src/daComposant/daAlgorithms/DerivativeFreeOptimization.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2017 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  = ["CurrentState", "CostFunctionJ", "CostFunctionJb", "CostFunctionJo", "CostFunctionJAtCurrentOptimum", "CurrentOptimum", "IndexOfOptimum", "InnovationAtCurrentState", "BMA", "OMA", "OMB", "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentOptimum", "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum"]
  87             )
  88         self.defineRequiredParameter( # Pas de type
  89             name     = "Bounds",
  90             message  = "Liste des valeurs de bornes",
  91             )
  92
  93     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
  94         self._pre_run(Parameters)
  95         #
  96         if not PlatformInfo.has_nlopt and not self._parameters["Minimizer"] in ["COBYLA", "POWELL", "SIMPLEX"]:
  97             self._parameters["Minimizer"] = "SIMPLEX"
  98         #
  99         # Opérateurs
 100         # ----------
 101         Hm = HO["Direct"].appliedTo
 102         #
 103         # Précalcul des inversions de B et R
 104         # ----------------------------------
 105         BI = B.getI()
 106         RI = R.getI()
 107         #
 108         # Définition de la fonction-coût
 109         # ------------------------------
 110         def CostFunction(x, QualityMeasure="AugmentedWeightedLeastSquares"):
 111             _X  = numpy.asmatrix(numpy.ravel( x )).T
 112             self.StoredVariables["CurrentState"].store( _X )
 113             _HX = Hm( _X )
 114             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 115             _Innovation = Y - _HX
 116             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 117                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 118                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 119             if "InnovationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 120                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 121             #
 122             if QualityMeasure in ["AugmentedWeightedLeastSquares","AWLS","DA"]:
 123                 if BI is None or RI is None:
 124                     raise ValueError("Background and Observation error covariance matrix has to be properly defined!")
 125                 Jb  = 0.5 * (_X - Xb).T * BI * (_X - Xb)
 126                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 127             elif QualityMeasure in ["WeightedLeastSquares","WLS"]:
 128                 if RI is None:
 129                     raise ValueError("Observation error covariance matrix has to be properly defined!")
 130                 Jb  = 0.
 131                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 132             elif QualityMeasure in ["LeastSquares","LS","L2"]:
 133                 Jb  = 0.
 134                 Jo  = 0.5 * (_Innovation).T * (_Innovation)
 135             elif QualityMeasure in ["AbsoluteValue","L1"]:
 136                 Jb  = 0.
 137                 Jo  = numpy.sum( numpy.abs(_Innovation) )
 138             elif QualityMeasure in ["MaximumError","ME"]:
 139                 Jb  = 0.
 140                 Jo  = numpy.max( numpy.abs(_Innovation) )
 141             #
 142             J   = float( Jb ) + float( Jo )
 143             #
 144             self.StoredVariables["CostFunctionJb"].store( Jb )
 145             self.StoredVariables["CostFunctionJo"].store( Jo )
 146             self.StoredVariables["CostFunctionJ" ].store( J )
 147             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 148                "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 149                "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 150                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 151                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 152             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 153                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 154             if "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 155                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 156             if "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 157                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 158             if "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 159                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 160                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 161                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 162             return J
 163         #
 164         # Point de démarrage de l'optimisation : Xini = Xb
 165         # ------------------------------------
 166         Xini = numpy.ravel(Xb)
 167         if len(Xini) < 2 and self._parameters["Minimizer"] == "NEWUOA":
 168             raise ValueError("The minimizer %s can not be used when the optimisation state dimension is 1. Please choose another minimizer."%self._parameters["Minimizer"])
 169         #
 170         # Minimisation de la fonctionnelle
 171         # --------------------------------
 172         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 173         #
 174         if self._parameters["Minimizer"] == "POWELL":
 175             Minimum, J_optimal, direc, niter, nfeval, rc = scipy.optimize.fmin_powell(
 176                 func        = CostFunction,
 177                 x0          = Xini,
 178                 args        = (self._parameters["QualityCriterion"],),
 179                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 180                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 181                 xtol        = self._parameters["StateVariationTolerance"],
 182                 ftol        = self._parameters["CostDecrementTolerance"],
 183                 full_output = True,
 184                 disp        = self._parameters["optdisp"],
 185                 )
 186         elif self._parameters["Minimizer"] == "COBYLA" and not PlatformInfo.has_nlopt:
 187             def make_constraints(bounds):
 188                 constraints = []
 189                 for (i,(a,b)) in enumerate(bounds):
 190                     lower = lambda x: x[i] - a
 191                     upper = lambda x: b - x[i]
 192                     constraints = constraints + [lower] + [upper]
 193                 return constraints
 194             if self._parameters["Bounds"] is None:
 195                 raise ValueError("Bounds have to be given for all axes as a list of lower/upper pairs!")
