..
- Copyright (C) 2008-2014 EDF R&D
+ Copyright (C) 2008-2015 EDF R&D
This file is part of SALOME ADAO module.
This algorithm performs a state estimation by variational minimization of the
classical :math:`J` function in static data assimilation:
-.. math:: J(\mathbf{x})=(\mathbf{x}-\mathbf{x}^b)^T.\mathbf{B}^{-1}.(\mathbf{x}-\mathbf{x}^b)+(\mathbf{y}^o-\mathbf{H}.\mathbf{x})^T.\mathbf{R}^{-1}.(\mathbf{y}^o-\mathbf{H}.\mathbf{x})
+.. 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}))
which is usually designed as the "*3D-VAR*" function (see for example
[Talagrand97]_).
Optional and required commands
++++++++++++++++++++++++++++++
+.. index:: single: AlgorithmParameters
.. index:: single: Background
.. index:: single: BackgroundError
.. index:: single: Observation
.. index:: single: CostDecrementTolerance
.. index:: single: ProjectedGradientTolerance
.. index:: single: GradientNormTolerance
-.. index:: single: StoreInternalVariables
.. index:: single: StoreSupplementaryCalculations
.. index:: single: Quantiles
.. index:: single: SetSeed
:math:`(X,U)`.
The general optional commands, available in the editing user interface, are
-indicated in :ref:`section_ref_assimilation_keywords`. In particular, the
-optional command "*AlgorithmParameters*" allows to choose the specific options,
+indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
+of the command "*AlgorithmParameters*" allows to choose the specific options,
described hereafter, of the algorithm. See
-:ref:`section_ref_options_AlgorithmParameters` for the good use of this command.
+:ref:`section_ref_options_Algorithm_Parameters` for the good use of this
+command.
The options of the algorithm are the following:
Example : ``{"GradientNormTolerance":1.e-5}``
- StoreInternalVariables
- This Boolean key allows to store default internal variables, mainly the
- current state during iterative optimization process. Be careful, this can be
- a numerically costly choice in certain calculation cases. The default is
- "False".
-
- Example : ``{"StoreInternalVariables":True}``
-
StoreSupplementaryCalculations
This list indicates the names of the supplementary variables that can be
available at the end of the algorithm. It involves potentially costly
calculations or memory consumptions. The default is a void list, none of
these variables being calculated and stored by default. The possible names
- are in the following list: ["APosterioriCovariance", "BMA", "OMA", "OMB",
- "Innovation", "SigmaObs2", "MahalanobisConsistency", "SimulationQuantiles"].
-
- Example : ``{"StoreSupplementaryCalculations":["BMA","Innovation"]}``
+ are in the following list: ["APosterioriCorrelations",
+ "APosterioriCovariance", "APosterioriStandardDeviations",
+ "APosterioriVariances", "BMA", "CostFunctionJ",
+ "CostFunctionJAtCurrentOptimum", "CurrentOptimum", "CurrentState",
+ "IndexOfOptimum", "Innovation", "InnovationAtCurrentState",
+ "MahalanobisConsistency", "OMA", "OMB", "SigmaObs2",
+ "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentOptimum",
+ "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum",
+ "SimulationQuantiles"].
+
+ Example : ``{"StoreSupplementaryCalculations":["BMA", "Innovation"]}``
Quantiles
This list indicates the values of quantile, between 0 and 1, to be estimated
Example : ``{"SimulationForQuantiles":"Linear"}``
+Information and variables available at the end of the algorithm
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+
+At the output, after executing the algorithm, there are variables and
+information originating from the calculation. The description of
+:ref:`section_ref_output_variables` show the way to obtain them by the method
+named ``get`` of the variable "*ADD*" of the post-processing. The input
+variables, available to the user at the output in order to facilitate the
+writing of post-processing procedures, are described in the
+:ref:`subsection_r_o_v_Inventaire`.
+
+The unconditional outputs of the algorithm are the following:
+
+ Analysis
+ *List of vectors*. Each element is an optimal state :math:`\mathbf{x}*` in
+ optimization or an analysis :math:`\mathbf{x}^a` in data assimilation.
+
+ Example : ``Xa = ADD.get("Analysis")[-1]``
+
+ CostFunctionJ
+ *List of values*. Each element is a value of the error function :math:`J`.
+
+ Example : ``J = ADD.get("CostFunctionJ")[:]``
+
+ CostFunctionJb
+ *List of values*. Each element is a value of the error function :math:`J^b`,
+ that is of the background difference part.
+
+ Example : ``Jb = ADD.get("CostFunctionJb")[:]``
+
+ CostFunctionJo
+ *List of values*. Each element is a value of the error function :math:`J^o`,
+ that is of the observation difference part.
+
+ Example : ``Jo = ADD.get("CostFunctionJo")[:]``
+
+The conditional outputs of the algorithm are the following:
+
+ APosterioriCorrelations
+ *List of matrices*. Each element is an *a posteriori* error correlations
+ matrix of the optimal state, coming from the :math:`\mathbf{A}*` covariance
+ matrix.
+
+ Example : ``C = ADD.get("APosterioriCorrelations")[-1]``
+
+ APosterioriCovariance
+ *List of matrices*. Each element is an *a posteriori* error covariance
+ matrix :math:`\mathbf{A}*` of the optimal state.
