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# 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 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

  `det`

  Notes

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

  New in version 1.6.0..

  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)

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