Sign & Log-Det

Shipping

matrix_slogdet

Numerically stable log-determinant: returns sign and ln|det A| separately

Signature

Inputs

aSignal|Arrayrequired— A square 2-D matrix.

Outputs

signScalar— The sign of the determinant: $+1$, $-1$, or $0$ if singular.
ln_abs_detScalar— The natural log of the absolute determinant, $\ln|\det A|$.

Description

Sign & Log-Det computes the determinant in a numerically stable, overflow-safe form: it returns the sign ( $+ 1$ , $- 1$ , or $0$ when singular) and $ln ∣ det A ∣$ on separate output ports. This mirrors numpy's slogdet and is the recommended way to reason about determinants of large or ill-scaled matrices, where the raw determinant would overflow to $\infty$ or underflow to $0$ .

To recover the ordinary determinant, combine the outputs as $det A = sign \cdot e^{l n ∣ d e t A ∣}$ . Both outputs are dimensionless scalars, and the computation runs through the MKL LAPACK backend.

Mathematics

det A = sign \cdot exp (ln ∣ det A ∣)

sign \in {- 1, 0, + 1}

Examples

Reconstructing the determinant

For a large positive-definite covariance matrix whose determinant is astronomically small, sign reads $+ 1$ and ln_abs_det reads a large negative number. Their combination $sign \cdot e^{ln_abs_det}$ reproduces $det A$ without ever underflowing to literal $0$ .

Applications

Gaussian / multivariate-normal log-likelihoods, which need $\ln\det\Sigma$ directly.
Comparing determinants across many matrices in the log domain to avoid overflow.
Robust singularity detection via the $0$ sign flag.

Neat

Working in the log domain keeps determinants of high-dimensional covariance matrices finite where the raw value would overflow floating point.

The sign is factored out cleanly, so a negative or singular determinant is unambiguous even when $|\det A|$ spans hundreds of orders of magnitude.

Known issues

For a singular matrix `sign` is $0$ and `ln_abs_det` is $-\infty$; downstream nodes should guard against the infinite log.

The two outputs must be recombined via $\text{sign}\cdot e^{\ln|\det|}$ to get a plain determinant — a single-port reading is incomplete.