def test_aca_func():
# check whether functional matrizitation is identical with original one
N = 50
for obj in ["B1", "B2"]:
C_list = []
ranks = np.array([N, N, N])
for mode in range(3):
if mode == 0:
if obj == "B1":
functional_generator = aca_fun.mode_m_matricization_fun(
aca_fun.b1, N, N, N)
C, U, R = aca_fun.aca_partial_pivoting(
functional_generator, N, N * N, N, 10e-4 / 3)
tensor = np.asarray(utilis.get_B_one(N))
else:
functional_generator = aca_fun.mode_m_matricization_fun(
aca_fun.b2, N, N, N)
C, U, R = aca_fun.aca_partial_pivoting(
functional_generator, N, N * N, N, 10e-4 / 3)
tensor = np.asarray(utilis.get_B_two(N))
else:
Core_mat = tl.unfold(Core_ten, mode)
C, U, R = aca_fun.aca_full_pivoting(Core_mat, 10e-4 / 3)
ranks[mode] = U.shape[0]
Core_ten = tl.fold(np.dot(U, R), mode, ranks)
C_list.append(C)
recon = utilis.reconstruct_tensor(C_list, Core_ten, tensor)
error = utilis.frobenius_norm_tensor(recon - tensor)
assert (error < 10e-4 * utilis.frobenius_norm_tensor(tensor))
def test_hosvd_B1():
# Full rank reconstruction should have low frob norm error
N = 50
tensor = np.asarray(utilis.get_B_one(N))
Core, U = utilis.compute_core(tensor, ranks=[N, N, N])
recon_tensor = utilis.reconstruct_tensor(U, Core, tensor)
error = utilis.frobenius_norm_tensor(recon_tensor - tensor)
assert (error < 10e-10)
def test_generator_B1():
# check whether functional and loop B1 generator are equal
N = 50
tensor = np.asarray(utilis.get_B_one(N))
gen_tensor = np.zeros((N, N, N))
for i in range(N):
for j in range(N):
for z in range(N):
gen_tensor[i, j, z] = aca_fun.b1(i, j, z, N)
assert (np.allclose(tensor, gen_tensor))
def test_fun_matriziation_b1():
# check whether functional matrizitation is identical with original one
N = 50
for mode in range(3):
tensor = np.asarray(utilis.get_B_one(N))
unfold_mat = tl.unfold(tensor, mode)
functional_generator = aca_fun.mode_m_matricization_fun(
aca_fun.b1, N, N, N)
gen_mat = np.zeros((N, N * N))
for i in range(N):
for j in range(N * N):
gen_mat[i, j] = functional_generator(i, j, N)
assert (np.allclose(unfold_mat, gen_mat))
def run_aca_full():
N = 200
C_list = []
ranks = np.array([N, N, N])
tensor = np.asarray(utilis.get_B_one(N))
for mode in range(3):
if mode == 0:
# Start with original matrix
Core_mat = tl.unfold(tensor, mode)
else:
Core_mat = tl.unfold(Core_ten, mode)
C, U, R = aca_fun.aca_full_pivoting(Core_mat, 10e-5)
ranks[mode] = U.shape[0]
print(f'Current ranks: {ranks}')
Core_ten = tl.fold(np.dot(U, R), mode, ranks)
C_list.append(C)
def test_speed_hosvd_B1_N200(benchmark):
# Benchmark speed for N=200 for decomposition without reconstruction
N = 200
tensor = np.asarray(utilis.get_B_one(N))
benchmark(utilis.compute_core, tensor, max_rel_error=10e-5)