t3_weighted_norm
================

.. py:function:: t3toolbox.backend.t3_linalg.t3_weighted_norm(x0, weights, use_orthogonalization = True)

   .. code-block:: python

      def t3_weighted_norm(
              x0:      typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # (tucker_cores, tt_cores)
              weights: typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # (tucker_weights, tt_weights)
              use_orthogonalization: bool = True,                                # for numerical stability
      ) -> NDArray:                                                              # weighted HS norm, shape=stack_shape


   Weighted Hilbert-Schmidt norm of a Tucker tensor train: ``t3_norm(absorb(x0, weights))`` -- the norm
   of the fully-weighted network. The plain norm squares the inserted diagonals (so ``diag(1/sigma)``
   penalises by ``1/sigma^2``).