246    :param dict constr: a single constraint entry of form::
247
248        {'var1': mult1, 'var2': mult2,... '_notVar': val,...}
249
250        (see :func:`GroupConstraints`)
251    :returns: a list of keys where any keys beginning with '_' are
252      removed.
253    """
254    return [i for i in constr.keys() if not i.startswith('_')]
255
256
257def GroupConstraints(constrDict):
258    """divide the constraints into groups that share no parameters.
259
260    :param dict constrDict: a list of dicts defining relationships/constraints
261
262    ::
263   
264       constrDict = [{<constr1>}, {<constr2>}, ...]
265
266    where {<constr1>} is {'var1': mult1, 'var2': mult2,... }
267
268    :returns: two lists of lists:
269   
270      * a list of grouped contraints where each constraint grouped containts a list
271        of indices for constraint constrDict entries
272      * a list containing lists of parameter names contained in each group
273     
274      """
275    assignedlist = [] # relationships that have been used
276    groups = [] # contains a list of grouplists
277    ParmList = []
278    for i,consi in enumerate(constrDict):
279        if i in assignedlist: continue # already in a group, skip
280        # starting a new group
281        grouplist = [i,]
282        assignedlist.append(i)
283        groupset = set(VarKeys(consi))
284        changes = True # always loop at least once
285        while(changes): # loop until we can't find anything to add to the current group
286            changes = False # but don't loop again unless we find something
287            for j,consj in enumerate(constrDict):
288                if j in assignedlist: continue # already in a group, skip
289                if len(set(VarKeys(consj)) & groupset) > 0: # true if this needs to be added
290                    changes = True
291                    grouplist.append(j)
292                    assignedlist.append(j)
293                    groupset = groupset | set(VarKeys(consj))
294        group = sorted(grouplist)
295        varlist = sorted(list(groupset))
296        groups.append(group)
297        ParmList.append(varlist)
298    return groups,ParmList
299
300def CheckConstraints(varyList,constrDict,fixedList):
301    '''Takes a list of relationship entries comprising a group of
302    constraints and checks for inconsistencies such as conflicts in
303    parameter/variable definitions and or inconsistently varied parameters.
304
305    :param list varyList: a list of parameters names that will be varied
306
307    :param dict constrDict: a list of dicts defining relationships/constraints
308      (as created in :func:`GSASIIstrIO.ProcessConstraints` and
309      documented in :func:`GroupConstraints`)
310
311    :param list fixedList: a list of values specifying a fixed value for each
312      dict in constrDict. Values are either strings that can be converted to
313      floats or ``None`` if the constraint defines a new parameter rather
314      than a constant.
315
316    :returns: two strings:
317
318      * the first lists conflicts internal to the specified constraints
319      * the second lists conflicts where the varyList specifies some
320        parameters in a constraint, but not all
321       
322      If there are no errors, both strings will be empty
323    '''
324    import re
325    global dependentParmList,arrayList,invarrayList,indParmList,consNum
326    errmsg = ''
327    warnmsg = ''
328    fixVlist = []
329    # process fixed variables (holds)
330    for cdict in constrDict:
331        # N.B. No "_" names in holds
332        if len(cdict) == 1:
333            fixVlist.append(cdict.keys()[0])
334   
335    # process equivalences: make a list of dependent and independent vars
336    #    and check for repeated uses (repetition of a parameter as an
337    #    independent var is OK)
338    indepVarList = []
339    depVarList = []
340    multdepVarList = []
341    for varlist,mapvars,multarr,invmultarr in zip(
342        dependentParmList,indParmList,arrayList,invarrayList):
343        if multarr is None: # an equivalence
344            zeromult = False
345            for mv in mapvars:
346                varied = 0
347                notvaried = ''
348                if mv in varyList:
349                    varied += 1
350                else:
351                    if notvaried: notvaried += ', '
352                    notvaried += mv
353                if mv not in indepVarList: indepVarList.append(mv)
354                for v,m in zip(varlist,invmultarr):
355                    if v in indepVarList:
356                        errmsg += '\nVariable '+v+' is used to set values in a constraint before its value is set in another constraint\n'
357                    if m == 0: zeromult = True
358                    if v in varyList:
359                        varied += 1
360                    else:
361                        if notvaried: notvaried += ', '
362                        notvaried += v
363                    if v in depVarList:
