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.
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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: Blue
25 .. _section_ref_algorithm_Blue:
27 Calculation algorithm "*Blue*"
28 ------------------------------
33 This algorithm realizes a BLUE (Best Linear Unbiased Estimator) type estimation
34 of the state of a system. More precisely, it is an Aitken estimator.
36 This algorithm is always the fastest of all the assimilation algorithms of ADAO.
37 It is theoretically reserved for observation operator cases which are linear,
38 even if it sometimes works in "slightly" non-linear cases. One can verify the
39 linearity of the observation operator with the help of the
40 :ref:`section_ref_algorithm_LinearityTest`.
42 In case of non-linearity, even slightly marked, it will be easily prefered the
43 :ref:`section_ref_algorithm_ExtendedBlue` or the
44 :ref:`section_ref_algorithm_3DVAR`.
46 Optional and required commands
47 ++++++++++++++++++++++++++++++
49 .. index:: single: Background
50 .. index:: single: BackgroundError
51 .. index:: single: Observation
52 .. index:: single: ObservationError
53 .. index:: single: ObservationOperator
54 .. index:: single: StoreInternalVariables
55 .. index:: single: StoreSupplementaryCalculations
56 .. index:: single: Quantiles
57 .. index:: single: SetSeed
58 .. index:: single: NumberOfSamplesForQuantiles
59 .. index:: single: SimulationForQuantiles
61 The general required commands, available in the editing user interface, are the
65 *Required command*. This indicates the background or initial vector used,
66 previously noted as :math:`\mathbf{x}^b`. Its value is defined as a
67 "*Vector*" or a *VectorSerie*" type object.
70 *Required command*. This indicates the background error covariance matrix,
71 previously noted as :math:`\mathbf{B}`. Its value is defined as a "*Matrix*"
72 type object, a "*ScalarSparseMatrix*" type object, or a
73 "*DiagonalSparseMatrix*" type object.
76 *Required command*. This indicates the observation vector used for data
77 assimilation or optimization, previously noted as :math:`\mathbf{y}^o`. It
78 is defined as a "*Vector*" or a *VectorSerie* type object.
81 *Required command*. This indicates the observation error covariance matrix,
82 previously noted as :math:`\mathbf{R}`. It is defined as a "*Matrix*" type
83 object, a "*ScalarSparseMatrix*" type object, or a "*DiagonalSparseMatrix*"
87 *Required command*. This indicates the observation operator, previously
88 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
89 results :math:`\mathbf{y}` to be compared to observations
90 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
91 a "*Matrix*" type one. In the case of "*Function*" type, different
92 functional forms can be used, as described in the section
93 :ref:`section_ref_operator_requirements`. If there is some control :math:`U`
94 included in the observation, the operator has to be applied to a pair
97 The general optional commands, available in the editing user interface, are
98 indicated in :ref:`section_ref_assimilation_keywords`. In particular, the
99 optional command "*AlgorithmParameters*" allows to choose the specific options,
100 described hereafter, of the algorithm. See
101 :ref:`section_ref_options_AlgorithmParameters` for the good use of this command.
103 The options of the algorithm are the following:
105 StoreInternalVariables
106 This Boolean key allows to store default internal variables, mainly the
107 current state during iterative optimization process. Be careful, this can be
108 a numerically costly choice in certain calculation cases. The default is
111 Example : ``{"StoreInternalVariables":True}``
113 StoreSupplementaryCalculations
114 This list indicates the names of the supplementary variables that can be
115 available at the end of the algorithm. It involves potentially costly
116 calculations or memory consumptions. The default is a void list, none of
117 these variables being calculated and stored by default. The possible names
118 are in the following list: ["APosterioriCovariance", "BMA", "OMA", "OMB",
119 "Innovation", "SigmaBck2", "SigmaObs2", "MahalanobisConsistency",
120 "SimulationQuantiles"].
122 Example : ``{"StoreSupplementaryCalculations":["BMA","Innovation"]}``
125 This list indicates the values of quantile, between 0 and 1, to be estimated
126 by simulation around the optimal state. The sampling uses a multivariate
127 gaussian random sampling, directed by the *a posteriori* covariance matrix.
128 This option is useful only if the supplementary calculation
129 "SimulationQuantiles" has been chosen. The default is a void list.
131 Example : ``{"Quantiles":[0.1,0.9]}``
134 This key allow to give an integer in order to fix the seed of the random
135 generator used to generate the ensemble. A convenient value is for example
136 1000. By default, the seed is left uninitialized, and so use the default
137 initialization from the computer.
139 Example : ``{"SetSeed":1000}``
141 NumberOfSamplesForQuantiles
142 This key indicates the number of simulation to be done in order to estimate
143 the quantiles. This option is useful only if the supplementary calculation
144 "SimulationQuantiles" has been chosen. The default is 100, which is often
145 sufficient for correct estimation of common quantiles at 5%, 10%, 90% or
148 Example : ``{"NumberOfSamplesForQuantiles":100}``
150 SimulationForQuantiles
151 This key indicates the type of simulation, linear (with the tangent
152 observation operator applied to perturbation increments around the optimal
153 state) or non-linear (with standard observation operator applied to
154 perturbated states), one want to do for each perturbation. It changes mainly
155 the time of each elementary calculation, usually longer in non-linear than
156 in linear. This option is useful only if the supplementary calculation
157 "SimulationQuantiles" has been chosen. The default value is "Linear", and
158 the possible choices are "Linear" and "NonLinear".
160 Example : ``{"SimulationForQuantiles":"Linear"}``
165 References to other sections:
166 - :ref:`section_ref_algorithm_ExtendedBlue`
167 - :ref:`section_ref_algorithm_3DVAR`
168 - :ref:`section_ref_algorithm_LinearityTest`
170 Bibliographical references: