def test_forme_bidiagonale(epsilon):
n = rd.randint(1,20)
m = rd.randint(1,20)
M = np.asmatrix(np.random.rand(n,m))
M = 100 * M
result = p2.forme_bidiagonale (M)
test_0_bidiagonale(result[1],epsilon)
for i in range (n):
for j in range (m):
assert (np.abs(M[i,j] - (result[0]*result[1]*result[2])[i,j])<epsilon)
def compression_matrice (Mat, k):
taille_x = Mat.shape[0]
taille_y = Mat.shape[1]
assert (k < min(taille_x, taille_y))
print "Mise sous forme bidiagonale"
(Ql, BD, Qr) = p2.forme_bidiagonale(Mat)
print "Diagonalisation"
(U,S,V,_) = p3.SVD_preliminaire(BD)
(U,S) = p3.organisation(U,S)
nouveau_U = np.asmatrix(Ql*(U[:,0:k]))
nouveau_S = np.asmatrix(S[0:k,0:k])
nouveau_V = np.asmatrix((V[0:k,:])*Qr)
return (nouveau_U, nouveau_S, nouveau_V)
def QR_optimise (A):
taille_x = A.shape[0]
taille_y = A.shape[1]
taille_max = max(taille_x, taille_y)
AprimTest = mat_identity(taille_x, taille_y)
AprimTest[:,:]=A[:,:]
tQ = mat_identity(taille_x, taille_y)
for i in range (taille_x - 1):
(Grot,Aprim,_) = p2.forme_bidiagonale( (AprimTest[i:i+2, i:i+2]))
Grot = Grot.T
G = mat_identity(taille_x, taille_x)
AprimTest[i:i+2,i:i+2]=Aprim
G[i:i+2, i:i+2] = Grot
tQ = G*tQ
Q = np.transpose(tQ)
return (Q, AprimTest)
def test_SVD (n, len_matrix, activate_plot = False, optimise = False):
if(n <= 0):
print("Erreur, veuillez entrer un nombre de test strictement positif\n")
return "FAILED"
else :
Matrix_list = []
Compare_list_S = []
Compare_list_V = []
Compare_list_U = []
x = range(0,n)
for i in range(0,n):
Matrix_list.append(p2.forme_bidiagonale(rand_square_Matrix(len_matrix, 0,100))[2])
if (optimise == False):
for i in range(0,n):
Compare_list_U.append(np.linalg.norm((np.linalg.svd(Matrix_list[i])[0]) - (p3.SVD_preliminaire(Matrix_list[i])[0])))
Compare_list_S.append(np.linalg.norm((np.linalg.svd(Matrix_list[i])[1]) - (p3.SVD_preliminaire(Matrix_list[i])[1])))
Compare_list_V.append(np.linalg.norm((np.linalg.svd(Matrix_list[i])[2]) - (p3.SVD_preliminaire(Matrix_list[i])[2])))
if(activate_plot == True):
mp.plot(x,Compare_list_U)
mp.title("Comparaison entre U implemente et celui du svd de numpy")
mp.show()
mp.plot(x,Compare_list_S)
mp.title("Comparaison entre S implemente et celui du svd de numpy")
mp.show()
mp.plot(x,Compare_list_V)
mp.title("Comparaison entre V implemente et celui du svd de numpy")
mp.show()
else :
Compare_list_U.append(np.linalg.norm((np.linalg.svd(Matrix_list[i])[0]) - (SVD_optimise(Matrix_list[i])[0])))
Compare_list_S.append(np.linalg.norm((np.linalg.svd(Matrix_list[i])[1]) - (SVD_optimise(Matrix_list[i])[1])))
Compare_list_V.append(np.linalg.norm((np.linalg.svd(Matrix_list[i])[2]) - (SVD_optimise(Matrix_list[i])[2])))
if(activate_plot == True):
mp.plot(x,Compare_list_U)
mp.title("Comparaison entre U implemente et celui du svd de numpy")
mp.show()
mp.plot(x,Compare_list_S)
mp.title("Comparaison entre S implemente et celui du svd de numpy")
mp.show()
mp.plot(x,Compare_list_V)
mp.title("Comparaison entre V implemente et celui du svd de numpy")
mp.show()
return "PASSED"
def test_QR_optimise (n, len_matrix, activate_plot = False):
if(n <= 0):
print("Erreur, veuillez entrer un nombre de test strictement positif\n")
return "FAILED"
else :
Matrix_list = []
Compare_list_Q = []
Compare_list_R = []
x = range(0,n)
for i in range(0,n):
Matrix_list.append(p2.forme_bidiagonale(rand_square_Matrix(len_matrix, 0,100))[2])
for i in range(0,n):
Compare_list_Q.append(np.linalg.norm((np.linalg.qr(Matrix_list[i])[0]) - (p3.QR_optimise(Matrix_list[i])[0])))
Compare_list_R.append(np.linalg.norm((np.linalg.qr(Matrix_list[i])[1]) - (p3.QR_optimise(Matrix_list[i])[1])))
if(activate_plot == True):
mp.plot(x,Compare_list_Q)
mp.title("Comparaison entre Q implemente et celui de numpy")
mp.show()
mp.plot(x,Compare_list_R)
mp.title("Comparaison entre R implemente et celui de numpy")
mp.show()
return "PASSED"
