src/daComposant/daAlgorithms/3DVAR.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, "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", "CostFunctionJ", "CostFunctionJb", "CostFunctionJo", "CurrentState", "CurrentOptimum", "IndexOfOptimum", "Innovation", "InnovationAtCurrentState", "CostFunctionJAtCurrentOptimum", "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 (sans cout)
 138         # ----------------------------------------------------------------
 139         if HO["AppliedToX"] is not None and HO["AppliedToX"].has_key("HXb"):
 140             HXb = Hm( Xb, HO["AppliedToX"]["HXb"])
 141         else:
 142             HXb = Hm( Xb )
 143         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 144         if Y.size != HXb.size:
 145             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))
 146         if max(Y.shape) != max(HXb.shape):
 147             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))
 148         #
 149         # Précalcul des inversions de B et R
 150         # ----------------------------------
 151         BI = B.getI()
 152         RI = R.getI()
 153         #
 154         # Définition de la fonction-coût
 155         # ------------------------------
 156         def CostFunction(x):
 157             _X  = numpy.asmatrix(numpy.ravel( x )).T
 158             if self._parameters["StoreInternalVariables"] or \
 159                 "CurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 160                 "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 161                 self.StoredVariables["CurrentState"].store( _X )
 162             _HX = Hm( _X )
 163             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 164             _Innovation = Y - _HX
 165             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 166                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 167                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 168             if "InnovationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 169                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 170             #
 171             Jb  = 0.5 * (_X - Xb).T * BI * (_X - Xb)
 172             Jo  = 0.5 * _Innovation.T * RI * _Innovation
 173             J   = float( Jb ) + float( Jo )
 174             #
 175             self.StoredVariables["CostFunctionJb"].store( Jb )
 176             self.StoredVariables["CostFunctionJo"].store( Jo )
 177             self.StoredVariables["CostFunctionJ" ].store( J )
 178             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 179                "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 180                "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 181                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 182                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 183             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 184                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 185             if "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 186                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 187             if "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 188                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 189             if "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 190                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 191                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 192                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 193             return J
 194         #
 195         def GradientOfCostFunction(x):
 196             _X      = numpy.asmatrix(numpy.ravel( x )).T
 197             _HX     = Hm( _X )
 198             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 199             GradJb  = BI * (_X - Xb)
 200             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 201             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 202             return GradJ.A1
 203         #
 204         # Point de démarrage de l'optimisation : Xini = Xb
 205         # ------------------------------------
 206         Xini = numpy.ravel(Xb)
 207         #
 208         # Minimisation de la fonctionnelle
 209         # --------------------------------
 210         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 211         #
 212         if self._parameters["Minimizer"] == "LBFGSB":
 213             Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 214                 func        = CostFunction,
 215                 x0          = Xini,
 216                 fprime      = GradientOfCostFunction,
 217                 args        = (),
 218                 bounds      = Bounds,
 219                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 220                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 221                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 222                 iprint      = self.__iprint,
 223                 )
 224             nfeval = Informations['funcalls']
 225             rc     = Informations['warnflag']
 226         elif self._parameters["Minimizer"] == "TNC":
 227             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 228                 func        = CostFunction,
 229                 x0          = Xini,
 230                 fprime      = GradientOfCostFunction,
 231                 args        = (),
 232                 bounds      = Bounds,
 233                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 234                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 235                 ftol        = self._parameters["CostDecrementTolerance"],
 236                 messages    = self.__message,
 237                 )
 238         elif self._parameters["Minimizer"] == "CG":
 239             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 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"] == "NCG":
 250             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 251                 f           = CostFunction,
 252                 x0          = Xini,
 253                 fprime      = GradientOfCostFunction,
 254                 args        = (),
 255                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 256                 avextol     = self._parameters["CostDecrementTolerance"],
 257                 disp        = self.__disp,
 258                 full_output = True,
 259                 )
 260         elif self._parameters["Minimizer"] == "BFGS":
 261             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 262                 f           = CostFunction,
 263                 x0          = Xini,
