doc/en/ref_algorithm_ExtendedBlue.rst

   1 ..
   2    Copyright (C) 2008-2024 EDF R&D
   3
   4    This file is part of SALOME ADAO module.
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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: 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 mono-objective optimization algorithm is naturally written for a single
  45 estimate, without any dynamic or iterative notion (there is no need in this
  46 case for an incremental evolution operator, nor for an evolution error
  47 covariance). In ADAO, it can also be used on a succession of observations,
  48 placing the estimate in a recursive framework partly similar to a
  49 :ref:`section_ref_algorithm_KalmanFilter`. A standard estimate is made at each
  50 observation step on the state predicted by the incremental evolution model,
  51 knowing that the state error covariance remains the background covariance
  52 initially provided by the user. To be explicit, unlike Kalman-type filters, the
  53 state error covariance is not updated.
  54
  55 .. ------------------------------------ ..
  56 .. include:: snippets/Header2Algo12.rst
  57
  58 .. include:: snippets/FeaturePropLocalOptimization.rst
  59
  60 .. include:: snippets/FeaturePropDerivativeNeeded.rst
  61
  62 .. include:: snippets/FeaturePropParallelDerivativesOnly.rst
  63
  64 .. ------------------------------------ ..
  65 .. include:: snippets/Header2Algo02.rst
  66
  67 .. include:: snippets/Background.rst
  68
  69 .. include:: snippets/BackgroundError.rst
  70
  71 .. include:: snippets/Observation.rst
  72
  73 .. include:: snippets/ObservationError.rst
  74
  75 .. include:: snippets/ObservationOperator.rst
  76
  77 .. ------------------------------------ ..
  78 .. include:: snippets/Header2Algo03AdOp.rst
  79
  80 .. include:: snippets/EstimationOf_Parameters.rst
  81
  82 .. include:: snippets/NumberOfSamplesForQuantiles.rst
  83
  84 .. include:: snippets/Quantiles.rst
  85
  86 .. include:: snippets/SetSeed.rst
  87
  88 .. include:: snippets/SimulationForQuantiles.rst
  89
  90 .. include:: snippets/StateBoundsForQuantilesWithNone.rst
  91
  92 StoreSupplementaryCalculations
  93   .. index:: single: StoreSupplementaryCalculations
  94
  95   *List of names*. This list indicates the names of the supplementary
  96   variables, that can be available during or at the end of the algorithm, if
  97   they are initially required by the user. Their availability involves,
  98   potentially, costly calculations or memory consumptions. The default is then
  99   a void list, none of these variables being calculated and stored by default
 100   (excepted the unconditional variables). The possible names are in the
 101   following list (the detailed description of each named variable is given in
 102   the following part of this specific algorithmic documentation, in the
 103   sub-section "*Information and variables available at the end of the
 104   algorithm*"): [
 105   "Analysis",
 106   "APosterioriCorrelations",
 107   "APosterioriCovariance",
 108   "APosterioriStandardDeviations",
 109   "APosterioriVariances",
 110   "BMA",
 111   "CostFunctionJ",
 112   "CostFunctionJAtCurrentOptimum",
 113   "CostFunctionJb",
 114   "CostFunctionJbAtCurrentOptimum",
 115   "CostFunctionJo",
 116   "CostFunctionJoAtCurrentOptimum",
 117   "CurrentOptimum",
 118   "CurrentState",
 119   "CurrentStepNumber",
 120   "ForecastState",
 121   "Innovation",
 122   "InnovationAtCurrentAnalysis",
 123   "MahalanobisConsistency",
 124   "OMA",
 125   "OMB",
 126   "SampledStateForQuantiles",
 127   "SigmaBck2",
 128   "SigmaObs2",
 129   "SimulatedObservationAtBackground",
 130   "SimulatedObservationAtCurrentOptimum",
 131   "SimulatedObservationAtCurrentState",
 132   "SimulatedObservationAtOptimum",
 133   "SimulationQuantiles",
 134   ].
 135
 136   Example :
 137   ``{"StoreSupplementaryCalculations":["CurrentState", "Residu"]}``
 138
 139 .. ------------------------------------ ..
 140 .. include:: snippets/Header2Algo04.rst
 141
 142 .. include:: snippets/Analysis.rst
 143
 144 .. ------------------------------------ ..
 145 .. include:: snippets/Header2Algo05.rst
 146
 147 .. include:: snippets/Analysis.rst
 148
 149 .. include:: snippets/APosterioriCorrelations.rst
 150
 151 .. include:: snippets/APosterioriCovariance.rst
 152
 153 .. include:: snippets/APosterioriStandardDeviations.rst
 154
 155 .. include:: snippets/APosterioriVariances.rst
 156
 157 .. include:: snippets/BMA.rst
 158
 159 .. include:: snippets/CostFunctionJ.rst
 160
 161 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 162
 163 .. include:: snippets/CostFunctionJb.rst
 164
 165 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 166
 167 .. include:: snippets/CostFunctionJo.rst
 168
 169 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 170
 171 .. include:: snippets/CurrentOptimum.rst
 172
 173 .. include:: snippets/CurrentState.rst
 174
 175 .. include:: snippets/CurrentStepNumber.rst
 176
 177 .. include:: snippets/ForecastState.rst
 178
 179 .. include:: snippets/Innovation.rst
 180
 181 .. include:: snippets/InnovationAtCurrentAnalysis.rst
 182
 183 .. include:: snippets/MahalanobisConsistency.rst
 184
 185 .. include:: snippets/OMA.rst
 186
 187 .. include:: snippets/OMB.rst
 188
 189 .. include:: snippets/SampledStateForQuantiles.rst
 190
 191 .. include:: snippets/SigmaBck2.rst
 192
 193 .. include:: snippets/SigmaObs2.rst
 194
 195 .. include:: snippets/SimulatedObservationAtBackground.rst
 196
 197 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 198
 199 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 200
 201 .. include:: snippets/SimulatedObservationAtOptimum.rst
 202
 203 .. include:: snippets/SimulationQuantiles.rst
 204
 205 .. ------------------------------------ ..
 206 .. _section_ref_algorithm_ExtendedBlue_examples:
 207
 208 .. include:: snippets/Header2Algo09.rst
 209
 210 .. include:: scripts/simple_ExtendedBlue.rst
 211
 212 .. literalinclude:: scripts/simple_ExtendedBlue.py
 213
 214 .. include:: snippets/Header2Algo10.rst
 215
 216 .. literalinclude:: scripts/simple_ExtendedBlue.res
 217
 218 .. ------------------------------------ ..
 219 .. include:: snippets/Header2Algo06.rst
 220
 221 - :ref:`section_ref_algorithm_Blue`
 222 - :ref:`section_ref_algorithm_3DVAR`
 223 - :ref:`section_ref_algorithm_LinearityTest`