def __init__(self,
num_rows,
multiplier,
is_non_singular=None,
is_self_adjoint=None,
is_positive_definite=None,
assert_proper_shapes=False,
name="LinearOperatorScaledIdentity"):
"""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.
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 = ops.convert_to_tensor(multiplier, name="multiplier")
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,
name=name)
# Shape [B1,...Bb, 1, 1]
self._multiplier_matrix = array_ops.expand_dims(
array_ops.expand_dims(self.multiplier, -1), -1)
self._multiplier_matrix_conj = math_ops.conj(
self._multiplier_matrix)
self._abs_multiplier = math_ops.abs(self.multiplier)
self._num_rows = linear_operator_util.shape_tensor(
num_rows, name="num_rows")
self._num_rows_static = tensor_util.constant_value(self._num_rows)
self._check_num_rows_possibly_add_asserts()
self._num_rows_cast_to_dtype = math_ops.cast(self._num_rows, self.dtype)
self._num_rows_cast_to_real_dtype = math_ops.cast(
self._num_rows, self.dtype.real_dtype)
def __init__(self,
num_rows,
multiplier,
is_non_singular=None,
is_self_adjoint=None,
is_positive_definite=None,
assert_proper_shapes=False,
name="LinearOperatorScaledIdentity"):
"""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.
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 = ops.convert_to_tensor(multiplier, name="multiplier")
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,
name=name)
# Shape [B1,...Bb, 1, 1]
self._multiplier_matrix = array_ops.expand_dims(
array_ops.expand_dims(self.multiplier, -1), -1)
self._multiplier_matrix_conj = math_ops.conj(
self._multiplier_matrix)
self._abs_multiplier = math_ops.abs(self.multiplier)
self._num_rows = linear_operator_util.shape_tensor(
num_rows, name="num_rows")
self._num_rows_static = tensor_util.constant_value(self._num_rows)
self._check_num_rows_possibly_add_asserts()
self._num_rows_cast_to_dtype = math_ops.cast(self._num_rows, self.dtype)
self._num_rows_cast_to_real_dtype = math_ops.cast(
self._num_rows, self.dtype.real_dtype)
def batch_shape_tensor(self, name="batch_shape_tensor"):
"""Shape of batch dimensions of this operator, determined at runtime.
If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns a `Tensor` holding
`[B1,...,Bb]`.
Args:
name: A name for this `Op.
Returns:
`int32` `Tensor`
"""
# Derived classes get this "for free" once .shape() is implemented.
with self._name_scope(name):
if self._cached_batch_shape_tensor is None:
# Prefer to use statically defined shape if available.
if self.batch_shape.is_fully_defined():
self._cached_batch_shape_tensor = linear_operator_util.shape_tensor(
self.batch_shape.as_list(), name="batch_shape")
else:
self._cached_batch_shape_tensor = self.shape_tensor()[:-2]
return self._cached_batch_shape_tensor
def shape_tensor(self, name="shape_tensor"):
"""Shape of this `LinearOperator`, determined at runtime.
If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns a `Tensor` holding
`[B1,...,Bb, M, N]`, equivalent to `tf.shape(A)`.
Args:
name: A name for this `Op.
Returns:
`int32` `Tensor`
"""
with self._name_scope(name):
# Be clean by avoiding adding shape Ops to the graph too many times.
if self._cached_shape_tensor is None:
# Prefer to use statically defined shape if available.
if self.shape.is_fully_defined():
self._cached_shape_tensor = linear_operator_util.shape_tensor(
self.shape.as_list())
else:
self._cached_shape_tensor = self._shape_tensor()
return self._cached_shape_tensor
def batch_shape_tensor(self, name="batch_shape_tensor"):
"""Shape of batch dimensions of this operator, determined at runtime.
If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns a `Tensor` holding
`[B1,...,Bb]`.
Args:
name: A name for this `Op.
Returns:
`int32` `Tensor`
"""
# Derived classes get this "for free" once .shape() is implemented.
with self._name_scope(name):
if self._cached_batch_shape_tensor is None:
# Prefer to use statically defined shape if available.
if self.batch_shape.is_fully_defined():
self._cached_batch_shape_tensor = linear_operator_util.shape_tensor(
self.batch_shape.as_list(), name="batch_shape")
else:
self._cached_batch_shape_tensor = self.shape_tensor()[:-2]
return self._cached_batch_shape_tensor
def shape_tensor(self, name="shape_tensor"):
"""Shape of this `LinearOperator`, determined at runtime.
If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns a `Tensor` holding
`[B1,...,Bb, M, N]`, equivalent to `tf.shape(A)`.
Args:
name: A name for this `Op.
