def testFrobeniusNormTens(self):
# Frobenius norm of a batch of TT-tensors.
with self.test_session() as sess:
tt = initializers.tensor_batch_with_random_cores((2, 1, 3), batch_size=3,
dtype=self.dtype)
norm_sq_actual = ops.frobenius_norm_squared(tt)
norm_actual = ops.frobenius_norm(tt)
vars = [norm_sq_actual, norm_actual, ops.full(tt)]
norm_sq_actual_val, norm_actual_val, tt_val = sess.run(vars)
tt_val = tt_val.reshape((3, -1))
norm_sq_desired_val = np.sum(tt_val * tt_val, axis=1)
norm_desired_val = np.sqrt(norm_sq_desired_val)
self.assertAllClose(norm_sq_actual_val, norm_sq_desired_val)
self.assertAllClose(norm_actual_val, norm_desired_val, atol=1e-5,
rtol=1e-5)
def testFrobeniusNormMatrix(self):
# Frobenius norm of a TT-matrix.
shape_list = (((2, 2), (3, 4)),
((2, 3, 4), (2, 2, 2)))
rank_list = (1, 2)
with self.test_session() as sess:
for tensor_shape in shape_list:
for rank in rank_list:
tt = initializers.random_matrix(tensor_shape, tt_rank=rank,
dtype=self.dtype)
norm_sq_actual = ops.frobenius_norm_squared(tt)
norm_actual = ops.frobenius_norm(tt)
vars = [norm_sq_actual, norm_actual, ops.full(tt)]
norm_sq_actual_val, norm_actual_val, tt_val = sess.run(vars)
tt_val = tt_val.flatten()
norm_sq_desired_val = tt_val.dot(tt_val)
norm_desired_val = np.linalg.norm(tt_val)
self.assertAllClose(norm_sq_actual_val, norm_sq_desired_val)
self.assertAllClose(norm_actual_val, norm_desired_val, atol=1e-5,
rtol=1e-5)
def testFrobeniusNormTens(self):
# Frobenius norm of a TT-tensor.
shape_list = ((2, 2), (2, 3, 4), (4, 2, 5, 2))
rank_list = (1, 2)
for shape in shape_list:
for rank in rank_list:
tt = initializers.random_tensor(shape,
tt_rank=rank,
dtype=self.dtype)
norm_sq_actual = ops.frobenius_norm_squared(tt)
norm_actual = ops.frobenius_norm(tt, epsilon=0.0)
vars = [norm_sq_actual, norm_actual, ops.full(tt)]
norm_sq_actual_val, norm_actual_val, tt_val = self.evaluate(
vars)
tt_val = tt_val.flatten()
norm_sq_desired_val = tt_val.dot(tt_val)
norm_desired_val = np.linalg.norm(tt_val)
self.assertAllClose(norm_sq_actual_val, norm_sq_desired_val)
self.assertAllClose(norm_actual_val,
norm_desired_val,
atol=1e-5,
rtol=1e-5)