source: trunk/GSASIImapvars.py @ 1818

Last change on this file since 1818 was 1818, checked in by toby, 6 years ago

fix immediate constraint problem; need to double check on skipped constraints

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1# -*- coding: utf-8 -*-
2########### SVN repository information ###################
3# $Date: 2015-04-28 19:49:55 +0000 (Tue, 28 Apr 2015) $
4# $Author: toby $
5# $Revision: 1818 $
6# $URL: trunk/GSASIImapvars.py $
7# $Id: GSASIImapvars.py 1818 2015-04-28 19:49:55Z toby $
8########### SVN repository information ###################
9"""
10*GSASIImapvars: Parameter constraints*
11======================================
12
13Module to implements algebraic contraints, parameter redefinition
14and parameter simplification contraints.
15
16Parameter redefinition (new vars) is done by creating one or more relationships
17between a set of parameters
18
19::
20
21   Mx1 * Px + My1 * Py +...
22   Mx2 * Px + Mz2 * Pz + ...
23
24where Pj is a parameter name and Mjk is a constant.
25
26Constant constraint Relations can also be supplied in the form of an equation:
27
28::
29
30  nx1 * Px + ny1 * Py +... = C1
31
32where Cn is a constant. These equations define an algebraic
33constrant.
34
35Parameters can also be "fixed" (held), which prevents them from being refined.
36
37All of the above three cases are input using routines
38GroupConstraints and GenerateConstraints. The input consists of a list of
39relationship dictionaries:
40
41.. code-block:: python
42
43    constrDict = [
44         {'0:12:Scale': 2.0, '0:14:Scale': 4.0, '0:13:Scale': 3.0, '0:0:Scale': 0.5},
45         {'2::C(10,6,1)': 1.0, '1::C(10,6,1)': 1.0},
46         {'0::A0': 0.0}]
47    fixedList = ['5.0', None, '0']
48
49Where the dictionary defines the first part of an expression and the corresponding fixedList
50item is either None (for parameter redefinition) or the constant value, for a constant
51constraint equation. A dictionary that contains a single term defines a variable that
52will be fixed (held). The multiplier and the fixedList value in this case are ignored.
53
54Parameters can also be equivalenced or "slaved" to another parameter, such that one
55(independent) parameter is equated to several (now dependent) parameters. In
56algebraic form this is:
57
58::
59
60   P0 = M1 * P1 = M2 * P2 = ...
61
62Thus parameters P0, P1 and P2,... are linearly equivalent. Routine StoreEquivalence is
63used to specify these equivalences.
64
65Parameter redefinition (new vars) describes a new, independent, parameter, which
66is defined in terms of dependent parameters that are defined in the
67Model, while fixed constrained relations effectively reduce the complexity
68of the Model by removing a degree of freedom. It is possible for a parameter to appear
69in both a parameter redefinition expression and a fixed constraint equation, but a
70parameter cannot be used a parameter equivalance cannot be used elsewhere (not fixed,
71constrained or redefined). Likewise a fixed parameter cannot be used elsewhere (not
72equivalanced, constrained or redefined).
73
74Relationships are grouped so that a set of dependent parameters appear
75in only one group (done in routine GroupConstraints.) Note that if a
76group contains relationships/equations that involve N dependent
77parameters, there must exist N-C new parameters, where C is the number
78of contraint equations in the group. Routine GenerateConstraints takes
79the output from GroupConstraints and generates the
80"missing" relationships and saves that information in the module's
81global variables. Each generated parameter is named sequentially using paramPrefix.
82
83A list of parameters that will be varied is specified as input to GenerateConstraints
84(varyList). A fixed parameter will simply be removed from this list preventing that
85parameter from being varied. Note that all parameters in a constraint relationship
86must specified as varied (appear in varyList) or none can be varied. This is
87checked in GenerateConstraints. Likewise, if all parameters in a constraint are
88not referenced in a refinement, the constraint is ignored, but if some parameters
89in a constraint group are not referenced in a refinement, but others are this
90constitutes and error.
91
92* When a new variable is created, the variable is assigned the name associated
93  in the constraint definition or it is assigned a default name of form
94  ``::constr<n>`` (see paramPrefix). The vary setting for variables used in the
95  constraint are ignored.
96  Note that any generated "missing" relations are not varied. Only
97  the input relations can be are varied.
98 
99* If all parameters in a fixed constraint equation are varied, the generated "missing"
100  relations in the group are all varied. This provides the N-C degrees of freedom.
101
102*External Routines*
103-------------------
104
105To define a set of constrained and unconstrained relations, one
106defines a list of dictionary defining constraint parameters and their
107values, a list of fixed values for each constraint and a list of
108parameters to be varied. In addition, one uses
109:func:`StoreEquivalence` to define parameters that are equivalent. One
110can then use :func:`CheckConstraints` to check that the input is
111internally consistent and finally :func:`GroupConstraints` and
112:func:`GenerateConstraints` to generate the internally used
113tables. Routines :func:`Map2Dict` is used to initialize the parameter
114dictionary and :func:`Dict2Map`, :func:`Dict2Deriv`, and
115:func:`ComputeDepESD` are used to apply constraints. Routine
116:func:`VarRemapShow` is used to print out the constraint information,
117as stored by :func:`GenerateConstraints`.
118
119:func:`InitVars`
120  This is optionally used to clear out all defined previously defined constraint information
121 
122:func:`StoreEquivalence`
123  To implement parameter redefinition, one calls StoreEquivalence. This should be called for every set of
124  equivalence relationships. There is no harm in using StoreEquivalence with the same independent variable:
125
126  .. code-block:: python
127
128       StoreEquivalence('x',('y',))
129       StoreEquivalence('x',('z',))
130
131  or equivalently
132
133  .. code-block:: python
134
135       StoreEquivalence('x',('y','z'))
136
137  The latter will run more efficiently. Note that mixing independent and dependent variables is
138  problematic. This is not allowed:
139
140  .. code-block:: python
141
142        StoreEquivalence('x',('y',))
143        StoreEquivalence('y',('z',))
144       
145  Use StoreEquivalence before calling GenerateConstraints or CheckConstraints
146
147:func:`CheckConstraints`
148   To check that input in internally consistent, use CheckConstraints
149
150:func:`Map2Dict`
151   To determine values for the parameters created in this module, one
152   calls Map2Dict. This will not apply contraints.
