compute_deta_tilde
==================

.. py:function:: t3toolbox.backend.probing.compute_deta_tilde(up_tucker_cores, ztildes)

   .. code-block:: python

      def compute_deta_tilde(
              up_tucker_cores:    typ.Union[typ.Sequence[NDArray], NDArray],  # len=d, elm_shape=(nUi,Ni)
              ztildes:            typ.Union[typ.Sequence[NDArray], NDArray],  # len=d, elm_shape=(...,Ni)
      ) -> typ.Union[typ.Sequence[NDArray], NDArray]: # len=d, elm_shape=(...,nUi)


   Adjoint-var-upward edge variables deta_tilde.
   Used for computing the transpose of the map from a tangent vector to its probes.

   See Section 6.2.3, particularly Algorithm 8, in:
       Alger, N., Christierson, B., Chen, P., & Ghattas, O. (2026).
       "Tucker Tensor Train Taylor Series."
       arXiv preprint arXiv:2603.21141.
       `https://arxiv.org/abs/2603.21141 <https://arxiv.org/abs/2603.21141>`_