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

.. function:: warp._src.lang.tile_cholesky(A: Tile[Float, tuple[int, int]], fill_mode: str) -> Tile[Float, tuple[int, int]]

   .. hlist::
      :columns: 8

      * Kernel
      * Differentiable

   Compute the Cholesky factorization of a symmetric positive-definite matrix ``A``.
   
   When ``fill_mode="lower"`` (default), 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"`` (default) or ``"upper"``. Must be a compile-time constant.
   
   :returns: A triangular matrix ``L`` or ``U``.