LHD (version 1.4.1)

phi_p: Calculate the phi_p Criterion

Description

phi_p returns the phi_p criterion of an LHD

Usage

phi_p(X, p = 15, q = 1)

Value

If all inputs are logical, then the output will be a positive number indicating phi_p. \phi_p = (\sum_{i=1}^{n-1}\sum_{j=i+1}^{n}dij^{-p})^{1/p}, where dij = \left\{ \sum_{k=1}^{m} \vert x_{ik}-x_{jk}\vert ^q \right\}^{1/q}

Arguments

X

A matrix object. In general, X stands for the design matrix.

p

A positive integer, which is the parameter in the phi_p formula, and p is prefered to be large. The default is set to be 15.

q

The default is set to be 1, and it could be either 1 or 2. If q is 1, dij is the Manhattan (rectangular) distance. If q is 2, dij is the Euclidean distance.

References

Jin, R., Chen, W., and Sudjianto, A. (2005) An efficient algorithm for constructing optimal design of computer experiments. Journal of Statistical Planning and Inference, 134, 268-287.

Examples

#create a toy LHD with 5 rows and 3 columns
toy=rLHD(n=5,k=3);toy

#Calculate the phi_p criterion of toy with default setting
phi_p(X=toy)

#Calculate the phi_p criterion of toy with p=50 and q=2
phi_p(X=toy,p=50,q=2)