src/daComposant/daAlgorithms/DerivativeFreeOptimization.py

   1 #-*-coding:iso-8859-1-*-
   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 de 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()
  95         if logging.getLogger().level < logging.WARNING:
  96             self.__disp = 1
  97         else:
  98             self.__disp = 0
  99         #
 100         # Paramètres de pilotage
 101         # ----------------------
 102         self.setParameters(Parameters)
 103         #
 104         if self._parameters.has_key("Bounds") and (type(self._parameters["Bounds"]) is type([]) or type(self._parameters["Bounds"]) is type(())) and (len(self._parameters["Bounds"]) > 0):
 105             Bounds = self._parameters["Bounds"]
 106             logging.debug("%s Prise en compte des bornes effectuee"%(self._name,))
 107         else:
 108             Bounds = None
 109         #
 110         # Opérateurs
 111         # ----------
 112         Hm = HO["Direct"].appliedTo
 113         #
 114         # Précalcul des inversions de B et R
 115         # ----------------------------------
 116         BI = B.getI()
 117         RI = R.getI()
 118         #
 119         # Définition de la fonction-coût
 120         # ------------------------------
 121         def CostFunction(x, QualityMeasure="AugmentedWeightedLeastSquares"):
 122             _X  = numpy.asmatrix(numpy.ravel( x )).T
 123             self.StoredVariables["CurrentState"].store( _X )
 124             _HX = Hm( _X )
 125             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 126             _Innovation = Y - _HX
 127             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 128                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 129                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 130             if "InnovationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 131                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 132             #
 133             if QualityMeasure in ["AugmentedWeightedLeastSquares","AWLS","DA"]:
 134                 if BI is None or RI is None:
 135                     raise ValueError("Background and Observation error covariance matrix has to be properly defined!")
 136                 Jb  = 0.5 * (_X - Xb).T * BI * (_X - Xb)
 137                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 138             elif QualityMeasure in ["WeightedLeastSquares","WLS"]:
 139                 if RI is None:
 140                     raise ValueError("Observation error covariance matrix has to be properly defined!")
 141                 Jb  = 0.
 142                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 143             elif QualityMeasure in ["LeastSquares","LS","L2"]:
 144                 Jb  = 0.
 145                 Jo  = 0.5 * (_Innovation).T * (_Innovation)
 146             elif QualityMeasure in ["AbsoluteValue","L1"]:
 147                 Jb  = 0.
 148                 Jo  = numpy.sum( numpy.abs(_Innovation) )
 149             elif QualityMeasure in ["MaximumError","ME"]:
 150                 Jb  = 0.
 151                 Jo  = numpy.max( numpy.abs(_Innovation) )
 152             #
 153             J   = float( Jb ) + float( Jo )
 154             #
 155             self.StoredVariables["CostFunctionJb"].store( Jb )
 156             self.StoredVariables["CostFunctionJo"].store( Jo )
 157             self.StoredVariables["CostFunctionJ" ].store( J )
 158             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 159                "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 160                "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 161                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 162                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 163             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 164                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 165             if "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 166                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 167             if "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 168                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 169             if "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 170                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 171                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 172                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 173             return J
 174         #
 175         # Point de démarrage de l'optimisation : Xini = Xb
 176         # ------------------------------------
 177         Xini = numpy.ravel(Xb)
 178         #
 179         # Minimisation de la fonctionnelle
 180         # --------------------------------
 181         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 182         #
 183         if self._parameters["Minimizer"] == "POWELL":
 184             Minimum, J_optimal, direc, niter, nfeval, rc = scipy.optimize.fmin_powell(
 185                 func        = CostFunction,
 186                 x0          = Xini,
 187                 args        = (self._parameters["QualityCriterion"],),
 188                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 189                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 190                 xtol        = self._parameters["StateVariationTolerance"],
 191                 ftol        = self._parameters["CostDecrementTolerance"],
 192                 full_output = True,
 193                 disp        = self.__disp,
 194                 )
 195         elif self._parameters["Minimizer"] == "COBYLA" and not PlatformInfo.has_nlopt:
 196             def make_constraints(bounds):
 197                 constraints = []
 198                 for (i,(a,b)) in enumerate(bounds):
 199                     lower = lambda x: x[i] - a
 200                     upper = lambda x: b - x[i]
 201                     constraints = constraints + [lower] + [upper]
 202                 return constraints
 203             if Bounds is None:
 204                 raise ValueError("Bounds have to be given for all axes as a list of lower/upper pairs!")
