doc/en/ref_algorithm_Blue.rst

   1 ..
   2    Copyright (C) 2008-2023 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 algorithm is naturally written for a single estimate, without any dynamic
  44 or iterative notion (there is no need in this case for an incremental evolution
  45 operator, nor for an evolution error covariance). In ADAO, it can also be used
  46 on a succession of observations, placing the estimate in a recursive framework
  47 partly similar to a :ref:`section_ref_algorithm_KalmanFilter`. A standard
  48 estimate is made at each observation step on the state predicted by the
  49 incremental evolution model, knowing that the state error covariance remains
  50 the background covariance initially provided by the user. To be explicit,
  51 unlike Kalman-type filters, the state error covariance is not updated.
  52
  53 In case of non-linearity, even slightly marked, it will be easily preferred a
  54 :ref:`section_ref_algorithm_ExtendedBlue` or a
  55 :ref:`section_ref_algorithm_3DVAR`.
  56
  57 .. index:: single: Optimal Interpolation
  58 .. index:: single: OI
  59
  60 Additional remark: an algebraic simplification of the BLUE leads to the
  61 so-called optimal interpolation method, named "*Optimal Interpolation*" or
  62 "*OI*". It is a very simple and inexpensive method, especially adapted to very
  63 (very) large problems, but whose disadvantage is to provide a globally
  64 sub-optimal and noisy analysis result, even inconsistent. The way to avoid
  65 these disadvantages is to adapt very precisely the elements of the method to
  66 each physical model. For these reasons, this method is not proposed nor
  67 recommended.
  68
  69 .. ------------------------------------ ..
  70 .. include:: snippets/Header2Algo02.rst
  71
  72 .. include:: snippets/Background.rst
  73
  74 .. include:: snippets/BackgroundError.rst
  75
  76 .. include:: snippets/Observation.rst
  77
  78 .. include:: snippets/ObservationError.rst
  79
  80 .. include:: snippets/ObservationOperator.rst
  81
  82 .. ------------------------------------ ..
  83 .. include:: snippets/Header2Algo03AdOp.rst
  84
  85 .. include:: snippets/EstimationOf_Parameters.rst
  86
  87 .. include:: snippets/NumberOfSamplesForQuantiles.rst
  88
  89 .. include:: snippets/Quantiles.rst
  90
  91 .. include:: snippets/SetSeed.rst
  92
  93 .. include:: snippets/SimulationForQuantiles.rst
  94
  95 .. include:: snippets/StateBoundsForQuantilesWithNone.rst
  96
  97 StoreSupplementaryCalculations
  98   .. index:: single: StoreSupplementaryCalculations
  99
 100   *List of names*. This list indicates the names of the supplementary
 101   variables, that can be available during or at the end of the algorithm, if
 102   they are initially required by the user. Their avalability involves,
 103   potentially, costly calculations or memory consumptions. The default is then
 104   a void list, none of these variables being calculated and stored by default
 105   (excepted the unconditionnal variables). The possible names are in the
 106   following list (the detailed description of each named variable is given in
 107   the following part of this specific algorithmic documentation, in the
 108   sub-section "*Information and variables available at the end of the
 109   algorithm*"): [
 110   "Analysis",
 111   "APosterioriCorrelations",
 112   "APosterioriCovariance",
 113   "APosterioriStandardDeviations",
 114   "APosterioriVariances",
 115   "BMA",
 116   "CostFunctionJ",
 117   "CostFunctionJAtCurrentOptimum",
 118   "CostFunctionJb",
 119   "CostFunctionJbAtCurrentOptimum",
 120   "CostFunctionJo",
 121   "CostFunctionJoAtCurrentOptimum",
 122   "CurrentOptimum",
 123   "CurrentState",
 124   "CurrentStepNumber",
 125   "ForecastState",
 126   "Innovation",
 127   "InnovationAtCurrentAnalysis",
 128   "MahalanobisConsistency",
 129   "OMA",
 130   "OMB",
 131   "SampledStateForQuantiles",
 132   "SigmaBck2",
 133   "SigmaObs2",
 134   "SimulatedObservationAtBackground",
 135   "SimulatedObservationAtCurrentOptimum",
 136   "SimulatedObservationAtCurrentState",
 137   "SimulatedObservationAtOptimum",
 138   "SimulationQuantiles",
 139   ].
 140
 141   Example :
 142   ``{"StoreSupplementaryCalculations":["CurrentState", "Residu"]}``
 143
 144 .. ------------------------------------ ..
 145 .. include:: snippets/Header2Algo04.rst
 146
 147 .. include:: snippets/Analysis.rst
 148
 149 .. ------------------------------------ ..
 150 .. include:: snippets/Header2Algo05.rst
 151
 152 .. include:: snippets/Analysis.rst
 153
 154 .. include:: snippets/APosterioriCorrelations.rst
 155
 156 .. include:: snippets/APosterioriCovariance.rst
 157
 158 .. include:: snippets/APosterioriStandardDeviations.rst
 159
 160 .. include:: snippets/APosterioriVariances.rst
 161
 162 .. include:: snippets/BMA.rst
 163
 164 .. include:: snippets/CostFunctionJ.rst
 165
 166 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 167
 168 .. include:: snippets/CostFunctionJb.rst
 169
 170 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 171
 172 .. include:: snippets/CostFunctionJo.rst
 173
 174 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 175
 176 .. include:: snippets/CurrentOptimum.rst
 177
 178 .. include:: snippets/CurrentState.rst
 179
 180 .. include:: snippets/CurrentStepNumber.rst
 181
 182 .. include:: snippets/ForecastState.rst
 183
 184 .. include:: snippets/Innovation.rst
 185
 186 .. include:: snippets/InnovationAtCurrentAnalysis.rst
 187
 188 .. include:: snippets/MahalanobisConsistency.rst
 189
 190 .. include:: snippets/OMA.rst
 191
 192 .. include:: snippets/OMB.rst
 193
 194 .. include:: snippets/SampledStateForQuantiles.rst
 195
 196 .. include:: snippets/SigmaBck2.rst
 197
 198 .. include:: snippets/SigmaObs2.rst
 199
 200 .. include:: snippets/SimulatedObservationAtBackground.rst
 201
 202 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 203
 204 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 205
 206 .. include:: snippets/SimulatedObservationAtOptimum.rst
 207
 208 .. include:: snippets/SimulationQuantiles.rst
 209
 210 .. ------------------------------------ ..
 211 .. _section_ref_algorithm_Blue_examples:
 212
 213 .. include:: snippets/Header2Algo09.rst
 214
 215 .. include:: scripts/simple_Blue.rst
 216
 217 .. literalinclude:: scripts/simple_Blue.py
 218
 219 .. include:: snippets/Header2Algo10.rst
 220
 221 .. literalinclude:: scripts/simple_Blue.res
 222
 223 .. ------------------------------------ ..
 224 .. include:: snippets/Header2Algo06.rst
 225
 226 - :ref:`section_ref_algorithm_ExtendedBlue`
 227 - :ref:`section_ref_algorithm_3DVAR`
 228 - :ref:`section_ref_algorithm_LinearityTest`
 229
 230 .. ------------------------------------ ..
 231 .. include:: snippets/Header2Algo07.rst
 232
 233 - [Bouttier99]_