153
154:func:`Dict2Map`
155   To take values from the new independent parameters and constraints,
156   one calls Dict2Map. This will apply contraints.
157
158:func:`Dict2Deriv`
159   Use Dict2Deriv to determine derivatives on independent parameters
160   from those on dependent ones
161
162:func:`ComputeDepESD`     
163   Use ComputeDepESD to compute uncertainties on dependent variables
164
165:func:`VarRemapShow`
166   To show a summary of the parameter remapping, one calls VarRemapShow
167
168*Global Variables*
169------------------
170
171dependentParmList:
172   contains a list by group of lists of
173   parameters used in the group. Note that parameters listed in
174   dependentParmList should not be refined as they will not affect
175   the model
176
177indParmList:
178     a list of groups of Independent parameters defined in
179     each group. This contains both parameters used in parameter
180     redefinitions as well as names of generated new parameters.
181
182fixedVarList:
183     a list of variables that have been 'fixed'
184     by defining them as equal to a constant (::var: = 0). Note that
185     the constant value is ignored at present. These variables are
186     later removed from varyList which prevents them from being refined.
187     Unlikely to be used externally.
188
189arrayList:
190     a list by group of relationship matrices to relate
191     parameters in dependentParmList to those in indParmList. Unlikely
192     to be used externally.
193
194invarrayList:
195     a list by group of relationship matrices to relate
196     parameters in indParmList to those in dependentParmList. Unlikely
197     to be used externally.
198
199fixedDict:
200     a dictionary containing the fixed values corresponding
201     to parameter equations.  The dict key is an ascii string, but the
202     dict value is a float.  Unlikely to be used externally.
203
204*Routines*
205----------
206
207Note that parameter names in GSAS-II are strings of form ``<ph>:<hst>:<nam>``
208
209"""
210
211import numpy as np
212import GSASIIpath
213GSASIIpath.SetVersionNumber("$Revision: 1818 $")
214# data used for constraints;
215debug = False # turns on printing as constraint input is processed
216# note that constraints are stored listed by contraint groups, where each constraint
217# group contains those parameters that must be handled together
218dependentParmList = [] # contains a list of parameters in each group
219# note that parameters listed in dependentParmList should not be refined
220arrayList = [] # a list of of relationship matrices
221invarrayList = [] # a list of inverse relationship matrices
222indParmList = [] # a list of names for the new parameters
223fixedDict = {} # a dictionary containing the fixed values corresponding to defined parameter equations
224               # key is original ascii string, value is float
225fixedVarList = [] # List of variables that should not be refined
226
227# prefix for parameter names
228paramPrefix = "::constr"
229consNum = 0 # number of the next constraint to be created
230
231def InitVars():
232    '''Initializes all constraint information'''
233    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict,consNum
234    dependentParmList = [] # contains a list of parameters in each group
235    arrayList = [] # a list of of relationship matrices
236    invarrayList = [] # a list of inverse relationship matrices
237    indParmList = [] # a list of names for the new parameters
238    fixedDict = {} # a dictionary containing the fixed values corresponding to defined parameter equations
239    consNum = 0 # number of the next constraint to be created
240    fixedVarList = []
241
242def VarKeys(constr):
243    """Finds the keys in a constraint that represent variables
244    e.g. eliminates any that start with '_'
245
246    :param dict constr: a single constraint entry of form::
247
248        {'var1': mult1, 'var2': mult2,... '_notVar': val,...}
249
250        (see :func:`GroupConstraints`)
251    :returns: a list of keys where any keys beginning with '_' are
252      removed.
253    """
254    return [i for i in constr.keys() if not i.startswith('_')]
255
256
257def GroupConstraints(constrDict):
258    """divide the constraints into groups that share no parameters.
259
260    :param dict constrDict: a list of dicts defining relationships/constraints
261
262    ::
263   
264       constrDict = [{<constr1>}, {<constr2>}, ...]
265
266    where {<constr1>} is {'var1': mult1, 'var2': mult2,... }
267
268    :returns: two lists of lists:
269   
270      * a list of grouped contraints where each constraint grouped containts a list
271        of indices for constraint constrDict entries
272      * a list containing lists of parameter names contained in each group
273     
274      """
275    assignedlist = [] # relationships that have been used
276    groups = [] # contains a list of grouplists
277    ParmList = []
278    for i,consi in enumerate(constrDict):
279        if i in assignedlist: continue # already in a group, skip
280        # starting a new group
281        grouplist = [i,]
282        assignedlist.append(i)
283        groupset = set(VarKeys(consi))
284        changes = True # always loop at least once
285        while(changes): # loop until we can't find anything to add to the current group
286            changes = False # but don't loop again unless we find something
287            for j,consj in enumerate(constrDict):
288                if j in assignedlist: continue # already in a group, skip
289                if len(set(VarKeys(consj)) & groupset) > 0: # true if this needs to be added
290                    changes = True
291                    grouplist.append(j)
292                    assignedlist.append(j)
293                    groupset = groupset | set(VarKeys(consj))
294        group = sorted(grouplist)
295        varlist = sorted(list(groupset))
296        groups.append(group)
297        ParmList.append(varlist)
298    return groups,ParmList
299
300def CheckConstraints(varyList,constrDict,fixedList):
301    '''Takes a list of relationship entries comprising a group of
302    constraints and checks for inconsistencies such as conflicts in
303    parameter/variable definitions and or inconsistently varied parameters.
304
305    :param list varyList: a list of parameters names that will be varied
306
307    :param dict constrDict: a list of dicts defining relationships/constraints
308      (as created in :func:`GSASIIstrIO.ProcessConstraints` and
309      documented in :func:`GroupConstraints`)
310
311    :param list fixedList: a list of values specifying a fixed value for each
312      dict in constrDict. Values are either strings that can be converted to
313      floats or ``None`` if the constraint defines a new parameter rather
314      than a constant.