 205             Minimum = scipy.optimize.fmin_cobyla(
 206                 func        = CostFunction,
 207                 x0          = Xini,
 208                 cons        = make_constraints( Bounds ),
 209                 args        = (self._parameters["QualityCriterion"],),
 210                 consargs    = (), # To avoid extra-args
 211                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 212                 rhobeg      = 1.0,
 213                 rhoend      = self._parameters["StateVariationTolerance"],
 214                 catol       = 2.*self._parameters["StateVariationTolerance"],
 215                 disp        = self.__disp,
 216                 )
 217         elif self._parameters["Minimizer"] == "COBYLA" and PlatformInfo.has_nlopt:
 218             import nlopt
 219             opt = nlopt.opt(nlopt.LN_COBYLA, Xini.size)
 220             def _f(_Xx, Grad):
 221                 # DFO, so no gradient
 222                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 223             opt.set_min_objective(_f)
 224             if Bounds is not None:
 225                 lub = numpy.array(Bounds).reshape((Xini.size,2))
 226                 lb = lub[:,0]
 227                 ub = lub[:,1]
 228                 if self.__disp:
 229                     print "%s: upper bounds %s"%(opt.get_algorithm_name(),ub)
 230                     print "%s: lower bounds %s"%(opt.get_algorithm_name(),lb)
 231                 opt.set_upper_bounds(ub)
 232                 opt.set_lower_bounds(lb)
 233             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 234             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 235             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 236             Minimum = opt.optimize( Xini )
 237             if self.__disp:
 238                 print "%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum)
 239                 print "%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value())
 240                 print "%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result())
 241         elif self._parameters["Minimizer"] == "SIMPLEX" and not PlatformInfo.has_nlopt:
 242             Minimum, J_optimal, niter, nfeval, rc = scipy.optimize.fmin(
 243                 func        = CostFunction,
 244                 x0          = Xini,
 245                 args        = (self._parameters["QualityCriterion"],),
 246                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 247                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 248                 xtol        = self._parameters["StateVariationTolerance"],
 249                 ftol        = self._parameters["CostDecrementTolerance"],
 250                 full_output = True,
 251                 disp        = self.__disp,
 252                 )
 253         elif self._parameters["Minimizer"] == "SIMPLEX" and PlatformInfo.has_nlopt:
 254             import nlopt
 255             opt = nlopt.opt(nlopt.LN_NELDERMEAD, Xini.size)
 256             def _f(_Xx, Grad):
 257                 # DFO, so no gradient
 258                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 259             opt.set_min_objective(_f)
 260             if Bounds is not None:
 261                 lub = numpy.array(Bounds).reshape((Xini.size,2))
 262                 lb = lub[:,0]
 263                 ub = lub[:,1]
 264                 if self.__disp:
 265                     print "%s: upper bounds %s"%(opt.get_algorithm_name(),ub)
 266                     print "%s: lower bounds %s"%(opt.get_algorithm_name(),lb)
 267                 opt.set_upper_bounds(ub)
 268                 opt.set_lower_bounds(lb)
 269             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 270             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 271             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 272             Minimum = opt.optimize( Xini )
 273             if self.__disp:
 274                 print "%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum)
 275                 print "%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value())
 276                 print "%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result())
 277         elif self._parameters["Minimizer"] == "BOBYQA" and PlatformInfo.has_nlopt:
 278             import nlopt
 279             opt = nlopt.opt(nlopt.LN_BOBYQA, Xini.size)
 280             def _f(_Xx, Grad):
 281                 # DFO, so no gradient
 282                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 283             opt.set_min_objective(_f)
 284             if Bounds is not None:
 285                 lub = numpy.array(Bounds).reshape((Xini.size,2))
 286                 lb = lub[:,0]
 287                 ub = lub[:,1]
 288                 if self.__disp:
 289                     print "%s: upper bounds %s"%(opt.get_algorithm_name(),ub)
 290                     print "%s: lower bounds %s"%(opt.get_algorithm_name(),lb)
 291                 opt.set_upper_bounds(ub)
 292                 opt.set_lower_bounds(lb)
 293             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 294             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 295             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 296             Minimum = opt.optimize( Xini )
