slogdet

→Tensor

slogdet(A: Tensor)

source

Sign and natural log of the absolute determinant.

Returns the pair $(\mathrm{sign},\, \log|\det A|)$ such that

\det(A) \,=\, \mathrm{sign} \cdot \exp(\log|\det A|).

Numerically stable for matrices whose determinant would overflow or underflow if computed directly — for instance, large covariance matrices in log-likelihood calculations.

Parameters

ATensor

Square matrix of shape (*, n, n).

Returns

Tensor

$\pm 1$ (or $0$ for singular matrices), shape (*,).

Notes

Computed via LU as $\log|\det A| = \sum_i \log|U_{ii}|$ with the sign accumulated from row swaps. Cost is $O(n^3)$ .

Examples

>>> import lucid
>>> from lucid.linalg import slogdet
>>> sign, logabs = slogdet(lucid.tensor([[1.0, 2.0], [3.0, 4.0]]))
>>> sign, logabs
(Tensor(-1.0), Tensor(0.6931))