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
9 version 2.1 of the License, or (at your option) any later version.
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:
100 This key allow to give an integer in order to fix the seed of the random
101 generator used to generate the ensemble. A convenient value is for example
102 1000. By default, the seed is left uninitialized, and so use the default
103 initialization from the computer.
105 Example : ``{"SetSeed":1000}``
107 Information and variables available at the end of the algorithm
108 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
110 At the output, after executing the algorithm, there are variables and
111 information originating from the calculation. The description of
112 :ref:`section_ref_output_variables` show the way to obtain them by the method
113 named ``get`` of the variable "*ADD*" of the post-processing. The input
114 variables, available to the user at the output in order to facilitate the
115 writing of post-processing procedures, are described in the
116 :ref:`subsection_r_o_v_Inventaire`.
118 The unconditional outputs of the algorithm are the following:
121 *List of vectors*. Each element is an optimal state :math:`\mathbf{x}*` in
122 optimization or an analysis :math:`\mathbf{x}^a` in data assimilation.
124 Example : ``Xa = ADD.get("Analysis")[-1]``
127 *List of vectors*. Each element is a usual state vector used during the
128 optimization algorithm procedure.
130 Example : ``Xs = ADD.get("CurrentState")[:]``
133 *List of vectors*. Each element is an innovation vector, which is in static
134 the difference between the optimal and the background, and in dynamic the
137 Example : ``d = ADD.get("Innovation")[-1]``
142 References to other sections:
143 - :ref:`section_ref_algorithm_Blue`