dense_probe_derivatives
=======================

.. py:function:: t3toolbox.backend.sampling_derivatives.dense_probe_derivatives(ww, pp, T, order)

   .. code-block:: python

      def dense_probe_derivatives(
              ww:     typ.Sequence[NDArray],  # probe vectors X,        len=d, elm_shape=(Ni,)
              pp:     typ.Sequence[NDArray],  # perturbation vectors P, len=d, elm_shape=(Ni,)
              T:      NDArray,                # dense tensor, shape=(N0,...,N(d-1))
              order:  int,                    # highest derivative order K
      ) -> typ.List[NDArray]:                 # z_jets. len=d, elm_shape=(K+1,Ni)


   Exact dense symmetric probe derivatives, by the multilinear subset expansion (test oracle).

   Each action ``y_i`` is multilinear in the off-mode vectors, so ``y_i(X+sP)`` is a polynomial in
   ``s`` and the ``t``-th derivative at ``s=0`` is exact:

       ``y_i^(t) = t! * sum_{|S|=t, S subset of modes\{i}} T contracted with {p_j: j in S, x_j: else}``.

   Enumerates the size-``t`` subsets ``S`` -- only for small ``d``/``t`` (testing), unstacked, no
   rank structure.