Add docs

python/mxnet/_numpy_op_doc.py

@@ -20,6 +20,129 @@
 """Doc placeholder for numpy ops with prefix _np."""
 
 
+def _np_linalg_det(a):
+    """
+    det(a)
+
+    Compute the determinant of an array.
+
+    Parameters
+    ----------
+    a : (..., M, M) ndarray
+        Input array to compute determinants for.
+
+    Returns
+    -------
+    det : (...) ndarray
+        Determinant of `a`.
+
+    See Also
+    --------
+    slogdet : Another way to represent the determinant, more suitable
+    for large matrices where underflow/overflow may occur.
+
+    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]])
+    >>> np.linalg.det(a)
+    -2.0
+
+    Computing 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)
+    >>> np.linalg.det(a)
+    array([-2., -3., -8.])
+    """
+    pass
+
+
+def _np_linalg_slogdet(a):
+    """
+    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) 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. 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
+    -----
+
+    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)
+    """
+    pass
+
+
 def _np_ones_like(a):
     """Return an array of ones with the same shape and type as a given array.