standardSimplex_exp_sum-class: An S4 class to represent the function \exp(-c(x_1 + ... +...

In multIntTestFunc: Provides Test Functions for Multivariate Integration

Description

Implementation of the function

f \colon T_n \to (0,∞),\, \vec{x} \mapsto f(\vec{x}) = \exp(-c(x_1 + … + x_n)),

where n \in \{1,2,3,…\} is the dimension of the integration domain T_n = \{\vec{x} \in \R^n : x_i≥q 0, \Vert \vec{x} \Vert_1 ≤q 1\} and c>0 is a constant. The integral is known to be

\int_{T_n} f(\vec{x}) d\vec{x} = \frac{Γ(n)-Γ(n,c)}{Γ(n)c^n},

where Γ(s,x) is the incomplete gamma function.

Details

The instance needs to be created with two parameters representing the dimension n and the parameter c>0.

Slots

dim

An integer that captures the dimension

coeff

A strictly positive number representing the constant

Examples

n <- as.integer(3)
f <- new("standardSimplex_exp_sum",dim=n,coeff=1)

multIntTestFunc documentation built on Oct. 5, 2021, 5:08 p.m.