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

.. currentmodule:: warp._src.lang

.. function:: tile_cholesky_inplace(A: Tile[Float, tuple[int, int]], fill_mode: str = "lower") -> None

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

   Compute the Cholesky factorization of a symmetric positive-definite matrix ``A`` in place.
   
   With ``fill_mode="lower"`` the lower triangle of ``A`` is replaced by
   the factor ``L`` such that ``L @ L^T = A`` and the upper triangle is set to zero;
   with ``fill_mode="upper"`` the upper triangle is replaced by ``U`` such that
   ``U^T @ U = A`` and the lower triangle is set to zero. Only the triangle selected by
   ``fill_mode`` is read. ``fill_mode`` must be a compile-time constant.
   
   Supported dtypes, the positive-definiteness requirement, and backend selection match
   :func:`~warp.tile_cholesky`; see it for details and a usage example.
   
   This is a cooperative operation, so every thread in the block must call it.
   
   This in-place variant avoids the input copy and uses half the shared memory of
   :func:`~warp.tile_cholesky`, but is not differentiable.
   
   :param A: A square, symmetric positive-definite tile with ``shape=(N, N)``, overwritten
             by the factor.
   :param fill_mode: ``"lower"`` or ``"upper"``. Must be a compile-time constant.