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

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}) = ∏_{i=1}^{n}x_i^{v_i-1}(1 - x_1 - … - x_n)^{v_{n+1}-1},

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 v_i>0, i=1,…,n+1, are constants. The integral is known to be

\int_{T_n} f(\vec{x}) d\vec{x} = \frac{∏_{i=1}^{n+1}Γ(v_i)}{Γ(∑_{i=1}^{n+1}v_i)},

where v_i>0 for i=1,…,n+1.

Details

The instance needs to be created with two parameters representing the dimension n and the vector of positive parameters.

Slots

dim

An integer that captures the dimension

v

A vector of dimension n+1 with positive entries representing the constants

Examples

n <- as.integer(3)
f <- new("standardSimplex_Dirichlet",dim=n,v=c(1,2,3,4))

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