% Levy 13 function L. LAURENT -- 17/03/2017 -- luc.laurent@lecnam.net
0001 %% Levy 13 function 0002 %L. LAURENT -- 17/03/2017 -- 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 % 0025 %global minimum : f(x)=0 for xi=1 0026 % 0027 %Design space: -10<xi<10 0028 % 0029 0030 0031 function [p,dp]=funLevy13(xx) 0032 %constants 0033 a=1; 0034 b=3*pi; 0035 c=2*pi; 0036 0037 0038 %evaluation and derivatives 0039 x=xx(:,:,1); 0040 y=xx(:,:,2); 0041 % 0042 pa=sin(b*y).^2+a; 0043 pb=sin(c*y).^2+a; 0044 pc=x-a; 0045 pd=y-a; 0046 pe=sin(b*x); 0047 % 0048 p=pc.^2.*pa+pd.^2.*pb+pe.^2; 0049 0050 % 0051 if nargout==2 0052 % 0053 dp=zeros(size(xx)); 0054 % 0055 dp(:,:,1)=2*pc.*pa+2*b*pe.*cos(b*x); 0056 dp(:,:,2)=2*b.*pc.^2.*sin(b*y).*cos(b*y)... 0057 +2*pd.*pb... 0058 +2*c*pd.^2.*sin(c*y).*cos(c*y); 0059 end