% Ursem Waves function L. LAURENT -- 24/02/2017 -- luc.laurent@lecnam.net
0001 %% Ursem Waves function 0002 % L. LAURENT -- 24/02/2017 -- 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 %1 minimum global: f(1.2,1.2)=-8.5536 0025 % 0026 %Design space -2<xi<2 0027 0028 function [p,dp] = funUrsemWaves(xx) 0029 0030 %constants 0031 a=0.9; 0032 b=4.5; 0033 c=4.7; 0034 d=2; 0035 e=2.5*pi; 0036 0037 %evaluation and derivatives 0038 x=xx(:,:,1); 0039 y=xx(:,:,2); 0040 % 0041 xyA=y.^2-b*y.^2; 0042 xyB=d*x-y.^2.*(d+x); 0043 cdxy=c*cos(xyB); 0044 se=sin(e*x); 0045 % 0046 p=-a*x.^2 ... 0047 +xyA.*x.*y ... 0048 +cdxy.*se; 0049 0050 if nargout==2 0051 % 0052 dp=zeros(size(xx)); 0053 % 0054 sdxy=sin(xyB); 0055 % 0056 dp(:,:,1)=-2*a*x+xyA.*y ... 0057 -c*(d-y.^2).*sdxy.*se ... 0058 +e*cdxy.*cos(e*x); 0059 dp(:,:,2)=(1-b)*3*x.*y.^2 ... 0060 +2*c*y.*(d+x).*sdxy.*se; 0061 end 0062 end 0063