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stk_dist


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 STK_DIST computes a matrix of (Euclidean) distances

 CALL: D = stk_dist(X, Y)

    computes the matrix of distances between X and Y. More precisely, if
    X is an nX x d matrix, and Y an nY x d matrix, the D is an nX x nY
    matrix with

       D_{i,j} = norm(X(i,:) - Y(j,:)),

    where norm(.) denotes the Euclidean norm in R^d.

 See also: stk_mindist, stk_filldist, norm



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 STK_DIST computes a matrix of (Euclidean) distances



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stk_filldist


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 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



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 STK_FILLDIST computes the fill distance of a set of points



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stk_filldist_discretized


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 STK_FILLDIST_DISCRETIZED computes the (discrete) fill distance of a set of points

 CALL: FD = stk_filldist_discretized(X, Y)

    computes the fill distance FD of X using the "test set" Y. More precisely, 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,:)),

    where norm(.) denotes the Euclidean norm in R^d. 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 (see: stk_filldist_exact). Optimal designs with respect to the fill distance
    are sometimes called "minimax" designs (see, e.g., [1]).

 CALL: [D, ARGMAX] = stk_filldist_discretized(X, Y)

    also returns the value ARGMAX of the index j for which the maximum is attained.
    (If the maximum is obtained for several values of j, the smallest is returned.)

 REFERENCE

   [1] 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_filldist, stk_filldist_exact, stk_dist, stk_mindist



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 STK_FILLDIST_DISCRETIZED computes the (discrete) fill distance of a set of p...



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stk_filldist_exact


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 STK_FILLDIST_EXACT computes the (exact) fill distance of a set of points

 CALL: FD = stk_filldist_exact(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_exact(X)

    assumes that the fill distance is to be computed with respect to the
    hyperrectangle BOX = [0; 1]^d.

 CALL: [FD, YMAX] = stk_filldist_exact(...)

    also returns the point YMAX where the maximal distance is attained,
    i.e., the argmax in equation (1).

 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_filldist, stk_filldist_discretized, stk_dist, stk_mindist



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 STK_FILLDIST_EXACT computes the (exact) fill distance of a set of points



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stk_gpquadform


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 STK_GPQUADFORM   [experimental, not part of public API yet... UAYOR!]

 CALL: Q = stk_gpquadform (X, Y, RX, RY)

    computes a matrix Q, whose entries Q(i,j) are given by a Gibbs-
    Paciorek quadratic form

       Q(i,j) = \sum_{k = 1}^d (X(i,k) - Y(j,k))^2 / R(i,j,k)^2,

    where

       R(i,j,k)^2 = RX(i,k)^2 + RY(i,k)^2,

    assuming that

     * X and RX have size [nX d],
     * Y and RY have size [nY d].



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 STK_GPQUADFORM   [experimental, not part of public API yet...



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stk_mindist


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 STK_MINDIST computes the separation distance of a set of points

 CALL: D = stk_mindist(X)

    computes the separation distance D of X. More precisely, if X is an
    n x d matrix, then

       D = min_{1 <= i < j <= n} norm(X(i,:) - X(j,:)),

    where norm(.) denotes the Euclidean norm in R^d.

 See also: stk_dist, stk_filldist



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 STK_MINDIST computes the separation distance of a set of points





