utv_weighted_norm
=================

.. py:function:: t3toolbox.backend.utv_operations.utv_weighted_norm(variations, weights, n_stack)

   .. code-block:: python

      def utv_weighted_norm(
              variations: typ.Tuple,  # UT3Variations .data: (tkv, ttv, shape, masks), stack = K + C
              weights:    typ.Tuple,  # UT3FrameWeights .data: (up, down, left, right, masks), stack = C
              n_stack:    int,        # leading K+C stack axes to keep; 0 -> a single scalar
      ) -> NDArray:                   # weighted coordinate norm, shape = stack_shape[:n_stack]


   Weighted (Grasedyck-Kramer) coordinate norm of a uniform tangent's variations: absorb the metric
   into the variation supercores, then take the corewise stack-norm. Uniform twin of ``fv_weighted_norm``.

   The frame (orthonormal) is not needed and not touched, so this is O(ranks). The inserted diagonal is
   **squared** by the norm, so ``weights = 1/sigma`` penalises by ``1/sigma^2``. Like ``corewise_norm``
   this is the coordinate metric (= Hilbert-Schmidt only on an orthonormal, gauged frame) -- and note that
   absorbing weights **breaks the gauge**, so the HS reading does not survive the weighting.

   Weighting does not mask; the reduction does (``utv_corewise_inner`` masks its own input), so garbage
   padding is zeroed where the sum happens. **Precondition:** the weight's masks (broadcast over ``K``)
   must equal the variations' -- ``ufv_weights_consistent``; the frontend enforces it.

   Lives here, not in ``ufv_operations`` beside ``ufv_absorb_weights``, because the corewise reduction it
   needs is ``utv_corewise_inner`` and ``utv_operations`` already imports ``ufv_operations`` -- the other
   placement would be a circular import. (Ragged has no such constraint: its ``fv_weighted_norm`` reaches
   a standalone ``corewise`` module.)