src/daComposant/daAlgorithms/DerivativeFreeOptimization.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2018 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                 "BMA",
  88                 "CostFunctionJ",
  89                 "CostFunctionJb",
  90                 "CostFunctionJo",
  91                 "CostFunctionJAtCurrentOptimum",
  92                 "CostFunctionJbAtCurrentOptimum",
  93                 "CostFunctionJoAtCurrentOptimum",
  94                 "CurrentOptimum",
  95                 "CurrentState",
  96                 "IndexOfOptimum",
  97                 "Innovation",
  98                 "InnovationAtCurrentState",
  99                 "OMA",
 100                 "OMB",
 101                 "SimulatedObservationAtBackground",
 102                 "SimulatedObservationAtCurrentOptimum",
 103                 "SimulatedObservationAtCurrentState",
 104                 "SimulatedObservationAtOptimum",
 105                 ]
 106             )
 107         self.defineRequiredParameter( # Pas de type
 108             name     = "Bounds",
 109             message  = "Liste des valeurs de bornes",
 110             )
 111         self.requireInputArguments(
 112             mandatory= ("Xb", "Y", "HO", "R", "B" ),
 113             )
 114
 115     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 116         self._pre_run(Parameters, Xb, Y, R, B, Q)
 117         #
 118         if not PlatformInfo.has_nlopt and not self._parameters["Minimizer"] in ["COBYLA", "POWELL", "SIMPLEX"]:
 119             logging.warning("%s Minimization by SIMPLEX is forced because %s is unavailable (COBYLA, POWELL are also available)"%(self._name,self._parameters["Minimizer"]))
 120             self._parameters["Minimizer"] = "SIMPLEX"
 121         #
 122         # Opérateurs
 123         # ----------
 124         Hm = HO["Direct"].appliedTo
 125         #
 126         # Précalcul des inversions de B et R
 127         # ----------------------------------
 128         BI = B.getI()
 129         RI = R.getI()
 130         #
 131         # Définition de la fonction-coût
 132         # ------------------------------
 133         def CostFunction(x, QualityMeasure="AugmentedWeightedLeastSquares"):
 134             _X  = numpy.asmatrix(numpy.ravel( x )).T
 135             self.StoredVariables["CurrentState"].store( _X )
 136             _HX = Hm( _X )
 137             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 138             _Innovation = Y - _HX
 139             if self._toStore("SimulatedObservationAtCurrentState") or \
 140                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 141                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 142             if self._toStore("InnovationAtCurrentState"):
 143                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 144             #
 145             if QualityMeasure in ["AugmentedWeightedLeastSquares","AWLS","DA"]:
 146                 if BI is None or RI is None:
 147                     raise ValueError("Background and Observation error covariance matrix has to be properly defined!")
 148                 Jb  = 0.5 * (_X - Xb).T * BI * (_X - Xb)
 149                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 150             elif QualityMeasure in ["WeightedLeastSquares","WLS"]:
 151                 if RI is None:
 152                     raise ValueError("Observation error covariance matrix has to be properly defined!")
 153                 Jb  = 0.
 154                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 155             elif QualityMeasure in ["LeastSquares","LS","L2"]:
 156                 Jb  = 0.
 157                 Jo  = 0.5 * (_Innovation).T * (_Innovation)
 158             elif QualityMeasure in ["AbsoluteValue","L1"]:
 159                 Jb  = 0.
 160                 Jo  = numpy.sum( numpy.abs(_Innovation) )
 161             elif QualityMeasure in ["MaximumError","ME"]:
