def _cond(self):
if not self.is_self_adjoint:
# In general the condition number is the ratio of the
# absolute value of the largest and smallest singular values.
vals = linalg_ops.svd(self.to_dense(), compute_uv=False)
else:
# For self-adjoint matrices, and in general normal matrices,
# we can use eigenvalues.
vals = math_ops.abs(self._eigvals())
return (math_ops.reduce_max(vals, axis=-1) /
math_ops.reduce_min(vals, axis=-1))
def _assert_non_singular(self):
"""Private default implementation of _assert_non_singular."""
logging.warn(
"Using (possibly slow) default implementation of assert_non_singular."
" Requires conversion to a dense matrix and O(N^3) operations.")
if self._can_use_cholesky():
return self.assert_positive_definite()
else:
singular_values = linalg_ops.svd(self.to_dense(), compute_uv=False)
# TODO(langmore) Add .eig and .cond as methods.
cond = (math_ops.reduce_max(singular_values, axis=-1) /
math_ops.reduce_min(singular_values, axis=-1))
return check_ops.assert_less(
cond,
self._max_condition_number_to_be_non_singular(),
message="Singular matrix up to precision epsilon.")
def _min_matrix_dim_tensor(self):
"""Minimum of domain/range dimension, as a tensor."""
return math_ops.reduce_min(self.shape_tensor()[-2:])
def _cond(self):
abs_diag = math_ops.abs(self.diag)
return (math_ops.reduce_max(abs_diag, axis=-1) /
math_ops.reduce_min(abs_diag, axis=-1))
