src/daComposant/daAlgorithms/EnsembleKalmanFilter.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, 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                 "ForecastState",
  78                 "IndexOfOptimum",
  79                 "InnovationAtCurrentAnalysis",
  80                 "InnovationAtCurrentState",
  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         self.setAttributes(tags=(
  91             "DataAssimilation",
  92             "NonLinear",
  93             "Filter",
  94             "Ensemble",
  95             "Dynamic",
  96             ))
  97
  98     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
  99         self._pre_run(Parameters, Xb, Y, U, HO, EM, CM, R, B, Q)
 100         #
 101         if self._parameters["EstimationOf"] == "Parameters":
 102             self._parameters["StoreInternalVariables"] = True
 103         #
 104         # Opérateurs
 105         # ----------
 106         H = HO["Direct"].appliedControledFormTo
 107         #
 108         if self._parameters["EstimationOf"] == "State":
 109             M = EM["Direct"].appliedControledFormTo
 110         #
 111         if CM is not None and "Tangent" in CM and U is not None:
 112             Cm = CM["Tangent"].asMatrix(Xb)
 113         else:
 114             Cm = None
 115         #
 116         # Nombre de pas identique au nombre de pas d'observations
 117         # -------------------------------------------------------
 118         if hasattr(Y,"stepnumber"):
 119             duration = Y.stepnumber()
 120             __p = numpy.cumprod(Y.shape())[-1]
 121         else:
 122             duration = 2
 123             __p = numpy.array(Y).size
 124         #
 125         # Précalcul des inversions de B et R
 126         # ----------------------------------
 127         if self._parameters["StoreInternalVariables"] \
 128             or self._toStore("CostFunctionJ") \
 129             or self._toStore("CostFunctionJb") \
 130             or self._toStore("CostFunctionJo") \
 131             or self._toStore("CurrentOptimum") \
 132             or self._toStore("APosterioriCovariance"):
 133             BI = B.getI()
 134             RI = R.getI()
 135         # BIdemi = B.choleskyI()
 136         # RIdemi = R.choleskyI()
 137         #
 138         # Initialisation
 139         # --------------
 140         __n = Xb.size
 141         __m = self._parameters["NumberOfMembers"]
 142         Xn = numpy.asmatrix(numpy.dot( Xb.reshape(__n,1), numpy.ones((1,__m)) ))
 143         if hasattr(B,"asfullmatrix"): Pn = B.asfullmatrix(__n)
 144         else:                         Pn = B
 145         if hasattr(R,"asfullmatrix"): Rn = R.asfullmatrix(__p)
 146         else:                         Rn = R
 147         if hasattr(Q,"asfullmatrix"): Qn = Q.asfullmatrix(__n)
 148         else:                         Qn = Q
 149         #
 150         if len(self.StoredVariables["Analysis"])==0 or not self._parameters["nextStep"]:
 151             self.StoredVariables["Analysis"].store( numpy.ravel(Xb) )
 152             if self._toStore("APosterioriCovariance"):
 153                 self.StoredVariables["APosterioriCovariance"].store( Pn )
 154                 covarianceXa = Pn
 155         #
 156         Xa               = Xb
 157         XaMin            = Xb
 158         previousJMinimum = numpy.finfo(float).max
 159         #
 160         # Predimensionnement
 161         Xn_predicted = numpy.asmatrix(numpy.zeros((__n,__m)))
 162         HX_predicted = numpy.asmatrix(numpy.zeros((__p,__m)))
 163         #
 164         for step in range(duration-1):
 165             if hasattr(Y,"store"):
 166                 Ynpu = numpy.asmatrix(numpy.ravel( Y[step+1] )).T
 167             else:
 168                 Ynpu = numpy.asmatrix(numpy.ravel( Y )).T
 169             #
 170             if U is not None:
 171                 if hasattr(U,"store") and len(U)>1:
 172                     Un = numpy.asmatrix(numpy.ravel( U[step] )).T
 173                 elif hasattr(U,"store") and len(U)==1:
 174                     Un = numpy.asmatrix(numpy.ravel( U[0] )).T
 175                 else:
 176                     Un = numpy.asmatrix(numpy.ravel( U )).T
 177             else:
 178                 Un = None
 179             #
 180             if self._parameters["EstimationOf"] == "State":
 181                 for i in range(__m):
 182                     qi = numpy.asmatrix(numpy.random.multivariate_normal(numpy.zeros(__n), Qn, (1,1,1))).T
 183                     Xn_predicted[:,i] = numpy.asmatrix(numpy.ravel( M((Xn[:,i], Un)) )).T + qi
 184                     HX_predicted[:,i] = numpy.asmatrix(numpy.ravel( H((Xn_predicted[:,i], Un)) )).T
 185                 if Cm is not None and Un is not None: # Attention : si Cm est aussi dans M, doublon !
 186                     Cm = Cm.reshape(__n,Un.size) # ADAO & check shape
 187                     Xn_predicted = Xn_predicted + Cm * Un
 188             elif self._parameters["EstimationOf"] == "Parameters":
