def test_produit_house_matrix(epsilon):
n = rd.randint(2,20)
m = rd.randint(2,20)
result = p1.generate_x_y(n)
H = p1.determine_H (result[0],result[1])
U = p1.determine_U (result[0],result[1])
M = np.asmatrix(np.random.rand(n,m))
M = 100 * M
assert (np.allclose(p1.produit_house_matrix(U,M),H*M))
def forme_bidiagonale(A):
taille = A.shape
BD = A
Qleft = np.asmatrix(np.eye(taille[0]))
Qright = np.asmatrix(np.eye(taille[1]))
l = taille[1]
if (taille[0]<taille[1]):
l = taille[0]
for k in range (l):
Q = determine_Q_k(BD[:,k],taille[0],k)
BD = p1.produit_house_matrix (Q, BD)
Qleft = p1.produit_house_matrix(Q,Qleft.T)
Qleft = Qleft.T
if k < (taille[1] - 2):
P = determine_Q_k(BD[k,:].T,taille[1],k+1)
BD = p1.produit_house_matrix(P, BD.T)
BD = BD.T
Qright = p1.produit_house_matrix(P,Qright)
return (Qleft, BD, Qright)
def compare_time_produit_h(n):
prod_h = np.asmatrix(np.zeros([n-2,1]))
prod = np.asmatrix(np.zeros([n-2,1]))
for i in range(0,n-2):
result = p1.generate_x_y(i+2)
H = p1.determine_H (result[0],result[1])
U = p1.determine_U (result[0],result[1])
M = np.asmatrix(np.random.rand((i+2),(i+2)))
M = 100 * M
start_time = time.time()
A = p1.produit_house_matrix(U,M)
prod_h[i] = time.time() - start_time
start_time = time.time()
A = H*M
prod[i] = time.time() - start_time
mp.plot(range(2,n),prod)
PH = ["produit matrice Householder","produit matrice numpy"]
mp.plot(range(2,n),prod_h)
mp.legend(PH)
pl.show()