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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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: ParticleSwarmOptimization
25 .. _section_ref_algorithm_ParticleSwarmOptimization:
27 Calculation algorithm "*ParticleSwarmOptimization*"
28 ---------------------------------------------------
33 This algorithm realizes an estimation of the state of a dynamic system by a
36 This is an optimization method allowing for global minimum search of a general
37 error function :math:`J` of type :math:`L^1`, :math:`L^2` or :math:`L^{\infty}`,
38 with or without weights. The default error function is the augmented weighted
39 least squares function, classicaly used in data assimilation.
41 Optional and required commands
42 ++++++++++++++++++++++++++++++
44 .. index:: single: AlgorithmParameters
45 .. index:: single: Background
46 .. index:: single: BackgroundError
47 .. index:: single: Observation
48 .. index:: single: ObservationError
49 .. index:: single: ObservationOperator
50 .. index:: single: MaximumNumberOfSteps
51 .. index:: single: NumberOfInsects
52 .. index:: single: SwarmVelocity
53 .. index:: single: GroupRecallRate
54 .. index:: single: QualityCriterion
55 .. index:: single: BoxBounds
56 .. index:: single: SetSeed
57 .. index:: single: StoreSupplementaryCalculations
59 The general required commands, available in the editing user interface, are the
63 *Required command*. This indicates the background or initial vector used,
64 previously noted as :math:`\mathbf{x}^b`. Its value is defined as a
65 "*Vector*" or a *VectorSerie*" type object.
68 *Required command*. This indicates the background error covariance matrix,
69 previously noted as :math:`\mathbf{B}`. Its value is defined as a "*Matrix*"
70 type object, a "*ScalarSparseMatrix*" type object, or a
71 "*DiagonalSparseMatrix*" type object.
74 *Required command*. This indicates the observation vector used for data
75 assimilation or optimization, previously noted as :math:`\mathbf{y}^o`. It
76 is defined as a "*Vector*" or a *VectorSerie* type object.
79 *Required command*. This indicates the observation error covariance matrix,
80 previously noted as :math:`\mathbf{R}`. It is defined as a "*Matrix*" type
81 object, a "*ScalarSparseMatrix*" type object, or a "*DiagonalSparseMatrix*"
85 *Required command*. This indicates the observation operator, previously
86 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
87 results :math:`\mathbf{y}` to be compared to observations
88 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
89 a "*Matrix*" type one. In the case of "*Function*" type, different
90 functional forms can be used, as described in the section
91 :ref:`section_ref_operator_requirements`. If there is some control :math:`U`
92 included in the observation, the operator has to be applied to a pair
95 The general optional commands, available in the editing user interface, are
96 indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
97 of the command "*AlgorithmParameters*" allows to choose the specific options,
98 described hereafter, of the algorithm. See
99 :ref:`section_ref_options_Algorithm_Parameters` for the good use of this
102 The options of the algorithm are the following:
105 This key indicates the maximum number of iterations allowed for iterative
106 optimization. The default is 50, which is an arbitrary limit. It is then
107 recommended to adapt this parameter to the needs on real problems.
109 Example : ``{"MaximumNumberOfSteps":100}``
112 This key indicates the number of insects or particles in the swarm. The
113 default is 100, which is a usual default for this algorithm.
115 Example : ``{"NumberOfInsects":100}``
118 This key indicates the part of the insect velocity which is imposed by the
119 swarm. It is a positive floating point value. The default value is 1.
121 Example : ``{"SwarmVelocity":1.}``
124 This key indicates the recall rate at the best swarm insect. It is a
125 floating point value between 0 and 1. The default value is 0.5.
127 Example : ``{"GroupRecallRate":0.5}``
130 This key indicates the quality criterion, minimized to find the optimal
131 state estimate. The default is the usual data assimilation criterion named
132 "DA", the augmented weighted least squares. The possible criteria has to be
133 in the following list, where the equivalent names are indicated by the sign
134 "=": ["AugmentedWeightedLeastSquares"="AWLS"="DA",
135 "WeightedLeastSquares"="WLS", "LeastSquares"="LS"="L2",
136 "AbsoluteValue"="L1", "MaximumError"="ME"].
