doc/en/ref_algorithm_NonLinearLeastSquares.rst

   1 ..
   2    Copyright (C) 2008-2024 EDF R&D
   3
   4    This file is part of SALOME ADAO module.
   5
   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.
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  11    This library is distributed in the hope that it will be useful,
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  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Lesser General Public License for more details.
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  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
  19
  20    See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
  21
  22    Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
  23
  24 .. index:: single: NonLinearLeastSquares
  25 .. _section_ref_algorithm_NonLinearLeastSquares:
  26
  27 Calculation algorithm "*NonLinearLeastSquares*"
  28 -----------------------------------------------
  29
  30 .. ------------------------------------ ..
  31 .. include:: snippets/Header2Algo01.rst
  32
  33 This algorithm realizes a state estimation by variational minimization of the
  34 classical :math:`J` function of weighted "Least Squares":
  35
  36 .. math:: J(\mathbf{x})=(\mathbf{y}^o-\mathbf{H}.\mathbf{x})^T.\mathbf{R}^{-1}.(\mathbf{y}^o-\mathbf{H}.\mathbf{x})
  37
  38 It is similar to a :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.
  41
  42 This mono-objective optimization algorithm is naturally written for a single
  43 estimate, without any dynamic or iterative notion (there is no need in this
  44 case for an incremental evolution operator, nor for an evolution error
  45 covariance). In ADAO, it can also be used on a succession of observations,
  46 placing the estimate in a recursive framework partly similar to a Kalman
  47 Filter. A standard estimate is made at each observation step on the state
  48 predicted by the incremental evolution model.
  49
  50 In all cases, it is recommended to prefer a :ref:`section_ref_algorithm_3DVAR`
  51 for its stability as for its behavior during optimization.
  52
  53 .. ------------------------------------ ..
  54 .. include:: snippets/Header2Algo12.rst
  55
  56 .. include:: snippets/FeaturePropLocalOptimization.rst
  57
  58 .. include:: snippets/FeaturePropDerivativeNeeded.rst
  59
  60 .. include:: snippets/FeaturePropParallelDerivativesOnly.rst
  61
  62 .. ------------------------------------ ..
  63 .. include:: snippets/Header2Algo02.rst
  64
  65 .. include:: snippets/Background.rst
  66
  67 .. include:: snippets/Observation.rst
  68
  69 .. include:: snippets/ObservationError.rst
  70
  71 .. include:: snippets/ObservationOperator.rst
  72
  73 .. ------------------------------------ ..
  74 .. include:: snippets/Header2Algo03AdOp.rst
  75
  76 .. include:: snippets/BoundsWithNone.rst
  77
  78 .. include:: snippets/CostDecrementTolerance.rst
  79
  80 .. include:: snippets/EstimationOf_Parameters.rst
  81
  82 .. include:: snippets/GradientNormTolerance.rst
  83
  84 .. include:: snippets/InitializationPoint.rst
  85
  86 .. include:: snippets/MaximumNumberOfIterations.rst
  87
  88 .. include:: snippets/Minimizer_xDVAR.rst
  89
  90 .. include:: snippets/ProjectedGradientTolerance.rst
  91
  92
  93 StoreSupplementaryCalculations
  94   .. index:: single: StoreSupplementaryCalculations
  95
  96   *List of names*. This list indicates the names of the supplementary
  97   variables, that can be available during or at the end of the algorithm, if
  98   they are initially required by the user. Their availability involves,
  99   potentially, costly calculations or memory consumptions. The default is then
 100   a void list, none of these variables being calculated and stored by default
 101   (excepted the unconditional variables). The possible names are in the
 102   following list (the detailed description of each named variable is given in
 103   the following part of this specific algorithmic documentation, in the
 104   sub-section "*Information and variables available at the end of the
 105   algorithm*"): [
 106   "Analysis",
 107   "BMA",
 108   "CostFunctionJ",
 109   "CostFunctionJAtCurrentOptimum",
 110   "CostFunctionJb",
 111   "CostFunctionJbAtCurrentOptimum",
 112   "CostFunctionJo",
 113   "CostFunctionJoAtCurrentOptimum",
 114   "CurrentIterationNumber",
 115   "CurrentOptimum",
 116   "CurrentState",
 117   "CurrentStepNumber",
 118   "ForecastState",
 119   "IndexOfOptimum",
 120   "Innovation",
 121   "InnovationAtCurrentAnalysis",
 122   "InnovationAtCurrentState",
 123   "OMA",
 124   "OMB",
 125   "SimulatedObservationAtBackground",
 126   "SimulatedObservationAtCurrentOptimum",
 127   "SimulatedObservationAtCurrentState",
 128   "SimulatedObservationAtOptimum",
 129   ].
