warp.tile\_cholesky
===================

.. currentmodule:: warp._src.lang

.. function:: tile_cholesky(A: Tile[Float, tuple[int, int]], fill_mode: str = "lower") -> Tile[Float, tuple[int, int]]

   .. wp-function-tags::
      :kernel: true
      :python: false
      :differentiable: true

   Compute the Cholesky factorization of a symmetric positive-definite matrix ``A``.
   
   When ``fill_mode="lower"``, returns lower-triangular ``L`` such that ``LL^T = A``.
   When ``fill_mode="upper"``, returns upper-triangular ``U`` such that ``U^T U = A``.
   
   The ``fill_mode`` parameter must be a compile-time constant.
   
   Backward propagation computes gradients with respect to the corresponding
   triangular parameterization of ``A`` (lower triangle when ``fill_mode="lower"``,
   upper triangle when ``fill_mode="upper"``).
   
   Supported datatypes are:
       * float32
       * float64
   
   :param A: A square, symmetric positive-definite matrix.
   :param fill_mode: ``"lower"`` or ``"upper"``. Must be a compile-time constant.
   
   :returns: A triangular matrix ``L`` or ``U``.