fv_weighted_inner
=================

.. py:function:: t3toolbox.backend.fv_operations.fv_weighted_inner(variations_A, variations_B, weights, n_stack)

   .. code-block:: python

      def fv_weighted_inner(
              variations_A: typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # (V, H) of A
              variations_B: typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # (V, H) of B
              weights:      typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray],
                                      typ.Sequence[NDArray], typ.Sequence[NDArray]],   # one metric (up, down, left, right)
              n_stack:      int,                                                       # leading K+C stack axes kept
      ) -> NDArray:                                                                    # weighted inner, shape=stack


   Weighted coordinate inner product ``<absorb(W,A), absorb(W,B)>`` w.r.t. one metric ``weights`` --
   the corewise stack-dot of the two weight-absorbed variations. The caller checks same-frame. Backend
   twin of ``T3Tangent.weighted_inner``.