[GitHub] [incubator-mxnet] xidulu commented on a change in pull request #16667: [NumPy] Add NumPy support for Cholesky decomposition

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xidulu commented on a change in pull request #16667: [NumPy] Add NumPy support for Cholesky decomposition
URL: https://github.com/apache/incubator-mxnet/pull/16667#discussion_r340425892
 
 

 ##########
 File path: python/mxnet/symbol/numpy/linalg.py
 ##########
 @@ -128,3 +128,65 @@ def svd(a):
      - Does not support complex input.
     """
     return _npi.svd(a)
+
+
+def cholesky(a):
+    r"""
+    Cholesky decomposition.
+
+    Return the Cholesky decomposition, `L * L.T`, of the square matrix `a`,
+    where `L` is lower-triangular and .T is the transpose operator. `a` must be
+    symmetric and positive-definite. Only `L` is actually returned. Complex-valued
+    input is currently not supported.
+
+    Parameters
+    ----------
+    a : (..., M, M) ndarray
+        Symmetric, positive-definite input matrix.
+
+    Returns
+    -------
+    L : (..., M, M) ndarray
+        Lower-triangular Cholesky factor of `a`.
+
+    Raises
+    ------
+    MXNetError
+        If the dcomposition fails, for example, if `a` is not positive-definite.
+
+    Notes
+    -----
+    Broadcasting rules apply.
+
+    The Cholesky decomposition is often used as a fast way of solving
+
+    .. math:: A \mathbf{x} = \mathbf{b}
+
+    (when `A` is both symmetric and positive-definite).
+
+    First, we solve for :math:`\mathbf{y}` in
+
+    .. math:: L \mathbf{y} = \mathbf{b},
+
+    and then for :math:`\mathbf{x}` in
+
+    .. math:: L.T \mathbf{x} = \mathbf{y}.
+
+    Examples
+    --------
+    >>> A = np.array([[16, 4], [4, 10]])
+    >>> A
+    array([[16.,  4.],
+           [ 4., 10.]])
+    >>> L = np.linalg.cholesky(A)
+    >>> L
+    array([[4., 0.],
+           [1., 3.]])
+    >>> np.dot(L, L.T)
+    array([[16.,  4.],
+           [ 4., 10.]])
+    """
+    # if empty, behave the same as numpy
+    if len(a.as_nd_ndarray()) == 0:
 
 Review comment:
   You'd better cover the zero-size case in the unit tests, in both symbolic and imperative mode.

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