funUrsem4

PURPOSE ^

% Ursem 4 function

SYNOPSIS ^

function [p,dp] = funUrsem4(xx)

DESCRIPTION ^

% Ursem 4 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 4 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(0,0)=-1,5
0025 %
0026 %Design space -2<xi<2
0027 
0028 function [p,dp] = funUrsem4(xx)
0029 
0030 %constants
0031 a=3;
0032 b=pi/2;
0033 c=pi/2;
0034 d=2;
0035 e=4;
0036 
0037 %evaluation and derivatives
0038 x=xx(:,:,1);
0039 y=xx(:,:,2);
0040 %
0041 sxy=sqrt(x.^2+y.^2);
0042 %
0043 pa=-a*sin(b*x+c);
0044 pb=(d-sxy)./e;
0045 %
0046 pt=pa.*pb;
0047 %
0048 p=sum(pt,3);
0049 
0050 if nargout==2
0051     %
0052     dp=zeros(size(xx));
0053     %
0054     dp(:,:,1)=-a*b*cos(b*x+c).*pb-pa.*x./(e*sxy);
0055     dp(:,:,2)=-pa.*y./(e*sxy);
0056 end
0057 end
0058

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