src/daComposant/daAlgorithms/3DVAR.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, "3DVAR")
  31         self.defineRequiredParameter(
  32             name     = "Minimizer",
  33             default  = "LBFGSB",
  34             typecast = str,
  35             message  = "Minimiseur utilisé",
  36             listval  = ["LBFGSB","TNC", "CG", "NCG", "BFGS"],
  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  = ["APosterioriCorrelations", "APosterioriCovariance", "APosterioriStandardDeviations", "APosterioriVariances", "BMA", "OMA", "OMB", "CurrentState", "CostFunctionJ", "CurrentOptimum", "IndexOfOptimum", "Innovation", "SigmaObs2", "MahalanobisConsistency", "SimulationQuantiles", "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum", "SimulatedObservationAtCurrentOptimum"]
  76             )
  77         self.defineRequiredParameter(
  78             name     = "Quantiles",
  79             default  = [],
  80             typecast = tuple,
  81             message  = "Liste des valeurs de quantiles",
  82             minval   = 0.,
  83             maxval   = 1.,
  84             )
  85         self.defineRequiredParameter(
  86             name     = "SetSeed",
  87             typecast = numpy.random.seed,
  88             message  = "Graine fixée pour le générateur aléatoire",
  89             )
  90         self.defineRequiredParameter(
  91             name     = "NumberOfSamplesForQuantiles",
  92             default  = 100,
  93             typecast = int,
  94             message  = "Nombre d'échantillons simulés pour le calcul des quantiles",
  95             minval   = 1,
  96             )
  97         self.defineRequiredParameter(
  98             name     = "SimulationForQuantiles",
  99             default  = "Linear",
 100             typecast = str,
 101             message  = "Type de simulation pour l'estimation des quantiles",
 102             listval  = ["Linear", "NonLinear"]
 103             )
 104         self.defineRequiredParameter( # Pas de type
 105             name     = "Bounds",
 106             message  = "Liste des valeurs de bornes",
 107             )
 108
 109     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 110         self._pre_run()
 111         if logging.getLogger().level < logging.WARNING:
 112             self.__iprint, self.__disp = 1, 1
 113             self.__message = scipy.optimize.tnc.MSG_ALL
 114         else:
 115             self.__iprint, self.__disp = -1, 0
 116             self.__message = scipy.optimize.tnc.MSG_NONE
 117         #
 118         # Paramètres de pilotage
 119         # ----------------------
 120         self.setParameters(Parameters)
 121         #
 122         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):
 123             Bounds = self._parameters["Bounds"]
 124             logging.debug("%s Prise en compte des bornes effectuee"%(self._name,))
 125         else:
 126             Bounds = None
 127         #
 128         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 129         if self._parameters.has_key("Minimizer") == "TNC":
 130             self.setParameterValue("StoreInternalVariables",True)
 131         #
 132         # Opérateurs
 133         # ----------
 134         Hm = HO["Direct"].appliedTo
 135         Ha = HO["Adjoint"].appliedInXTo
 136         #
 137         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
 138         # ----------------------------------------------------
 139         if HO["AppliedToX"] is not None and HO["AppliedToX"].has_key("HXb"):
 140             HXb = HO["AppliedToX"]["HXb"]
 141         else:
 142             HXb = Hm( Xb )
 143         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 144         #
 145         # Calcul de l'innovation
 146         # ----------------------
 147         if Y.size != HXb.size:
 148             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))
 149         if max(Y.shape) != max(HXb.shape):
 150             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))
 151         d  = Y - HXb
 152         #
 153         # Précalcul des inversions de B et R
 154         # ----------------------------------
 155         BI = B.getI()
 156         RI = R.getI()
 157         #
 158         # Définition de la fonction-coût
 159         # ------------------------------
 160         def CostFunction(x):
 161             _X  = numpy.asmatrix(numpy.ravel( x )).T
 162             if self._parameters["StoreInternalVariables"] or \
 163                 "CurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 164                 "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 165                 self.StoredVariables["CurrentState"].store( _X )
 166             _HX = Hm( _X )
 167             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 168             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 169                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 170                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 171             Jb  = 0.5 * (_X - Xb).T * BI * (_X - Xb)
 172             Jo  = 0.5 * (Y - _HX).T * RI * (Y - _HX)
 173             J   = float( Jb ) + float( Jo )
 174             self.StoredVariables["CostFunctionJb"].store( Jb )
 175             self.StoredVariables["CostFunctionJo"].store( Jo )
 176             self.StoredVariables["CostFunctionJ" ].store( J )
 177             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 178                "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 179                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 180                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 181             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 182                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 183             if "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 184                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 185             if "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 186                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 187             return J
 188         #
 189         def GradientOfCostFunction(x):
 190             _X      = numpy.asmatrix(numpy.ravel( x )).T
 191             _HX     = Hm( _X )
 192             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 193             GradJb  = BI * (_X - Xb)
 194             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 195             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 196             return GradJ.A1
 197         #
 198         # Point de démarrage de l'optimisation : Xini = Xb
 199         # ------------------------------------
 200         if type(Xb) is type(numpy.matrix([])):
 201             Xini = Xb.A1.tolist()
 202         else:
 203             Xini = list(Xb)
 204         #
 205         # Minimisation de la fonctionnelle
 206         # --------------------------------
 207         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 208         #
 209         if self._parameters["Minimizer"] == "LBFGSB":
 210             Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 211                 func        = CostFunction,
 212                 x0          = Xini,
 213                 fprime      = GradientOfCostFunction,
 214                 args        = (),
 215                 bounds      = Bounds,
 216                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 217                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 218                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 219                 iprint      = self.__iprint,
 220                 )
 221             nfeval = Informations['funcalls']
 222             rc     = Informations['warnflag']
 223         elif self._parameters["Minimizer"] == "TNC":
 224             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 225                 func        = CostFunction,
 226                 x0          = Xini,
 227                 fprime      = GradientOfCostFunction,
 228                 args        = (),
 229                 bounds      = Bounds,
