doc/en/ref_algorithm_NonLinearLeastSquares.rst

   1 ..
   2    Copyright (C) 2008-2020 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
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   8    License as published by the Free Software Foundation; either
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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
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  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 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.
  41
  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.
  44
  45 .. ------------------------------------ ..
  46 .. include:: snippets/Header2Algo02.rst
  47
  48 .. include:: snippets/Background.rst
  49
  50 .. include:: snippets/Observation.rst
  51
  52 .. include:: snippets/ObservationError.rst
  53
  54 .. include:: snippets/ObservationOperator.rst
  55
  56 .. ------------------------------------ ..
  57 .. include:: snippets/Header2Algo03AdOp.rst
  58
  59 Minimizer
  60   .. index:: single: Minimizer
  61
  62   This key allows to choose the optimization minimizer. The default choice is
  63   "LBFGSB", and the possible ones are "LBFGSB" (nonlinear constrained
  64   minimizer, see [Byrd95]_, [Morales11]_ and [Zhu97]_), "TNC" (nonlinear
  65   constrained minimizer), "CG" (nonlinear unconstrained minimizer), "BFGS"
  66   (nonlinear unconstrained minimizer), "NCG" (Newton CG minimizer). It is
  67   strongly recommended to stay with the default.
  68
  69   Example :
  70   ``{"Minimizer":"LBFGSB"}``
  71
  72 .. include:: snippets/BoundsWithNone.rst
  73
  74 .. include:: snippets/MaximumNumberOfSteps.rst
  75
  76 .. include:: snippets/CostDecrementTolerance.rst
  77
  78 .. include:: snippets/ProjectedGradientTolerance.rst
  79
  80 .. include:: snippets/GradientNormTolerance.rst
  81
  82 StoreSupplementaryCalculations
  83   .. index:: single: StoreSupplementaryCalculations
  84
  85   This list indicates the names of the supplementary variables that can be
  86   available at the end of the algorithm, if they are initially required by the
  87   user. It involves potentially costly calculations or memory consumptions. The
  88   default is a void list, none of these variables being calculated and stored
  89   by default excepted the unconditionnal variables. The possible names are in
  90   the following list: [
  91   "Analysis",
  92   "BMA",
  93   "CostFunctionJ",
  94   "CostFunctionJAtCurrentOptimum",
  95   "CostFunctionJb",
  96   "CostFunctionJbAtCurrentOptimum",
  97   "CostFunctionJo",
  98   "CostFunctionJoAtCurrentOptimum",
  99   "CurrentOptimum",
 100   "CurrentState",
 101   "IndexOfOptimum",
 102   "Innovation",
 103   "InnovationAtCurrentState",
 104   "OMA",
 105   "OMB",
 106   "SimulatedObservationAtBackground",
 107   "SimulatedObservationAtCurrentOptimum",
 108   "SimulatedObservationAtCurrentState",
 109   "SimulatedObservationAtOptimum",
 110   ].
 111
 112   Example :
 113   ``{"StoreSupplementaryCalculations":["BMA", "CurrentState"]}``
 114
 115 *Tips for this algorithm:*
 116
 117     As the *"BackgroundError"* command is required for ALL the calculation
 118     algorithms in the graphical interface ADAO EFICAS, you have to provide a
 119     value, even if this command is not required for this algorithm, and will
 120     not be used. The simplest way is to give "1" as a STRING.
 121
 122 .. ------------------------------------ ..
 123 .. include:: snippets/Header2Algo04.rst
 124
 125 .. include:: snippets/Analysis.rst
 126
 127 .. include:: snippets/CostFunctionJ.rst
 128
 129 .. include:: snippets/CostFunctionJb.rst
 130
 131 .. include:: snippets/CostFunctionJo.rst
 132
 133 .. ------------------------------------ ..
 134 .. include:: snippets/Header2Algo05.rst
 135
 136 .. include:: snippets/Analysis.rst
 137
 138 .. include:: snippets/BMA.rst
 139
 140 .. include:: snippets/CostFunctionJ.rst
 141
 142 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 143
 144 .. include:: snippets/CostFunctionJb.rst
 145
 146 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 147
 148 .. include:: snippets/CostFunctionJo.rst
 149
 150 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 151
 152 .. include:: snippets/CurrentOptimum.rst
 153
 154 .. include:: snippets/CurrentState.rst
 155
 156 .. include:: snippets/IndexOfOptimum.rst
 157
 158 .. include:: snippets/Innovation.rst
 159
 160 .. include:: snippets/InnovationAtCurrentState.rst
 161
 162 .. include:: snippets/OMA.rst
 163
 164 .. include:: snippets/OMB.rst
 165
 166 .. include:: snippets/SimulatedObservationAtBackground.rst
 167
 168 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 169
 170 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 171
 172 .. include:: snippets/SimulatedObservationAtOptimum.rst
 173
 174 .. ------------------------------------ ..
 175 .. include:: snippets/Header2Algo09.rst
 176
 177 .. literalinclude:: scripts/simple_NonLinearLeastSquares.py
 178
 179 .. include:: snippets/Header2Algo10.rst
 180
 181 .. literalinclude:: scripts/simple_NonLinearLeastSquares.res
 182
 183 .. ------------------------------------ ..
 184 .. include:: snippets/Header2Algo06.rst
 185
 186 - :ref:`section_ref_algorithm_3DVAR`
 187
 188 .. ------------------------------------ ..
 189 .. include:: snippets/Header2Algo07.rst
 190
 191 - [Byrd95]_
 192 - [Morales11]_
 193 - [Zhu97]_