% JACOBI_EXAMPLE This is the example on page 13.
global sigma 
%
sigma=0;
l=6;
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
f=zeros(nt,1);
vtest=zeros(nt,4);
vtest(:,1)=evecs(:,1);
vtest(:,2)=evecs(:,3);
vtest(:,3)=evecs(:,6);
vtest(:,4)=(evecs(:,1)+evecs(:,6)+evecs(:,32))/3;
errnorm=zeros(101,3);
for ic=1:4
	v=vtest(:,ic); v2=v;
	errnorm(1,ic)=norm(v,inf);
%
% Do 100 damped Jacobi's and see what happens.
%
	for ij=1:100
		v=dampj(v,f);
		errnorm(ij+1,ic)=norm(v,inf);
	end
end
itct=[0:100]';
figure(1);
plot(itct,errnorm(:,1),'-',itct,errnorm(:,2),'--',itct,errnorm(:,3),'-.');
legend('k=1','k=3','k=6');
title('Figure 2.3(a), page 15');
xlabel('iterations'); ylabel('error');
figure(2);
semilogy(itct,errnorm(:,1),'-',itct,errnorm(:,2),'--',itct,errnorm(:,3),'-.');
legend('k=1','k=3','k=6');
title('Figure 2.4, page 16');
xlabel('iterations'); ylabel('error');
figure(3);
plot(itct,errnorm(:,4));
xlabel('iterations'); ylabel('error');
title('Figure 2.5, page 16');