code: def slogdet(a):
      r"""
      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) ndarray
          Input array, has to be a square 2-D array.
  
      Returns
      -------
      sign : (...) ndarray
          A number representing the sign of the determinant. For a real matrix,
          this is 1, 0, or -1.
      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
      -----
      Broadcasting rules apply, see the `numpy.linalg` documentation for
      details.
      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)
  
      >>> 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)
      """
      return tuple(_api_internal.slogdet(a))
  
file_path: mxnet/python/mxnet/ndarray/numpy/linalg.py
imports: import numpy
  from .None import _op
  from .None import _api_internal
label_desc: Use image node_id 10 for calling a global function with example usage: slogdet(a) and returns: tuple