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: TangentTest
25 .. _section_ref_algorithm_TangentTest:
27 Checking algorithm "*TangentTest*"
28 ----------------------------------
33 This algorithm allows to check the quality of the tangent operator, by
34 calculating a residue with known theoretical properties.
36 One can observe the following residue, which is the comparison of increments
37 using the tangent linear operator:
39 .. math:: R(\alpha) = \frac{|| F(\mathbf{x}+\alpha*\mathbf{dx}) - F(\mathbf{x}) ||}{|| \alpha * TangentF_x * \mathbf{dx} ||}
41 which has to remain stable in :math:`1+O(\alpha)` until the calculation
44 When :math:`|R-1|/\alpha` is less or equal to a stable value when :math:`\alpha`
45 is varying, the tangent is valid, until the calculation precision is reached.
47 If :math:`|R-1|/\alpha` is really small, the calculation code :math:`F` is
48 almost linear or quasi-linear (which can be verified by the
49 :ref:`section_ref_algorithm_LinearityTest`), and the tangent is valid until the
50 calculation precision is reached.
52 One take :math:`\mathbf{dx}_0=Normal(0,\mathbf{x})` and
53 :math:`\mathbf{dx}=\alpha*\mathbf{dx}_0`. :math:`F` is the calculation code.
55 Optional and required commands
56 ++++++++++++++++++++++++++++++
58 .. index:: single: CheckingPoint
59 .. index:: single: ObservationOperator
60 .. index:: single: AmplitudeOfInitialDirection
61 .. index:: single: EpsilonMinimumExponent
62 .. index:: single: InitialDirection
63 .. index:: single: SetSeed
65 The general required commands, available in the editing user interface, are the
69 *Required command*. This indicates the vector used as the state around which
70 to perform the required check, noted :math:`\mathbf{x}` and similar to the
71 background :math:`\mathbf{x}^b`. It is defined as a "*Vector*" type object.
74 *Required command*. This indicates the observation operator, previously
75 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
76 results :math:`\mathbf{y}` to be compared to observations
77 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
78 a "*Matrix*" type one. In the case of "*Function*" type, different
79 functional forms can be used, as described in the section
80 :ref:`section_ref_operator_requirements`. If there is some control
81 :math:`U` included in the observation, the operator has to be applied to a
84 The general optional commands, available in the editing user interface, are
85 indicated in :ref:`section_ref_assimilation_keywords`. In particular, the
86 optional command "*AlgorithmParameters*" allows to choose the specific options,
87 described hereafter, of the algorithm. See
88 :ref:`section_ref_options_AlgorithmParameters` for the good use of this command.
90 The options of the algorithm are the following:
92 AmplitudeOfInitialDirection
93 This key indicates the scaling of the initial perturbation build as a vector
94 used for the directional derivative around the nominal checking point. The
95 default is 1, that means no scaling.
97 EpsilonMinimumExponent
98 This key indicates the minimal exponent value of the power of 10 coefficient
99 to be used to decrease the increment multiplier. The default is -8, and it
100 has to be between 0 and -20. For example, its default value leads to
101 calculate the residue of the scalar product formula with a fixed increment
102 multiplied from 1.e0 to 1.e-8.
105 This key indicates the vector direction used for the directional derivative
106 around the nominal checking point. It has to be a vector. If not specified,
107 this direction defaults to a random perturbation around zero of the same
108 vector size than the checking point.
111 This key allow to give an integer in order to fix the seed of the random
112 generator used to generate the ensemble. A convenient value is for example
113 1000. By default, the seed is left uninitialized, and so use the default
114 initialization from the computer.
119 References to other sections:
120 - :ref:`section_ref_algorithm_FunctionTest`
121 - :ref:`section_ref_algorithm_AdjointTest`
122 - :ref:`section_ref_algorithm_GradientTest`