tv_precompute_probe_frame_sweep
===============================

.. py:function:: t3toolbox.backend.probing.tv_precompute_probe_frame_sweep(frame, ww)

   .. code-block:: python

      def tv_precompute_probe_frame_sweep(
              frame:   typ.Tuple[
                  typ.Sequence[NDArray],          # up_tucker_cores  U. len=d
                  typ.Sequence[NDArray],          # down_tt_cores    O. len=d
                  typ.Sequence[NDArray],          # left_tt_cores    P. len=d
                  typ.Sequence[NDArray],          # right_tt_cores   Q. len=d
              ],                                  # frame order = T3Frame.data = (up, down, left, right)
              ww:     typ.Sequence[NDArray],      # probe vectors, len=d, elm_shape=W+(Ni,)
      ) -> typ.Tuple[
          typ.Sequence[NDArray],  # xis.  len=d, elm_shape=W+C+(nUi,)
          typ.Sequence[NDArray],  # mus.  len=d, elm_shape=W+C+(rLi,)
          typ.Sequence[NDArray],  # nus.  len=d, elm_shape=W+C+(rR(i+1),)
          typ.Sequence[NDArray],  # etas. len=d, elm_shape=W+C+(nOi,)
      ]:                                          # full frame sweep -- (xis, mus, nus, etas)


   The **probe** frame sweep (full): all four frame edge variables ``(xi, mu, nu, eta)``. The probe
   leaves one mode free, so its transpose's per-mode (vector) residual must be propagated through both
   the left ``mu`` and right ``nu`` sweeps + the central ``eta`` combine -- it cannot use the
   scalar-residual adjoint-state shortcut that lets apply/entries drop ``nu``/``eta``
   (:py:func:`tv_precompute_apply_frame_sweep`). Reused across the probe forward / transpose of an inner
   solve. §6.2.2 of Alger et al. (2026); no gauge projector ``Π``.

   .. seealso:: :py:obj:`tv_probe_jacobian_from_sweep`, :py:obj:`tv_probe_transpose_from_sweep`, :py:obj:`tv_precompute_apply_frame_sweep`