%
 %  set up matrix
 %
  format short e
  n = 50; k = 10;
 
% [Q,R] = qr(randn(n));
% A = Q*R*Q';
  A = randn(n); A = A + A';
 %
 %
  v =  randn(n,1); 

 [V,H,f] = ArnoldiC(A,n,v);

 ek = zeros(n,1); ek(n)= 1;
 Resid = norm(A*V - V*H -  f*ek')

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

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

 k1 = 10;
 for j = k1:n-1,
     [Y,D] = eig(H(1:j,1:j));
     d = diag(D);
     [s,ii] = sort(abs(d));

     ritz = abs(H(j+1,j))*abs(Y(j,ii(j-k1+1:j))); ritz = ritz';

     t__s__diff__ritz = [ritz abs(t(n-k1+1:n) - s(j-k1+1:j)) t(n-k1+1:n) s(j-k1+1:j)]


     y = Y(:,ii(j));   x = V(:,1:j)*y;   theta = d(ii(j));

     normRTZ = norm(A*x - x*theta) 
     pause
 end