def _determinant(self):
logging.warn(
"Using (possibly slow) default implementation of determinant."
" Requires conversion to a dense matrix and O(N^3) operations.")
if self._can_use_cholesky():
return math_ops.exp(self.log_abs_determinant())
return linalg_ops.matrix_determinant(self.to_dense())
def _determinant(self):
if all(op.is_positive_definite for op in self._diagonal_operators):
return math_ops.exp(self._log_abs_determinant())
result = self._diagonal_operators[0].determinant()
for op in self._diagonal_operators[1:]:
result *= op.determinant()
return result
def _determinant(self):
if self.is_positive_definite:
return math_ops.exp(self.log_abs_determinant())
# The matrix determinant lemma gives
# https://en.wikipedia.org/wiki/Matrix_determinant_lemma
# det(L + UDV^H) = det(D^{-1} + V^H L^{-1} U) det(D) det(L)
# = det(C) det(D) det(L)
# where C is sometimes known as the capacitance matrix,
# C := D^{-1} + V^H L^{-1} U
det_c = _linalg.det(self._make_capacitance())
det_d = self.diag_operator.determinant()
det_l = self.base_operator.determinant()
return det_c * det_d * det_l
