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% STK_IS_LHS tests if a given set of points forms a LHS
%
% CALL: OK = stk_is_lhs (X, N, DIM, BOX)
%
% tests if X is a Latin Hypercube Sample (LHS) of size N, over the hyper-
% rectangle BOX of dimension DIM. The result OK is true if X is a LHS and
% false otherwise.
%
% CALL: OK = stk_is_lhs (X, N, DIM)
%
% tests if X is a Latin Hypercube Sample (LHS) of size N, over the hyper-
% rectangle [0; 1]^DIM.
%
% CALL: OK = stk_is_lhs (X)
%
% tests if X is a Latin Hypercube Sample (LHS). Both the size N and the
% number DIM of factors are inferred from X.
%
% All three calling syntaxes accept both matrix-type inputs or data structures
% (with an 'a' field) for X.
% Copyright Notice
%
% Copyright (C) 2018 CentraleSupelec
% Copyright (C) 2012-2014 SUPELEC
%
% Author: Julien Bect <julien.bect@centralesupelec.fr>
% Copying Permission Statement
%
% This file is part of
%
% STK: a Small (Matlab/Octave) Toolbox for Kriging
% (https://github.com/stk-kriging/stk/)
%
% 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 b = stk_is_lhs (x, n, dim, box)
x = double (x);
if nargin == 1
[n, dim] = size (x);
elseif nargin == 2
if size (x, 1) ~= n
b = false; return;
end
dim = size (x, 2);
else % nargin > 2
if ~ isequal (size (x), [n dim])
b = false; return;
end
end
% read argument 'box'
if (nargin < 4) || (isempty (box))
xmin = zeros (1, dim);
xmax = ones (1, dim);
else
if ~ isa (box, 'stk_hrect')
box = stk_hrect (box);
end
xmin = box.lower_bounds;
xmax = box.upper_bounds;
end
for j = 1:dim
y = x(:,j);
if (xmin(j) > min(y)) || (xmax(j) < max(y))
b = false; return;
end
y = (y - xmin(j)) / (xmax(j) - xmin(j));
y = ceil (y * n);
if ~ isequal (sort (y), (1:n)')
b = false; return;
end
end
b = true;
end % function
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