 130
 131   Example :
 132   ``{"StoreSupplementaryCalculations":["CurrentState", "Residu"]}``
 133
 134 *Tips for this algorithm:*
 135
 136     As the *"BackgroundError"* command is required for ALL the calculation
 137     algorithms in the graphical interface ADAO EFICAS, you have to provide a
 138     value, even if this command is not required for this algorithm, and will
 139     not be used. The simplest way is to give "1" as a STRING.
 140
 141 .. ------------------------------------ ..
 142 .. include:: snippets/Header2Algo04.rst
 143
 144 .. include:: snippets/Analysis.rst
 145
 146 .. include:: snippets/CostFunctionJ.rst
 147
 148 .. include:: snippets/CostFunctionJb.rst
 149
 150 .. include:: snippets/CostFunctionJo.rst
 151
 152 .. ------------------------------------ ..
 153 .. include:: snippets/Header2Algo05.rst
 154
 155 .. include:: snippets/Analysis.rst
 156
 157 .. include:: snippets/BMA.rst
 158
 159 .. include:: snippets/CostFunctionJ.rst
 160
 161 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 162
 163 .. include:: snippets/CostFunctionJb.rst
 164
 165 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 166
 167 .. include:: snippets/CostFunctionJo.rst
 168
 169 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 170
 171 .. include:: snippets/CurrentIterationNumber.rst
 172
 173 .. include:: snippets/CurrentOptimum.rst
 174
 175 .. include:: snippets/CurrentState.rst
 176
 177 .. include:: snippets/CurrentStepNumber.rst
 178
 179 .. include:: snippets/ForecastState.rst
 180
 181 .. include:: snippets/IndexOfOptimum.rst
 182
 183 .. include:: snippets/Innovation.rst
 184
 185 .. include:: snippets/InnovationAtCurrentAnalysis.rst
 186
 187 .. include:: snippets/InnovationAtCurrentState.rst
 188
 189 .. include:: snippets/OMA.rst
 190
 191 .. include:: snippets/OMB.rst
 192
 193 .. include:: snippets/SimulatedObservationAtBackground.rst
 194
 195 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 196
 197 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 198
 199 .. include:: snippets/SimulatedObservationAtOptimum.rst
 200
 201 .. ------------------------------------ ..
 202 .. _section_ref_algorithm_NonLinearLeastSquares_examples:
 203
 204 .. include:: snippets/Header2Algo09.rst
 205
 206 .. include:: scripts/simple_NonLinearLeastSquares.rst
 207
 208 .. literalinclude:: scripts/simple_NonLinearLeastSquares.py
 209
 210 .. include:: snippets/Header2Algo10.rst
 211
 212 .. literalinclude:: scripts/simple_NonLinearLeastSquares.res
 213
 214 .. include:: snippets/Header2Algo11.rst
 215
 216 .. _simple_NonLinearLeastSquares:
 217 .. image:: scripts/simple_NonLinearLeastSquares.png
 218   :align: center
 219   :width: 90%
 220
 221 .. ------------------------------------ ..
 222 .. include:: snippets/Header2Algo06.rst
 223
 224 - :ref:`section_ref_algorithm_LinearLeastSquares`
 225 - :ref:`section_ref_algorithm_3DVAR`
 226 - :ref:`section_ref_algorithm_LinearityTest`
 227
 228 .. ------------------------------------ ..
 229 .. include:: snippets/Header2Algo07.rst
 230
 231 - [Byrd95]_
 232 - [Morales11]_
 233 - [Zhu97]_