src/daComposant/daAlgorithms/NonLinearLeastSquares.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
  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  = ["BMA", "OMA", "OMB", "CostFunctionJ", "CostFunctionJb", "CostFunctionJo", "CurrentState", "CurrentOptimum", "IndexOfOptimum", "Innovation", "InnovationAtCurrentState", "CostFunctionJAtCurrentOptimum", "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum", "SimulatedObservationAtCurrentOptimum"]
  76             )
  77         self.defineRequiredParameter( # Pas de type
  78             name     = "Bounds",
  79             message  = "Liste des valeurs de bornes",
  80             )
  81
  82     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
  83         self._pre_run(Parameters)
  84         #
  85         # Correction pour pallier a un bug de TNC sur le retour du Minimum
  86         if "Minimizer" in self._parameters and self._parameters["Minimizer"] == "TNC":
  87             self.setParameterValue("StoreInternalVariables",True)
  88         #
  89         # Opérateurs
  90         # ----------
  91         Hm = HO["Direct"].appliedTo
  92         Ha = HO["Adjoint"].appliedInXTo
  93         #
  94         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
  95         # ----------------------------------------------------
  96         if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
  97             HXb = Hm( Xb, HO["AppliedInX"]["HXb"])
  98         else:
  99             HXb = Hm( Xb )
 100         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 101         if Y.size != HXb.size:
 102             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))
 103         if max(Y.shape) != max(HXb.shape):
 104             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))
 105         #
 106         # Précalcul des inversions de B et R
 107         # ----------------------------------
 108         RI = R.getI()
 109         if self._parameters["Minimizer"] == "LM":
 110             RdemiI = R.choleskyI()
 111         #
 112         # Définition de la fonction-coût
 113         # ------------------------------
 114         def CostFunction(x):
 115             _X  = numpy.asmatrix(numpy.ravel( x )).T
 116             if self._parameters["StoreInternalVariables"] or \
 117                 "CurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 118                 "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 119                 self.StoredVariables["CurrentState"].store( _X )
 120             _HX = Hm( _X )
 121             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 122             _Innovation = Y - _HX
 123             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 124                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 125                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 126             if "InnovationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 127                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 128             #
 129             Jb  = 0.
 130             Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 131             J   = Jb + Jo
 132             #
 133             self.StoredVariables["CostFunctionJb"].store( Jb )
 134             self.StoredVariables["CostFunctionJo"].store( Jo )
 135             self.StoredVariables["CostFunctionJ" ].store( J )
 136             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 137                "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 138                "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 139                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 140                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 141             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 142                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 143             if "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 144                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 145             if "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 146                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 147             if "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 148                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 149                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 150                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 151             return J
 152         #
 153         def GradientOfCostFunction(x):
 154             _X      = numpy.asmatrix(numpy.ravel( x )).T
 155             _HX     = Hm( _X )
 156             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 157             GradJb  = 0.
 158             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 159             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 160             return GradJ.A1
 161         #
 162         def CostFunctionLM(x):
 163             _X  = numpy.asmatrix(numpy.ravel( x )).T
 164             _HX = Hm( _X )
 165             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 166             _Innovation = Y - _HX
