def rqi(A, x, k, verbose=False):
    partida = time()
    """
    Program 12.3 Rayleigh Quotient Iteration
    Input: matrix A, initial (nonzero) vector x, number of steps k
    Output: eigenvalue lam, eigenvector of inv(A-sI)
    """
    if verbose: print("Rayleigh Quotient Iteration\n%s"%('='*80))
    for j in range(k):
        u = x/np.linalg.norm(x)
        lam = np.dot(u.T, np.dot(A, u))
        try:
            x = solve(A -lam*np.eye(*A.shape), u)
        except np.linalg.LinAlgError:
            break
        if verbose: print("k=%d, lambda=%+.3f, u=%s"%(j,lam,str(u.T)))
    u = x/np.linalg.norm(x)
    lam = float(np.dot(u.T, np.dot(A, u)))
    if verbose: print("k=%d, lambda=%+.3f, u=%s\n"%(j+1,lam,str(u.T)))
    final = time()
    tiempo = final - partida
    iteracion = tiempo/k
    return (lam, u, iteracion)

# Probamos el algoritmo
lam, v, tiempo = rqi(A, x, k=2)
print("lambda = {0}".format(lam))
print("v = {0}".format(v))