unitCube_floor-class {multIntTestFunc}R Documentation

An S4 class to represent the function x1++xn\lfloor x_1 + \ldots + x_n \rfloor on [0,1]n[0,1]^n

Description

Implementation of the function

f ⁣:[0,1]n[0,n],xf(x)=x1++xn,f \colon [0,1]^n \to [0,n],\, \vec{x} \mapsto f(\vec{x}) = \lfloor x_1 + \ldots + x_n \rfloor,

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

Cnf(x)dx=n12.\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 nn.

Slots

dim

An integer that captures the dimension

Author(s)

Klaus Herrmann

Examples

n <- as.integer(3)
f <- new("unitCube_floor",dim=n)

[Package multIntTestFunc version 0.2.0 Index]