def _log_abs_determinant(self):
# Recall
# det(L + UDV^H) = det(D^{-1} + V^H L^{-1} U) det(D) det(L)
# = det(C) det(D) det(L)
log_abs_det_d = self.diag_operator.log_abs_determinant()
log_abs_det_l = self.base_operator.log_abs_determinant()
if self._use_cholesky:
chol_cap_diag = _linalg.diag_part(self._chol_capacitance)
log_abs_det_c = 2 * math_ops.reduce_sum(
math_ops.log(chol_cap_diag), axis=[-1])
else:
det_c = linalg_ops.matrix_determinant(self._capacitance)
log_abs_det_c = math_ops.log(math_ops.abs(det_c))
if np.issubdtype(self.dtype, np.complexfloating):
log_abs_det_c = _ops.cast(log_abs_det_c, dtype=self.dtype)
return log_abs_det_c + log_abs_det_d + log_abs_det_l
def _log_abs_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():
diag = _linalg.diag_part(linalg_ops.cholesky(self.to_dense()))
return 2 * math_ops.reduce_sum(math_ops.log(diag), axis=[-1])
_, log_abs_det = linalg.slogdet(self.to_dense())
return log_abs_det
def _log_abs_determinant(self):
axis = [-(i + 1) for i in range(self.block_depth)]
lad = math_ops.reduce_sum(math_ops.log(self._abs_spectrum), axis=axis)
return _ops.cast(lad, self.dtype)
def _log_abs_determinant(self):
log_det = math_ops.reduce_sum(math_ops.log(math_ops.abs(self._diag)),
axis=[-1])
if np.issubdtype(self.dtype, np.complexfloating):
log_det = _ops.cast(log_det, dtype=self.dtype)
return log_det
def _log_abs_determinant(self):
return math_ops.reduce_sum(math_ops.log(math_ops.abs(
self._get_diag())),
axis=[-1])
def _log_abs_determinant(self):
return self._num_rows_cast_to_real_dtype * math_ops.log(
math_ops.abs(self.multiplier))