compute_deta_jets
=================

.. py:function:: t3toolbox.backend.sampling_derivatives.compute_deta_jets(var_tt_cores, left_tt_cores, right_tt_cores, mu_jets, nu_jets, sigma_jets, tau_jets, trs)

   .. code-block:: python

      def compute_deta_jets(
              var_tt_cores:   typ.Sequence[NDArray],  # dG. len=d, elm_shape=K+C+(rLi,nUi,rR(i+1))
              left_tt_cores:  typ.Sequence[NDArray],  # P.  len=d, elm_shape=C+(rLi,nUi,rL(i+1))
              right_tt_cores: typ.Sequence[NDArray],  # Q.  len=d, elm_shape=C+(rRi,nUi,rR(i+1))
              mu_jets:        typ.Sequence[NDArray],  # len=d, elm_shape=(order+1,)+W+C+(rLi,)
              nu_jets:        typ.Sequence[NDArray],  # len=d, elm_shape=(order+1,)+W+C+(rR(i+1),)
              sigma_jets:     typ.Sequence[NDArray],  # len=d, elm_shape=(order+1,)+W+K+C+(rR(i+1),)
              tau_jets:       typ.Sequence[NDArray],  # len=d, elm_shape=(order+1,)+W+K+C+(rL(i+1),)
              trs:            NDArray,                # binomial tensor, shape=(order+1,order+1,order+1)
      ) -> typ.Tuple[NDArray, ...]:                   # deta_jets. len=d, elm_shape=(order+1,)+W+K+C+(nUi,)


   Tangent combine at each free mode (standard order-scan form).

   Dense reference: :py:func:`compute_deta_jets_trs` (equal to tolerance).

   The three-term tangent analog of :py:func:`compute_eta_jets`: ``deta_i = sigma Q nu +
   mu dG nu + mu P tau``, three FULL convolutions (mode ``i`` free). The dense uniform d-einsum forms
   the ``(order+1)*W*K*r^2`` spatial product for every core at once; this scans the input order ``r``
   (one order slice of ``jetL . core`` live at a time) and folds in all of the right jet + the
   binomial weights -- peak ``W*K*r^2``. The K tangent stack sits on a *different* operand in each
   term (sigma / dG / tau), so several of the grouped contractions need ``len_C`` (the W|C split
   is not pinned by their operands). Memory win needs
   the uniform path (real ``lax.map``/``lax.scan``); see :py:func:`compute_eta_jets`. Verified
   equal to :py:func:`compute_deta_jets_trs` to 1e-12.