% Bukin 13's function L. LAURENT -- 01/11/2016 -- luc.laurent@lecnam.net
0001 %% Bukin 13'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]=funBukin13(xx) 0027 0028 %constants 0029 a=100; 0030 b=3; 0031 c=0.5; 0032 0033 %evaluation and derivatives 0034 pa=xx(:,:,1)+b; 0035 pb=xx(:,:,2)-c; 0036 rho=sqrt(pa.^2+pb.^2); 0037 m=sin(b*rho).*pa-cos(b*rho).*pb; 0038 p=rho+a./rho.^2.*m.^2; 0039 if nargout==2 0040 dRhoX=pa./rho; 0041 dRhoY=pb./rho; 0042 dp(:,:,1)=dRhoX-2*a./rho.^3.*dRhoX.*(m.^2)... 0043 +2*a./rho.^2.*(b*dRhoX.*cos(b*rho).*pa+sin(b*rho)+b*dRhoX.*sin(b*rho).*pb).*m; 0044 dp(:,:,2)=dRhoY-2*a./rho.^3.*dRhoY.*(m.^2)... 0045 +2*a./rho.^2.*(b*dRhoY.*cos(b*rho).*pa-cos(b*rho)+b*dRhoY.*sin(b*rho).*pb).*m; 0046 end 0047 end 0048