% Levy 03 function L. LAURENT -- 17/03/2017 -- luc.laurent@lecnam.net
0001 %% Levy 03 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]=funLevy03(xx) 0032 %constants 0033 a=pi; 0034 b=1; 0035 c=4; 0036 d=10; 0037 0038 %evaluation and derivatives 0039 y=b+(xx-b)./c; 0040 % 0041 pa=sin(a*y(:,:,1)); 0042 pb=y(:,:,1:end-1)-b; 0043 sc=sin(a*y(:,:,1:end-1)+b); 0044 pc=b+d*sc.^2; 0045 pd=y(:,:,end)-b; 0046 se=sin(2*a*y(:,:,end)); 0047 pe=b+se.^2; 0048 % 0049 p=pa.^2+sum(pb.^2.*pc,3)+pd.^2.*pe; 0050 0051 % 0052 if nargout==2 0053 % 0054 dp=zeros(size(xx)); 0055 % 0056 cc=cos(a*y(:,:,1:end-1)+b); 0057 ce=cos(2*a*y(:,:,end)); 0058 % 0059 dp(:,:,1)=2*a/c*pa.*cos(a*y(:,:,1))... 0060 +2/c.*pb(:,:,1).*pc(:,:,1)... 0061 +2*d*a/c*sc(:,:,1).*cc(:,:,1).*pb(:,:,1).^2; 0062 dp(:,:,end)=2/c*pd.*pe... 0063 +4*a/c*se.*ce.*pd.^2; 0064 dp(:,:,2:end-1)=2/c*pb(:,:,2:end).*pc(:,:,2:end)... 0065 +2*d*a/c*sc(:,:,2:end).*cc(:,:,2:end).*pb(:,:,2:end).^2; 0066 end