% Schmidt-Vetters's function L. LAURENT -- 19/02/2017 -- luc.laurent@lecnam.net
0001 %% Schmidt-Vetters's function 0002 % L. LAURENT -- 19/02/2017 -- 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(0.78547,0.78547,0.78547)=2.99845 0025 % 0026 %Design space 0<xi<10 (other minima outside of this space) 0027 0028 0029 function [p,dp] = funSchmidtVetters(xx) 0030 0031 %constants 0032 a=1; 0033 b=pi; 0034 c=2; 0035 0036 %evaluation and derivatives 0037 x=xx(:,:,1); 0038 y=xx(:,:,2); 0039 z=xx(:,:,3); 0040 % 0041 pa=a+(x-y).^2; 0042 ga=a./pa; 0043 pb=(b*y+z)./c; 0044 gb=sin(pb); 0045 pc=((x+y)./y-c); 0046 gc=exp(pc.^2); 0047 % 0048 p=ga+gb+gc; 0049 0050 if nargout==2 0051 % 0052 ax=-2*a*(x-y)./pa.^2; 0053 ay=-ax; 0054 by=b/c*cos(pb); 0055 bz=1/c*cos(pb); 0056 cx=2./y.*pc.*gc; 0057 cy=-2*x./y.^2.*pc.*gc; 0058 % 0059 dp=zeros(size(xx)); 0060 dp(:,:,1)=ax+cx; 0061 dp(:,:,2)=ay+by+cy; 0062 dp(:,:,3)=bz; 0063 end 0064 end