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

.. currentmodule:: warp._src.lang

.. function:: tile_cholesky_solve(L: Tile[Float, tuple[int, int]], y: Tile[Float, tuple[int]], fill_mode: str = "lower") -> Tile[Float, tuple[int]]

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

   Solve for ``x`` in ``Ax = y`` given the Cholesky factor of ``A``.
   
   When ``fill_mode="lower"``, ``L`` is lower-triangular such that ``LL^T = A``.
   When ``fill_mode="upper"``, ``L`` is upper-triangular ``U`` such that ``U^T U = A``.
   
   The ``fill_mode`` parameter must be a compile-time constant.
   
   Note that computing the adjoint is not yet supported.
   
   Supported datatypes are:
       * float32
       * float64
   
   :param L: A square triangular Cholesky factor of ``A``.
   :param y: A 1D or 2D tile of length ``M``.
   :param fill_mode: ``"lower"`` or ``"upper"``. Must be a compile-time constant.
   
   :returns: A tile of the same shape as ``y`` such that ``Ax = y``.