uniform.crit: Uniform criterion

In SFDesign: Space-Filling Designs

Uniform criterion

Description

This function calculates the wrap-around discrepancy of a design.

Usage

uniform.crit(design)

Arguments

design

a design matrix.

Details

uniform.crit calculates the wrap-around discrepancy of a design. The wrap-around discrepancy for a design D=[\bm x_1, \dots, \bm x_n]^T is defined as (Hickernell, 1998):

\phi_{wa} = -\left(\frac{4}{3}\right)^p + \frac{1}{n^2}\sum_{i,j=1}^n\prod_{k=1}^p\left[\frac{3}{2} - |x_{ik}-x_{jk}|(1-|x_{ik}-x_{jk}|)\right].

Value

wrap-around discrepancy of the design

References

Hickernell, F. (1998), “A generalized discrepancy and quadrature error bound,” Mathematics of computation, 67, 299–322.

Examples

n = 20
p = 3
D = randomLHD(n, p)
uniform.crit(D)

SFDesign documentation built on June 22, 2025, 1:06 a.m.