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% STK_SAMPLING_MAXIMINLHS generates a "maximin" LHS design
%
% CALL: X = stk_sampling_maximinlhs (N, DIM)
%
% generates a "maximin" Latin Hypercube Sample of size N in the
% DIM-dimensional hypercube [0; 1]^DIM. More precisely, NITER = 1000
% independent random LHS are generated, and the one with the biggest
% separation distance is returned.
%
% CALL: X = stk_sampling_maximinlhs (N, DIM, BOX)
%
% does the same thing in the DIM-dimensional hyperrectangle specified by the
% argument BOX, which is a 2 x DIM matrix where BOX(1, j) and BOX(2, j) are
% the lower- and upper-bound of the interval on the j^th coordinate.
%
% CALL: X = stk_sampling_maximinlhs (N, DIM, BOX, NITER)
%
% allows to change the number of independent random LHS that are used.
%
% See also: stk_mindist, stk_sampling_randomlhs
% Copyright Notice
%
% Copyright (C) 2017, 2018 CentraleSupelec
% Copyright (C) 2011-2014 SUPELEC
%
% Authors: Julien Bect <julien.bect@centralesupelec.fr>
% Emmanuel Vazquez <emmanuel.vazquez@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 x = stk_sampling_maximinlhs (n, d, box, niter)
% Read argument dim
if (nargin < 2) || ((nargin < 3) && (isempty (d)))
d = 1; % Default dimension
elseif (nargin > 2) && (~ isempty (box))
d = size (box, 2);
end
% Read argument 'box'
if (nargin < 3) || isempty (box)
box = stk_hrect (d); % build a default box
else
box = stk_hrect (box); % convert input argument to a proper box
end
if nargin < 4,
niter = 1000;
end
if n == 0, % no input => no output
xdata = zeros (0, d);
else % at least one input point
xx = lhsdesign_ (n, d, niter);
xdata = stk_rescale (xx, [], box);
end
x = stk_dataframe (xdata, box.colnames);
end % function
%%%%%%%%%%%%%%%%%%
%%% lhsdesign_ %%%
%%%%%%%%%%%%%%%%%%
function x = lhsdesign_ (n, d, niter)
x = generatedesign_ (n, d);
if niter > 1,
bestscore = stk_mindist (x);
for j = 2:niter
y = generatedesign_ (n, d);
score = stk_mindist (y);
if score > bestscore
x = y;
bestscore = score;
end
end
end
end % function
%%%%%%%%%%%%%%%%%%%%%%%
%%% generatedesign_ %%%
%%%%%%%%%%%%%%%%%%%%%%%
function x = generatedesign_ (n, d)
x = zeros (n, d);
for i = 1:d % for each dimension, draw a random permutation
[ignd, x(:,i)] = sort (rand (n,1)); %#ok<ASGLU> CG#07
end
x = (x - rand (size (x))) / n;
end % function
%%
% Check error for incorrect number of input arguments
%!shared x, n, dim, box, niter
%! n = 20; dim = 2; box = [0, 0; 1, 1]; niter = 1;
%!error x = stk_sampling_maximinlhs ();
%!test x = stk_sampling_maximinlhs (n);
%!test x = stk_sampling_maximinlhs (n, dim);
%!test x = stk_sampling_maximinlhs (n, dim, box);
%!test x = stk_sampling_maximinlhs (n, dim, box, niter);
%%
% Check that the output is a dataframe
% (all stk_sampling_* functions should behave similarly in this respect)
%!assert (isa (x, 'stk_dataframe'));
%%
% Check that column names are properly set, if available in box
%!assert (isequal (x.colnames, {}));
%!test
%! cn = {'W', 'H'}; box = stk_hrect (box, cn);
%! x = stk_sampling_maximinlhs (n, dim, box);
%! assert (isequal (x.colnames, cn));
%%
% Check output argument
%!test
%! for dim = 1:5,
%! x = stk_sampling_randomlhs (n, dim);
%! assert (isequal (size (x), [n dim]));
%! u = double (x); u = u(:);
%! assert (~ any (isnan (u) | isinf (u)));
%! assert ((min (u) >= 0) && (max (u) <= 1));
%! assert (stk_is_lhs (x, n, dim));
%! end
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