src/daComposant/daAlgorithms/DerivativeFreeOptimization.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2020 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  = ["BOBYQA", "COBYLA", "NEWUOA", "POWELL", "SIMPLEX", "SUBPLEX"],
  37             )
  38         self.defineRequiredParameter(
  39             name     = "MaximumNumberOfSteps",
  40             default  = 15000,
  41             typecast = int,
  42             message  = "Nombre maximal de pas d'optimisation",
  43             minval   = -1,
  44             )
  45         self.defineRequiredParameter(
  46             name     = "MaximumNumberOfFunctionEvaluations",
  47             default  = 15000,
  48             typecast = int,
  49             message  = "Nombre maximal d'évaluations de la fonction",
  50             minval   = -1,
  51             )
  52         self.defineRequiredParameter(
  53             name     = "StateVariationTolerance",
  54             default  = 1.e-4,
  55             typecast = float,
  56             message  = "Variation relative maximale de l'état lors de l'arrêt",
  57             )
  58         self.defineRequiredParameter(
  59             name     = "CostDecrementTolerance",
  60             default  = 1.e-7,
  61             typecast = float,
  62             message  = "Diminution relative minimale du cout lors de l'arrêt",
  63             )
  64         self.defineRequiredParameter(
  65             name     = "QualityCriterion",
  66             default  = "AugmentedWeightedLeastSquares",
  67             typecast = str,
  68             message  = "Critère de qualité utilisé",
  69             listval  = ["AugmentedWeightedLeastSquares","AWLS","DA",
  70                         "WeightedLeastSquares","WLS",
  71                         "LeastSquares","LS","L2",
  72                         "AbsoluteValue","L1",
  73                         "MaximumError","ME"],
  74             )
  75         self.defineRequiredParameter(
  76             name     = "StoreInternalVariables",
  77             default  = False,
  78             typecast = bool,
  79             message  = "Stockage des variables internes ou intermédiaires du calcul",
  80             )
  81         self.defineRequiredParameter(
  82             name     = "StoreSupplementaryCalculations",
  83             default  = [],
  84             typecast = tuple,
  85             message  = "Liste de calculs supplémentaires à stocker et/ou effectuer",
  86             listval  = [
  87                 "Analysis",
  88                 "BMA",
  89                 "CostFunctionJ",
  90                 "CostFunctionJb",
  91                 "CostFunctionJo",
  92                 "CostFunctionJAtCurrentOptimum",
  93                 "CostFunctionJbAtCurrentOptimum",
  94                 "CostFunctionJoAtCurrentOptimum",
  95                 "CurrentIterationNumber",
  96                 "CurrentOptimum",
  97                 "CurrentState",
  98                 "IndexOfOptimum",
  99                 "Innovation",
 100                 "InnovationAtCurrentState",
 101                 "OMA",
 102                 "OMB",
 103                 "SimulatedObservationAtBackground",
 104                 "SimulatedObservationAtCurrentOptimum",
 105                 "SimulatedObservationAtCurrentState",
 106                 "SimulatedObservationAtOptimum",
 107                 ]
 108             )
 109         self.defineRequiredParameter( # Pas de type
 110             name     = "Bounds",
 111             message  = "Liste des valeurs de bornes",
 112             )
 113         self.requireInputArguments(
 114             mandatory= ("Xb", "Y", "HO", "R", "B" ),
 115             )
 116         self.setAttributes(tags=(
 117             "Optimization",
 118             "NonLinear",
 119             "MetaHeuristic",
 120             ))
 121
 122     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 123         self._pre_run(Parameters, Xb, Y, U, HO, EM, CM, R, B, Q)
 124         #
 125         if not PlatformInfo.has_nlopt and not self._parameters["Minimizer"] in ["COBYLA", "POWELL", "SIMPLEX"]:
 126             logging.warning("%s Minimization by SIMPLEX is forced because %s is unavailable (COBYLA, POWELL are also available)"%(self._name,self._parameters["Minimizer"]))
 127             self._parameters["Minimizer"] = "SIMPLEX"
 128         #
 129         # Opérateurs
 130         # ----------
 131         Hm = HO["Direct"].appliedTo
 132         #
 133         # Précalcul des inversions de B et R
 134         # ----------------------------------
 135         BI = B.getI()
 136         RI = R.getI()
 137         #
 138         # Définition de la fonction-coût
 139         # ------------------------------
 140         def CostFunction(x, QualityMeasure="AugmentedWeightedLeastSquares"):
 141             _X  = numpy.asmatrix(numpy.ravel( x )).T
 142             self.StoredVariables["CurrentState"].store( _X )
 143             _HX = Hm( _X )
 144             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 145             _Innovation = Y - _HX
 146             if self._toStore("SimulatedObservationAtCurrentState") or \
 147                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 148                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 149             if self._toStore("InnovationAtCurrentState"):
 150                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 151             #
 152             if QualityMeasure in ["AugmentedWeightedLeastSquares","AWLS","DA"]:
 153                 if BI is None or RI is None:
 154                     raise ValueError("Background and Observation error covariance matrix has to be properly defined!")
