src/daComposant/daAlgorithms/NonLinearLeastSquares.py

   1 #-*-coding:iso-8859-1-*-
   2 #
   3 #  Copyright (C) 2008-2015 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", "Innovation", "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum"]
  76             )
  77
  78     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
  79         self._pre_run()
  80         if logging.getLogger().level < logging.WARNING:
  81             self.__iprint, self.__disp = 1, 1
  82             self.__message = scipy.optimize.tnc.MSG_ALL
  83         else:
  84             self.__iprint, self.__disp = -1, 0
  85             self.__message = scipy.optimize.tnc.MSG_NONE
  86         #
  87         # Paramètres de pilotage
  88         # ----------------------
  89         self.setParameters(Parameters)
  90         #
  91         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):
  92             Bounds = self._parameters["Bounds"]
  93             logging.debug("%s Prise en compte des bornes effectuee"%(self._name,))
  94         else:
  95             Bounds = None
  96         #
  97         # Correction pour pallier a un bug de TNC sur le retour du Minimum
  98         if self._parameters.has_key("Minimizer") == "TNC":
  99             self.setParameterValue("StoreInternalVariables",True)
 100         #
 101         # Opérateurs
 102         # ----------
 103         Hm = HO["Direct"].appliedTo
 104         Ha = HO["Adjoint"].appliedInXTo
 105         #
 106         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
 107         # ----------------------------------------------------
 108         if HO["AppliedToX"] is not None and HO["AppliedToX"].has_key("HXb"):
 109             HXb = HO["AppliedToX"]["HXb"]
 110         else:
 111             HXb = Hm( Xb )
 112         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 113         #
 114         # Calcul de l'innovation
 115         # ----------------------
 116         if Y.size != HXb.size:
 117             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))
 118         if max(Y.shape) != max(HXb.shape):
 119             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))
 120         d  = Y - HXb
 121         #
 122         # Précalcul des inversions de B et R
 123         # ----------------------------------
 124         RI = R.getI()
 125         if self._parameters["Minimizer"] == "LM":
 126             RdemiI = R.choleskyI()
 127         #
 128         # Définition de la fonction-coût
 129         # ------------------------------
 130         def CostFunction(x):
 131             _X  = numpy.asmatrix(numpy.ravel( x )).T
 132             _HX = Hm( _X )
 133             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 134             Jb  = 0.
 135             Jo  = 0.5 * (Y - _HX).T * RI * (Y - _HX)
 136             J   = float( Jb ) + float( Jo )
 137             if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 138                 self.StoredVariables["CurrentState"].store( _X )
 139             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 140                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 141             self.StoredVariables["CostFunctionJb"].store( Jb )
 142             self.StoredVariables["CostFunctionJo"].store( Jo )
 143             self.StoredVariables["CostFunctionJ" ].store( J )
 144             return J
 145         #
 146         def GradientOfCostFunction(x):
 147             _X      = numpy.asmatrix(numpy.ravel( x )).T
 148             _HX     = Hm( _X )
 149             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 150             GradJb  = 0.
 151             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 152             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 153             return GradJ.A1
 154         #
 155         def CostFunctionLM(x):
 156             _X  = numpy.asmatrix(numpy.ravel( x )).T
 157             _HX = Hm( _X )
 158             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 159             Jb  = 0.
 160             Jo  = 0.5 * (Y - _HX).T * RI * (Y - _HX)
 161             J   = float( Jb ) + float( Jo )
 162             if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 163                 self.StoredVariables["CurrentState"].store( _X )
 164             self.StoredVariables["CostFunctionJb"].store( Jb )
 165             self.StoredVariables["CostFunctionJo"].store( Jo )
 166             self.StoredVariables["CostFunctionJ" ].store( J )
 167             #
 168             return numpy.ravel( RdemiI*(Y - _HX) )
 169         #
 170         def GradientOfCostFunctionLM(x):
 171             _X      = numpy.asmatrix(numpy.ravel( x )).T
 172             _HX     = Hm( _X )
 173             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 174             GradJb  = 0.
