src/daComposant/daAlgorithms/DerivativeFreeOptimization.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2021 EDF R&D
   4 #
   5 # This library is free software; you can redistribute it and/or
   6 # modify it under the terms of the GNU Lesser General Public
   7 # License as published by the Free Software Foundation; either
   8 # version 2.1 of the License.
   9 #
  10 # This library is distributed in the hope that it will be useful,
  11 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  12 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13 # Lesser General Public License for more details.
  14 #
  15 # You should have received a copy of the GNU Lesser General Public
  16 # License along with this library; if not, write to the Free Software
  17 # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA
  18 #
  19 # See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
  20 #
  21 # Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
  22
  23 import logging
  24 from daCore import BasicObjects, PlatformInfo
  25 import numpy, scipy.optimize
  26
  27 # ==============================================================================
  28 class ElementaryAlgorithm(BasicObjects.Algorithm):
  29     def __init__(self):
  30         BasicObjects.Algorithm.__init__(self, "DERIVATIVEFREEOPTIMIZATION")
  31         self.defineRequiredParameter(
  32             name     = "Minimizer",
  33             default  = "BOBYQA",
  34             typecast = str,
  35             message  = "Minimiseur utilisé",
  36             listval  = [
  37                 "BOBYQA",
  38                 "COBYLA",
  39                 "NEWUOA",
  40                 "POWELL",
  41                 "SIMPLEX",
  42                 "SUBPLEX",
  43                 ],
  44             )
  45         self.defineRequiredParameter(
  46             name     = "MaximumNumberOfSteps",
  47             default  = 15000,
  48             typecast = int,
  49             message  = "Nombre maximal de pas d'optimisation",
  50             minval   = -1,
  51             )
  52         self.defineRequiredParameter(
  53             name     = "MaximumNumberOfFunctionEvaluations",
  54             default  = 15000,
  55             typecast = int,
  56             message  = "Nombre maximal d'évaluations de la fonction",
  57             minval   = -1,
  58             )
  59         self.defineRequiredParameter(
  60             name     = "StateVariationTolerance",
  61             default  = 1.e-4,
  62             typecast = float,
  63             message  = "Variation relative maximale de l'état lors de l'arrêt",
  64             )
  65         self.defineRequiredParameter(
  66             name     = "CostDecrementTolerance",
  67             default  = 1.e-7,
  68             typecast = float,
  69             message  = "Diminution relative minimale du cout lors de l'arrêt",
  70             )
  71         self.defineRequiredParameter(
  72             name     = "QualityCriterion",
  73             default  = "AugmentedWeightedLeastSquares",
  74             typecast = str,
  75             message  = "Critère de qualité utilisé",
  76             listval  = ["AugmentedWeightedLeastSquares","AWLS","DA",
  77                         "WeightedLeastSquares","WLS",
  78                         "LeastSquares","LS","L2",
  79                         "AbsoluteValue","L1",
  80                         "MaximumError","ME"],
  81             )
  82         self.defineRequiredParameter(
  83             name     = "StoreInternalVariables",
  84             default  = False,
  85             typecast = bool,
  86             message  = "Stockage des variables internes ou intermédiaires du calcul",
  87             )
  88         self.defineRequiredParameter(
  89             name     = "StoreSupplementaryCalculations",
  90             default  = [],
  91             typecast = tuple,
  92             message  = "Liste de calculs supplémentaires à stocker et/ou effectuer",
  93             listval  = [
