tv_entries_derivatives_transpose
================================

.. py:function:: t3toolbox.backend.sampling_derivatives.tv_entries_derivatives_transpose(c, index, pp, frame, order, sum_over_probes = False)

   .. code-block:: python

      def tv_entries_derivatives_transpose(
              c:          NDArray,                # residual jet (scalar), shape=(order+1)+W+K+C
              index:      NDArray,                # int, shape=(d,)+W -- the grid points
              pp:         typ.Sequence[NDArray],  # perturbation vectors P, len=d, elm_shape=W+(Ni,)
              frame:       typ.Tuple[
                  typ.Sequence[NDArray], typ.Sequence[NDArray],
                  typ.Sequence[NDArray], typ.Sequence[NDArray],
              ],                                  # = T3Frame.data = (U, O, P, Q)
              order:      int,                    # highest derivative order
              sum_over_probes: bool = False,      # True: sum the sample stack W (the J^T r back-projection)
      ) -> typ.Tuple[
          typ.Tuple[NDArray, ...],  # dU_tildes
          typ.Tuple[NDArray, ...],  # dG_tildes
      ]:                                          # = T3Variations.data


   Transpose of :py:func:`tv_entries_derivatives`: scatter residual jets ``c`` at ``index``
   into a variation gradient. Identical to :py:func:`tv_apply_derivatives_transpose` with the
   frame up-index jet from fiber slicing at ``index`` (order 0) + contracting ``P`` (order 1), and the
   ambient ``w_jet`` from the unit vectors ``e_{index}`` (order 0) + ``P`` (order 1) -- so the
   Tucker-variation gradient scatters onto the indexed rows.

   .. seealso:: :py:obj:`tv_entries_derivatives`, :py:obj:`tv_apply_derivatives_transpose`