t3variations_to_ut3variations
=============================

.. py:function:: t3toolbox.backend.ufv_conversions.t3variations_to_ut3variations(variations_data, N = None, nU = None, nD = None, rL = None, rR = None)

   .. code-block:: python

      def t3variations_to_ut3variations(
              variations_data: typ.Tuple[
                  typ.Tuple[NDArray, ...],  # tucker_variations, len=d, elm_shape=C+(nDi, Ni)
                  typ.Tuple[NDArray, ...],  # tt_variations,     len=d, elm_shape=C+(rLi, nUi, rR(i+1))
              ],
              N:  typ.Optional[int] = None,   # padded mode dim   (default max(shape))
              nU: typ.Optional[int] = None,   # padded up rank    (default max(up_ranks))
              nD: typ.Optional[int] = None,   # padded down rank  (default max(down_ranks))
              rL: typ.Optional[int] = None,   # padded left rank  (default max(left_ranks))
              rR: typ.Optional[int] = None,   # padded right rank (default max(right_ranks))
      ) -> typ.Tuple[
          NDArray,                          # tucker_variations supercore, (d,)+C+(nD, N)
          NDArray,                          # tt_variations supercore,     (d,)+C+(rL, nU, rR)
          typ.Tuple[int, ...],              # shape
          typ.Tuple[NDArray, NDArray, NDArray, NDArray],  # (variations up, down, left, right) masks, all (d,)-leading
      ]:


   Pack a ragged ``T3Variations`` core-tuple into uniform variation ``.data``.

   Inverse of :py:func:`ut3variations_to_t3variations`. The variation masks are all ``(d,)``-leading (a
   variation occupies one TT slot, not a boundary edge), so the left/right ranks are the per-slot bonds
   ``rLi`` / ``rR(i+1)`` -- NOT a ``(d+1,)`` edge sequence. ``ufv_make_frame_masks`` builds the prefix masks
   from whatever leading shape its rank args carry, so it serves here too.