Simple Lanczos algorithm code to obtain eigenvalues and eigenvectors of a symmetric matrix

Question

I would like to write a simple program (in C) using Lanczos algorithm. I came across a Matlab example which helped me to understand a bit further the algorithm, however from this piece of code I can't find the way of getting the eigenvalues and eigenvectors. I can follow the algorithm but I think I must be missing something. Can someone guide me to get the eigenvalues from this example so I can understand the method and then code it in C?

% Create a random symmetric matrix 
D=6
for i=1:D,
    for j=1:i,
        A(i,j)=rand; 
        A(j,i)=A(i,j);
    end 
end

% Iteration with j=0 
r0 = rand(D,1); 
b0 = sqrt(r0'*r0); 
q1 = r0/b0; 
a1 = q1'*A*q1

%Iteration with j=1
r1 = A*q1 - a1*q1
b1 = sqrt(r1'*r1)
q2 = r1/b1;
a2 = q2'*A*q2

%Iteration with j=2
r2 = A*q2 - a2*q2 - b1*q1;
b2 = sqrt(r2'*r2)
q3 = r2/b2
a3 = q3'*A*q3

% Create Matrix Q
Q = [q1 q2 q3];

%Check orthogonality
EYE = Q'*Q
T = Q'*A*Q

Answer 1

The Lanczos algorithm can be used to put the matrix into tridiagonal form, but it doesn't actually find the eigenvalues and eigenvectors of that tridiagonal matrix. Once you have the matrix in tridiagonal form, the QR algorithm is typically used to find the eigenvalues of the tridiagonal matrix.