 297             if self.__disp:
 298                 print "%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum)
 299                 print "%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value())
 300                 print "%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result())
 301         elif self._parameters["Minimizer"] == "NEWUOA" and PlatformInfo.has_nlopt:
 302             import nlopt
 303             opt = nlopt.opt(nlopt.LN_NEWUOA, Xini.size)
 304             def _f(_Xx, Grad):
 305                 # DFO, so no gradient
 306                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 307             opt.set_min_objective(_f)
 308             if Bounds is not None:
 309                 lub = numpy.array(Bounds).reshape((Xini.size,2))
 310                 lb = lub[:,0]
 311                 ub = lub[:,1]
 312                 if self.__disp:
 313                     print "%s: upper bounds %s"%(opt.get_algorithm_name(),ub)
 314                     print "%s: lower bounds %s"%(opt.get_algorithm_name(),lb)
 315                 opt.set_upper_bounds(ub)
 316                 opt.set_lower_bounds(lb)
 317             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 318             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 319             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 320             Minimum = opt.optimize( Xini )
 321             if self.__disp:
 322                 print "%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum)
 323                 print "%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value())
 324                 print "%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result())
 325         elif self._parameters["Minimizer"] == "SUBPLEX" and PlatformInfo.has_nlopt:
 326             import nlopt
 327             opt = nlopt.opt(nlopt.LN_SBPLX, Xini.size)
 328             def _f(_Xx, Grad):
 329                 # DFO, so no gradient
 330                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 331             opt.set_min_objective(_f)
 332             if Bounds is not None:
 333                 lub = numpy.array(Bounds).reshape((Xini.size,2))
 334                 lb = lub[:,0]
 335                 ub = lub[:,1]
 336                 if self.__disp:
 337                     print "%s: upper bounds %s"%(opt.get_algorithm_name(),ub)
 338                     print "%s: lower bounds %s"%(opt.get_algorithm_name(),lb)
 339                 opt.set_upper_bounds(ub)
 340                 opt.set_lower_bounds(lb)
 341             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 342             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 343             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 344             Minimum = opt.optimize( Xini )
 345             if self.__disp:
 346                 print "%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum)
 347                 print "%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value())
 348                 print "%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result())
 349         else:
 350             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 351         #
 352         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 353         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 354         Minimum  = self.StoredVariables["CurrentState"][IndexMin]
 355         #
 356         # Obtention de l'analyse
 357         # ----------------------
 358         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 359         #
 360         self.StoredVariables["Analysis"].store( Xa.A1 )
 361         #
 362         if "OMA"                           in self._parameters["StoreSupplementaryCalculations"] or \
 363            "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 364             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 365                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 366             elif "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 367                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 368             else:
 369                 HXa = Hm(Xa)
 370         #
 371         if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 372             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 373         if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 374             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 375         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 376             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 377         if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
 378             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 379         if "SimulatedObservationAtBackground" in self._parameters["StoreSupplementaryCalculations"]:
 380             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(Hm(Xb)) )
 381         if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 382             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 383         #
 384         self._post_run()
 385         return 0
 386
 387 # ==============================================================================
 388 if __name__ == "__main__":
 389     print '\n AUTODIAGNOSTIC \n'