meshRatio {DiceDesign}

MeshRatio measure

Description

The meshRatio criterion is the ratio between the maximimum and the minimum distance between two points of the experimental design.

Usage

meshRatio(design)

Arguments

design

a matrix (or a data.frame) representing the design of experiments in the unit cube [0,1]^d. If this last condition is not fulfilled, a transformation into [0,1]^{d} is applied before the computation of the criteria.

Details

The meshRatio criterion is defined by

meshRatio=\frac{\max_{1\leq i \leq n} \gamma_{i}}{\min_{1\leq i \leq n} \gamma_{i}}

where \gamma_{i} denotes the minimal distance between the point x_{i} and the other points of the design.

Note that for a regular mesh, meshRatio=1.

Value

A real number equal to the value of the meshRatio criterion for the design.

Author(s)

J. Franco

References

Gunzburer M. and Burkdart J. (2004), Uniformity measures for point samples in hypercubes, https://people.sc.fsu.edu/~jburkardt/.

See Also

Other distance criteria like meshRatio, phiP and mindist.

Discrepancy measures provided by discrepancyCriteria.

Examples

dimension <- 2
n <- 40
X <- matrix(runif(n*dimension), n, dimension)
meshRatio(X)