%
% Test of intergrid transfer
%
coltab=7;
errtab=zeros(coltab,4);
for l=3:2+coltab
nl=2^l; h=1/nl; nv=nl-1; nt=nl+1;
x=0:nl; x=h*x'; evecs=zeros(nt,nv);
for k=1:nv
	evecs(:,k)=sin(k*pi*x);
end
w=evecs(:,6).*exp(x);
wfc=ftoc(ctof(w)); wcf=ctof(ftoc(w));
%
% Columns 1 and 3 are errors between w and ftoc(ctof(w)) or ctof(ftoc(w))
%
errtab(l-2,1:2:3)=[norm(wfc-w,inf),norm(wcf-w,inf)];
end
%
% Columns 2 and 4 are ratios of errors. These should converge to .25 as
% the problem size increases, and they do!
%
errtab(2:coltab,2)=errtab(2:coltab,1)./errtab(1:coltab-1,1);
errtab(2:coltab,4)=errtab(2:coltab,3)./errtab(1:coltab-1,3);
errtab
%
% Now check the formula on page 92 for ftoc
%
l=6;
nl=2^l; h=1/nl; nv=nl-1; nt=nl+1; nf=nl;
x=0:nl; x=h*x'; evecs=zeros(nt,nv);
for k=1:nv
	evecsf(:,k)=sin(k*pi*x);
end
kv=[1:nl/2]; kv=pi*kv/(2*nl); ce=cos(kv).^2; se=-sin(kv).^2;
l=5;
nl=2^l; h=1/nl; nv=nl-1; nt=nl+1;
x=0:nl; x=h*x'; evecs=zeros(nt,nv);
for k=1:nv
	evecsc(:,k)=sin(k*pi*x);
end
err92=0;
for k=1:nv
	err92=err92+norm(ftoc(evecsf(:,k))-ce(k)*evecsc(:,k));
end
for k=1:nv
	err92=err92+norm(ftoc(evecsf(:,nf-k))-se(k)*evecsc(:,k));
end
%
% err92 is supposed to be small and is.
%
err92