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
 101     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 102         self._pre_run(Parameters, Xb, Y, R, B, Q)
 103         #
 104         Hm = HO["Tangent"].asMatrix(Xb)
 105         Hm = Hm.reshape(Y.size,Xb.size) # ADAO & check shape
 106         Ha = HO["Adjoint"].asMatrix(Xb)
 107         Ha = Ha.reshape(Xb.size,Y.size) # ADAO & check shape
 108         H  = HO["Direct"].appliedTo
 109         #
 110         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
 111         # ----------------------------------------------------
 112         if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
 113             HXb = H( Xb, HO["AppliedInX"]["HXb"])
 114         else:
 115             HXb = H( Xb )
 116         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 117         if Y.size != HXb.size:
 118             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))
 119         if max(Y.shape) != max(HXb.shape):
 120             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))
 121         #
 122         # Précalcul des inversions de B et R
 123         # ----------------------------------
 124         BI = B.getI()
 125         RI = R.getI()
 126         #
 127         # Calcul de l'innovation
 128         # ----------------------
 129         d  = Y - HXb
 130         #
 131         # Calcul de la matrice de gain et de l'analyse
 132         # --------------------------------------------
 133         if Y.size <= Xb.size:
 134             _A = R + numpy.dot(Hm, B * Ha)
 135             _u = numpy.linalg.solve( _A , d )
 136             Xa = Xb + B * Ha * _u
 137         else:
 138             _A = BI + numpy.dot(Ha, RI * Hm)
 139             _u = numpy.linalg.solve( _A , numpy.dot(Ha, RI * d) )
 140             Xa = Xb + _u
 141         self.StoredVariables["Analysis"].store( Xa.A1 )
 142         #
 143         # Calcul de la fonction coût
 144         # --------------------------
 145         if self._parameters["StoreInternalVariables"] or \
 146             self._toStore("CostFunctionJ")  or self._toStore("CostFunctionJAtCurrentOptimum") or \
 147             self._toStore("CostFunctionJb") or self._toStore("CostFunctionJbAtCurrentOptimum") or \
 148             self._toStore("CostFunctionJo") or self._toStore("CostFunctionJoAtCurrentOptimum") or \
 149             self._toStore("OMA") or \
 150             self._toStore("SigmaObs2") or \
 151             self._toStore("MahalanobisConsistency") or \
 152             self._toStore("SimulatedObservationAtCurrentOptimum") or \
 153             self._toStore("SimulatedObservationAtCurrentState") or \
 154             self._toStore("SimulatedObservationAtOptimum") or \
 155             self._toStore("SimulationQuantiles"):
 156             HXa  = numpy.matrix(numpy.ravel( H( Xa ) )).T
 157             oma = Y - HXa
 158         if self._parameters["StoreInternalVariables"] or \
 159             self._toStore("CostFunctionJ")  or self._toStore("CostFunctionJAtCurrentOptimum") or \
 160             self._toStore("CostFunctionJb") or self._toStore("CostFunctionJbAtCurrentOptimum") or \
 161             self._toStore("CostFunctionJo") or self._toStore("CostFunctionJoAtCurrentOptimum") or \
 162             self._toStore("MahalanobisConsistency"):
 163             Jb  = float( 0.5 * (Xa - Xb).T * BI * (Xa - Xb) )
 164             Jo  = float( 0.5 * oma.T * RI * oma )
 165             J   = Jb + Jo
 166             self.StoredVariables["CostFunctionJb"].store( Jb )
 167             self.StoredVariables["CostFunctionJo"].store( Jo )
 168             self.StoredVariables["CostFunctionJ" ].store( J )
 169             self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( Jb )
 170             self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( Jo )
 171             self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( J )
 172         #
 173         # Calcul de la covariance d'analyse
 174         # ---------------------------------
 175         if self._toStore("APosterioriCovariance") or \
 176             self._toStore("SimulationQuantiles"):
 177             if   (Y.size <= Xb.size): K  = B * Ha * (R + numpy.dot(Hm, B * Ha)).I
 178             elif (Y.size >  Xb.size): K = (BI + numpy.dot(Ha, RI * Hm)).I * Ha * RI
 179             A = B - K * Hm * B
 180             if min(A.shape) != max(A.shape):
 181                 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)))
 182             if (numpy.diag(A) < 0).any():
 183                 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,))
 184             if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
 185                 try:
 186                     L = numpy.linalg.cholesky( A )
 187                 except:
 188                     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,))
 189             self.StoredVariables["APosterioriCovariance"].store( A )
 190         #
 191         # Calculs et/ou stockages supplémentaires
 192         # ---------------------------------------
 193         if self._parameters["StoreInternalVariables"] or self._toStore("CurrentState"):
 194             self.StoredVariables["CurrentState"].store( numpy.ravel(Xa) )
 195         if self._toStore("CurrentOptimum"):
 196             self.StoredVariables["CurrentOptimum"].store( numpy.ravel(Xa) )
 197         if self._toStore("Innovation"):
 198             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 199         if self._toStore("BMA"):
 200             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 201         if self._toStore("OMA"):
 202             self.StoredVariables["OMA"].store( numpy.ravel(oma) )
 203         if self._toStore("OMB"):
 204             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 205         if self._toStore("SigmaObs2"):
 206             TraceR = R.trace(Y.size)
 207             self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(oma)).T)) ) / TraceR )
 208         if self._toStore("SigmaBck2"):
 209             self.StoredVariables["SigmaBck2"].store( float( (d.T * Hm * (Xa - Xb))/(Hm * B * Hm.T).trace() ) )
 210         if self._toStore("MahalanobisConsistency"):
 211             self.StoredVariables["MahalanobisConsistency"].store( float( 2.*J/d.size ) )
 212         if self._toStore("SimulationQuantiles"):
 213             nech = self._parameters["NumberOfSamplesForQuantiles"]
 214             HtM  = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 215             HtM  = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
 216             YfQ  = None
 217             for i in range(nech):
 218                 if self._parameters["SimulationForQuantiles"] == "Linear":
 219                     dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
 220                     dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
 221                     Yr = HXa + dYr
 222                 elif self._parameters["SimulationForQuantiles"] == "NonLinear":
 223                     Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
 224                     Yr = numpy.matrix(numpy.ravel( H( Xr ) )).T
 225                 if YfQ is None:
 226                     YfQ = Yr
 227                 else:
 228                     YfQ = numpy.hstack((YfQ,Yr))
 229             YfQ.sort(axis=-1)
 230             YQ = None
 231             for quantile in self._parameters["Quantiles"]:
 232                 if not (0. <= float(quantile) <= 1.): continue
 233                 indice = int(nech * float(quantile) - 1./nech)
 234                 if YQ is None: YQ = YfQ[:,indice]
 235                 else:          YQ = numpy.hstack((YQ,YfQ[:,indice]))
 236             self.StoredVariables["SimulationQuantiles"].store( YQ )
 237         if self._toStore("SimulatedObservationAtBackground"):
 238             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
 239         if self._toStore("SimulatedObservationAtCurrentState"):
 240             self.StoredVariables["SimulatedObservationAtCurrentState"].store( numpy.ravel(HXa) )
 241         if self._toStore("SimulatedObservationAtCurrentOptimum"):
 242             self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( numpy.ravel(HXa) )
 243         if self._toStore("SimulatedObservationAtOptimum"):
 244             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 245         #
 246         self._post_run(HO)
 247         return 0
 248
 249 # ==============================================================================
 250 if __name__ == "__main__":
 251     print('\n AUTODIAGNOSTIC\n')