R: MeshRatio measure

meshRatio {DiceDesign} | R Documentation

## 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(\code{design})=max(g_1, ..., g_n)/min(g_1, ..., g_n)

where g_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)

[Package DiceDesign version 1.9 Index]