  94                 "Analysis",
  95                 "BMA",
  96                 "CostFunctionJ",
  97                 "CostFunctionJb",
  98                 "CostFunctionJo",
  99                 "CostFunctionJAtCurrentOptimum",
 100                 "CostFunctionJbAtCurrentOptimum",
 101                 "CostFunctionJoAtCurrentOptimum",
 102                 "CurrentIterationNumber",
 103                 "CurrentOptimum",
 104                 "CurrentState",
 105                 "IndexOfOptimum",
 106                 "Innovation",
 107                 "InnovationAtCurrentState",
 108                 "OMA",
 109                 "OMB",
 110                 "SimulatedObservationAtBackground",
 111                 "SimulatedObservationAtCurrentOptimum",
 112                 "SimulatedObservationAtCurrentState",
 113                 "SimulatedObservationAtOptimum",
 114                 ]
 115             )
 116         self.defineRequiredParameter( # Pas de type
 117             name     = "Bounds",
 118             message  = "Liste des valeurs de bornes",
 119             )
 120         self.requireInputArguments(
 121             mandatory= ("Xb", "Y", "HO", "R", "B" ),
 122             )
 123         self.setAttributes(tags=(
 124             "Optimization",
 125             "NonLinear",
 126             "MetaHeuristic",
 127             ))
 128
 129     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 130         self._pre_run(Parameters, Xb, Y, U, HO, EM, CM, R, B, Q)
 131         #
 132         if not PlatformInfo.has_nlopt and not self._parameters["Minimizer"] in ["COBYLA", "POWELL", "SIMPLEX"]:
 133             logging.warning("%s Minimization by SIMPLEX is forced because %s is unavailable (COBYLA, POWELL are also available)"%(self._name,self._parameters["Minimizer"]))
 134             self._parameters["Minimizer"] = "SIMPLEX"
 135         #
 136         # Opérateurs
 137         # ----------
 138         Hm = HO["Direct"].appliedTo
 139         #
 140         # Précalcul des inversions de B et R
 141         # ----------------------------------
 142         BI = B.getI()
 143         RI = R.getI()
 144         #
 145         # Définition de la fonction-coût
 146         # ------------------------------
 147         def CostFunction(x, QualityMeasure="AugmentedWeightedLeastSquares"):
 148             _X  = numpy.asmatrix(numpy.ravel( x )).T
 149             self.StoredVariables["CurrentState"].store( _X )
 150             _HX = Hm( _X )
 151             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 152             _Innovation = Y - _HX
 153             if self._toStore("SimulatedObservationAtCurrentState") or \
 154                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 155                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 156             if self._toStore("InnovationAtCurrentState"):
 157                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 158             #
 159             if QualityMeasure in ["AugmentedWeightedLeastSquares","AWLS","DA"]:
 160                 if BI is None or RI is None:
 161                     raise ValueError("Background and Observation error covariance matrix has to be properly defined!")
 162                 Jb  = 0.5 * (_X - Xb).T * BI * (_X - Xb)
 163                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 164             elif QualityMeasure in ["WeightedLeastSquares","WLS"]:
 165                 if RI is None:
 166                     raise ValueError("Observation error covariance matrix has to be properly defined!")
 167                 Jb  = 0.
 168                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 169             elif QualityMeasure in ["LeastSquares","LS","L2"]:
 170                 Jb  = 0.
 171                 Jo  = 0.5 * (_Innovation).T * (_Innovation)
 172             elif QualityMeasure in ["AbsoluteValue","L1"]:
 173                 Jb  = 0.
 174                 Jo  = numpy.sum( numpy.abs(_Innovation) )
 175             elif QualityMeasure in ["MaximumError","ME"]:
