coverage {DiceDesign}

Coverage

Description

Compute the coverage measure

Usage

coverage(design)

Arguments

design

a matrix (or a data.frame) representing the design of experiments 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 coverage criterion is defined by

coverage=\frac{1}{\bar{\gamma}} \left[ \frac{1}{n} \sum_{i=1}^{n} \left( \gamma_{i} - \bar{\gamma} \right)^2 \right]^{1/2}

where \gamma_{i} is the minimal distance between the point x_{i} and the other points of the design and \bar{\gamma} is the mean of the \gamma_{i}.

Note that for a regular mesh, cov=0. Then, a small value of cov means that the design is close to a regular grid.

Value

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

Author(s)

J. Franco

References

Gunzburer M., 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)
coverage(X)