format short e
 %
 %  set up matrix
 %
  n = 200; k = 10;
 
  A = randn(n); A = A + A';
 %
 %
  v =  randn(n,1); 
 [V,T,f] = Lanczos(A,k,v);

 ek = zeros(k,1); ek(k)= 1;
 Resid = norm(A*V - V*T -  f*ek')


 orthtestV = norm(eye(k) - V'*V)
 ortestf = norm(V'*f)

 t = eig(A);
 t = sort(t);

 s = sort(eig(T));
 k1 = 8;
 t1 = [t(1:k1);t(n-k1+1:n)];
 s1 = [s(1:k1);s(k-k1+1:k)];
 t__s__diff = [t1 s1 abs(t1-s1)]