t3_entries_corewise_transpose
=============================

.. py:function:: t3toolbox.backend.entries.t3_entries_corewise_transpose(c, index, core_pair, sum_over_probes = False)

   .. code-block:: python

      def t3_entries_corewise_transpose(
              c:          NDArray,                # residual, shape=W+C
              index:      NDArray,                # int, shape=(d,)+W
              core_pair:  typ.Tuple[
                  typ.Sequence[NDArray],          # tucker_cores, len=d, elm_shape=C+(ni,Ni)
                  typ.Sequence[NDArray],          # tt_cores,     len=d, elm_shape=C+(ri,ni,r(i+1))
              ],
              sum_over_probes: bool = False,      # True: sum the apply stack W (scatter-adds collisions)
      ) -> typ.Tuple[
          typ.Tuple[NDArray, ...],  # tucker-core gradients, same shapes as tucker_cores
          typ.Tuple[NDArray, ...],  # tt-core gradients,     same shapes as tt_cores
      ]:


   Corewise (non-manifold) transpose of :py:func:`t3_entries`: gradient of the
   sampled entries w.r.t. the frame's cores.

   The ``entries`` counterpart of :py:func:`t3_apply_corewise_transpose` -- the Section 6.3 substitution
   into :py:func:`tv_entries_transpose`. Needs no ambient ``shape`` argument: the dims come from
   the frame ``tucker_cores``. ``sum_over_probes=True`` scatter-adds colliding indices (the gradient
   ``J^T r``).