 155                 Jb  = 0.5 * (_X - Xb).T * BI * (_X - Xb)
 156                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 157             elif QualityMeasure in ["WeightedLeastSquares","WLS"]:
 158                 if RI is None:
 159                     raise ValueError("Observation error covariance matrix has to be properly defined!")
 160                 Jb  = 0.
 161                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 162             elif QualityMeasure in ["LeastSquares","LS","L2"]:
 163                 Jb  = 0.
 164                 Jo  = 0.5 * (_Innovation).T * (_Innovation)
 165             elif QualityMeasure in ["AbsoluteValue","L1"]:
 166                 Jb  = 0.
 167                 Jo  = numpy.sum( numpy.abs(_Innovation) )
 168             elif QualityMeasure in ["MaximumError","ME"]:
 169                 Jb  = 0.
 170                 Jo  = numpy.max( numpy.abs(_Innovation) )
 171             #
 172             J   = float( Jb ) + float( Jo )
 173             #
 174             self.StoredVariables["CurrentIterationNumber"].store( len(self.StoredVariables["CostFunctionJ"]) )
 175             self.StoredVariables["CostFunctionJb"].store( Jb )
 176             self.StoredVariables["CostFunctionJo"].store( Jo )
 177             self.StoredVariables["CostFunctionJ" ].store( J )
 178             if self._toStore("IndexOfOptimum") or \
 179                 self._toStore("CurrentOptimum") or \
 180                 self._toStore("CostFunctionJAtCurrentOptimum") or \
 181                 self._toStore("CostFunctionJbAtCurrentOptimum") or \
 182                 self._toStore("CostFunctionJoAtCurrentOptimum") or \
 183                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 184                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 185             if self._toStore("IndexOfOptimum"):
 186                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 187             if self._toStore("CurrentOptimum"):
 188                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 189             if self._toStore("SimulatedObservationAtCurrentOptimum"):
 190                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 191             if self._toStore("CostFunctionJAtCurrentOptimum"):
 192                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 193             if self._toStore("CostFunctionJbAtCurrentOptimum"):
 194                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 195             if self._toStore("CostFunctionJoAtCurrentOptimum"):
 196                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 197             return J
 198         #
 199         # Point de démarrage de l'optimisation : Xini = Xb
 200         # ------------------------------------
 201         Xini = numpy.ravel(Xb)
 202         if len(Xini) < 2 and self._parameters["Minimizer"] == "NEWUOA":
 203             raise ValueError("The minimizer %s can not be used when the optimisation state dimension is 1. Please choose another minimizer."%self._parameters["Minimizer"])
 204         #
 205         # Minimisation de la fonctionnelle
 206         # --------------------------------
 207         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 208         #
 209         if self._parameters["Minimizer"] == "POWELL":
 210             Minimum, J_optimal, direc, niter, nfeval, rc = scipy.optimize.fmin_powell(
 211                 func        = CostFunction,
 212                 x0          = Xini,
 213                 args        = (self._parameters["QualityCriterion"],),
 214                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 215                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 216                 xtol        = self._parameters["StateVariationTolerance"],
 217                 ftol        = self._parameters["CostDecrementTolerance"],
 218                 full_output = True,
 219                 disp        = self._parameters["optdisp"],
 220                 )
 221         elif self._parameters["Minimizer"] == "COBYLA" and not PlatformInfo.has_nlopt:
 222             def make_constraints(bounds):
 223                 constraints = []
 224                 for (i,(a,b)) in enumerate(bounds):
 225                     lower = lambda x: x[i] - a
 226                     upper = lambda x: b - x[i]
 227                     constraints = constraints + [lower] + [upper]
 228                 return constraints
 229             if self._parameters["Bounds"] is None:
 230                 raise ValueError("Bounds have to be given for all axes as a list of lower/upper pairs!")
