# -*- coding: utf-8 -*-
"""
Created on Thu Jan 08 14:47:46 2015

Exercice 10-4 : puissance n-ième de l'inverse avec 
décalage et quotient de Rayleigh

@author: grivet
"""

import numpy as np
import scipy.linalg as lg

F = np.array([[1.0,1.0,0.5],[1.0,1.0,0.25],[0.5,0.25,2.0]])
x0 = np.array([1.0,0.0,0.0])
E = np.eye(3,3)
nit = int(input('nombre d iterations: '))
print()
x = np.copy(x0)
print (' rang ', '  valeur propre')
for it in range(nit):
    dec = np.dot(x,np.dot(F,x))
    Fd = F-dec*E
    x = lg.solve(Fd,x)
    x /= lg.norm(x)
    print ('  %d    %12.6f' %(it+1,dec))