2 Copyright (C) 2008-2014 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: 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: CheckingPoint
51 .. index:: single: ObservationOperator
52 .. index:: single: AmplitudeOfInitialDirection
53 .. index:: single: EpsilonMinimumExponent
54 .. index:: single: InitialDirection
55 .. index:: single: SetSeed
57 The general required commands, available in the editing user interface, are the
61 *Required command*. This indicates the vector used as the state around which
62 to perform the required check, noted :math:`\mathbf{x}` and similar to the
63 background :math:`\mathbf{x}^b`. It is defined as a "*Vector*" type object.
66 *Required command*. This indicates the observation operator, previously
67 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
68 results :math:`\mathbf{y}` to be compared to observations
69 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
70 a "*Matrix*" type one. In the case of "*Function*" type, different
71 functional forms can be used, as described in the section
72 :ref:`section_ref_operator_requirements`. If there is some control
73 :math:`U` included in the observation, the operator has to be applied to a
76 The general optional commands, available in the editing user interface, are
77 indicated in :ref:`section_ref_assimilation_keywords`. In particular, the
78 optional command "*AlgorithmParameters*" allows to choose the specific options,
79 described hereafter, of the algorithm. See
80 :ref:`section_ref_options_AlgorithmParameters` for the good use of this command.
82 The options of the algorithm are the following:
84 AmplitudeOfInitialDirection
85 This key indicates the scaling of the initial perturbation build as a vector
86 used for the directional derivative around the nominal checking point. The
87 default is 1, that means no scaling.
89 EpsilonMinimumExponent
90 This key indicates the minimal exponent value of the power of 10 coefficient
91 to be used to decrease the increment multiplier. The default is -8, and it
92 has to be between 0 and -20. For example, its default value leads to
93 calculate the residue of the formula with a fixed increment multiplied from
97 This key indicates the vector direction used for the directional derivative
98 around the nominal checking point. It has to be a vector. If not specified,
99 this direction defaults to a random perturbation around zero of the same
100 vector size than the checking point.
103 This key allow to give an integer in order to fix the seed of the random
104 generator used to generate the ensemble. A convenient value is for example
105 1000. By default, the seed is left uninitialized, and so use the default
106 initialization from the computer.
111 References to other sections:
112 - :ref:`section_ref_algorithm_FunctionTest`
113 - :ref:`section_ref_algorithm_TangentTest`
114 - :ref:`section_ref_algorithm_GradientTest`