phiP criterion
Compute the φ_p criterion (strongly linked to mindist criterion)
phiP(design, p=50)
design |
a matrix (or a data.frame) corresponding to the design of experiments. |
p |
the "p" in the Lp norm which is taken |
The φ_p criterion is defined by the L_p norm of the sum of the inverses of the design inter-point euclidean distances:
A higher value corresponds to a more regular scaterring of design points.
When p tends to infinity, optimizing a design with φ_p is equivalent to optimizing a design with mindist.
A real number equal to the value of the φ_p criterion for the design.
G. Damblin & B.Iooss
Damblin G., Couplet M., and Iooss B. (2013). Numerical studies of sapce filling designs: optimization of Latin Hypercube Samples and subprojection properties, Journal of Simulation, 7:276-289, 2013.
Fang K.-T., Li R. and Sudjianto A. (2006). Design and Modeling for Computer Experiments, Chapman & Hall.
Pronzato, L. and Muller, W. (2012). Design of computer experiments: space filling and beyond, Statistics and Computing, 22:681-701.
geometric criterion (mindist)
dimension <- 2 n <- 40 X <- matrix(runif(n*dimension), n, dimension) phiP(X)
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