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