 231             Minimum = scipy.optimize.fmin_cobyla(
 232                 func        = CostFunction,
 233                 x0          = Xini,
 234                 cons        = make_constraints( self._parameters["Bounds"] ),
 235                 args        = (self._parameters["QualityCriterion"],),
 236                 consargs    = (), # To avoid extra-args
 237                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 238                 rhobeg      = 1.0,
 239                 rhoend      = self._parameters["StateVariationTolerance"],
 240                 catol       = 2.*self._parameters["StateVariationTolerance"],
 241                 disp        = self._parameters["optdisp"],
 242                 )
 243         elif self._parameters["Minimizer"] == "COBYLA" and PlatformInfo.has_nlopt:
 244             import nlopt
 245             opt = nlopt.opt(nlopt.LN_COBYLA, Xini.size)
 246             def _f(_Xx, Grad):
 247                 # DFO, so no gradient
 248                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 249             opt.set_min_objective(_f)
 250             if self._parameters["Bounds"] is not None:
 251                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 252                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 253                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 254                 if self._parameters["optdisp"]:
 255                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 256                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 257                 opt.set_upper_bounds(ub)
 258                 opt.set_lower_bounds(lb)
 259             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 260             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 261             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 262             Minimum = opt.optimize( Xini )
 263             if self._parameters["optdisp"]:
 264                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 265                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 266                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 267         elif self._parameters["Minimizer"] == "SIMPLEX" and not PlatformInfo.has_nlopt:
 268             Minimum, J_optimal, niter, nfeval, rc = scipy.optimize.fmin(
 269                 func        = CostFunction,
 270                 x0          = Xini,
 271                 args        = (self._parameters["QualityCriterion"],),
 272                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 273                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 274                 xtol        = self._parameters["StateVariationTolerance"],
 275                 ftol        = self._parameters["CostDecrementTolerance"],
 276                 full_output = True,
 277                 disp        = self._parameters["optdisp"],
 278                 )
 279         elif self._parameters["Minimizer"] == "SIMPLEX" and PlatformInfo.has_nlopt:
 280             import nlopt
 281             opt = nlopt.opt(nlopt.LN_NELDERMEAD, Xini.size)
 282             def _f(_Xx, Grad):
 283                 # DFO, so no gradient
 284                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 285             opt.set_min_objective(_f)
 286             if self._parameters["Bounds"] is not None:
 287                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 288                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 289                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 290                 if self._parameters["optdisp"]:
 291                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 292                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 293                 opt.set_upper_bounds(ub)
 294                 opt.set_lower_bounds(lb)
 295             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 296             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 297             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 298             Minimum = opt.optimize( Xini )
 299             if self._parameters["optdisp"]:
 300                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 301                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 302                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 303         elif self._parameters["Minimizer"] == "BOBYQA" and PlatformInfo.has_nlopt:
 304             import nlopt
 305             opt = nlopt.opt(nlopt.LN_BOBYQA, Xini.size)
 306             def _f(_Xx, Grad):
 307                 # DFO, so no gradient
 308                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 309             opt.set_min_objective(_f)
 310             if self._parameters["Bounds"] is not None:
 311                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 312                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 313                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 314                 if self._parameters["optdisp"]:
 315                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 316                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 317                 opt.set_upper_bounds(ub)
 318                 opt.set_lower_bounds(lb)
 319             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 320             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 321             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 322             Minimum = opt.optimize( Xini )
 323             if self._parameters["optdisp"]:
 324                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 325                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 326                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 327         elif self._parameters["Minimizer"] == "NEWUOA" and PlatformInfo.has_nlopt:
 328             import nlopt
 329             opt = nlopt.opt(nlopt.LN_NEWUOA, Xini.size)
 330             def _f(_Xx, Grad):
 331                 # DFO, so no gradient
 332                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 333             opt.set_min_objective(_f)
 334             if self._parameters["Bounds"] is not None:
 335                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 336                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 337                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 338                 if self._parameters["optdisp"]:
 339                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 340                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 341                 opt.set_upper_bounds(ub)
 342                 opt.set_lower_bounds(lb)
 343             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 344             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 345             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 346             Minimum = opt.optimize( Xini )
 347             if self._parameters["optdisp"]:
 348                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 349                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 350                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 351         elif self._parameters["Minimizer"] == "SUBPLEX" and PlatformInfo.has_nlopt:
 352             import nlopt
 353             opt = nlopt.opt(nlopt.LN_SBPLX, Xini.size)
 354             def _f(_Xx, Grad):
 355                 # DFO, so no gradient
 356                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 357             opt.set_min_objective(_f)
 358             if self._parameters["Bounds"] is not None:
 359                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 360                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 361                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 362                 if self._parameters["optdisp"]:
 363                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 364                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 365                 opt.set_upper_bounds(ub)
 366                 opt.set_lower_bounds(lb)
 367             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 368             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 369             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 370             Minimum = opt.optimize( Xini )
 371             if self._parameters["optdisp"]:
 372                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 373                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 374                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 375         else:
 376             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 377         #
 378         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 379         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 380         Minimum  = self.StoredVariables["CurrentState"][IndexMin]
 381         #
 382         # Obtention de l'analyse
 383         # ----------------------
 384         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 385         #
 386         self.StoredVariables["Analysis"].store( Xa.A1 )
 387         #
 388         # Calculs et/ou stockages supplémentaires
 389         # ---------------------------------------
 390         if self._toStore("OMA" ) or \
 391             self._toStore("SimulatedObservationAtOptimum"):
 392             if self._toStore("SimulatedObservationAtCurrentState"):
 393                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 394             elif self._toStore("SimulatedObservationAtCurrentOptimum"):
 395                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 396             else:
 397                 HXa = Hm(Xa)
 398         if self._toStore("Innovation") or \
 399             self._toStore("OMB"):
 400             d  = Y - HXb
 401         if self._toStore("Innovation"):
 402             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 403         if self._toStore("OMB"):
 404             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 405         if self._toStore("BMA"):
 406             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 407         if self._toStore("OMA"):
 408             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 409         if self._toStore("SimulatedObservationAtBackground"):
 410             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(Hm(Xb)) )
 411         if self._toStore("SimulatedObservationAtOptimum"):
 412             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 413         #
 414         self._post_run()
 415         return 0
 416
 417 # ==============================================================================
 418 if __name__ == "__main__":
 419     print('\n AUTODIAGNOSTIC\n')