funLangermann52

PURPOSE ^

% Langermann 5 2D function

SYNOPSIS ^

function [p,dp]=funLangermann52(xx)

DESCRIPTION ^

% Langermann 5 2D function
L. LAURENT -- 17/11/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Langermann 5 2D 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)=-1.4 for (x1,x2)=()
0026 %
0027 %Design space:0<xi<10
0028 
0029 
0030 function [p,dp]=funLangermann52(xx)
0031 %constants
0032 ma = [3,5,2,1,7];
0033 mb = [5,2,1,4,9];
0034 mc = [1,2,5,2,3];
0035 d=pi;
0036 m=5;
0037 %variables
0038 xxx=xx(:,:,1);
0039 yyy=xx(:,:,2);
0040 
0041 %evaluation and derivatives
0042 vx=bsxfun(@minus,xxx,reshape(ma,1,1,m));
0043 vy=bsxfun(@minus,yyy,reshape(mb,1,1,m));
0044 vxy=vx.^2+vy.^2;
0045 ex=exp(-1/d*vxy);
0046 cx=cos(d*vxy);
0047 cc=bsxfun(@times,cx,reshape(mc,1,1,m));
0048 %
0049 p=sum(-ex.*cc,3);
0050 %
0051 if nargout==2
0052     sx=sin(d*vxy);
0053     cs=bsxfun(@times,sx,reshape(mc,1,1,m));
0054     pvx=vx.*ex;
0055     pvy=vy.*ex;
0056     %
0057     dp(:,:,1)=sum(2/d*pvx.*cc+2*d*pvx.*cs,3);
0058     dp(:,:,2)=sum(2/d*pvy.*cc+2*d*pvy.*cs,3);
0059 end
0060 end

Generated on Tue 28-May-2019 16:00:34 by m2html © 2005