 230                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 231                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 232                 ftol        = self._parameters["CostDecrementTolerance"],
 233                 messages    = self.__message,
 234                 )
 235         elif self._parameters["Minimizer"] == "CG":
 236             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 237                 f           = CostFunction,
 238                 x0          = Xini,
 239                 fprime      = GradientOfCostFunction,
 240                 args        = (),
 241                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 242                 gtol        = self._parameters["GradientNormTolerance"],
 243                 disp        = self.__disp,
 244                 full_output = True,
 245                 )
 246         elif self._parameters["Minimizer"] == "NCG":
 247             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 248                 f           = CostFunction,
 249                 x0          = Xini,
 250                 fprime      = GradientOfCostFunction,
 251                 args        = (),
 252                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 253                 avextol     = self._parameters["CostDecrementTolerance"],
 254                 disp        = self.__disp,
 255                 full_output = True,
 256                 )
 257         elif self._parameters["Minimizer"] == "BFGS":
 258             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 259                 f           = CostFunction,
 260                 x0          = Xini,
 261                 fprime      = GradientOfCostFunction,
 262                 args        = (),
 263                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 264                 gtol        = self._parameters["GradientNormTolerance"],
 265                 disp        = self.__disp,
 266                 full_output = True,
 267                 )
 268         else:
 269             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 270         #
 271         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 272         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 273         #
 274         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 275         # ----------------------------------------------------------------
 276         if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 277             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 278         #
 279         # Obtention de l'analyse
 280         # ----------------------
 281         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 282         #
 283         self.StoredVariables["Analysis"].store( Xa.A1 )
 284         #
 285         if "OMA"                           in self._parameters["StoreSupplementaryCalculations"] or \
 286            "SigmaObs2"                     in self._parameters["StoreSupplementaryCalculations"] or \
 287            "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 288            "SimulationQuantiles"           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         # Calcul de la covariance d'analyse
 297         # ---------------------------------
 298         if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"] or \
 299            "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
 300             HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 301             HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
 302             HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
 303             HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
 304             HessienneI = []
 305             nb = Xa.size
 306             for i in range(nb):
 307                 _ee    = numpy.matrix(numpy.zeros(nb)).T
 308                 _ee[i] = 1.
 309                 _HtEE  = numpy.dot(HtM,_ee)
 310                 _HtEE  = numpy.asmatrix(numpy.ravel( _HtEE )).T
 311                 HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
 312             HessienneI = numpy.matrix( HessienneI )
 313             A = HessienneI.I
 314             if min(A.shape) != max(A.shape):
 315                 raise ValueError("The %s a posteriori covariance matrix A is of shape %s, despites it has to be a squared matrix. There is an error in the observation operator, please check it."%(self._name,str(A.shape)))
 316             if (numpy.diag(A) < 0).any():
 317                 raise ValueError("The %s a posteriori covariance matrix A has at least one negative value on its diagonal. There is an error in the observation operator, please check it."%(self._name,))
 318             if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
 319                 try:
 320                     L = numpy.linalg.cholesky( A )
 321                 except:
 322                     raise ValueError("The %s a posteriori covariance matrix A is not symmetric positive-definite. Please check your a priori covariances and your observation operator."%(self._name,))
 323             self.StoredVariables["APosterioriCovariance"].store( A )
 324         #
 325         # Calculs et/ou stockages supplémentaires
 326         # ---------------------------------------
 327         if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 328             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 329         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 330             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 331         if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
 332             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 333         if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 334             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 335         if "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"]:
 336             TraceR = R.trace(Y.size)
 337             self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
 338         if "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
 339             self.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
 340         if "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
 341             Qtls = map(float, self._parameters["Quantiles"])
 342             nech = self._parameters["NumberOfSamplesForQuantiles"]
 343             HXa  = numpy.matrix(numpy.ravel( HXa )).T
 344             YfQ  = None
 345             for i in range(nech):
 346                 if self._parameters["SimulationForQuantiles"] == "Linear":
 347                     dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
 348                     dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
 349                     Yr = HXa + dYr
 350                 elif self._parameters["SimulationForQuantiles"] == "NonLinear":
 351                     Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
 352                     Yr = numpy.matrix(numpy.ravel( Hm( Xr ) )).T
 353                 if YfQ is None:
 354                     YfQ = Yr
 355                 else:
 356                     YfQ = numpy.hstack((YfQ,Yr))
 357             YfQ.sort(axis=-1)
 358             YQ = None
 359             for quantile in Qtls:
 360                 if not (0. <= quantile <= 1.): continue
 361                 indice = int(nech * quantile - 1./nech)
 362                 if YQ is None: YQ = YfQ[:,indice]
 363                 else:          YQ = numpy.hstack((YQ,YfQ[:,indice]))
 364             self.StoredVariables["SimulationQuantiles"].store( YQ )
 365         if "SimulatedObservationAtBackground" in self._parameters["StoreSupplementaryCalculations"]:
 366             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
 367         if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 368             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 369         #
 370         self._post_run(HO)
 371         return 0
 372
 373 # ==============================================================================
 374 if __name__ == "__main__":
 375     print '\n AUTODIAGNOSTIC \n'