unitCube_cos2-class: An S4 class to represent the function...

In multIntTestFunc: Provides Test Functions for Multivariate Integration

An S4 class to represent the function (\cos(\vec{x}\cdot\vec{v}))^2 on [0,1]^n

Description

Implementation of the function

f \colon [0,1]^n \to [0,1],\, \vec{x} \mapsto f(\vec{x}) = (\cos(\vec{x}\cdot\vec{v}))^2,

where n \in \{1,2,3,\ldots\} is the dimension of the integration domain C_n = [0,1]^n and \vec{v} is a n-dimensional parameter vector where each entry is different from 0. The integral is known to be

\int_{C_n} f(\vec{x}) d\vec{x} = \frac{1}{2}+\frac{1}{2}\cos(\sum_{j=1}^{n}v_j)\prod_{j=1}^{n}\frac{\sin(v_j)}{v_j}.

Details

The instance needs to be created with two parameters representing the dimension n and the n-dimensional parameter vector where each entry is different from 0.

Slots

dim

An integer that captures the dimension

coeffs

A vector of non-zero parameters

Author(s)

Klaus Herrmann

Examples

n <- as.integer(3)
f <- new("unitCube_cos2",dim=n, coeffs=c(-1,2,-2))

multIntTestFunc documentation built on Sept. 11, 2024, 5:18 p.m.