src/daComposant/daAlgorithms/3DVAR.py

   1 #-*-coding:iso-8859-1-*-
   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, "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(Parameters)
 111         #
 112         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 113         if self._parameters.has_key("Minimizer") == "TNC":
 114             self.setParameterValue("StoreInternalVariables",True)
 115         #
 116         # Opérateurs
 117         # ----------
 118         Hm = HO["Direct"].appliedTo
 119         Ha = HO["Adjoint"].appliedInXTo
 120         #
 121         # Utilisation éventuelle d'un vecteur H(Xb) précalculé (sans cout)
 122         # ----------------------------------------------------------------
 123         if HO["AppliedToX"] is not None and HO["AppliedToX"].has_key("HXb"):
 124             HXb = Hm( Xb, HO["AppliedToX"]["HXb"])
 125         else:
 126             HXb = Hm( Xb )
 127         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 128         if Y.size != HXb.size:
 129             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))
 130         if max(Y.shape) != max(HXb.shape):
 131             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))
 132         #
 133         # Précalcul des inversions de B et R
 134         # ----------------------------------
 135         BI = B.getI()
 136         RI = R.getI()
 137         #
 138         # Définition de la fonction-coût
 139         # ------------------------------
 140         def CostFunction(x):
 141             _X  = numpy.asmatrix(numpy.ravel( x )).T
 142             if self._parameters["StoreInternalVariables"] or \
 143                 "CurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 144                 "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 145                 self.StoredVariables["CurrentState"].store( _X )
 146             _HX = Hm( _X )
 147             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 148             _Innovation = Y - _HX
 149             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 150                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 151                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 152             if "InnovationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 153                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 154             #
 155             Jb  = float( 0.5 * (_X - Xb).T * BI * (_X - Xb) )
 156             Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 157             J   = Jb + Jo
 158             #
 159             self.StoredVariables["CostFunctionJb"].store( Jb )
 160             self.StoredVariables["CostFunctionJo"].store( Jo )
 161             self.StoredVariables["CostFunctionJ" ].store( J )
 162             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 163                "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 164                "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 165                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 166                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 167             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 168                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 169             if "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 170                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 171             if "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 172                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 173             if "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 174                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 175                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 176                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 177             return J
 178         #
 179         def GradientOfCostFunction(x):
 180             _X      = numpy.asmatrix(numpy.ravel( x )).T
 181             _HX     = Hm( _X )
 182             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 183             GradJb  = BI * (_X - Xb)
 184             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 185             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 186             return GradJ.A1
 187         #
 188         # Point de démarrage de l'optimisation : Xini = Xb
 189         # ------------------------------------
 190         Xini = numpy.ravel(Xb)
 191         #
 192         # Minimisation de la fonctionnelle
 193         # --------------------------------
 194         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 195         #
 196         if self._parameters["Minimizer"] == "LBFGSB":
 197             Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 198                 func        = CostFunction,
 199                 x0          = Xini,
 200                 fprime      = GradientOfCostFunction,
 201                 args        = (),
 202                 bounds      = self._parameters["Bounds"],
 203                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 204                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 205                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 206                 iprint      = self._parameters["optiprint"],
 207                 )
 208             nfeval = Informations['funcalls']
 209             rc     = Informations['warnflag']
 210         elif self._parameters["Minimizer"] == "TNC":
 211             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 212                 func        = CostFunction,
 213                 x0          = Xini,
 214                 fprime      = GradientOfCostFunction,
 215                 args        = (),
 216                 bounds      = self._parameters["Bounds"],
 217                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 218                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 219                 ftol        = self._parameters["CostDecrementTolerance"],
 220                 messages    = self._parameters["optmessages"],
 221                 )
 222         elif self._parameters["Minimizer"] == "CG":
 223             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 224                 f           = CostFunction,
 225                 x0          = Xini,
 226                 fprime      = GradientOfCostFunction,
 227                 args        = (),
 228                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 229                 gtol        = self._parameters["GradientNormTolerance"],
 230                 disp        = self._parameters["optdisp"],
 231                 full_output = True,
 232                 )
 233         elif self._parameters["Minimizer"] == "NCG":
 234             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 235                 f           = CostFunction,
 236                 x0          = Xini,
 237                 fprime      = GradientOfCostFunction,
 238                 args        = (),
 239                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 240                 avextol     = self._parameters["CostDecrementTolerance"],
