t3_weighted_inner
=================

.. py:function:: t3toolbox.backend.t3_linalg.t3_weighted_inner(x0_A, weights_A, x0_B, weights_B, use_orthogonalization = True)

   .. code-block:: python

      def t3_weighted_inner(
              x0_A:      typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # (tucker_cores, tt_cores) of A
              weights_A: typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # weights of A
              x0_B:      typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # (tucker_cores, tt_cores) of B
              weights_B: typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # weights of B
              use_orthogonalization: bool = True,                                  # for numerical stability
      ) -> NDArray:                                                                # weighted HS inner, shape=stack_shape


   Weighted Hilbert-Schmidt inner product ``<absorb(A), absorb(B)>`` of two weighted Tucker tensor
   trains. A and B must share physical shape (same ambient space); ranks/weights may differ.