src/daComposant/daAlgorithms/DerivativeFreeOptimization.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2019 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                 "CurrentOptimum",
  96                 "CurrentState",
  97                 "IndexOfOptimum",
  98                 "Innovation",
  99                 "InnovationAtCurrentState",
 100                 "OMA",
 101                 "OMB",
 102                 "SimulatedObservationAtBackground",
 103                 "SimulatedObservationAtCurrentOptimum",
 104                 "SimulatedObservationAtCurrentState",
 105                 "SimulatedObservationAtOptimum",
 106                 ]
 107             )
 108         self.defineRequiredParameter( # Pas de type
 109             name     = "Bounds",
 110             message  = "Liste des valeurs de bornes",
 111             )
 112         self.requireInputArguments(
 113             mandatory= ("Xb", "Y", "HO", "R", "B" ),
 114             )
 115
 116     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 117         self._pre_run(Parameters, Xb, Y, R, B, Q)
 118         #
 119         if not PlatformInfo.has_nlopt and not self._parameters["Minimizer"] in ["COBYLA", "POWELL", "SIMPLEX"]:
 120             logging.warning("%s Minimization by SIMPLEX is forced because %s is unavailable (COBYLA, POWELL are also available)"%(self._name,self._parameters["Minimizer"]))
 121             self._parameters["Minimizer"] = "SIMPLEX"
 122         #
 123         # Opérateurs
 124         # ----------
 125         Hm = HO["Direct"].appliedTo
 126         #
 127         # Précalcul des inversions de B et R
 128         # ----------------------------------
 129         BI = B.getI()
 130         RI = R.getI()
 131         #
 132         # Définition de la fonction-coût
 133         # ------------------------------
 134         def CostFunction(x, QualityMeasure="AugmentedWeightedLeastSquares"):
 135             _X  = numpy.asmatrix(numpy.ravel( x )).T
 136             self.StoredVariables["CurrentState"].store( _X )
 137             _HX = Hm( _X )
 138             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 139             _Innovation = Y - _HX
 140             if self._toStore("SimulatedObservationAtCurrentState") or \
 141                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 142                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 143             if self._toStore("InnovationAtCurrentState"):
 144                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 145             #
 146             if QualityMeasure in ["AugmentedWeightedLeastSquares","AWLS","DA"]:
 147                 if BI is None or RI is None:
 148                     raise ValueError("Background and Observation error covariance matrix has to be properly defined!")
 149                 Jb  = 0.5 * (_X - Xb).T * BI * (_X - Xb)
 150                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 151             elif QualityMeasure in ["WeightedLeastSquares","WLS"]:
 152                 if RI is None:
 153                     raise ValueError("Observation error covariance matrix has to be properly defined!")
 154                 Jb  = 0.
 155                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 156             elif QualityMeasure in ["LeastSquares","LS","L2"]:
 157                 Jb  = 0.
 158                 Jo  = 0.5 * (_Innovation).T * (_Innovation)
 159             elif QualityMeasure in ["AbsoluteValue","L1"]:
 160                 Jb  = 0.
 161                 Jo  = numpy.sum( numpy.abs(_Innovation) )
 162             elif QualityMeasure in ["MaximumError","ME"]:
