funPowell

PURPOSE ^

% Powell function

SYNOPSIS ^

function [p,dp]=funPowell(xx)

DESCRIPTION ^

% Powell function
L. LAURENT -- 23/03/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Powell function
0002 %L. LAURENT -- 23/03/2017 -- 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 %
0025 %global minimum : f(x)=0 for xi=0
0026 %
0027 %Design space: -4<xi<5
0028 %
0029 
0030 function [p,dp]=funPowell(xx)
0031 %constants
0032 a=10;
0033 b=5;
0034 c=2;
0035 d=10;
0036 
0037 %evaluation and derivatives
0038 x=xx(:,:,1);
0039 y=xx(:,:,2);
0040 z=xx(:,:,3);
0041 v=xx(:,:,4);
0042 %
0043 pa=z+a*x;
0044 pb=y-v;
0045 pc=x-c*y;
0046 pd=z-v;
0047 %
0048 p=sum(pa.^2+b*pb.^2+pc.^4+d*pd.^4,3);
0049 %
0050 if nargout==2
0051     %
0052     dp=zeros(size(xx));
0053     %
0054     dp(:,:,1)=2*a*pa+4*pc.^3;
0055     dp(:,:,2)=2*b*pb-4*c*pc.^3;
0056     dp(:,:,3)=2*pa+4*d*pd.^3;
0057     dp(:,:,4)=-2*b*pb-4*d*pd.^3;
0058 end

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