def test_scalar_row_col_raises(self):
with self.assertRaisesRegex(ValueError, "must have at least 1 dimension"):
linear_operator_toeplitz.LinearOperatorToeplitz(1., 1.)
with self.assertRaisesRegex(ValueError, "must have at least 1 dimension"):
linear_operator_toeplitz.LinearOperatorToeplitz([1.], 1.)
with self.assertRaisesRegex(ValueError, "must have at least 1 dimension"):
linear_operator_toeplitz.LinearOperatorToeplitz(1., [1.])
def test_convert_variables_to_tensors(self):
col = variables_module.Variable([1.])
row = variables_module.Variable([1.])
operator = linear_operator_toeplitz.LinearOperatorToeplitz(
col, row, is_self_adjoint=True, is_positive_definite=True)
with self.cached_session() as sess:
sess.run([x.initializer for x in operator.variables])
self.check_convert_variables_to_tensors(operator)
def operator_and_matrix(self,
build_info,
dtype,
use_placeholder,
ensure_self_adjoint_and_pd=False):
shape = list(build_info.shape)
row = np.random.uniform(low=1., high=5., size=shape[:-1])
col = np.random.uniform(low=1., high=5., size=shape[:-1])
# Make sure first entry is the same
row[..., 0] = col[..., 0]
if ensure_self_adjoint_and_pd:
# Note that a Toeplitz matrix generated from a linearly decreasing
# non-negative sequence is positive definite. See
# https://www.math.cinvestav.mx/~grudsky/Papers/118_29062012_Albrecht.pdf
# for details.
row = np.linspace(start=10., stop=1., num=shape[-1])
# The entries for the first row and column should be the same to guarantee
# symmetric.
row = col
lin_op_row = math_ops.cast(row, dtype=dtype)
lin_op_col = math_ops.cast(col, dtype=dtype)
if use_placeholder:
lin_op_row = array_ops.placeholder_with_default(lin_op_row,
shape=None)
lin_op_col = array_ops.placeholder_with_default(lin_op_col,
shape=None)
operator = linear_operator_toeplitz.LinearOperatorToeplitz(
row=lin_op_row,
col=lin_op_col,
is_self_adjoint=True if ensure_self_adjoint_and_pd else None,
is_positive_definite=True if ensure_self_adjoint_and_pd else None)
flattened_row = np.reshape(row, (-1, shape[-1]))
flattened_col = np.reshape(col, (-1, shape[-1]))
flattened_toeplitz = np.zeros(
[flattened_row.shape[0], shape[-1], shape[-1]])
for i in range(flattened_row.shape[0]):
flattened_toeplitz[i] = scipy.linalg.toeplitz(
flattened_col[i], flattened_row[i])
matrix = np.reshape(flattened_toeplitz, shape)
matrix = math_ops.cast(matrix, dtype=dtype)
return operator, matrix
def test_tape_safe(self):
col = variables_module.Variable([1.])
row = variables_module.Variable([1.])
operator = linear_operator_toeplitz.LinearOperatorToeplitz(
col, row, is_self_adjoint=True, is_positive_definite=True)
self.check_tape_safe(
operator,
skip_options=[
# .diag_part, .trace depend only on `col`, so test explicitly below.
linear_operator_test_util.CheckTapeSafeSkipOptions.DIAG_PART,
linear_operator_test_util.CheckTapeSafeSkipOptions.TRACE,
])
with backprop.GradientTape() as tape:
self.assertIsNotNone(tape.gradient(operator.diag_part(), col))
with backprop.GradientTape() as tape:
self.assertIsNotNone(tape.gradient(operator.trace(), col))
