phiP criterion

Description

Compute the φ_p criterion (strongly linked to mindist criterion)

Usage

phiP(design,p=50)

Arguments

Details

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.

Value

A real number equal to the value of the φ_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. http://www.gdr-mascotnum.fr/doku.php?id=iooss1

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)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(DiceDesign)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DiceDesign/phiP.Rd_%03d_medium.png", width=480, height=480)
> ### Name: phiP
> ### Title: phiP criterion
> ### Aliases: phiP
> ### Keywords: design
> 
> ### ** Examples
> 
> dimension <- 2
> n <- 40
> X <- matrix(runif(n*dimension),n,dimension)
> phiP(X)
[1] 51.12943
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>