 175             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 176             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 177             return - RdemiI*HO["Tangent"].asMatrix( _X )
 178         #
 179         # Point de démarrage de l'optimisation : Xini = Xb
 180         # ------------------------------------
 181         if type(Xb) is type(numpy.matrix([])):
 182             Xini = Xb.A1.tolist()
 183         else:
 184             Xini = list(Xb)
 185         #
 186         # Minimisation de la fonctionnelle
 187         # --------------------------------
 188         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 189         #
 190         if self._parameters["Minimizer"] == "LBFGSB":
 191             Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 192                 func        = CostFunction,
 193                 x0          = Xini,
 194                 fprime      = GradientOfCostFunction,
 195                 args        = (),
 196                 bounds      = Bounds,
 197                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 198                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 199                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 200                 iprint      = self.__iprint,
 201                 )
 202             nfeval = Informations['funcalls']
 203             rc     = Informations['warnflag']
 204         elif self._parameters["Minimizer"] == "TNC":
 205             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 206                 func        = CostFunction,
 207                 x0          = Xini,
 208                 fprime      = GradientOfCostFunction,
 209                 args        = (),
 210                 bounds      = Bounds,
 211                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 212                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 213                 ftol        = self._parameters["CostDecrementTolerance"],
 214                 messages    = self.__message,
 215                 )
 216         elif self._parameters["Minimizer"] == "CG":
 217             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 218                 f           = CostFunction,
 219                 x0          = Xini,
 220                 fprime      = GradientOfCostFunction,
 221                 args        = (),
 222                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 223                 gtol        = self._parameters["GradientNormTolerance"],
 224                 disp        = self.__disp,
 225                 full_output = True,
 226                 )
 227         elif self._parameters["Minimizer"] == "NCG":
 228             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 229                 f           = CostFunction,
 230                 x0          = Xini,
 231                 fprime      = GradientOfCostFunction,
 232                 args        = (),
 233                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 234                 avextol     = self._parameters["CostDecrementTolerance"],
 235                 disp        = self.__disp,
 236                 full_output = True,
 237                 )
 238         elif self._parameters["Minimizer"] == "BFGS":
 239             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 240                 f           = CostFunction,
 241                 x0          = Xini,
 242                 fprime      = GradientOfCostFunction,
 243                 args        = (),
 244                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 245                 gtol        = self._parameters["GradientNormTolerance"],
 246                 disp        = self.__disp,
 247                 full_output = True,
 248                 )
 249         elif self._parameters["Minimizer"] == "LM":
 250             Minimum, cov_x, infodict, mesg, rc = scipy.optimize.leastsq(
 251                 func        = CostFunctionLM,
 252                 x0          = Xini,
 253                 Dfun        = GradientOfCostFunctionLM,
 254                 args        = (),
 255                 ftol        = self._parameters["CostDecrementTolerance"],
 256                 maxfev      = self._parameters["MaximumNumberOfSteps"],
 257                 gtol        = self._parameters["GradientNormTolerance"],
 258                 full_output = True,
 259                 )
 260             nfeval = infodict['nfev']
 261         else:
 262             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 263         #
 264         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 265         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 266         #
 267         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 268         # ----------------------------------------------------------------
 269         if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 270             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 271         #
 272         # Obtention de l'analyse
 273         # ----------------------
 274         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 275         #
 276         self.StoredVariables["Analysis"].store( Xa.A1 )
 277         #
 278         if "OMA"                           in self._parameters["StoreSupplementaryCalculations"] or \
 279            "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 280             HXa = Hm(Xa)
 281         #
 282         #
 283         # Calculs et/ou stockages supplémentaires
 284         # ---------------------------------------
 285         if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 286             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 287         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 288             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 289         if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
 290             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 291         if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 292             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 293         if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 294             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 295         #
 296         self._post_run(HO)
 297         return 0
 298
 299 # ==============================================================================
 300 if __name__ == "__main__":
 301     print '\n AUTODIAGNOSTIC \n'