# numpy.linalg.slogdet

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, then 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(…, M, M) array_like

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

  Returns
    sign(…) array_like

      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(…) array_like

      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

  New in version 1.8.0.

  Broadcasting rules apply, see the `numpy.linalg` documentation for details.

  New in version 1.6.0.

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

  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) # may vary
      >>> sign * np.exp(logdet)
      -2.0

  Computing log-determinants for a stack of matrices:

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

  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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