 167             Jb  = 0.
 168             Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 169             J   = Jb + Jo
 170             if self._parameters["StoreInternalVariables"] or \
 171                 "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 172                 self.StoredVariables["CurrentState"].store( _X )
 173             self.StoredVariables["CostFunctionJb"].store( Jb )
 174             self.StoredVariables["CostFunctionJo"].store( Jo )
 175             self.StoredVariables["CostFunctionJ" ].store( J )
 176             #
 177             return numpy.ravel( RdemiI*_Innovation )
 178         #
 179         def GradientOfCostFunctionLM(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 - RdemiI*HO["Tangent"].asMatrix( _X )
 187         #
 188         # Point de démarrage de l'optimisation : Xini = Xb
 189         # ------------------------------------
 190         Xini = numpy.ravel(Xb)
 191         #
 192         # Minimisation de la fonctionnelle
 193         # --------------------------------
 194         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 195         #
 196         if self._parameters["Minimizer"] == "LBFGSB":
 197             Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 198                 func        = CostFunction,
 199                 x0          = Xini,
 200                 fprime      = GradientOfCostFunction,
 201                 args        = (),
 202                 bounds      = self._parameters["Bounds"],
 203                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 204                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 205                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 206                 iprint      = self._parameters["optiprint"],
 207                 )
 208             nfeval = Informations['funcalls']
 209             rc     = Informations['warnflag']
 210         elif self._parameters["Minimizer"] == "TNC":
 211             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 212                 func        = CostFunction,
 213                 x0          = Xini,
 214                 fprime      = GradientOfCostFunction,
 215                 args        = (),
 216                 bounds      = self._parameters["Bounds"],
 217                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 218                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 219                 ftol        = self._parameters["CostDecrementTolerance"],
 220                 messages    = self._parameters["optmessages"],
 221                 )
 222         elif self._parameters["Minimizer"] == "CG":
 223             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 224                 f           = CostFunction,
 225                 x0          = Xini,
 226                 fprime      = GradientOfCostFunction,
 227                 args        = (),
 228                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 229                 gtol        = self._parameters["GradientNormTolerance"],
 230                 disp        = self._parameters["optdisp"],
 231                 full_output = True,
 232                 )
 233         elif self._parameters["Minimizer"] == "NCG":
 234             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 235                 f           = CostFunction,
 236                 x0          = Xini,
 237                 fprime      = GradientOfCostFunction,
 238                 args        = (),
 239                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 240                 avextol     = self._parameters["CostDecrementTolerance"],
 241                 disp        = self._parameters["optdisp"],
 242                 full_output = True,
 243                 )
 244         elif self._parameters["Minimizer"] == "BFGS":
 245             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 246                 f           = CostFunction,
 247                 x0          = Xini,
 248                 fprime      = GradientOfCostFunction,
 249                 args        = (),
 250                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 251                 gtol        = self._parameters["GradientNormTolerance"],
 252                 disp        = self._parameters["optdisp"],
 253                 full_output = True,
 254                 )
 255         elif self._parameters["Minimizer"] == "LM":
 256             Minimum, cov_x, infodict, mesg, rc = scipy.optimize.leastsq(
 257                 func        = CostFunctionLM,
 258                 x0          = Xini,
 259                 Dfun        = GradientOfCostFunctionLM,
 260                 args        = (),
 261                 ftol        = self._parameters["CostDecrementTolerance"],
 262                 maxfev      = self._parameters["MaximumNumberOfSteps"],
 263                 gtol        = self._parameters["GradientNormTolerance"],
 264                 full_output = True,
 265                 )
 266             nfeval = infodict['nfev']
 267         else:
 268             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 269         #
 270         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 271         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 272         #
 273         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 274         # ----------------------------------------------------------------
 275         if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 276             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 277         #
 278         # Obtention de l'analyse
 279         # ----------------------
 280         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 281         #
 282         self.StoredVariables["Analysis"].store( Xa.A1 )
 283         #
 284         if "OMA"                           in self._parameters["StoreSupplementaryCalculations"] or \
 285            "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 286             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 287                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 288             elif "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 289                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 290             else:
 291                 HXa = Hm(Xa)
 292         #
 293         #
 294         # Calculs et/ou stockages supplémentaires
 295         # ---------------------------------------
 296         if "Innovation" in self._parameters["StoreSupplementaryCalculations"] or \
 297             "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 298             d  = Y - HXb
 299         if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 300             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 301         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 302             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 303         if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
 304             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 305         if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 306             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 307         if "SimulatedObservationAtBackground" in self._parameters["StoreSupplementaryCalculations"]:
 308             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
 309         if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 310             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 311         #
 312         self._post_run(HO)
 313         return 0
 314
 315 # ==============================================================================
 316 if __name__ == "__main__":
 317     print('\n AUTODIAGNOSTIC \n')