doc/en/ref_algorithm_3DVAR.rst

   1 ..
   2    Copyright (C) 2008-2020 EDF R&D
   3
   4    This file is part of SALOME ADAO module.
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   6    This library is free software; you can redistribute it and/or
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  11    This library is distributed in the hope that it will be useful,
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  14    Lesser General Public License for more details.
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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: 3DVAR
  25 .. _section_ref_algorithm_3DVAR:
  26
  27 Calculation algorithm "*3DVAR*"
  28 -------------------------------
  29
  30 .. ------------------------------------ ..
  31 .. include:: snippets/Header2Algo01.rst
  32
  33 This algorithm performs a state estimation by variational minimization of the
  34 classical :math:`J` function in static data assimilation:
  35
  36 .. 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}))
  37
  38 which is usually designed as the "*3D-VAR*" function (see for example
  39 [Talagrand97]_).
  40
  41 .. ------------------------------------ ..
  42 .. include:: snippets/Header2Algo02.rst
  43
  44 .. include:: snippets/Background.rst
  45
  46 .. include:: snippets/BackgroundError.rst
  47
  48 .. include:: snippets/Observation.rst
  49
  50 .. include:: snippets/ObservationError.rst
  51
  52 .. include:: snippets/ObservationOperator.rst
  53
  54 .. ------------------------------------ ..
  55 .. include:: snippets/Header2Algo03AdOp.rst
  56
  57 .. include:: snippets/BoundsWithNone.rst
  58
  59 .. include:: snippets/CostDecrementTolerance.rst
  60
  61 .. include:: snippets/GradientNormTolerance.rst
  62
  63 .. include:: snippets/MaximumNumberOfSteps.rst
  64
  65 Minimizer
  66   .. index:: single: Minimizer
  67
  68   This key allows to choose the optimization minimizer. The default choice is
  69   "LBFGSB", and the possible ones are "LBFGSB" (nonlinear constrained
  70   minimizer, see [Byrd95]_, [Morales11]_ and [Zhu97]_), "TNC" (nonlinear
  71   constrained minimizer), "CG" (nonlinear unconstrained minimizer), "BFGS"
  72   (nonlinear unconstrained minimizer), "NCG" (Newton CG minimizer). It is
  73   strongly recommended to stay with the default.
  74
  75   Example :
  76   ``{"Minimizer":"LBFGSB"}``
  77
  78 .. include:: snippets/NumberOfSamplesForQuantiles.rst
  79
  80 .. include:: snippets/ProjectedGradientTolerance.rst
  81
  82 .. include:: snippets/Quantiles.rst
  83
  84 .. include:: snippets/SetSeed.rst
  85
  86 .. include:: snippets/SimulationForQuantiles.rst
  87
  88 StoreSupplementaryCalculations
  89   .. index:: single: StoreSupplementaryCalculations
  90
  91   This list indicates the names of the supplementary variables that can be
  92   available at the end of the algorithm, if they are initially required by the
  93   user. It involves potentially costly calculations or memory consumptions. The
  94   default is a void list, none of these variables being calculated and stored
  95   by default excepted the unconditionnal variables. The possible names are in
  96   the following list: [
  97   "Analysis",
  98   "APosterioriCorrelations",
  99   "APosterioriCovariance",
 100   "APosterioriStandardDeviations",
 101   "APosterioriVariances",
 102   "BMA",
 103   "CostFunctionJ",
 104   "CostFunctionJAtCurrentOptimum",
 105   "CostFunctionJb",
 106   "CostFunctionJbAtCurrentOptimum",
 107   "CostFunctionJo",
 108   "CostFunctionJoAtCurrentOptimum",
 109   "CurrentOptimum",
 110   "CurrentState",
 111   "IndexOfOptimum",
 112   "Innovation",
 113   "InnovationAtCurrentState",
 114   "JacobianMatrixAtBackground",
 115   "JacobianMatrixAtOptimum",
 116   "KalmanGainAtOptimum",
 117   "MahalanobisConsistency",
 118   "OMA",
 119   "OMB",
 120   "SigmaObs2",
 121   "SimulatedObservationAtBackground",
 122   "SimulatedObservationAtCurrentOptimum",
 123   "SimulatedObservationAtCurrentState",
 124   "SimulatedObservationAtOptimum",
 125   "SimulationQuantiles",
 126   ].
 127
 128   Example :
 129   ``{"StoreSupplementaryCalculations":["BMA", "CurrentState"]}``
 130
 131 .. ------------------------------------ ..
 132 .. include:: snippets/Header2Algo04.rst
 133
 134 .. include:: snippets/Analysis.rst
 135
 136 .. include:: snippets/CostFunctionJ.rst
 137
 138 .. include:: snippets/CostFunctionJb.rst
 139
 140 .. include:: snippets/CostFunctionJo.rst
 141
 142 .. ------------------------------------ ..
 143 .. include:: snippets/Header2Algo05.rst
 144
 145 .. include:: snippets/Analysis.rst
 146
 147 .. include:: snippets/APosterioriCorrelations.rst
 148
 149 .. include:: snippets/APosterioriCovariance.rst
 150
 151 .. include:: snippets/APosterioriStandardDeviations.rst
 152
 153 .. include:: snippets/APosterioriVariances.rst
 154
 155 .. include:: snippets/BMA.rst
 156
 157 .. include:: snippets/CostFunctionJ.rst
 158
 159 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 160
 161 .. include:: snippets/CostFunctionJb.rst
 162
 163 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 164
 165 .. include:: snippets/CostFunctionJo.rst
 166
 167 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 168
 169 .. include:: snippets/CurrentOptimum.rst
 170
 171 .. include:: snippets/CurrentState.rst
 172
 173 .. include:: snippets/IndexOfOptimum.rst
 174
 175 .. include:: snippets/Innovation.rst
 176
 177 .. include:: snippets/InnovationAtCurrentState.rst
 178
 179 .. include:: snippets/JacobianMatrixAtBackground.rst
 180
 181 .. include:: snippets/JacobianMatrixAtOptimum.rst
 182
 183 .. include:: snippets/KalmanGainAtOptimum.rst
 184
 185 .. include:: snippets/MahalanobisConsistency.rst
 186
 187 .. include:: snippets/OMA.rst
 188
 189 .. include:: snippets/OMB.rst
 190
 191 .. include:: snippets/SigmaObs2.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 .. include:: snippets/SimulationQuantiles.rst
 202
 203 .. ------------------------------------ ..
 204 .. include:: snippets/Header2Algo06.rst
 205
 206 - :ref:`section_ref_algorithm_Blue`
 207 - :ref:`section_ref_algorithm_ExtendedBlue`
 208 - :ref:`section_ref_algorithm_LinearityTest`
 209
 210 .. ------------------------------------ ..
 211 .. include:: snippets/Header2Algo07.rst
 212
 213 - [Byrd95]_
 214 - [Morales11]_
 215 - [Talagrand97]_
 216 - [Zhu97]_