 162                 Jb  = 0.
 163                 Jo  = numpy.max( numpy.abs(_Innovation) )
 164             #
 165             J   = float( Jb ) + float( Jo )
 166             #
 167             self.StoredVariables["CostFunctionJb"].store( Jb )
 168             self.StoredVariables["CostFunctionJo"].store( Jo )
 169             self.StoredVariables["CostFunctionJ" ].store( J )
 170             if self._toStore("IndexOfOptimum") or \
 171                 self._toStore("CurrentOptimum") or \
 172                 self._toStore("CostFunctionJAtCurrentOptimum") or \
 173                 self._toStore("CostFunctionJbAtCurrentOptimum") or \
 174                 self._toStore("CostFunctionJoAtCurrentOptimum") or \
 175                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 176                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 177             if self._toStore("IndexOfOptimum"):
 178                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 179             if self._toStore("CurrentOptimum"):
 180                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 181             if self._toStore("SimulatedObservationAtCurrentOptimum"):
 182                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 183             if self._toStore("CostFunctionJAtCurrentOptimum"):
 184                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 185             if self._toStore("CostFunctionJbAtCurrentOptimum"):
 186                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 187             if self._toStore("CostFunctionJoAtCurrentOptimum"):
 188                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 189             return J
 190         #
 191         # Point de démarrage de l'optimisation : Xini = Xb
 192         # ------------------------------------
 193         Xini = numpy.ravel(Xb)
 194         if len(Xini) < 2 and self._parameters["Minimizer"] == "NEWUOA":
 195             raise ValueError("The minimizer %s can not be used when the optimisation state dimension is 1. Please choose another minimizer."%self._parameters["Minimizer"])
 196         #
 197         # Minimisation de la fonctionnelle
 198         # --------------------------------
 199         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 200         #
 201         if self._parameters["Minimizer"] == "POWELL":
 202             Minimum, J_optimal, direc, niter, nfeval, rc = scipy.optimize.fmin_powell(
 203                 func        = CostFunction,
 204                 x0          = Xini,
 205                 args        = (self._parameters["QualityCriterion"],),
 206                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 207                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 208                 xtol        = self._parameters["StateVariationTolerance"],
 209                 ftol        = self._parameters["CostDecrementTolerance"],
 210                 full_output = True,
 211                 disp        = self._parameters["optdisp"],
 212                 )
 213         elif self._parameters["Minimizer"] == "COBYLA" and not PlatformInfo.has_nlopt:
 214             def make_constraints(bounds):
 215                 constraints = []
 216                 for (i,(a,b)) in enumerate(bounds):
 217                     lower = lambda x: x[i] - a
 218                     upper = lambda x: b - x[i]
 219                     constraints = constraints + [lower] + [upper]
 220                 return constraints
 221             if self._parameters["Bounds"] is None:
 222                 raise ValueError("Bounds have to be given for all axes as a list of lower/upper pairs!")
 223             Minimum = scipy.optimize.fmin_cobyla(
 224                 func        = CostFunction,
 225                 x0          = Xini,
 226                 cons        = make_constraints( self._parameters["Bounds"] ),
 227                 args        = (self._parameters["QualityCriterion"],),
 228                 consargs    = (), # To avoid extra-args
 229                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 230                 rhobeg      = 1.0,
 231                 rhoend      = self._parameters["StateVariationTolerance"],
 232                 catol       = 2.*self._parameters["StateVariationTolerance"],
 233                 disp        = self._parameters["optdisp"],
 234                 )
 235         elif self._parameters["Minimizer"] == "COBYLA" and PlatformInfo.has_nlopt:
 236             import nlopt
 237             opt = nlopt.opt(nlopt.LN_COBYLA, Xini.size)
 238             def _f(_Xx, Grad):
 239                 # DFO, so no gradient
 240                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 241             opt.set_min_objective(_f)
 242             if self._parameters["Bounds"] is not None:
 243                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 244                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 245                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 246                 if self._parameters["optdisp"]:
 247                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 248                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 249                 opt.set_upper_bounds(ub)
 250                 opt.set_lower_bounds(lb)
 251             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 252             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 253             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 254             Minimum = opt.optimize( Xini )
 255             if self._parameters["optdisp"]:
 256                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 257                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 258                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 259         elif self._parameters["Minimizer"] == "SIMPLEX" and not PlatformInfo.has_nlopt:
 260             Minimum, J_optimal, niter, nfeval, rc = scipy.optimize.fmin(
 261                 func        = CostFunction,
 262                 x0          = Xini,
 263                 args        = (self._parameters["QualityCriterion"],),
 264                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 265                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 266                 xtol        = self._parameters["StateVariationTolerance"],
 267                 ftol        = self._parameters["CostDecrementTolerance"],
 268                 full_output = True,
 269                 disp        = self._parameters["optdisp"],
 270                 )
 271         elif self._parameters["Minimizer"] == "SIMPLEX" and PlatformInfo.has_nlopt:
 272             import nlopt
 273             opt = nlopt.opt(nlopt.LN_NELDERMEAD, Xini.size)
 274             def _f(_Xx, Grad):
 275                 # DFO, so no gradient
 276                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 277             opt.set_min_objective(_f)
 278             if self._parameters["Bounds"] is not None:
 279                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 280                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 281                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 282                 if self._parameters["optdisp"]:
