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