364                        multdepVarList.append(v)
365                    else:
366                        depVarList.append(v)
367            if varied > 0 and varied != len(varlist)+1:
368                warnmsg += "\nNot all variables refined in equivalence:\n\t"
369                s = ""
370                for v in varlist:
371                    if s != "": s+= " & "
372                    s += str(v)           
373                warnmsg += str(mv) + " => " + s
374                warnmsg += '\nNot refined: ' + notvaried + '\n'
375            if zeromult:
376                errmsg += "\nZero multiplier is invalid in equivalence:\n\t"
377                s = ""
378                for v in varlist:
379                    if s != "": s+= " & "
380                    s += str(v)           
381                errmsg += str(mv) + " => " + s + '\n'
382
383    # check for errors:
384    if len(multdepVarList) > 0:
385        errmsg += "\nThe following parameters(s) are used in conflicting Equivalence relations as dependent variables:\n"
386        s = ''
387        for var in sorted(set(multdepVarList)):
388            if s != "": s+= ", "
389            s += str(var)           
390        errmsg += '\t'+ s + '\n'
391    equivVarList = list(set(indepVarList).union(set(depVarList)))
392    if debug: print 'equivVarList',equivVarList
393    inboth = set(fixVlist).intersection(set(equivVarList))
394    if len(inboth) > 0:
395        errmsg += "\nThe following parameter(s) are used in both Equivalence and Fixed constraints:\n"
396        s = ''
397        for var in sorted(inboth):
398            if s != "": s+= ", "
399            s += str(var)
400        errmsg += '\t'+ s + '\n'
401
402    groups,parmlist = GroupConstraints(constrDict)
403    # scan through parameters in each relationship. Are all varied? If only some are
404    # varied, create a warning message.
405    for group,varlist in zip(groups,parmlist):
406        if len(varlist) == 1: continue
407        for rel in group:
408            varied = 0
409            notvaried = ''
410            for var in constrDict[rel]:
411                if var.startswith('_'): continue
412                if not re.match('[0-9]*:[0-9\*]*:',var):
413                    warnmsg += "\nVariable "+str(var)+" does not begin with a ':'"
414                if var in varyList:
415                    varied += 1
416                else:
417                    if notvaried: notvaried += ', '
418                    notvaried += var
419                if var in fixVlist:
420                    errmsg += '\nParameter '+var+" is Fixed and used in a constraint:\n\t"
421                    errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])+"\n"
422            if varied > 0 and varied != len(VarKeys(constrDict[rel])):
423                warnmsg += "\nNot all variables refined in constraint:\n\t"
424                warnmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
425                warnmsg += '\nNot refined: ' + notvaried + '\n'
426    if errmsg or warnmsg:
427        return errmsg,warnmsg
428
429    # now look for process each group and create the relations that are needed to form
430    # non-singular square matrix
431    for group,varlist in zip(groups,parmlist):
432        if len(varlist) == 1: continue # a constraint group with a single variable can be ignored
433        if len(varlist) < len(group): # too many relationships -- no can do
434            errmsg += "\nOver-constrained input. "
435            errmsg += "There are more constraints " + str(len(group))
436            errmsg += "\n\tthan variables " + str(len(varlist)) + "\n"
437            for rel in group:
438                errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
439                errmsg += "\n"
440                continue
441        try:
442            multarr = _FillArray(group,constrDict,varlist)
443            _RowEchelon(len(group),multarr,varlist)
444        except:
445            errmsg += "\nSingular input. "
446            errmsg += "There are internal inconsistencies in these constraints\n"
447            for rel in group:
448                errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
449                errmsg += "\n"
450            continue
451        try:
452            multarr = _FillArray(group,constrDict,varlist,FillDiagonals=True)
453            GramSchmidtOrtho(multarr,len(group))
454        except:
455            errmsg += "\nUnexpected singularity with constraints (in Gram-Schmidt)\n"
456            for rel in group:
457                errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
458                errmsg += "\n"
459            continue
460        mapvar = []
461        group = group[:]
462        # scan through all generated and input variables
463        # Check again for inconsistent variable use
464        # for new variables -- where varied and unvaried parameters get grouped
465        # together. I don't think this can happen when not flagged before, but
466        # it does not hurt to check again.