 196             Minimum = scipy.optimize.fmin_cobyla(
 197                 func        = CostFunction,
 198                 x0          = Xini,
 199                 cons        = make_constraints( self._parameters["Bounds"] ),
 200                 args        = (self._parameters["QualityCriterion"],),
 201                 consargs    = (), # To avoid extra-args
 202                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 203                 rhobeg      = 1.0,
 204                 rhoend      = self._parameters["StateVariationTolerance"],
 205                 catol       = 2.*self._parameters["StateVariationTolerance"],
 206                 disp        = self._parameters["optdisp"],
 207                 )
 208         elif self._parameters["Minimizer"] == "COBYLA" and PlatformInfo.has_nlopt:
 209             import nlopt
 210             opt = nlopt.opt(nlopt.LN_COBYLA, Xini.size)
 211             def _f(_Xx, Grad):
 212                 # DFO, so no gradient
 213                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 214             opt.set_min_objective(_f)
 215             if self._parameters["Bounds"] is not None:
 216                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 217                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 218                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 219                 if self._parameters["optdisp"]:
 220                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 221                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 222                 opt.set_upper_bounds(ub)
 223                 opt.set_lower_bounds(lb)
 224             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 225             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 226             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 227             Minimum = opt.optimize( Xini )
 228             if self._parameters["optdisp"]:
 229                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 230                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 231                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 232         elif self._parameters["Minimizer"] == "SIMPLEX" and not PlatformInfo.has_nlopt:
 233             Minimum, J_optimal, niter, nfeval, rc = scipy.optimize.fmin(
 234                 func        = CostFunction,
 235                 x0          = Xini,
 236                 args        = (self._parameters["QualityCriterion"],),
 237                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 238                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 239                 xtol        = self._parameters["StateVariationTolerance"],
 240                 ftol        = self._parameters["CostDecrementTolerance"],
 241                 full_output = True,
 242                 disp        = self._parameters["optdisp"],
 243                 )
 244         elif self._parameters["Minimizer"] == "SIMPLEX" and PlatformInfo.has_nlopt:
 245             import nlopt
 246             opt = nlopt.opt(nlopt.LN_NELDERMEAD, Xini.size)
 247             def _f(_Xx, Grad):
 248                 # DFO, so no gradient
 249                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 250             opt.set_min_objective(_f)
 251             if self._parameters["Bounds"] is not None:
 252                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 253                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 254                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 255                 if self._parameters["optdisp"]:
 256                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 257                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 258                 opt.set_upper_bounds(ub)
 259                 opt.set_lower_bounds(lb)
 260             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 261             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 262             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 263             Minimum = opt.optimize( Xini )
 264             if self._parameters["optdisp"]:
 265                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 266                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 267                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 268         elif self._parameters["Minimizer"] == "BOBYQA" and PlatformInfo.has_nlopt:
 269             import nlopt
 270             opt = nlopt.opt(nlopt.LN_BOBYQA, Xini.size)
 271             def _f(_Xx, Grad):
 272                 # DFO, so no gradient
 273                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 274             opt.set_min_objective(_f)
 275             if self._parameters["Bounds"] is not None:
 276                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 277                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 278                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 279                 if self._parameters["optdisp"]:
 280                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 281                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 282                 opt.set_upper_bounds(ub)
 283                 opt.set_lower_bounds(lb)
 284             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 285             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 286             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 287             Minimum = opt.optimize( Xini )
 288             if self._parameters["optdisp"]:
 289                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 290                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 291                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 292         elif self._parameters["Minimizer"] == "NEWUOA" and PlatformInfo.has_nlopt:
 293             import nlopt
 294             opt = nlopt.opt(nlopt.LN_NEWUOA, Xini.size)
 295             def _f(_Xx, Grad):
 296                 # DFO, so no gradient
 297                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 298             opt.set_min_objective(_f)
 299             if self._parameters["Bounds"] is not None:
 300                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 301                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 302                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 303                 if self._parameters["optdisp"]:
 304                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 305                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 306                 opt.set_upper_bounds(ub)
 307                 opt.set_lower_bounds(lb)
 308             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 309             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 310             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 311             Minimum = opt.optimize( Xini )
 312             if self._parameters["optdisp"]:
 313                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 314                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 315                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 316         elif self._parameters["Minimizer"] == "SUBPLEX" and PlatformInfo.has_nlopt:
 317             import nlopt
 318             opt = nlopt.opt(nlopt.LN_SBPLX, Xini.size)
 319             def _f(_Xx, Grad):
 320                 # DFO, so no gradient
 321                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 322             opt.set_min_objective(_f)
 323             if self._parameters["Bounds"] is not None:
 324                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 325                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 326                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 327                 if self._parameters["optdisp"]:
 328                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 329                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 330                 opt.set_upper_bounds(ub)
 331                 opt.set_lower_bounds(lb)
 332             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 333             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 334             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 335             Minimum = opt.optimize( Xini )
 336             if self._parameters["optdisp"]:
 337                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 338                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 339                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 340         else:
 341             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 342         #
 343         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 344         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 345         Minimum  = self.StoredVariables["CurrentState"][IndexMin]
 346         #
 347         # Obtention de l'analyse
 348         # ----------------------
 349         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 350         #
 351         self.StoredVariables["Analysis"].store( Xa.A1 )
 352         #
 353         if "OMA"                           in self._parameters["StoreSupplementaryCalculations"] or \
 354            "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 355             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 356                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 357             elif "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 358                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 359             else:
 360                 HXa = Hm(Xa)
 361         #
 362         if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 363             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 364         if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 365             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 366         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 367             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 368         if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
 369             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 370         if "SimulatedObservationAtBackground" in self._parameters["StoreSupplementaryCalculations"]:
 371             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(Hm(Xb)) )
 372         if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 373             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 374         #
 375         self._post_run()
 376         return 0
 377
 378 # ==============================================================================
 379 if __name__ == "__main__":
 380     print('\n AUTODIAGNOSTIC \n')