+
+ Example : ``A = ADD.get("APosterioriCovariance")[-1]``
+
+ APosterioriStandardDeviations
+ *List of matrices*. Each element is an *a posteriori* error standard
+ errors diagonal matrix of the optimal state, coming from the
+ :math:`\mathbf{A}*` covariance matrix.
+
+ Exemple : ``S = ADD.get("APosterioriStandardDeviations")[-1]``
+
+ APosterioriVariances
+ *List of matrices*. Each element is an *a posteriori* error variance
+ errors diagonal matrix of the optimal state, coming from the
+ :math:`\mathbf{A}*` covariance matrix.
+
+ Example : ``V = ADD.get("APosterioriVariances")[-1]``
+
+ BMA
+ *List of vectors*. Each element is a vector of difference between the
+ background and the optimal state.
+
+ Example : ``bma = ADD.get("BMA")[-1]``
+
+ CostFunctionJAtCurrentOptimum
+ *List of values*. Each element is a value of the error function :math:`J`.
+ At each step, the value corresponds to the optimal state found from the
+ beginning.
+
+ Example : ``JACO = ADD.get("CostFunctionJAtCurrentOptimum")[:]``
+
+ CostFunctionJbAtCurrentOptimum
+ *List of values*. Each element is a value of the error function :math:`J^b`,
+ that is of the background difference part. At each step, the value
+ corresponds to the optimal state found from the beginning.
+
+ Example : ``JbACO = ADD.get("CostFunctionJbAtCurrentOptimum")[:]``
+
+ CostFunctionJoAtCurrentOptimum
+ *List of values*. Each element is a value of the error function :math:`J^o`,
+ that is of the observation difference part. At each step, the value
+ corresponds to the optimal state found from the beginning.
+
+ Example : ``JoACO = ADD.get("CostFunctionJoAtCurrentOptimum")[:]``
+
+ CurrentOptimum
+ *List of vectors*. Each element is the optimal state obtained at the current
+ step of the optimization algorithm. It is not necessarely the last state.
+
+ Exemple : ``Xo = ADD.get("CurrentOptimum")[:]``
+
+ CurrentState
+ *List of vectors*. Each element is a usual state vector used during the
+ optimization algorithm procedure.
+
+ Example : ``Xs = ADD.get("CurrentState")[:]``
+
+ IndexOfOptimum
+ *List of integers*. Each element is the iteration index of the optimum
+ obtained at the current step the optimization algorithm. It is not
+ necessarely the number of the last iteration.
+
+ Exemple : ``i = ADD.get("IndexOfOptimum")[-1]``
+
+ Innovation
+ *List of vectors*. Each element is an innovation vector, which is in static
+ the difference between the optimal and the background, and in dynamic the
+ evolution increment.
+
+ Example : ``d = ADD.get("Innovation")[-1]``
+
+ InnovationAtCurrentState
+ *List of vectors*. Each element is an innovation vector at current state.
+
+ Example : ``ds = ADD.get("InnovationAtCurrentState")[-1]``
+
+ MahalanobisConsistency
+ *List of values*. Each element is a value of the Mahalanobis quality
+ indicator.
+
+ Example : ``m = ADD.get("MahalanobisConsistency")[-1]``
+
+ OMA
+ *List of vectors*. Each element is a vector of difference between the
+ observation and the optimal state in the observation space.
+
+ Example : ``oma = ADD.get("OMA")[-1]``
+
+ OMB
+ *List of vectors*. Each element is a vector of difference between the
+ observation and the background state in the observation space.
+
+ Example : ``omb = ADD.get("OMB")[-1]``
+
+ SigmaObs2
+ *List of values*. Each element is a value of the quality indicator
+ :math:`(\sigma^o)^2` of the observation part.
+
+ Example : ``so2 = ADD.get("SigmaObs")[-1]``
+
+ SimulatedObservationAtBackground
+ *List of vectors*. Each element is a vector of observation simulated from
+ the background :math:`\mathbf{x}^b`.
+
+ Example : ``hxb = ADD.get("SimulatedObservationAtBackground")[-1]``
+
+ SimulatedObservationAtCurrentOptimum
+ *List of vectors*. Each element is a vector of observation simulated from
+ the optimal state obtained at the current step the optimization algorithm,
+ that is, in the observation space.
+
+ Exemple : ``hxo = ADD.get("SimulatedObservationAtCurrentOptimum")[-1]``
+
+ SimulatedObservationAtCurrentState
+ *List of vectors*. Each element is an observed vector at the current state,
+ that is, in the observation space.
+
+ Example : ``hxs = ADD.get("SimulatedObservationAtCurrentState")[-1]``
+
+ SimulatedObservationAtOptimum
+ *List of vectors*. Each element is a vector of observation simulated from
+ the analysis or optimal state :math:`\mathbf{x}^a`.
+
+ Example : ``hxa = ADD.get("SimulatedObservationAtOptimum")[-1]``
+
+ SimulationQuantiles
+ *List of vectors*. Each element is a vector corresponding to the observed
+ state which realize the required quantile, in the same order than the
+ quantiles required by the user.
+
+ Example : ``sQuantiles = ADD.get("SimulationQuantiles")[:]``
+
See also
++++++++