315
316    :returns: two strings:
317
318      * the first lists conflicts internal to the specified constraints
319      * the second lists conflicts where the varyList specifies some
320        parameters in a constraint, but not all
321       
322      If there are no errors, both strings will be empty
323    '''
324    import re
325    global dependentParmList,arrayList,invarrayList,indParmList,consNum
326    errmsg = ''
327    warnmsg = ''
328    fixVlist = []
329    # process fixed variables (holds)
330    for cdict in constrDict:
331        # N.B. No "_" names in holds
332        if len(cdict) == 1:
333            fixVlist.append(cdict.keys()[0])
334   
335    # process equivalences: make a list of dependent and independent vars
336    #    and check for repeated uses (repetition of a parameter as an
337    #    independent var is OK)
338    indepVarList = []
339    depVarList = []
340    multdepVarList = []
341    for varlist,mapvars,multarr,invmultarr in zip(
342        dependentParmList,indParmList,arrayList,invarrayList):
343        if multarr is None: # an equivalence
344            zeromult = False
345            for mv in mapvars:
346                varied = 0
347                notvaried = ''
348                if mv in varyList:
349                    varied += 1
350                else:
351                    if notvaried: notvaried += ', '
352                    notvaried += mv
353                if mv not in indepVarList: indepVarList.append(mv)
354                for v,m in zip(varlist,invmultarr):
355                    if v in indepVarList:
356                        errmsg += '\nVariable '+v+' is used to set values in a constraint before its value is set in another constraint\n'
357                    if m == 0: zeromult = True
358                    if v in varyList:
359                        varied += 1
360                    else:
361                        if notvaried: notvaried += ', '
362                        notvaried += v
363                    if v in depVarList:
364                        multdepVarList.append(v)
365                    else:
366                        depVarList.append(v)
367            if varied > 0 and varied != len(varlist)+1:
368                warnmsg += "\nNot all variables refined in equivalence:\n\t"
369                s = ""
370                for v in varlist:
371                    if s != "": s+= " & "
372                    s += str(v)           
373                warnmsg += str(mv) + " => " + s
374                warnmsg += '\nNot refined: ' + notvaried + '\n'
375            if zeromult:
376                errmsg += "\nZero multiplier is invalid in equivalence:\n\t"
377                s = ""
378                for v in varlist:
379                    if s != "": s+= " & "
380                    s += str(v)           
381                errmsg += str(mv) + " => " + s + '\n'
382
383    # check for errors:
384    if len(multdepVarList) > 0:
385        errmsg += "\nThe following parameters(s) are used in conflicting Equivalence relations as dependent variables:\n"
386        s = ''
387        for var in sorted(set(multdepVarList)):
388            if s != "": s+= ", "
389            s += str(var)           
390        errmsg += '\t'+ s + '\n'
391    equivVarList = list(set(indepVarList).union(set(depVarList)))
392    if debug: print 'equivVarList',equivVarList
393    inboth = set(fixVlist).intersection(set(equivVarList))
394    if len(inboth) > 0:
395        errmsg += "\nThe following parameter(s) are used in both Equivalence and Fixed constraints:\n"
396        s = ''
397        for var in sorted(inboth):
398            if s != "": s+= ", "
399            s += str(var)
400        errmsg += '\t'+ s + '\n'
401
402    groups,parmlist = GroupConstraints(constrDict)
403    # scan through parameters in each relationship. Are all varied? If only some are
404    # varied, create a warning message.
405    for group,varlist in zip(groups,parmlist):
406        if len(varlist) == 1: continue
407        for rel in group:
408            varied = 0
409            notvaried = ''
410            for var in constrDict[rel]:
411                if var.startswith('_'): continue
412                if not re.match('[0-9]*:[0-9\*]*:',var):
413                    warnmsg += "\nVariable "+str(var)+" does not begin with a ':'"
414                if var in varyList:
415                    varied += 1
416                else:
417                    if notvaried: notvaried += ', '
418                    notvaried += var
419                if var in fixVlist:
420                    errmsg += '\nParameter '+var+" is Fixed and used in a constraint:\n\t"
421                    errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])+"\n"
422            if varied > 0 and varied != len(VarKeys(constrDict[rel])):
423                warnmsg += "\nNot all variables refined in constraint:\n\t"
424                warnmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
425                warnmsg += '\nNot refined: ' + notvaried + '\n'
426    if errmsg or warnmsg:
427        return errmsg,warnmsg
428
429    # now look for process each group and create the relations that are needed to form
430    # non-singular square matrix
431    for group,varlist in zip(groups,parmlist):
432        if len(varlist) == 1: continue # a constraint group with a single variable can be ignored
433        if len(varlist) < len(group): # too many relationships -- no can do
434            errmsg += "\nOver-constrained input. "
435            errmsg += "There are more constraints " + str(len(group))
436            errmsg += "\n\tthan variables " + str(len(varlist)) + "\n"
437            for rel in group:
438                errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
439                errmsg += "\n"
440                continue
441        try:
442            multarr = _FillArray(group,constrDict,varlist)
443            _RowEchelon(len(group),multarr,varlist)
444        except:
445            errmsg += "\nSingular input. "
446            errmsg += "There are internal inconsistencies in these constraints\n"
447            for rel in group:
448                errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
449                errmsg += "\n"
450            continue
451        try:
452            multarr = _FillArray(group,constrDict,varlist,FillDiagonals=True)
453            GramSchmidtOrtho(multarr,len(group))
454        except:
455            errmsg += "\nUnexpected singularity with constraints (in Gram-Schmidt)\n"
456            for rel in group:
457                errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
458                errmsg += "\n"
459            continue
460        mapvar = []
461        group = group[:]
462        # scan through all generated and input variables
463        # Check again for inconsistent variable use
464        # for new variables -- where varied and unvaried parameters get grouped
465        # together. I don't think this can happen when not flagged before, but
466        # it does not hurt to check again.
