utv_weighted_inner
==================

.. py:function:: t3toolbox.backend.utv_operations.utv_weighted_inner(variations_a, variations_b, weights, n_stack)

   .. code-block:: python

      def utv_weighted_inner(
              variations_a: typ.Tuple,  # UT3Variations .data of A, stack = K + C
              variations_b: typ.Tuple,  # UT3Variations .data of B, stack = K + C (same frame as A)
              weights:      typ.Tuple,  # ONE metric: UT3FrameWeights .data, stack = C
              n_stack:      int,        # leading K+C stack axes to keep; 0 -> a single scalar
      ) -> NDArray:                     # weighted coordinate inner product, shape = stack_shape[:n_stack]


   Weighted coordinate inner product ``<absorb(W, A), absorb(W, B)>`` w.r.t. **one** metric -- absorb
   into both tangents' variations and dot. Uniform twin of ``fv_weighted_inner``. The caller checks
   same-frame; the frontend also checks the metric against the frame.