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% STK_MAXABSCORR computes the maximal absolute correlation for a set of points
%
% CALL: MAC = stk_maxabscorr (X)
%
% computes the Maximum Absolute (linear) Correlation MAC between the columns
% of the array X.
%
% NOTES:
%
% * The construction of experimental designs (more specifically, Latin
% hypercubes samples) with a small MAC is considered, e.g., by Florian
% (1992) and Cioppa & Lucas (2007).
%
% * When X is a Latin hypercube sample, the linear (Pearson) correlation
% coefficients and Spearman's rank correlation coefficients coincide.
%
% REFERENCES
%
% [1] Ales Florian, "An Efficient Sampling Scheme: Updated Latin Hypercube
% Sampling", Probabilistic Engineering Mechanics, 7:123-130, 1992.
% http://dx.doi.org/10.1016/0266-8920(92)90015-A
%
% [2] Thomas M. Cioppa and Thomas W. Lucas, "Efficient Nearly Orthogonal and
% Space-Filling Latin Hypercubes, Technometrics, 49:1, 45-55, 2007.
% http://dx.doi.org/10.1198/004017006000000453
%
% See also: stk_mindist, stk_filldist, stk_phipcrit
% Copyright Notice
%
% Copyright (C) 2015, 2018 CentraleSupelec
% Copyright (C) 2013 SUPELEC
%
% Author: Julien Bect <julien.bect@centralesupelec.fr>
% Copying Permission Statement
%
% This file is part of
%
% STK: a Small (Matlab/Octave) Toolbox for Kriging
% (http://sourceforge.net/projects/kriging)
%
% STK is free software: you can redistribute it and/or modify it under
% the terms of the GNU General Public License as published by the Free
% Software Foundation, either version 3 of the License, or (at your
% option) any later version.
%
% STK is distributed in the hope that it will be useful, but WITHOUT
% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
% or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
% License for more details.
%
% You should have received a copy of the GNU General Public License
% along with STK. If not, see <http://www.gnu.org/licenses/>.
function mac = stk_maxabscorr (x)
x = double (x);
x = bsxfun (@minus, x, mean (x));
n = size (x, 2);
M = 0;
for i = 1:(n-1)
for j = (i+1):n
M = max (M, abs (sum (x(:, i) .* x(:, j))));
end
end
mac = M / n;
end % function
%!assert (stk_isequal_tolabs (0.0, ... % Test on an OLHS(5)
%! stk_maxabscorr ([0.4 0.8 0 -0.4 -0.8; -0.8 0.4 0 0.8 -0.4]')));
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