# numpy.linalg.slogdet¶

numpy.linalg.slogdet(a)

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, shape (M, M) Input array. 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)`. :

det

Notes

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

New in version 2.0.0..

Examples

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)
-2.0
```

This routine succeeds where ordinary det does not:

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

numpy.linalg.det

numpy.trace