% Jennrich-Sampson's function L. LAURENT -- 17/11/2016 -- luc.laurent@lecnam.net
0001 %% Jennrich-Sampson's 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)=124.3622 for (x1,x2)=(0.257825,0.257825) 0026 % 0027 %Design space: -1<xi<1 0028 0029 0030 function [p,dp]=funJennrichSampson(xx) 0031 %constants 0032 a=2; 0033 b=10; 0034 0035 %variables 0036 xxx=xx(:,:,1); 0037 yyy=xx(:,:,2); 0038 0039 %evaluation and derivatives 0040 ii=reshape(1:b,1,1,b); 0041 ex=bsxfun(@power,exp(xxx),ii); 0042 ey=bsxfun(@power,exp(yyy),ii); 0043 se=bsxfun(@minus,a*ii,ex+ey); 0044 % 0045 p=sum((a+se).^2,3); 0046 0047 if nargout==2 0048 iex=bsxfun(@times,ii,ex); 0049 iey=bsxfun(@times,ii,ey); 0050 % 0051 dp(:,:,1)=sum(-iex*2.*(a+se),3); 0052 dp(:,:,2)=sum(-iey*2.*(a+se),3); 0053 end 0054 end