def _solve_linear_operator(linop_a, linop_b):
"""Generic solve of two `LinearOperator`s."""
is_square = registrations_util.is_square(linop_a, linop_b)
is_non_singular = None
is_self_adjoint = None
is_positive_definite = None
if is_square:
is_non_singular = registrations_util.combined_non_singular_hint(
linop_a, linop_b)
elif is_square is False: # pylint:disable=g-bool-id-comparison
is_non_singular = False
is_self_adjoint = False
is_positive_definite = False
return linear_operator_composition.LinearOperatorComposition(
operators=[
linear_operator_inversion.LinearOperatorInversion(linop_a),
linop_b
],
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
)
def _solve_linear_operator_circulant_circulant(linop_a, linop_b):
return linear_operator_circulant.LinearOperatorCirculant(
spectrum=linop_b.spectrum / linop_a.spectrum,
is_non_singular=registrations_util.combined_non_singular_hint(
linop_a, linop_b),
is_self_adjoint=registrations_util.
combined_commuting_self_adjoint_hint(linop_a, linop_b),
is_positive_definite=(
registrations_util.combined_commuting_positive_definite_hint(
linop_a, linop_b)),
is_square=True)
def _solve_linear_operator_diag_tril(linop_diag, linop_triangular):
return linear_operator_lower_triangular.LinearOperatorLowerTriangular(
tril=linop_triangular.to_dense() / linop_diag.diag[..., None],
is_non_singular=registrations_util.combined_non_singular_hint(
linop_diag, linop_triangular),
# This is safe to do since the Triangular matrix is only self-adjoint
# when it is a diagonal matrix, and hence commutes.
is_self_adjoint=registrations_util.
combined_commuting_self_adjoint_hint(linop_diag, linop_triangular),
is_positive_definite=None,
is_square=True)
def _solve_linear_operator_diag(linop_a, linop_b):
return linear_operator_diag.LinearOperatorDiag(
diag=linop_b.diag / linop_a.diag,
is_non_singular=registrations_util.combined_non_singular_hint(
linop_a, linop_b),
is_self_adjoint=registrations_util.
combined_commuting_self_adjoint_hint(linop_a, linop_b),
is_positive_definite=(
registrations_util.combined_commuting_positive_definite_hint(
linop_a, linop_b)),
is_square=True)
def _solve_linear_operator_diag(linop_a, linop_b):
return linear_operator_diag.LinearOperatorDiag(
diag=linop_b.diag / linop_a.diag,
is_non_singular=registrations_util.combined_non_singular_hint(
linop_a, linop_b),
is_self_adjoint=registrations_util.combined_commuting_self_adjoint_hint(
linop_a, linop_b),
is_positive_definite=(
registrations_util.combined_commuting_positive_definite_hint(
linop_a, linop_b)),
is_square=True)
def _solve_linear_operator_circulant_circulant(linop_a, linop_b):
return linear_operator_circulant.LinearOperatorCirculant(
spectrum=linop_b.spectrum / linop_a.spectrum,
is_non_singular=registrations_util.combined_non_singular_hint(
linop_a, linop_b),
is_self_adjoint=registrations_util.combined_commuting_self_adjoint_hint(
linop_a, linop_b),
is_positive_definite=(
registrations_util.combined_commuting_positive_definite_hint(
linop_a, linop_b)),
is_square=True)
def _solve_linear_operator_diag_tril(linop_diag, linop_triangular):
