unitCube_Genz1-class: An S4 class to represent the function \cos<=ft(2pi u +...

In multIntTestFunc: Provides Test Functions for Multivariate Integration

An S4 class to represent the function \cos\left(2\pi u + \sum^{n}_{i=1} a_i x_i \right) on [0,1]^n

Description

Implementation of the function

f \colon [0,1]^n \to (-\infty,\infty),\, \vec{x} \mapsto f(\vec{x}) = \cos\left(2\pi u + \sum^{n}_{i=1} a_i x_i \right)

, where n \in \{1,2,3,\ldots\} is the dimension of the integration domain C_n = [0,1]^n. The integral is known to be

\int_{C_n} f(\vec{x}) d\vec{x} = \frac{2^n \cos\left(2\pi u + \sum_{i=1}^{n}a_i/2\right) \prod_{i=1}^n \sin(a_i/2)}{\prod_{i=1}^n a_i}.

Details

The instance needs to be created with three parameter representing the dimension n, the real number u and the vector (a_1,...,a_n).

Slots

dim

An integer that captures the dimension

u

A real number representing a shift in the integrand

a

A vector of real numbers, each non-zero, increasing the difficulty of the integrand with higher absolute values

Author(s)

Klaus Herrmann

Examples

n <- as.integer(3)
u <- pi
a <- rep(exp(1),n)
f <- new("unitCube_Genz1",dim=n, u=u, a=a)

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