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         self.requireInputArguments(
  93             mandatory= ("Xb", "Y", "HO", "R", "B" ),
  94             )
  95
  96     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
  97         self._pre_run(Parameters, Xb, Y, R, B, Q)
  98         #
  99         if not PlatformInfo.has_nlopt and not self._parameters["Minimizer"] in ["COBYLA", "POWELL", "SIMPLEX"]:
 100             logging.debug("%s Absence de NLopt, utilisation forcee du minimiseur SIMPLEX"%(self._name,))
 101             self._parameters["Minimizer"] = "SIMPLEX"
 102         #
 103         # Opérateurs
 104         # ----------
 105         Hm = HO["Direct"].appliedTo
 106         #
 107         # Précalcul des inversions de B et R
 108         # ----------------------------------
 109         BI = B.getI()
 110         RI = R.getI()
 111         #
 112         # Définition de la fonction-coût
 113         # ------------------------------
 114         def CostFunction(x, QualityMeasure="AugmentedWeightedLeastSquares"):
 115             _X  = numpy.asmatrix(numpy.ravel( x )).T
 116             self.StoredVariables["CurrentState"].store( _X )
 117             _HX = Hm( _X )
 118             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 119             _Innovation = Y - _HX
 120             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 121                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 122                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 123             if "InnovationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 124                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 125             #
 126             if QualityMeasure in ["AugmentedWeightedLeastSquares","AWLS","DA"]:
 127                 if BI is None or RI is None:
 128                     raise ValueError("Background and Observation error covariance matrix has to be properly defined!")
 129                 Jb  = 0.5 * (_X - Xb).T * BI * (_X - Xb)
 130                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 131             elif QualityMeasure in ["WeightedLeastSquares","WLS"]:
 132                 if RI is None:
 133                     raise ValueError("Observation error covariance matrix has to be properly defined!")
 134                 Jb  = 0.
 135                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 136             elif QualityMeasure in ["LeastSquares","LS","L2"]:
 137                 Jb  = 0.
 138                 Jo  = 0.5 * (_Innovation).T * (_Innovation)
 139             elif QualityMeasure in ["AbsoluteValue","L1"]:
 140                 Jb  = 0.
 141                 Jo  = numpy.sum( numpy.abs(_Innovation) )
 142             elif QualityMeasure in ["MaximumError","ME"]:
 143                 Jb  = 0.
 144                 Jo  = numpy.max( numpy.abs(_Innovation) )
 145             #
 146             J   = float( Jb ) + float( Jo )
 147             #
 148             self.StoredVariables["CostFunctionJb"].store( Jb )
 149             self.StoredVariables["CostFunctionJo"].store( Jo )
 150             self.StoredVariables["CostFunctionJ" ].store( J )
 151             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 152                "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 153                "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 154                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 155                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 156             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 157                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 158             if "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 159                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 160             if "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 161                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 162             if "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 163                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 164                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 165                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 166             return J
 167         #
 168         # Point de démarrage de l'optimisation : Xini = Xb
 169         # ------------------------------------
 170         Xini = numpy.ravel(Xb)
 171         if len(Xini) < 2 and self._parameters["Minimizer"] == "NEWUOA":
 172             raise ValueError("The minimizer %s can not be used when the optimisation state dimension is 1. Please choose another minimizer."%self._parameters["Minimizer"])
 173         #
 174         # Minimisation de la fonctionnelle
 175         # --------------------------------
 176         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 177         #
 178         if self._parameters["Minimizer"] == "POWELL":
 179             Minimum, J_optimal, direc, niter, nfeval, rc = scipy.optimize.fmin_powell(
 180                 func        = CostFunction,
 181                 x0          = Xini,
 182                 args        = (self._parameters["QualityCriterion"],),
 183                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 184                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 185                 xtol        = self._parameters["StateVariationTolerance"],
 186                 ftol        = self._parameters["CostDecrementTolerance"],
 187                 full_output = True,
 188                 disp        = self._parameters["optdisp"],
 189                 )
 190         elif self._parameters["Minimizer"] == "COBYLA" and not PlatformInfo.has_nlopt:
 191             def make_constraints(bounds):
 192                 constraints = []
 193                 for (i,(a,b)) in enumerate(bounds):
 194                     lower = lambda x: x[i] - a
 195                     upper = lambda x: b - x[i]
 196                     constraints = constraints + [lower] + [upper]
 197                 return constraints
 198             if self._parameters["Bounds"] is None:
 199                 raise ValueError("Bounds have to be given for all axes as a list of lower/upper pairs!")