467        for i in range(len(varlist)):
468            varied = 0
469            notvaried = ''
470            if len(group) > 0:
471                rel = group.pop(0)
472                fixedval = fixedList[rel]
473                for var in VarKeys(constrDict[rel]):
474                    if var in varyList:
475                        varied += 1
476                    else:
477                        if notvaried: notvaried += ', '
478                        notvaried += var
479            else:
480                fixedval = None
481            if fixedval is None:
482                varname = paramPrefix + str(consNum) # assign a name to a variable
483                mapvar.append(varname)
484                consNum += 1
485            else:
486                mapvar.append(fixedval)
487            if varied > 0 and notvaried != '':
488                warnmsg += "\nNot all variables refined in generated constraint"
489                warnmsg += '\nPlease report this unexpected error\n'
490                for rel in group:
491                    warnmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
492                    warnmsg += "\n"
493                warnmsg += '\n\tNot refined: ' + notvaried + '\n'
494        try:
495            np.linalg.inv(multarr)           
496        except:
497            errmsg += "\nSingular input. "
498            errmsg += "The following constraints are not "
499            errmsg += "linearly independent\n\tor do not "
500            errmsg += "allow for generation of a non-singular set\n"
501            errmsg += 'Please report this unexpected error\n'
502            for rel in group:
503                errmsg += _FormatConstraint(constrDict[rel],fixedList[rel])
504                errmsg += "\n"
505    return errmsg,warnmsg
506
507def GenerateConstraints(groups,parmlist,varyList,constrDict,fixedList,parmDict=None,SeqHist=None):
508    '''Takes a list of relationship entries comprising a group of
509    constraints and builds the relationship lists and their inverse
510    and stores them in global variables Also checks for internal
511    conflicts or inconsistencies in parameter/variable definitions.
512
513    :param list groups: a list of grouped contraints where each constraint
514      grouped containts a list of indices for constraint constrDict entries,
515      created in :func:`GroupConstraints` (returned as 1st value)
516
517    :param list parmlist: a list containing lists of parameter names
518      contained in each group, created in :func:`GroupConstraints`
519      (returned as 2nd value)
520
521    :param list varyList: a list of parameters names (strings of form
522      ``<ph>:<hst>:<nam>``) that will be varied. Note that this is changed here.
523   
524    :param dict constrDict: a list of dicts defining relationships/constraints
525      (as defined in :func:`GroupConstraints`)
526
527    :param list fixedList: a list of values specifying a fixed value for each
528      dict in constrDict. Values are either strings that can be converted to
529      floats, float values or None if the constraint defines a new parameter.
530     
531    :param dict parmDict: a dict containing all parameters defined in current
532      refinement.
533
534    :param int SeqHist: number of current histogram, when used in a sequential
535      refinement. None (default) otherwise. Wildcard variable names are
536      set to the current histogram, when found if not None.
537    '''
538    global dependentParmList,arrayList,invarrayList,indParmList,consNum
539    msg = ''
540
541    # process fixed (held) variables
542    for cdict in constrDict:
543        if len(cdict) == 1:
544            fixedVarList.append(cdict.keys()[0])
545   
546    # process equivalences: make a list of dependent and independent vars
547    #    and check for repeated uses (repetition of a parameter as an
548    #    independent var is OK [A=B; A=C], but chaining: [A=B; B=C] is not good)
549    indepVarList = []
550    depVarList = []
551    multdepVarList = []
552    translateTable = {} # lookup table for wildcard referenced variables
553    for varlist,mapvars,multarr,invmultarr in zip(       # process equivalences
554        dependentParmList,indParmList,arrayList,invarrayList):
555        if multarr is None: # true only if an equivalence
556            zeromult = False
557            for mv in mapvars:
558                #s = ''
559                varied = 0
560                notvaried = ''
561                if mv in varyList:
562                    varied += 1
563                else:
564                    if notvaried: notvaried += ', '
565                    notvaried += mv
566                if parmDict is not None and mv not in parmDict:
567                    print "Dropping equivalence for variable "+str(mv)+". Not defined in this refinement"
568                    #msg += "\nCannot equivalence to variable "+str(mv)+". Not defined in this refinement"
569                    #continue
570                else: 
571                    if mv not in indepVarList: indepVarList.append(mv)
572                for v,m in zip(varlist,invmultarr):
573                    if parmDict is not None and v not in parmDict:
574                        print "Dropping equivalence for dep. variable "+str(v)+". Not defined in this refinement"
575                        continue
576                    if m == 0: zeromult = True
577                    if v in varyList:
578                        varied += 1
579                    else:
580                        if notvaried: notvaried += ', '
581                        notvaried += v
582                    if v in depVarList:
583                        multdepVarList.append(v)
584                    else:
585                        depVarList.append(v)
586            if varied > 0 and varied != len(varlist)+1:
587                msg += "\nNot all variables refined in equivalence:\n\t"
588                s = ""
589                for v in varlist:
590                    if s != "": s+= " & "
591                    s += str(v)           
592                msg += str(mv) + " => " + s
593                msg += '\nNot refined: ' + notvaried + '\n'
594            if zeromult:
595                msg += "\nZero multiplier is invalid in equivalence:\n\t"
596                s = ""
597                for v in varlist:
598                    if s != "": s+= " & "
599                    s += str(v)           
600                msg += str(mv) + " => " + s + '\n'
601    # save the lists of dep. and indep. vars (after dropping unused)
602    global independentVars
603    independentVars = indepVarList
604    #print 'independentVars=',independentVars
605    equivVarList = list(set(indepVarList).union(set(depVarList)))
606
607    # scan through parameters in each relationship. Are all varied? If only some are
608    # varied, create an error message.
