% TIME_TEST
%
% test of solvers for
%
% -u'' + sigma u = f
%
% where the solution is u(x) = exp(x) sin(pi x) and 
%
% f(x) = -2 pi exp(x) cos(pi x) + (pi^2 +sigma -1)u(x)
%
% We solve the problem on a sequence of grids and (I hope!) observe
% the errors decrease by roughly a factor of 4 and the compute times
% increase by roughly a factor of 2.
%
% Why are the increases in compute times so hard to measure?
%
% You can pick direct, or three flavors of FMG by editing the 
% commented out calls to the solvers.
%
global sigma
sigma=10;
lmin=5; lmax=10; ld=lmax-lmin+1;
errdata=zeros(ld,5);
for l=lmin:lmax
	nl=2^l; x=0:nl; x=x'/nl;
        h=1/nl; 
	u=exp(x).*sin(pi*x); fe=-2*pi*exp(x).*cos(pi*x)+(pi^2 + sigma -1)*u;
        tin=cputime;
%
% Pick your favorite solver and compare errors and work as
% the mesh is refined
%
% Do the solve many times to make sure you get something measurable.
        repeats=1000;
%
%         for i=1:repeats; v=fmg1(fe,2,1,1); end
%        for i=1:repeats; v=fmg2(fe,3,3,3); end
        for i=1:repeats; v=fmg(fe,3,3,3); end
%
% 	repeats=1000; v=helmholtz(fe,repeats);
	tout=cputime-tin; 
	errdata(l-lmin+1,1)=h;
	errdata(l-lmin+1,4)=tout;
	errdata(l-lmin+1,2)=norm(v-u,inf);
end
errdata(2:ld,3)=errdata(2:ld,2)./errdata(1:ld-1,2);
errdata(2:ld,5)=errdata(2:ld,4)./errdata(1:ld-1,4)