\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)
abs_eval¶
View page sourceabs_normal: Evaluate First Order Approximation¶
Syntax¶
g_tilde = abs_eval ( n , m , s , g_hat , g_jac , delta_x )
Prototype¶
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 .