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: AdjointTest
25 .. _section_ref_algorithm_AdjointTest:
27 Checking algorithm "*AdjointTest*"
28 ----------------------------------
33 This algorithm allows to check the quality of the adjoint operator, by
34 calculating a residue with known theoretical properties.
36 One can observe the following residue, which is the difference of two scalar
39 .. math:: R(\alpha) = | < TangentF_x(\mathbf{dx}) , \mathbf{y} > - < \mathbf{dx} , AdjointF_x(\mathbf{y}) > |
41 that has to remain equal to zero at the calculation precision. One take
42 :math:`\mathbf{dx}_0=Normal(0,\mathbf{x})` and
43 :math:`\mathbf{dx}=\alpha*\mathbf{dx}_0`. :math:`F` is the calculation code.
44 :math:`\mathbf{y}` has to be in the image of :math:`F`. If it is not given, one
45 take :math:`\mathbf{y} = F(\mathbf{x})`.
47 Optional and required commands
48 ++++++++++++++++++++++++++++++
50 .. index:: single: AlgorithmParameters
51 .. index:: single: CheckingPoint
52 .. index:: single: ObservationOperator
53 .. index:: single: AmplitudeOfInitialDirection
54 .. index:: single: EpsilonMinimumExponent
55 .. index:: single: InitialDirection
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 vector used as the state around which
64 to perform the required check, noted :math:`\mathbf{x}` and similar to the
65 background :math:`\mathbf{x}^b`. It is defined as a "*Vector*" type object.
68 *Required command*. This indicates the observation operator, previously
69 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
70 results :math:`\mathbf{y}` to be compared to observations
71 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
72 a "*Matrix*" type one. In the case of "*Function*" type, different
73 functional forms can be used, as described in the section
74 :ref:`section_ref_operator_requirements`. If there is some control
75 :math:`U` included in the observation, the operator has to be applied to a
78 The general optional commands, available in the editing user interface, are
79 indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
80 of the command "*AlgorithmParameters*" allow to choose the specific options,
81 described hereafter, of the algorithm. See
82 :ref:`section_ref_options_Algorithm_Parameters` for the good use of this
85 The options of the algorithm are the following:
87 AmplitudeOfInitialDirection
88 This key indicates the scaling of the initial perturbation build as a vector
89 used for the directional derivative around the nominal checking point. The
90 default is 1, that means no scaling.
92 Example : ``{"AmplitudeOfInitialDirection":0.5}``
94 EpsilonMinimumExponent
95 This key indicates the minimal exponent value of the power of 10 coefficient
96 to be used to decrease the increment multiplier. The default is -8, and it
97 has to be between 0 and -20. For example, its default value leads to
98 calculate the residue of the formula with a fixed increment multiplied from
101 Example : ``{"EpsilonMinimumExponent":-12}``
104 This key indicates the vector direction used for the directional derivative
105 around the nominal checking point. It has to be a vector. If not specified,
106 this direction defaults to a random perturbation around zero of the same
107 vector size than the checking point.
109 Example : ``{"InitialDirection":[0.1,0.1,100.,3}``
112 This key allow to give an integer in order to fix the seed of the random
113 generator used to generate the ensemble. A convenient value is for example
114 1000. By default, the seed is left uninitialized, and so use the default
115 initialization from the computer.
117 Example : ``{"SetSeed":1000}``
119 StoreSupplementaryCalculations
120 This list indicates the names of the supplementary variables that can be
121 available at the end of the algorithm. It involves potentially costly
122 calculations or memory consumptions. The default is a void list, none of
123 these variables being calculated and stored by default. The possible names
124 are in the following list: ["CurrentState", "Residu",
125 "SimulatedObservationAtCurrentState"].
127 Example : ``{"StoreSupplementaryCalculations":["CurrentState"]}``
129 Information and variables available at the end of the algorithm
130 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
132 At the output, after executing the algorithm, there are variables and
133 information originating from the calculation. The description of
134 :ref:`section_ref_output_variables` show the way to obtain them by the method
135 named ``get`` of the variable "*ADD*" of the post-processing. The input
136 variables, available to the user at the output in order to facilitate the
137 writing of post-processing procedures, are described in the
138 :ref:`subsection_r_o_v_Inventaire`.
140 The unconditional outputs of the algorithm are the following:
143 *List of values*. Each element is the value of the particular residu
144 verified during a checking algorithm, in the order of the tests.
146 Example : ``r = ADD.get("Residu")[:]``
148 The conditional outputs of the algorithm are the following:
151 *List of vectors*. Each element is a usual state vector used during the
152 optimization algorithm procedure.
154 Example : ``Xs = ADD.get("CurrentState")[:]``
156 SimulatedObservationAtCurrentState
157 *List of vectors*. Each element is an observed vector at the current state,
158 that is, in the observation space.
160 Example : ``hxs = ADD.get("SimulatedObservationAtCurrentState")[-1]``
165 References to other sections:
166 - :ref:`section_ref_algorithm_FunctionTest`
167 - :ref:`section_ref_algorithm_LinearityTest`
168 - :ref:`section_ref_algorithm_TangentTest`
169 - :ref:`section_ref_algorithm_GradientTest`