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% STK_PARETOFIND finds non-dominated rows in an array
%
% CALL: [NDPOS, DRANK] = stk_paretofind (X)
%
% returns the indices NDPOS such that X(NDPOS, :) contains all non-
% dominated rows of X, sorted in (ascending) lexical order. A row
% X(i, :) is said to dominate another row X(j, :) if
%
% X(i, k) <= X(j, k) for all k in {1, 2, ..., d}
%
% and
%
% X(i, k) < X(j, k) for at least one such k,
%
% where d is the number of columns. In other words: smaller is better.
% For each row X(i, :), DRANK(i) is equal to zero if the row is non-
% dominated, and equal to the smallest j such that X(i, :) is dominated
% by X(NDPOS(j), :) otherwise.
%
% See also: sortrows, stk_isdominated, stk_dominatedhv
% Copyright Notice
%
% Copyright (C) 2015 CentraleSupelec
% Copyright (C) 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/>.
function varargout = stk_paretofind (x)
varargout = cell (1, max (1, nargout));
[varargout{:}] = __stk_paretofind_mex__ (double (x));
end % function
%!shared x, ndpos, drank
%! x = [ ...
%! 0 2; ...
%! 2 2; ...
%! ];
%!test [ndpos, drank] = stk_paretofind (x);
%!assert (isequal (ndpos, 1));
%!assert (isequal (drank, [0; 1]));
%!shared x, ndpos, drank
%! x = [ ...
%! 3 2; ...
%! 2 2; ...
%! ];
%!test [ndpos, drank] = stk_paretofind (x);
%!assert (isequal (ndpos, 2));
%!assert (isequal (drank, [1; 0]));
%!shared x, ndpos, drank
%! x = [ ...
%! 1 0; ...
%! 2 0; ...
%! 0 2; ...
%! 2 2; ...
%! -1 3 ];
%!test [ndpos, drank] = stk_paretofind (x);
%!assert (isequal (ndpos, [5; 3; 1]));
%!assert (isequal (drank, [0; 3; 0; 2; 0]));
%!shared x, ndpos, drank
%! x = [ ...
%! 1 0; ...
%! 2 0; ...
%! 0 2; ...
%! 2 2; ...
%! -1 3; ...
%! -1 4; ...
%! 2 2 ];
%!test [ndpos, drank] = stk_paretofind (x);
%!assert (isequal (ndpos, [5; 3; 1]));
%!assert (isequal (drank, [0; 3; 0; 2; 0; 1; 2]));
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