funSchmidtVetters

PURPOSE ^

% Schmidt-Vetters's function

SYNOPSIS ^

function [p,dp] = funSchmidtVetters(xx)

DESCRIPTION ^

% Schmidt-Vetters's function
 L. LAURENT -- 19/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Schmidt-Vetters's function
0002 % L. LAURENT -- 19/02/2017 -- 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(0.78547,0.78547,0.78547)=2.99845
0025 %
0026 %Design space 0<xi<10 (other minima outside of this space)
0027 
0028 
0029 function [p,dp] = funSchmidtVetters(xx)
0030 
0031 %constants
0032 a=1;
0033 b=pi;
0034 c=2;
0035 
0036 %evaluation and derivatives
0037 x=xx(:,:,1);
0038 y=xx(:,:,2);
0039 z=xx(:,:,3);
0040 %
0041 pa=a+(x-y).^2;
0042 ga=a./pa;
0043 pb=(b*y+z)./c;
0044 gb=sin(pb);
0045 pc=((x+y)./y-c);
0046 gc=exp(pc.^2);
0047 %
0048 p=ga+gb+gc;
0049 
0050 if nargout==2
0051     %
0052     ax=-2*a*(x-y)./pa.^2;
0053     ay=-ax;
0054     by=b/c*cos(pb);
0055     bz=1/c*cos(pb);
0056     cx=2./y.*pc.*gc;
0057     cy=-2*x./y.^2.*pc.*gc;
0058     %
0059     dp=zeros(size(xx));
0060     dp(:,:,1)=ax+cx;
0061     dp(:,:,2)=ay+by+cy;
0062     dp(:,:,3)=bz;
0063 end
0064 end

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