template <class Vector>
Vector abs_eval(
size_t n ,
size_t m ,
size_t s ,
const Vector& g_hat ,
const Vector& g_jac ,
const Vector& delta_x )
Source
This following is a link to the source code for this example:
abs_eval.hpp
.
Purpose
Given a current that abs-normal representation at a point
@(@
\hat{x} \in \B{R}^n
@)@,
and a @(@
\Delta x \in \B{R}^n
@)@,
this routine evaluates the abs-normal
approximation for f(x)
where @(@
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
f
.
n
This is the dimension of the domain space for
f
; see
n
.
m
This is the dimension of the range space for
f
; see
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 g
.
g_hat
This vector has size
m + s
and is the value of
g(x, u)
at @(@
x = \hat{x}
@)@ and @(@
u = a( \hat{x} )
@)@.
g_jac
This vector has size
(m + s) * (n + s)
and is the Jacobian of
@(@
g(x, u)
@)@ at @(@
x = \hat{x}
@)@ and @(@
u = a( \hat{x} )
@)@.
delta_x
This vector has size
n
and is the difference
@(@
\Delta x = x - \hat{x}
@)@,
where @(@
x
@)@ is the point that we are approximating @(@
f(x)
@)@.
g_tilde
This vector has size
m + s
and is a the
first order approximation for
g
that corresponds to the point
@(@
x = \hat{x} + \Delta x
@)@ and @(@
u = a(x)
@)@.
Example
The file abs_eval.cpp
contains an example and test of
abs_eval.
It returns true if the test passes and false otherwise.
Input File: example/abs_normal/abs_eval.hpp
