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

Exercice 10-2
puissance n-ième de l'inverse avec décalage
@author: grivet
"""

import numpy as np
from numpy.linalg import norm,solve

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: '))
dec = float(input('valeur du decalage: '))
x = np.copy(x0)
Fd = F-dec*E
for it in range(nit):
    x = solve(Fd,x)
    x /= norm(x)
    print ('  %d  %10.5f %10.5f %10.5f' %(it+1, x[0], x[1], x[2]))