src/daComposant/daAlgorithms/NonLinearLeastSquares.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2021 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
  25 import numpy, scipy.optimize, scipy.version
  26
  27 # ==============================================================================
  28 class ElementaryAlgorithm(BasicObjects.Algorithm):
  29     def __init__(self):
  30         BasicObjects.Algorithm.__init__(self, "NONLINEARLEASTSQUARES")
  31         self.defineRequiredParameter(
  32             name     = "Minimizer",
  33             default  = "LBFGSB",
  34             typecast = str,
  35             message  = "Minimiseur utilisé",
  36             listval  = ["LBFGSB","TNC", "CG", "NCG", "BFGS", "LM"],
  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     = "CostDecrementTolerance",
  47             default  = 1.e-7,
  48             typecast = float,
  49             message  = "Diminution relative minimale du coût lors de l'arrêt",
  50             minval   = 0.,
  51             )
  52         self.defineRequiredParameter(
  53             name     = "ProjectedGradientTolerance",
  54             default  = -1,
  55             typecast = float,
  56             message  = "Maximum des composantes du gradient projeté lors de l'arrêt",
  57             minval   = -1,
  58             )
  59         self.defineRequiredParameter(
  60             name     = "GradientNormTolerance",
  61             default  = 1.e-05,
  62             typecast = float,
  63             message  = "Maximum des composantes du gradient lors de l'arrêt",
  64             minval   = 0.,
  65             )
  66         self.defineRequiredParameter(
  67             name     = "StoreInternalVariables",
  68             default  = False,
  69             typecast = bool,
  70             message  = "Stockage des variables internes ou intermédiaires du calcul",
  71             )
  72         self.defineRequiredParameter(
  73             name     = "StoreSupplementaryCalculations",
  74             default  = [],
  75             typecast = tuple,
  76             message  = "Liste de calculs supplémentaires à stocker et/ou effectuer",
  77             listval  = [
  78                 "Analysis",
  79                 "BMA",
  80                 "CostFunctionJ",
  81                 "CostFunctionJAtCurrentOptimum",
  82                 "CostFunctionJb",
  83                 "CostFunctionJbAtCurrentOptimum",
  84                 "CostFunctionJo",
  85                 "CostFunctionJoAtCurrentOptimum",
  86                 "CurrentIterationNumber",
  87                 "CurrentOptimum",
  88                 "CurrentState",
  89                 "IndexOfOptimum",
  90                 "Innovation",
  91                 "InnovationAtCurrentState",
  92                 "OMA",
  93                 "OMB",
  94                 "SimulatedObservationAtBackground",
  95                 "SimulatedObservationAtCurrentOptimum",
  96                 "SimulatedObservationAtCurrentState",
  97                 "SimulatedObservationAtOptimum",
  98                 ]
  99             )
 100         self.defineRequiredParameter( # Pas de type
 101             name     = "Bounds",
 102             message  = "Liste des valeurs de bornes",
 103             )
 104         self.defineRequiredParameter(
 105             name     = "InitializationPoint",
 106             typecast = numpy.ravel,
 107             message  = "État initial imposé (par défaut, c'est l'ébauche si None)",
 108             )
 109         self.requireInputArguments(
 110             mandatory= ("Xb", "Y", "HO", "R"),
 111             )
 112         self.setAttributes(tags=(
 113             "Optimization",
 114             "NonLinear",
 115             "Variational",
 116             ))
 117
 118     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 119         self._pre_run(Parameters, Xb, Y, U, HO, EM, CM, R, B, Q)
 120         #
 121         # Opérateurs
 122         # ----------
 123         Hm = HO["Direct"].appliedTo
 124         Ha = HO["Adjoint"].appliedInXTo
 125         #
 126         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
 127         # ----------------------------------------------------
 128         if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
 129             HXb = Hm( Xb, HO["AppliedInX"]["HXb"] )
 130         else:
 131             HXb = Hm( Xb )
 132         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 133         if Y.size != HXb.size:
 134             raise ValueError("The size %i of observations Y and %i of observed calculation H(X) are different, they have to be identical."%(Y.size,HXb.size))
 135         if max(Y.shape) != max(HXb.shape):
 136             raise ValueError("The shapes %s of observations Y and %s of observed calculation H(X) are different, they have to be identical."%(Y.shape,HXb.shape))
 137         #
 138         # Précalcul des inversions de B et R
 139         # ----------------------------------
 140         RI = R.getI()
 141         if self._parameters["Minimizer"] == "LM":
 142             RdemiI = R.choleskyI()
 143         #
 144         # Définition de la fonction-coût
 145         # ------------------------------
 146         def CostFunction(x):
 147             _X  = numpy.asmatrix(numpy.ravel( x )).T
 148             if self._parameters["StoreInternalVariables"] or \
 149                 self._toStore("CurrentState") or \
 150                 self._toStore("CurrentOptimum"):
 151                 self.StoredVariables["CurrentState"].store( _X )
 152             _HX = Hm( _X )
 153             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 154             _Innovation = Y - _HX
 155             if self._toStore("SimulatedObservationAtCurrentState") or \
 156                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 157                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 158             if self._toStore("InnovationAtCurrentState"):
 159                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 160             #