 241                 disp        = self._parameters["optdisp"],
 242                 full_output = True,
 243                 )
 244         elif self._parameters["Minimizer"] == "BFGS":
 245             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 246                 f           = CostFunction,
 247                 x0          = Xini,
 248                 fprime      = GradientOfCostFunction,
 249                 args        = (),
 250                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 251                 gtol        = self._parameters["GradientNormTolerance"],
 252                 disp        = self._parameters["optdisp"],
 253                 full_output = True,
 254                 )
 255         else:
 256             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 257         #
 258         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 259         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 260         #
 261         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 262         # ----------------------------------------------------------------
 263         if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 264             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 265         #
 266         # Obtention de l'analyse
 267         # ----------------------
 268         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 269         #
 270         self.StoredVariables["Analysis"].store( Xa.A1 )
 271         #
 272         if "OMA"                           in self._parameters["StoreSupplementaryCalculations"] or \
 273            "SigmaObs2"                     in self._parameters["StoreSupplementaryCalculations"] or \
 274            "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 275            "SimulationQuantiles"           in self._parameters["StoreSupplementaryCalculations"]:
 276             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 277                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 278             elif "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 279                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 280             else:
 281                 HXa = Hm(Xa)
 282         #
 283         # Calcul de la covariance d'analyse
 284         # ---------------------------------
 285         if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"] or \
 286            "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
 287             HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 288             HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
 289             HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
 290             HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
 291             HessienneI = []
 292             nb = Xa.size
 293             for i in range(nb):
 294                 _ee    = numpy.matrix(numpy.zeros(nb)).T
 295                 _ee[i] = 1.
 296                 _HtEE  = numpy.dot(HtM,_ee)
 297                 _HtEE  = numpy.asmatrix(numpy.ravel( _HtEE )).T
 298                 HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
 299             HessienneI = numpy.matrix( HessienneI )
 300             A = HessienneI.I
 301             if min(A.shape) != max(A.shape):
 302                 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)))
 303             if (numpy.diag(A) < 0).any():
 304                 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,))
 305             if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
 306                 try:
 307                     L = numpy.linalg.cholesky( A )
 308                 except:
 309                     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,))
 310             self.StoredVariables["APosterioriCovariance"].store( A )
 311         #
 312         # Calculs et/ou stockages supplémentaires
 313         # ---------------------------------------
 314         if "Innovation" in self._parameters["StoreSupplementaryCalculations"] or \
 315             "OMB" in self._parameters["StoreSupplementaryCalculations"] or \
 316             "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"] or \
 317             "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
 318             d  = Y - HXb
 319         if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 320             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 321         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 322             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 323         if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
 324             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 325         if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 326             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 327         if "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"]:
 328             TraceR = R.trace(Y.size)
 329             self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
 330         if "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
 331             self.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
 332         if "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
 333             Qtls = map(float, self._parameters["Quantiles"])
 334             nech = self._parameters["NumberOfSamplesForQuantiles"]
 335             HXa  = numpy.matrix(numpy.ravel( HXa )).T
 336             YfQ  = None
 337             for i in range(nech):
 338                 if self._parameters["SimulationForQuantiles"] == "Linear":
 339                     dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
 340                     dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
 341                     Yr = HXa + dYr
 342                 elif self._parameters["SimulationForQuantiles"] == "NonLinear":
 343                     Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
 344                     Yr = numpy.matrix(numpy.ravel( Hm( Xr ) )).T
 345                 if YfQ is None:
 346                     YfQ = Yr
 347                 else:
 348                     YfQ = numpy.hstack((YfQ,Yr))
 349             YfQ.sort(axis=-1)
 350             YQ = None
 351             for quantile in Qtls:
 352                 if not (0. <= quantile <= 1.): continue
 353                 indice = int(nech * quantile - 1./nech)
 354                 if YQ is None: YQ = YfQ[:,indice]
 355                 else:          YQ = numpy.hstack((YQ,YfQ[:,indice]))
 356             self.StoredVariables["SimulationQuantiles"].store( YQ )
 357         if "SimulatedObservationAtBackground" in self._parameters["StoreSupplementaryCalculations"]:
 358             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
 359         if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 360             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 361         #
 362         self._post_run(HO)
 363         return 0
 364
 365 # ==============================================================================
 366 if __name__ == "__main__":
 367     print '\n AUTODIAGNOSTIC \n'