def efficacite(M):
n = len(M)
QL, BD, QR = bi.bi_diagonal(M, 0)
U, S, V = qr.transfo_USV(BD, 100)
U, S = qr.ordre_vp(U, S)
x = range(n-1, 0, -1)
distances = []
for i in x:
S[i][i] = 0
M_comp = np.dot(QL,np.dot(U, np.dot(S, np.dot(V, QR))))
distances += [norme(M - M_comp)]
pl.plot(x[::-1], distances[::-1])
pl.xlabel("Rang de compression k")
pl.ylabel("Efficacite de la compression")
pl.show()
def compress(M, k):
n = len(M)
QL, BD, QR = bi.bi_diagonal(M, 0)
U, S, V = qr.transfo_USV(BD, 100)
U, S = qr.ordre_vp(U, S)
if (k < n):
for i in range(k + 1, n):
S[i][i] = 0
res = np.dot(QL,np.dot(U, np.dot(S, np.dot(V, QR))))
for i in range(n):
for j in range(n):
if (res[i][j] > 1):
res[i][j] = 1
if (res[i][j] < 0):
res[i][j] = 0
return res
