def __init__(self,
col,
row,
is_non_singular=None,
is_self_adjoint=None,
is_positive_definite=None,
is_square=None,
name="LinearOperatorToeplitz"):
r"""Initialize a `LinearOperatorToeplitz`.
Args:
col: Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`.
The first column of the operator. Allowed dtypes: `float16`, `float32`,
`float64`, `complex64`, `complex128`. Note that the first entry of
`col` is assumed to be the same as the first entry of `row`.
row: Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`.
The first row of the operator. Allowed dtypes: `float16`, `float32`,
`float64`, `complex64`, `complex128`. Note that the first entry of
`row` is assumed to be the same as the first entry of `col`.
is_non_singular: Expect that this operator is non-singular.
is_self_adjoint: Expect that this operator is equal to its hermitian
transpose. If `diag.dtype` is real, this is auto-set to `True`.
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.
name: A name for this `LinearOperator`.
"""
parameters = dict(col=col,
row=row,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
name=name)
with ops.name_scope(name, values=[row, col]):
self._row = linear_operator_util.convert_nonref_to_tensor(
row, name="row")
self._col = linear_operator_util.convert_nonref_to_tensor(
col, name="col")
self._check_row_col(self._row, self._col)
if is_square is False: # pylint:disable=g-bool-id-comparison
raise ValueError(
"Only square Toeplitz operators currently supported.")
is_square = True
super(LinearOperatorToeplitz,
self).__init__(dtype=self._row.dtype,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
parameters=parameters,
name=name)
self._set_graph_parents([self._row, self._col])
def __init__(self,
tril,
is_non_singular=None,
is_self_adjoint=None,
is_positive_definite=None,
is_square=None,
name="LinearOperatorLowerTriangular"):
r"""Initialize a `LinearOperatorLowerTriangular`.
Args:
tril: Shape `[B1,...,Bb, N, N]` with `b >= 0`, `N >= 0`.
The lower triangular part of `tril` defines this operator. The strictly
upper triangle is ignored.
is_non_singular: Expect that this operator is non-singular.
This operator is non-singular if and only if its diagonal elements are
all non-zero.
is_self_adjoint: Expect that this operator is equal to its hermitian
transpose. This operator is self-adjoint only if it is diagonal with
real-valued diagonal entries. In this case it is advised to use
`LinearOperatorDiag`.
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.
name: A name for this `LinearOperator`.
Raises:
ValueError: If `is_square` is `False`.
"""
parameters = dict(tril=tril,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
name=name)
if is_square is False:
raise ValueError(
"Only square lower triangular operators supported at this time."
)
is_square = True
with ops.name_scope(name, values=[tril]):
self._tril = linear_operator_util.convert_nonref_to_tensor(
tril, name="tril")
self._check_tril(self._tril)
super(LinearOperatorLowerTriangular,
self).__init__(dtype=self._tril.dtype,
graph_parents=None,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
parameters=parameters,
name=name)
self._set_graph_parents([self._tril])
def __init__(self,
diag,
is_non_singular=None,
is_self_adjoint=None,
is_positive_definite=None,
is_square=None,
name="LinearOperatorDiag"):
r"""Initialize a `LinearOperatorDiag`.
Args:
diag: Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`.
The diagonal of the operator. Allowed dtypes: `float16`, `float32`,
`float64`, `complex64`, `complex128`.
is_non_singular: Expect that this operator is non-singular.
is_self_adjoint: Expect that this operator is equal to its hermitian
transpose. If `diag.dtype` is real, this is auto-set to `True`.
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.
name: A name for this `LinearOperator`.
Raises:
TypeError: If `diag.dtype` is not an allowed type.
ValueError: If `diag.dtype` is real, and `is_self_adjoint` is not `True`.
"""
with ops.name_scope(name, values=[diag]):
self._diag = linear_operator_util.convert_nonref_to_tensor(
diag, name="diag")
self._check_diag(self._diag)
# Check and auto-set hints.
if not np.issubdtype(self._diag.dtype, np.complexfloating):
if is_self_adjoint is False:
raise ValueError(
"A real diagonal operator is always self adjoint.")
else:
is_self_adjoint = True
if is_square is False:
raise ValueError(
"Only square diagonal operators currently supported.")
is_square = True
super(LinearOperatorDiag,
self).__init__(dtype=self._diag.dtype,
graph_parents=None,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
name=name)
# TODO(b/143910018) Remove graph_parents in V3.
self._set_graph_parents([self._diag])
def _check_spectrum_and_return_tensor(self, spectrum):
"""Static check of spectrum. Then return `Tensor` version."""
