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% STK_SAMPLING_HALTON_RR2 generates points from the Halton/RR2 sequence
%
% CALL: X = stk_sampling_halton_rr2 (N, D)
%
% computes the first N terms of the D-dimensional RR2-scrambled Halton
% sequence.
%
% REFERENCE
%
% Ladislav Kocis and William J. Whiten, "Computational investigations of low
% discrepancy sequences", ACM Transactions on Mathematical Software,
% 23(2):266-294, 1997. http://dx.doi.org/10.1145/264029.264064
%
% SEE ALSO: __stk_sampling_vdc_rr2__
% Copyright Notice
%
% Copyright (C) 2017, 2018 CentraleSupelec
% Copyright (C) 2014 SUPELEC
% Copyright (C) 2013 Alexandra Krauth, Elham Rahali & SUPELEC
%
% Authors: Julien Bect <julien.bect@centralesupelec.fr>
% Alexandra Krauth <alexandrakrauth@gmail.com>
% Elham Rahali <elham.rahali@gmail.com>
% 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 x = stk_sampling_halton_rr2 (n, d, box)
% 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)
colnames = {};
else
box = stk_hrect (box); % convert input argument to a proper box
colnames = box.colnames;
end
xdata = zeros (n, d);
for j = 1:d,
xdata(:, j) = double (__stk_sampling_vdc_rr2__ (n, j));
end
x = stk_dataframe (xdata, colnames);
if nargin > 2,
x = stk_rescale (x, [], box);
end
end % function
%!error stk_sampling_halton_rr2 () % nargin < 1
%!test
%! n = 300; d = 25;
%! x = stk_sampling_halton_rr2 (n, d);
%! assert (isequal (size (x), [n d]))
%!test
%! x = stk_sampling_halton_rr2 (1000, 3);
%! y = double (x(end, :));
%! yref = [0.9052734375 0.028349336991312 0.74848];
%! assert (stk_isequal_tolrel (y, yref, 1e-13));
%%
% Check that column names are properly set, if available in box
%!test
%! dim = 2; box = stk_hrect (dim);
%! x = stk_sampling_halton_rr2 (5, dim, box);
%! assert (isequal (x.colnames, {}));
%!test
%! dim = 2; cn = {'W', 'H'}; box = stk_hrect (dim, cn);
%! x = stk_sampling_halton_rr2 (5, dim, box);
%! assert (isequal (x.colnames, cn));
%%
% Comparison with Scilab+lowdisc
% % Matlab/Octave STK test script
%
% NREP = 10;
% M = 1e5;
% DIM = 20;
%
% tic;
% for i = 1:NREP
% x = stk_sampling_halton_rr2(M, DIM);
% end;
% t1 = toc/NREP;
% fprintf('time elapsed: %.2e seconds\n', t1);
%
% fprintf('%.15f\n', x(1:5, 2))
% // Scilab lowdisc test script
%
% NREP = 10;
% M = 1e5;
% DIM = 20;
%
% tic();
% for i = 1:NREP,
% rng = lowdisc_new("halton");
% rng = lowdisc_configure(rng, "-dimension", DIM);
% rng = lowdisc_configure(rng, "-scrambling", "RR2");
% rng = lowdisc_startup(rng);
% [rng, x] = lowdisc_next(rng, M);
% rng = lowdisc_destroy(rng);
% end
% t = toc() / NREP
%
% mprintf('%.15f\n', x(1:9, 2))
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