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: SamplingTest
25 .. _section_ref_algorithm_SamplingTest:
27 Checking algorithm "*SamplingTest*"
28 -----------------------------------
33 This algorithm allows to calculate the values, linked to a :math:`\mathbf{x}`
34 state, of a general error function :math:`J` of type :math:`L^1`, :math:`L^2` or
35 :math:`L^{\infty}`, with or without weights, and of the observation operator,
36 for an priori given states sample. The default error function is the augmented
37 weighted least squares function, classicaly used in data assimilation.
39 It is useful to test the sensitivity, of the error function :math:`J`, in
40 particular, to the state :math:`\mathbf{x}` variations. When a state is not
41 observable, a *"NaN"* value is returned.
43 The sampling of the states :math:`\mathbf{x}` can be given explicitly or under
44 the form of hyper-cubes, explicit or sampled using classic distributions. Be
45 careful to the size of the hyper-cube (and then to the number of calculations)
46 that can be reached, it can be big very quickly.
48 To perform distributed or complex sampling, see other modules available in
49 SALOME : PARAMETRIC or OPENTURNS.
51 Optional and required commands
52 ++++++++++++++++++++++++++++++
54 .. index:: single: CheckingPoint
55 .. index:: single: BackgroundError
56 .. index:: single: Observation
57 .. index:: single: ObservationError
58 .. index:: single: ObservationOperator
59 .. index:: single: SampleAsnUplet
60 .. index:: single: SampleAsExplicitHyperCube
61 .. index:: single: SampleAsMinMaxStepHyperCube
62 .. index:: single: SampleAsIndependantRandomVariables
63 .. index:: single: QualityCriterion
64 .. index:: single: SetDebug
65 .. index:: single: SetSeed
66 .. index:: single: StoreSupplementaryCalculations
68 The general required commands, available in the editing user interface, are the
72 *Required command*. This indicates the vector used as the state around which
73 to perform the required check, noted :math:`\mathbf{x}` and similar to the
74 background :math:`\mathbf{x}^b`. It is defined as a "*Vector*" type object.
77 *Required command*. This indicates the background error covariance matrix,
78 previously noted as :math:`\mathbf{B}`. Its value is defined as a "*Matrix*"
79 type object, a "*ScalarSparseMatrix*" type object, or a
80 "*DiagonalSparseMatrix*" type object.
83 *Required command*. This indicates the observation vector used for data
84 assimilation or optimization, previously noted as :math:`\mathbf{y}^o`. It
85 is defined as a "*Vector*" or a *VectorSerie* type object.
88 *Required command*. This indicates the observation error covariance matrix,
89 previously noted as :math:`\mathbf{R}`. It is defined as a "*Matrix*" type
90 object, a "*ScalarSparseMatrix*" type object, or a "*DiagonalSparseMatrix*"
94 *Required command*. This indicates the observation operator, previously
95 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
96 results :math:`\mathbf{y}` to be compared to observations
97 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
98 a "*Matrix*" type one. In the case of "*Function*" type, different
99 functional forms can be used, as described in the section
100 :ref:`section_ref_operator_requirements`. If there is some control :math:`U`
101 included in the observation, the operator has to be applied to a pair
104 The general optional commands, available in the editing user interface, are
105 indicated in :ref:`section_ref_assimilation_keywords`. In particular, the
106 optional command "*AlgorithmParameters*" allows to choose the specific options,
107 described hereafter, of the algorithm. See
108 :ref:`section_ref_options_AlgorithmParameters` for the good use of this command.
110 The options of the algorithm are the following:
113 This key describes the calculations points as a list of n-uplets, each
114 n-uplet being a state.
116 Example : ``{"SampleAsnUplet":[[0,1,2,3],[4,3,2,1],[-2,3,-4,5]]}`` for 3 points in a state space of dimension 4
118 SampleAsExplicitHyperCube
119 This key describes the calculations points as an hyper-cube, from a given
120 list of explicit sampling of each variable as a list. That is then a list of
121 lists, each of them being potentially of different size.
123 Example : ``{"SampleAsExplicitHyperCube":[[0.,0.25,0.5,0.75,1.],[-2,2,1]]}`` for a state space of dimension 2
125 SampleAsMinMaxStepHyperCube
126 This key describes the calculations points as an hyper-cube, from a given
127 list of implicit sampling of each variable by a triplet *[min,max,step]*.
128 That is then a list of the same size than the one of the state. The bounds
131 Example : ``{"SampleAsMinMaxStepHyperCube":[[0.,1.,0.25],[-1,3,1]]}`` for a state space of dimension 2
133 SampleAsIndependantRandomVariables
134 This key describes the calculations points as an hyper-cube, for which the
135 points on each axis come from a independant random sampling of the axis
136 variable, under the specification of the distribution, its parameters and
137 the number of points in the sample, as a list ``['distribution',
138 [parametres], nombre]`` for each axis. The possible distributions are
139 'normal' of parameters (mean,std), 'lognormal' of parameters (mean,sigma),
140 'uniform' of parameters (low,high), or 'weibull' of parameter (shape). That
141 is then a list of the same size than the one of the state.
143 Example : ``{"SampleAsIndependantRandomVariables":[['normal',[0.,1.],3],['uniform',[-2,2],4]]`` for a state space of dimension 2
146 This key indicates the quality criterion, used to find the state estimate.
147 The default is the usual data assimilation criterion named "DA", the
148 augmented weighted least squares. The possible criteria has to be in the
149 following list, where the equivalent names are indicated by the sign "=":
150 ["AugmentedWeightedLeastSquares"="AWLS"="DA", "WeightedLeastSquares"="WLS",
151 "LeastSquares"="LS"="L2", "AbsoluteValue"="L1", "MaximumError"="ME"].
153 Example : ``{"QualityCriterion":"DA"}``
156 This key requires the activation, or not, of the debug mode during the
157 function evaluation. The default is "True", the choices are "True" or
160 Example : ``{"SetDebug":False}``
163 This key allow to give an integer in order to fix the seed of the random
164 generator used to generate the ensemble. A convenient value is for example
165 1000. By default, the seed is left uninitialized, and so use the default
166 initialization from the computer.
168 Example : ``{"SetSeed":1000}``
170 StoreSupplementaryCalculations
171 This list indicates the names of the supplementary variables that can be
172 available at the end of the algorithm. It involves potentially costly
173 calculations or memory consumptions. The default is a void list, none of
174 these variables being calculated and stored by default. The possible names
175 are in the following list: ["CostFunctionJ", "CurrentState", "Innovation",
178 Example : ``{"StoreSupplementaryCalculations":["CostFunctionJ", "ObservedState"]}``
183 References to other sections:
184 - :ref:`section_ref_algorithm_FunctionTest`
186 References to other SALOME modules:
187 - PARAMETRIC, see the *User guide of PARAMETRIC module* in the main "*Help*" menu of SALOME platform
188 - OPENTURNS, see the *User guide of OPENTURNS module* in the main "*Help*" menu of SALOME platform