spectrum = linear_operator_util.convert_nonref_to_tensor(spectrum,
name="spectrum")
if tensor_shape.TensorShape(spectrum.shape).ndims is not None:
if tensor_shape.TensorShape(spectrum.shape).ndims < self.block_depth:
raise ValueError(
"Argument spectrum must have at least %d dimensions. Found: %s" %
(self.block_depth, spectrum))
return spectrum
def _check_spectrum_and_return_tensor(self, spectrum):
"""Static check of spectrum. Then return `Tensor` version."""
spectrum = linear_operator_util.convert_nonref_to_tensor(
spectrum, name="spectrum")
if tensor_shape.TensorShape(spectrum.shape).ndims is not None:
if tensor_shape.TensorShape(
spectrum.shape).ndims < self.block_depth:
raise ValueError(
f"Argument `spectrum` must have at least {self.block_depth} "
f"dimensions. Received: {spectrum}.")
return spectrum
def __init__(self,
matrix,
is_non_singular=None,
is_self_adjoint=None,
is_positive_definite=None,
is_square=None,
name="LinearOperatorFullMatrix"):
r"""Initialize a `LinearOperatorFullMatrix`.
Args:
matrix: Shape `[B1,...,Bb, M, N]` with `b >= 0`, `M, N >= 0`.
Allowed dtypes: `float16`, `float32`, `float64`, `complex64`,
`complex128`.
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.
name: A name for this `LinearOperator`.
Raises:
TypeError: If `diag.dtype` is not an allowed type.
"""
parameters = dict(
matrix=matrix,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
name=name
)
with ops.name_scope(name, values=[matrix]):
self._matrix = linear_operator_util.convert_nonref_to_tensor(
matrix, name="matrix")
self._check_matrix(self._matrix)
super(LinearOperatorFullMatrix, self).__init__(
dtype=self._matrix.dtype,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
parameters=parameters,
name=name)
# TODO(b/143910018) Remove graph_parents in V3.
self._set_graph_parents([self._matrix])
def __init__(self,
reflection_axis,
is_non_singular=None,
is_self_adjoint=None,
is_positive_definite=None,
is_square=None,
name="LinearOperatorHouseholder"):
r"""Initialize a `LinearOperatorHouseholder`.
Args:
reflection_axis: Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`.
The vector defining the hyperplane to reflect about.
Allowed dtypes: `float16`, `float32`, `float64`, `complex64`,
`complex128`.
is_non_singular: Expect that this operator is non-singular.
is_self_adjoint: Expect that this operator is equal to its hermitian
transpose. This is autoset to true
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
This is autoset to false.
is_square: Expect that this operator acts like square [batch] matrices.
This is autoset to true.
name: A name for this `LinearOperator`.
Raises:
ValueError: `is_self_adjoint` is not `True`, `is_positive_definite` is
not `False` or `is_square` is not `True`.
"""
parameters = dict(
reflection_axis=reflection_axis,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
name=name
)
with ops.name_scope(name, values=[reflection_axis]):
self._reflection_axis = linear_operator_util.convert_nonref_to_tensor(
reflection_axis, name="reflection_axis")
self._check_reflection_axis(self._reflection_axis)
# Check and auto-set hints.
if is_self_adjoint is False: # pylint:disable=g-bool-id-comparison
raise ValueError("A Householder operator is always self adjoint.")
else:
is_self_adjoint = True
if is_positive_definite is True: # pylint:disable=g-bool-id-comparison
raise ValueError(
"A Householder operator is always non-positive definite.")
else:
is_positive_definite = False
if is_square is False: # pylint:disable=g-bool-id-comparison
raise ValueError("A Householder operator is always square.")
is_square = True
super(LinearOperatorHouseholder, self).__init__(
dtype=self._reflection_axis.dtype,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
parameters=parameters,
name=name)
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))
def __init__(self,
base_operator,
u,
diag_update=None,
v=None,
is_diag_update_positive=None,
is_non_singular=None,
is_self_adjoint=None,
is_positive_definite=None,
is_square=None,
name="LinearOperatorLowRankUpdate"):
"""Initialize a `LinearOperatorLowRankUpdate`.
This creates a `LinearOperator` of the form `A = L + U D V^H`, with
`L` a `LinearOperator`, `U, V` both [batch] matrices, and `D` a [batch]
diagonal matrix.
If `L` is non-singular, solves and determinants are available.
Solves/determinants both involve a solve/determinant of a `K x K` system.