 176                 Jb  = 0.
 177                 Jo  = numpy.max( numpy.abs(_Innovation) )
 178             #
 179             J   = float( Jb ) + float( Jo )
 180             #
 181             self.StoredVariables["CurrentIterationNumber"].store( len(self.StoredVariables["CostFunctionJ"]) )
 182             self.StoredVariables["CostFunctionJb"].store( Jb )
 183             self.StoredVariables["CostFunctionJo"].store( Jo )
 184             self.StoredVariables["CostFunctionJ" ].store( J )
 185             if self._toStore("IndexOfOptimum") or \
 186                 self._toStore("CurrentOptimum") or \
 187                 self._toStore("CostFunctionJAtCurrentOptimum") or \
 188                 self._toStore("CostFunctionJbAtCurrentOptimum") or \
 189                 self._toStore("CostFunctionJoAtCurrentOptimum") or \
 190                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 191                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 192             if self._toStore("IndexOfOptimum"):
 193                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 194             if self._toStore("CurrentOptimum"):
 195                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 196             if self._toStore("SimulatedObservationAtCurrentOptimum"):
 197                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 198             if self._toStore("CostFunctionJAtCurrentOptimum"):
 199                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 200             if self._toStore("CostFunctionJbAtCurrentOptimum"):
 201                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 202             if self._toStore("CostFunctionJoAtCurrentOptimum"):
 203                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 204             return J
 205         #
 206         # Point de démarrage de l'optimisation : Xini = Xb
 207         # ------------------------------------
 208         Xini = numpy.ravel(Xb)
 209         if len(Xini) < 2 and self._parameters["Minimizer"] == "NEWUOA":
 210             raise ValueError("The minimizer %s can not be used when the optimisation state dimension is 1. Please choose another minimizer."%self._parameters["Minimizer"])
 211         #
 212         # Minimisation de la fonctionnelle
 213         # --------------------------------
 214         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 215         #
 216         if self._parameters["Minimizer"] == "POWELL":
 217             Minimum, J_optimal, direc, niter, nfeval, rc = scipy.optimize.fmin_powell(
 218                 func        = CostFunction,
 219                 x0          = Xini,
 220                 args        = (self._parameters["QualityCriterion"],),
 221                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 222                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 223                 xtol        = self._parameters["StateVariationTolerance"],
 224                 ftol        = self._parameters["CostDecrementTolerance"],
 225                 full_output = True,
 226                 disp        = self._parameters["optdisp"],
 227                 )
 228         elif self._parameters["Minimizer"] == "COBYLA" and not PlatformInfo.has_nlopt:
 229             def make_constraints(bounds):
 230                 constraints = []
 231                 for (i,(a,b)) in enumerate(bounds):
 232                     lower = lambda x: x[i] - a
 233                     upper = lambda x: b - x[i]
 234                     constraints = constraints + [lower] + [upper]
 235                 return constraints
 236             if self._parameters["Bounds"] is None:
 237                 raise ValueError("Bounds have to be given for all axes as a list of lower/upper pairs!")
 238             Minimum = scipy.optimize.fmin_cobyla(
 239                 func        = CostFunction,
 240                 x0          = Xini,
 241                 cons        = make_constraints( self._parameters["Bounds"] ),
 242                 args        = (self._parameters["QualityCriterion"],),
 243                 consargs    = (), # To avoid extra-args
 244                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 245                 rhobeg      = 1.0,
 246                 rhoend      = self._parameters["StateVariationTolerance"],
 247                 catol       = 2.*self._parameters["StateVariationTolerance"],
 248                 disp        = self._parameters["optdisp"],
 249                 )
 250         elif self._parameters["Minimizer"] == "COBYLA" and PlatformInfo.has_nlopt:
 251             import nlopt
 252             opt = nlopt.opt(nlopt.LN_COBYLA, Xini.size)
 253             def _f(_Xx, Grad):
 254                 # DFO, so no gradient
 255                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 256             opt.set_min_objective(_f)
 257             if self._parameters["Bounds"] is not None:
 258                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 259                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 260                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 261                 if self._parameters["optdisp"]:
 262                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 263                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 264                 opt.set_upper_bounds(ub)
 265                 opt.set_lower_bounds(lb)
 266             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 267             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 268             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 269             Minimum = opt.optimize( Xini )
 270             if self._parameters["optdisp"]:
 271                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 272                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 273                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 274         elif self._parameters["Minimizer"] == "SIMPLEX" and not PlatformInfo.has_nlopt:
 275             Minimum, J_optimal, niter, nfeval, rc = scipy.optimize.fmin(
 276                 func        = CostFunction,
 277                 x0          = Xini,
 278                 args        = (self._parameters["QualityCriterion"],),
 279                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 280                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 281                 xtol        = self._parameters["StateVariationTolerance"],
 282                 ftol        = self._parameters["CostDecrementTolerance"],
 283                 full_output = True,
 284                 disp        = self._parameters["optdisp"],
 285                 )
 286         elif self._parameters["Minimizer"] == "SIMPLEX" and PlatformInfo.has_nlopt:
 287             import nlopt
 288             opt = nlopt.opt(nlopt.LN_NELDERMEAD, Xini.size)
 289             def _f(_Xx, Grad):
 290                 # DFO, so no gradient
 291                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 292             opt.set_min_objective(_f)
 293             if self._parameters["Bounds"] is not None:
 294                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 295                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 296                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 297                 if self._parameters["optdisp"]:
