..
- Copyright (C) 2008-2015 EDF R&D
+ Copyright (C) 2008-2017 EDF R&D
This file is part of SALOME ADAO module.
through the GUI, using the keyword "*CenteredFiniteDifference*", with 0 for an
uncentered schema of first order (which is the default value), and with 1 for a
centered schema of second order (of twice the first order computational cost).
-If necessary and if possible, :ref:`subsection_ref_parallel_df` can be used.
+If necessary and if possible, :ref:`subsection_ref_parallel_df` can be used. In
+all cases, an internal cache mechanism is used to restrict the number of
+operator evaluations at the minimum possible in a sequential or parallel
+execution scheme for numerical approximations of the tangent and adjoint
+operators, to avoid redundant calculations.
This first operator definition form allows easily to test the functional form
before its use in an ADAO case, greatly reducing the complexity of operator
All various modifications could be done from this template hypothesis.
-Special case of controlled evolution or observation operator
-++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+.. _section_ref_operator_control:
+
+Special case of controled evolution or observation operator
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
In some cases, the evolution or the observation operator is required to be
controlled by an external input control, given *a priori*. In this case, the
In such a case with explicit control, only the second functional form (using
"*ScriptWithFunctions*") and third functional form (using "*ScriptWithSwitch*")
can be used.
+
+Additional notes on nondimensionalization of operators
+++++++++++++++++++++++++++++++++++++++++++++++++++++++
+
+.. index:: single: Nondimensionalization
+.. index:: single: Dimensionless
+
+It is common that physical quantities, in input or output of the operators, have
+significant differences in magnitude or rate of change. One way to avoid
+numerical difficulties is to use, or to set, a nondimensionalization of the
+calculations carried out in operators [WikipediaND]_. In principle, since
+physical simulation should be as dimensionless as possible, it is firstly
+recommended to use the existing capacity of nondimensionalization of the
+calculation code.
+
+However, in the common case where we can not dispose of it, it is often useful
+to surround the calculation to remove dimension for input or output. A simple
+way to do this is to convert the input parameters :math:`\mathbf{x}` which are
+arguments of a function like "*DirectOperator*". One mostly use the default
+values :math:`\mathbf{x}^b` (background, or nominal value). Provided that each
+component of :math:`\mathbf{x}^b` is non zero, one can indeed put:
+
+.. math:: \mathbf{x} = \mathbf{\alpha}\mathbf{x}^b
+
+and then optimize the multiplicative parameter :math:`\mathbf{\alpha}`. This
+parameter has as default value (or as background) a vector of 1. Be careful,
+applying a process of nondimensionalization also requires changing the error
+covariances associated in an ADAO formulation of the optimization problem.
+
+Such a process is rarely enough to avoid all the numerical problems, but it
+often improves a lot the numeric conditioning of the optimization.
