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

prog_10_1
puissance n-ième
@author: grivet
"""

import numpy as np
import numpy.linalg as la

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])
print("vecteurs itérés : ")
x1 = np.dot(F,x0)
x1 /= la.norm(x1)
print (x1)
x2 = np.dot(F,x1)
x2 /= la.norm(x2)
print (x2)
x3 = np.dot(F,x2)
x3 /= la.norm(x3)
print (x3)
x4 = np.dot(F,x3)
x4 /= la.norm(x4)
print (x4)
x5 = np.dot(F,x4)
x5 /= la.norm(x5)
print (x5)
print("valeur propre: ")
print (np.dot(x5,np.dot(F,x5)))