.. [Buchinsky98] Buchinsky M., *Recent Advances in Quantile Regression Models: A Practical Guidline for Empirical Research*, Journal of Human Resources, 33(1), pp.88-126, 1998
+.. [Burgers98] Burgers G., Van Leuween P. J., Evensen G., *Analysis scheme in the Ensemble Kalman Filter*, Monthly Weather Review, 126, 1719–1724, 1998
+
.. [Byrd95] Byrd R. H., Lu P., Nocedal J., *A Limited Memory Algorithm for Bound Constrained Optimization*, SIAM Journal on Scientific and Statistical Computing, 16(5), pp.1190-1208, 1995
.. [Cade03] Cade B. S., Noon B. R., *A Gentle Introduction to Quantile Regression for Ecologists*, Frontiers in Ecology and the Environment, 1(8), pp.412-420, 2003
+.. [Evensen94] Evensen G., *Sequential data assimilation with a nonlinear quasi-geostrophic model using monte carlo methods to forecast error statistics*, Journal of Geophysical Research, 99(C5), 10,143–10,162, 1994
+
+.. [Evensen03] Evensen G., *The Ensemble Kalman Filter: theoretical formulation and practical implementation*, Seminar on Recent developments in data assimilation for atmosphere and ocean, ECMWF, 8 to 12 September 2003
+
.. [Ide97] Ide K., Courtier P., Ghil M., Lorenc A. C., *Unified notation for data assimilation: operational, sequential and variational*, Journal of the Meteorological Society of Japan, 75(1B), pp.181-189, 1997
.. [Johnson08] Johnson S. G., *The NLopt nonlinear-optimization package*, http://ab-initio.mit.edu/nlopt
.. [WikipediaDA] Wikipedia, *Data assimilation*, http://en.wikipedia.org/wiki/Data_assimilation
+.. [WikipediaEnKF] Wikipedia, *Ensemble Kalman Filter*, http://en.wikipedia.org/wiki/Ensemble_Kalman_filter
+
.. [WikipediaMO] Wikipedia, *Mathematical optimization*, https://en.wikipedia.org/wiki/Mathematical_optimization
.. [WikipediaND] Wikipedia, *Nondimensionalization*, https://en.wikipedia.org/wiki/Nondimensionalization
-.. [WikipediaPSO] Wikipedia, *Particle swarm optimization*, https://en.wikipedia.org/wiki/Particle_swarm_optimization
+.. [WikipediaPSO] Wikipedia, *Particle Swarm Optimization*, https://en.wikipedia.org/wiki/Particle_swarm_optimization
.. [WikipediaQR] Wikipedia, *Quantile regression*, https://en.wikipedia.org/wiki/Quantile_regression
.. [WikipediaTI] Wikipedia, *Tikhonov regularization*, https://en.wikipedia.org/wiki/Tikhonov_regularization
-.. [WikipediaUKF] Wikipedia, *Unscented Kalman filter*, https://en.wikipedia.org/wiki/Unscented_Kalman_filter
+.. [WikipediaUKF] Wikipedia, *Unscented Kalman Filter*, https://en.wikipedia.org/wiki/Unscented_Kalman_filter
.. [Zhu97] Zhu C., Byrd R. H., Nocedal J., *L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization*, ACM Transactions on Mathematical Software, 23(4), pp.550-560, 1997
--- /dev/null
+..
+ Copyright (C) 2008-2018 EDF R&D
+
+ This file is part of SALOME ADAO module.
+
+ 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, or (at your option) any later version.
+
+ 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
+
+.. index:: single: EnsembleKalmanFilter
+.. _section_ref_algorithm_EnsembleKalmanFilter:
+
+Calculation algorithm "*EnsembleKalmanFilter*"
+----------------------------------------------
+
+.. warning::
+
+ in its present version, this algorithm is experimental, and so changes can be
+ required in forthcoming versions.
+
+Description
++++++++++++
+
+This algorithm realizes an estimation of the state of a dynamic system by a
+Ensemble Kalman Filter (EnKF), avoiding to have to perform the tangent and
+adjoint operators for the observation and evolution operators, as in the simple
+or extended Kalman filter.
+
+It applies to non-linear observation and incremental evolution (process)
+operators with excellent robustness and performance qualities. It can be
+compared to the :ref:`section_ref_algorithm_UnscentedKalmanFilter`, whose
+qualities are similar for non-linear systems.
+
+In case of linear of "slightly" non-linear operators, one can easily use the
+:ref:`section_ref_algorithm_ExtendedKalmanFilter` or even the
+:ref:`section_ref_algorithm_KalmanFilter`, which are often far less expensive
+to evaluate on small systems. One can verify the linearity of the operators
+with the help of the :ref:`section_ref_algorithm_LinearityTest`.
