doc/en/ref_algorithm_Blue.rst

   1 ..
   2    Copyright (C) 2008-2024 EDF R&D
   3
   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
  21
  22    Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
  23
  24 .. index:: single: Blue
  25 .. _section_ref_algorithm_Blue:
  26
  27 Calculation algorithm "*Blue*"
  28 ------------------------------
  29
  30 .. ------------------------------------ ..
  31 .. include:: snippets/Header2Algo01.rst
  32
  33 This algorithm realizes a BLUE (Best Linear Unbiased Estimator) type estimation
  34 of the state of a system. It is a linear, unbiased and optimal estimation.
  35 Technically, it is here an Aitken estimator. It performs the best linear
  36 estimate of the state using the initial background state and the observations.
  37 It is theoretically reserved for observation operator cases which are linear,
  38 even if it sometimes works in "slightly" non-linear cases. One can verify the
  39 linearity of the observation operator with the help of the
  40 :ref:`section_ref_algorithm_LinearityTest`. This algorithm is always the
  41 fastest of all the assimilation algorithms of ADAO.
  42
  43 This mono-objective optimization algorithm is naturally written for a single
  44 estimate, without any dynamic or iterative notion (there is no need in this
  45 case for an incremental evolution operator, nor for an evolution error
  46 covariance). In ADAO, it can also be used on a succession of observations,
  47 placing the estimate in a recursive framework partly similar to a
  48 :ref:`section_ref_algorithm_KalmanFilter`. A standard estimate is made at each
  49 observation step on the state predicted by the incremental evolution model,
  50 knowing that the state error covariance remains the background covariance
  51 initially provided by the user. To be explicit, unlike Kalman-type filters, the
  52 state error covariance is not updated.
  53
  54 In case of non-linearity, even slightly marked, it will be easily preferred a
  55 :ref:`section_ref_algorithm_ExtendedBlue` or a
  56 :ref:`section_ref_algorithm_3DVAR`.
  57
  58 .. index:: single: Optimal Interpolation
  59 .. index:: single: OI
  60
  61 Additional remark: an algebraic simplification of the BLUE leads to the
  62 so-called optimal interpolation method, named "*Optimal Interpolation*" or
  63 "*OI*". It is a very simple and inexpensive method, especially adapted to very
  64 (very) large problems, but whose disadvantage is to provide a globally
  65 sub-optimal and noisy analysis result, even inconsistent. The way to avoid
  66 these disadvantages is to adapt very precisely the elements of the method to
  67 each physical model, making the method not robust. For these reasons, this
  68 method is not proposed nor recommended.
  69
  70 .. ------------------------------------ ..
  71 .. include:: snippets/Header2Algo12.rst
  72
  73 .. include:: snippets/FeaturePropLocalOptimization.rst
  74
  75 .. include:: snippets/FeaturePropDerivativeNeeded.rst
  76
  77 .. include:: snippets/FeaturePropParallelDerivativesOnly.rst
  78
  79 .. ------------------------------------ ..
  80 .. include:: snippets/Header2Algo02.rst
  81
  82 .. include:: snippets/Background.rst
  83
  84 .. include:: snippets/BackgroundError.rst
  85
  86 .. include:: snippets/Observation.rst
  87
  88 .. include:: snippets/ObservationError.rst
  89
  90 .. include:: snippets/ObservationOperator.rst
  91
  92 .. ------------------------------------ ..
