coverage: Coverage In DiceDesign: Designs of Computer Experiments

Description

Compute the coverage measure

Usage

 `1` ```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) =1/gMean *[ 1/n * [( g_1 - gMean )^2 + ... + (g_n - gMean)^2] ]^(1/2)

where g_i is the minimal distance between the point x_i and the other points of the `design` and gMean is the mean of the g_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`.

J. Franco

References

Gunzburer M., 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`.
 ```1 2 3 4``` ```dimension <- 2 n <- 40 X <- matrix(runif(n*dimension), n, dimension) coverage(X) ```