function [vout,fout]=twog(vin,fin,nu1,nu2)
% TWOG two grid method with the full data structure
%
global sigma 
%
% cheap hack to back out the level
%
ntl=length(fin); l=max(1,floor(log2(ntl))-1);
%
% lower and upper bounds for the current mesh and the one below
%
fout=fin; vout=vin;
ifu=ntl; ifl=ntl-2^l; icu=ifl-1; icl=icu-2^(l-1);
nl=2^l; h=1/nl; hm2=nl*nl; nt=nl+1;
for ij=1:nu1
	vout(ifl:ifu)=dampj(vout(ifl:ifu),fin(ifl:ifu));
end
av=zeros(nt,1);
av(2:nt-1)=-vout(ifl:ifu-2) +(2+sigma*h*h)*vout(ifl+1:ifu-1) -vout(ifl+2:ifu);
%
% prepare coarse mesh data
%
r=fin(ifl:ifu)-hm2*av;  fout(icl:icu)=ftoc(r);
%
% call direct solver
%
vout(icl:icu)=helmholtz(fout(icl:icu));
vout(ifl:ifu)=vout(ifl:ifu)+ctof(vout(icl:icu));
for ij=1:nu2
	vout(ifl:ifu)=dampj(vout(ifl:ifu),fin(ifl:ifu));
end