doc/fr/ref_algorithm_3DVAR.rst

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   4    This file is part of SALOME ADAO module.
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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 .. index:: single: 3D-Var
  26 .. _section_ref_algorithm_3DVAR:
  27
  28 Algorithme de calcul "*3DVAR*"
  29 ------------------------------
  30
  31 .. ------------------------------------ ..
  32 .. include:: snippets/Header2Algo01.rst
  33
  34 Cet algorithme réalise une estimation d'état par minimisation variationnelle de
  35 la fonctionnelle :math:`J` d'écart classique en assimilation de données
  36 statique:
  37
  38 .. 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}))
  39
  40 qui est usuellement désignée comme la fonctionnelle "*3D-Var*" (voir par
  41 exemple [Talagrand97]_). Les dénominations "*3D-Var*", "*3D-VAR*" et "*3DVAR*"
  42 sont équivalentes.
  43
  44 .. ------------------------------------ ..
  45 .. include:: snippets/Header2Algo02.rst
  46
  47 .. include:: snippets/Background.rst
  48
  49 .. include:: snippets/BackgroundError.rst
  50
  51 .. include:: snippets/Observation.rst
  52
  53 .. include:: snippets/ObservationError.rst
  54
  55 .. include:: snippets/ObservationOperator.rst
  56
  57 .. ------------------------------------ ..
  58 .. include:: snippets/Header2Algo03AdOp.rst
  59
  60 .. include:: snippets/BoundsWithNone.rst
  61
  62 .. include:: snippets/CostDecrementTolerance.rst
  63
  64 .. include:: snippets/GradientNormTolerance.rst
  65
  66 .. include:: snippets/InitializationPoint.rst
  67
  68 .. include:: snippets/MaximumNumberOfSteps.rst
  69
  70 .. include:: snippets/Minimizer_xDVAR.rst
  71
  72 .. include:: snippets/NumberOfSamplesForQuantiles.rst
  73
  74 .. include:: snippets/ProjectedGradientTolerance.rst
  75
  76 .. include:: snippets/Quantiles.rst
  77
  78 .. include:: snippets/SetSeed.rst
  79
  80 .. include:: snippets/SimulationForQuantiles.rst
  81
  82 StoreSupplementaryCalculations
  83   .. index:: single: StoreSupplementaryCalculations
  84
  85   *Liste de noms*. Cette liste indique les noms des variables supplémentaires
  86   qui peuvent être disponibles au cours du déroulement ou à la fin de
  87   l'algorithme, si elles sont initialement demandées par l'utilisateur. Cela
  88   implique potentiellement des calculs ou du stockage coûteux. La valeur par
  89   défaut est une liste vide, aucune de ces variables n'étant calculée et
  90   stockée par défaut sauf les variables inconditionnelles. Les noms possibles
  91   sont dans la liste suivante : [
  92   "Analysis",
  93   "APosterioriCorrelations",
  94   "APosterioriCovariance",
  95   "APosterioriStandardDeviations",
  96   "APosterioriVariances",
  97   "BMA",
  98   "CostFunctionJ",
  99   "CostFunctionJAtCurrentOptimum",
 100   "CostFunctionJb",
 101   "CostFunctionJbAtCurrentOptimum",
 102   "CostFunctionJo",
 103   "CostFunctionJoAtCurrentOptimum",
 104   "CurrentIterationNumber",
 105   "CurrentOptimum",
 106   "CurrentState",
 107   "IndexOfOptimum",
 108   "Innovation",
 109   "InnovationAtCurrentState",
 110   "JacobianMatrixAtBackground",
 111   "JacobianMatrixAtOptimum",
 112   "KalmanGainAtOptimum",
 113   "MahalanobisConsistency",
 114   "OMA",
 115   "OMB",
 116   "SigmaObs2",
 117   "SimulatedObservationAtBackground",
 118   "SimulatedObservationAtCurrentOptimum",
 119   "SimulatedObservationAtCurrentState",
 120   "SimulatedObservationAtOptimum",
 121   "SimulationQuantiles",
 122   ].
 123
 124   Exemple :
 125   ``{"StoreSupplementaryCalculations":["BMA", "CurrentState"]}``
 126
 127 .. ------------------------------------ ..
 128 .. include:: snippets/Header2Algo04.rst
 129
 130 .. include:: snippets/Analysis.rst
 131
 132 .. include:: snippets/CostFunctionJ.rst
 133
 134 .. include:: snippets/CostFunctionJb.rst
 135
 136 .. include:: snippets/CostFunctionJo.rst
 137
 138 .. ------------------------------------ ..
 139 .. include:: snippets/Header2Algo05.rst
 140
 141 .. include:: snippets/Analysis.rst
 142
 143 .. include:: snippets/APosterioriCorrelations.rst
 144
 145 .. include:: snippets/APosterioriCovariance.rst
 146
 147 .. include:: snippets/APosterioriStandardDeviations.rst
 148
 149 .. include:: snippets/APosterioriVariances.rst
 150
 151 .. include:: snippets/BMA.rst
 152
 153 .. include:: snippets/CostFunctionJ.rst
 154
 155 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 156
 157 .. include:: snippets/CostFunctionJb.rst
 158
 159 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 160
 161 .. include:: snippets/CostFunctionJo.rst
 162
 163 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 164
 165 .. include:: snippets/CurrentIterationNumber.rst
 166
 167 .. include:: snippets/CurrentOptimum.rst
 168
 169 .. include:: snippets/CurrentState.rst
 170
 171 .. include:: snippets/IndexOfOptimum.rst
 172
 173 .. include:: snippets/Innovation.rst
 174
 175 .. include:: snippets/InnovationAtCurrentState.rst
 176
 177 .. include:: snippets/JacobianMatrixAtBackground.rst
 178
 179 .. include:: snippets/JacobianMatrixAtOptimum.rst
 180
 181 .. include:: snippets/KalmanGainAtOptimum.rst
 182
 183 .. include:: snippets/MahalanobisConsistency.rst
 184
 185 .. include:: snippets/OMA.rst
 186
 187 .. include:: snippets/OMB.rst
 188
 189 .. include:: snippets/SigmaObs2.rst
 190
 191 .. include:: snippets/SimulatedObservationAtBackground.rst
 192
 193 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 194
 195 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 196
 197 .. include:: snippets/SimulatedObservationAtOptimum.rst
 198
 199 .. include:: snippets/SimulationQuantiles.rst
 200
 201 .. ------------------------------------ ..
 202 .. include:: snippets/Header2Algo09.rst
 203
 204 .. include:: scripts/simple_3DVAR.rst
 205
 206 .. literalinclude:: scripts/simple_3DVAR.py
 207
 208 .. include:: snippets/Header2Algo10.rst
 209
 210 .. literalinclude:: scripts/simple_3DVAR.res
 211
 212 .. ------------------------------------ ..
 213 .. include:: snippets/Header2Algo06.rst
 214
 215 - :ref:`section_ref_algorithm_Blue`
 216 - :ref:`section_ref_algorithm_ExtendedBlue`
 217 - :ref:`section_ref_algorithm_LinearityTest`
 218
 219 .. ------------------------------------ ..
 220 .. include:: snippets/Header2Algo07.rst
 221
 222 - [Byrd95]_
 223 - [Morales11]_
 224 - [Talagrand97]_
 225 - [Zhu97]_