return linear_operator_lower_triangular.LinearOperatorLowerTriangular(
tril=linop_triangular.to_dense() / linop_diag.diag[..., None],
is_non_singular=registrations_util.combined_non_singular_hint(
linop_diag, linop_triangular),
# This is safe to do since the Triangular matrix is only self-adjoint
# when it is a diagonal matrix, and hence commutes.
is_self_adjoint=registrations_util.combined_commuting_self_adjoint_hint(
linop_diag, linop_triangular),
is_positive_definite=None,
is_square=True)
def _solve_linear_operator_diag_scaled_identity_left(
linop_scaled_identity, linop_diag):
return linear_operator_diag.LinearOperatorDiag(
diag=linop_diag.diag / linop_scaled_identity.multiplier,
is_non_singular=registrations_util.combined_non_singular_hint(
linop_diag, linop_scaled_identity),
is_self_adjoint=registrations_util.combined_commuting_self_adjoint_hint(
linop_diag, linop_scaled_identity),
is_positive_definite=(
registrations_util.combined_commuting_positive_definite_hint(
linop_diag, linop_scaled_identity)),
is_square=True)
def _matmul_linear_operator_diag_scaled_identity_left(
linop_scaled_identity, linop_diag):
return linear_operator_diag.LinearOperatorDiag(
diag=linop_diag.diag * linop_scaled_identity.multiplier,
is_non_singular=registrations_util.combined_non_singular_hint(
linop_diag, linop_scaled_identity),
is_self_adjoint=registrations_util.combined_commuting_self_adjoint_hint(
linop_diag, linop_scaled_identity),
is_positive_definite=(
registrations_util.combined_commuting_positive_definite_hint(
linop_diag, linop_scaled_identity)),
is_square=True)
def _solve_linear_operator_scaled_identity(linop_a, linop_b):
"""Solve of two ScaledIdentity `LinearOperators`."""
return linear_operator_identity.LinearOperatorScaledIdentity(
num_rows=linop_a.domain_dimension_tensor(),
multiplier=linop_b.multiplier / linop_a.multiplier,
is_non_singular=registrations_util.combined_non_singular_hint(
linop_a, linop_b),
is_self_adjoint=registrations_util.
combined_commuting_self_adjoint_hint(linop_a, linop_b),
is_positive_definite=(
registrations_util.combined_commuting_positive_definite_hint(
linop_a, linop_b)),
is_square=True)
def _matmul_linear_operator_circulant_circulant(linop_a, linop_b):
if not isinstance(linop_a, linop_b.__class__):
return _matmul_linear_operator(linop_a, linop_b)
return linop_a.__class__(
spectrum=linop_a.spectrum * linop_b.spectrum,
is_non_singular=registrations_util.combined_non_singular_hint(
linop_a, linop_b),
is_self_adjoint=registrations_util.
combined_commuting_self_adjoint_hint(linop_a, linop_b),
is_positive_definite=(
registrations_util.combined_commuting_positive_definite_hint(
linop_a, linop_b)),
is_square=True)
def _solve_linear_operator_block_diag_block_diag(linop_a, linop_b):
return linear_operator_block_diag.LinearOperatorBlockDiag(
operators=[
o1.solve(o2)
for o1, o2 in zip(linop_a.operators, linop_b.operators)
],
is_non_singular=registrations_util.combined_non_singular_hint(
linop_a, linop_b),
# In general, a solve of self-adjoint positive-definite block diagonal
# matrices is not self-=adjoint.
is_self_adjoint=None,
# In general, a solve of positive-definite block diagonal matrices is
# not positive-definite.
is_positive_definite=None,
is_square=True)
def _matmul_linear_operator(linop_a, linop_b):
"""Generic matmul of two `LinearOperator`s."""
is_square = registrations_util.is_square(linop_a, linop_b)
is_non_singular = None
is_self_adjoint = None
is_positive_definite = None
if is_square:
is_non_singular = registrations_util.combined_non_singular_hint(
linop_a, linop_b)
elif is_square is False: # pylint:disable=g-bool-id-comparison
is_non_singular = False
is_self_adjoint = False
is_positive_definite = False
return linear_operator_composition.LinearOperatorComposition(
operators=[linop_a, linop_b],
is_non_singular=is_non_singular,
is_self_adjoint=is_self_adjoint,
is_positive_definite=is_positive_definite,
is_square=is_square,
)
