src/daComposant/daAlgorithms/NonLinearLeastSquares.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2020 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                 "CurrentOptimum",
  87                 "CurrentState",
  88                 "IndexOfOptimum",
  89                 "Innovation",
  90                 "InnovationAtCurrentState",
  91                 "OMA",
  92                 "OMB",
  93                 "SimulatedObservationAtBackground",
  94                 "SimulatedObservationAtCurrentOptimum",
  95                 "SimulatedObservationAtCurrentState",
  96                 "SimulatedObservationAtOptimum",
  97                 ]
  98             )
  99         self.defineRequiredParameter( # Pas de type
 100             name     = "Bounds",
 101             message  = "Liste des valeurs de bornes",
 102             )
 103         self.requireInputArguments(
 104             mandatory= ("Xb", "Y", "HO", "R"),
 105             )
 106         self.setAttributes(tags=(
 107             "Optimization",
 108             "NonLinear",
 109             "Variational",
 110             ))
 111
 112     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 113         self._pre_run(Parameters, Xb, Y, U, HO, EM, CM, R, B, Q)
 114         #
 115         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 116         if "Minimizer" in self._parameters and self._parameters["Minimizer"] == "TNC":
 117             self.setParameterValue("StoreInternalVariables",True)
 118         #
 119         # Opérateurs
 120         # ----------
 121         Hm = HO["Direct"].appliedTo
 122         Ha = HO["Adjoint"].appliedInXTo
 123         #
 124         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
 125         # ----------------------------------------------------
 126         if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
 127             HXb = Hm( Xb, HO["AppliedInX"]["HXb"] )
 128         else:
 129             HXb = Hm( Xb )
 130         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 131         if Y.size != HXb.size:
 132             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))
 133         if max(Y.shape) != max(HXb.shape):
 134             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))
 135         #
 136         # Précalcul des inversions de B et R
 137         # ----------------------------------
 138         RI = R.getI()
 139         if self._parameters["Minimizer"] == "LM":
 140             RdemiI = R.choleskyI()
 141         #
 142         # Définition de la fonction-coût
 143         # ------------------------------
 144         def CostFunction(x):
 145             _X  = numpy.asmatrix(numpy.ravel( x )).T
 146             if self._parameters["StoreInternalVariables"] or \
 147                 self._toStore("CurrentState") or \
 148                 self._toStore("CurrentOptimum"):
 149                 self.StoredVariables["CurrentState"].store( _X )
 150             _HX = Hm( _X )
 151             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 152             _Innovation = Y - _HX
 153             if self._toStore("SimulatedObservationAtCurrentState") or \
 154                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 155                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 156             if self._toStore("InnovationAtCurrentState"):
 157                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 158             #
 159             Jb  = 0.
 160             Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 161             J   = Jb + Jo
 162             #
 163             self.StoredVariables["CostFunctionJb"].store( Jb )
 164             self.StoredVariables["CostFunctionJo"].store( Jo )
 165             self.StoredVariables["CostFunctionJ" ].store( J )
 166             if self._toStore("IndexOfOptimum") or \
 167                 self._toStore("CurrentOptimum") or \
 168                 self._toStore("CostFunctionJAtCurrentOptimum") or \
 169                 self._toStore("CostFunctionJbAtCurrentOptimum") or \
 170                 self._toStore("CostFunctionJoAtCurrentOptimum") or \
 171                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 172                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 173             if self._toStore("IndexOfOptimum"):
 174                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 175             if self._toStore("CurrentOptimum"):
 176                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 177             if self._toStore("SimulatedObservationAtCurrentOptimum"):
 178                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 179             if self._toStore("CostFunctionJbAtCurrentOptimum"):
 180                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 181             if self._toStore("CostFunctionJoAtCurrentOptimum"):
 182                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 183             if self._toStore("CostFunctionJAtCurrentOptimum"):
 184                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 185             return J
 186         #
 187         def GradientOfCostFunction(x):
 188             _X      = numpy.asmatrix(numpy.ravel( x )).T
 189             _HX     = Hm( _X )
 190             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 191             GradJb  = 0.
 192             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 193             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 194             return GradJ.A1
 195         #
 196         def CostFunctionLM(x):
 197             _X  = numpy.asmatrix(numpy.ravel( x )).T
 198             _HX = Hm( _X )
 199             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 200             _Innovation = Y - _HX
 201             Jb  = 0.
 202             Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 203             J   = Jb + Jo
 204             if self._parameters["StoreInternalVariables"] or \
 205                 self._toStore("CurrentState"):
 206                 self.StoredVariables["CurrentState"].store( _X )
 207             self.StoredVariables["CostFunctionJb"].store( Jb )
 208             self.StoredVariables["CostFunctionJo"].store( Jo )
 209             self.StoredVariables["CostFunctionJ" ].store( J )
 210             #
 211             return numpy.ravel( RdemiI*_Innovation )
 212         #
 213         def GradientOfCostFunctionLM(x):
 214             _X      = numpy.asmatrix(numpy.ravel( x )).T
 215             _HX     = Hm( _X )
 216             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 217             GradJb  = 0.
