tv_gauge_residual
=================

.. py:function:: t3toolbox.backend.tv_operations.tv_gauge_residual(frame, variations)

   .. code-block:: python

      def tv_gauge_residual(
              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
              ],
              variations: typ.Tuple[
                  typ.Sequence[NDArray],  # tucker_variations
                  typ.Sequence[NDArray],  # tt_variations
              ],
      ) -> NDArray:  # shape = variation stack_shape (K+C); per stack element (scalar/0-d when unstacked)


   Max violation of the gauge conditions for a tangent vector, **per stack element**.

   The gauged tangent space requires each tucker variation orthogonal to its up-core, and each
   left-interior tt variation orthogonal to its left-core (see :py:func:`tv_orthogonal_gauge_projection`).
   Returns the max absolute gauge inner product reduced over the **non-stack** axes (shape = the variation
   stack ``K+C``); a caller thresholds it (``<= atol``).