609    for group,varlist in zip(groups,parmlist):
610        if len(varlist) == 1: continue
611        for rel in group:
612            varied = 0
613            notvaried = ''
614            unused = 0
615            notused = ''
616            for var in constrDict[rel]:
617                if var.startswith('_'): continue
618                if var.split(':')[1] == '*' and SeqHist is not None:
619                    # convert wildcard var to reference current histogram; save translation in table
620                    sv = var.split(':')
621                    sv[1] = str(SeqHist)
622                    translateTable[var] = ':'.join(sv)
623                    var = translateTable[var]
624                if parmDict is not None and var not in parmDict:
625                    unused += 1
626                    if notvaried: notused += ', '
627                    notused += var
628                if var in varyList:
629                    varied += 1
630                else:
631                    if notvaried: notvaried += ', '
632                    notvaried += var
633                if var in fixedVarList:
634                    msg += '\nError: parameter '+var+" is Fixed and used in a constraint:\n\t"
635                    msg += _FormatConstraint(constrDict[rel],fixedList[rel])+"\n"
636            #if unused > 0:# and unused != len(VarKeys(constrDict[rel])):
637            if unused > 0 and unused != len(VarKeys(constrDict[rel])):
638                msg += "\nSome (but not all) variables in constraint are not defined:\n\t"
639                msg += _FormatConstraint(constrDict[rel],fixedList[rel])
640                msg += '\nNot used: ' + notused + '\n'
641            if varied > 0 and varied != len(VarKeys(constrDict[rel])):
642                msg += "\nNot all variables refined in constraint:\n\t"
643                msg += _FormatConstraint(constrDict[rel],fixedList[rel])
644                msg += '\nNot refined: ' + notvaried + '\n'
645    # if there were errors found, go no farther
646    if msg:
647        print ' *** ERROR in constraint definitions! ***'
648        print msg
649        raise Exception
650               
651    # now process each group and create the relations that are needed to form
652    # a non-singular square matrix
653    # If all are varied and this is a constraint equation, then set VaryFree flag
654    # so that the newly created relationships will be varied
655    for group,varlist in zip(groups,parmlist):
656        if len(varlist) == 1: continue
657        # for constraints, if all included variables are refined,
658        # set the VaryFree flag, and remaining degrees of freedom will be
659        # varied (since consistency was checked, if any one variable is
660        # refined, then assume that all are)
661        varsList = [] # make a list of all the referenced variables as well
662        VaryFree = False
663        for rel in group:
664            varied = 0
665            unused = 0
666            for var in VarKeys(constrDict[rel]):
667                var = translateTable.get(var,var) # replace wildcards
668                if parmDict is not None and var not in parmDict:
669                    unused += 1                   
670                if var not in varsList: varsList.append(var)
671                if var in varyList: varied += 1
672            if fixedList[rel] is not None and varied > 0:
673                VaryFree = True
674        if len(varlist) < len(group): # too many relationships -- no can do
675            msg = 'too many relationships'
676            break
677        # Since we checked before, if any variables are unused, then all must be.
678        # If so, this set of relationships can be ignored
679        if unused:
680            if debug: print('Constraint ignored (all variables undefined)')
681            if debug: print ('    '+_FormatConstraint(constrDict[rel],fixedList[rel]))
682            continue
683        # fill in additional degrees of freedom
684        try:
685            arr = _FillArray(group,constrDict,varlist)
686            _RowEchelon(len(group),arr,varlist)
687            constrArr = _FillArray(group,constrDict,varlist,FillDiagonals=True)
688            GramSchmidtOrtho(constrArr,len(group))
689        except:
690            msg = 'Singular relationships'
691            break
692        mapvar = []
693        group = group[:]
694        # scan through all generated and input relationships, we need to add to the varied list
695        # all the new parameters where VaryFree has been set or where a New Var is varied.
696        #
697        # If a group does not contain any fixed values (constraint equations)
698        # and nothing in the group is varied, drop this group, so that the
699        # dependent parameters can be refined individually.
700        unused = True
701        for i in range(len(varlist)):
702            if len(group) > 0: # get the original equation reference
703                rel = group.pop(0)
704                fixedval = fixedList[rel]
705                varyflag = constrDict[rel].get('_vary',False)
706                varname = constrDict[rel].get('_name','')
707            else: # this relationship has been generated
708                varyflag = False
709                varname = ''
710                fixedval = None
711            if fixedval is None: # this is a new variable, not a constraint
712                if not varname:
713                    varname = paramPrefix + str(consNum) # no assigned name, create one
714                    consNum += 1
715                mapvar.append(varname)
716                # vary the new relationship if it is a degree of freedom in
717                # a set of contraint equations or if a New Var is flagged to be varied.
718                if VaryFree or varyflag: 
719                    unused = False
720                    varyList.append(varname)
721                    # fix (prevent varying) of all the variables inside the constraint group
722                    # (dependent vars)
723                    for var in varsList:
724                        if var in varyList: varyList.remove(var)
725            else:
726                unused = False
727                mapvar.append(fixedval)
728        if unused: # skip over constraints that don't matter (w/o fixed value or any refined variables)
729            if debug: print('Constraint ignored (all variables unrefined)')
730            if debug: print ('   '+_FormatConstraint(constrDict[rel],fixedList[rel]))
731            continue 
732        dependentParmList.append([translateTable.get(var,var) for var in varlist])
733        arrayList.append(constrArr)
734        invarrayList.append(np.linalg.inv(constrArr))
735        indParmList.append(mapvar)
736    if msg:
737        print ' *** ERROR in constraint definitions! ***'
738        print msg
739        print VarRemapShow(varyList)
740        raise Exception
741    # setup dictionary containing the fixed values
742    global fixedDict
743    # key is original ascii string, value is float
744    for fixedval in fixedList:
745        if fixedval:
746            fixedDict[fixedval] = float(fixedval)
747
748    # make list of dependent variables
749    global dependentVars
750    depVarList = []
751    for varlist,mapvars,invmultarr in zip(       # process equivalences
752        dependentParmList,indParmList,invarrayList):
753        for i,mv in enumerate(varlist):
754            if mv not in depVarList: depVarList.append(mv)
755    dependentVars = depVarList
756    if debug: # on debug, show what is parsed & generated, semi-readable
