T3Tangent.weighted_norm
=======================

.. py:method:: t3toolbox.manifold.T3Tangent.weighted_norm(weights)

   .. code-block:: python

      def weighted_norm(self, weights: 'bvf.T3FrameWeights'):


   The **weighted** (Grasedyck-Kramer) coordinate norm: absorb the metric ``weights`` into the
   variation cores (``down``->V, ``up``/``left``/``right``->H) and take the coordinate norm. The frame
   stays orthonormal (untouched). Vectorized over the stack (returns shape ``K + C``). The inserted
   diagonal is squared by the norm, so ``weights = 1/sigma`` penalises by ``1/sigma^2``. As with
   :py:meth:`corewise_norm`, this is the coordinate metric (= HS on an orthonormal, gauged frame).
   ``weights`` is frame-like: its stack must equal the frame's ``C`` (checked --
   :py:func:`~t3toolbox.frame_variations_format.check_fw_pair`), and it broadcasts over ``K``.
   Backend twin: :py:func:`~t3toolbox.backend.fv_operations.fv_weighted_norm`.