funBeale

PURPOSE ^

% Beale function

SYNOPSIS ^

function [p,dp]=funBeale(xx)

DESCRIPTION ^

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

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Beale 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)=0 pour (x1,x2)=(3,0.5)
0026 %
0027 %Design space: -4.5<x1<4.5, -4.5<x<4.5
0028 
0029 
0030 
0031 function [p,dp]=funBeale(xx)
0032 
0033 %responses and derivatives
0034 xxx=xx(:,:,1);
0035 yyy=xx(:,:,2);
0036 
0037 p = (1.5 - xxx + xxx.*yyy).^2 + (2.25 - xxx + xxx.*yyy.^2).^2 + (2.625 - xxx + xxx.*yyy.^3).^2;
0038 
0039 if nargout==2
0040     dp(:,:,1)=2*(yyy-1).*(1.5-xxx+xxx.*yyy)+...
0041         2*(yyy.^2-1).*(2.25 - xxx + xxx.*yyy.^2) +...
0042         2*(yyy.^3-1).*(2.625 - xxx + xxx.*yyy.^3);
0043     dp(:,:,2)=2*xxx.*(1.5-xxx+xxx.*yyy)+...
0044         4*xxx.*yyy.*(2.25 - xxx + xxx.*yyy.^2) +...
0045         6*xxx.*yyy.^2.*(2.625 - xxx + xxx.*yyy.^3);
0046 end
0047 end

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