funTrigonometric2

PURPOSE ^

% Trigonometric 2 function

SYNOPSIS ^

function [p,dp] = funTrigonometric2(xx)

DESCRIPTION ^

% Trigonometric 2 function
 L. LAURENT -- 23/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Trigonometric 2 function
0002 % L. LAURENT -- 23/02/2017 -- 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 %1 minimum global: f(0.9,...,0.9)=1
0025 %
0026 %Design space -500<xi<500 (focus on 0<xi<2)
0027 
0028 
0029 function [p,dp] = funTrigonometric2(xx)
0030 
0031 %constants
0032 a=1;
0033 b=8;
0034 c=7;
0035 d=0.9;
0036 e=6;
0037 f=14;
0038 
0039 %evaluation and derivatives
0040 xd=xx-d;
0041 xd2=xd.^2;
0042 scx=sin(c*xd2);
0043 sfx=sin(f*xd2);
0044 %
0045 pa=b*scx.^2;%+e*sfx.^2+xd2;
0046 %
0047 p=a+sum(pa,3);
0048 
0049 if nargout==2
0050     %
0051     ccx=cos(c*xd2);
0052     cfx=cos(f*xd2);
0053     %
0054     dp=4*b*c*xd.*ccx.*scx; ...
0055         +4*e*f*xd.*cfx.*sfx ...
0056         +2*xd;
0057 end
0058 end

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