funTrefethen

PURPOSE ^

% Trefethen function

SYNOPSIS ^

function [p,dp] = funTrefethen(xx)

DESCRIPTION ^

% Trefethen function
 L. LAURENT -- 23/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Trefethen function
0002 % L. LAURENT -- 23/02/2017 -- 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 %1 minimum global: f(-0.02440307923,0.2106124261)=-3.3068686474
0025 %
0026 %Design space -5<xi<5
0027 
0028 
0029 function [p,dp] = funTrefethen(xx)
0030 
0031 %constants
0032 a=0.25;
0033 b=0.25;
0034 c=50;
0035 d=10;
0036 e=60;
0037 f=70;
0038 g=80;
0039 
0040 %evaluation and derivatives
0041 x=xx(:,:,1);
0042 y=xx(:,:,2);
0043 %
0044 sx=sin(c*x);
0045 sa=sin(d*x+d*y);
0046 sb=sin(e*exp(y));
0047 sc=sin(f*sin(x));
0048 sd=sin(sin(g*y));
0049 %
0050 p=a*x.^2+b*y.^2+exp(sx)-sa ...
0051     +sb+sc+sd;
0052 
0053 if nargout==2
0054     %
0055     dp=zeros(size(xx));
0056     %
0057     ca=cos(d*x+d*y);
0058     %
0059     dp(:,:,1)=2*a*x+c*cos(c*x).*exp(sx) ...
0060         -d*ca+f*cos(x).*cos(f*sin(x));
0061     dp(:,:,2)=2*b*y-d*ca ...
0062         +e*exp(y).*cos(e*exp(y)) ...
0063         +g*cos(g*y).*cos(sin(g*y));
0064 end
0065 end

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