ut3_probe_derivatives
=====================

.. py:function:: t3toolbox.backend.ut3_sampling.ut3_probe_derivatives(ww, pp, data, order)

   .. code-block:: python

      def ut3_probe_derivatives(
              ww:    typ.Sequence[NDArray],  # probe vectors X,        len=d, ith elm_shape=W+(Ni,)
              pp:    typ.Sequence[NDArray],  # perturbation vectors P, len=d, ith elm_shape=W+(Ni,)
              data:  UT3Data,
              order: int,                    # highest derivative order
      ) -> typ.Union[typ.Tuple[NDArray, ...], NDArray]:  # MIRRORS ww: ragged -> len=d tuple; packed -> (d,)+(order+1,)+W+(N,)


   Symmetric probe derivatives of a uniform Tucker tensor train (shares
   ``sampling_derivatives.t3_probe_derivatives``). **Mirrors** ``ww``'s packedness (ragged -> ``len=d`` tuple of
   real widths; packed -> the packed ``(d,)+(order+1,)+W+(N,)`` array).