 163                 Jb  = 0.
 164                 Jo  = numpy.max( numpy.abs(_Innovation) )
 165             #
 166             J   = float( Jb ) + float( Jo )
 167             #
 168             self.StoredVariables["CostFunctionJb"].store( Jb )
 169             self.StoredVariables["CostFunctionJo"].store( Jo )
 170             self.StoredVariables["CostFunctionJ" ].store( J )
 171             if self._toStore("IndexOfOptimum") or \
 172                 self._toStore("CurrentOptimum") or \
 173                 self._toStore("CostFunctionJAtCurrentOptimum") or \
 174                 self._toStore("CostFunctionJbAtCurrentOptimum") or \
 175                 self._toStore("CostFunctionJoAtCurrentOptimum") or \
 176                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 177                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 178             if self._toStore("IndexOfOptimum"):
 179                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 180             if self._toStore("CurrentOptimum"):
 181                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 182             if self._toStore("SimulatedObservationAtCurrentOptimum"):
 183                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 184             if self._toStore("CostFunctionJAtCurrentOptimum"):
 185                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 186             if self._toStore("CostFunctionJbAtCurrentOptimum"):
 187                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 188             if self._toStore("CostFunctionJoAtCurrentOptimum"):
 189                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 190             return J
 191         #
 192         # Point de démarrage de l'optimisation : Xini = Xb
 193         # ------------------------------------
 194         Xini = numpy.ravel(Xb)
 195         if len(Xini) < 2 and self._parameters["Minimizer"] == "NEWUOA":
 196             raise ValueError("The minimizer %s can not be used when the optimisation state dimension is 1. Please choose another minimizer."%self._parameters["Minimizer"])
 197         #
 198         # Minimisation de la fonctionnelle
 199         # --------------------------------
 200         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 201         #
 202         if self._parameters["Minimizer"] == "POWELL":
 203             Minimum, J_optimal, direc, niter, nfeval, rc = scipy.optimize.fmin_powell(
 204                 func        = CostFunction,
 205                 x0          = Xini,
 206                 args        = (self._parameters["QualityCriterion"],),
 207                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 208                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 209                 xtol        = self._parameters["StateVariationTolerance"],
 210                 ftol        = self._parameters["CostDecrementTolerance"],
 211                 full_output = True,
 212                 disp        = self._parameters["optdisp"],
 213                 )
 214         elif self._parameters["Minimizer"] == "COBYLA" and not PlatformInfo.has_nlopt:
 215             def make_constraints(bounds):
 216                 constraints = []
 217                 for (i,(a,b)) in enumerate(bounds):
 218                     lower = lambda x: x[i] - a
 219                     upper = lambda x: b - x[i]
 220                     constraints = constraints + [lower] + [upper]
 221                 return constraints
 222             if self._parameters["Bounds"] is None:
 223                 raise ValueError("Bounds have to be given for all axes as a list of lower/upper pairs!")
 224             Minimum = scipy.optimize.fmin_cobyla(
 225                 func        = CostFunction,
 226                 x0          = Xini,
 227                 cons        = make_constraints( self._parameters["Bounds"] ),
 228                 args        = (self._parameters["QualityCriterion"],),
 229                 consargs    = (), # To avoid extra-args
 230                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 231                 rhobeg      = 1.0,
 232                 rhoend      = self._parameters["StateVariationTolerance"],
 233                 catol       = 2.*self._parameters["StateVariationTolerance"],
 234                 disp        = self._parameters["optdisp"],
 235                 )
 236         elif self._parameters["Minimizer"] == "COBYLA" and PlatformInfo.has_nlopt:
 237             import nlopt
 238             opt = nlopt.opt(nlopt.LN_COBYLA, Xini.size)
 239             def _f(_Xx, Grad):
 240                 # DFO, so no gradient
 241                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 242             opt.set_min_objective(_f)
 243             if self._parameters["Bounds"] is not None:
 244                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 245                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 246                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 247                 if self._parameters["optdisp"]:
 248                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 249                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 250                 opt.set_upper_bounds(ub)
 251                 opt.set_lower_bounds(lb)
 252             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 253             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 254             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 255             Minimum = opt.optimize( Xini )
 256             if self._parameters["optdisp"]:
 257                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 258                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 259                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 260         elif self._parameters["Minimizer"] == "SIMPLEX" and not PlatformInfo.has_nlopt:
 261             Minimum, J_optimal, niter, nfeval, rc = scipy.optimize.fmin(
 262                 func        = CostFunction,
 263                 x0          = Xini,
 264                 args        = (self._parameters["QualityCriterion"],),
 265                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 266                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 267                 xtol        = self._parameters["StateVariationTolerance"],
 268                 ftol        = self._parameters["CostDecrementTolerance"],
 269                 full_output = True,
 270                 disp        = self._parameters["optdisp"],
 271                 )
 272         elif self._parameters["Minimizer"] == "SIMPLEX" and PlatformInfo.has_nlopt:
 273             import nlopt
 274             opt = nlopt.opt(nlopt.LN_NELDERMEAD, Xini.size)
 275             def _f(_Xx, Grad):
 276                 # DFO, so no gradient
 277                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 278             opt.set_min_objective(_f)
 279             if self._parameters["Bounds"] is not None:
 280                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 281                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 282                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 283                 if self._parameters["optdisp"]:
