% Rump function L. LAURENT -- 14/02/2017 -- luc.laurent@lecnam.net
0001 %% Rump function 0002 % L. LAURENT -- 14/02/2017 -- 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(0,0)=0 0025 % 0026 %Design space -500<xi<500 0027 0028 0029 function [p,dp] = funRump(xx) 0030 0031 %constants 0032 a=333.75; 0033 b=11; 0034 c=121; 0035 d=2; 0036 e=5.5; 0037 f=2; 0038 0039 %evaluation and derivatives 0040 x=xx(:,:,1); 0041 y=xx(:,:,2); 0042 p=(a-x.^2).*y.^6 ... 0043 +x.^2.*(b*x.^2.*y.^2-c*y.^4-d) ... 0044 +e*y.^8+x./(f*y); 0045 0046 if nargout==2 0047 % 0048 dp=zeros(size(xx)); 0049 dp(:,:,1)=-2*x.*y.^6 ... 0050 +2*x.*(b*x.^2.*y.^2-c*y.^4-d) ... 0051 +2*b*x.^3.*y.^2 ... 0052 +1./(f*y); 0053 dp(:,:,2)=6*y.^5.*(a-x.^2) ... 0054 +x.^2.*(2*b*x.^2.*y-4*c*y.^3) ... 0055 +8*e*y.^7 ... 0056 -x./(f*y.^2); 0057 end 0058 end