+
+Commandes requises et optionnelles
+++++++++++++++++++++++++++++++++++
+
+The general required commands, available in the editing user interface, are the
+following:
+
+ .. include:: snippets/Background.rst
+
+ .. include:: snippets/BackgroundError.rst
+
+ .. include:: snippets/EvolutionError.rst
+
+ .. include:: snippets/EvolutionModel.rst
+
+ .. include:: snippets/Observation.rst
+
+ .. include:: snippets/ObservationError.rst
+
+ .. include:: snippets/ObservationOperator.rst
+
+The general optional commands, available in the editing user interface, are
+indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
+of the command "*AlgorithmParameters*" allows to choose the specific options,
+described hereafter, of the algorithm. See
+:ref:`section_ref_options_Algorithm_Parameters` for the good use of this
+command.
+
+The options of the algorithm are the following:
+
+ .. include:: snippets/NumberOfMembers.rst
+
+ .. include:: snippets/EstimationOf.rst
+
+ .. include:: snippets/SetSeed.rst
+
+ StoreSupplementaryCalculations
+ .. index:: single: 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 or memory consumptions. The default is a void list, none of
+ these variables being calculated and stored by default. The possible names
+ are in the following list: ["APosterioriCorrelations",
+ "APosterioriCovariance", "APosterioriStandardDeviations",
+ "APosterioriVariances", "BMA", "CostFunctionJ", "CostFunctionJb",
+ "CostFunctionJo", "CurrentState"].
+
+ Example :
+ ``{"StoreSupplementaryCalculations":["CurrentState"]}``
+
+Information and variables available at the end of the algorithm
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+
+At the output, after executing the algorithm, there are variables and
+information originating from the calculation. The description of
+:ref:`section_ref_output_variables` show the way to obtain them by the method
+named ``get`` of the variable "*ADD*" of the post-processing. The input
+variables, available to the user at the output in order to facilitate the
+writing of post-processing procedures, are described in the
+:ref:`subsection_r_o_v_Inventaire`.
+
+The unconditional outputs of the algorithm are the following:
+
+ .. include:: snippets/Analysis.rst
+
+The conditional outputs of the algorithm are the following:
+
+ .. include:: snippets/APosterioriCorrelations.rst
+
+ .. include:: snippets/APosterioriCovariance.rst
+
+ .. include:: snippets/APosterioriStandardDeviations.rst
+
+ .. include:: snippets/APosterioriVariances.rst
+
+ .. include:: snippets/BMA.rst
+
+ .. include:: snippets/CostFunctionJ.rst
+
+ .. include:: snippets/CostFunctionJb.rst
+
+ .. include:: snippets/CostFunctionJo.rst
+
+ .. include:: snippets/CurrentState.rst
+
+ .. include:: snippets/Innovation.rst
+
+See also
+++++++++
+
+References to other sections:
+ - :ref:`section_ref_algorithm_KalmanFilter`
+ - :ref:`section_ref_algorithm_ExtendedKalmanFilter`
+ - :ref:`section_ref_algorithm_UnscentedKalmanFilter`
+
+Bibliographical references:
+ - [Evensen94]_
+ - [Burgers98]_
+ - [Evensen03]_
+ - [WikipediaEnKF]_
ref_algorithm_Blue
ref_algorithm_DerivativeFreeOptimization
ref_algorithm_EnsembleBlue
+ ref_algorithm_EnsembleKalmanFilter
ref_algorithm_ExtendedBlue
ref_algorithm_ExtendedKalmanFilter
ref_algorithm_KalmanFilter
.. [Buchinsky98] Buchinsky M., *Recent Advances in Quantile Regression Models: A Practical Guidline for Empirical Research*, Journal of Human Resources, 33(1), pp.88-126, 1998
+.. [Burgers98] Burgers G., Van Leuween P. J., Evensen G., *Analysis scheme in the Ensemble Kalman Filter*, Monthly Weather Review, 126, 1719–1724, 1998
+
.. [Byrd95] Byrd R. H., Lu P., Nocedal J., *A Limited Memory Algorithm for Bound Constrained Optimization*, SIAM Journal on Scientific and Statistical Computing, 16(5), pp.1190-1208, 1995
.. [Cade03] Cade B. S., Noon B. R., *A Gentle Introduction to Quantile Regression for Ecologists*, Frontiers in Ecology and the Environment, 1(8), pp.412-420, 2003
