STK_PHIPCRIT computes the "phi_p" criterion of Morris & Mitchell
CALL: D = stk_phipcrit (X, P)
computes the phi_P criterion on the set of points X, which is defined for
an n x d array X as
D = (sum_{1 <= i < j <= n} d_ij ^ (-p)) ^ (1/p)
where d_ij is the Euclidean distance in R^d between X(i,:) and X(j,:).
CALL: D = stk_phipcrit (X)
computes the phi_P criterion with P = 50.
NOTES:
* In the special case P = 2, this criterion has first been introduced by
Audze & Eglais (1977).
* When p -> +Inf, the value of the phi_p criterion tends to the inverse of
the mindist criterion. The phi_p criterion with a high value of p is
often used in place of the mindist criterion for its being easier to
optimize. Morris & Mitchell recommend using p in the range 20-50 for this
purpose.
REFERENCES
[1] Max D. Morris and Toby J. Mitchell, "Exploratory Designs for Computer
Experiments", Journal of Statistical Planning and Inference,
43(3):381-402, 1995.
[2] P. Audze and V. Eglais, "New approach for planning out experiments",
Problems of Dynamics and Strengths, 35:104-107, 1977.
[3] Luc Pronzato and Werner G. Muller, "Design of computer
experiments: space filling and beyond", Statistics and Computing,
22(3):681-701, 2012.
[4] G. Damblin, M. Couplet and B. Iooss, "Numerical studies of space filling
designs: optimization of Latin hypercube samples and subprojection
properties", Journal of Simulation, in press.
See also: stk_mindist, stk_filldist