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