edge_condition_numbers
======================

.. py:function:: t3toolbox.backend.ranks.edge_condition_numbers(tucker_singular_values, tt_singular_values)

   .. code-block:: python

      def edge_condition_numbers(
              tucker_singular_values: typ.Sequence[NDArray],  # len=d,   elm_shape=(n_i,), descending
              tt_singular_values:     typ.Sequence[NDArray],  # len=d+1, elm_shape=(r_i,), descending
      ) -> typ.Tuple[
          typ.Tuple[float, ...],  # len=d,   Tucker edge condition numbers (kappa^Tucker)
          typ.Tuple[float, ...],  # len=d+1, TT edge condition numbers (kappa^TT); length-1 boundary bonds = 1.0
      ]:


   Edge condition numbers ``kappa_i = sigma_{i,1} / sigma_{i,r_i}`` of the matrix unfoldings.

   Section 5.4.1 of Alger et al. (2026), "Tucker Tensor Train Taylor Series" (arXiv:2603.21141): the
   ratio of the largest to the smallest *retained* singular value on each Tucker matricization and each
   TT unfolding, as returned by the implicit T3-SVD (:py:meth:`TuckerTensorTrain.t3svd`). The two
   length-1 boundary TT bonds give ``1.0``. Degenerate-edge conventions keep the value defined on any
   iterate (including the zero tensor): an all-zero edge -> ``1.0``; a rank-deficient edge -> ``+inf``.