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diff --git a/inst/examples/test_functions/stk_testfun_hartman4.m b/inst/examples/test_functions/stk_testfun_hartman4.m new file mode 100644 index 0000000..620332d --- /dev/null +++ b/inst/examples/test_functions/stk_testfun_hartman4.m @@ -0,0 +1,123 @@ +% STK_TESTFUN_HARTMAN4 computes the "Hartman4" function +% +% CALL: Y = stk_testfun_hartman4 (X) +% +% computes the value Y of the Hartman4 function at X. +% +% The Hartman4 function is a test function in dimension 4, +% which is usually minimized over [0, 1]^4. +% +% HISTORICAL REMARKS +% +% This function belongs to a general class of test functions introduced +% by Hartman [1]. The particular set of coefficients used in the +% Hartman4 function seems to have been introduced by [2]. +% +% Note that the test function used in [2] is a scaled version of the +% one implemented here, which can be recovered as follows: +% +% y = (1.1 + stk_testfun_hartman4 (x)) / 0.839; +% +% Picheny & co-authors [2] refer to Dixon & Szego [3] for this test +% function, but it turns out that [3] only contains two sorts of +% "Hartman functions", in dimensions three and six. +% +% In fact, this function appears to have been obtained by truncating +% the sum at the fourth coordinate in the six-dimensional Hartman +% function of [3]. +% +% GLOBAL MINIMUM +% +% According to [4], the function has one global minimum at +% +% x = [0.1873 0.1906 0.5566 0.2647]. +% +% The corresponding function value, with our definition of the test +% function, is: +% +% f(x) = -3.729722308557300. +% +% Slightly better function values can be found in the neighborhood of +% this point. For instance, with +% +% x = [0.18744768 0.19414868 0.558005333 0.26476409] +% +% we get +% +% f(x) = -3.729840440436292. +% +% REFERENCES +% +% [1] J. K. Hartman (1973). Some experiments in global optimization. +% Naval Research Logistics Quarterly, 20(3):569-576. +% +% [2] V. Picheny, T. Wagner & D. Ginsbourger (2013). A benchmark +% of kriging-based infill criteria for noisy optimization. +% Structural and Multidisciplinary Optimization, 48:607-626. +% +% [3] L. C. W. Dixon & G. P. Szego (1978). Towards Global +% Optimization 2, North-Holland, Amsterdam, The Netherlands +% +% [4] V. Picheny, D. Ginsbourger & O. Roustant (2021). DiceOptim: +% Kriging-Based Optimization for Computer Experiments. R package +% version 2.1.1. URL: https://CRAN.R-project.org/package=DiceOptim. + +% Author +% +% Julien Bect <julien.bect@centralesupelec.fr> + +% Copying Permission Statement (this file) +% +% To the extent possible under law, CentraleSupelec has waived all +% copyright and related or neighboring rights to +% stk_testfun_hartman4.m. This work is published from France. +% +% License: CC0 <http://creativecommons.org/publicdomain/zero/1.0/> + +% Copying Permission Statement (STK toolbox as a whole) +% +% 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 y = stk_testfun_hartman4 (x) + +a = [ ... + [ 10.00 0.05 3.00 17.00 ]; ... + [ 3.00 10.00 3.50 8.00 ]; ... + [ 17.00 17.00 1.70 0.05 ]; ... + [ 3.50 0.10 10.00 10.00 ]]; + +p = [ ... + [ 0.1312 0.2329 0.2348 0.4047]; ... + [ 0.1696 0.4135 0.1451 0.8828]; ... + [ 0.5569 0.8307 0.3522 0.8732]; ... + [ 0.0124 0.3736 0.2883 0.5743]]; + +c = [1.0 1.2 3.0 3.2]; + +y = stk_testfun_hartman_generic (x, a, p, c); + +end % function + + +%!test +%! x = [0.1873 0.1906 0.5566 0.2647 ; +%! 0.18744768 0.19414868 0.558005333 0.26476409]; +%! y = stk_testfun_hartman4 (x); +%! assert (stk_isequal_tolabs (y, ... +%! [-3.729722308557300; -3.729840440436292], 1e-15)); |