funColville

PURPOSE ^

% Colville function

SYNOPSIS ^

function [p,dp]=funColville(xx)

DESCRIPTION ^

% Colville function
L. LAURENT -- 16/09/2011 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Colville function
0002 %L. LAURENT -- 16/09/2011 -- 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,x4)=0 for (x1,x2,x3,x4)=(1,1,1,1)
0026 %
0027 %Design space: -10<xi<10
0028 
0029 
0030 function [p,dp]=funColville(xx)
0031 
0032 %constants
0033 a=100;
0034 b=1;
0035 c=90;
0036 d=10.1;
0037 e=19.8;
0038 
0039 %evaluation and derivatives
0040 pa=xx(:,:,1)-xx(:,:,2).^2;
0041 pb=b-xx(:,:,1);
0042 pc=xx(:,:,4)-xx(:,:,3).^2;
0043 pd=b-xx(:,:,3);
0044 pe=xx(:,:,2)-b;
0045 pf=xx(:,:,4)-b;
0046 %
0047 p=a*pa.^2+pb.^2+c*pc.^2+pd.^2+d*pe.^2+d*pf.^2+e*pe.*pf;
0048 %
0049 if nargout==2
0050     dp(:,:,1)=2*a*pa-2*pb;
0051     dp(:,:,2)=-4*a*xx(:,:,2).*pa+2*d*pe+e*pf;
0052     dp(:,:,3)=-4*c*xx(:,:,3).*pc-2*pd;
0053     dp(:,:,4)=2*c*pc+2*d*pf+e*pe;
0054 end
0055 end

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