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 test_determine_H(epsilon):
n = rd.randint(2,20)
result = p1.generate_x_y(n)
H = p1.determine_H (result[0],result[1])
Hx = H * result[0]
#on teste H*x = y
for i in range(n):
assert (np.abs(Hx[i] - result[1][i])<epsilon)
#on teste la symetrie
for i in range (n):
for j in range (n):
assert (np.abs(H[i,j] - (H.T)[i,j]) < epsilon)
I = np.asmatrix(np.eye(n,n))
HH = H * H
#on teste H*H = identity
for i in range (n):
for j in range (n):
assert (np.abs(HH[i,j] - I[i,j]) < epsilon)
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()
def test_generate_x_y(epsilon):
n = rd.randint(2,20)
result = p1.generate_x_y(n)
#on teste si on a la meme norme
assert(np.abs(np.linalg.norm(result[0]) - np.linalg.norm(result[1]))<epsilon)