% Beale function L. LAURENT -- 16/09/2011 -- luc.laurent@lecnam.net
0001 %% Beale function 0002 %L. LAURENT -- 16/09/2011 -- luc.laurent@lecnam.net 0003 0004 % sources available here: 0005 % https://bitbucket.org/luclaurent/optigtest/ 0006 % https://github.com/luclaurent/optigtest/ 0007 0008 % optiGTest - set of testing functions A toolbox to easy manipulate functions. 0009 % Copyright (C) 2017 Luc LAURENT <luc.laurent@lecnam.net> 0010 % 0011 % This program is free software: you can redistribute it and/or modify 0012 % it under the terms of the GNU General Public License as published by 0013 % the Free Software Foundation, either version 3 of the License, or 0014 % (at your option) any later version. 0015 % 0016 % This program is distributed in the hope that it will be useful, 0017 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0018 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0019 % GNU General Public License for more details. 0020 % 0021 % You should have received a copy of the GNU General Public License 0022 % along with this program. If not, see <http://www.gnu.org/licenses/>. 0023 0024 % 0025 %global minimum : f(x1,x2)=0 pour (x1,x2)=(3,0.5) 0026 % 0027 %Design space: -4.5<x1<4.5, -4.5<x<4.5 0028 0029 0030 0031 function [p,dp]=funBeale(xx) 0032 0033 %responses and derivatives 0034 xxx=xx(:,:,1); 0035 yyy=xx(:,:,2); 0036 0037 p = (1.5 - xxx + xxx.*yyy).^2 + (2.25 - xxx + xxx.*yyy.^2).^2 + (2.625 - xxx + xxx.*yyy.^3).^2; 0038 0039 if nargout==2 0040 dp(:,:,1)=2*(yyy-1).*(1.5-xxx+xxx.*yyy)+... 0041 2*(yyy.^2-1).*(2.25 - xxx + xxx.*yyy.^2) +... 0042 2*(yyy.^3-1).*(2.625 - xxx + xxx.*yyy.^3); 0043 dp(:,:,2)=2*xxx.*(1.5-xxx+xxx.*yyy)+... 0044 4*xxx.*yyy.*(2.25 - xxx + xxx.*yyy.^2) +... 0045 6*xxx.*yyy.^2.*(2.625 - xxx + xxx.*yyy.^3); 0046 end 0047 end