tv_project_t3_onto_tangent_space
================================

.. py:function:: t3toolbox.backend.tv_operations.tv_project_t3_onto_tangent_space(frame, x)

   .. code-block:: python

      def tv_project_t3_onto_tangent_space(
              frame:      typ.Tuple[
                  typ.Sequence[NDArray],  # up_tucker_cores
                  typ.Sequence[NDArray],  # down_tt_cores
                  typ.Sequence[NDArray],  # left_tt_cores
                  typ.Sequence[NDArray],  # right_tt_cores
              ],
              x:          typ.Tuple[
                  typ.Sequence[NDArray],  # tucker_cores
                  typ.Sequence[NDArray],  # tt_cores
              ],
      ) -> typ.Tuple[
          typ.Tuple[NDArray, ...],  # gauged tucker_variations
          typ.Tuple[NDArray, ...],  # gauged tt_variations
      ]:


   Orthogonal projection of a Tucker tensor train onto the tangent space at an orthogonal frame.

   Returns gauged variations representing the orthogonal projection of ``x`` *directly* onto the
   tangent space (a linear subspace); it does not subtract the base point. The frame must be an
   orthogonal representation (minimal rank is *not* required). Stack-aware. Ragged path only (uniform
   deferred).