src/daComposant/daAlgorithms/ExtendedBlue.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2020 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
  26
  27 # ==============================================================================
  28 class ElementaryAlgorithm(BasicObjects.Algorithm):
  29     def __init__(self):
  30         BasicObjects.Algorithm.__init__(self, "EXTENDEDBLUE")
  31         self.defineRequiredParameter(
  32             name     = "StoreInternalVariables",
  33             default  = False,
  34             typecast = bool,
  35             message  = "Stockage des variables internes ou intermédiaires du calcul",
  36             )
  37         self.defineRequiredParameter(
  38             name     = "StoreSupplementaryCalculations",
  39             default  = [],
  40             typecast = tuple,
  41             message  = "Liste de calculs supplémentaires à stocker et/ou effectuer",
  42             listval  = [
  43                 "Analysis",
  44                 "APosterioriCorrelations",
  45                 "APosterioriCovariance",
  46                 "APosterioriStandardDeviations",
  47                 "APosterioriVariances",
  48                 "BMA",
  49                 "CostFunctionJ",
  50                 "CostFunctionJAtCurrentOptimum",
  51                 "CostFunctionJb",
  52                 "CostFunctionJbAtCurrentOptimum",
  53                 "CostFunctionJo",
  54                 "CostFunctionJoAtCurrentOptimum",
  55                 "CurrentOptimum",
  56                 "CurrentState",
  57                 "Innovation",
  58                 "MahalanobisConsistency",
  59                 "OMA",
  60                 "OMB",
  61                 "SigmaBck2",
  62                 "SigmaObs2",
  63                 "SimulatedObservationAtBackground",
  64                 "SimulatedObservationAtCurrentOptimum",
  65                 "SimulatedObservationAtCurrentState",
  66                 "SimulatedObservationAtOptimum",
  67                 "SimulationQuantiles",
  68                 ]
  69             )
  70         self.defineRequiredParameter(
  71             name     = "Quantiles",
  72             default  = [],
  73             typecast = tuple,
  74             message  = "Liste des valeurs de quantiles",
  75             minval   = 0.,
  76             maxval   = 1.,
  77             )
  78         self.defineRequiredParameter(
  79             name     = "SetSeed",
  80             typecast = numpy.random.seed,
  81             message  = "Graine fixée pour le générateur aléatoire",
  82             )
  83         self.defineRequiredParameter(
  84             name     = "NumberOfSamplesForQuantiles",
  85             default  = 100,
  86             typecast = int,
  87             message  = "Nombre d'échantillons simulés pour le calcul des quantiles",
  88             minval   = 1,
  89             )
  90         self.defineRequiredParameter(
  91             name     = "SimulationForQuantiles",
  92             default  = "Linear",
  93             typecast = str,
  94             message  = "Type de simulation pour l'estimation des quantiles",
  95             listval  = ["Linear", "NonLinear"]
  96             )
  97         self.requireInputArguments(
  98             mandatory= ("Xb", "Y", "HO", "R", "B"),
  99             )
 100         self.setAttributes(tags=(
 101             "DataAssimilation",
 102             "NonLinear",
 103             "Filter",
 104             ))
 105
 106     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 107         self._pre_run(Parameters, Xb, Y, U, HO, EM, CM, R, B, Q)
 108         #
 109         Hm = HO["Tangent"].asMatrix(Xb)
 110         Hm = Hm.reshape(Y.size,Xb.size) # ADAO & check shape
 111         Ha = HO["Adjoint"].asMatrix(Xb)
 112         Ha = Ha.reshape(Xb.size,Y.size) # ADAO & check shape
 113         H  = HO["Direct"].appliedTo
 114         #
 115         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
 116         # ----------------------------------------------------
 117         if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
 118             HXb = H( Xb, HO["AppliedInX"]["HXb"])
 119         else:
 120             HXb = H( Xb )
 121         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 122         if Y.size != HXb.size:
 123             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))
 124         if max(Y.shape) != max(HXb.shape):
 125             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))
 126         #
 127         # Précalcul des inversions de B et R
 128         # ----------------------------------
 129         BI = B.getI()
 130         RI = R.getI()
 131         #
 132         # Calcul de l'innovation
 133         # ----------------------
 134         d  = Y - HXb
 135         #
 136         # Calcul de la matrice de gain et de l'analyse
 137         # --------------------------------------------
 138         if Y.size <= Xb.size:
 139             _A = R + numpy.dot(Hm, B * Ha)
 140             _u = numpy.linalg.solve( _A , d )
 141             Xa = Xb + B * Ha * _u
 142         else:
 143             _A = BI + numpy.dot(Ha, RI * Hm)
 144             _u = numpy.linalg.solve( _A , numpy.dot(Ha, RI * d) )
 145             Xa = Xb + _u
 146         self.StoredVariables["Analysis"].store( Xa.A1 )
 147         #
 148         # Calcul de la fonction coût
 149         # --------------------------
 150         if self._parameters["StoreInternalVariables"] or \
 151             self._toStore("CostFunctionJ")  or self._toStore("CostFunctionJAtCurrentOptimum") or \
 152             self._toStore("CostFunctionJb") or self._toStore("CostFunctionJbAtCurrentOptimum") or \
 153             self._toStore("CostFunctionJo") or self._toStore("CostFunctionJoAtCurrentOptimum") or \
 154             self._toStore("OMA") or \
 155             self._toStore("SigmaObs2") or \
 156             self._toStore("MahalanobisConsistency") or \
 157             self._toStore("SimulatedObservationAtCurrentOptimum") or \
