unitCube_BFN3-class: An S4 class to represent the function prod^{n}_{i=1}...

In multIntTestFunc: Provides Test Functions for Multivariate Integration

An S4 class to represent the function \prod^{n}_{i=1} T_{\nu(i)}(2x_i-1) on [0,1]^n

Description

Implementation of the function

f \colon [0,1]^n \to (-\infty,\infty),\, \vec{x} \mapsto f(\vec{x}) = \prod^{n}_{i=1} T_{\nu(i)}(2x_i-1)

, where n \in \{1,2,3,\ldots\} is the dimension of the integration domain C_n = [0,1]^n and T_k is the Chebyshev polynomial of degree k and \nu(i) = (i \mod 4) + 1. The integral is known to be

\int_{C_n} f(\vec{x}) d\vec{x} = 0.

Details

The instance needs to be created with one parameter representing the dimension n.

Slots

dim

An integer that captures the dimension

Author(s)

Klaus Herrmann

Examples

n <- as.integer(3)
f <- new("unitCube_BFN3",dim=n)

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