 264                 fprime      = GradientOfCostFunction,
 265                 args        = (),
 266                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 267                 gtol        = self._parameters["GradientNormTolerance"],
 268                 disp        = self.__disp,
 269                 full_output = True,
 270                 )
 271         else:
 272             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 273         #
 274         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 275         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 276         #
 277         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 278         # ----------------------------------------------------------------
 279         if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 280             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 281         #
 282         # Obtention de l'analyse
 283         # ----------------------
 284         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 285         #
 286         self.StoredVariables["Analysis"].store( Xa.A1 )
 287         #
 288         if "OMA"                           in self._parameters["StoreSupplementaryCalculations"] or \
 289            "SigmaObs2"                     in self._parameters["StoreSupplementaryCalculations"] or \
 290            "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 291            "SimulationQuantiles"           in self._parameters["StoreSupplementaryCalculations"]:
 292             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 293                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 294             elif "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 295                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 296             else:
 297                 HXa = Hm(Xa)
 298         #
 299         # Calcul de la covariance d'analyse
 300         # ---------------------------------
 301         if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"] or \
 302            "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
 303             HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 304             HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
 305             HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
 306             HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
 307             HessienneI = []
 308             nb = Xa.size
 309             for i in range(nb):
 310                 _ee    = numpy.matrix(numpy.zeros(nb)).T
 311                 _ee[i] = 1.
 312                 _HtEE  = numpy.dot(HtM,_ee)
 313                 _HtEE  = numpy.asmatrix(numpy.ravel( _HtEE )).T
 314                 HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
 315             HessienneI = numpy.matrix( HessienneI )
 316             A = HessienneI.I
 317             if min(A.shape) != max(A.shape):
 318                 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)))
 319             if (numpy.diag(A) < 0).any():
 320                 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,))
 321             if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
 322                 try:
 323                     L = numpy.linalg.cholesky( A )
 324                 except:
 325                     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,))
 326             self.StoredVariables["APosterioriCovariance"].store( A )
 327         #
 328         # Calculs et/ou stockages supplémentaires
 329         # ---------------------------------------
 330         if "Innovation" in self._parameters["StoreSupplementaryCalculations"] or \
 331             "OMB" in self._parameters["StoreSupplementaryCalculations"] or \
 332             "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"] or \
 333             "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
 334             d  = Y - HXb
 335         if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 336             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 337         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 338             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 339         if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
 340             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 341         if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 342             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 343         if "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"]:
 344             TraceR = R.trace(Y.size)
 345             self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
 346         if "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
 347             self.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
 348         if "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
 349             Qtls = map(float, self._parameters["Quantiles"])
 350             nech = self._parameters["NumberOfSamplesForQuantiles"]
 351             HXa  = numpy.matrix(numpy.ravel( HXa )).T
 352             YfQ  = None
 353             for i in range(nech):
 354                 if self._parameters["SimulationForQuantiles"] == "Linear":
 355                     dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
 356                     dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
 357                     Yr = HXa + dYr
 358                 elif self._parameters["SimulationForQuantiles"] == "NonLinear":
 359                     Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
 360                     Yr = numpy.matrix(numpy.ravel( Hm( Xr ) )).T
 361                 if YfQ is None:
 362                     YfQ = Yr
 363                 else:
 364                     YfQ = numpy.hstack((YfQ,Yr))
 365             YfQ.sort(axis=-1)
 366             YQ = None
 367             for quantile in Qtls:
 368                 if not (0. <= quantile <= 1.): continue
 369                 indice = int(nech * quantile - 1./nech)
 370                 if YQ is None: YQ = YfQ[:,indice]
 371                 else:          YQ = numpy.hstack((YQ,YfQ[:,indice]))
 372             self.StoredVariables["SimulationQuantiles"].store( YQ )
 373         if "SimulatedObservationAtBackground" in self._parameters["StoreSupplementaryCalculations"]:
 374             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
 375         if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 376             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 377         #
 378         self._post_run(HO)
 379         return 0
 380
 381 # ==============================================================================
 382 if __name__ == "__main__":
 383     print '\n AUTODIAGNOSTIC \n'