def test_left_orthonormalization(self):
"""test left-orthonormalization"""
# construct non-operator tensor train
cores = [self.cores[i][:, :, 0:1, :] for i in range(self.order)]
t_col = TT(cores)
# left-orthonormalize t
t_left = t_col.ortho_left()
# test if cores are left-orthonormal
err = 0
for i in range(self.order - 1):
c = np.tensordot(t_left.cores[i],
t_left.cores[i],
axes=([0, 1], [0, 1])).squeeze()
if np.linalg.norm(c - np.eye(t_left.ranks[i + 1])) > self.tol:
err += 1
# convert t_col to full format and flatten
t_full = t_col.full().flatten()
# compute relative error
rel_err = np.linalg.norm(t_left.full().flatten() -
t_full) / np.linalg.norm(t_full)
# check if t_left is left-orthonormal and equal to t_col
self.assertEqual(err, 0)
self.assertLess(rel_err, self.tol)
def test_left_orthonormalization(self):
"""test left-orthonormalization"""
# construct non-operator tensor train
cores = [self.cores[i][:, :, 0:1, :] for i in range(self.order)]
t_col = TT(cores)
# left-orthonormalize t
t_left = t_col.ortho_left(threshold=1e-14)
# test if cores are left-orthonormal
err = 0
for i in range(self.order - 1):
c = np.tensordot(t_left.cores[i],
t_left.cores[i],
axes=([0, 1], [0, 1])).squeeze()
if np.linalg.norm(c - np.eye(t_left.ranks[i + 1])) > self.tol:
err += 1
# convert t_col to full format and flatten
t_full = t_col.full().flatten()
# compute relative error
rel_err = np.linalg.norm(t_left.full().flatten() -
t_full) / np.linalg.norm(t_full)
# check if t_left is left-orthonormal and equal to t_col
self.assertEqual(err, 0)
self.assertLess(rel_err, self.tol)
# check if orthonormalization fails if maximum rank is not positive
with self.assertRaises(ValueError):
t_col.ortho_left(max_rank=0)
# check if orthonormalization fails if threshold is negative
with self.assertRaises(ValueError):
t_col.ortho_left(threshold=-1)
# check if orthonormalization fails if start and end indices are not integers
with self.assertRaises(TypeError):
t_col.ortho_left(start_index="a")
t_col.ortho_left(end_index="b")
