DiceDesign (version 1.8)

coverage: 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.

Value

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

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.

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

# NOT RUN {
dimension <- 2
n <- 40
X <- matrix(runif(n*dimension), n, dimension)
coverage(X)
# }