src/daComposant/daAlgorithms/NonLinearLeastSquares.py

   1 #-*-coding:iso-8859-1-*-
   2 #
   3 # Copyright (C) 2008-2016 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", "CurrentState", "CostFunctionJ", "CostFunctionJb", "CostFunctionJo", "Innovation", "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum"]
  76             )
  77         self.defineRequiredParameter( # Pas de type
  78             name     = "Bounds",
  79             message  = "Liste des valeurs de bornes",
  80             )
  81
  82     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
  83         self._pre_run()
  84         if logging.getLogger().level < logging.WARNING:
  85             self.__iprint, self.__disp = 1, 1
  86             self.__message = scipy.optimize.tnc.MSG_ALL
  87         else:
  88             self.__iprint, self.__disp = -1, 0
  89             self.__message = scipy.optimize.tnc.MSG_NONE
  90         #
  91         # Paramètres de pilotage
  92         # ----------------------
  93         self.setParameters(Parameters)
  94         #
  95         if self._parameters.has_key("Bounds") and (type(self._parameters["Bounds"]) is type([]) or type(self._parameters["Bounds"]) is type(())) and (len(self._parameters["Bounds"]) > 0):
  96             Bounds = self._parameters["Bounds"]
  97             logging.debug("%s Prise en compte des bornes effectuee"%(self._name,))
  98         else:
  99             Bounds = None
 100         #
 101         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 102         if self._parameters.has_key("Minimizer") == "TNC":
 103             self.setParameterValue("StoreInternalVariables",True)
 104         #
 105         # Opérateurs
 106         # ----------
 107         Hm = HO["Direct"].appliedTo
 108         Ha = HO["Adjoint"].appliedInXTo
 109         #
 110         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
 111         # ----------------------------------------------------
 112         if HO["AppliedToX"] is not None and HO["AppliedToX"].has_key("HXb"):
 113             HXb = Hm( Xb, HO["AppliedToX"]["HXb"])
 114         else:
 115             HXb = Hm( Xb )
 116         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 117         #
 118         # Calcul de l'innovation
 119         # ----------------------
 120         if Y.size != HXb.size:
 121             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))
 122         if max(Y.shape) != max(HXb.shape):
 123             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))
 124         d  = Y - HXb
 125         #
 126         # Précalcul des inversions de B et R
 127         # ----------------------------------
 128         RI = R.getI()
 129         if self._parameters["Minimizer"] == "LM":
 130             RdemiI = R.choleskyI()
 131         #
 132         # Définition de la fonction-coût
 133         # ------------------------------
 134         def CostFunction(x):
 135             _X  = numpy.asmatrix(numpy.ravel( x )).T
 136             if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 137                 self.StoredVariables["CurrentState"].store( _X )
 138             _HX = Hm( _X )
 139             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 140             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 141                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 142             Jb  = 0.
 143             Jo  = 0.5 * (Y - _HX).T * RI * (Y - _HX)
 144             J   = float( Jb ) + float( Jo )
 145             self.StoredVariables["CostFunctionJb"].store( Jb )
 146             self.StoredVariables["CostFunctionJo"].store( Jo )
 147             self.StoredVariables["CostFunctionJ" ].store( J )
 148             return J
 149         #
 150         def GradientOfCostFunction(x):
 151             _X      = numpy.asmatrix(numpy.ravel( x )).T
 152             _HX     = Hm( _X )
 153             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 154             GradJb  = 0.
 155             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 156             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 157             return GradJ.A1
 158         #
 159         def CostFunctionLM(x):
 160             _X  = numpy.asmatrix(numpy.ravel( x )).T
 161             _HX = Hm( _X )
 162             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 163             Jb  = 0.
 164             Jo  = 0.5 * (Y - _HX).T * RI * (Y - _HX)
 165             J   = float( Jb ) + float( Jo )
 166             if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 167                 self.StoredVariables["CurrentState"].store( _X )
 168             self.StoredVariables["CostFunctionJb"].store( Jb )
 169             self.StoredVariables["CostFunctionJo"].store( Jo )
 170             self.StoredVariables["CostFunctionJ" ].store( J )
 171             #
 172             return numpy.ravel( RdemiI*(Y - _HX) )
 173         #
 174         def GradientOfCostFunctionLM(x):
 175             _X      = numpy.asmatrix(numpy.ravel( x )).T
 176             _HX     = Hm( _X )
 177             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 178             GradJb  = 0.