467        for i in range(len(varlist)):
468            varied = 0
469            notvaried = ''
470            if len(group) > 0:
471                rel = group.pop(0)
472                fixedval = fixedList[rel]
473                for var in VarKeys(constrDict[rel]):
474                    if var in varyList:
475                        varied += 1
476                    else:
477                        if notvaried: notvaried += ', '
478                        notvaried += var
479            else:
480                fixedval = None
481            if fixedval is None:
482                varname = paramPrefix + str(consNum) # assign a name to a variable
483                mapvar.append(varname)
484                consNum += 1
485            else:
486                mapvar.append(fixedval)
487            if varied > 0 and notvaried != '':
488                warnmsg += "\nNot all variables refined in generated constraint"
489                warnmsg += '\nPlease report this unexpected error\n'
490                for rel in group:
491                    warnmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
492                    warnmsg += "\n"
493                warnmsg += '\n\tNot refined: ' + notvaried + '\n'
494        try:
495            np.linalg.inv(multarr)           
496        except:
497            errmsg += "\nSingular input. "
498            errmsg += "The following constraints are not "
499            errmsg += "linearly independent\n\tor do not "
500            errmsg += "allow for generation of a non-singular set\n"
501            errmsg += 'Please report this unexpected error\n'
502            for rel in group:
503                errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
504                errmsg += "\n"
505    return errmsg,warnmsg
506
507def GenerateConstraints(groups,parmlist,varyList,constrDict,fixedList,parmDict=None,SeqHist=None):
508    '''Takes a list of relationship entries comprising a group of
509    constraints and builds the relationship lists and their inverse
510    and stores them in global variables Also checks for internal
511    conflicts or inconsistencies in parameter/variable definitions.
512
513    :param list groups: a list of grouped contraints where each constraint
514      grouped containts a list of indices for constraint constrDict entries,
515      created in :func:`GroupConstraints` (returned as 1st value)
516
517    :param list parmlist: a list containing lists of parameter names
518      contained in each group, created in :func:`GroupConstraints`
519      (returned as 2nd value)
520
521    :param list varyList: a list of parameters names (strings of form
522      ``<ph>:<hst>:<nam>``) that will be varied. Note that this is changed here.
523   
524    :param dict constrDict: a list of dicts defining relationships/constraints
525      (as defined in :func:`GroupConstraints`)
526
527    :param list fixedList: a list of values specifying a fixed value for each
528      dict in constrDict. Values are either strings that can be converted to
529      floats, float values or None if the constraint defines a new parameter.
530     
531    :param dict parmDict: a dict containing all parameters defined in current
532      refinement.
533
534    :param int SeqHist: number of current histogram, when used in a sequential
535      refinement. None (default) otherwise. Wildcard variable names are
536      set to the current histogram, when found if not None.
