funHolzman

PURPOSE ^

% Holzman function

SYNOPSIS ^

function [p,dp]=funHolzman(xx)

DESCRIPTION ^

% Holzman function
L. LAURENT -- 16/03/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

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

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