+.. [Evensen94] Evensen G., *Sequential data assimilation with a nonlinear quasi-geostrophic model using monte carlo methods to forecast error statistics*, Journal of Geophysical Research, 99(C5), 10,143–10,162, 1994
+
+.. [Evensen03] Evensen G., *The Ensemble Kalman Filter: theoretical formulation and practical implementation*, Seminar on Recent developments in data assimilation for atmosphere and ocean, ECMWF, 8 to 12 September 2003
+
.. [Ide97] Ide K., Courtier P., Ghil M., Lorenc A. C., *Unified notation for data assimilation: operational, sequential and variational*, Journal of the Meteorological Society of Japan, 75(1B), pp.181-189, 1997
.. [Johnson08] Johnson S. G., *The NLopt nonlinear-optimization package*, http://ab-initio.mit.edu/nlopt
.. [Tikhonov77] Tikhonov A. N., Arsenin V. Y., *Solution of Ill-posed Problems*, Winston & Sons, 1977
-.. [WikipediaDA] Wikipédia, *Data assimilation*, http://en.wikipedia.org/wiki/Data_assimilation
+.. [WikipediaDA] Wikipedia, *Data assimilation*, http://en.wikipedia.org/wiki/Data_assimilation
+
+.. [WikipediaEnKF] Wikipedia, *Ensemble Kalman Filter*, http://en.wikipedia.org/wiki/Ensemble_Kalman_filter
-.. [WikipediaMO] Wikipédia, *Mathematical optimization*, https://en.wikipedia.org/wiki/Mathematical_optimization
+.. [WikipediaMO] Wikipedia, *Mathematical optimization*, https://en.wikipedia.org/wiki/Mathematical_optimization
-.. [WikipediaND] Wikipédia, *Nondimensionalization*, https://en.wikipedia.org/wiki/Nondimensionalization
+.. [WikipediaND] Wikipedia, *Nondimensionalization*, https://en.wikipedia.org/wiki/Nondimensionalization
-.. [WikipediaPSO] Wikipédia, *Particle swarm optimization*, https://en.wikipedia.org/wiki/Particle_swarm_optimization
+.. [WikipediaPSO] Wikipedia, *Particle Swarm Optimization*, https://en.wikipedia.org/wiki/Particle_swarm_optimization
-.. [WikipediaQR] Wikipédia, *Quantile regression*, https://en.wikipedia.org/wiki/Quantile_regression
+.. [WikipediaQR] Wikipedia, *Quantile regression*, https://en.wikipedia.org/wiki/Quantile_regression
-.. [WikipediaTI] Wikipédia, *Tikhonov regularization*, https://en.wikipedia.org/wiki/Tikhonov_regularization
+.. [WikipediaTI] Wikipedia, *Tikhonov regularization*, https://en.wikipedia.org/wiki/Tikhonov_regularization
-.. [WikipediaUKF] Wikipédia, *Unscented Kalman filter*, https://en.wikipedia.org/wiki/Unscented_Kalman_filter
+.. [WikipediaUKF] Wikipedia, *Unscented Kalman Filter*, https://en.wikipedia.org/wiki/Unscented_Kalman_filter
.. [Zhu97] Zhu C., Byrd R. H., Nocedal J., *L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization*, ACM Transactions on Mathematical Software, 23(4), pp.550-560, 1997
--- /dev/null
+..
+ Copyright (C) 2008-2018 EDF R&D
+
+ This file is part of SALOME ADAO module.
+
+ 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, or (at your option) any later version.
+
+ 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
+
+.. index:: single: EnsembleKalmanFilter
+.. _section_ref_algorithm_EnsembleKalmanFilter:
+
+Algorithme de calcul "*EnsembleKalmanFilter*"
+---------------------------------------------
+
+.. warning::
+
+ dans sa présente version, cet algorithme est expérimental, et reste donc
+ susceptible de changements dans les prochaines versions.
+
+Description
++++++++++++
+
+Cet algorithme réalise une estimation de l'état d'un système dynamique par un
+filtre de Kalman d'ensemble (EnKF), permettant d'éviter de devoir calculer les
+opérateurs tangent ou adjoint pour les opérateurs d'observation ou d'évolution,
+comme dans les filtres de Kalman simple ou étendu.
+
+Il s'applique aux cas d'opérateurs d'observation et d'évolution incrémentale
+(processus) non-linéaires et présente d'excellentes qualités de robustesse et
+de performances. Il peut être comparé à
+l':ref:`section_ref_algorithm_UnscentedKalmanFilter` dont les qualités sont
+similaires pour les systèmes non-linéaires.
