2 Copyright (C) 2008-2014 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: Background
47 .. index:: single: BackgroundError
48 .. index:: single: Observation
49 .. index:: single: ObservationError
50 .. index:: single: ObservationOperator
51 .. index:: single: SetSeed
53 The general required commands, available in the editing user interface, are the
57 *Required command*. This indicates the background or initial vector used,
58 previously noted as :math:`\mathbf{x}^b`. Its value is defined as a
59 "*Vector*" or a *VectorSerie*" type object.
62 *Required command*. This indicates the background error covariance matrix,
63 previously noted as :math:`\mathbf{B}`. Its value is defined as a "*Matrix*"
64 type object, a "*ScalarSparseMatrix*" type object, or a
65 "*DiagonalSparseMatrix*" type object.
68 *Required command*. This indicates the observation vector used for data
69 assimilation or optimization, previously noted as :math:`\mathbf{y}^o`. It
70 is defined as a "*Vector*" or a *VectorSerie* type object.
73 *Required command*. This indicates the observation error covariance matrix,
74 previously noted as :math:`\mathbf{R}`. It is defined as a "*Matrix*" type
75 object, a "*ScalarSparseMatrix*" type object, or a "*DiagonalSparseMatrix*"
79 *Required command*. This indicates the observation operator, previously
80 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
81 results :math:`\mathbf{y}` to be compared to observations
82 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
83 a "*Matrix*" type one. In the case of "*Function*" type, different
84 functional forms can be used, as described in the section
85 :ref:`section_ref_operator_requirements`. If there is some control :math:`U`
86 included in the observation, the operator has to be applied to a pair
89 The general optional commands, available in the editing user interface, are
90 indicated in :ref:`section_ref_assimilation_keywords`. In particular, the
91 optional command "*AlgorithmParameters*" allows to choose the specific options,
92 described hereafter, of the algorithm. See
93 :ref:`section_ref_options_AlgorithmParameters` for the good use of this command.
95 The options of the algorithm are the following:
98 This key allow to give an integer in order to fix the seed of the random
99 generator used to generate the ensemble. A convenient value is for example
100 1000. By default, the seed is left uninitialized, and so use the default
101 initialization from the computer.
103 Example : ``{"SetSeed":1000}``
108 References to other sections:
109 - :ref:`section_ref_algorithm_Blue`