compute_sigma
=============

.. py:function:: t3toolbox.backend.probing.compute_sigma(var_tt_cores, right_tt_cores, down_tt_cores, xis, dxis, mus)

   .. code-block:: python

      def compute_sigma(
              var_tt_cores:       typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(rLi,nUi,rR(i+1))
              right_tt_cores:     typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(rRi,nUi,rR(i+1))
              down_tt_cores:     typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(rLi,nOi,rR(i+1))
              xis:                typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,nUi),
              dxis:               typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,nOi)
              mus:                typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,rLi)
      ) -> typ.Union[typ.Sequence[NDArray], NDArray]: # sigmas. len=d, elm_shape=(...,rR(i+1))


   Compute var-leftward edge variables sigma.
   Used for probing a tangent vector.

   See Section 6.2.2, particularly Algorithm 7, 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>`_

   .. seealso:: :py:obj:`compute_dxi`, :py:obj:`compute_tau`, :py:obj:`compute_deta`, :py:obj:`assemble_tangent_z`, :py:obj:`tv_probe`