flopscope.

flopscope.numpy.linalg.slogdet

fnp.linalg.slogdet(a)[flopscope source][numpy source]

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

Adapted from NumPy docs np.linalg.slogdet

Arealinalg
Typecustom
NumPy Refnp.linalg.slogdet
Cost
4×n3n^3
Flopscope Context

Sign + log determinant. Cost: $n^3$.

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 * flops.exp(logabsdet)``.

See also

Notes

Broadcasting rules apply, see the flops.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 flopscope.numpy as fnp
>>> a = flops.array([[1, 2], [3, 4]])
>>> (sign, logabsdet) = flops.linalg.slogdet(a)
>>> (sign, logabsdet)
(-1, 0.69314718055994529) # may vary
>>> sign * flops.exp(logabsdet)
-2.0

Computing log-determinants for a stack of matrices:

>>> a = flops.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ])
>>> a.shape
(3, 2, 2)
>>> sign, logabsdet = flops.linalg.slogdet(a)
>>> (sign, logabsdet)
(array([-1., -1., -1.]), array([ 0.69314718,  1.09861229,  2.07944154]))
>>> sign * flops.exp(logabsdet)
array([-2., -3., -8.])

This routine succeeds where ordinary det does not:

>>> flops.linalg.det(flops.eye(500) * 0.1)
0.0
>>> flops.linalg.slogdet(flops.eye(500) * 0.1)
(1, -1151.2925464970228)