def _assert_positive_definite(self):
# This operator has the action Ax = F^H D F x,
# where D is the diagonal matrix with self.spectrum on the diag. Therefore,
# <x, Ax> = <Fx, DFx>,
# Since F is bijective, the condition for positive definite is the same as
# for a diagonal matrix, i.e. real part of spectrum is positive.
message = (
"Not positive definite: Real part of spectrum was not all positive.")
return check_ops.assert_positive(
math_ops.real(self.spectrum), message=message)
def _assert_positive_definite(self):
if np.issubdtype(self.dtype, np.complexfloating):
message = (
"Diagonal operator had diagonal entries with non-positive real part, "
"thus was not positive definite.")
else:
message = (
"Real diagonal operator had non-positive diagonal entries, "
"thus was not positive definite.")
return check_ops.assert_positive(math_ops.real(self._diag),
message=message)
def _assert_positive_definite(self):
"""Default implementation of _assert_positive_definite."""
logging.warn(
"Using (possibly slow) default implementation of "
"assert_positive_definite."
" Requires conversion to a dense matrix and O(N^3) operations.")
# If the operator is self-adjoint, then checking that
# Cholesky decomposition succeeds + results in positive diag is necessary
# and sufficient.
if self.is_self_adjoint:
return check_ops.assert_positive(
_linalg.diag_part(linalg_ops.cholesky(self.to_dense())),
message="Matrix was not positive definite.")
# We have no generic check for positive definite.
raise NotImplementedError("assert_positive_definite is not implemented.")
def _assert_positive_definite(self):
return check_ops.assert_positive(
math_ops.real(self.multiplier),
message="LinearOperator was not positive definite.")
def _assert_non_singular(self):
return check_ops.assert_positive(math_ops.abs(self.multiplier),
message="LinearOperator was singular")
