ut3_inner
=========

.. py:function:: t3toolbox.backend.ut3_linalg.ut3_inner(x, y, use_orthogonalization = True)

   .. code-block:: python

      def ut3_inner(
              x:  UT3Data,                                  # (tucker_supercore, tt_supercore, shape, masks)
              y:  UT3Data,                                  # same physical shape; ranks/masks/padding may differ
              use_orthogonalization: bool = True,           # True (default): orthogonalize both first (stable)
      ) -> NDArray:                                         # HS inner product <T(x), T(y)>, shape=stack_shape


   Hilbert-Schmidt inner product of two uniform Tucker tensor trains -- the twin of the ragged
   ``t3_inner_product``. See :py:func:`ut3_norm` for the orthogonalization / autodiff story.