2 Copyright (C) 2008-2015 EDF R&D
4 This file is part of SALOME ADAO module.
6 This library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
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11 This library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
16 You should have received a copy of the GNU Lesser General Public
17 License along with this library; if not, write to the Free Software
18 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
20 See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
22 Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
24 .. index:: single: EnsembleBlue
25 .. _section_ref_algorithm_EnsembleBlue:
27 Calculation algorithm "*EnsembleBlue*"
28 --------------------------------------
33 This algorithm realizes a BLUE (Best Linear Unbiased Estimator, which is here an
34 Aitken estimator) type estimation of the state of a system by an ensemble
35 method. To work, one must give a set of backgrounds, their number determining
36 the size of the ensemble for the estimation.
38 It is theoretically reserved for observation operator cases which are linear,
39 but has to work also in "slightly" non-linear cases. One can verify the
40 linearity of the observation operator with the help of the
41 :ref:`section_ref_algorithm_LinearityTest`.
43 Optional and required commands
44 ++++++++++++++++++++++++++++++
46 .. index:: single: AlgorithmParameters
47 .. index:: single: Background
48 .. index:: single: BackgroundError
49 .. index:: single: Observation
50 .. index:: single: ObservationError
51 .. index:: single: ObservationOperator
52 .. index:: single: SetSeed
54 The general required commands, available in the editing user interface, are the
58 *Required command*. This indicates the background or initial vector used,
59 previously noted as :math:`\mathbf{x}^b`. Its value is defined as a
60 "*Vector*" or a *VectorSerie*" type object.
63 *Required command*. This indicates the background error covariance matrix,
64 previously noted as :math:`\mathbf{B}`. Its value is defined as a "*Matrix*"
65 type object, a "*ScalarSparseMatrix*" type object, or a
66 "*DiagonalSparseMatrix*" type object.
69 *Required command*. This indicates the observation vector used for data
70 assimilation or optimization, previously noted as :math:`\mathbf{y}^o`. It
71 is defined as a "*Vector*" or a *VectorSerie* type object.
74 *Required command*. This indicates the observation error covariance matrix,
75 previously noted as :math:`\mathbf{R}`. It is defined as a "*Matrix*" type
76 object, a "*ScalarSparseMatrix*" type object, or a "*DiagonalSparseMatrix*"
80 *Required command*. This indicates the observation operator, previously
81 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
82 results :math:`\mathbf{y}` to be compared to observations
83 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
84 a "*Matrix*" type one. In the case of "*Function*" type, different
85 functional forms can be used, as described in the section
86 :ref:`section_ref_operator_requirements`. If there is some control :math:`U`
87 included in the observation, the operator has to be applied to a pair
90 The general optional commands, available in the editing user interface, are
91 indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
92 of the command "*AlgorithmParameters*" allows to choose the specific options,
93 described hereafter, of the algorithm. See
94 :ref:`section_ref_options_Algorithm_Parameters` for the good use of this
97 The options of the algorithm are the following:
99 StoreSupplementaryCalculations
100 This list indicates the names of the supplementary variables that can be
101 available at the end of the algorithm. It involves potentially costly
102 calculations or memory consumptions. The default is a void list, none of
103 these variables being calculated and stored by default. The possible names
104 are in the following list: ["CurrentState", "Innovation",
105 "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentState",
106 "SimulatedObservationAtOptimum"].
108 Example : ``{"StoreSupplementaryCalculations":["CurrentState", "Innovation"]}``
111 This key allow to give an integer in order to fix the seed of the random
112 generator used to generate the ensemble. A convenient value is for example
113 1000. By default, the seed is left uninitialized, and so use the default
114 initialization from the computer.
116 Example : ``{"SetSeed":1000}``
118 Information and variables available at the end of the algorithm
119 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
121 At the output, after executing the algorithm, there are variables and
122 information originating from the calculation. The description of
123 :ref:`section_ref_output_variables` show the way to obtain them by the method
124 named ``get`` of the variable "*ADD*" of the post-processing. The input
125 variables, available to the user at the output in order to facilitate the
126 writing of post-processing procedures, are described in the
127 :ref:`subsection_r_o_v_Inventaire`.
129 The unconditional outputs of the algorithm are the following:
132 *List of vectors*. Each element is an optimal state :math:`\mathbf{x}*` in
133 optimization or an analysis :math:`\mathbf{x}^a` in data assimilation.
135 Example : ``Xa = ADD.get("Analysis")[-1]``
138 *List of vectors*. Each element is a usual state vector used during the
139 optimization algorithm procedure.
141 Example : ``Xs = ADD.get("CurrentState")[:]``
144 *List of vectors*. Each element is an innovation vector, which is in static
145 the difference between the optimal and the background, and in dynamic the
148 Example : ``d = ADD.get("Innovation")[-1]``
153 References to other sections:
154 - :ref:`section_ref_algorithm_Blue`