  93 .. include:: snippets/Header2Algo03AdOp.rst
  94
  95 .. include:: snippets/EstimationOf_Parameters.rst
  96
  97 .. include:: snippets/NumberOfSamplesForQuantiles.rst
  98
  99 .. include:: snippets/Quantiles.rst
 100
 101 .. include:: snippets/SetSeed.rst
 102
 103 .. include:: snippets/SimulationForQuantiles.rst
 104
 105 .. include:: snippets/StateBoundsForQuantilesWithNone.rst
 106
 107 StoreSupplementaryCalculations
 108   .. index:: single: StoreSupplementaryCalculations
 109
 110   *List of names*. This list indicates the names of the supplementary
 111   variables, that can be available during or at the end of the algorithm, if
 112   they are initially required by the user. Their availability involves,
 113   potentially, costly calculations or memory consumptions. The default is then
 114   a void list, none of these variables being calculated and stored by default
 115   (excepted the unconditional variables). The possible names are in the
 116   following list (the detailed description of each named variable is given in
 117   the following part of this specific algorithmic documentation, in the
 118   sub-section "*Information and variables available at the end of the
 119   algorithm*"): [
 120   "Analysis",
 121   "APosterioriCorrelations",
 122   "APosterioriCovariance",
 123   "APosterioriStandardDeviations",
 124   "APosterioriVariances",
 125   "BMA",
 126   "CostFunctionJ",
 127   "CostFunctionJAtCurrentOptimum",
 128   "CostFunctionJb",
 129   "CostFunctionJbAtCurrentOptimum",
 130   "CostFunctionJo",
 131   "CostFunctionJoAtCurrentOptimum",
 132   "CurrentOptimum",
 133   "CurrentState",
 134   "CurrentStepNumber",
 135   "ForecastState",
 136   "Innovation",
 137   "InnovationAtCurrentAnalysis",
 138   "MahalanobisConsistency",
 139   "OMA",
 140   "OMB",
 141   "SampledStateForQuantiles",
 142   "SigmaBck2",
 143   "SigmaObs2",
 144   "SimulatedObservationAtBackground",
 145   "SimulatedObservationAtCurrentOptimum",
 146   "SimulatedObservationAtCurrentState",
 147   "SimulatedObservationAtOptimum",
 148   "SimulationQuantiles",
 149   ].
 150
 151   Example :
 152   ``{"StoreSupplementaryCalculations":["CurrentState", "Residu"]}``
 153
 154 .. ------------------------------------ ..
 155 .. include:: snippets/Header2Algo04.rst
 156
 157 .. include:: snippets/Analysis.rst
 158
 159 .. ------------------------------------ ..
 160 .. include:: snippets/Header2Algo05.rst
 161
 162 .. include:: snippets/Analysis.rst
 163
 164 .. include:: snippets/APosterioriCorrelations.rst
 165
 166 .. include:: snippets/APosterioriCovariance.rst
 167
 168 .. include:: snippets/APosterioriStandardDeviations.rst
 169
 170 .. include:: snippets/APosterioriVariances.rst
 171
 172 .. include:: snippets/BMA.rst
 173
 174 .. include:: snippets/CostFunctionJ.rst
 175
 176 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 177
 178 .. include:: snippets/CostFunctionJb.rst
 179
 180 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 181
 182 .. include:: snippets/CostFunctionJo.rst
 183
 184 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 185
 186 .. include:: snippets/CurrentOptimum.rst
 187
 188 .. include:: snippets/CurrentState.rst
 189
 190 .. include:: snippets/CurrentStepNumber.rst
 191
 192 .. include:: snippets/ForecastState.rst
 193
 194 .. include:: snippets/Innovation.rst
 195
 196 .. include:: snippets/InnovationAtCurrentAnalysis.rst
 197
 198 .. include:: snippets/MahalanobisConsistency.rst
 199
 200 .. include:: snippets/OMA.rst
 201
 202 .. include:: snippets/OMB.rst
 203
 204 .. include:: snippets/SampledStateForQuantiles.rst
 205
 206 .. include:: snippets/SigmaBck2.rst
 207
 208 .. include:: snippets/SigmaObs2.rst
 209
 210 .. include:: snippets/SimulatedObservationAtBackground.rst
 211
 212 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 213
 214 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 215
 216 .. include:: snippets/SimulatedObservationAtOptimum.rst
 217
 218 .. include:: snippets/SimulationQuantiles.rst
 219
 220 .. ------------------------------------ ..
 221 .. _section_ref_algorithm_Blue_examples:
 222
 223 .. include:: snippets/Header2Algo09.rst
 224
 225 .. include:: scripts/simple_Blue.rst
 226
 227 .. literalinclude:: scripts/simple_Blue.py
 228
 229 .. include:: snippets/Header2Algo10.rst
 230
 231 .. literalinclude:: scripts/simple_Blue.res
 232
 233 .. ------------------------------------ ..
 234 .. include:: snippets/Header2Algo06.rst
 235
 236 - :ref:`section_ref_algorithm_ExtendedBlue`
 237 - :ref:`section_ref_algorithm_3DVAR`
 238 - :ref:`section_ref_algorithm_LinearityTest`
 239
 240 .. ------------------------------------ ..
 241 .. include:: snippets/Header2Algo07.rst
 242
 243 - [Bouttier99]_