standardSimplex_exp_sum-class {multIntTestFunc}

An S4 class to represent the function \exp(-c(x_1 + \ldots + x_n)) on T_n

Description

Implementation of the function

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

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

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

where \Gamma(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

Author(s)

Klaus Herrmann

Examples

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