src/daComposant/daAlgorithms/EnsembleKalmanFilter.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2019 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, PlatformInfo
  25 import numpy, math
  26 mfp = PlatformInfo.PlatformInfo().MaximumPrecision()
  27
  28 # ==============================================================================
  29 class ElementaryAlgorithm(BasicObjects.Algorithm):
  30     def __init__(self):
  31         BasicObjects.Algorithm.__init__(self, "ENSEMBLEKALMANFILTER")
  32         self.defineRequiredParameter(
  33             name     = "NumberOfMembers",
  34             default  = 100,
  35             typecast = int,
  36             message  = "Nombre de membres dans l'ensemble",
  37             minval   = -1,
  38             )
  39         self.defineRequiredParameter(
  40             name     = "EstimationOf",
  41             default  = "State",
  42             typecast = str,
  43             message  = "Estimation d'etat ou de parametres",
  44             listval  = ["State", "Parameters"],
  45             )
  46         self.defineRequiredParameter(
  47             name     = "SetSeed",
  48             typecast = numpy.random.seed,
  49             message  = "Graine fixée pour le générateur aléatoire",
  50             )
  51         self.defineRequiredParameter(
  52             name     = "StoreInternalVariables",
  53             default  = False,
  54             typecast = bool,
  55             message  = "Stockage des variables internes ou intermédiaires du calcul",
  56             )
  57         self.defineRequiredParameter(
  58             name     = "StoreSupplementaryCalculations",
  59             default  = [],
  60             typecast = tuple,
  61             message  = "Liste de calculs supplémentaires à stocker et/ou effectuer",
  62             listval  = [
  63                 "Analysis",
  64                 "APosterioriCorrelations",
  65                 "APosterioriCovariance",
  66                 "APosterioriStandardDeviations",
  67                 "APosterioriVariances",
  68                 "BMA",
  69                 "CostFunctionJ",
  70                 "CostFunctionJAtCurrentOptimum",
  71                 "CostFunctionJb",
  72                 "CostFunctionJbAtCurrentOptimum",
  73                 "CostFunctionJo",
  74                 "CostFunctionJoAtCurrentOptimum",
  75                 "CurrentOptimum",
  76                 "CurrentState",
  77                 "IndexOfOptimum",
  78                 "InnovationAtCurrentAnalysis",
  79                 "InnovationAtCurrentState",
  80                 "PredictedState",
  81                 "SimulatedObservationAtCurrentAnalysis",
  82                 "SimulatedObservationAtCurrentOptimum",
  83                 "SimulatedObservationAtCurrentState",
  84                 ]
  85             )
  86         self.requireInputArguments(
  87             mandatory= ("Xb", "Y", "HO", "R", "B"),
  88             optional = ("U", "EM", "CM", "Q"),
  89             )
  90
  91     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
  92         self._pre_run(Parameters, Xb, Y, R, B, Q)
  93         #
  94         if self._parameters["EstimationOf"] == "Parameters":
  95             self._parameters["StoreInternalVariables"] = True
  96         #
  97         # Opérateurs
  98         # ----------
  99         H = HO["Direct"].appliedControledFormTo
 100         #
 101         if self._parameters["EstimationOf"] == "State":
 102             M = EM["Direct"].appliedControledFormTo
 103         #
 104         if CM is not None and "Tangent" in CM and U is not None:
 105             Cm = CM["Tangent"].asMatrix(Xb)
 106         else:
 107             Cm = None
 108         #
 109         # Nombre de pas identique au nombre de pas d'observations
 110         # -------------------------------------------------------
 111         if hasattr(Y,"stepnumber"):
 112             duration = Y.stepnumber()
 113             __p = numpy.cumprod(Y.shape())[-1]
 114         else:
 115             duration = 2
 116             __p = numpy.array(Y).size
 117         #
 118         # Précalcul des inversions de B et R
 119         # ----------------------------------
 120         if self._parameters["StoreInternalVariables"] \
 121             or self._toStore("CostFunctionJ") \
 122             or self._toStore("CostFunctionJb") \
 123             or self._toStore("CostFunctionJo") \
 124             or self._toStore("CurrentOptimum") \
 125             or self._toStore("APosterioriCovariance"):
 126             BI = B.getI()
 127             RI = R.getI()
 128         BIdemi = B.choleskyI()
 129         RIdemi = R.choleskyI()
 130         #
 131         # Initialisation
 132         # --------------
 133         __n = Xb.size