+
+Dans le cas d'opérateurs linéaires ou "faiblement" non-linéaire, on peut
+aisément utiliser l':ref:`section_ref_algorithm_ExtendedKalmanFilter` ou même
+l':ref:`section_ref_algorithm_KalmanFilter`, qui sont souvent largement moins
+coûteux en évaluations sur de petits systèmes. On peut vérifier la linéarité
+des opérateurs à l'aide de l':ref:`section_ref_algorithm_LinearityTest`.
+
+Commandes requises et optionnelles
+++++++++++++++++++++++++++++++++++
+
+Les commandes requises générales, disponibles dans l'interface en édition, sont
+les suivantes:
+
+ .. include:: snippets/Background.rst
+
+ .. include:: snippets/BackgroundError.rst
+
+ .. include:: snippets/EvolutionError.rst
+
+ .. include:: snippets/EvolutionModel.rst
+
+ .. include:: snippets/Observation.rst
+
+ .. include:: snippets/ObservationError.rst
+
+ .. include:: snippets/ObservationOperator.rst
+
+Les commandes optionnelles générales, disponibles dans l'interface en édition,
+sont indiquées dans la :ref:`section_ref_assimilation_keywords`. De plus, les
+paramètres de la commande "*AlgorithmParameters*" permettent d'indiquer les
+options particulières, décrites ci-après, de l'algorithme. On se reportera à la
+:ref:`section_ref_options_Algorithm_Parameters` pour le bon usage de cette
+commande.
+
+Les options de l'algorithme sont les suivantes:
+
+ .. include:: snippets/NumberOfMembers.rst
+
+ .. include:: snippets/EstimationOf.rst
+
+ .. include:: snippets/SetSeed.rst
+
+ StoreSupplementaryCalculations
+ .. index:: single: StoreSupplementaryCalculations
+
+ Cette liste indique les noms des variables supplémentaires qui peuvent être
+ disponibles à la fin de l'algorithme. Cela implique potentiellement des
+ calculs ou du stockage coûteux. La valeur par défaut est une liste vide,
+ aucune de ces variables n'étant calculée et stockée par défaut. Les noms
+ possibles sont dans la liste suivante : ["APosterioriCorrelations",
+ "APosterioriCovariance", "APosterioriStandardDeviations",
+ "APosterioriVariances", "BMA", "CostFunctionJ", "CostFunctionJb",
+ "CostFunctionJo", "CurrentState"].
+
+ Exemple :
+ ``{"StoreSupplementaryCalculations":["CurrentState"]}``
+
+Informations et variables disponibles à la fin de l'algorithme
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+
+En sortie, après exécution de l'algorithme, on dispose d'informations et de
+variables issues du calcul. La description des
+:ref:`section_ref_output_variables` indique la manière de les obtenir par la
+méthode nommée ``get`` de la variable "*ADD*" du post-processing. Les variables
+d'entrée, mises à disposition de l'utilisateur en sortie pour faciliter
+l'écriture des procédures de post-processing, sont décrites dans
+l':ref:`subsection_r_o_v_Inventaire`.
+
+Les sorties non conditionnelles de l'algorithme sont les suivantes:
+
+ .. include:: snippets/Analysis.rst
+
+Les sorties conditionnelles de l'algorithme sont les suivantes:
+
+ .. include:: snippets/APosterioriCorrelations.rst
+
+ .. include:: snippets/APosterioriCovariance.rst
+
+ .. include:: snippets/APosterioriStandardDeviations.rst
+
+ .. include:: snippets/APosterioriVariances.rst
+
+ .. include:: snippets/BMA.rst
+
+ .. include:: snippets/CostFunctionJ.rst
+
+ .. include:: snippets/CostFunctionJb.rst
+
+ .. include:: snippets/CostFunctionJo.rst
+
+ .. include:: snippets/CurrentState.rst
+
+ .. include:: snippets/Innovation.rst
+
+Voir aussi
+++++++++++
+
+Références vers d'autres sections :
+ - :ref:`section_ref_algorithm_KalmanFilter`
+ - :ref:`section_ref_algorithm_ExtendedKalmanFilter`
+ - :ref:`section_ref_algorithm_UnscentedKalmanFilter`
+
+Références bibliographiques :
+ - [Evensen94]_
+ - [Burgers98]_
+ - [Evensen03]_
+ - [WikipediaEnKF]_
ref_algorithm_Blue
ref_algorithm_DerivativeFreeOptimization
ref_algorithm_EnsembleBlue
+ ref_algorithm_EnsembleKalmanFilter
ref_algorithm_ExtendedBlue
ref_algorithm_ExtendedKalmanFilter
ref_algorithm_KalmanFilter