757        print 50*'-'
758        print VarRemapShow(varyList)
759        print 'Varied: ',varyList
760        print 'Not Varied: ',fixedVarList
761
762def StoreEquivalence(independentVar,dependentList):
763    '''Takes a list of dependent parameter(s) and stores their
764    relationship to a single independent parameter (independentVar)
765
766    :param str independentVar: name of master parameter that will be used to determine the value
767      to set the dependent variables
768
769    :param list dependentList: a list of parameters that will set from
770         independentVar. Each item in the list can be a string with the parameter
771         name or a tuple containing a name and multiplier:
772         ``['parm1',('parm2',.5),]``
773
774    '''
775   
776    global dependentParmList,arrayList,invarrayList,indParmList
777    mapList = []
778    multlist = []
779    for var in dependentList:
780        if isinstance(var, basestring):
781            mult = 1.0
782        elif len(var) == 2:
783            var,mult = var
784        else:
785            raise Exception("Cannot parse "+repr(var) + " as var or (var,multiplier)")
786        mapList.append(var)
787        multlist.append(tuple((mult,)))
788    # added relationships to stored values
789    arrayList.append(None)
790    invarrayList.append(np.array(multlist))
791    indParmList.append(tuple((independentVar,)))
792    dependentParmList.append(mapList)
793    return
794
795def GetDependentVars():
796    '''Return a list of dependent variables: e.g. variables that are
797    constrained in terms of other variables
798
799    :returns: a list of variable names
800
801    '''
802    return dependentVars
803
804def GetIndependentVars():
805    '''Return a list of independent variables: e.g. variables that are
806    created by constraints of other variables
807
808    :returns: a list of variable names
809
810    '''
811    return independentVars
812
813def PrintIndependentVars(parmDict,varyList,sigDict,PrintAll=False,pFile=None):
814    '''Print the values and uncertainties on the independent variables'''
815    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
816    printlist = []
817    mapvars = GetIndependentVars()
818    for i,name in enumerate(mapvars):
819        if name in fixedDict: continue
820        if PrintAll or name in varyList:
821            sig = sigDict.get(name)
822            printlist.append([name,parmDict[name],sig])
823    if len(printlist) == 0: return
824    s1 = ''
825    print >>pFile,130*'-'
826    print >>pFile,"Variables generated by constraints"
827    printlist.append(3*[None])
828    for name,val,esd in printlist:
829        if len(s1) > 120 or name is None:
830            print >>pFile,''
831            print >>pFile,s1
832            print >>pFile,s2
833            print >>pFile,s3
834            s1 = ''
835            if name is None: break
836        if s1 == "":
837            s1 = ' name  :'
838            s2 = ' value :'
839            s3 = ' sig   :'
840        s1 += '%15s' % (name)
841        s2 += '%15.4f' % (val)
842        if esd is None:
843            s3 += '%15s' % ('n/a')
844        else:   
845            s3 += '%15.4f' % (esd)
846
847def ComputeDepESD(covMatrix,varyList,parmDict):
848    '''Compute uncertainties for dependent parameters from independent ones
849    returns a dictionary containing the esd values for dependent parameters
850    '''
851    sigmaDict = {}
852    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
853        #if invmultarr is None: continue # probably not needed
854        try: 
855            valuelist = [parmDict[var] for var in mapvars]
856        except KeyError:
857            continue
858        # get the v-covar matrix for independent parameters
859        vcov = np.zeros((len(mapvars),len(mapvars)))
860        for i1,name1 in enumerate(mapvars):
861            if name1 not in varyList: continue
862            iv1 = varyList.index(name1)
863            for i2,name2 in enumerate(mapvars):
864                if name2 not in varyList: continue
865                iv2 = varyList.index(name2)
866                vcov[i1][i2] = covMatrix[iv1][iv2]
867        # vec is the vector that multiplies each of the independent values
868        for v,vec in zip(varlist,invmultarr):
869            sigmaDict[v] = np.sqrt(np.inner(vec.T,np.inner(vcov,vec)))
870    return sigmaDict
871
872def _FormatConstraint(RelDict,RelVal):
873    '''Formats a Constraint or Function for use in a convenient way'''
874    linelen = 45
875    s = [""]
876    for var,val in RelDict.items():
877        if var.startswith('_'): continue
878        if len(s[-1]) > linelen: s.append(' ')
879        m = val
880        if s[-1] != "" and m >= 0:
881            s[-1] += ' + '
882        elif s[-1] != "":
883            s[-1] += ' - '
884            m = abs(m)
885        s[-1] += '%.3f*%s '%(m,var)
886    if len(s[-1]) > linelen: s.append(' ')
887    if RelVal is None:
888        s[-1] += ' = New variable'
889    else:
890        s[-1] += ' = ' + RelVal
891    s1 = ''
892    for s2 in s:
893        if s1 != '': s1 += '\n\t'
894        s1 += s2
895    return s1
896
897def VarRemapShow(varyList,inputOnly=False):
898    '''List out the saved relationships. This should be done after the constraints have been
899    defined using :func:`StoreEquivalence`, :func:`GroupConstraints` and :func:`GenerateConstraints`.
900
901    :returns: a string containing the details of the contraint relationships
902    '''
903    s = ''
904    if len(fixedVarList) > 0:
905        s += 'Fixed Variables:\n'
906        for v in fixedVarList:
907            s += '    ' + v + '\n'
908    s += 'Variable mapping relations:\n'
909    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
910    for varlist,mapvars,multarr,invmultarr in zip(
911        dependentParmList,indParmList,arrayList,invarrayList):
912        for i,mv in enumerate(mapvars):
913            if multarr is None:
914                s += '  ' + str(mv) + ' is equivalent to parameter(s): '
915                j = 0
916                for v,m in zip(varlist,invmultarr):
917                    if debug: print 'v,m[0]: ',v,m[0]
918                    if j > 0: s += '  & '
919                    j += 1
920                    s += str(v)
921                    if m != 1:
922                        s += " / " + str(m[0])                       
923                s += '\n'
924                continue
925            s += %s = ' % mv
926            j = 0
927            for m,v in zip(multarr[i,:],varlist):
928                if m == 0: continue
929                if j > 0: s += ' + '
930                j += 1
931                s += '(%s * %s)' % (m,v)
932            if mv in varyList: s += ' VARY'
933            s += '\n'
934    if inputOnly: return s
935    s += 'Inverse variable mapping relations:\n'
936    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
937        for i,mv in enumerate(varlist):
938            s += %s = ' % mv
939            j = 0
940            for m,v in zip(invmultarr[i,:],mapvars):
941                if m == 0: continue
942                if j > 0: s += ' + '
943                j += 1
944                s += '(%s * %s)' % (m,v)
945            s += '\n'
946    return s
947
948def Dict2Deriv(varyList,derivDict,dMdv):
949    '''Compute derivatives for Independent Parameters from the
950    derivatives for the original parameters
951
952    :param list varyList: a list of parameters names that will be varied
953
954    :param dict derivDict: a dict containing derivatives for parameter values keyed by the
955      parameter names.
