unitCube_floor-class {multIntTestFunc}

An S4 class to represent the function \lfloor x_1 + \ldots + x_n \rfloor on [0,1]^n

Description

Implementation of the function

f \colon [0,1]^n \to [0,n],\, \vec{x} \mapsto f(\vec{x}) = \lfloor x_1 + \ldots + x_n \rfloor,

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{n-1}{2}.

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_floor",dim=n)