doc/fr/ref_algorithm_3DVAR.rst

   1 ..
   2    Copyright (C) 2008-2020 EDF R&D
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   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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  20    See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
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  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 Algorithme de calcul "*3DVAR*"
  28 ------------------------------
  29
  30 .. ------------------------------------ ..
  31 .. include:: snippets/Header2Algo01.rst
  32
  33 Cet algorithme réalise une estimation d'état par minimisation variationnelle de
  34 la fonctionnelle :math:`J` d'écart classique en assimilation de données
  35 statique:
  36
  37 .. 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}))
  38
  39 qui est usuellement désignée comme la fonctionnelle "*3D-VAR*" (voir par exemple
  40 [Talagrand97]_).
  41
  42 .. ------------------------------------ ..
  43 .. include:: snippets/Header2Algo02.rst
  44
  45 .. include:: snippets/Background.rst
  46
  47 .. include:: snippets/BackgroundError.rst
  48
  49 .. include:: snippets/Observation.rst
  50
  51 .. include:: snippets/ObservationError.rst
  52
  53 .. include:: snippets/ObservationOperator.rst
  54
  55 .. ------------------------------------ ..
  56 .. include:: snippets/Header2Algo03AdOp.rst
  57
  58 .. include:: snippets/BoundsWithNone.rst
  59
  60 .. include:: snippets/CostDecrementTolerance.rst
  61
  62 .. include:: snippets/GradientNormTolerance.rst
  63
  64 .. include:: snippets/MaximumNumberOfSteps.rst
  65
  66 .. include:: snippets/Minimizer_xDVAR.rst
  67
  68 .. include:: snippets/NumberOfSamplesForQuantiles.rst
  69
  70 .. include:: snippets/ProjectedGradientTolerance.rst
  71
  72 .. include:: snippets/Quantiles.rst
  73
  74 .. include:: snippets/SetSeed.rst
  75
  76 .. include:: snippets/SimulationForQuantiles.rst
  77
  78 StoreSupplementaryCalculations
  79   .. index:: single: StoreSupplementaryCalculations
  80
  81   Cette liste indique les noms des variables supplémentaires qui peuvent être
  82   disponibles à la fin de l'algorithme, si elles sont initialement demandées par
  83   l'utilisateur. Cela implique potentiellement des calculs ou du stockage
  84   coûteux. La valeur par défaut est une liste vide, aucune de ces variables
  85   n'étant calculée et stockée par défaut sauf les variables inconditionnelles.
  86   Les noms possibles sont dans la liste suivante : [
  87   "Analysis",
  88   "APosterioriCorrelations",
  89   "APosterioriCovariance",
  90   "APosterioriStandardDeviations",
  91   "APosterioriVariances",
  92   "BMA",
  93   "CostFunctionJ",
  94   "CostFunctionJAtCurrentOptimum",
  95   "CostFunctionJb",
  96   "CostFunctionJbAtCurrentOptimum",
  97   "CostFunctionJo",
  98   "CostFunctionJoAtCurrentOptimum",
  99   "CurrentIterationNumber",
 100   "CurrentOptimum",
 101   "CurrentState",
 102   "IndexOfOptimum",
 103   "Innovation",
 104   "InnovationAtCurrentState",
 105   "JacobianMatrixAtBackground",
 106   "JacobianMatrixAtOptimum",
 107   "KalmanGainAtOptimum",
 108   "MahalanobisConsistency",
 109   "OMA",
 110   "OMB",
 111   "SigmaObs2",
 112   "SimulatedObservationAtBackground",
 113   "SimulatedObservationAtCurrentOptimum",
 114   "SimulatedObservationAtCurrentState",
 115   "SimulatedObservationAtOptimum",
 116   "SimulationQuantiles",
 117   ].
 118
 119   Exemple :
 120   ``{"StoreSupplementaryCalculations":["BMA", "CurrentState"]}``
 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/APosterioriCorrelations.rst
 139
 140 .. include:: snippets/APosterioriCovariance.rst
 141
 142 .. include:: snippets/APosterioriStandardDeviations.rst
 143
 144 .. include:: snippets/APosterioriVariances.rst
 145
 146 .. include:: snippets/BMA.rst
 147
 148 .. include:: snippets/CostFunctionJ.rst
 149
 150 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 151
 152 .. include:: snippets/CostFunctionJb.rst
 153
 154 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 155
 156 .. include:: snippets/CostFunctionJo.rst
 157
 158 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 159
 160 .. include:: snippets/CurrentIterationNumber.rst
 161
 162 .. include:: snippets/CurrentOptimum.rst
 163
 164 .. include:: snippets/CurrentState.rst
 165
 166 .. include:: snippets/IndexOfOptimum.rst
 167
 168 .. include:: snippets/Innovation.rst
 169
 170 .. include:: snippets/InnovationAtCurrentState.rst
 171
 172 .. include:: snippets/JacobianMatrixAtBackground.rst
 173
 174 .. include:: snippets/JacobianMatrixAtOptimum.rst
 175
 176 .. include:: snippets/KalmanGainAtOptimum.rst
 177
 178 .. include:: snippets/MahalanobisConsistency.rst
 179
 180 .. include:: snippets/OMA.rst
 181
 182 .. include:: snippets/OMB.rst
 183
 184 .. include:: snippets/SigmaObs2.rst
 185
 186 .. include:: snippets/SimulatedObservationAtBackground.rst
 187
 188 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 189
 190 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 191
 192 .. include:: snippets/SimulatedObservationAtOptimum.rst
 193
 194 .. include:: snippets/SimulationQuantiles.rst
 195
 196 .. ------------------------------------ ..
 197 .. include:: snippets/Header2Algo09.rst
 198
 199 .. literalinclude:: scripts/simple_3DVAR.py
 200
 201 .. include:: snippets/Header2Algo10.rst
 202
 203 .. literalinclude:: scripts/simple_3DVAR.res
 204
 205 .. ------------------------------------ ..
 206 .. include:: snippets/Header2Algo06.rst
 207
 208 - :ref:`section_ref_algorithm_Blue`
 209 - :ref:`section_ref_algorithm_ExtendedBlue`
 210 - :ref:`section_ref_algorithm_LinearityTest`
 211
 212 .. ------------------------------------ ..
 213 .. include:: snippets/Header2Algo07.rst
 214
 215 - [Byrd95]_
 216 - [Morales11]_
 217 - [Talagrand97]_
 218 - [Zhu97]_