--- /dev/null
+# -*- coding: utf-8 -*-
+#
+# Copyright (C) 2008-2017 EDF R&D
+#
+# This library is free software; you can redistribute it and/or
+# modify it under the terms of the GNU Lesser General Public
+# License as published by the Free Software Foundation; either
+# version 2.1 of the License.
+#
+# This library is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+# Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public
+# License along with this library; if not, write to the Free Software
+# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+#
+# See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
+#
+# Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
+
+import logging
+from daCore import BasicObjects, PlatformInfo
+import numpy, math
+mfp = PlatformInfo.PlatformInfo().MaximumPrecision()
+
+# Using "Ensemble Kalman filtering", L. HOUTEKAMER and HERSCHEL L. MITCHELL, QJRMS (2005), 131, pp. 3269–3289
+
+# ==============================================================================
+class ElementaryAlgorithm(BasicObjects.Algorithm):
+ def __init__(self):
+ BasicObjects.Algorithm.__init__(self, "ENSEMBLEKALMANFILTER")
+ self.defineRequiredParameter(
+ name = "NumberOfMembers",
+ default = 100,
+ typecast = int,
+ message = "Nombre de membres dans l'ensemble",
+ minval = -1,
+ )
+ self.defineRequiredParameter(
+ name = "Minimizer",
+ default = "EnKF",
+ typecast = str,
+ message = "Schéma de mise a jour des informations d'ensemble",
+ listval = ["EnKF", "ETKF", "DEnKF"],
+ )
+ self.defineRequiredParameter(
+ name = "ConstrainedBy",
+ default = "EstimateProjection",
+ typecast = str,
+ message = "Prise en compte des contraintes",
+ listval = ["EstimateProjection"],
+ )
+ self.defineRequiredParameter(
+ name = "EstimationOf",
+ default = "State",
+ typecast = str,
+ message = "Estimation d'etat ou de parametres",
+ listval = ["State", "Parameters"],
+ )
+ self.defineRequiredParameter(
+ name = "StoreInternalVariables",
+ default = False,
+ typecast = bool,
+ message = "Stockage des variables internes ou intermédiaires du calcul",
+ )
+ self.defineRequiredParameter(
+ name = "StoreSupplementaryCalculations",
+ default = [],
+ typecast = tuple,
+ message = "Liste de calculs supplémentaires à stocker et/ou effectuer",
+ listval = ["APosterioriCorrelations", "APosterioriCovariance", "APosterioriStandardDeviations", "APosterioriVariances", "BMA", "CurrentState", "CostFunctionJ", "CostFunctionJb", "CostFunctionJo", "Innovation"]
+ )
+ self.defineRequiredParameter( # Pas de type
+ name = "Bounds",
+ message = "Liste des valeurs de bornes",
+ )
+ self.defineRequiredParameter(
+ name = "SetSeed",
+ typecast = numpy.random.seed,
+ message = "Graine fixée pour le générateur aléatoire",
+ )
+ self.requireInputArguments(
+ mandatory= ("Xb", "Y", "HO", "R", "B"),
+ optional = ("U", "EM", "CM", "Q"),
+ )
+
+ def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
+ self._pre_run(Parameters, Xb, Y, R, B, Q)
+ #
+ if self._parameters["EstimationOf"] == "Parameters":
+ self._parameters["StoreInternalVariables"] = True
+ #
+ # Opérateurs
+ # ----------
+ H = HO["Direct"].appliedControledFormTo
+ #
+ if self._parameters["EstimationOf"] == "State":
+ M = EM["Direct"].appliedControledFormTo
+ #
+ if CM is not None and "Tangent" in CM and U is not None:
+ Cm = CM["Tangent"].asMatrix(Xb)
+ else:
+ Cm = None
+ #
+ # Nombre de pas identique au nombre de pas d'observations
+ # -------------------------------------------------------