In the event that L and D are self-adjoint positive-definite, and U = V,
this can be done using a Cholesky factorization. The user should set the
`is_X` matrix property hints, which will trigger the appropriate code path.
Args:
base_operator: Shape `[B1,...,Bb, M, N]`.
u: Shape `[B1,...,Bb, M, K]` `Tensor` of same `dtype` as `base_operator`.
This is `U` above.
diag_update: Optional shape `[B1,...,Bb, K]` `Tensor` with same `dtype`
as `base_operator`. This is the diagonal of `D` above.
Defaults to `D` being the identity operator.
v: Optional `Tensor` of same `dtype` as `u` and shape `[B1,...,Bb, N, K]`
Defaults to `v = u`, in which case the perturbation is symmetric.
If `M != N`, then `v` must be set since the perturbation is not square.
is_diag_update_positive: Python `bool`.
If `True`, expect `diag_update > 0`.
is_non_singular: Expect that this operator is non-singular.
Default is `None`, unless `is_positive_definite` is auto-set to be
`True` (see below).
is_self_adjoint: Expect that this operator is equal to its hermitian
transpose. Default is `None`, unless `base_operator` is self-adjoint
and `v = None` (meaning `u=v`), in which case this defaults to `True`.
is_positive_definite: Expect that this operator is positive definite.
Default is `None`, unless `base_operator` is positive-definite
`v = None` (meaning `u=v`), and `is_diag_update_positive`, in which case
this defaults to `True`.
Note that we say an operator is positive definite when the quadratic
form `x^H A x` has positive real part for all nonzero `x`.
is_square: Expect that this operator acts like square [batch] matrices.
name: A name for this `LinearOperator`.
Raises:
ValueError: If `is_X` flags are set in an inconsistent way.
"""
parameters = dict(base_operator=base_operator,
u=u,
diag_update=diag_update,
v=v,
is_diag_update_positive=is_diag_update_positive,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
name=name)
dtype = base_operator.dtype
if diag_update is not None:
if is_diag_update_positive and np.issubdtype(
dtype, np.complexfloating):
logging.warn(
"Note: setting is_diag_update_positive with a complex "
"dtype means that diagonal is real and positive.")
if diag_update is None:
if is_diag_update_positive is False:
raise ValueError(
"Default diagonal is the identity, which is positive. However, "
"user set 'is_diag_update_positive' to False.")
is_diag_update_positive = True
# In this case, we can use a Cholesky decomposition to help us solve/det.
self._use_cholesky = (base_operator.is_positive_definite
and base_operator.is_self_adjoint
and is_diag_update_positive and v is None)
# Possibly auto-set some characteristic flags from None to True.
# If the Flags were set (by the user) incorrectly to False, then raise.
if base_operator.is_self_adjoint and v is None and not np.issubdtype(
dtype, np.complexfloating):
if is_self_adjoint is False:
raise ValueError(
"A = L + UDU^H, with L self-adjoint and D real diagonal. Since"
" UDU^H is self-adjoint, this must be a self-adjoint operator."
)
is_self_adjoint = True
# The condition for using a cholesky is sufficient for SPD, and
# we no weaker choice of these hints leads to SPD. Therefore,
# the following line reads "if hints indicate SPD..."
if self._use_cholesky:
if (is_positive_definite is False or is_self_adjoint is False
or is_non_singular is False):
raise ValueError(
"Arguments imply this is self-adjoint positive-definite operator."
)
is_positive_definite = True
is_self_adjoint = True
values = base_operator.graph_parents + [u, diag_update, v]
with ops.name_scope(name, values=values):
# Create U and V.
self._u = linear_operator_util.convert_nonref_to_tensor(u,
name="u")
if v is None:
self._v = self._u
else:
self._v = linear_operator_util.convert_nonref_to_tensor(
v, name="v")
if diag_update is None:
self._diag_update = None
else:
self._diag_update = linear_operator_util.convert_nonref_to_tensor(
diag_update, name="diag_update")
# Create base_operator L.
self._base_operator = base_operator
graph_parents = base_operator.graph_parents + [
self.u, self._diag_update, self.v
]
graph_parents = [p for p in graph_parents if p is not None]
super(LinearOperatorLowRankUpdate,
self).__init__(dtype=self._base_operator.dtype,
graph_parents=None,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
parameters=parameters,
name=name)
self._set_graph_parents(graph_parents)
# Create the diagonal operator D.
self._set_diag_operators(diag_update, is_diag_update_positive)
self._is_diag_update_positive = is_diag_update_positive
self._check_shapes()