 200             Minimum = scipy.optimize.fmin_cobyla(
 201                 func        = CostFunction,
 202                 x0          = Xini,
 203                 cons        = make_constraints( self._parameters["Bounds"] ),
 204                 args        = (self._parameters["QualityCriterion"],),
 205                 consargs    = (), # To avoid extra-args
 206                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 207                 rhobeg      = 1.0,
 208                 rhoend      = self._parameters["StateVariationTolerance"],
 209                 catol       = 2.*self._parameters["StateVariationTolerance"],
 210                 disp        = self._parameters["optdisp"],
 211                 )
 212         elif self._parameters["Minimizer"] == "COBYLA" and PlatformInfo.has_nlopt:
 213             import nlopt
 214             opt = nlopt.opt(nlopt.LN_COBYLA, Xini.size)
 215             def _f(_Xx, Grad):
 216                 # DFO, so no gradient
 217                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 218             opt.set_min_objective(_f)
 219             if self._parameters["Bounds"] is not None:
 220                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 221                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 222                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 223                 if self._parameters["optdisp"]:
 224                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 225                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 226                 opt.set_upper_bounds(ub)
 227                 opt.set_lower_bounds(lb)
 228             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 229             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 230             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 231             Minimum = opt.optimize( Xini )
 232             if self._parameters["optdisp"]:
 233                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 234                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 235                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 236         elif self._parameters["Minimizer"] == "SIMPLEX" and not PlatformInfo.has_nlopt:
 237             Minimum, J_optimal, niter, nfeval, rc = scipy.optimize.fmin(
 238                 func        = CostFunction,
 239                 x0          = Xini,
 240                 args        = (self._parameters["QualityCriterion"],),
 241                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 242                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 243                 xtol        = self._parameters["StateVariationTolerance"],
 244                 ftol        = self._parameters["CostDecrementTolerance"],
 245                 full_output = True,
 246                 disp        = self._parameters["optdisp"],
 247                 )
 248         elif self._parameters["Minimizer"] == "SIMPLEX" and PlatformInfo.has_nlopt:
 249             import nlopt
 250             opt = nlopt.opt(nlopt.LN_NELDERMEAD, Xini.size)
 251             def _f(_Xx, Grad):
 252                 # DFO, so no gradient
 253                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 254             opt.set_min_objective(_f)
 255             if self._parameters["Bounds"] is not None:
 256                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 257                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 258                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 259                 if self._parameters["optdisp"]:
 260                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 261                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 262                 opt.set_upper_bounds(ub)
 263                 opt.set_lower_bounds(lb)
 264             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 265             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 266             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 267             Minimum = opt.optimize( Xini )
 268             if self._parameters["optdisp"]:
 269                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 270                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 271                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 272         elif self._parameters["Minimizer"] == "BOBYQA" and PlatformInfo.has_nlopt:
 273             import nlopt
 274             opt = nlopt.opt(nlopt.LN_BOBYQA, 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"] == "NEWUOA" and PlatformInfo.has_nlopt:
 297             import nlopt
 298             opt = nlopt.opt(nlopt.LN_NEWUOA, 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"] == "SUBPLEX" and PlatformInfo.has_nlopt:
 321             import nlopt
 322             opt = nlopt.opt(nlopt.LN_SBPLX, 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         else:
 345             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 346         #
 347         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 348         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 349         Minimum  = self.StoredVariables["CurrentState"][IndexMin]
 350         #
 351         # Obtention de l'analyse
 352         # ----------------------
 353         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 354         #
 355         self.StoredVariables["Analysis"].store( Xa.A1 )
 356         #
 357         if "OMA"                           in self._parameters["StoreSupplementaryCalculations"] or \
 358            "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 359             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 360                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 361             elif "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 362                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 363             else:
 364                 HXa = Hm(Xa)
 365         #
 366         if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 367             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 368         if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 369             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 370         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 371             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 372         if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
 373             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 374         if "SimulatedObservationAtBackground" in self._parameters["StoreSupplementaryCalculations"]:
 375             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(Hm(Xb)) )
 376         if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 377             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 378         #
 379         self._post_run()
 380         return 0
 381
 382 # ==============================================================================
 383 if __name__ == "__main__":
 384     print('\n AUTODIAGNOSTIC \n')