funTripod

PURPOSE ^

% Tripod function

SYNOPSIS ^

function [p,dp] = funTripod(xx)

DESCRIPTION ^

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

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SUBFUNCTIONS ^

SOURCE CODE ^

0001 %% Tripod 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,-50)=0
0025 %
0026 %Design space -100<xi<100
0027 
0028 
0029 function [p,dp] = funTripod(xx)
0030 
0031 %constants
0032 a=1;
0033 b=50;
0034 c=2;
0035 
0036 %evaluation and derivatives
0037 x=xx(:,:,1);
0038 y=xx(:,:,2);
0039 %
0040 pX=ps(x);
0041 pY=ps(y);
0042 %
0043 pa=pY.*(a+pX);
0044 pb=x+b*pY.*(a-c*pX);
0045 pc=y+b*(a-c*pY);
0046 %
0047 p=pa+abs(pb)+abs(pc);
0048 
0049 if nargout==2
0050     %
0051     dp=zeros(size(xx));
0052     %
0053     dpX=dps(x);
0054     dpY=dps(y);
0055     %
0056     dp(:,:,1)=pY.*dpX+sign(pb).*(1-b*c*pY.*dpX);
0057     dp(:,:,2)=(a+pX).*dpY ... 
0058         +b*sign(pb).*dpY.*(a-c*pX) ...
0059         +sign(pc).*(1-b*c*dpY);      
0060 end
0061 end
0062 
0063 function ev=ps(x)
0064     ev=ones(size(x));
0065     IX=(x<0);
0066     ev(IX)=0;
0067 end
0068 
0069 function ev=dps(x)
0070     ev=zeros(size(x));
0071     IX=(x==0);
0072     ev(IX)=1/eps;
0073 end

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