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DiceDesign (version 1.10)

meshRatio: 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)

Value

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

Author

J. Franco

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.

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

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

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