STK_FILLDIST computes the fill distance of a set of points CALL: FD = stk_filldist(X, BOX) computes the fill distance FD of the dataset X in the hyper-rectangle BOX, using the computational-geometric algorithm of L. Pronzato and W. G. Muller [1]. Recall that D = max_{Y in BOX} min_{1 <= i <= n} norm(X(i,:) - Y), (1) where norm(.) denotes the Euclidean norm in R^d. Optimal designs with respect to the fill distance are sometimes called "minimax" designs (see, e.g., [2]). CALL: FD = stk_filldist(X) assumes that the fill distance is to be computed with respect to the hyperrectangle BOX = [0; 1]^d. CALL: FD = stk_filldist(X, Y) computes the fill distance FD of X using the "test set" Y. More preci- sely, if X and Y are respectively n x d and m x d, then FD = max_{1 <= j <= m} min_{1 <= i <= n} norm(X(i,:) - Y(j,:)), If Y is dense enough in some subset BOX of R^d, then FD should be close to the actual fill distance of X in BOX. CALL: [FD, YMAX] = stk_filldist(...) also returns the point YMAX where the maximal distance is attained. NOTE: stk_filldist is actually a wrapper around stk_filldist_discretized and stk_filldist_exact. Which function to call is guessed based on the number of rows of the second argument. Because of that, the test set Y is required to have at least 3 rows. REFERENCES [1] Luc Pronzato and Werner G. Muller, "Design of computer experiments: space filling and beyond", Statistics and Computing, 22(3):681-701, 2012. [2] Mark E. Johnson, Leslie M. Moore and Donald Ylvisaker, "Minimax and maximin distance designs", Journal of Statistical Planning and Inference, 26(2):131-148, 1990. See also: stk_dist, stk_mindist, stk_filldist_exact, stk_filldist_discretized
Package: stk