% Bukin 12's function L. LAURENT -- 01/11/2016 -- luc.laurent@lecnam.net
0001 %% Bukin 12's function 0002 %L. LAURENT -- 01/11/2016 -- 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 0026 function [p,dp]=funBukin12(xx) 0027 0028 %constants 0029 a=1000; 0030 b=5; 0031 0032 %evaluation and derivatives 0033 pa=xx(:,:,1)+b; 0034 pb=xx(:,:,2)+b; 0035 rho=sqrt(pa.^2+pb.^2); 0036 pc=xx(:,:,1)+b-rho.*cos(rho); 0037 pd=xx(:,:,2)+b+rho.*sin(rho); 0038 p=a*abs(pc)+a*abs(pd)+rho; 0039 if nargout==2 0040 dRhoX=pa./rho; 0041 dRhoY=pb./rho; 0042 dp(:,:,1)=a*sign(pc).*(1+rho.*dRhoX.*sin(rho)-dRhoX.*cos(rho))... 0043 +a*sign(pd).*(rho.*dRhoX.*cos(rho)+dRhoX.*sin(rho))+dRhoX; 0044 dp(:,:,2)=a*sign(pc).*(rho.*dRhoY.*sin(rho)-dRhoY.*cos(rho))... 0045 +a*sign(pd).*(1+rho.*dRhoY.*cos(rho)+dRhoY.*sin(rho))+dRhoY; 0046 end 0047 end 0048