| phiP {DiceDesign} | R Documentation |
phiP criterion
Description
Compute the \phi_p criterion (strongly linked to mindist criterion)
Usage
phiP(design, p=50)Arguments
design |
a matrix (or a data.frame) corresponding to the design of experiments. |
p |
the "p" in the Lp norm which is taken |
Details
The \phi_p criterion is defined by the L_p norm of the sum of the inverses of the design inter-point euclidean distances:
\phi_{p}=\left[\sum_{i,j=1\ldots N,i<j}\,\,d_{ij}^{-p}\right]^{\frac{1}{p}}
A higher value corresponds to a more regular scaterring of design points.
When p tends to infinity, optimizing a design with \phi_p is equivalent to optimizing a design with mindist.
Value
A real number equal to the value of the \phi_p criterion for the design.
Author(s)
G. Damblin & B.Iooss
References
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.
See Also
geometric criterion (mindist)
Examples
dimension <- 2
n <- 40
X <- matrix(runif(n*dimension), n, dimension)
phiP(X)