 158             self._toStore("SimulatedObservationAtCurrentState") or \
 159             self._toStore("SimulatedObservationAtOptimum") or \
 160             self._toStore("SimulationQuantiles"):
 161             HXa  = numpy.matrix(numpy.ravel( H( Xa ) )).T
 162             oma = Y - HXa
 163         if self._parameters["StoreInternalVariables"] or \
 164             self._toStore("CostFunctionJ")  or self._toStore("CostFunctionJAtCurrentOptimum") or \
 165             self._toStore("CostFunctionJb") or self._toStore("CostFunctionJbAtCurrentOptimum") or \
 166             self._toStore("CostFunctionJo") or self._toStore("CostFunctionJoAtCurrentOptimum") or \
 167             self._toStore("MahalanobisConsistency"):
 168             Jb  = float( 0.5 * (Xa - Xb).T * BI * (Xa - Xb) )
 169             Jo  = float( 0.5 * oma.T * RI * oma )
 170             J   = Jb + Jo
 171             self.StoredVariables["CostFunctionJb"].store( Jb )
 172             self.StoredVariables["CostFunctionJo"].store( Jo )
 173             self.StoredVariables["CostFunctionJ" ].store( J )
 174             self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( Jb )
 175             self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( Jo )
 176             self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( J )
 177         #
 178         # Calcul de la covariance d'analyse
 179         # ---------------------------------
 180         if self._toStore("APosterioriCovariance") or \
 181             self._toStore("SimulationQuantiles"):
 182             if   (Y.size <= Xb.size): K  = B * Ha * (R + numpy.dot(Hm, B * Ha)).I
 183             elif (Y.size >  Xb.size): K = (BI + numpy.dot(Ha, RI * Hm)).I * Ha * RI
 184             A = B - K * Hm * B
 185             if min(A.shape) != max(A.shape):
 186                 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)))
 187             if (numpy.diag(A) < 0).any():
 188                 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,))
 189             if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
 190                 try:
 191                     L = numpy.linalg.cholesky( A )
 192                 except:
 193                     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,))
 194             self.StoredVariables["APosterioriCovariance"].store( A )
 195         #
 196         # Calculs et/ou stockages supplémentaires
 197         # ---------------------------------------
 198         if self._parameters["StoreInternalVariables"] or self._toStore("CurrentState"):
 199             self.StoredVariables["CurrentState"].store( numpy.ravel(Xa) )
 200         if self._toStore("CurrentOptimum"):
 201             self.StoredVariables["CurrentOptimum"].store( numpy.ravel(Xa) )
 202         if self._toStore("Innovation"):
 203             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 204         if self._toStore("BMA"):
 205             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 206         if self._toStore("OMA"):
 207             self.StoredVariables["OMA"].store( numpy.ravel(oma) )
 208         if self._toStore("OMB"):
 209             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 210         if self._toStore("SigmaObs2"):
 211             TraceR = R.trace(Y.size)
 212             self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(oma)).T)) ) / TraceR )
 213         if self._toStore("SigmaBck2"):
 214             self.StoredVariables["SigmaBck2"].store( float( (d.T * Hm * (Xa - Xb))/(Hm * B * Hm.T).trace() ) )
 215         if self._toStore("MahalanobisConsistency"):
 216             self.StoredVariables["MahalanobisConsistency"].store( float( 2.*J/d.size ) )
 217         if self._toStore("SimulationQuantiles"):
 218             nech = self._parameters["NumberOfSamplesForQuantiles"]
 219             HtM  = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 220             HtM  = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
 221             YfQ  = None
 222             for i in range(nech):
 223                 if self._parameters["SimulationForQuantiles"] == "Linear":
 224                     dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
 225                     dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
 226                     Yr = HXa + dYr
 227                 elif self._parameters["SimulationForQuantiles"] == "NonLinear":
 228                     Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
 229                     Yr = numpy.matrix(numpy.ravel( H( Xr ) )).T
 230                 if YfQ is None:
 231                     YfQ = Yr
 232                 else:
 233                     YfQ = numpy.hstack((YfQ,Yr))
 234             YfQ.sort(axis=-1)
 235             YQ = None
 236             for quantile in self._parameters["Quantiles"]:
 237                 if not (0. <= float(quantile) <= 1.): continue
 238                 indice = int(nech * float(quantile) - 1./nech)
 239                 if YQ is None: YQ = YfQ[:,indice]
 240                 else:          YQ = numpy.hstack((YQ,YfQ[:,indice]))
 241             self.StoredVariables["SimulationQuantiles"].store( YQ )
 242         if self._toStore("SimulatedObservationAtBackground"):
 243             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
 244         if self._toStore("SimulatedObservationAtCurrentState"):
 245             self.StoredVariables["SimulatedObservationAtCurrentState"].store( numpy.ravel(HXa) )
 246         if self._toStore("SimulatedObservationAtCurrentOptimum"):
 247             self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( numpy.ravel(HXa) )
 248         if self._toStore("SimulatedObservationAtOptimum"):
 249             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 250         #
 251         self._post_run(HO)
 252         return 0
 253
 254 # ==============================================================================
 255 if __name__ == "__main__":
 256     print('\n AUTODIAGNOSTIC\n')