src/daComposant/daAlgorithms/NonLinearLeastSquares.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2019 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
 107     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 108         self._pre_run(Parameters, Xb, Y, R, B, Q)
 109         #
 110         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 111         if "Minimizer" in self._parameters and self._parameters["Minimizer"] == "TNC":
 112             self.setParameterValue("StoreInternalVariables",True)
 113         #
 114         # Opérateurs
 115         # ----------
 116         Hm = HO["Direct"].appliedTo
 117         Ha = HO["Adjoint"].appliedInXTo
 118         #
 119         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
 120         # ----------------------------------------------------
 121         if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
 122             HXb = Hm( Xb, HO["AppliedInX"]["HXb"] )
 123         else:
 124             HXb = Hm( Xb )
 125         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 126         if Y.size != HXb.size:
 127             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))
 128         if max(Y.shape) != max(HXb.shape):
 129             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))
 130         #
 131         # Précalcul des inversions de B et R
 132         # ----------------------------------
 133         RI = R.getI()
 134         if self._parameters["Minimizer"] == "LM":
 135             RdemiI = R.choleskyI()
 136         #
 137         # Définition de la fonction-coût
 138         # ------------------------------
 139         def CostFunction(x):
 140             _X  = numpy.asmatrix(numpy.ravel( x )).T
 141             if self._parameters["StoreInternalVariables"] or \
 142                 self._toStore("CurrentState") or \
 143                 self._toStore("CurrentOptimum"):
 144                 self.StoredVariables["CurrentState"].store( _X )
 145             _HX = Hm( _X )
 146             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 147             _Innovation = Y - _HX
 148             if self._toStore("SimulatedObservationAtCurrentState") or \
 149                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 150                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 151             if self._toStore("InnovationAtCurrentState"):
 152                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 153             #
 154             Jb  = 0.
 155             Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 156             J   = Jb + Jo
 157             #
 158             self.StoredVariables["CostFunctionJb"].store( Jb )
 159             self.StoredVariables["CostFunctionJo"].store( Jo )
 160             self.StoredVariables["CostFunctionJ" ].store( J )
 161             if self._toStore("IndexOfOptimum") or \
 162                 self._toStore("CurrentOptimum") or \
 163                 self._toStore("CostFunctionJAtCurrentOptimum") or \
 164                 self._toStore("CostFunctionJbAtCurrentOptimum") or \
 165                 self._toStore("CostFunctionJoAtCurrentOptimum") or \
 166                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 167                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 168             if self._toStore("IndexOfOptimum"):
 169                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 170             if self._toStore("CurrentOptimum"):
 171                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 172             if self._toStore("SimulatedObservationAtCurrentOptimum"):
 173                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 174             if self._toStore("CostFunctionJbAtCurrentOptimum"):
 175                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 176             if self._toStore("CostFunctionJoAtCurrentOptimum"):
 177                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 178             if self._toStore("CostFunctionJAtCurrentOptimum"):
 179                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 180             return J
 181         #
 182         def GradientOfCostFunction(x):
 183             _X      = numpy.asmatrix(numpy.ravel( x )).T
 184             _HX     = Hm( _X )
 185             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 186             GradJb  = 0.
 187             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 188             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 189             return GradJ.A1
 190         #
 191         def CostFunctionLM(x):
 192             _X  = numpy.asmatrix(numpy.ravel( x )).T
 193             _HX = Hm( _X )
 194             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 195             _Innovation = Y - _HX
 196             Jb  = 0.
 197             Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 198             J   = Jb + Jo
 199             if self._parameters["StoreInternalVariables"] or \
 200                 self._toStore("CurrentState"):
 201                 self.StoredVariables["CurrentState"].store( _X )
 202             self.StoredVariables["CostFunctionJb"].store( Jb )
 203             self.StoredVariables["CostFunctionJo"].store( Jo )
 204             self.StoredVariables["CostFunctionJ" ].store( J )
 205             #
 206             return numpy.ravel( RdemiI*_Innovation )
 207         #
 208         def GradientOfCostFunctionLM(x):
 209             _X      = numpy.asmatrix(numpy.ravel( x )).T
 210             _HX     = Hm( _X )
 211             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 212             GradJb  = 0.
