t3_entries_ambient_transpose
============================

.. py:function:: t3toolbox.backend.entries.t3_entries_ambient_transpose(c, index, shape, sum_over_probes = False)

   .. code-block:: python

      def t3_entries_ambient_transpose(
              c:                  NDArray,                # residual, shape=W+C
              index:              NDArray,                # int, shape=(d,)+W
              shape:              typ.Sequence[int],      # ambient dims (N0,...,N(d-1)) -- to size the one-hots
              sum_over_probes:    bool = False,           # True: W becomes the CP rank (scatter-adds collisions)
      ) -> typ.Sequence[NDArray]:  # canonical (CP) factors. len=d, ith elm_shape=stack_shape+(R, Ni)


   Ambient transpose of :py:func:`t3_entries`: scatter ``c`` at ``index`` into CP factors.

   The ``entries`` counterpart of :py:func:`t3_apply_ambient_transpose` -- identical
   with the apply vectors replaced by the unit vectors ``e_{index_k}``, so the CP factors are one-hots
   and the back-projection is ``c * e_{idx_0} (x) ... (x) e_{idx_{d-1}}``. ``sum_over_probes=True``
   makes ``W`` the CP rank (scatter-adding colliding indices -- the ``J^T r`` for entry sampling).
   ``shape`` supplies the ambient dims, which (unlike the apply case, where ``ww`` carries them) the
   residual and index alone do not determine. Returns CP factors (see the apply version).