956
957    :param list dMdv: a Jacobian, as a list of np.array containing derivatives for dependent
958      parameter computed from derivDict
959
960    '''
961    global dependentParmList,arrayList,invarrayList,indParmList,invarrayList
962    for varlist,mapvars,multarr,invmultarr in zip(dependentParmList,indParmList,arrayList,invarrayList):
963        for i,name in enumerate(mapvars):
964            # grouped variables: need to add in the derv. w/r
965            # dependent variables to the independent ones
966            if name not in varyList: continue # skip if independent var not varied
967            if multarr is None:
968                for v,m in zip(varlist,invmultarr):
969                    if debug: print 'start dMdv',dMdv[varyList.index(name)]
970                    if debug: print 'add derv',v,'/',m[0],'to derv',name,'add=',derivDict[v] / m[0]
971                    if m == 0: continue
972                    dMdv[varyList.index(name)] += derivDict[v] / m[0]
973            else:
974                for v,m in zip(varlist,multarr[i,:]):
975                    if debug: print 'start dMdv',dMdv[varyList.index(name)]
976                    if debug: print 'add derv',v,'*',m,'to derv',name,'add=',m * derivDict[v]
977                    if m == 0: continue
978                    dMdv[varyList.index(name)] += m * derivDict[v]
979
980def Map2Dict(parmDict,varyList):
981    '''Create (or update) the Independent Parameters from the original
982    set of Parameters
983
984    Removes dependent variables from the varyList
985
986    This should be done once, after the constraints have been
987    defined using :func:`StoreEquivalence`,
988    :func:`GroupConstraints` and :func:`GenerateConstraints` and
989    before any variable refinement is done. This completes the parameter
990    dictionary by defining independent parameters and it satisfies the
991    constraint equations in the initial parameters
992
993    :param dict parmDict: a dict containing parameter values keyed by the
994      parameter names.
995      This will contain updated values for both dependent and independent
996      parameters after Dict2Map is called. It will also contain some
997      unexpected entries of every constant value {'0':0.0} & {'1.0':1.0},
998      which do not cause any problems.
999
1000    :param list varyList: a list of parameters names that will be varied
1001   
1002
1003    '''
1004    # process the Independent vars: remove dependent ones from varylist
1005    # and then compute values for the Independent ones from their dependents
1006    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
1007    for varlist,mapvars,multarr in zip(dependentParmList,indParmList,arrayList):
1008        for item in varlist:
1009            try:
1010                varyList.remove(item)
1011            except ValueError:
1012                pass
1013        if multarr is None: continue
1014        valuelist = [parmDict[var] for var in varlist]
1015        parmDict.update(zip(mapvars,
1016                            np.dot(multarr,np.array(valuelist)))
1017                        )
1018    # now remove fixed variables from the varyList
1019    global fixedVarList
1020    for item in fixedVarList:
1021        try:
1022            varyList.remove(item)
1023        except ValueError:
1024            pass
1025    # Set constrained parameters to their fixed values
1026    parmDict.update(fixedDict)
1027
1028def Dict2Map(parmDict,varyList):
1029    '''Applies the constraints defined using :func:`StoreEquivalence`,
1030    :func:`GroupConstraints` and :func:`GenerateConstraints` by changing
1031    values in a dict containing the parameters. This should be
1032    done before the parameters are used for any computations
1033
1034    :param dict parmDict: a dict containing parameter values keyed by the
1035      parameter names.
1036      This will contain updated values for both dependent and independent
1037      parameters after Dict2Map is called. It will also contain some
1038      unexpected entries of every constant value {'0':0.0} & {'1.0':1.0},
1039      which do not cause any problems.
1040
1041    :param list varyList: a list of parameters names that will be varied
1042   
1043    '''
1044    global dependentParmList,arrayList,invarrayList,indParmList,fixedDict
1045    # reset fixed values (should not be needed, but very quick)
1046    # - this seems to update parmDict with {'0':0.0} & {'1.0':1.0} - probably not what was intended
1047    # not needed, but also not a problem - BHT
1048    parmDict.update(fixedDict)
1049    for varlist,mapvars,invmultarr in zip(dependentParmList,indParmList,invarrayList):
1050        #if invmultarr is None: continue
1051        try: 
1052            valuelist = [parmDict[var] for var in mapvars]
1053        except KeyError:
1054            continue
1055        parmDict.update(zip(varlist,
1056                            np.dot(invmultarr,np.array(valuelist)))
1057                        )
1058
1059#======================================================================
1060# internal routines follow (these routines are unlikely to be called
1061# from outside the module)
1062
1063def GramSchmidtOrtho(a,nkeep=0):
1064    '''Use the Gram-Schmidt process (http://en.wikipedia.org/wiki/Gram-Schmidt) to
1065    find orthonormal unit vectors relative to first row.
