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