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