def PartialHosvd(X, ranks):
U = [None for _ in range(X.ndims())]
dims = X.ndims()
S = X
for d in range(dims):
C = base.unfold(X, d)
U1, _, _ = SVD.PartialSvd(C, ranks[d])
U[d] = U1
S = base.tensor_times_mat(S, U[d].T, d)
return U, S
def hosvd(X):
U = [None for _ in range(X.ndims())]
dims = X.ndims()
S = X
for d in range(dims):
C = base.unfold(X, d)
U1, S1, V1 = np.linalg.svd(C, full_matrices=False)
S = base.tensor_times_mat(S, U1.T, d)
U[d] = U1
core = S
return U, core
def TruncatedHosvd(X, ranks):
U = [None for _ in range(X.ndims())]
dims = X.ndims()
S = X
R = [None for _ in range(X.ndims())]
for d in range(dims):
C = base.unfold(X, d)
U1, S1, r = SVD.TruncatedSvd(C, rank=ranks[d])
R[d] = r
U[d] = U1
S = base.tensor_times_mat(S, U[d].T, d)
return U, S
def randomized_hosvd(X):
U = [None for _ in range(X.ndims())]
dims = X.ndims()
S = X
for d in range(dims):
C = base.unfold(X, d)
U1, S1, V1 = randomized_svd(C,
n_components=3,
n_oversamples=10,
n_iter='auto',
power_iteration_normalizer='auto',
transpose='auto',
flip_sign=True,
random_state=42)
S = base.tensor_times_mat(S, U1.T, d)
U[d] = U1
core = S
return U, core
def TestUnfoldAndFold():
ten1 = tensor(np.arange(24).reshape(3, 4, 2))
U = [base.unfold(ten1, i) for i in range(3)]
print([U[i].shape for i in range(3)])
ten = [base.fold(U[i], ten1.shape, i) for i in range(3)]
print([ten[i].shape for i in range(3)])
def hooi(X,
ranks=None,
maxiter=1000,
init='svd',
tol=1e-10,
print_enable=False,
plot_enable=False):
time0 = time.time()
dims = X.ndims()
modelist = list(range(dims))
if init == 'hosvd':
U, core = TruncatedHosvd(X, ranks)
data = base.tensor_multi_times_mat(core,
U,
modelist=modelist,
transpose=False)
error_init = base.tennorm(base.tensor_sub(data, X)) / base.tennorm(X)
if init == 'random':
U, core = randomized_hosvd(X)
data = base.tensor_multi_times_mat(core,
U,
modelist=modelist,
transpose=False)
error_init = base.tennorm(base.tensor_sub(data, X)) / base.tennorm(X)
error_original = []
error_iter = []
error_original.append(error_init)
normx = base.tennorm(X)
S1 = X
for iteration in range(maxiter):
Uk = [None for _ in range(dims)]
for i in range(dims):
U1 = U.copy()
U1.pop(i)
L = list(range(dims))
L.pop(i)
Y = base.tensor_multi_times_mat(X, U1, modelist=L, transpose=True)
C = base.unfold(Y, i)
Uk[i], _, _ = SVD.PartialSvd(C, ranks[i])
U = Uk
core = base.tensor_multi_times_mat(X,
Uk,
list(range(dims)),
transpose=True)
tensor_reconstruction = base.tensor_multi_times_mat(core,
Uk,
list(range(dims)),
transpose=False)
relative_error = base.tennorm(base.tensor_sub(
X, tensor_reconstruction)) / normx
error_original.append(relative_error)
error_iter_relative = abs(error_original[-2] - error_original[-1])
error_iter.append(error_iter_relative)
if error_iter_relative < tol:
if print_enable:
print('---------------------------->>>>>>')
print('TruncatedHosvd Init:')
print('TruncatedHosvd Ranks:\t' + str(ranks))
print("Truncated error:", error_init)
print('---------------------------->>>>>>')
print('\t\tHOOI\tInformation')
table = PrettyTable(
['Iteration', 'Error_iter', 'Error_original', 'Cost Time'])
table.add_row([
iteration, error_iter_relative, relative_error,
time.time() - time0
])
table.reversesort = False
table.border = 1
print(table)
break
if plot_enable:
plt.plot(error_original, 'g*-')
plt.title(
'The norm difference between the reduction tensor and the original tensor'
)
plt.xlabel('Iteration')
plt.ylabel('Norm difference')
plt.show()
plt.plot(error_iter, 'rs-.')
plt.title(
'The difference between the norm of restoring tensors in two consecutive iterations'
)
plt.xlabel('Iteration')
plt.ylabel('Norm difference')
plt.show()
return U, core