% Helical Valley function L. LAURENT -- 17/11/2016 -- luc.laurent@lecnam.net
0001 %% Helical Valley function 0002 %L. LAURENT -- 17/11/2016 -- 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,x3)=0 for (x1,x2,x3)=(1,0,0) 0026 % 0027 %Design space: -10<xi<10 0028 0029 0030 function [p,dp]=funHelicalValley(xx) 0031 %constants 0032 a=100; 0033 b=10; 0034 c=1; 0035 d=1/(2*pi); 0036 0037 %variables 0038 xxx=xx(:,:,1); 0039 yyy=xx(:,:,2); 0040 zzz=xx(:,:,3); 0041 0042 %evaluation and derivatives 0043 th=atan2(yyy,xxx)*d; 0044 pa=yyy-b*th; 0045 pb=sqrt(xxx.^2+yyy.^2)-c; 0046 % 0047 p=a*(pa.^2+pb.^2)+zzz.^2; 0048 0049 if nargout==2 0050 dthX=-d*yyy./(xxx.^2+yyy.^2); 0051 dthY=d.*xxx./(xxx.^2+yyy.^2); 0052 pbX=2*a*xxx./sqrt(xxx.^2+yyy.^2).*pb; 0053 pbY=2*a*yyy./sqrt(xxx.^2+yyy.^2).*pb; 0054 paX=-2*a*b*dthX.*pa; 0055 paY=2*a*(1-b*dthY).*pa; 0056 % 0057 dp(:,:,1)=paX+pbX; 0058 dp(:,:,2)=paY+pbY; 0059 dp(:,:,3)=2*zzz; 0060 end 0061 end