 179             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 180             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 181             return - RdemiI*HO["Tangent"].asMatrix( _X )
 182         #
 183         # Point de démarrage de l'optimisation : Xini = Xb
 184         # ------------------------------------
 185         if type(Xb) is type(numpy.matrix([])):
 186             Xini = Xb.A1.tolist()
 187         else:
 188             Xini = list(Xb)
 189         #
 190         # Minimisation de la fonctionnelle
 191         # --------------------------------
 192         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 193         #
 194         if self._parameters["Minimizer"] == "LBFGSB":
 195             Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 196                 func        = CostFunction,
 197                 x0          = Xini,
 198                 fprime      = GradientOfCostFunction,
 199                 args        = (),
 200                 bounds      = Bounds,
 201                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 202                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 203                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 204                 iprint      = self.__iprint,
 205                 )
 206             nfeval = Informations['funcalls']
 207             rc     = Informations['warnflag']
 208         elif self._parameters["Minimizer"] == "TNC":
 209             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 210                 func        = CostFunction,
 211                 x0          = Xini,
 212                 fprime      = GradientOfCostFunction,
 213                 args        = (),
 214                 bounds      = Bounds,
 215                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 216                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 217                 ftol        = self._parameters["CostDecrementTolerance"],
 218                 messages    = self.__message,
 219                 )
 220         elif self._parameters["Minimizer"] == "CG":
 221             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 222                 f           = CostFunction,
 223                 x0          = Xini,
 224                 fprime      = GradientOfCostFunction,
 225                 args        = (),
 226                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 227                 gtol        = self._parameters["GradientNormTolerance"],
 228                 disp        = self.__disp,
 229                 full_output = True,
 230                 )
 231         elif self._parameters["Minimizer"] == "NCG":
 232             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 233                 f           = CostFunction,
 234                 x0          = Xini,
 235                 fprime      = GradientOfCostFunction,
 236                 args        = (),
 237                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 238                 avextol     = self._parameters["CostDecrementTolerance"],
 239                 disp        = self.__disp,
 240                 full_output = True,
 241                 )
 242         elif self._parameters["Minimizer"] == "BFGS":
 243             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 244                 f           = CostFunction,
 245                 x0          = Xini,
 246                 fprime      = GradientOfCostFunction,
 247                 args        = (),
 248                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 249                 gtol        = self._parameters["GradientNormTolerance"],
 250                 disp        = self.__disp,
 251                 full_output = True,
 252                 )
 253         elif self._parameters["Minimizer"] == "LM":
 254             Minimum, cov_x, infodict, mesg, rc = scipy.optimize.leastsq(
 255                 func        = CostFunctionLM,
 256                 x0          = Xini,
 257                 Dfun        = GradientOfCostFunctionLM,
 258                 args        = (),
 259                 ftol        = self._parameters["CostDecrementTolerance"],
 260                 maxfev      = self._parameters["MaximumNumberOfSteps"],
 261                 gtol        = self._parameters["GradientNormTolerance"],
 262                 full_output = True,
 263                 )
 264             nfeval = infodict['nfev']
 265         else:
 266             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 267         #
 268         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 269         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 270         #
 271         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 272         # ----------------------------------------------------------------
 273         if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 274             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 275         #
 276         # Obtention de l'analyse
 277         # ----------------------
 278         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 279         #
 280         self.StoredVariables["Analysis"].store( Xa.A1 )
 281         #
 282         if "OMA"                           in self._parameters["StoreSupplementaryCalculations"] or \
 283            "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 284             HXa = Hm(Xa)
 285         #
 286         #
 287         # Calculs et/ou stockages supplémentaires
 288         # ---------------------------------------
 289         if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 290             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 291         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 292             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 293         if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
 294             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 295         if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 296             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 297         if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 298             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 299         #
 300         self._post_run(HO)
 301         return 0
 302
 303 # ==============================================================================
 304 if __name__ == "__main__":
 305     print '\n AUTODIAGNOSTIC \n'