funMishra06

PURPOSE ^

% Mishra 6 function

SYNOPSIS ^

function [p,dp]=funMishra06(xx)

DESCRIPTION ^

% Mishra 6 function
L. LAURENT -- 17/11/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Mishra 6 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(x)=-2.67507597 for x=(2.94777, 1.82174)
0026 %
0027 %Design space: -10<xi<10
0028 
0029 
0030 function [p,dp]=funMishra06(xx)
0031 
0032 %constants
0033 a=1e-2;
0034 b=1;
0035 
0036 %variables
0037 xxx=xx(:,:,1);
0038 yyy=xx(:,:,2);
0039 
0040 %evaluation and derivatives
0041 g=cos(xxx)+cos(yyy);
0042 h=sin(xxx)+sin(yyy);
0043 kx=xxx-b;
0044 ky=yyy-b;
0045 pa=sin(g.^2).^2-cos(h.^2).^2+xxx;
0046 %
0047 p=-log(pa.^2)+a*(kx.^2+ky.^2);
0048 
0049 if nargout==2
0050     dgX=-sin(xxx);
0051     dgY=-sin(yyy);
0052     dhX=cos(xxx);
0053     dhY=cos(yyy);
0054     %
0055     dp(:,:,1)=-2*pa.*(4*dgX.*g.*cos(g.^2).*sin(g.^2)...
0056         +4*dhX.*h.*sin(h.^2).*cos(h.^2)+1)./pa.^2 ...
0057         +2*a*kx;
0058     dp(:,:,2)=-2*pa.*(4*dgY.*g.*cos(g.^2).*sin(g.^2)...
0059         +4*dhY.*h.*sin(h.^2).*cos(h.^2))./pa.^2 ...
0060         +2*a*ky;
0061 end
0062 end

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