2 Copyright (C) 2008-2020 EDF R&D
4 This file is part of SALOME ADAO module.
6 This library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
11 This library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
16 You should have received a copy of the GNU Lesser General Public
17 License along with this library; if not, write to the Free Software
18 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
20 See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
22 Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
24 .. index:: single: 3DVAR
25 .. _section_ref_algorithm_3DVAR:
27 Algorithme de calcul "*3DVAR*"
28 ------------------------------
30 .. ------------------------------------ ..
31 .. include:: snippets/Header2Algo01.rst
33 Cet algorithme réalise une estimation d'état par minimisation variationnelle de
34 la fonctionnelle :math:`J` d'écart classique en assimilation de données
37 .. math:: J(\mathbf{x})=(\mathbf{x}-\mathbf{x}^b)^T.\mathbf{B}^{-1}.(\mathbf{x}-\mathbf{x}^b)+(\mathbf{y}^o-H(\mathbf{x}))^T.\mathbf{R}^{-1}.(\mathbf{y}^o-H(\mathbf{x}))
39 qui est usuellement désignée comme la fonctionnelle "*3D-VAR*" (voir par exemple
42 .. ------------------------------------ ..
43 .. include:: snippets/Header2Algo02.rst
45 .. include:: snippets/Background.rst
47 .. include:: snippets/BackgroundError.rst
49 .. include:: snippets/Observation.rst
51 .. include:: snippets/ObservationError.rst
53 .. include:: snippets/ObservationOperator.rst
55 .. ------------------------------------ ..
56 .. include:: snippets/Header2Algo03AdOp.rst
58 .. include:: snippets/BoundsWithNone.rst
60 .. include:: snippets/CostDecrementTolerance.rst
62 .. include:: snippets/GradientNormTolerance.rst
64 .. include:: snippets/MaximumNumberOfSteps.rst
67 .. index:: single: Minimizer
69 Cette clé permet de changer le minimiseur pour l'optimiseur. Le choix par
70 défaut est "LBFGSB", et les choix possibles sont "LBFGSB" (minimisation non
71 linéaire sous contraintes, voir [Byrd95]_, [Morales11]_ et [Zhu97]_), "TNC"
72 (minimisation non linéaire sous contraintes), "CG" (minimisation non
73 linéaire sans contraintes), "BFGS" (minimisation non linéaire sans
74 contraintes), "NCG" (minimisation de type gradient conjugué de Newton). Il
75 est fortement conseillé de conserver la valeur par défaut.
78 ``{"Minimizer":"LBFGSB"}``
80 .. include:: snippets/NumberOfSamplesForQuantiles.rst
82 .. include:: snippets/ProjectedGradientTolerance.rst
84 .. include:: snippets/Quantiles.rst
86 .. include:: snippets/SetSeed.rst
88 .. include:: snippets/SimulationForQuantiles.rst
90 StoreSupplementaryCalculations
91 .. index:: single: StoreSupplementaryCalculations
93 Cette liste indique les noms des variables supplémentaires qui peuvent être
94 disponibles à la fin de l'algorithme, si elles sont initialement demandées par
95 l'utilisateur. Cela implique potentiellement des calculs ou du stockage
96 coûteux. La valeur par défaut est une liste vide, aucune de ces variables
97 n'étant calculée et stockée par défaut sauf les variables inconditionnelles.
98 Les noms possibles sont dans la liste suivante : [
100 "APosterioriCorrelations",
101 "APosterioriCovariance",
102 "APosterioriStandardDeviations",
103 "APosterioriVariances",
106 "CostFunctionJAtCurrentOptimum",
108 "CostFunctionJbAtCurrentOptimum",
110 "CostFunctionJoAtCurrentOptimum",
115 "InnovationAtCurrentState",
116 "JacobianMatrixAtBackground",
117 "JacobianMatrixAtOptimum",
118 "KalmanGainAtOptimum",
119 "MahalanobisConsistency",
123 "SimulatedObservationAtBackground",
124 "SimulatedObservationAtCurrentOptimum",
125 "SimulatedObservationAtCurrentState",
126 "SimulatedObservationAtOptimum",
127 "SimulationQuantiles",
131 ``{"StoreSupplementaryCalculations":["BMA", "CurrentState"]}``
133 .. ------------------------------------ ..
134 .. include:: snippets/Header2Algo04.rst
136 .. include:: snippets/Analysis.rst
138 .. include:: snippets/CostFunctionJ.rst
140 .. include:: snippets/CostFunctionJb.rst
142 .. include:: snippets/CostFunctionJo.rst
144 .. ------------------------------------ ..
145 .. include:: snippets/Header2Algo05.rst
147 .. include:: snippets/Analysis.rst
149 .. include:: snippets/APosterioriCorrelations.rst
151 .. include:: snippets/APosterioriCovariance.rst
153 .. include:: snippets/APosterioriStandardDeviations.rst
155 .. include:: snippets/APosterioriVariances.rst
157 .. include:: snippets/BMA.rst
159 .. include:: snippets/CostFunctionJ.rst
161 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
163 .. include:: snippets/CostFunctionJb.rst
165 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
167 .. include:: snippets/CostFunctionJo.rst
169 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
171 .. include:: snippets/CurrentOptimum.rst
173 .. include:: snippets/CurrentState.rst
175 .. include:: snippets/IndexOfOptimum.rst
177 .. include:: snippets/Innovation.rst
179 .. include:: snippets/InnovationAtCurrentState.rst
181 .. include:: snippets/JacobianMatrixAtBackground.rst
183 .. include:: snippets/JacobianMatrixAtOptimum.rst
185 .. include:: snippets/KalmanGainAtOptimum.rst
187 .. include:: snippets/MahalanobisConsistency.rst
189 .. include:: snippets/OMA.rst
191 .. include:: snippets/OMB.rst
193 .. include:: snippets/SigmaObs2.rst
195 .. include:: snippets/SimulatedObservationAtBackground.rst
197 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
199 .. include:: snippets/SimulatedObservationAtCurrentState.rst
201 .. include:: snippets/SimulatedObservationAtOptimum.rst
203 .. include:: snippets/SimulationQuantiles.rst
205 .. ------------------------------------ ..
206 .. include:: snippets/Header2Algo06.rst
208 - :ref:`section_ref_algorithm_Blue`
209 - :ref:`section_ref_algorithm_ExtendedBlue`
210 - :ref:`section_ref_algorithm_LinearityTest`
212 .. ------------------------------------ ..
213 .. include:: snippets/Header2Algo07.rst