dpnp.linalg.slogdet

dpnp.linalg.slogdet(a)

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

For full documentation refer to numpy.linalg.slogdet.

Parameters:

a(..., M, M) {dpnp.ndarray, usm_ndarray}

Input array, has to be a square 2-D array.

Returns:

A namedtuple with the following attributes:

sign(...) dpnp.ndarray

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(...) dpnp.ndarray

The natural log of the absolute value of the determinant.

See also

dpnp.det

Returns the determinant of an array.

Examples

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

>>> import dpnp as dp
>>> a = dp.array([[1, 2], [3, 4]])
>>> (sign, logabsdet) = dp.linalg.slogdet(a)
>>> (sign, logabsdet)
(array(-1.), array(0.69314718))
>>> sign * dp.exp(logabsdet)
array(-2.)

Computing log-determinants for a stack of matrices:

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