 213             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 214             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 215             return - RdemiI*HO["Tangent"].asMatrix( _X )
 216         #
 217         # Point de démarrage de l'optimisation : Xini = Xb
 218         # ------------------------------------
 219         Xini = numpy.ravel(Xb)
 220         #
 221         # Minimisation de la fonctionnelle
 222         # --------------------------------
 223         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 224         #
 225         if self._parameters["Minimizer"] == "LBFGSB":
 226             # Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 227             if "0.19" <= scipy.version.version <= "1.1.0":
 228                 import lbfgsbhlt as optimiseur
 229             else:
 230                 import scipy.optimize as optimiseur
 231             Minimum, J_optimal, Informations = optimiseur.fmin_l_bfgs_b(
 232                 func        = CostFunction,
 233                 x0          = Xini,
 234                 fprime      = GradientOfCostFunction,
 235                 args        = (),
 236                 bounds      = self._parameters["Bounds"],
 237                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 238                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 239                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 240                 iprint      = self._parameters["optiprint"],
 241                 )
 242             nfeval = Informations['funcalls']
 243             rc     = Informations['warnflag']
 244         elif self._parameters["Minimizer"] == "TNC":
 245             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 246                 func        = CostFunction,
 247                 x0          = Xini,
 248                 fprime      = GradientOfCostFunction,
 249                 args        = (),
 250                 bounds      = self._parameters["Bounds"],
 251                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 252                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 253                 ftol        = self._parameters["CostDecrementTolerance"],
 254                 messages    = self._parameters["optmessages"],
 255                 )
 256         elif self._parameters["Minimizer"] == "CG":
 257             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 258                 f           = CostFunction,
 259                 x0          = Xini,
 260                 fprime      = GradientOfCostFunction,
 261                 args        = (),
 262                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 263                 gtol        = self._parameters["GradientNormTolerance"],
 264                 disp        = self._parameters["optdisp"],
 265                 full_output = True,
 266                 )
 267         elif self._parameters["Minimizer"] == "NCG":
 268             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 269                 f           = CostFunction,
 270                 x0          = Xini,
 271                 fprime      = GradientOfCostFunction,
 272                 args        = (),
 273                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 274                 avextol     = self._parameters["CostDecrementTolerance"],
 275                 disp        = self._parameters["optdisp"],
 276                 full_output = True,
 277                 )
 278         elif self._parameters["Minimizer"] == "BFGS":
 279             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 280                 f           = CostFunction,
 281                 x0          = Xini,
 282                 fprime      = GradientOfCostFunction,
 283                 args        = (),
 284                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 285                 gtol        = self._parameters["GradientNormTolerance"],
 286                 disp        = self._parameters["optdisp"],
 287                 full_output = True,
 288                 )
 289         elif self._parameters["Minimizer"] == "LM":
 290             Minimum, cov_x, infodict, mesg, rc = scipy.optimize.leastsq(
 291                 func        = CostFunctionLM,
 292                 x0          = Xini,
 293                 Dfun        = GradientOfCostFunctionLM,
 294                 args        = (),
 295                 ftol        = self._parameters["CostDecrementTolerance"],
 296                 maxfev      = self._parameters["MaximumNumberOfSteps"],
 297                 gtol        = self._parameters["GradientNormTolerance"],
 298                 full_output = True,
 299                 )
 300             nfeval = infodict['nfev']
 301         else:
 302             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 303         #
 304         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 305         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 306         #
 307         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 308         # ----------------------------------------------------------------
 309         if self._parameters["StoreInternalVariables"] or self._toStore("CurrentState"):
 310             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 311         #
 312         # Obtention de l'analyse
 313         # ----------------------
 314         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 315         #
 316         self.StoredVariables["Analysis"].store( Xa.A1 )
 317         #
 318         if self._toStore("OMA") or \
 319             self._toStore("SimulatedObservationAtOptimum"):
 320             if self._toStore("SimulatedObservationAtCurrentState"):
 321                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 322             elif self._toStore("SimulatedObservationAtCurrentOptimum"):
 323                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 324             else:
 325                 HXa = Hm( Xa )
 326         #
 327         #
 328         # Calculs et/ou stockages supplémentaires
 329         # ---------------------------------------
 330         if self._toStore("Innovation") or \
 331             self._toStore("OMB"):
 332             d  = Y - HXb
 333         if self._toStore("Innovation"):
 334             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 335         if self._toStore("BMA"):
 336             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 337         if self._toStore("OMA"):
 338             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 339         if self._toStore("OMB"):
 340             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 341         if self._toStore("SimulatedObservationAtBackground"):
 342             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
 343         if self._toStore("SimulatedObservationAtOptimum"):
 344             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 345         #
 346         self._post_run(HO)
 347         return 0
 348
 349 # ==============================================================================
 350 if __name__ == "__main__":
 351     print('\n AUTODIAGNOSTIC\n')