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