tv_apply_transpose
==================

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

   .. code-block:: python

      def tv_apply_transpose(
              c:          NDArray,                # residual, shape = W + C (one per probe-set, per base point)
              ww:         typ.Sequence[NDArray],  # the apply vectors, len=d, elm_shape=W+(Ni,)
              frame:       typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray],
                                    typ.Sequence[NDArray], typ.Sequence[NDArray]],   # (up, down, left, right)
              sum_over_probes: bool = False,
      ) -> typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]]:  # (dU_tildes, dG_tildes) = T3Variations.data


   Apply the transpose of :py:func:`tv_apply` -- back-project a residual ``c`` into a tangent.

   The adjoint of the (linear-in-the-variation) all-modes apply. Needs only the frame sweep
   (xi-hat, mu-hat, nu-hat, eta-hat) and a single-term scatter assembly (it skips the adjoint
   perturbation sweep that tv_probe_transpose runs). With ``sum_over_probes=False`` the probe
   stack W becomes the output tangent stack; with ``True`` it is summed (the ``J^T r`` back-projection).

   .. seealso:: :py:obj:`tv_apply`, :py:obj:`tv_entries_transpose`