 161             Jb  = 0.
 162             Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 163             J   = Jb + Jo
 164             #
 165             self.StoredVariables["CurrentIterationNumber"].store( len(self.StoredVariables["CostFunctionJ"]) )
 166             self.StoredVariables["CostFunctionJb"].store( Jb )
 167             self.StoredVariables["CostFunctionJo"].store( Jo )
 168             self.StoredVariables["CostFunctionJ" ].store( J )
 169             if self._toStore("IndexOfOptimum") or \
 170                 self._toStore("CurrentOptimum") or \
 171                 self._toStore("CostFunctionJAtCurrentOptimum") or \
 172                 self._toStore("CostFunctionJbAtCurrentOptimum") or \
 173                 self._toStore("CostFunctionJoAtCurrentOptimum") or \
 174                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 175                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 176             if self._toStore("IndexOfOptimum"):
 177                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 178             if self._toStore("CurrentOptimum"):
 179                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 180             if self._toStore("SimulatedObservationAtCurrentOptimum"):
 181                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 182             if self._toStore("CostFunctionJbAtCurrentOptimum"):
 183                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 184             if self._toStore("CostFunctionJoAtCurrentOptimum"):
 185                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 186             if self._toStore("CostFunctionJAtCurrentOptimum"):
 187                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 188             return J
 189         #
 190         def GradientOfCostFunction(x):
 191             _X      = numpy.asmatrix(numpy.ravel( x )).T
 192             _HX     = Hm( _X )
 193             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 194             GradJb  = 0.
 195             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 196             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 197             return GradJ.A1
 198         #
 199         def CostFunctionLM(x):
 200             _X  = numpy.asmatrix(numpy.ravel( x )).T
 201             _HX = Hm( _X )
 202             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 203             _Innovation = Y - _HX
 204             Jb  = 0.
 205             Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 206             J   = Jb + Jo
 207             if self._parameters["StoreInternalVariables"] or \
 208                 self._toStore("CurrentState"):
 209                 self.StoredVariables["CurrentState"].store( _X )
 210             self.StoredVariables["CostFunctionJb"].store( Jb )
 211             self.StoredVariables["CostFunctionJo"].store( Jo )
 212             self.StoredVariables["CostFunctionJ" ].store( J )
 213             #
 214             return numpy.ravel( RdemiI*_Innovation )
 215         #
 216         def GradientOfCostFunctionLM(x):
 217             _X      = numpy.asmatrix(numpy.ravel( x )).T
 218             _HX     = Hm( _X )
 219             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 220             GradJb  = 0.
