2 Copyright (C) 2008-2021 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 .. index:: single: 3D-Var
26 .. _section_ref_algorithm_3DVAR:
28 Algorithme de calcul "*3DVAR*"
29 ------------------------------
31 .. ------------------------------------ ..
32 .. include:: snippets/Header2Algo01.rst
34 Cet algorithme réalise une estimation d'état par minimisation variationnelle de
35 la fonctionnelle :math:`J` d'écart classique en assimilation de données
38 .. 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}))
40 qui est usuellement désignée comme la fonctionnelle "*3D-Var*" (voir par
41 exemple [Talagrand97]_). Les dénominations "*3D-Var*", "*3D-VAR*" et "*3DVAR*"
44 .. ------------------------------------ ..
45 .. include:: snippets/Header2Algo02.rst
47 .. include:: snippets/Background.rst
49 .. include:: snippets/BackgroundError.rst
51 .. include:: snippets/Observation.rst
53 .. include:: snippets/ObservationError.rst
55 .. include:: snippets/ObservationOperator.rst
57 .. ------------------------------------ ..
58 .. include:: snippets/Header2Algo03AdOp.rst
60 .. include:: snippets/BoundsWithNone.rst
62 .. include:: snippets/CostDecrementTolerance.rst
64 .. include:: snippets/GradientNormTolerance.rst
66 .. include:: snippets/InitializationPoint.rst
68 .. include:: snippets/MaximumNumberOfSteps.rst
70 .. include:: snippets/Minimizer_xDVAR.rst
72 .. include:: snippets/NumberOfSamplesForQuantiles.rst
74 .. include:: snippets/ProjectedGradientTolerance.rst
76 .. include:: snippets/Quantiles.rst
78 .. include:: snippets/SetSeed.rst
80 .. include:: snippets/SimulationForQuantiles.rst
82 StoreSupplementaryCalculations
83 .. index:: single: StoreSupplementaryCalculations
85 *Liste de noms*. Cette liste indique les noms des variables supplémentaires
86 qui peuvent être disponibles au cours du déroulement ou à la fin de
87 l'algorithme, si elles sont initialement demandées par l'utilisateur. Cela
88 implique potentiellement des calculs ou du stockage coûteux. La valeur par
89 défaut est une liste vide, aucune de ces variables n'étant calculée et
90 stockée par défaut sauf les variables inconditionnelles. Les noms possibles
91 sont dans la liste suivante : [
93 "APosterioriCorrelations",
94 "APosterioriCovariance",
95 "APosterioriStandardDeviations",
96 "APosterioriVariances",
99 "CostFunctionJAtCurrentOptimum",
101 "CostFunctionJbAtCurrentOptimum",
103 "CostFunctionJoAtCurrentOptimum",
104 "CurrentIterationNumber",
109 "InnovationAtCurrentState",
110 "JacobianMatrixAtBackground",
111 "JacobianMatrixAtOptimum",
112 "KalmanGainAtOptimum",
113 "MahalanobisConsistency",
117 "SimulatedObservationAtBackground",
118 "SimulatedObservationAtCurrentOptimum",
119 "SimulatedObservationAtCurrentState",
120 "SimulatedObservationAtOptimum",
121 "SimulationQuantiles",
125 ``{"StoreSupplementaryCalculations":["BMA", "CurrentState"]}``
127 .. include:: snippets/Variant_3DVAR.rst
129 .. ------------------------------------ ..
130 .. include:: snippets/Header2Algo04.rst
132 .. include:: snippets/Analysis.rst
134 .. include:: snippets/CostFunctionJ.rst
136 .. include:: snippets/CostFunctionJb.rst
138 .. include:: snippets/CostFunctionJo.rst
140 .. ------------------------------------ ..
141 .. include:: snippets/Header2Algo05.rst
143 .. include:: snippets/Analysis.rst
145 .. include:: snippets/APosterioriCorrelations.rst
147 .. include:: snippets/APosterioriCovariance.rst
149 .. include:: snippets/APosterioriStandardDeviations.rst
151 .. include:: snippets/APosterioriVariances.rst
153 .. include:: snippets/BMA.rst
155 .. include:: snippets/CostFunctionJ.rst
157 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
159 .. include:: snippets/CostFunctionJb.rst
161 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
163 .. include:: snippets/CostFunctionJo.rst
165 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
167 .. include:: snippets/CurrentIterationNumber.rst
169 .. include:: snippets/CurrentOptimum.rst
171 .. include:: snippets/CurrentState.rst
173 .. include:: snippets/IndexOfOptimum.rst
175 .. include:: snippets/Innovation.rst
177 .. include:: snippets/InnovationAtCurrentState.rst
179 .. include:: snippets/JacobianMatrixAtBackground.rst
181 .. include:: snippets/JacobianMatrixAtOptimum.rst
183 .. include:: snippets/KalmanGainAtOptimum.rst
185 .. include:: snippets/MahalanobisConsistency.rst
187 .. include:: snippets/OMA.rst
189 .. include:: snippets/OMB.rst
191 .. include:: snippets/SigmaObs2.rst
193 .. include:: snippets/SimulatedObservationAtBackground.rst
195 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
197 .. include:: snippets/SimulatedObservationAtCurrentState.rst
199 .. include:: snippets/SimulatedObservationAtOptimum.rst
201 .. include:: snippets/SimulationQuantiles.rst
203 .. ------------------------------------ ..
204 .. include:: snippets/Header2Algo09.rst
206 .. include:: scripts/simple_3DVAR.rst
208 .. literalinclude:: scripts/simple_3DVAR.py
210 .. include:: snippets/Header2Algo10.rst
212 .. literalinclude:: scripts/simple_3DVAR.res
214 .. ------------------------------------ ..
215 .. include:: snippets/Header2Algo06.rst
217 - :ref:`section_ref_algorithm_Blue`
218 - :ref:`section_ref_algorithm_ExtendedBlue`
219 - :ref:`section_ref_algorithm_LinearityTest`
221 .. ------------------------------------ ..
222 .. include:: snippets/Header2Algo07.rst