537    '''
538    global dependentParmList,arrayList,invarrayList,indParmList,consNum
539    msg = ''
540
541    # process fixed (held) variables
542    for cdict in constrDict:
543        if len(cdict) == 1:
544            fixedVarList.append(cdict.keys()[0])
545   
546    # process equivalences: make a list of dependent and independent vars
547    #    and check for repeated uses (repetition of a parameter as an
548    #    independent var is OK [A=B; A=C], but chaining: [A=B; B=C] is not good)
549    dropVarList = []
550    translateTable = {} # lookup table for wildcard referenced variables
551    for varlist,mapvars,multarr,invmultarr in zip(       # process equivalences
552        dependentParmList,indParmList,arrayList,invarrayList):
553        if multarr is None: # true only if an equivalence
554            zeromult = False
555            for mv in mapvars:
556                #s = ''
557                varied = 0
558                notvaried = ''
559                if mv in varyList:
560                    varied += 1
561                else:
562                    if notvaried: notvaried += ', '
563                    notvaried += mv
564                if parmDict is not None and mv not in parmDict:
565                    print "Dropping equivalence for variable "+str(mv)+". Not defined in this refinement"
566                    if mv not in dropVarList: dropVarList.append(mv)
567                    #msg += "\nCannot equivalence to variable "+str(mv)+". Not defined in this refinement"
568                    #continue
569            for v,m in zip(varlist,invmultarr):
570                if parmDict is not None and v not in parmDict:
571                    print "Dropping equivalence for dep. variable "+str(v)+". Not defined in this refinement"
572                    if v not in dropVarList: dropVarList.append(v)
573                    continue
574                if m == 0: zeromult = True
575                if v in varyList:
576                    varied += 1
577                else:
578                    if notvaried: notvaried += ', '
579                    notvaried += v
580            if varied > 0 and varied != len(varlist)+1:
581                msg += "\nNot all variables refined in equivalence:\n\t"
582                s = ""
583                for v in varlist:
584                    if s != "": s+= " & "
585                    s += str(v)           
586                msg += str(mv) + " => " + s
587                msg += '\nNot refined: ' + notvaried + '\n'
588            if zeromult:
589                msg += "\nZero multiplier is invalid in equivalence:\n\t"
590                s = ""
591                for v in varlist:
592                    if s != "": s+= " & "
593                    s += str(v)           
594                msg += str(mv) + " => " + s + '\n'
595
596    # scan through parameters in each relationship. Are all varied? If only some are
597    # varied, create an error message.
598    for group,varlist in zip(groups,parmlist):
599        if len(varlist) == 1: continue
600        for rel in group:
601            varied = 0
602            notvaried = ''
603            unused = 0
604            notused = ''
605            for var in constrDict[rel]:
606                if var.startswith('_'): continue
607                if var.split(':')[1] == '*' and SeqHist is not None:
608                    # convert wildcard var to reference current histogram; save translation in table
609                    sv = var.split(':')
610                    sv[1] = str(SeqHist)
611                    translateTable[var] = ':'.join(sv)
612                    var = translateTable[var]
613                if parmDict is not None and var not in parmDict:
614                    unused += 1
615                    if notvaried: notused += ', '
616                    notused += var
617                if var in varyList:
618                    varied += 1
619                else:
620                    if notvaried: notvaried += ', '
621                    notvaried += var
622                if var in fixedVarList:
623                    msg += '\nError: parameter '+var+" is Fixed and used in a constraint:\n\t"
624                    msg += _FormatConstraint(constrDict[rel],fixedList[rel])+"\n"
625            #if unused > 0:# and unused != len(VarKeys(constrDict[rel])):
626            if unused > 0 and unused != len(VarKeys(constrDict[rel])):
627                msg += "\nSome (but not all) variables in constraint are not defined:\n\t"
628                msg += _FormatConstraint(constrDict[rel],fixedList[rel])
629                msg += '\nNot used: ' + notused + '\n'
630            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    s2 = ''
819    s3 = ''
820    print >>pFile,130*'-'
821    print >>pFile,"Variables generated by constraints"
822    printlist.append(3*[None])
823    for name,val,esd in printlist:
824        if len(s1) > 120 or name is None:
