fv_weights_from_t3_weights
==========================

.. py:function:: t3toolbox.backend.fv_operations.fv_weights_from_t3_weights(t3_weights)

   .. code-block:: python

      def fv_weights_from_t3_weights(
              t3_weights: typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # (tucker_weights, tt_weights)
      ) -> typ.Tuple[
          typ.Tuple[NDArray, ...],  # up_weights    = tucker_weights
          typ.Tuple[NDArray, ...],  # down_weights  = tucker_weights
          typ.Tuple[NDArray, ...],  # left_weights  = tt_weights[:-1]
          typ.Tuple[NDArray, ...],  # right_weights = tt_weights[1:]
      ]:


   Build frame weights (a tangent metric) from base-point edge weights ``(tucker_weights, tt_weights)``.

   ``up = down = tucker_weights``; ``left = tt_weights[:-1]``, ``right = tt_weights[1:]``. The TT slicing
   encodes the convention that ``H_i``'s left bond is TT bond ``i`` and its right bond is bond ``i+1`` --
   non-obvious, hence a named function. The result is a valid ``T3FrameWeights``; it pairs with a
   **minimal-rank** tangent (where the down/complement rank ``nD`` equals the Tucker rank ``nU``, e.g. from
   ``t3svd``). A non-minimal tangent has ``nD < nU`` and would mismatch the down family at use.