compute_mu_jets
===============

.. py:function:: t3toolbox.backend.sampling_derivatives.compute_mu_jets(tt_cores, xi_jets, trs)

   .. code-block:: python

      def compute_mu_jets(
              tt_cores:   typ.Sequence[NDArray],  # len=d, elm_shape=C+(rLi,nUi,rR(i+1))
              xi_jets:    typ.Sequence[NDArray],  # input jets,  len=d, elm_shape=(2,)+W+C+(nUi,)
              trs:        NDArray,                # binomial tensor -- ONLY its shape (order) is read here
      ) -> typ.Tuple[NDArray, ...]:               # mu_jets. len=d, elm_shape=(order+1,)+W+C+(rLi,). mu_jets[i][t]=mu_{i-1}^(t)


   Left derivative-pushthrough jets (standard fused-recurrence form).

   ``mu_jets[i]`` is the left edge variable entering core ``i`` (``mu_{i-1}``), stacked over derivative
   orders. The affine input jet (``xi`` nonzero only at orders ``s in {0,1}``) collapses each binomial
   pushthrough to a two-term recurrence ``mu_i^(t) = mu^(t).G.xi^(0) + t * mu^(t-1).G.xi^(1)`` -- no
   dense ``trs`` tensor, no ``(order+1)^2`` work. The two terms are folded into ONE contraction per core:
   stack ``[mu^(t), t * mu^(t-1)]`` on a jet-pair axis ``s`` and contract it together with the bond ``a``
   against ``[G.xi^(0), G.xi^(1)]`` (``'stWCa,sWCab->tWCb'``) -- one larger GEMM for XLA to
   schedule turns the two-einsum form's ~parity with the dense ``trs`` into a win. Equal to the dense
   :py:func:`compute_mu_jets_trs` to tolerance; see it for the binomial-tensor reference form.