mlx.core.linalg.slogdet

slogdet(a: array, *, stream: None | Stream | Device = None) → Tuple[array, array]

Compute the sign and natural log of the absolute value of the determinant of a square matrix.

This function supports arrays with at least 2 dimensions. When the input has more than two dimensions, the sign and log-absolute-determinant are computed for each matrix in the last two dimensions.

For a singular matrix, sign is 0 and logabsdet is -inf.

The determinant can be reconstructed as det = sign * exp(logabsdet). This is more numerically stable than computing the determinant directly for matrices with large or small determinants.

Parameters:

• a (array) – Input array.

• stream (Stream, optional) – Stream or device. Defaults to None in which case the default stream of the default device is used.

Returns:

The sign and logabsdet of the

determinant. sign is -1, 0, or +1. logabsdet is the natural log of the absolute value of the determinant.

Return type:

tuple(array, array)

Example

>>> A = mx.array([[1., 2.], [3., 4.]])
>>> sign, logabsdet = mx.linalg.slogdet(A, stream=mx.cpu)
>>> sign
array(-1, dtype=float32)
>>> logabsdet
array(0.693147, dtype=float32)