825            print >>pFile,''
826            print >>pFile,s1
827            print >>pFile,s2
828            print >>pFile,s3
829            s1 = ''
830            if name is None: break
831        if s1 == "":
832            s1 = ' name  :'
833            s2 = ' value :'
834            s3 = ' sig   :'
835        s1 += '%15s' % (name)
836        s2 += '%15.4f' % (val)
837        if esd is None:
838            s3 += '%15s' % ('n/a')
839        else:   
840            s3 += '%15.4f' % (esd)
841
842def ComputeDepESD(covMatrix,varyList,parmDict):
843    '''Compute uncertainties for dependent parameters from independent ones
844    returns a dictionary containing the esd values for dependent parameters
845    '''
846    sigmaDict = {}
847    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
848        #if invmultarr is None: continue # probably not needed
849#        try:
850#            valuelist = [parmDict[var] for var in mapvars]
851#        except KeyError:
852#            continue
853        # get the v-covar matrix for independent parameters
854        vcov = np.zeros((len(mapvars),len(mapvars)))
855        for i1,name1 in enumerate(mapvars):
856            if name1 not in varyList: continue
857            iv1 = varyList.index(name1)
858            for i2,name2 in enumerate(mapvars):
859                if name2 not in varyList: continue
860                iv2 = varyList.index(name2)
861                vcov[i1][i2] = covMatrix[iv1][iv2]
862        # vec is the vector that multiplies each of the independent values
863        for v,vec in zip(varlist,invmultarr):
864            sigmaDict[v] = np.sqrt(np.inner(vec.T,np.inner(vcov,vec)))
865    return sigmaDict
866
867def _FormatConstraint(RelDict,RelVal):
868    '''Formats a Constraint or Function for use in a convenient way'''
869    linelen = 45
870    s = [""]
871    for var,val in RelDict.items():
872        if var.startswith('_'): continue
873        if len(s[-1]) > linelen: s.append(' ')
874        m = val
875        if s[-1] != "" and m >= 0:
876            s[-1] += ' + '
877        elif s[-1] != "":
878            s[-1] += ' - '
879            m = abs(m)
880        s[-1] += '%.3f*%s '%(m,var)
881    if len(s[-1]) > linelen: s.append(' ')
882    if RelVal is None:
883        s[-1] += ' = New variable'
884    else:
885        s[-1] += ' = ' + RelVal
886    s1 = ''
887    for s2 in s:
888        if s1 != '': s1 += '\n\t'
889        s1 += s2
890    return s1
891
892def VarRemapShow(varyList,inputOnly=False):
893    '''List out the saved relationships. This should be done after the constraints have been
894    defined using :func:`StoreEquivalence`, :func:`GroupConstraints` and :func:`GenerateConstraints`.
895
896    :returns: a string containing the details of the contraint relationships
897    '''
898    s = ''
899    if len(fixedVarList) > 0:
900        s += 'Fixed Variables:\n'
901        for v in fixedVarList:
902            s += '    ' + v + '\n'
903    s += 'Variable mapping relations:\n'
904    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
905    for varlist,mapvars,multarr,invmultarr in zip(
906        dependentParmList,indParmList,arrayList,invarrayList):
907        for i,mv in enumerate(mapvars):
908            if multarr is None:
909                s += '  ' + str(mv) + ' is equivalent to parameter(s): '
910                j = 0
911                for v,m in zip(varlist,invmultarr):
912                    if debug: print 'v,m[0]: ',v,m[0]
913                    if j > 0: s += '  & '
914                    j += 1
915                    s += str(v)
916                    if m != 1:
917                        s += " / " + str(m[0])                       
918                s += '\n'
919                continue
920            s += %s = ' % mv
921            j = 0
922            for m,v in zip(multarr[i,:],varlist):
923                if m == 0: continue
924                if j > 0: s += ' + '
925                j += 1
926                s += '(%s * %s)' % (m,v)
927            if mv in varyList: s += ' VARY'
928            s += '\n'
929    if inputOnly: return s
930    s += 'Inverse variable mapping relations:\n'
931    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
932        for i,mv in enumerate(varlist):
933            s += %s = ' % mv
934            j = 0
935            for m,v in zip(invmultarr[i,:],mapvars):
936                if m == 0: continue
937                if j > 0: s += ' + '
938                j += 1
939                s += '(%s * %s)' % (m,v)
940            s += '\n'
941    return s
942
943def Dict2Deriv(varyList,derivDict,dMdv):
944    '''Compute derivatives for Independent Parameters from the
945    derivatives for the original parameters
946
947    :param list varyList: a list of parameters names that will be varied
948
949    :param dict derivDict: a dict containing derivatives for parameter values keyed by the
950      parameter names.
