2 Copyright (C) 2008-2018 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 Calculation algorithm "*NonLinearLeastSquares*"
28 -----------------------------------------------
33 This algorithm realizes a state estimation by variational minimization of the
34 classical :math:`J` function of weighted "Least Squares":
36 .. math:: J(\mathbf{x})=(\mathbf{y}^o-\mathbf{H}.\mathbf{x})^T.\mathbf{R}^{-1}.(\mathbf{y}^o-\mathbf{H}.\mathbf{x})
38 It is similar to the :ref:`section_ref_algorithm_3DVAR`, without its background
39 part. The background, required in the interface, is only used as an initial
40 point for the variational minimization.
42 In all cases, it is recommended to prefer the :ref:`section_ref_algorithm_3DVAR`
43 for its stability as for its behavior during optimization.
45 Optional and required commands
46 ++++++++++++++++++++++++++++++
48 The general required commands, available in the editing user interface, are the
51 .. include:: snippets/Background.rst
53 .. include:: snippets/Observation.rst
55 .. include:: snippets/ObservationError.rst
57 .. include:: snippets/ObservationOperator.rst
59 The general optional commands, available in the editing user interface, are
60 indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
61 of the command "*AlgorithmParameters*" allows to choose the specific options,
62 described hereafter, of the algorithm. See
63 :ref:`section_ref_options_Algorithm_Parameters` for the good use of this
66 The options of the algorithm are the following:
69 .. index:: single: Minimizer
71 This key allows to choose the optimization minimizer. The default choice is
72 "LBFGSB", and the possible ones are "LBFGSB" (nonlinear constrained
73 minimizer, see [Byrd95]_, [Morales11]_ and [Zhu97]_), "TNC" (nonlinear
74 constrained minimizer), "CG" (nonlinear unconstrained minimizer), "BFGS"
75 (nonlinear unconstrained minimizer), "NCG" (Newton CG minimizer). It is
76 strongly recommended to stay with the default.
79 ``{"Minimizer":"LBFGSB"}``
81 .. include:: snippets/BoundsWithNone.rst
83 .. include:: snippets/MaximumNumberOfSteps.rst
85 .. include:: snippets/CostDecrementTolerance.rst
87 .. include:: snippets/ProjectedGradientTolerance.rst
89 .. include:: snippets/GradientNormTolerance.rst
91 StoreSupplementaryCalculations
92 .. index:: single: StoreSupplementaryCalculations
94 This list indicates the names of the supplementary variables that can be
95 available at the end of the algorithm. It involves potentially costly
96 calculations or memory consumptions. The default is a void list, none of
97 these variables being calculated and stored by default. The possible names
98 are in the following list: ["BMA", "CostFunctionJ",
99 "CostFunctionJb", "CostFunctionJo", "CostFunctionJAtCurrentOptimum",
100 "CostFunctionJbAtCurrentOptimum", "CostFunctionJoAtCurrentOptimum",
101 "CurrentState", "CurrentOptimum", "IndexOfOptimum", "Innovation",
102 "InnovationAtCurrentState", "OMA", "OMB",
103 "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentState",
104 "SimulatedObservationAtOptimum", "SimulatedObservationAtCurrentOptimum"].
107 ``{"StoreSupplementaryCalculations":["BMA", "Innovation"]}``
109 *Tips for this algorithm:*
111 As the *"BackgroundError"* command is required for ALL the calculation
112 algorithms in the interface, you have to provide a value, even if this
113 command is not required for this algorithm, and will not be used. The
114 simplest way is to give "1" as a STRING.
116 Information and variables available at the end of the algorithm
117 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
119 At the output, after executing the algorithm, there are variables and
120 information originating from the calculation. The description of
121 :ref:`section_ref_output_variables` show the way to obtain them by the method
122 named ``get`` of the variable "*ADD*" of the post-processing. The input
123 variables, available to the user at the output in order to facilitate the
124 writing of post-processing procedures, are described in the
125 :ref:`subsection_r_o_v_Inventaire`.
127 The unconditional outputs of the algorithm are the following:
129 .. include:: snippets/Analysis.rst
131 .. include:: snippets/CostFunctionJ.rst
133 .. include:: snippets/CostFunctionJb.rst
135 .. include:: snippets/CostFunctionJo.rst
137 The conditional outputs of the algorithm are the following:
139 .. include:: snippets/BMA.rst
141 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
143 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
145 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
147 .. include:: snippets/CurrentOptimum.rst
149 .. include:: snippets/CurrentState.rst
151 .. include:: snippets/IndexOfOptimum.rst
153 .. include:: snippets/Innovation.rst
155 .. include:: snippets/InnovationAtCurrentState.rst
157 .. include:: snippets/OMA.rst
159 .. include:: snippets/OMB.rst
161 .. include:: snippets/SimulatedObservationAtBackground.rst
163 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
165 .. include:: snippets/SimulatedObservationAtCurrentState.rst
167 .. include:: snippets/SimulatedObservationAtOptimum.rst
172 References to other sections:
173 - :ref:`section_ref_algorithm_3DVAR`
175 Bibliographical references: