phi_p: Calculate the phi_p Criterion
In LHD: Latin Hypercube Designs (LHDs)

Description Usage Arguments Value References Examples

phi_p returns the phi_p criterion of an LHD

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

`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.

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}

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.

#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)