funBranin1

PURPOSE ^

% Branin's function 1

SYNOPSIS ^

function [p,dp]=funBranin1(xx)

DESCRIPTION ^

% Branin's function 1
L. LAURENT -- 13/12/2010 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Branin's function 1
0002 %L. LAURENT -- 13/12/2010 -- 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 %3 global minima :
0026 %f(x1,x2)=0 for (x1,x2)={(-pi,12.275),(pi,2.275),(3*pi,2.475)}
0027 %
0028 %Design space: -5<x1<10, 0<x2<15
0029 
0030 
0031 
0032 function [p,dp]=funBranin1(xx)
0033 
0034 %constants
0035 a=5.1/(4*pi^2);
0036 b=5/pi;
0037 c=6;
0038 d=10;
0039 e=1/(8*pi);
0040 
0041 %responses and derivatives
0042 xxx=xx(:,:,1);
0043 yyy=xx(:,:,2);
0044 
0045 p = (yyy-a*xxx.^2+b*xxx-c).^2+d*(1-e)*cos(xxx)+d;
0046 
0047 if nargout==2
0048     dp(:,:,1)=2*(yyy-a*xxx.^2+b*xxx-c).*(b-2*a*xxx)-d*(1-e)*sin(xxx);
0049     dp(:,:,2)=2*(yyy-a*xxx.^2+b*xxx-c);
0050 end
0051 end

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