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% STK_EXAMPLE_DOE02 "Sequential Maximin" design
%
% In this example, a two-dimensional space-filling design is progressively
% enriched with new points using a "sequential maximin" approach. More
% precisely, the k-th point X(k, :) is selected to maximize the distance to the
% set of all previously selected points X(1, :), X(2, :), ..., X(k-1, :).
%
% NOTES:
%
% * The resulting design is NOT optimal with respect to the maximin criterion
% (separation distance).
%
% * This procedure is not truly a *sequential* design procedure, since the
% choice of the k-th point X(k, :) does NOT depend on the response at the
% previously selected locations X(i, :), i < k.
%
% REFERENCE
%
% [1] Emmanuel Vazquez and Julien Bect, "Sequential search based on kriging:
% convergence analysis of some algorithms", In: ISI - 58th World
% Statistics Congress of the International Statistical Institute (ISI'11),
% Dublin, Ireland, August 21-26, 2011.
% Copyright Notice
%
% Copyright (C) 2013, 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
% (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/>.
stk_disp_examplewelcome; stk_figure ('stk_example_doe02');
%% Preliminaries
DIM = 2; BOX = repmat ([0; 1], 1, DIM);
% start from, e. g., a random/maximin LHS
N0 = 10; x = stk_sampling_maximinlhs (N0, DIM, BOX);
% final size of the desired DoE
NB_ITER = 10;
% plot styles
STYLE_CURRENT = {'bo', 'MarkerFaceColor', 0.7 * ones(1, 3)};
STYLE_NEXT = {'ro', 'MarkerFaceColor', 'y'};
%% Sequential design
%
% This section can be run several times, to produce a bigger DoE !
%
for i = 1:NB_ITER,
% compute the current fill distance
% & the point where the maximum is attained
[fd, next_x] = stk_filldist (x, BOX);
% plot
cla; plot (x(:, 1), x(:, 2), STYLE_CURRENT{:});
hold on; plot (next_x(:, 1), next_x(:, 2), STYLE_NEXT{:});
stk_title (sprintf ('n = %d, fd = %.2e\n', size (x, 1), fd));
drawnow; pause (0.5);
% enrich the DoE
x = [x; next_x];
end
%!test stk_example_doe02; close all;
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