tv_apply_transpose_from_sweep
=============================

.. py:function:: t3toolbox.backend.apply.tv_apply_transpose_from_sweep(c, ww, frame, frame_sweep, sum_over_probes = False)

   .. code-block:: python

      def tv_apply_transpose_from_sweep(
              c:          NDArray,                # residual, shape = W + K + C (K optional)
              ww:         typ.Sequence[NDArray],  # apply vectors (one-hot e_index for entries), len=d, elm_shape=W+(Ni,)
              frame:       typ.Tuple[
                  typ.Sequence[NDArray],          # up_tucker_cores  U. len=d  (unused; uniform call signature)
                  typ.Sequence[NDArray],          # down_tt_cores    O. len=d
                  typ.Sequence[NDArray],          # left_tt_cores    P. len=d  (unused)
                  typ.Sequence[NDArray],          # right_tt_cores   Q. len=d
              ],                                  # frame order = T3Frame.data = (up, down, left, right)
              frame_sweep: typ.Tuple[
                  typ.Sequence[NDArray],          # xis
                  typ.Sequence[NDArray],          # mus
              ],                                  # = tv_precompute_apply_frame_sweep(frame, ww)  (lean: no nu/eta)
              sum_over_probes: bool = False,
      ) -> typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]]:  # (dU_tildes, dG_tildes) = T3Variations.data


   Transpose of the all-modes apply reusing a precomputed frame sweep -- the bare ``𝒥ᵀ``, by the
   **adjoint-state** method (the scalar residual ``c`` seeds one reverse ``sigma_hat`` sweep; see
   :py:func:`_apply_transpose_adjoint`). Takes the **lean** ``(xis, mus)`` sweep + the frame cores ``O,
   Q`` (it recomputes the right context rather than storing ``nu``/``eta`` -- half the memory). Reuse
   hook for ``fitting.py`` (one frame sweep feeds the forward and this transpose). Full ``W + K + C``
   (the residual ``c`` may carry the tangent stack ``K``). No gauge projector ``Π``.

   .. seealso:: :py:obj:`tv_precompute_apply_frame_sweep`, :py:obj:`tv_apply_transpose`