 189                 # --- > Par principe, M = Id, Q = 0
 190                 Xn_predicted = Xn
 191             #
 192             Xfm = numpy.asmatrix(numpy.ravel(Xn_predicted.mean(axis=1, dtype=mfp))).T
 193             Hfm = numpy.asmatrix(numpy.ravel(HX_predicted.mean(axis=1, dtype=mfp))).T
 194             #
 195             PfHT, HPfHT = 0., 0.
 196             for i in range(__m):
 197                 Exfi = Xn_predicted[:,i] - Xfm
 198                 Eyfi = HX_predicted[:,i] - Hfm
 199                 PfHT  += Exfi * Eyfi.T
 200                 HPfHT += Eyfi * Eyfi.T
 201             PfHT  = (1./(__m-1)) * PfHT
 202             HPfHT = (1./(__m-1)) * HPfHT
 203             K     = PfHT * ( R + HPfHT ).I
 204             del PfHT, HPfHT
 205             #
 206             for i in range(__m):
 207                 ri = numpy.asmatrix(numpy.random.multivariate_normal(numpy.zeros(__p), Rn, (1,1,1))).T
 208                 Xn[:,i] = Xn_predicted[:,i] + K * (Ynpu + ri - HX_predicted[:,i])
 209             #
 210             Xa = Xn.mean(axis=1, dtype=mfp)
 211             #
 212             if self._parameters["StoreInternalVariables"] \
 213                 or self._toStore("CostFunctionJ") \
 214                 or self._toStore("CostFunctionJb") \
 215                 or self._toStore("CostFunctionJo") \
 216                 or self._toStore("APosterioriCovariance") \
 217                 or self._toStore("InnovationAtCurrentAnalysis") \
 218                 or self._toStore("SimulatedObservationAtCurrentAnalysis") \
 219                 or self._toStore("SimulatedObservationAtCurrentOptimum"):
 220                 _HXa = numpy.asmatrix(numpy.ravel( H((Xa, Un)) )).T
 221                 _Innovation = Ynpu - _HXa
 222             #
 223             # ---> avec analysis
 224             self.StoredVariables["Analysis"].store( Xa )
 225             if self._toStore("SimulatedObservationAtCurrentAnalysis"):
 226                 self.StoredVariables["SimulatedObservationAtCurrentAnalysis"].store( _HXa )
 227             if self._toStore("InnovationAtCurrentAnalysis"):
 228                 self.StoredVariables["InnovationAtCurrentAnalysis"].store( _Innovation )
 229             # ---> avec current state
 230             if self._parameters["StoreInternalVariables"] \
 231                 or self._toStore("CurrentState"):
 232                 self.StoredVariables["CurrentState"].store( Xn )
 233             if self._toStore("ForecastState"):
 234                 self.StoredVariables["ForecastState"].store( Xn_predicted )
 235             if self._toStore("BMA"):
 236                 self.StoredVariables["BMA"].store( Xn_predicted - Xa )
 237             if self._toStore("InnovationAtCurrentState"):
 238                 self.StoredVariables["InnovationAtCurrentState"].store( - HX_predicted + Ynpu )
 239             if self._toStore("SimulatedObservationAtCurrentState") \
 240                 or self._toStore("SimulatedObservationAtCurrentOptimum"):
 241                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( HX_predicted )
 242             # ---> autres
 243             if self._parameters["StoreInternalVariables"] \
 244                 or self._toStore("CostFunctionJ") \
 245                 or self._toStore("CostFunctionJb") \
 246                 or self._toStore("CostFunctionJo") \
 247                 or self._toStore("CurrentOptimum") \
 248                 or self._toStore("APosterioriCovariance"):
 249                 Jb  = float( 0.5 * (Xa - Xb).T * BI * (Xa - Xb) )
 250                 Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 251                 J   = Jb + Jo
 252                 self.StoredVariables["CostFunctionJb"].store( Jb )
 253                 self.StoredVariables["CostFunctionJo"].store( Jo )
 254                 self.StoredVariables["CostFunctionJ" ].store( J )
 255                 #
 256                 if self._toStore("IndexOfOptimum") \
 257                     or self._toStore("CurrentOptimum") \
 258                     or self._toStore("CostFunctionJAtCurrentOptimum") \
 259                     or self._toStore("CostFunctionJbAtCurrentOptimum") \
 260                     or self._toStore("CostFunctionJoAtCurrentOptimum") \
 261                     or self._toStore("SimulatedObservationAtCurrentOptimum"):
 262                     IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 263                 if self._toStore("IndexOfOptimum"):
 264                     self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 265                 if self._toStore("CurrentOptimum"):
 266                     self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["Analysis"][IndexMin] )
 267                 if self._toStore("SimulatedObservationAtCurrentOptimum"):
 268                     self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentAnalysis"][IndexMin] )
 269                 if self._toStore("CostFunctionJbAtCurrentOptimum"):
 270                     self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 271                 if self._toStore("CostFunctionJoAtCurrentOptimum"):
 272                     self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 273                 if self._toStore("CostFunctionJAtCurrentOptimum"):
 274                     self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 275             if self._toStore("APosterioriCovariance"):
 276                 Pn = 0.
 277                 for i in range(__m):
 278                     Eai = Xn[:,i] - Xa
 279                     Pn += Eai * Eai.T
 280                 Pn  = (1./(__m-1)) * Pn
 281                 self.StoredVariables["APosterioriCovariance"].store( Pn )
 282             if self._parameters["EstimationOf"] == "Parameters" \
 283                 and J < previousJMinimum:
 284                 previousJMinimum    = J
 285                 XaMin               = Xa
 286                 if self._toStore("APosterioriCovariance"):
 287                     covarianceXaMin = Pn
 288         #
 289         # Stockage final supplémentaire de l'optimum en estimation de paramètres
 290         # ----------------------------------------------------------------------
 291         if self._parameters["EstimationOf"] == "Parameters":
 292             self.StoredVariables["Analysis"].store( XaMin )
 293             if self._toStore("APosterioriCovariance"):
 294                 self.StoredVariables["APosterioriCovariance"].store( covarianceXaMin )
 295             if self._toStore("BMA"):
 296                 self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(XaMin) )
 297         #
 298         self._post_run(HO)
 299         return 0
 300
 301 # ==============================================================================
 302 if __name__ == "__main__":
 303     print('\n AUTODIAGNOSTIC\n')