.. index:: single: 3DVAR
.. index:: single: Blue
+.. index:: single: ExtendedBlue
.. index:: single: EnsembleBlue
.. index:: single: KalmanFilter
.. index:: single: ExtendedKalmanFilter
list: ["APosterioriCovariance", "BMA", "OMA", "OMB", "Innovation",
"SigmaBck2", "SigmaObs2", "MahalanobisConsistency"].
+**"ExtendedBlue"**
+
+ *Required commands*
+ *"Background", "BackgroundError",
+ "Observation", "ObservationError",
+ "ObservationOperator"*
+
+ StoreInternalVariables
+ This boolean key allows to store default internal variables, mainly the
+ current state during iterative optimization process. Be careful, this can be
+ a numerically costly choice in certain calculation cases. The default is
+ "False".
+
+ StoreSupplementaryCalculations
+ This list indicates the names of the supplementary variables that can be
+ available at the end of the algorithm. It involves potentially costly
+ calculations. The default is a void list, none of these variables being
+ calculated and stored by default. The possible names are in the following
+ list: ["APosterioriCovariance", "BMA", "OMA", "OMB", "Innovation",
+ "SigmaBck2", "SigmaObs2", "MahalanobisConsistency"].
+
**"LinearLeastSquares"**
*Required commands*
--- /dev/null
+#-*-coding:iso-8859-1-*-
+#
+# Copyright (C) 2008-2013 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
+m = PlatformInfo.SystemUsage()
+
+import numpy
+
+# ==============================================================================
+class ElementaryAlgorithm(BasicObjects.Algorithm):
+ def __init__(self):
+ BasicObjects.Algorithm.__init__(self, "EXTENDEDBLUE")
+ 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 = ["APosterioriCovariance", "BMA", "OMA", "OMB", "Innovation", "SigmaBck2", "SigmaObs2", "MahalanobisConsistency"]
+ )
+
+ def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
+ logging.debug("%s Lancement"%self._name)
+ logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("M")))
+ #
+ # Paramètres de pilotage
+ # ----------------------
+ self.setParameters(Parameters)
+ #
+ # Opérateur d'observation
+ # -----------------------
+ H = HO["Direct"].appliedTo
+ Hm = HO["Tangent"].asMatrix(Xb)
+ Hm = Hm.reshape(Y.size,Xb.size) # ADAO & check shape
+ Ha = HO["Adjoint"].asMatrix(Xb)
+ Ha = Ha.reshape(Xb.size,Y.size) # ADAO & check shape
+ #
+ # Utilisation éventuelle d'un vecteur H(Xb) précalculé
+ # ----------------------------------------------------
+ if HO["AppliedToX"] is not None and HO["AppliedToX"].has_key("HXb"):
+ HXb = HO["AppliedToX"]["HXb"]
+ else:
+ HXb = H( Xb )
+ HXb = numpy.asmatrix(numpy.ravel( HXb )).T
+ #
+ # Précalcul des inversions de B et R
+ # ----------------------------------
+ BI = B.getI()
+ RI = R.getI()
+ #
+ # Calcul de l'innovation
+ # ----------------------
+ if Y.size != HXb.size:
+ 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))
+ if max(Y.shape) != max(HXb.shape):
+ 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))
+ d = Y - HXb
+ #
+ # Calcul de la matrice de gain et de l'analyse
+ # --------------------------------------------
+ if Y.size <= Xb.size:
+ if Y.size > 100: # len(R)
+ _A = R + Hm * B * Ha
+ _u = numpy.linalg.solve( _A , d )
+ Xa = Xb + B * Ha * _u
+ else:
+ K = B * Ha * (R + Hm * B * Ha).I
+ Xa = Xb + K*d
+ else:
+ if Y.size > 100: # len(R)
+ _A = BI + Ha * RI * Hm
+ _u = numpy.linalg.solve( _A , Ha * RI * d )
+ Xa = Xb + _u
+ else:
+ K = (BI + Ha * RI * Hm).I * Ha * RI
+ Xa = Xb + K*d
+ self.StoredVariables["Analysis"].store( Xa.A1 )
+ #
+ # Calcul de la fonction coût
+ # --------------------------
+ if self._parameters["StoreInternalVariables"] or "OMA" in self._parameters["StoreSupplementaryCalculations"] or "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"] or "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
+ oma = Y - Hm * Xa
+ if self._parameters["StoreInternalVariables"] or "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
+ Jb = 0.5 * (Xa - Xb).T * BI * (Xa - Xb)
+ Jo = 0.5 * oma.T * RI * oma
+ J = float( Jb ) + float( Jo )
+ self.StoredVariables["CostFunctionJb"].store( Jb )
+ self.StoredVariables["CostFunctionJo"].store( Jo )
+ self.StoredVariables["CostFunctionJ" ].store( J )
+ #
+ # Calcul de la covariance d'analyse
+ # ---------------------------------
+ if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
+ A = B - K * Hm * B
+ if min(A.shape) != max(A.shape):
+ 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)))
+ if (numpy.diag(A) < 0).any():
+ 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,))
+ if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
+ try:
+ L = numpy.linalg.cholesky( A )
+ except:
+ 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,))
+ self.StoredVariables["APosterioriCovariance"].store( A )
+ #
+ # Calculs et/ou stockages supplémentaires
+ # ---------------------------------------
+ if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["Innovation"].store( numpy.ravel(d) )
+ if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
+ if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["OMA"].store( numpy.ravel(oma) )
+ if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["OMB"].store( numpy.ravel(d) )
+ if "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"]:
+ TraceR = R.trace(Y.size)
+ self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(oma)).T)) ) / TraceR )
+ if "SigmaBck2" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["SigmaBck2"].store( float( (d.T * Hm * (Xa - Xb))/(Hm * B * Hm.T).trace() ) )
+ if "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["MahalanobisConsistency"].store( float( 2.*J/d.size ) )
+ #
+ logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("M")))
+ logging.debug("%s Terminé"%self._name)
+ #
+ return 0
+
+# ==============================================================================
+if __name__ == "__main__":
+ print '\n AUTODIAGNOSTIC \n'
