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=\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.

J. Franco

### References

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

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]