ut3_pad_ranks
=============

.. py:function:: t3toolbox.backend.ut3_operations.ut3_pad_ranks(data, n, r)

   .. code-block:: python

      def ut3_pad_ranks(
              data: UT3Data,
              n:    int,          # target padded Tucker rank (>= the current padded n)
              r:    int,          # target padded TT rank    (>= the current padded r)
      ) -> UT3Data:               # the same tensor, ranks and masks, stored at padded dims (n, r)


   Zero-pad the rank dims of a uniform T3 to ``(n, r)`` -- the storage changes, the represented tensor,
   the ranks and the mask CONTENT do not (the new slots are padding: mask False, value 0). The inverse of
   the pad-shrinking ``ut3svd`` does (which slices to the max rank it kept); ``utv_retract`` uses it to
   return a point at the frame's padded dims, so the optimizers' loop-invariant masks stay valid.