ut3_weighted_inner
==================

.. py:function:: t3toolbox.backend.ut3_linalg.ut3_weighted_inner(x_A, weights_A, x_B, weights_B, use_orthogonalization = True)

   .. code-block:: python

      def ut3_weighted_inner(
              x_A:       UT3Data,                        # (tucker_supercore, tt_supercore, shape, masks) of A
              weights_A: ut3_operations.UT3WeightsData,  # weights of A
              x_B:       UT3Data,                        # (tucker_supercore, tt_supercore, shape, masks) of B
              weights_B: ut3_operations.UT3WeightsData,  # weights of B
              use_orthogonalization: bool = True,        # for numerical stability
      ) -> NDArray:                                      # weighted HS inner, shape=stack_shape


   Weighted Hilbert-Schmidt inner product ``<absorb(A, weights_A), absorb(B, weights_B)>`` of two
   weighted uniform Tucker tensor trains. Uniform twin of ``t3_weighted_inner``.

   A and B must share physical ``shape`` (the same ambient space); their ranks, masks and weights may
   differ from each other. Each operand's weights must match *its own* object's masks
   (:py:func:`~t3toolbox.backend.ut3_operations.ut3_weights_consistent`); the frontend enforces it.