lines 8-101 of file: example/abs_normal/abs_eval.hpp

{xrst_begin abs_eval}
{xrst_spell
   tilde
}
abs_normal: Evaluate First Order Approximation
##############################################

Syntax
******
*g_tilde* = ``abs_eval`` ( *n* , *m* , *s* , *g_hat* , *g_jac* , *delta_x* )

Prototype
*********
{xrst_literal
   // BEGIN PROTOTYPE
   // END PROTOTYPE
}

Source
******
This following is a link to the source code for this example:
:ref:`abs_eval.hpp-name` .

Purpose
*******
Given a current that abs-normal representation at a point
:math:`\hat{x} \in \B{R}^n`,
and a :math:`\Delta x \in \B{R}^n`,
this routine evaluates the abs-normal
:ref:`approximation for f(x)<abs_normal_fun@Abs-normal Approximation@Approximating f(x)>`
where :math:`x = \hat{x} + \Delta x`.

Vector
******
The type *Vector* is a
simple vector with elements of type ``double`` .

f
*
We use the notation *f* for the original function; see
:ref:`abs_normal_fun@f` .

n
*
This is the dimension of the domain space for *f* ; see
:ref:`abs_normal_fun@f@n` .

m
*
This is the dimension of the range space for *f* ; see
:ref:`abs_normal_fun@f@m` .

s
*
This is the number of absolute value terms in *f* ; see

g
*
We use the notation *g* for the abs-normal representation of *f* ;
see :ref:`abs_normal_fun@g` .

g_hat
*****
This vector has size *m* + *s* and is the value of
*g* ( *x* , *u* ) at :math:`x = \hat{x}` and :math:`u = a( \hat{x} )`.

g_jac
*****
This vector has size ( *m* + *s* ) * ( *n* + *s* ) and is the Jacobian of
:math:`g(x, u)` at :math:`x = \hat{x}` and :math:`u = a( \hat{x} )`.

delta_x
*******
This vector has size *n* and is the difference
:math:`\Delta x = x - \hat{x}`,
where :math:`x` is the point that we are approximating :math:`f(x)`.

g_tilde
*******
This vector has size *m* + *s* and is a the
first order approximation for
:ref:`abs_normal_fun@g`
that corresponds to the point
:math:`x = \hat{x} + \Delta x` and :math:`u = a(x)`.
{xrst_toc_hidden
   example/abs_normal/abs_eval.cpp
   example/abs_normal/abs_eval.xrst
}
Example
*******
The file :ref:`abs_eval.cpp-name` contains an example and test of
``abs_eval`` .

{xrst_end abs_eval}