abs_eval¶

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abs_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 .