funHelicalValley

PURPOSE ^

% Helical Valley function

SYNOPSIS ^

function [p,dp]=funHelicalValley(xx)

DESCRIPTION ^

% Helical Valley function
L. LAURENT -- 17/11/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Helical Valley function
0002 %L. LAURENT -- 17/11/2016 -- 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 %
0025 %global minimum : f(x1,x2,x3)=0 for (x1,x2,x3)=(1,0,0)
0026 %
0027 %Design space: -10<xi<10
0028 
0029 
0030 function [p,dp]=funHelicalValley(xx)
0031 %constants
0032 a=100;
0033 b=10;
0034 c=1;
0035 d=1/(2*pi);
0036 
0037 %variables
0038 xxx=xx(:,:,1);
0039 yyy=xx(:,:,2);
0040 zzz=xx(:,:,3);
0041 
0042 %evaluation and derivatives
0043 th=atan2(yyy,xxx)*d;
0044 pa=yyy-b*th;
0045 pb=sqrt(xxx.^2+yyy.^2)-c;
0046 %
0047 p=a*(pa.^2+pb.^2)+zzz.^2;
0048 
0049 if nargout==2
0050     dthX=-d*yyy./(xxx.^2+yyy.^2);
0051     dthY=d.*xxx./(xxx.^2+yyy.^2);
0052     pbX=2*a*xxx./sqrt(xxx.^2+yyy.^2).*pb;
0053     pbY=2*a*yyy./sqrt(xxx.^2+yyy.^2).*pb;
0054     paX=-2*a*b*dthX.*pa;
0055     paY=2*a*(1-b*dthY).*pa;
0056     %
0057     dp(:,:,1)=paX+pbX;
0058     dp(:,:,2)=paY+pbY;  
0059     dp(:,:,3)=2*zzz;
0060 end
0061 end

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