# -*- coding: utf-8 -*-
"""
Created on Thu Jan 08 15:31:02 2015

Listing 10.1 : Formation de la matrice de Householder
@author: grivet

"""
import numpy as np
from scipy.linalg import norm

N = 5
x = np.array([1.0,-2.0,3.0,1.0,-1.0])
E5 = np.eye(5,5)
e0 = np.zeros(N)
e0[0] = 1.0
v = np.sign(x[0])*norm(x)*e0 + x
v /= norm(v)
P  = E5 -2*np.outer(v,v)
print ('vecteur x: ', x)
print ('norme de x: ',norm(x))
print ('matrice P: ')
print (P)
print ('produit P.x: ')
print (np.dot(P,x))