% CrownedCross function L. LAURENT -- 14/03/2017 -- luc.laurent@lecnam.net
0001 %% CrownedCross function 0002 %L. LAURENT -- 14/03/2017 -- 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 % 0025 %global minimum : f(x)=1e-4 for x1=0 (forall x2) or x2=0 (forall x1) 0026 % 0027 %Design space: -10<xi<10 0028 0029 0030 function [p,dp]=funCrownedCross(xx) 0031 %constants 0032 a=0.1; 0033 b=100; 0034 c=pi; 0035 d=1; 0036 e=1e-4; 0037 0038 %evaluation and derivatives 0039 x=xx(:,:,1); 0040 y=xx(:,:,2); 0041 % 0042 xy=sqrt(x.^2+y.^2); 0043 fxy=b-xy./c; 0044 % 0045 pa=exp(abs(fxy)); 0046 sx=sin(x); 0047 sy=sin(y); 0048 % 0049 h=pa.*sx.*sy; 0050 g=abs(h)+d; 0051 % 0052 p=e*g.^a; 0053 % 0054 if nargout==2 0055 % 0056 dh=cos(xx).*sin(xx(:,:,[2 1])).*pa-1/c*xx./xy.*sign(fxy).*h; 0057 % 0058 dg=sign(h).*dh; 0059 % 0060 dp=e*a*dg.*g.^(a-1); 0061 end 0062 end