`numpy.linalg:slogdet`

source: build-install/usr/lib/python3.14/site-packages/numpy/linalg/_linalg.py :2271

Signature

def slogdet ( a )

Summary

Compute the sign and (natural) logarithm of the determinant of an array.

Extended Summary

If an array has a very small or very large determinant, then a call to det may overflow or underflow. This routine is more robust against such issues, because it computes the logarithm of the determinant rather than the determinant itself.

Parameters

a : (..., M, M) array_like: Input array, has to be a square 2-D array.

Returns

: A namedtuple with the following attributes:
sign : (...) array_like: A number representing the sign of the determinant. For a real matrix, this is 1, 0, or -1. For a complex matrix, this is a complex number with absolute value 1 (i.e., it is on the unit circle), or else 0.
logabsdet : (...) array_like: The natural log of the absolute value of the determinant.
: If the determinant is zero, then `sign` will be 0 and `logabsdet`
: will be -inf. In all cases, the determinant is equal to
: ``sign * np.exp(logabsdet)``.

Notes

Broadcasting rules apply, see the numpy.linalg documentation for details.

The determinant is computed via LU factorization using the LAPACK routine z/dgetrf.

Examples

The determinant of a 2-D array ``[[a, b], [c, d]]`` is ``ad - bc``:

import numpy as np
a = np.array([[1, 2], [3, 4]])
(sign, logabsdet) = np.linalg.slogdet(a)

✓

(sign, logabsdet)
sign * np.exp(logabsdet)

✗

Computing log-determinants for a stack of matrices:

a = np.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ])
a.shape
sign, logabsdet = np.linalg.slogdet(a)

✓

(sign, logabsdet)

✗

sign * np.exp(logabsdet)

✓

This routine succeeds where ordinary `det` does not:

np.linalg.det(np.eye(500) * 0.1)
np.linalg.slogdet(np.eye(500) * 0.1)

✗

Aliases

numpy.linalg.slogdet