1066
1067    If nkeep is non-zero, the first nkeep rows in the array are not changed
1068   
1069    input:
1070       arrayin: a 2-D non-singular square array
1071    returns:
1072       a orthonormal set of unit vectors as a square array
1073    '''
1074    def proj(a,b):
1075        'Projection operator'
1076        return a*(np.dot(a,b)/np.dot(a,a))
1077    for j in range(nkeep,len(a)):
1078        for i in range(j):
1079            a[j] -= proj(a[i],a[j])
1080        if np.allclose(np.linalg.norm(a[j]),0.0):
1081            raise Exception,"Singular input to GramSchmidtOrtho"
1082        a[j] /= np.linalg.norm(a[j])
1083    return a
1084
1085def _FillArray(sel,dict,collist,FillDiagonals=False):
1086    '''Construct a n by n matrix (n = len(collist)
1087    filling in the rows using the relationships defined
1088    in the dictionaries selected by sel
1089
1090    If FillDiagonals is True, diagonal elements in the
1091    array are set to 1.0
1092    '''
1093    n = len(collist)
1094    if FillDiagonals:
1095        arr = np.eye(n)
1096    else:
1097        arr = np.zeros(2*[n,])
1098    # fill the top rows
1099    for i,cnum in enumerate(sel):
1100        for j,var in enumerate(collist):
1101            arr[i,j] = dict[cnum].get(var,0)
1102    return arr
1103
1104def _SwapColumns(i,m,v):
1105    '''Swap columns in matrix m as well as the labels in v
1106    so that element (i,i) is replaced by the first non-zero element in row i after that element
1107
1108    Throws an exception if there are no non-zero elements in that row
1109    '''
1110    for j in range(i+1,len(v)):
1111        if not np.allclose(m[i,j],0):
1112            m[:,(i,j)] = m[:,(j,i)]
1113            v[i],v[j] = v[j],v[i]
1114            return
1115    else:
1116        raise Exception,'Singular input'
1117
1118def _RowEchelon(m,arr,collist):
1119    '''Convert the first m rows in Matrix arr to row-echelon form
1120    exchanging columns in the matrix and collist as needed.
1121
1122    throws an exception if the matrix is singular because
1123    the first m rows are not linearly independent
1124    '''
1125    n = len(collist)
1126    for i in range(m):
1127        if np.allclose(arr[i,i],0):
1128            _SwapColumns(i,arr,collist)
1129        arr[i,:] /= arr[i,i] # normalize row
1130        # subtract current row from subsequent rows to set values to left of diagonal to 0
1131        for j in range(i+1,m):
1132            arr[j,:] -= arr[i,:] * arr[j,i]
1133
1134if __name__ == "__main__":
1135    parmdict = {}
1136    constrDict = [
1137        {'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},
1138        {'0:0:eA': 0.0},
1139        {'2::C(10,6,1)': 1.0, '1::C(10,6,1)': 1.0},
1140        {'1::C(10,0,1)': 1.0, '2::C(10,0,1)': 1.0},
1141        {'1::AUiso:0': 1.0, '0::AUiso:0': 1.0},
1142        {'0::A0': 0.0}
1143        ]
1144    fixedList = ['5.0', '0', None, None, '1.0', '0']
1145    StoreEquivalence('2::atomx:3',('2::atomy:3', ('2::atomz:3',2,), ))
1146    #StoreEquivalence('1::atomx:3',('2::atomx:3', ('2::atomz:3',2,), )) # error: dependent & independent vars mixed
1147    #StoreEquivalence('1::atomx:3',('2::atomy:3', ('2::atomz:3',2,), )) # error: dependent vars repeated
1148    #StoreEquivalence('0:1:eA',('0:0:eA',)) # error: equiv & fixed
1149    #StoreEquivalence('0:99:Scale',('0:12:Scale',)) # error: equiv & constrained
1150    #StoreEquivalence('0:12:Scale',('0:99:Scale',)) # error: equiv & constrained
1151    varylist = ['2::atomx:3',
1152                '2::C(10,6,1)', '1::C(10,6,1)',
1153                '2::atomy:3', '2::atomz:3',
1154                '0:12:Scale', '0:11:Scale', '0:14:Scale', '0:13:Scale', '0:0:Scale']
1155#    e,w = CheckConstraints([,
1156#                     [{'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}],
1157#                     ['1.0'])
1158#    if e: print 'error=',e
1159#    if w: print 'error=',w
1160#    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']
1161#    constrDict = [
1162#        {'0::Afrac:4': 24.0, '0::Afrac:1': 16.0, '0::Afrac:3': 24.0, '0::Afrac:2': 16.0},
1163#        {'0::Afrac:1': 1.0, '0::Afrac:2': 1.0},
1164#        {'0::Afrac:4': 1.0, '0::Afrac:3': 1.0}]
1165#    fixedList = ['40.0', '1.0', '1.0']
1166
1167    errmsg, warnmsg = CheckConstraints(varylist,constrDict,fixedList)
1168    if errmsg:
1169        print "*** Error ********************"
1170        print errmsg
1171    if warnmsg:
1172        print "*** Warning ********************"
1173        print warnmsg
1174    if errmsg or warnmsg:
1175        sys.exit()
1176    groups,parmlist = GroupConstraints(constrDict)
1177    GenerateConstraints(groups,parmlist,varylist,constrDict,fixedList)
1178    print VarRemapShow(varylist)
1179    parmdict.update( {
1180        '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,
1181        '0:0:eA': 0.0,
1182        '2::C(10,6,1)': 0.2, '1::C(10,6,1)': 0.3,
1183        '1::C(10,0,1)': 0.2, '2::C(10,0,1)': 0.3,
1184        '1::AUiso:0': 0.02, '0::AUiso:0': 0.03,
1185        '0::A0': 0.0,
1186        '2::atomx:3':0.23,'2::atomy:3':-.23, '2::atomz:3':-0.11,
1187        })
1188    print 'parmdict start',parmdict
1189    print 'varylist start',varylist
1190    before = parmdict.copy()
1191    Map2Dict(parmdict,varylist)
1192    print 'parmdict before and after Map2Dict'
1193    print '  key / before / after'
1194    for key in sorted(parmdict.keys()):
1195        print '  '+key,'\t',before.get(key),'\t',parmdict[key]
1196    print 'varylist after',varylist
1197    before = parmdict.copy()
1198    Dict2Map(parmdict,varylist)
1199    print 'after Dict2Map'
1200    print '  key / before / after'
1201    for key in sorted(parmdict.keys()):
1202        print '  '+key,'\t',before.get(key),'\t',parmdict[key]
1203#    dMdv = len(varylist)*[0]
1204#    deriv = {}
1205#    for i,v in enumerate(parmdict.keys()): deriv[v]=i
1206#    Dict2Deriv(varylist,deriv,dMdv)
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