diff options
Diffstat (limited to 'inst/examples/test_functions/stk_testfun_hartman_generic.m')
| -rw-r--r-- | inst/examples/test_functions/stk_testfun_hartman_generic.m | 103 |
1 files changed, 103 insertions, 0 deletions
diff --git a/inst/examples/test_functions/stk_testfun_hartman_generic.m b/inst/examples/test_functions/stk_testfun_hartman_generic.m new file mode 100644 index 0000000..c7eb5e4 --- /dev/null +++ b/inst/examples/test_functions/stk_testfun_hartman_generic.m @@ -0,0 +1,103 @@ +% STK_TESTFUN_HARTMAN_GENERIC compute the value of a Hartman function +% +% CALL: Y = stk_testfun_hartman_generic (X, A, P, C) +% +% computes the value Y of the Hartman function with parameters A, P, C, +% at the points contained in X. +% +% The size of Y is N x 1, where N is the number of rows of X. +% +% The parameters A, P and C should have size N x D, N x D and 1 x D +% respectively, where D is the number of columns of X. +% +% HISTORICAL NOTE +% +% This class of test functions has been introduced by Hartman [2], +% hence the name. The particular form of Hartman functions considered +% here, however, seems to have been introduced by [1]. +% +% The only difference between the particular form considered in [1] and +% the general form in [2] is that the weighting matrix for the quadratic +% form in the exponential is assumed to be diagonal. +% +% REFERENCES +% +% [1] L. C. W. Dixon & G. P. Szego (1978). Towards Global +% Optimization 2, North-Holland, Amsterdam, The Netherlands +% +% [2] J. K. Hartman (1973). Some experiments in global optimization. +% Naval Research Logistics Quarterly, 20(3):569-576. +% +% [3] V. Picheny, T. Wagner & D. Ginsbourger (2013). A benchmark +% of kriging-based infill criteria for noisy optimization. +% Structural and Multidisciplinary Optimization, 48:607-626. +% +% [4] MCS: Global Optimization by Multilevel Coordinate Search. +% Version 2.0 from Feb. 8, 2000. Retrieved on March 10, 2022, +% from https://www.mat.univie.ac.at/~neum/software/mcs/ +% +% [5] S. Surjanovic & D. Bingham. Virtual Library of Simulation +% Experiments: Test Functions and Datasets. Retrieved March 3, +% 2022, https://www.sfu.ca/~ssurjano/hart4.html. +% +% See also stk_testfun_hartman3, stk_testfun_hartman4, stk_testfun_hartman6 + +% Author +% +% Julien Bect <julien.bect@centralesupelec.fr> + +% IMPLEMENTATION +% +% This implementation has been written from scratch using [1, 3] as +% references (omitting the scaling in [3]). Other implementations +% available on the web, such as [4, 5], have only been used to check +% the results for some special cases (Hartman3 and Hartman6 functions). + +% Copying Permission Statement (this file) +% +% To the extent possible under law, CentraleSupelec has waived all +% copyright and related or neighboring rights to +% stk_testfun_hartman_generic.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_hartman_generic (x, A, P, C) + +x = double (x); + +d = size (x, 2); +m = size (A, 2); + +assert (isequal (size (A), [d m])); +assert (isequal (size (P), [d m])); +assert (isequal (size (C), [1 m])); + +% Compute inner sum +inner_sum = sum ( ... + bsxfun (@times, shiftdim (A, -1), ... + (bsxfun (@minus, x, shiftdim (P, -1))) .^ 2), 2); + +% Compute the outer sum +y = - sum (bsxfun (@times, shiftdim (C, -1), exp (- inner_sum)), 3); + +end % function |