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

If an array has a very small or very large determinant, than 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 : array_like

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

Returns :

sign : float or complex

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.

logdet : float

The natural log of the absolute value of the determinant.

If the determinant is zero, then `sign` will be 0 and `logdet` will be :

-Inf. In all cases, the determinant is equal to ``sign * np.exp(logdet)``. :

See also



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

New in version 1.6.0..


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

>>> a = np.array([[1, 2], [3, 4]])
>>> (sign, logdet) = np.linalg.slogdet(a)
>>> (sign, logdet)
(-1, 0.69314718055994529)
>>> sign * np.exp(logdet)

This routine succeeds where ordinary det does not:

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

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