def _make_multiplier_matrix(self, conjugate=False):
# Shape [B1,...Bb, 1, 1]
multiplier_matrix = array_ops.expand_dims(
array_ops.expand_dims(self.multiplier, -1), -1)
if conjugate:
multiplier_matrix = math_ops.conj(multiplier_matrix)
return multiplier_matrix
def _adjoint_diag(diag_operator):
diag = diag_operator.diag
if np.issubdtype(diag.dtype, np.complexfloating):
diag = math_ops.conj(diag)
return linear_operator_diag.LinearOperatorDiag(
diag=diag,
is_non_singular=diag_operator.is_non_singular,
is_self_adjoint=diag_operator.is_self_adjoint,
is_positive_definite=diag_operator.is_positive_definite,
is_square=True)
def _adjoint_scaled_identity(identity_operator):
multiplier = identity_operator.multiplier
if np.issubdtype(multiplier.dtype, np.complexfloating):
multiplier = math_ops.conj(multiplier)
return linear_operator_identity.LinearOperatorScaledIdentity(
num_rows=identity_operator._num_rows, # pylint: disable=protected-access
multiplier=multiplier,
is_non_singular=identity_operator.is_non_singular,
is_self_adjoint=identity_operator.is_self_adjoint,
is_positive_definite=identity_operator.is_positive_definite,
is_square=True)
def _adjoint_circulant(circulant_operator):
spectrum = circulant_operator.spectrum
if np.issubdtype(spectrum.dtype, np.complexfloating):
spectrum = math_ops.conj(spectrum)
# Conjugating the spectrum is sufficient to get the adjoint.
return linear_operator_circulant.LinearOperatorCirculant(
spectrum=spectrum,
is_non_singular=circulant_operator.is_non_singular,
is_self_adjoint=circulant_operator.is_self_adjoint,
is_positive_definite=circulant_operator.is_positive_definite,
is_square=True)
def __init__(self,
spectrum,
block_depth,
input_output_dtype=dtypes.complex64,
is_non_singular=None,
is_self_adjoint=None,
is_positive_definite=None,
is_square=True,
name="LinearOperatorCirculant"):
r"""Initialize an `_BaseLinearOperatorCirculant`.
Args:
spectrum: Shape `[B1,...,Bb, N]` `Tensor`. Allowed dtypes: `float16`,
`float32`, `float64`, `complex64`, `complex128`. Type can be different
than `input_output_dtype`
block_depth: Python integer, either 1, 2, or 3. Will be 1 for circulant,
2 for block circulant, and 3 for nested block circulant.
input_output_dtype: `dtype` for input/output.
is_non_singular: Expect that this operator is non-singular.
is_self_adjoint: Expect that this operator is equal to its hermitian
transpose. If `spectrum` is real, this will always be 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 to prepend to all ops created by this class.
Raises:
ValueError: If `block_depth` is not an allowed value.
TypeError: If `spectrum` is not an allowed type.
"""
allowed_block_depths = [1, 2, 3]
self._name = name
if block_depth not in allowed_block_depths:
raise ValueError("Expected block_depth to be in %s. Found: %s." %
(allowed_block_depths, block_depth))
self._block_depth = block_depth
with ops.name_scope(name, values=[spectrum]):
self._spectrum = self._check_spectrum_and_return_tensor(spectrum)
# Check and auto-set hints.
if not np.issubdtype(self.spectrum.dtype, np.complexfloating):
if is_self_adjoint is False:
raise ValueError(
"A real spectrum always corresponds to a self-adjoint operator."
)
is_self_adjoint = True
if is_square is False:
raise ValueError(
"A [[nested] block] circulant operator is always square.")
is_square = True
# If _ops.TensorShape(spectrum.shape) = [s0, s1, s2], and block_depth = 2,
# block_shape = [s1, s2]
s_shape = array_ops.shape(self.spectrum)
self._block_shape_tensor = s_shape[-self.block_depth:]
# Add common variants of spectrum to the graph.
self._spectrum_complex = _to_complex(self.spectrum)
self._abs_spectrum = math_ops.abs(self.spectrum)
self._conj_spectrum = math_ops.conj(self._spectrum_complex)
super(_BaseLinearOperatorCirculant,
self).__init__(dtype=dtypes.as_dtype(input_output_dtype),
graph_parents=[self.spectrum],
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
name=name)
def _solve(self, rhs, adjoint=False, adjoint_arg=False):
diag_term = math_ops.conj(self._diag) if adjoint else self._diag
rhs = linalg.adjoint(rhs) if adjoint_arg else rhs
inv_diag_mat = array_ops.expand_dims(1. / diag_term, -1)
return rhs * inv_diag_mat
def _matvec(self, x, adjoint=False):
diag_term = math_ops.conj(self._diag) if adjoint else self._diag
return diag_term * x
def _matmul(self, x, adjoint=False, adjoint_arg=False):
diag_term = math_ops.conj(self._diag) if adjoint else self._diag
x = linalg.adjoint(x) if adjoint_arg else x
diag_mat = array_ops.expand_dims(diag_term, -1)
return diag_mat * x
def _trace(self):
if self.is_self_adjoint:
return self.operator.trace()
return math_ops.conj(self.operator.trace())
def _determinant(self):
if self.is_self_adjoint:
return self.operator.determinant()
return math_ops.conj(self.operator.determinant())
def _diag_part(self):
normalized_axis = self.reflection_axis / linalg.norm(
self.reflection_axis, axis=-1, keepdims=True)
return 1. - 2 * normalized_axis * math_ops.conj(normalized_axis)
