ut3_norm
========

.. py:function:: t3toolbox.backend.ut3_linalg.ut3_norm(x, use_orthogonalization = True)

   .. code-block:: python

      def ut3_norm(
              x:  UT3Data,                                  # (tucker_supercore, tt_supercore, shape, masks)
              use_orthogonalization: bool = True,           # True (default): orthogonalize first -- the stable path
      ) -> NDArray:                                         # HS norm ‖T(x)‖, shape=stack_shape


   Hilbert-Schmidt norm of a uniform Tucker tensor train -- the twin of the ragged ``t3_norm``.
   ``use_orthogonalization=True`` (default) left-orthogonalizes first and reads the last core's norm
   (numerically stable; the zipper alternative accumulates roundoff along the chain); its jax derivative is
   the exact multilinear rule above, so ``jax.grad`` through it is finite on any padded train.
   ``False`` is the raw zipper ``sqrt(<x, x>)`` (cheaper, less stable; differentiable by plain autodiff).