 221             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 222             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 223             return - RdemiI*HO["Tangent"].asMatrix( _X )
 224         #
 225         # Point de démarrage de l'optimisation : Xini = Xb
 226         # ------------------------------------
 227         Xini = self._parameters["InitializationPoint"]
 228         #
 229         # Minimisation de la fonctionnelle
 230         # --------------------------------
 231         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 232         #
 233         if self._parameters["Minimizer"] == "LBFGSB":
 234             # Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 235             if "0.19" <= scipy.version.version <= "1.1.0":
 236                 import lbfgsbhlt as optimiseur
 237             else:
 238                 import scipy.optimize as optimiseur
 239             Minimum, J_optimal, Informations = optimiseur.fmin_l_bfgs_b(
 240                 func        = CostFunction,
 241                 x0          = Xini,
 242                 fprime      = GradientOfCostFunction,
 243                 args        = (),
 244                 bounds      = self._parameters["Bounds"],
 245                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 246                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 247                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 248                 iprint      = self._parameters["optiprint"],
 249                 )
 250             nfeval = Informations['funcalls']
 251             rc     = Informations['warnflag']
 252         elif self._parameters["Minimizer"] == "TNC":
 253             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 254                 func        = CostFunction,
 255                 x0          = Xini,
 256                 fprime      = GradientOfCostFunction,
 257                 args        = (),
 258                 bounds      = self._parameters["Bounds"],
 259                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 260                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 261                 ftol        = self._parameters["CostDecrementTolerance"],
 262                 messages    = self._parameters["optmessages"],
 263                 )
 264         elif self._parameters["Minimizer"] == "CG":
 265             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 266                 f           = CostFunction,
 267                 x0          = Xini,
 268                 fprime      = GradientOfCostFunction,
 269                 args        = (),
 270                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 271                 gtol        = self._parameters["GradientNormTolerance"],
 272                 disp        = self._parameters["optdisp"],
 273                 full_output = True,
 274                 )
 275         elif self._parameters["Minimizer"] == "NCG":
 276             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 277                 f           = CostFunction,
 278                 x0          = Xini,
 279                 fprime      = GradientOfCostFunction,
 280                 args        = (),
 281                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 282                 avextol     = self._parameters["CostDecrementTolerance"],
 283                 disp        = self._parameters["optdisp"],
 284                 full_output = True,
 285                 )
 286         elif self._parameters["Minimizer"] == "BFGS":
 287             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 288                 f           = CostFunction,
 289                 x0          = Xini,
 290                 fprime      = GradientOfCostFunction,
 291                 args        = (),
 292                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 293                 gtol        = self._parameters["GradientNormTolerance"],
 294                 disp        = self._parameters["optdisp"],
 295                 full_output = True,
 296                 )
 297         elif self._parameters["Minimizer"] == "LM":
 298             Minimum, cov_x, infodict, mesg, rc = scipy.optimize.leastsq(
 299                 func        = CostFunctionLM,
 300                 x0          = Xini,
 301                 Dfun        = GradientOfCostFunctionLM,
 302                 args        = (),
 303                 ftol        = self._parameters["CostDecrementTolerance"],
 304                 maxfev      = self._parameters["MaximumNumberOfSteps"],
 305                 gtol        = self._parameters["GradientNormTolerance"],
 306                 full_output = True,
 307                 )
 308             nfeval = infodict['nfev']
 309         else:
 310             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 311         #
 312         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 313         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 314         #
 315         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 316         # ----------------------------------------------------------------
 317         if self._parameters["StoreInternalVariables"] or self._toStore("CurrentState"):
 318             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 319         #
 320         # Obtention de l'analyse
 321         # ----------------------
 322         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 323         #
 324         self.StoredVariables["Analysis"].store( Xa.A1 )
 325         #
 326         if self._toStore("OMA") or \
 327             self._toStore("SimulatedObservationAtOptimum"):
 328             if self._toStore("SimulatedObservationAtCurrentState"):
 329                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 330             elif self._toStore("SimulatedObservationAtCurrentOptimum"):
 331                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 332             else:
 333                 HXa = Hm( Xa )
 334         #
 335         #
 336         # Calculs et/ou stockages supplémentaires
 337         # ---------------------------------------
 338         if self._toStore("Innovation") or \
 339             self._toStore("OMB"):
 340             d  = Y - HXb
 341         if self._toStore("Innovation"):
 342             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 343         if self._toStore("BMA"):
 344             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 345         if self._toStore("OMA"):
 346             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 347         if self._toStore("OMB"):
 348             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 349         if self._toStore("SimulatedObservationAtBackground"):
 350             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
 351         if self._toStore("SimulatedObservationAtOptimum"):
 352             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 353         #
 354         self._post_run(HO)
 355         return 0
 356
 357 # ==============================================================================
 358 if __name__ == "__main__":
 359     print('\n AUTODIAGNOSTIC\n')