 284                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 285                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 286                 opt.set_upper_bounds(ub)
 287                 opt.set_lower_bounds(lb)
 288             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 289             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 290             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 291             Minimum = opt.optimize( Xini )
 292             if self._parameters["optdisp"]:
 293                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 294                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 295                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 296         elif self._parameters["Minimizer"] == "BOBYQA" and PlatformInfo.has_nlopt:
 297             import nlopt
 298             opt = nlopt.opt(nlopt.LN_BOBYQA, Xini.size)
 299             def _f(_Xx, Grad):
 300                 # DFO, so no gradient
 301                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 302             opt.set_min_objective(_f)
 303             if self._parameters["Bounds"] is not None:
 304                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 305                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 306                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 307                 if self._parameters["optdisp"]:
 308                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 309                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 310                 opt.set_upper_bounds(ub)
 311                 opt.set_lower_bounds(lb)
 312             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 313             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 314             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 315             Minimum = opt.optimize( Xini )
 316             if self._parameters["optdisp"]:
 317                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 318                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 319                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 320         elif self._parameters["Minimizer"] == "NEWUOA" and PlatformInfo.has_nlopt:
 321             import nlopt
 322             opt = nlopt.opt(nlopt.LN_NEWUOA, Xini.size)
 323             def _f(_Xx, Grad):
 324                 # DFO, so no gradient
 325                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 326             opt.set_min_objective(_f)
 327             if self._parameters["Bounds"] is not None:
 328                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 329                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 330                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 331                 if self._parameters["optdisp"]:
 332                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 333                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 334                 opt.set_upper_bounds(ub)
 335                 opt.set_lower_bounds(lb)
 336             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 337             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 338             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 339             Minimum = opt.optimize( Xini )
 340             if self._parameters["optdisp"]:
 341                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 342                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 343                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 344         elif self._parameters["Minimizer"] == "SUBPLEX" and PlatformInfo.has_nlopt:
 345             import nlopt
 346             opt = nlopt.opt(nlopt.LN_SBPLX, Xini.size)
 347             def _f(_Xx, Grad):
 348                 # DFO, so no gradient
 349                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 350             opt.set_min_objective(_f)
 351             if self._parameters["Bounds"] is not None:
 352                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 353                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 354                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 355                 if self._parameters["optdisp"]:
 356                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 357                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 358                 opt.set_upper_bounds(ub)
 359                 opt.set_lower_bounds(lb)
 360             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 361             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 362             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 363             Minimum = opt.optimize( Xini )
 364             if self._parameters["optdisp"]:
 365                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 366                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 367                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 368         else:
 369             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 370         #
 371         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 372         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 373         Minimum  = self.StoredVariables["CurrentState"][IndexMin]
 374         #
 375         # Obtention de l'analyse
 376         # ----------------------
 377         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 378         #
 379         self.StoredVariables["Analysis"].store( Xa.A1 )
 380         #
 381         # Calculs et/ou stockages supplémentaires
 382         # ---------------------------------------
 383         if self._toStore("OMA" ) or \
 384             self._toStore("SimulatedObservationAtOptimum"):
 385             if self._toStore("SimulatedObservationAtCurrentState"):
 386                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 387             elif self._toStore("SimulatedObservationAtCurrentOptimum"):
 388                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 389             else:
 390                 HXa = Hm(Xa)
 391         if self._toStore("Innovation") or \
 392             self._toStore("OMB"):
 393             d  = Y - HXb
 394         if self._toStore("Innovation"):
 395             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 396         if self._toStore("OMB"):
 397             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 398         if self._toStore("BMA"):
 399             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 400         if self._toStore("OMA"):
 401             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 402         if self._toStore("SimulatedObservationAtBackground"):
 403             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(Hm(Xb)) )
 404         if self._toStore("SimulatedObservationAtOptimum"):
 405             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 406         #
 407         self._post_run()
 408         return 0
 409
 410 # ==============================================================================
 411 if __name__ == "__main__":
 412     print('\n AUTODIAGNOSTIC\n')