doc/fr/ref_algorithm_3DVAR.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
   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.
  10
  11    This library is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  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: 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   *Liste de noms*. Cette liste indique les noms des variables supplémentaires
  82   qui peuvent être disponibles au cours du déroulement ou à la fin de
  83   l'algorithme, si elles sont initialement demandées par l'utilisateur. Cela
  84   implique potentiellement des calculs ou du stockage coûteux. La valeur par
  85   défaut est une liste vide, aucune de ces variables n'étant calculée et
  86   stockée par défaut sauf les variables inconditionnelles. Les noms possibles
  87   sont dans la liste suivante : [
  88   "Analysis",
  89   "APosterioriCorrelations",
  90   "APosterioriCovariance",
  91   "APosterioriStandardDeviations",
  92   "APosterioriVariances",
  93   "BMA",
  94   "CostFunctionJ",
  95   "CostFunctionJAtCurrentOptimum",
  96   "CostFunctionJb",
  97   "CostFunctionJbAtCurrentOptimum",
  98   "CostFunctionJo",
  99   "CostFunctionJoAtCurrentOptimum",
 100   "CurrentIterationNumber",
 101   "CurrentOptimum",
 102   "CurrentState",
 103   "IndexOfOptimum",
 104   "Innovation",
 105   "InnovationAtCurrentState",
 106   "JacobianMatrixAtBackground",
 107   "JacobianMatrixAtOptimum",
 108   "KalmanGainAtOptimum",
 109   "MahalanobisConsistency",
 110   "OMA",
 111   "OMB",
 112   "SigmaObs2",
 113   "SimulatedObservationAtBackground",
 114   "SimulatedObservationAtCurrentOptimum",
 115   "SimulatedObservationAtCurrentState",
 116   "SimulatedObservationAtOptimum",
 117   "SimulationQuantiles",
 118   ].
 119
 120   Exemple :
 121   ``{"StoreSupplementaryCalculations":["BMA", "CurrentState"]}``
 122
 123 .. ------------------------------------ ..
 124 .. include:: snippets/Header2Algo04.rst
 125
 126 .. include:: snippets/Analysis.rst
 127
 128 .. include:: snippets/CostFunctionJ.rst
 129
 130 .. include:: snippets/CostFunctionJb.rst
 131
 132 .. include:: snippets/CostFunctionJo.rst
 133
 134 .. ------------------------------------ ..
 135 .. include:: snippets/Header2Algo05.rst
 136
 137 .. include:: snippets/Analysis.rst
 138
 139 .. include:: snippets/APosterioriCorrelations.rst
 140
 141 .. include:: snippets/APosterioriCovariance.rst
 142
 143 .. include:: snippets/APosterioriStandardDeviations.rst
 144
 145 .. include:: snippets/APosterioriVariances.rst
 146
 147 .. include:: snippets/BMA.rst
 148
 149 .. include:: snippets/CostFunctionJ.rst
 150
 151 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 152
 153 .. include:: snippets/CostFunctionJb.rst
 154
 155 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 156
 157 .. include:: snippets/CostFunctionJo.rst
 158
 159 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 160
 161 .. include:: snippets/CurrentIterationNumber.rst
 162
 163 .. include:: snippets/CurrentOptimum.rst
 164
 165 .. include:: snippets/CurrentState.rst
 166
 167 .. include:: snippets/IndexOfOptimum.rst
 168
 169 .. include:: snippets/Innovation.rst
 170
 171 .. include:: snippets/InnovationAtCurrentState.rst
 172
 173 .. include:: snippets/JacobianMatrixAtBackground.rst
 174
 175 .. include:: snippets/JacobianMatrixAtOptimum.rst
 176
 177 .. include:: snippets/KalmanGainAtOptimum.rst
 178
 179 .. include:: snippets/MahalanobisConsistency.rst
 180
 181 .. include:: snippets/OMA.rst
 182
 183 .. include:: snippets/OMB.rst
 184
 185 .. include:: snippets/SigmaObs2.rst
 186
 187 .. include:: snippets/SimulatedObservationAtBackground.rst
 188
 189 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 190
 191 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 192
 193 .. include:: snippets/SimulatedObservationAtOptimum.rst
 194
 195 .. include:: snippets/SimulationQuantiles.rst
 196
 197 .. ------------------------------------ ..
 198 .. include:: snippets/Header2Algo09.rst
 199
 200 .. include:: scripts/simple_3DVAR.rst
 201
 202 .. literalinclude:: scripts/simple_3DVAR.py
 203
 204 .. include:: snippets/Header2Algo10.rst
 205
 206 .. literalinclude:: scripts/simple_3DVAR.res
 207
 208 .. ------------------------------------ ..
 209 .. include:: snippets/Header2Algo06.rst
 210
 211 - :ref:`section_ref_algorithm_Blue`
 212 - :ref:`section_ref_algorithm_ExtendedBlue`
 213 - :ref:`section_ref_algorithm_LinearityTest`
 214
 215 .. ------------------------------------ ..
 216 .. include:: snippets/Header2Algo07.rst
 217
 218 - [Byrd95]_
 219 - [Morales11]_
 220 - [Talagrand97]_
 221 - [Zhu97]_