\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)
abs_eval¶
abs_normal: Evaluate First Order Approximation¶
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 \(x = \hat{x} + \Delta x\).
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 \(f(x)\).