funUrsemWaves

PURPOSE ^

% Ursem Waves function

SYNOPSIS ^

function [p,dp] = funUrsemWaves(xx)

DESCRIPTION ^

% Ursem Waves function
 L. LAURENT -- 24/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Ursem Waves function
0002 % L. LAURENT -- 24/02/2017 -- 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(1.2,1.2)=-8.5536
0025 %
0026 %Design space -2<xi<2
0027 
0028 function [p,dp] = funUrsemWaves(xx)
0029 
0030 %constants
0031 a=0.9;
0032 b=4.5;
0033 c=4.7;
0034 d=2;
0035 e=2.5*pi;
0036 
0037 %evaluation and derivatives
0038 x=xx(:,:,1);
0039 y=xx(:,:,2);
0040 %
0041 xyA=y.^2-b*y.^2;
0042 xyB=d*x-y.^2.*(d+x);
0043 cdxy=c*cos(xyB);
0044 se=sin(e*x);
0045 %
0046 p=-a*x.^2 ...
0047     +xyA.*x.*y ...
0048     +cdxy.*se;
0049 
0050 if nargout==2
0051     %
0052     dp=zeros(size(xx));
0053     %
0054     sdxy=sin(xyB);
0055     %
0056     dp(:,:,1)=-2*a*x+xyA.*y ...
0057         -c*(d-y.^2).*sdxy.*se ...
0058         +e*cdxy.*cos(e*x);
0059     dp(:,:,2)=(1-b)*3*x.*y.^2 ...
0060         +2*c*y.*(d+x).*sdxy.*se;
0061 end
0062 end
0063

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