951
952    :param list dMdv: a Jacobian, as a list of np.array containing derivatives for dependent
953      parameter computed from derivDict
954
955    '''
956    global dependentParmList,arrayList,invarrayList,indParmList,invarrayList
957    for varlist,mapvars,multarr,invmultarr in zip(dependentParmList,indParmList,arrayList,invarrayList):
958        for i,name in enumerate(mapvars):
959            # grouped variables: need to add in the derv. w/r
960            # dependent variables to the independent ones
961            if name not in varyList: continue # skip if independent var not varied
962            if multarr is None:
963                for v,m in zip(varlist,invmultarr):
964                    if debug: print 'start dMdv',dMdv[varyList.index(name)]
965                    if debug: print 'add derv',v,'/',m[0],'to derv',name,'add=',derivDict[v] / m[0]
966                    if m == 0: continue
967                    dMdv[varyList.index(name)] += derivDict[v] / m[0]
968            else:
969                for v,m in zip(varlist,multarr[i,:]):
970                    if debug: print 'start dMdv',dMdv[varyList.index(name)]
971                    if debug: print 'add derv',v,'*',m,'to derv',name,'add=',m * derivDict[v]
972                    if m == 0: continue
973                    dMdv[varyList.index(name)] += m * derivDict[v]
974
975def Map2Dict(parmDict,varyList):
976    '''Create (or update) the Independent Parameters from the original
977    set of Parameters
978
979    Removes dependent variables from the varyList
980
981    This should be done once, after the constraints have been
982    defined using :func:`StoreEquivalence`,
983    :func:`GroupConstraints` and :func:`GenerateConstraints` and
984    before any variable refinement is done. This completes the parameter
985    dictionary by defining independent parameters and it satisfies the
986    constraint equations in the initial parameters
987
988    :param dict parmDict: a dict containing parameter values keyed by the
989      parameter names.
990      This will contain updated values for both dependent and independent
991      parameters after Dict2Map is called. It will also contain some
992      unexpected entries of every constant value {'0':0.0} & {'1.0':1.0},
993      which do not cause any problems.
994
995    :param list varyList: a list of parameters names that will be varied
996   
997
998    '''
999    # process the Independent vars: remove dependent ones from varylist
1000    # and then compute values for the Independent ones from their dependents
1001    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
1002    for varlist,mapvars,multarr in zip(dependentParmList,indParmList,arrayList):
1003        for item in varlist:
1004            try:
1005                varyList.remove(item)
1006            except ValueError:
1007                pass
1008        if multarr is None: continue
1009        valuelist = [parmDict[var] for var in varlist]
1010        parmDict.update(zip(mapvars,
1011                            np.dot(multarr,np.array(valuelist)))
1012                        )
1013    # now remove fixed variables from the varyList
1014    global fixedVarList
1015    for item in fixedVarList:
1016        try:
1017            varyList.remove(item)
1018        except ValueError:
1019            pass
1020    # Set constrained parameters to their fixed values
1021    parmDict.update(fixedDict)
1022
1023def Dict2Map(parmDict,varyList):
1024    '''Applies the constraints defined using :func:`StoreEquivalence`,
1025    :func:`GroupConstraints` and :func:`GenerateConstraints` by changing
1026    values in a dict containing the parameters. This should be
1027    done before the parameters are used for any computations
1028
1029    :param dict parmDict: a dict containing parameter values keyed by the
1030      parameter names.
