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
Package: stk