 134         __m = self._parameters["NumberOfMembers"]
 135         Xn = numpy.asmatrix(numpy.dot( Xb.reshape(__n,1), numpy.ones((1,__m)) ))
 136         if hasattr(B,"asfullmatrix"): Pn = B.asfullmatrix(__n)
 137         else:                         Pn = B
 138         if hasattr(R,"asfullmatrix"): Rn = R.asfullmatrix(__p)
 139         else:                         Rn = R
 140         if hasattr(Q,"asfullmatrix"): Qn = Q.asfullmatrix(__n)
 141         else:                         Qn = Q
 142         #
 143         self.StoredVariables["Analysis"].store( Xb.A1 )
 144         if self._toStore("APosterioriCovariance"):
 145             self.StoredVariables["APosterioriCovariance"].store( Pn )
 146             covarianceXa = Pn
 147         Xa = XaMin       = Xb
 148         previousJMinimum = numpy.finfo(float).max
 149         #
 150         # Predimensionnement
 151         Xn_predicted = numpy.asmatrix(numpy.zeros((__n,__m)))
 152         HX_predicted = numpy.asmatrix(numpy.zeros((__p,__m)))
 153         #
 154         for step in range(duration-1):
 155             if hasattr(Y,"store"):
 156                 Ynpu = numpy.asmatrix(numpy.ravel( Y[step+1] )).T
 157             else:
 158                 Ynpu = numpy.asmatrix(numpy.ravel( Y )).T
 159             #
 160             if U is not None:
 161                 if hasattr(U,"store") and len(U)>1:
 162                     Un = numpy.asmatrix(numpy.ravel( U[step] )).T
 163                 elif hasattr(U,"store") and len(U)==1:
 164                     Un = numpy.asmatrix(numpy.ravel( U[0] )).T
 165                 else:
 166                     Un = numpy.asmatrix(numpy.ravel( U )).T
 167             else:
 168                 Un = None
 169             #
 170             if self._parameters["EstimationOf"] == "State":
 171                 for i in range(__m):
 172                     qi = numpy.asmatrix(numpy.random.multivariate_normal(numpy.zeros(__n), Qn)).T
 173                     Xn_predicted[:,i] = numpy.asmatrix(numpy.ravel( M((Xn[:,i], Un)) )).T + qi
 174                     HX_predicted[:,i] = numpy.asmatrix(numpy.ravel( H((Xn_predicted[:,i], Un)) )).T
 175                 if Cm is not None and Un is not None: # Attention : si Cm est aussi dans M, doublon !
 176                     Cm = Cm.reshape(__n,Un.size) # ADAO & check shape
 177                     Xn_predicted = Xn_predicted + Cm * Un
 178             elif self._parameters["EstimationOf"] == "Parameters":
 179                 # --- > Par principe, M = Id, Q = 0
 180                 Xn_predicted = Xn
 181             #
 182             Xfm = numpy.asmatrix(numpy.ravel(Xn_predicted.mean(axis=1, dtype=mfp))).T
 183             Hfm = numpy.asmatrix(numpy.ravel(HX_predicted.mean(axis=1, dtype=mfp))).T
 184             Af  = Xn_predicted - Xfm
 185             Hf  = HX_predicted - Hfm
 186             #
 187             PfHT, HPfHT = 0., 0.
 188             for i in range(__m):
 189                 PfHT  += Af[:,i] * Hf[:,i].T
 190                 HPfHT += Hf[:,i] * Hf[:,i].T
 191             PfHT  = (1./(__m-1)) * PfHT
 192             HPfHT = (1./(__m-1)) * HPfHT
 193             #
 194             K = PfHT * ( R + HPfHT ).I
 195             #
 196             Yo = numpy.asmatrix(numpy.zeros((__p,__m)))
 197             for i in range(__m):
 198                 ri = numpy.asmatrix(numpy.random.multivariate_normal(numpy.zeros(__p), Rn)).T
 199                 Yo[:,i] = Ynpu + ri
 200             #
 201             for i in range(__m):
 202                 Xn[:,i] = Xn_predicted[:,i] + K * (Yo[:,i] - HX_predicted[:,i])
 203             del PfHT, HPfHT
 204             #
 205             Xa = Xn.mean(axis=1, dtype=mfp)
 206             #
 207             if self._parameters["StoreInternalVariables"] \
 208                 or self._toStore("CostFunctionJ") \
 209                 or self._toStore("CostFunctionJb") \
 210                 or self._toStore("CostFunctionJo") \
 211                 or self._toStore("APosterioriCovariance") \
 212                 or self._toStore("InnovationAtCurrentAnalysis") \
 213                 or self._toStore("SimulatedObservationAtCurrentAnalysis") \
 214                 or self._toStore("SimulatedObservationAtCurrentOptimum"):
 215                 _HXa = numpy.asmatrix(numpy.ravel( H((Xa, Un)) )).T
 216                 _Innovation = Ynpu - _HXa
 217             #
 218             # ---> avec analysis
 219             self.StoredVariables["Analysis"].store( Xa )
 220             if self._toStore("SimulatedObservationAtCurrentAnalysis"):
 221                 self.StoredVariables["SimulatedObservationAtCurrentAnalysis"].store( _HXa )
 222             if self._toStore("InnovationAtCurrentAnalysis"):
 223                 self.StoredVariables["InnovationAtCurrentAnalysis"].store( _Innovation )