Returns:
`int32` `Tensor`
"""
with self._name_scope(name):
# Be clean by avoiding adding shape Ops to the graph too many times.
if self._cached_shape_tensor is None:
# Prefer to use statically defined shape if available.
if self.shape.is_fully_defined():
self._cached_shape_tensor = linear_operator_util.shape_tensor(
self.shape.as_list())
else:
self._cached_shape_tensor = self._shape_tensor()
return self._cached_shape_tensor
def __init__(self,
num_rows,
batch_shape=None,
dtype=None,
is_non_singular=True,
is_self_adjoint=True,
is_positive_definite=True,
assert_proper_shapes=False,
name="LinearOperatorIdentity"):
r"""Initialize a `LinearOperatorIdentity`.
The `LinearOperatorIdentity` is initialized with arguments defining `dtype`
and shape.
This operator is able to broadcast the leading (batch) dimensions, which
sometimes requires copying data. If `batch_shape` is `None`, the operator
can take arguments of any batch shape without copying. See examples.
Args:
num_rows: Scalar non-negative integer `Tensor`. Number of rows in the
corresponding identity matrix.
batch_shape: Optional `1-D` integer `Tensor`. The shape of the leading
dimensions. If `None`, this operator has no leading dimensions.
dtype: Data type of the matrix that this operator represents.
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
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.
ValueError: If `batch_shape` is determined statically to not be 1-D, or
negative.
ValueError: If any of the following is not `True`:
`{is_self_adjoint, is_non_singular, is_positive_definite}`.
"""
dtype = dtype or dtypes.float32
self._assert_proper_shapes = assert_proper_shapes
with ops.name_scope(name):
dtype = dtypes.as_dtype(dtype)
if not is_self_adjoint:
raise ValueError(
"An identity operator is always self adjoint.")
if not is_non_singular:
raise ValueError(
"An identity operator is always non-singular.")
if not is_positive_definite:
raise ValueError(
"An identity operator is always positive-definite.")
super(LinearOperatorIdentity,
self).__init__(dtype=dtype,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
name=name)
self._num_rows = linear_operator_util.shape_tensor(num_rows,
name="num_rows")
self._num_rows_static = tensor_util.constant_value(self._num_rows)
self._check_num_rows_possibly_add_asserts()
if batch_shape is None:
self._batch_shape_arg = None
else:
self._batch_shape_arg = linear_operator_util.shape_tensor(
batch_shape, name="batch_shape_arg")
self._batch_shape_static = tensor_util.constant_value(
self._batch_shape_arg)
self._check_batch_shape_possibly_add_asserts()
def __init__(self,
num_rows,
batch_shape=None,
dtype=None,
is_non_singular=True,
is_self_adjoint=True,
is_positive_definite=True,
assert_proper_shapes=False,
name="LinearOperatorIdentity"):
"""Initialize a `LinearOperatorIdentity`.
The `LinearOperatorIdentity` is initialized with arguments defining `dtype`
and shape.
This operator is able to broadcast the leading (batch) dimensions, which
sometimes requires copying data. If `batch_shape` is `None`, the operator
can take arguments of any batch shape without copying. See examples.
Args:
num_rows: Scalar non-negative integer `Tensor`. Number of rows in the
corresponding identity matrix.
batch_shape: Optional `1-D` integer `Tensor`. The shape of the leading
dimensions. If `None`, this operator has no leading dimensions.
dtype: Data type of the matrix that this operator represents.
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.
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.
ValueError: If `batch_shape` is determined statically to not be 1-D, or
negative.
ValueError: If any of the following is not `True`:
`{is_self_adjoint, is_non_singular, is_positive_definite}`.
"""
dtype = dtype or dtypes.float32
self._assert_proper_shapes = assert_proper_shapes
with ops.name_scope(name):
dtype = dtypes.as_dtype(dtype)
if not is_self_adjoint:
raise ValueError("An identity operator is always self adjoint.")
if not is_non_singular:
raise ValueError("An identity operator is always non-singular.")
if not is_positive_definite:
raise ValueError("An identity operator is always positive-definite.")
super(LinearOperatorIdentity, self).__init__(
dtype=dtype,
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
name=name)
self._num_rows = linear_operator_util.shape_tensor(
num_rows, name="num_rows")
self._num_rows_static = tensor_util.constant_value(self._num_rows)
self._check_num_rows_possibly_add_asserts()
if batch_shape is None:
self._batch_shape_arg = None
else:
self._batch_shape_arg = linear_operator_util.shape_tensor(
batch_shape, name="batch_shape_arg")
self._batch_shape_static = tensor_util.constant_value(
self._batch_shape_arg)
self._check_batch_shape_possibly_add_asserts()
