def assert_no_entries_with_modulus_zero(
x, message=None, name="assert_no_entries_with_modulus_zero"):
"""Returns `Op` that asserts Tensor `x` has no entries with modulus zero.
Args:
x: Numeric `Tensor`, real, integer, or complex.
message: A string message to prepend to failure message.
name: A name to give this `Op`.
Returns:
An `Op` that asserts `x` has no entries with modulus zero.
"""
with ops.name_scope(name, values=[x]):
x = ops.convert_to_tensor(x, name="x")
dtype = x.dtype
should_be_nonzero = math_ops.abs(x)
zero = ops.convert_to_tensor(0, dtype=dtypes.real_dtype(dtype))
return check_ops.assert_less(zero, should_be_nonzero, message=message)
def assert_zero_imag_part(x, message=None, name="assert_zero_imag_part"):
"""Returns `Op` that asserts Tensor `x` has no non-zero imaginary parts.
Args:
x: Numeric `Tensor`, real, integer, or complex.
message: A string message to prepend to failure message.
name: A name to give this `Op`.
Returns:
An `Op` that asserts `x` has no entries with modulus zero.
"""
with ops.name_scope(name, values=[x]):
x = ops.convert_to_tensor(x, name="x")
dtype = x.dtype
if dtype.is_floating:
return control_flow_ops.no_op()
zero = ops.convert_to_tensor(0, dtype=dtypes.real_dtype(dtype))
return check_ops.assert_equal(zero, math_ops.imag(x), message=message)
def assert_hermitian_spectrum(self, name="assert_hermitian_spectrum"):
"""Returns an `Op` that asserts this operator has Hermitian spectrum.
This operator corresponds to a real-valued matrix if and only if its
spectrum is Hermitian.
Args:
name: A name to give this `Op`.
Returns:
An `Op` that asserts this operator has Hermitian spectrum.
"""
eps = np.finfo(dtypes.real_dtype(self.dtype)).eps
with self._name_scope(name): # pylint: disable=not-callable
# Assume linear accumulation of error.
max_err = eps * self.domain_dimension_tensor()
imag_convolution_kernel = math_ops.imag(self.convolution_kernel())
return check_ops.assert_less(math_ops.abs(imag_convolution_kernel),
max_err,
message="Spectrum was not Hermitian")
def __init__(self,
num_rows,
multiplier,
is_non_singular=None,
is_self_adjoint=None,
is_positive_definite=None,
is_square=True,
assert_proper_shapes=False,
name="LinearOperatorScaledIdentity"):
r"""Initialize a `LinearOperatorScaledIdentity`.
The `LinearOperatorScaledIdentity` is initialized with `num_rows`, which
determines the size of each identity matrix, and a `multiplier`,
which defines `dtype`, batch shape, and scale of each matrix.
This operator is able to broadcast the leading (batch) dimensions.
Args:
num_rows: Scalar non-negative integer `Tensor`. Number of rows in the
corresponding identity matrix.
multiplier: `Tensor` of shape `[B1,...,Bb]`, or `[]` (a scalar).
is_non_singular: Expect that this operator is non-singular.
is_self_adjoint: Expect that this operator is equal to its hermitian
transpose.
is_positive_definite: Expect that this operator is positive definite,
meaning the quadratic form `x^H A x` has positive real part for all
nonzero `x`. Note that we do not require the operator to be
self-adjoint to be positive-definite. See:
https://en.wikipedia.org/wiki/Positive-definite_matrix#Extension_for_non-symmetric_matrices
is_square: Expect that this operator acts like square [batch] matrices.
assert_proper_shapes: Python `bool`. If `False`, only perform static
checks that initialization and method arguments have proper shape.
If `True`, and static checks are inconclusive, add asserts to the graph.
name: A name for this `LinearOperator`
Raises:
ValueError: If `num_rows` is determined statically to be non-scalar, or
negative.
"""
self._assert_proper_shapes = assert_proper_shapes
with ops.name_scope(name, values=[multiplier, num_rows]):
self._multiplier = linear_operator_util.convert_nonref_to_tensor(
multiplier, name="multiplier")
# Check and auto-set hints.
if not np.issubdtype(self._multiplier.dtype, np.complexfloating):
if is_self_adjoint is False: # pylint: disable=g-bool-id-comparison
raise ValueError(
"A real diagonal operator is always self adjoint.")
else:
is_self_adjoint = True
if not is_square:
raise ValueError("A ScaledIdentity operator is always square.")
linear_operator_util.assert_not_ref_type(num_rows, "num_rows")
super(LinearOperatorScaledIdentity,
self).__init__(dtype=self._multiplier.dtype,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
name=name)
self._num_rows = linear_operator_util.shape_tensor(num_rows,
name="num_rows")
self._num_rows_static = (self._num_rows)
self._check_num_rows_possibly_add_asserts()
self._num_rows_cast_to_dtype = _ops.cast(self._num_rows,
self.dtype)
self._num_rows_cast_to_real_dtype = _ops.cast(
self._num_rows, dtypes.real_dtype(self.dtype))
