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: ExtendedBlue
25 .. _section_ref_algorithm_ExtendedBlue:
27 Calculation algorithm "*ExtendedBlue*"
28 --------------------------------------
33 This algorithm realizes an extended BLUE (Best Linear Unbiased Estimator) type
34 estimation of the state of a system.
36 This algorithm is a partially non-linear generalization of the
37 :ref:`section_ref_algorithm_Blue`. It is equivalent for a linear observation
38 operator. One can verify the linearity of the observation operator with the help
39 of the :ref:`section_ref_algorithm_LinearityTest`.
41 In case of non-linearity, it is close to the :ref:`section_ref_algorithm_3DVAR`,
42 without being entirely equivalent.
44 Optional and required commands
45 ++++++++++++++++++++++++++++++
47 .. index:: single: Background
48 .. index:: single: BackgroundError
49 .. index:: single: Observation
50 .. index:: single: ObservationError
51 .. index:: single: ObservationOperator
52 .. index:: single: StoreInternalVariables
53 .. index:: single: StoreSupplementaryCalculations
55 The general required commands, available in the editing user interface, are the
59 *Required command*. This indicates the background or initial vector used,
60 previously noted as :math:`\mathbf{x}^b`. Its value is defined as a
61 "*Vector*" or a *VectorSerie*" type object.
64 *Required command*. This indicates the background error covariance matrix,
65 previously noted as :math:`\mathbf{B}`. Its value is defined as a "*Matrix*"
66 type object, a "*ScalarSparseMatrix*" type object, or a
67 "*DiagonalSparseMatrix*" type object.
70 *Required command*. This indicates the observation vector used for data
71 assimilation or optimization, previously noted as :math:`\mathbf{y}^o`. It
72 is defined as a "*Vector*" or a *VectorSerie* type object.
75 *Required command*. This indicates the observation error covariance matrix,
76 previously noted as :math:`\mathbf{R}`. It is defined as a "*Matrix*" type
77 object, a "*ScalarSparseMatrix*" type object, or a "*DiagonalSparseMatrix*"
81 *Required command*. This indicates the observation operator, previously
82 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
83 results :math:`\mathbf{y}` to be compared to observations
84 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
85 a "*Matrix*" type one. In the case of "*Function*" type, different
86 functional forms can be used, as described in the section
87 :ref:`section_ref_operator_requirements`. If there is some control :math:`U`
88 included in the observation, the operator has to be applied to a pair
91 The general optional commands, available in the editing user interface, are
92 indicated in :ref:`section_ref_assimilation_keywords`. In particular, the
93 optional command "*AlgorithmParameters*" allows to choose the specific options,
94 described hereafter, of the algorithm. See
95 :ref:`section_ref_options_AlgorithmParameters` for the good use of this command.
97 The options of the algorithm are the following:
99 StoreInternalVariables
100 This Boolean key allows to store default internal variables, mainly the
101 current state during iterative optimization process. Be careful, this can be
102 a numerically costly choice in certain calculation cases. The default is
105 Example : ``{"StoreInternalVariables":True}``
107 StoreSupplementaryCalculations
108 This list indicates the names of the supplementary variables that can be
109 available at the end of the algorithm. It involves potentially costly
110 calculations or memory consumptions. The default is a void list, none of
111 these variables being calculated and stored by default. The possible names
112 are in the following list: ["APosterioriCovariance", "BMA", "OMA", "OMB",
113 "Innovation", "SigmaBck2", "SigmaObs2", "MahalanobisConsistency"].
115 Example : ``{"StoreSupplementaryCalculations":["BMA","Innovation"]}``
120 References to other sections:
121 - :ref:`section_ref_algorithm_Blue`
122 - :ref:`section_ref_algorithm_3DVAR`
123 - :ref:`section_ref_algorithm_LinearityTest`