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: NonLinearLeastSquares
25 .. _section_ref_algorithm_NonLinearLeastSquares:
27 Algorithme de calcul "*NonLinearLeastSquares*"
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 de "Moindres Carrés" pondérés:
36 .. math:: J(\mathbf{x})=(\mathbf{y}^o-\mathbf{H}.\mathbf{x})^T.\mathbf{R}^{-1}.(\mathbf{y}^o-\mathbf{H}.\mathbf{x})
38 Il est similaire à l':ref:`section_ref_algorithm_3DVAR` privé de sa partie
39 ébauche. L'ébauche, requise dans l'interface, ne sert que de point initial pour
40 la minimisation variationnelle.
42 Dans tous les cas, il est recommandé de lui préférer
43 l':ref:`section_ref_algorithm_3DVAR` pour sa stabilité comme pour son
44 comportement lors de l'optimisation.
46 .. ------------------------------------ ..
47 .. include:: snippets/Header2Algo02.rst
49 .. include:: snippets/Background.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/MaximumNumberOfSteps.rst
68 .. include:: snippets/Minimizer_xDVAR.rst
70 .. include:: snippets/ProjectedGradientTolerance.rst
73 StoreSupplementaryCalculations
74 .. index:: single: StoreSupplementaryCalculations
76 *Liste de noms*. Cette liste indique les noms des variables supplémentaires
77 qui peuvent être disponibles au cours du déroulement ou à la fin de
78 l'algorithme, si elles sont initialement demandées par l'utilisateur. Cela
79 implique potentiellement des calculs ou du stockage coûteux. La valeur par
80 défaut est une liste vide, aucune de ces variables n'étant calculée et
81 stockée par défaut sauf les variables inconditionnelles. Les noms possibles
82 sont dans la liste suivante : [
86 "CostFunctionJAtCurrentOptimum",
88 "CostFunctionJbAtCurrentOptimum",
90 "CostFunctionJoAtCurrentOptimum",
91 "CurrentIterationNumber",
96 "InnovationAtCurrentState",
99 "SimulatedObservationAtBackground",
100 "SimulatedObservationAtCurrentOptimum",
101 "SimulatedObservationAtCurrentState",
102 "SimulatedObservationAtOptimum",
106 ``{"StoreSupplementaryCalculations":["BMA", "CurrentState"]}``
108 *Astuce pour cet algorithme :*
110 Comme la commande *"BackgroundError"* est requise pour TOUS les algorithmes
111 de calcul dans l'interface graphique EFICAS d'ADAO, vous devez fournir une
112 valeur, malgré le fait que cette commande ne soit pas nécessaire pour cet
113 algorithme, et n'est donc pas utilisée. La manière la plus simple est de
114 donner "1" comme un STRING.
116 .. ------------------------------------ ..
117 .. include:: snippets/Header2Algo04.rst
119 .. include:: snippets/Analysis.rst
121 .. include:: snippets/CostFunctionJ.rst
123 .. include:: snippets/CostFunctionJb.rst
125 .. include:: snippets/CostFunctionJo.rst
127 .. ------------------------------------ ..
128 .. include:: snippets/Header2Algo05.rst
130 .. include:: snippets/Analysis.rst
132 .. include:: snippets/BMA.rst
134 .. include:: snippets/CostFunctionJ.rst
136 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
138 .. include:: snippets/CostFunctionJb.rst
140 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
142 .. include:: snippets/CostFunctionJo.rst
144 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
146 .. include:: snippets/CurrentIterationNumber.rst
148 .. include:: snippets/CurrentOptimum.rst
150 .. include:: snippets/CurrentState.rst
152 .. include:: snippets/IndexOfOptimum.rst
154 .. include:: snippets/Innovation.rst
156 .. include:: snippets/InnovationAtCurrentState.rst
158 .. include:: snippets/OMA.rst
160 .. include:: snippets/OMB.rst
162 .. include:: snippets/SimulatedObservationAtBackground.rst
164 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
166 .. include:: snippets/SimulatedObservationAtCurrentState.rst
168 .. include:: snippets/SimulatedObservationAtOptimum.rst
170 .. ------------------------------------ ..
171 .. include:: snippets/Header2Algo09.rst
173 .. literalinclude:: scripts/simple_NonLinearLeastSquares.py
175 .. include:: snippets/Header2Algo10.rst
177 .. literalinclude:: scripts/simple_NonLinearLeastSquares.res
179 .. ------------------------------------ ..
180 .. include:: snippets/Header2Algo06.rst
182 - :ref:`section_ref_algorithm_3DVAR`
184 .. ------------------------------------ ..
185 .. include:: snippets/Header2Algo07.rst