doc/en/ref_algorithm_ExtendedBlue.rst

   1 ..
   2    Copyright (C) 2008-2023 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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  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: ExtendedBlue
  25 .. _section_ref_algorithm_ExtendedBlue:
  26
  27 Calculation algorithm "*ExtendedBlue*"
  28 --------------------------------------
  29
  30 .. ------------------------------------ ..
  31 .. include:: snippets/Header2Algo01.rst
  32
  33 This algorithm realizes an extended BLUE (Best Linear Unbiased Estimator) type
  34 estimation of the state of a system.
  35
  36 This algorithm is a partially non-linear generalization of a
  37 :ref:`section_ref_algorithm_Blue`. It is equivalent for a linear observation
  38 operator. One can verify the linearity of the observation operator with the
  39 help of a :ref:`section_ref_algorithm_LinearityTest`.
  40
  41 In case of non-linearity, its results are close to a
  42 :ref:`section_ref_algorithm_3DVAR`, without being entirely equivalent.
  43
  44 This algorithm is naturally written for a single estimate, without any dynamic
  45 or iterative notion (there is no need in this case for an incremental evolution
  46 operator, nor for an evolution error covariance). In ADAO, it can also be used
  47 on a succession of observations, placing the estimate in a recursive framework
  48 partly similar to a :ref:`section_ref_algorithm_KalmanFilter`. A standard
  49 estimate is made at each observation step on the state predicted by the
  50 incremental evolution model, knowing that the state error covariance remains
  51 the background covariance initially provided by the user. To be explicit,
  52 unlike Kalman-type filters, the state error covariance is not updated.
  53
  54 .. ------------------------------------ ..
  55 .. include:: snippets/Header2Algo02.rst
  56
  57 .. include:: snippets/Background.rst
  58
  59 .. include:: snippets/BackgroundError.rst
  60
  61 .. include:: snippets/Observation.rst
  62
  63 .. include:: snippets/ObservationError.rst
  64
  65 .. include:: snippets/ObservationOperator.rst
  66
  67 .. ------------------------------------ ..
  68 .. include:: snippets/Header2Algo03AdOp.rst
  69
  70 .. include:: snippets/EstimationOf_Parameters.rst
  71
  72 .. include:: snippets/NumberOfSamplesForQuantiles.rst
  73
  74 .. include:: snippets/Quantiles.rst
  75
  76 .. include:: snippets/SetSeed.rst
  77
  78 .. include:: snippets/SimulationForQuantiles.rst
  79
  80 .. include:: snippets/StateBoundsForQuantilesWithNone.rst
  81
  82 StoreSupplementaryCalculations
  83   .. index:: single: StoreSupplementaryCalculations
  84
  85   *List of names*. This list indicates the names of the supplementary
  86   variables, that can be available during or at the end of the algorithm, if
  87   they are initially required by the user. Their avalability involves,
  88   potentially, costly calculations or memory consumptions. The default is then
  89   a void list, none of these variables being calculated and stored by default
  90   (excepted the unconditionnal variables). The possible names are in the
  91   following list (the detailed description of each named variable is given in
  92   the following part of this specific algorithmic documentation, in the
  93   sub-section "*Information and variables available at the end of the
  94   algorithm*"): [
  95   "Analysis",
  96   "APosterioriCorrelations",
  97   "APosterioriCovariance",
  98   "APosterioriStandardDeviations",
  99   "APosterioriVariances",
 100   "BMA",
 101   "CostFunctionJ",
 102   "CostFunctionJAtCurrentOptimum",
 103   "CostFunctionJb",
 104   "CostFunctionJbAtCurrentOptimum",
 105   "CostFunctionJo",
 106   "CostFunctionJoAtCurrentOptimum",
 107   "CurrentOptimum",
 108   "CurrentState",
 109   "CurrentStepNumber",
 110   "ForecastState",
 111   "Innovation",
 112   "InnovationAtCurrentAnalysis",
 113   "MahalanobisConsistency",
 114   "OMA",
 115   "OMB",
 116   "SampledStateForQuantiles",
 117   "SigmaBck2",
 118   "SigmaObs2",
 119   "SimulatedObservationAtBackground",
 120   "SimulatedObservationAtCurrentOptimum",
 121   "SimulatedObservationAtCurrentState",
 122   "SimulatedObservationAtOptimum",
 123   "SimulationQuantiles",
 124   ].
 125
 126   Example :
 127   ``{"StoreSupplementaryCalculations":["CurrentState", "Residu"]}``
 128
 129 .. ------------------------------------ ..
 130 .. include:: snippets/Header2Algo04.rst
 131
 132 .. include:: snippets/Analysis.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/CurrentOptimum.rst
 162
 163 .. include:: snippets/CurrentState.rst
 164
 165 .. include:: snippets/CurrentStepNumber.rst
 166
 167 .. include:: snippets/ForecastState.rst
 168
 169 .. include:: snippets/Innovation.rst
 170
 171 .. include:: snippets/InnovationAtCurrentAnalysis.rst
 172
 173 .. include:: snippets/MahalanobisConsistency.rst
 174
 175 .. include:: snippets/OMA.rst
 176
 177 .. include:: snippets/OMB.rst
 178
 179 .. include:: snippets/SampledStateForQuantiles.rst
 180
 181 .. include:: snippets/SigmaBck2.rst
 182
 183 .. include:: snippets/SigmaObs2.rst
 184
 185 .. include:: snippets/SimulatedObservationAtBackground.rst
 186
 187 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 188
 189 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 190
 191 .. include:: snippets/SimulatedObservationAtOptimum.rst
 192
 193 .. include:: snippets/SimulationQuantiles.rst
 194
 195 .. ------------------------------------ ..
 196 .. _section_ref_algorithm_ExtendedBlue_examples:
 197 .. include:: snippets/Header2Algo09.rst
 198
 199 .. include:: scripts/simple_ExtendedBlue.rst
 200
 201 .. literalinclude:: scripts/simple_ExtendedBlue.py
 202
 203 .. include:: snippets/Header2Algo10.rst
 204
 205 .. literalinclude:: scripts/simple_ExtendedBlue.res
 206
 207 .. ------------------------------------ ..
 208 .. include:: snippets/Header2Algo06.rst
 209
 210 - :ref:`section_ref_algorithm_Blue`
 211 - :ref:`section_ref_algorithm_3DVAR`
 212 - :ref:`section_ref_algorithm_LinearityTest`