 298                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 299                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 300                 opt.set_upper_bounds(ub)
 301                 opt.set_lower_bounds(lb)
 302             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 303             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 304             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 305             Minimum = opt.optimize( Xini )
 306             if self._parameters["optdisp"]:
 307                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 308                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 309                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 310         elif self._parameters["Minimizer"] == "BOBYQA" and PlatformInfo.has_nlopt:
 311             import nlopt
 312             opt = nlopt.opt(nlopt.LN_BOBYQA, Xini.size)
 313             def _f(_Xx, Grad):
 314                 # DFO, so no gradient
 315                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 316             opt.set_min_objective(_f)
 317             if self._parameters["Bounds"] is not None:
 318                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 319                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 320                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 321                 if self._parameters["optdisp"]:
 322                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 323                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 324                 opt.set_upper_bounds(ub)
 325                 opt.set_lower_bounds(lb)
 326             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 327             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 328             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 329             Minimum = opt.optimize( Xini )
 330             if self._parameters["optdisp"]:
 331                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 332                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 333                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 334         elif self._parameters["Minimizer"] == "NEWUOA" and PlatformInfo.has_nlopt:
 335             import nlopt
 336             opt = nlopt.opt(nlopt.LN_NEWUOA, Xini.size)
 337             def _f(_Xx, Grad):
 338                 # DFO, so no gradient
 339                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 340             opt.set_min_objective(_f)
 341             if self._parameters["Bounds"] is not None:
 342                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 343                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 344                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 345                 if self._parameters["optdisp"]:
 346                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 347                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 348                 opt.set_upper_bounds(ub)
 349                 opt.set_lower_bounds(lb)
 350             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 351             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 352             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 353             Minimum = opt.optimize( Xini )
 354             if self._parameters["optdisp"]:
 355                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 356                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 357                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 358         elif self._parameters["Minimizer"] == "SUBPLEX" and PlatformInfo.has_nlopt:
 359             import nlopt
 360             opt = nlopt.opt(nlopt.LN_SBPLX, Xini.size)
 361             def _f(_Xx, Grad):
 362                 # DFO, so no gradient
 363                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 364             opt.set_min_objective(_f)
 365             if self._parameters["Bounds"] is not None:
 366                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 367                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 368                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 369                 if self._parameters["optdisp"]:
 370                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 371                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 372                 opt.set_upper_bounds(ub)
 373                 opt.set_lower_bounds(lb)
 374             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 375             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 376             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 377             Minimum = opt.optimize( Xini )
 378             if self._parameters["optdisp"]:
 379                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 380                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 381                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 382         else:
 383             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 384         #
 385         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 386         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 387         Minimum  = self.StoredVariables["CurrentState"][IndexMin]
 388         #
 389         # Obtention de l'analyse
 390         # ----------------------
 391         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 392         #
 393         self.StoredVariables["Analysis"].store( Xa.A1 )
 394         #
 395         # Calculs et/ou stockages supplémentaires
 396         # ---------------------------------------
 397         if self._toStore("OMA" ) or \
 398             self._toStore("SimulatedObservationAtOptimum"):
 399             if self._toStore("SimulatedObservationAtCurrentState"):
 400                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 401             elif self._toStore("SimulatedObservationAtCurrentOptimum"):
 402                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 403             else:
 404                 HXa = Hm(Xa)
 405         if self._toStore("Innovation") or \
 406             self._toStore("OMB"):
 407             d  = Y - HXb
 408         if self._toStore("Innovation"):
 409             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 410         if self._toStore("OMB"):
 411             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 412         if self._toStore("BMA"):
 413             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 414         if self._toStore("OMA"):
 415             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 416         if self._toStore("SimulatedObservationAtBackground"):
 417             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(Hm(Xb)) )
 418         if self._toStore("SimulatedObservationAtOptimum"):
 419             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 420         #
 421         self._post_run()
 422         return 0
 423
 424 # ==============================================================================
 425 if __name__ == "__main__":
 426     print('\n AUTODIAGNOSTIC\n')