1031      This will contain updated values for both dependent and independent
1032      parameters after Dict2Map is called. It will also contain some
1033      unexpected entries of every constant value {'0':0.0} & {'1.0':1.0},
1034      which do not cause any problems.
1035
1036    :param list varyList: a list of parameters names that will be varied
1037   
1038    '''
1039    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
1040    # reset fixed values (should not be needed, but very quick)
1041    # - this seems to update parmDict with {'0':0.0} & {'1.0':1.0} - probably not what was intended
1042    # not needed, but also not a problem - BHT
1043    parmDict.update(fixedDict)
1044    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
1045        #if invmultarr is None: continue
1046        try: 
1047            valuelist = [parmDict[var] for var in mapvars]
1048        except KeyError:
1049            continue
1050        parmDict.update(zip(varlist,np.dot(invmultarr,np.array(valuelist))))
1051
1052#======================================================================
1053# internal routines follow (these routines are unlikely to be called
1054# from outside the module)
1055
1056def GramSchmidtOrtho(a,nkeep=0):
1057    '''Use the Gram-Schmidt process (http://en.wikipedia.org/wiki/Gram-Schmidt) to
1058    find orthonormal unit vectors relative to first row.
1059
1060    If nkeep is non-zero, the first nkeep rows in the array are not changed
1061   
1062    input:
1063       arrayin: a 2-D non-singular square array
1064    returns:
1065       a orthonormal set of unit vectors as a square array
1066    '''
1067    def proj(a,b):
1068        'Projection operator'
1069        return a*(np.dot(a,b)/np.dot(a,a))
1070    for j in range(nkeep,len(a)):
1071        for i in range(j):
1072            a[j] -= proj(a[i],a[j])
1073        if np.allclose(np.linalg.norm(a[j]),0.0):
1074            raise Exception,"Singular input to GramSchmidtOrtho"
1075        a[j] /= np.linalg.norm(a[j])
1076    return a
1077
1078def _FillArray(sel,dict,collist,FillDiagonals=False):
1079    '''Construct a n by n matrix (n = len(collist)
1080    filling in the rows using the relationships defined
1081    in the dictionaries selected by sel
1082
1083    If FillDiagonals is True, diagonal elements in the
1084    array are set to 1.0
1085    '''
1086    n = len(collist)
1087    if FillDiagonals:
1088        arr = np.eye(n)
1089    else:
1090        arr = np.zeros(2*[n,])
1091    # fill the top rows
1092    for i,cnum in enumerate(sel):
1093        for j,var in enumerate(collist):
1094            arr[i,j] = dict[cnum].get(var,0)
1095    return arr
1096
1097def _SwapColumns(i,m,v):
1098    '''Swap columns in matrix m as well as the labels in v
1099    so that element (i,i) is replaced by the first non-zero element in row i after that element
1100
1101    Throws an exception if there are no non-zero elements in that row
1102    '''
1103    for j in range(i+1,len(v)):
1104        if not np.allclose(m[i,j],0):
1105            m[:,(i,j)] = m[:,(j,i)]
1106            v[i],v[j] = v[j],v[i]
1107            return
1108    else:
1109        raise Exception,'Singular input'
1110
1111def _RowEchelon(m,arr,collist):
1112    '''Convert the first m rows in Matrix arr to row-echelon form
1113    exchanging columns in the matrix and collist as needed.
1114
1115    throws an exception if the matrix is singular because
1116    the first m rows are not linearly independent
1117    '''
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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