warp.tile\_lower\_solve
=======================

.. function:: warp._src.lang.tile_lower_solve(L: Tile[Float, tuple[int, int]], y: Tile[Float, tuple[int]]) -> Tile[Float, tuple[int]]

   .. hlist::
      :columns: 8

      * Kernel
      * Differentiable

   Solve for ``z`` in ``Lz = y``, where ``L`` is a lower triangular matrix.
   
   This performs general forward substitution for a lower triangular system.
   
   Backward propagation computes gradients with respect to ``y`` and the
   lower-triangular parameterization of ``L``. The strictly upper triangle of
   ``L`` does not affect the solve and receives zero gradient.
   
   Supported datatypes are:
       * float32
       * float64
   
   :param L: A square, non-singular, lower triangular matrix
   :param y: A 1D or 2D tile with compatible shape
   
   :returns: A tile of the same shape as ``y`` such that ``Lz = y``.