funSineEnveloppe

PURPOSE ^

% Sine Enveloppe function

SYNOPSIS ^

function [p,dp] = funSineEnveloppe(xx)

DESCRIPTION ^

% Sine Enveloppe function
 L. LAURENT -- 20/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Sine Enveloppe function
0002 % L. LAURENT -- 20/02/2017 -- 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,...,0)=0
0025 %
0026 %Design space -100<xi<100
0027 
0028 
0029 function [p,dp] = funSineEnveloppe(xx)
0030 
0031 %constants
0032 a=1/2;
0033 b=1e-3;
0034 c=1;
0035 
0036 %evaluation and derivatives
0037 sX=size(xx);
0038 %
0039 funH=@(x,y)sin(sqrt(x.^2+y.^2)).^2-a;
0040 funG=@(x,y)(b*(x.^2+y.^2)+c).^2;
0041 %
0042 xkp=xx(:,:,2:end);
0043 xk=xx(:,:,1:end-1);
0044 pa=funH(xkp,xk)./funG(xkp,xk)+a;
0045 %
0046 p=sum(pa,3);
0047 
0048 if nargout==2
0049     %
0050     funHx=@(x,y)2*x./sqrt(x.^2+y.^2) ...
0051         .*cos(sqrt(x.^2+y.^2)) ...
0052         .*sin(sqrt(x.^2+y.^2));
0053     funHy=@(x,y)2*y./sqrt(x.^2+y.^2) ...
0054         .*cos(sqrt(x.^2+y.^2)) ...
0055         .*sin(sqrt(x.^2+y.^2));
0056     funGx=@(x,y)4*b*x.*(b*(x.^2+y.^2)+c);
0057     funGy=@(x,y)4*b*y.*(b*(x.^2+y.^2)+c);
0058     %
0059     dp=zeros(sX);
0060     %
0061     for itX=1:sX(3)
0062         if itX==1
0063             x=xx(:,:,2);
0064             y=xx(:,:,1);
0065             dp(:,:,itX)=(funHy(x,y).*funG(x,y)-funH(x,y).*funGy(x,y))./funG(x,y).^2;
0066         elseif itX==sX(3)
0067             x=xx(:,:,sX(3));
0068             y=xx(:,:,sX(3)-1);
0069             dp(:,:,itX)=(funHx(x,y).*funG(x,y)-funH(x,y).*funGx(x,y))./funG(x,y).^2;
0070         else
0071             xk=xx(:,:,itX);
0072             xkp=xx(:,:,itX+1);
0073             xkm=xx(:,:,itX-1);
0074             dp(:,:,itX)=(funHx(xk,xkm).*funG(xk,xkm)-funH(xk,xkm).*funGx(xk,xkm))./funG(xk,xkm).^2 ...
0075                 +(funHy(xkp,xk).*funG(xkp,xk)-funH(xkp,xk).*funGy(xkp,xk))./funG(xkp,xk).^2;
0076         end
0077     end
0078 end
0079 end

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