 218             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 219             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 220             return - RdemiI*HO["Tangent"].asMatrix( _X )
 221         #
 222         # Point de démarrage de l'optimisation : Xini = Xb
 223         # ------------------------------------
 224         Xini = numpy.ravel(Xb)
 225         #
 226         # Minimisation de la fonctionnelle
 227         # --------------------------------
 228         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 229         #
 230         if self._parameters["Minimizer"] == "LBFGSB":
 231             # Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 232             if "0.19" <= scipy.version.version <= "1.1.0":
 233                 import lbfgsbhlt as optimiseur
 234             else:
 235                 import scipy.optimize as optimiseur
 236             Minimum, J_optimal, Informations = optimiseur.fmin_l_bfgs_b(
 237                 func        = CostFunction,
 238                 x0          = Xini,
 239                 fprime      = GradientOfCostFunction,
 240                 args        = (),
 241                 bounds      = self._parameters["Bounds"],
 242                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 243                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 244                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 245                 iprint      = self._parameters["optiprint"],
 246                 )
 247             nfeval = Informations['funcalls']
 248             rc     = Informations['warnflag']
 249         elif self._parameters["Minimizer"] == "TNC":
 250             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 251                 func        = CostFunction,
 252                 x0          = Xini,
 253                 fprime      = GradientOfCostFunction,
 254                 args        = (),
 255                 bounds      = self._parameters["Bounds"],
 256                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 257                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 258                 ftol        = self._parameters["CostDecrementTolerance"],
 259                 messages    = self._parameters["optmessages"],
 260                 )
 261         elif self._parameters["Minimizer"] == "CG":
 262             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 263                 f           = CostFunction,
 264                 x0          = Xini,
 265                 fprime      = GradientOfCostFunction,
 266                 args        = (),
 267                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 268                 gtol        = self._parameters["GradientNormTolerance"],
 269                 disp        = self._parameters["optdisp"],
 270                 full_output = True,
 271                 )
 272         elif self._parameters["Minimizer"] == "NCG":
 273             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 274                 f           = CostFunction,
 275                 x0          = Xini,
 276                 fprime      = GradientOfCostFunction,
 277                 args        = (),
 278                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 279                 avextol     = self._parameters["CostDecrementTolerance"],
 280                 disp        = self._parameters["optdisp"],
 281                 full_output = True,
 282                 )
 283         elif self._parameters["Minimizer"] == "BFGS":
 284             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 285                 f           = CostFunction,
 286                 x0          = Xini,
 287                 fprime      = GradientOfCostFunction,
 288                 args        = (),
 289                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 290                 gtol        = self._parameters["GradientNormTolerance"],
 291                 disp        = self._parameters["optdisp"],
 292                 full_output = True,
 293                 )
 294         elif self._parameters["Minimizer"] == "LM":
 295             Minimum, cov_x, infodict, mesg, rc = scipy.optimize.leastsq(
 296                 func        = CostFunctionLM,
 297                 x0          = Xini,
 298                 Dfun        = GradientOfCostFunctionLM,
 299                 args        = (),
 300                 ftol        = self._parameters["CostDecrementTolerance"],
 301                 maxfev      = self._parameters["MaximumNumberOfSteps"],
 302                 gtol        = self._parameters["GradientNormTolerance"],
 303                 full_output = True,
 304                 )
 305             nfeval = infodict['nfev']
 306         else:
 307             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 308         #
 309         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 310         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 311         #
 312         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 313         # ----------------------------------------------------------------
 314         if self._parameters["StoreInternalVariables"] or self._toStore("CurrentState"):
 315             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 316         #
 317         # Obtention de l'analyse
 318         # ----------------------
 319         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 320         #
 321         self.StoredVariables["Analysis"].store( Xa.A1 )
 322         #
 323         if self._toStore("OMA") or \
 324             self._toStore("SimulatedObservationAtOptimum"):
 325             if self._toStore("SimulatedObservationAtCurrentState"):
 326                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 327             elif self._toStore("SimulatedObservationAtCurrentOptimum"):
 328                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 329             else:
 330                 HXa = Hm( Xa )
 331         #
 332         #
 333         # Calculs et/ou stockages supplémentaires
 334         # ---------------------------------------
 335         if self._toStore("Innovation") or \
 336             self._toStore("OMB"):
 337             d  = Y - HXb
 338         if self._toStore("Innovation"):
 339             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 340         if self._toStore("BMA"):
 341             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 342         if self._toStore("OMA"):
 343             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 344         if self._toStore("OMB"):
 345             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 346         if self._toStore("SimulatedObservationAtBackground"):
 347             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
 348         if self._toStore("SimulatedObservationAtOptimum"):
 349             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 350         #
 351         self._post_run(HO)
 352         return 0
 353
 354 # ==============================================================================
 355 if __name__ == "__main__":
 356     print('\n AUTODIAGNOSTIC\n')