% Holzman function L. LAURENT -- 16/03/2017 -- luc.laurent@lecnam.net
0001 %% Holzman function 0002 %L. LAURENT -- 16/03/2017 -- 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)=0 for x=[50 25 1.5] 0026 % 0027 %Design space: 0<x1<100, 0<x2<25.6, 0<x3<5 0028 % 0029 0030 0031 0032 function [p,dp]=funHolzman(xx) 0033 %constants 0034 a=0.01; 0035 b=1; 0036 c=25; 0037 d=50; 0038 e=2/3; 0039 f=1e-2; 0040 m=99; 0041 0042 %evaluation and derivatives 0043 x=xx(:,:,1); 0044 y=xx(:,:,2); 0045 z=xx(:,:,3); 0046 % 0047 listI=reshape(0:m,1,1,m+1); 0048 u=c+(-d.*log(f*(listI+1))).^e; 0049 % 0050 pa=(u-y); 0051 pax=pa.^z; 0052 paxx=pax./x; 0053 pb=exp(-paxx)-a*(listI+b); % ajustement "-paxx" 0054 % 0055 p=sum(pb,3); 0056 0057 % 0058 if nargout==2 0059 % 0060 dp=zeros(size(xx)); 0061 % 0062 dp(:,:,1)=sum(paxx./x.*exp(-paxx),3); 0063 dp(:,:,2)=sum(z.*pa.^(z-1)./x.*exp(-paxx),3); 0064 dp(:,:,3)=sum(-log(pa).*paxx.*exp(-paxx),3); 0065 end 0066 end