% Constraint function used in problems: Townsend L. LAURENT -- 02/05/2018 -- luc.laurent@lecnam.net
0001 %% Constraint function used in problems: Townsend 0002 %L. LAURENT -- 02/05/2018 -- 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 function [g,dg]=funConsTownsend(xx) 0025 0026 %constants 0027 a=2; 0028 b=1/2; 0029 c=1/4; 0030 d=1/8; 0031 e=3; 0032 f=4; 0033 0034 % contraint 0035 xxx=xx(:,:,1); 0036 yyy=xx(:,:,2); 0037 % 0038 t=atan2(xxx,yyy); 0039 st=sin(t); 0040 ct=cos(t); 0041 cat=cos(a*t); 0042 cet=cos(e*t); 0043 cft=cos(f*t); 0044 % 0045 td=a*ct-b*cat-c*cet-d*cft; 0046 % 0047 g=xxx.^2+yyy.^2-f*st.^2-td.^2; 0048 0049 %and their derivatives 0050 if nargout>1 0051 dtx=yyy./(xxx.^2+yyy.^2); 0052 dty=-xxx./(xxx.^2+yyy.^2); 0053 % 0054 sat=sin(a*t); 0055 set=sin(e*t); 0056 sft=sin(f*t); 0057 % 0058 dg(:,:,1)=2*xxx-2*f*dtx.*ct.*st-2*dtx.*(-a*st+sat+e*c*set+b*sft).*td; 0059 dg(:,:,2)=2*yyy-2*f*dty.*ct.*st-2*dty.*(-a*st+sat+e*c*set+b*sft).*td; 0060 end 0061 end