2 Copyright (C) 2008-2023 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 -----------------------------------
30 .. ------------------------------------ ..
31 .. include:: snippets/Header2Algo01.rst
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`
35 or :math:`L^{\infty}`, with or without weights, and of the observation
36 operator, for an priori given :math:`\mathbf{x}` states sample. The default
37 error function is the augmented weighted least squares function, classically
38 used in data assimilation, using observation :math:`\mathbf{y}^o`.
40 It is useful to test the sensitivity, of the error function :math:`J`, in
41 particular, to the state :math:`\mathbf{x}` variations. When a state is not
42 observable, a *"NaN"* value is returned.
44 The sampling of the states :math:`\mathbf{x}` can be given explicitly or under
45 form of hyper-cubes, explicit or sampled according to classic distributions.
46 Beware of the size of the hyper-cube (and then to the number of computations)
47 that can be reached, it can grow quickly to be quite large.
49 To be visible by the user while reducing the risk of storage difficulties, the
50 results of sampling or simulations has to be **explicitly** asked for. One use
51 for that, on the desired variable, the final saving through
52 "*UserPostAnalysis*" or the treatment during the calculation by "*observer*".
54 To perform distributed or more complex sampling, see OPENTURNS module available
57 .. ------------------------------------ ..
58 .. include:: snippets/Header2Algo02.rst
60 .. include:: snippets/CheckingPoint.rst
62 .. include:: snippets/BackgroundError.rst
64 .. include:: snippets/Observation.rst
66 .. include:: snippets/ObservationError.rst
68 .. include:: snippets/ObservationOperator.rst
70 .. ------------------------------------ ..
71 .. include:: snippets/Header2Algo03Chck.rst
73 .. include:: snippets/QualityCriterion.rst
75 .. include:: snippets/SampleAsExplicitHyperCube.rst
77 .. include:: snippets/SampleAsIndependantRandomVariables.rst
79 .. include:: snippets/SampleAsMinMaxStepHyperCube.rst
81 .. include:: snippets/SampleAsnUplet.rst
83 .. include:: snippets/SetDebug.rst
85 .. include:: snippets/SetSeed.rst
87 StoreSupplementaryCalculations
88 .. index:: single: StoreSupplementaryCalculations
90 *List of names*. This list indicates the names of the supplementary
91 variables, that can be available during or at the end of the algorithm, if
92 they are initially required by the user. Their avalability involves,
93 potentially, costly calculations or memory consumptions. The default is then
94 a void list, none of these variables being calculated and stored by default
95 (excepted the unconditionnal variables). The possible names are in the
96 following list (the detailed description of each named variable is given in
97 the following part of this specific algorithmic documentation, in the
98 sub-section "*Information and variables available at the end of the
104 "EnsembleOfSimulations",
106 "InnovationAtCurrentState",
107 "SimulatedObservationAtCurrentState",
111 ``{"StoreSupplementaryCalculations":["CurrentState", "Residu"]}``
113 .. ------------------------------------ ..
114 .. include:: snippets/Header2Algo04.rst
116 .. include:: snippets/CostFunctionJ.rst
118 .. include:: snippets/CostFunctionJb.rst
120 .. include:: snippets/CostFunctionJo.rst
122 .. ------------------------------------ ..
123 .. include:: snippets/Header2Algo05.rst
125 .. include:: snippets/CostFunctionJ.rst
127 .. include:: snippets/CostFunctionJb.rst
129 .. include:: snippets/CostFunctionJo.rst
131 .. include:: snippets/CurrentState.rst
133 .. include:: snippets/EnsembleOfSimulations.rst
135 .. include:: snippets/EnsembleOfStates.rst
137 .. include:: snippets/InnovationAtCurrentState.rst
139 .. include:: snippets/SimulatedObservationAtCurrentState.rst
141 .. ------------------------------------ ..
142 .. _section_ref_algorithm_SamplingTest_examples:
143 .. include:: snippets/Header2Algo06.rst
145 - :ref:`section_ref_algorithm_FunctionTest`
146 - :ref:`section_ref_algorithm_LocalSensitivityTest`
148 .. ------------------------------------ ..
149 .. include:: snippets/Header2Algo08.rst
151 - OPENTURNS, see the *User guide of OPENTURNS module* in the main "*Help*" menu of SALOME platform