 224             # ---> avec current state
 225             if self._parameters["StoreInternalVariables"] \
 226                 or self._toStore("CurrentState"):
 227                 self.StoredVariables["CurrentState"].store( Xn )
 228             if self._toStore("PredictedState"):
 229                 self.StoredVariables["PredictedState"].store( Xn_predicted )
 230             if self._toStore("BMA"):
 231                 self.StoredVariables["BMA"].store( Xn_predicted - Xa )
 232             if self._toStore("InnovationAtCurrentState"):
 233                 self.StoredVariables["InnovationAtCurrentState"].store( - HX_predicted + Ynpu )
 234             if self._toStore("SimulatedObservationAtCurrentState") \
 235                 or self._toStore("SimulatedObservationAtCurrentOptimum"):
 236                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( HX_predicted )
 237             # ---> autres
 238             if self._parameters["StoreInternalVariables"] \
 239                 or self._toStore("CostFunctionJ") \
 240                 or self._toStore("CostFunctionJb") \
 241                 or self._toStore("CostFunctionJo") \
 242                 or self._toStore("CurrentOptimum") \
 243                 or self._toStore("APosterioriCovariance"):
 244                 Jb  = float( 0.5 * (Xa - Xb).T * BI * (Xa - Xb) )
 245                 Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 246                 J   = Jb + Jo
 247                 self.StoredVariables["CostFunctionJb"].store( Jb )
 248                 self.StoredVariables["CostFunctionJo"].store( Jo )
 249                 self.StoredVariables["CostFunctionJ" ].store( J )
 250                 #
 251                 if self._toStore("IndexOfOptimum") \
 252                     or self._toStore("CurrentOptimum") \
 253                     or self._toStore("CostFunctionJAtCurrentOptimum") \
 254                     or self._toStore("CostFunctionJbAtCurrentOptimum") \
 255                     or self._toStore("CostFunctionJoAtCurrentOptimum") \
 256                     or self._toStore("SimulatedObservationAtCurrentOptimum"):
 257                     IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 258                 if self._toStore("IndexOfOptimum"):
 259                     self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 260                 if self._toStore("CurrentOptimum"):
 261                     self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["Analysis"][IndexMin] )
 262                 if self._toStore("SimulatedObservationAtCurrentOptimum"):
 263                     self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentAnalysis"][IndexMin] )
 264                 if self._toStore("CostFunctionJbAtCurrentOptimum"):
 265                     self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 266                 if self._toStore("CostFunctionJoAtCurrentOptimum"):
 267                     self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 268                 if self._toStore("CostFunctionJAtCurrentOptimum"):
 269                     self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 270             if self._toStore("APosterioriCovariance"):
 271                 Ht = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 272                 Ht = Ht.reshape(__p,__n) # ADAO & check shape
 273                 Pf = 0.
 274                 for i in range(__m):
 275                     Pf += Af[:,i] * Af[:,i].T
 276                 Pf = (1./(__m-1)) * Pf
 277                 Pn = (1. - K * Ht) * Pf
 278                 self.StoredVariables["APosterioriCovariance"].store( Pn )
 279             if self._parameters["EstimationOf"] == "Parameters" \
 280                 and J < previousJMinimum:
 281                 previousJMinimum    = J
 282                 XaMin               = Xa
 283                 if self._toStore("APosterioriCovariance"):
 284                     covarianceXaMin = Pn
 285         #
 286         # Stockage final supplémentaire de l'optimum en estimation de paramètres
 287         # ----------------------------------------------------------------------
 288         if self._parameters["EstimationOf"] == "Parameters":
 289             self.StoredVariables["Analysis"].store( XaMin )
 290             if self._toStore("APosterioriCovariance"):
 291                 self.StoredVariables["APosterioriCovariance"].store( covarianceXaMin )
 292             if self._toStore("BMA"):
 293                 self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(XaMin) )
 294         #
 295         self._post_run(HO)
 296         return 0
 297
 298 # ==============================================================================
 299 if __name__ == "__main__":
 300     print('\n AUTODIAGNOSTIC \n')