warp.tile\_upper\_solve
=======================

.. currentmodule:: warp._src.lang

.. function:: tile_upper_solve(U: Tile[Float, tuple[int, int]], z: Tile[Float, tuple[int]]) -> Tile[Float, tuple[int]]

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

   Solve for ``x`` in ``Ux = z``, where ``U`` is an upper triangular matrix.
   
   This performs general back substitution for upper triangular systems.
   
   Note that computing the adjoint is not yet supported.
   
   Supported datatypes are:
       * float32
       * float64
   
   :param U: A square, non-singular, upper triangular matrix
   :param z: A 1D or 2D tile with compatible shape
   
   :returns: A tile of the same shape as ``z`` such that ``Ux = z``.