138 Example : ``{"QualityCriterion":"DA"}``
141 This key allows to define upper and lower bounds for *increments* on every
142 state variable being optimized (and not on state variables themselves).
143 Bounds have to be given by a list of list of pairs of lower/upper bounds for
144 each increment on variable, with extreme values every time there is no bound
145 (``None`` is not allowed when there is no bound). This key is required and
146 there is no default values.
148 Example : ``{"BoxBounds":[[-0.5,0.5], [0.01,2.], [0.,1.e99], [-1.e99,1.e99]]}``
151 This key allow to give an integer in order to fix the seed of the random
152 generator used to generate the ensemble. A convenient value is for example
153 1000. By default, the seed is left uninitialized, and so use the default
154 initialization from the computer.
156 Example : ``{"SetSeed":1000}``
158 StoreSupplementaryCalculations
159 This list indicates the names of the supplementary variables that can be
160 available at the end of the algorithm. It involves potentially costly
161 calculations or memory consumptions. The default is a void list, none of
162 these variables being calculated and stored by default. The possible names
163 are in the following list: ["BMA", "CostFunctionJ", "CurrentState", "OMA",
164 "OMB", "Innovation", "SimulatedObservationAtBackground",
165 "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum"].
167 Example : ``{"StoreSupplementaryCalculations":["BMA", "Innovation"]}``
169 Information and variables available at the end of the algorithm
170 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
172 At the output, after executing the algorithm, there are variables and
173 information originating from the calculation. The description of
174 :ref:`section_ref_output_variables` show the way to obtain them by the method
175 named ``get`` of the variable "*ADD*" of the post-processing. The input
176 variables, available to the user at the output in order to facilitate the
177 writing of post-processing procedures, are described in the
178 :ref:`subsection_r_o_v_Inventaire`.
180 The unconditional outputs of the algorithm are the following:
183 *List of vectors*. Each element is an optimal state :math:`\mathbf{x}*` in
184 optimization or an analysis :math:`\mathbf{x}^a` in data assimilation.
186 Example : ``Xa = ADD.get("Analysis")[-1]``
189 *List of values*. Each element is a value of the error function :math:`J`.
191 Example : ``J = ADD.get("CostFunctionJ")[:]``
194 *List of values*. Each element is a value of the error function :math:`J^b`,
195 that is of the background difference part.
197 Example : ``Jb = ADD.get("CostFunctionJb")[:]``
200 *List of values*. Each element is a value of the error function :math:`J^o`,
201 that is of the observation difference part.
203 Example : ``Jo = ADD.get("CostFunctionJo")[:]``
205 The conditional outputs of the algorithm are the following:
208 *List of vectors*. Each element is a vector of difference between the
209 background and the optimal state.
211 Example : ``bma = ADD.get("BMA")[-1]``
214 *List of vectors*. Each element is a usual state vector used during the
215 optimization algorithm procedure.
217 Example : ``Xs = ADD.get("CurrentState")[:]``
220 *List of vectors*. Each element is an innovation vector, which is in static
221 the difference between the optimal and the background, and in dynamic the
224 Example : ``d = ADD.get("Innovation")[-1]``
227 *List of vectors*. Each element is a vector of difference between the
228 observation and the optimal state in the observation space.
230 Example : ``oma = ADD.get("OMA")[-1]``
233 *List of vectors*. Each element is a vector of difference between the
234 observation and the background state in the observation space.
236 Example : ``omb = ADD.get("OMB")[-1]``
238 SimulatedObservationAtBackground
239 *List of vectors*. Each element is a vector of observation simulated from
240 the background :math:`\mathbf{x}^b`.
242 Example : ``hxb = ADD.get("SimulatedObservationAtBackground")[-1]``
244 SimulatedObservationAtCurrentState
245 *List of vectors*. Each element is an observed vector at the current state,
246 that is, in the observation space.
248 Example : ``Ys = ADD.get("SimulatedObservationAtCurrentState")[-1]``
250 SimulatedObservationAtOptimum
251 *List of vectors*. Each element is a vector of observation simulated from
252 the analysis or optimal state :math:`\mathbf{x}^a`.
254 Example : ``hxa = ADD.get("SimulatedObservationAtOptimum")[-1]``
259 References to other sections: