code: def cholesky(a, upper=False):
      r"""
      Cholesky decomposition.
  
      Notes
      -----
      `upper` param is requested by API standardization in
      https://data-apis.org/array-api/latest/extensions/generated/signatures.linalg.cholesky.html
      instead of parameter in official NumPy operator.
  
      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.
      upper : bool
          If `True`, the result must be the upper-triangular Cholesky factor.
          If `False`, the result must be the lower-triangular Cholesky factor.
          Default: `False`.
  
      Returns
      -------
      L : (..., M, M) ndarray
          Lower-triangular Cholesky factor of `a`.
  
      Raises
      ------
      MXNetError
          If the decomposition 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.]])
      """
      return _api_internal.cholesky(a, not upper)
  
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 6 for calling a global function with example usage: cholesky(a, upper) and returns: _api_internal