 283                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 284                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 285                 opt.set_upper_bounds(ub)
 286                 opt.set_lower_bounds(lb)
 287             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 288             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 289             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 290             Minimum = opt.optimize( Xini )
 291             if self._parameters["optdisp"]:
 292                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 293                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 294                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 295         elif self._parameters["Minimizer"] == "BOBYQA" and PlatformInfo.has_nlopt:
 296             import nlopt
 297             opt = nlopt.opt(nlopt.LN_BOBYQA, Xini.size)
 298             def _f(_Xx, Grad):
 299                 # DFO, so no gradient
 300                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 301             opt.set_min_objective(_f)
 302             if self._parameters["Bounds"] is not None:
 303                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 304                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 305                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 306                 if self._parameters["optdisp"]:
 307                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 308                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 309                 opt.set_upper_bounds(ub)
 310                 opt.set_lower_bounds(lb)
 311             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 312             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 313             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 314             Minimum = opt.optimize( Xini )
 315             if self._parameters["optdisp"]:
 316                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 317                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 318                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 319         elif self._parameters["Minimizer"] == "NEWUOA" and PlatformInfo.has_nlopt:
 320             import nlopt
 321             opt = nlopt.opt(nlopt.LN_NEWUOA, Xini.size)
 322             def _f(_Xx, Grad):
 323                 # DFO, so no gradient
 324                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 325             opt.set_min_objective(_f)
 326             if self._parameters["Bounds"] is not None:
 327                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 328                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 329                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 330                 if self._parameters["optdisp"]:
 331                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 332                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 333                 opt.set_upper_bounds(ub)
 334                 opt.set_lower_bounds(lb)
 335             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 336             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 337             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 338             Minimum = opt.optimize( Xini )
 339             if self._parameters["optdisp"]:
 340                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 341                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 342                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 343         elif self._parameters["Minimizer"] == "SUBPLEX" and PlatformInfo.has_nlopt:
 344             import nlopt
 345             opt = nlopt.opt(nlopt.LN_SBPLX, Xini.size)
 346             def _f(_Xx, Grad):
 347                 # DFO, so no gradient
 348                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 349             opt.set_min_objective(_f)
 350             if self._parameters["Bounds"] is not None:
 351                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 352                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 353                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 354                 if self._parameters["optdisp"]:
 355                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 356                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 357                 opt.set_upper_bounds(ub)
 358                 opt.set_lower_bounds(lb)
 359             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 360             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 361             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 362             Minimum = opt.optimize( Xini )
 363             if self._parameters["optdisp"]:
 364                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 365                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 366                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 367         else:
 368             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 369         #
 370         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 371         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 372         Minimum  = self.StoredVariables["CurrentState"][IndexMin]
 373         #
 374         # Obtention de l'analyse
 375         # ----------------------
 376         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 377         #
 378         self.StoredVariables["Analysis"].store( Xa.A1 )
 379         #
 380         # Calculs et/ou stockages supplémentaires
 381         # ---------------------------------------
 382         if self._toStore("OMA" ) or \
 383             self._toStore("SimulatedObservationAtOptimum"):
 384             if self._toStore("SimulatedObservationAtCurrentState"):
 385                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 386             elif self._toStore("SimulatedObservationAtCurrentOptimum"):
 387                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 388             else:
 389                 HXa = Hm(Xa)
 390         if self._toStore("Innovation") or \
 391             self._toStore("OMB"):
 392             d  = Y - HXb
 393         if self._toStore("Innovation"):
 394             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 395         if self._toStore("OMB"):
 396             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 397         if self._toStore("BMA"):
 398             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 399         if self._toStore("OMA"):
 400             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 401         if self._toStore("SimulatedObservationAtBackground"):
 402             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(Hm(Xb)) )
 403         if self._toStore("SimulatedObservationAtOptimum"):
 404             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 405         #
 406         self._post_run()
 407         return 0
 408
 409 # ==============================================================================
 410 if __name__ == "__main__":
 411     print('\n AUTODIAGNOSTIC \n')