+ if hasattr(Y,"stepnumber"):
+ duration = Y.stepnumber()
+ __p = numpy.cumprod(Y.shape())[-1]
+ else:
+ duration = 2
+ __p = numpy.array(Y).size
+ #
+ # Précalcul des inversions de B et R
+ # ----------------------------------
+ if self._parameters["StoreInternalVariables"]:
+ BI = B.getI()
+ RI = R.getI()
+ BIdemi = B.choleskyI()
+ RIdemi = R.choleskyI()
+ #
+ # Initialisation
+ # --------------
+ __n = Xb.size
+ __m = self._parameters["NumberOfMembers"]
+ Xn = numpy.asmatrix(numpy.dot( Xb.reshape(__n,1), numpy.ones((1,__m)) ))
+ if hasattr(B,"asfullmatrix"): Pn = B.asfullmatrix(__n)
+ else: Pn = B
+ if hasattr(R,"asfullmatrix"): Rn = R.asfullmatrix(__p)
+ else: Rn = R
+ if hasattr(Q,"asfullmatrix"): Qn = Q.asfullmatrix(__n)
+ else: Qn = Q
+ #
+ self.StoredVariables["Analysis"].store( Xb.A1 )
+ if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["APosterioriCovariance"].store( Pn )
+ covarianceXa = Pn
+ Xa = Xb
+ previousJMinimum = numpy.finfo(float).max
+ #
+ # Predimensionnement
+ Xn_predicted = numpy.asmatrix(numpy.zeros((__n,__m)))
+ HX_predicted = numpy.asmatrix(numpy.zeros((__p,__m)))
+ #
+ for step in range(duration-1):
+ if hasattr(Y,"store"):
+ Ynpu = numpy.asmatrix(numpy.ravel( Y[step+1] )).T
+ else:
+ Ynpu = numpy.asmatrix(numpy.ravel( Y )).T
+ #
+ if U is not None:
+ if hasattr(U,"store") and len(U)>1:
+ Un = numpy.asmatrix(numpy.ravel( U[step] )).T
+ elif hasattr(U,"store") and len(U)==1:
+ Un = numpy.asmatrix(numpy.ravel( U[0] )).T
+ else:
+ Un = numpy.asmatrix(numpy.ravel( U )).T
+ else:
+ Un = None
+ #
+ if self._parameters["EstimationOf"] == "State":
+ for i in range(__m):
+ qi = numpy.asmatrix(numpy.random.multivariate_normal(numpy.zeros(__n), Qn)).T
+ Xn_predicted[:,i] = numpy.asmatrix(numpy.ravel( M((Xn[:,i], Un)) )).T + qi
+ HX_predicted[:,i] = numpy.asmatrix(numpy.ravel( H((Xn_predicted[:,i], Un)) )).T
+ if Cm is not None and Un is not None: # Attention : si Cm est aussi dans M, doublon !
+ Cm = Cm.reshape(__n,Un.size) # ADAO & check shape
+ Xn_predicted = Xn_predicted + Cm * Un
+ elif self._parameters["EstimationOf"] == "Parameters":
+ # --- > Par principe, M = Id, Q = 0
+ Xn_predicted = Xn
+ #
+ Xfm = numpy.asmatrix(numpy.ravel(Xn_predicted.mean(axis=1, dtype=mfp))).T
+ Hfm = numpy.asmatrix(numpy.ravel(HX_predicted.mean(axis=1, dtype=mfp))).T
+ Af = Xn_predicted - Xfm
+ Hf = HX_predicted - Hfm
+ #
+ PfHT, HPfHT = 0., 0.
+ for i in range(__m):
+ PfHT += Af[:,i] * Hf[:,i].T
+ HPfHT += Hf[:,i] * Hf[:,i].T
+ PfHT = (1./(__m-1)) * PfHT
+ HPfHT = (1./(__m-1)) * HPfHT
+ #
+ K = PfHT * ( R + HPfHT ).I
+ #
+ Yo = numpy.asmatrix(numpy.zeros((__p,__m)))
+ for i in range(__m):
+ ri = numpy.asmatrix(numpy.random.multivariate_normal(numpy.zeros(__p), Rn)).T
+ Yo[:,i] = Ynpu + ri
+ #
+ for i in range(__m):
+ Xn[:,i] = Xn_predicted[:,i] + K * (Yo[:,i] - HX_predicted[:,i])
+ #
+ Xa = Xn.mean(axis=1, dtype=mfp)
+ self.StoredVariables["Analysis"].store( Xa )
+ #
+ del Yo, PfHT, HPfHT
+ if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
+ Ht = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
+ Ht = Ht.reshape(__p,__n) # ADAO & check shape
+ Pf = 0.
+ for i in range(__m):
+ Pf += Af[:,i] * Af[:,i].T
+ Pf = (1./(__m-1)) * Pf
+ Pn = (1. - K * Ht) * Pf
+ self.StoredVariables["APosterioriCovariance"].store( Pn )
+ #
+ self._post_run(HO)
+ return 0
+
+# ==============================================================================
+if __name__ == "__main__":
+ print('\n AUTODIAGNOSTIC \n')
