UT3Tangent.apply_transpose
==========================

.. py:method:: t3toolbox.uniform_manifold.UT3Tangent.apply_transpose(c, ww, frame, sum_over_probes = False)
   :staticmethod:


   .. code-block:: python

      def apply_transpose(
              c,                         # residual, shape=W+K+C (a scalar per stack element)
              ww,                        # apply vectors, len=d, ith elm_shape=W+(Ni,)
              frame:  ubv.UT3Frame,
              sum_over_probes:  bool = False,
      ) -> 'UT3Tangent':  # tangent stack W+K (sum_over_probes=False) or K (True); frame stack C


   Apply the transpose ``𝒥ᵀ`` of :py:meth:`apply` -- back-project a residual ``c`` into a tangent
   at ``frame``. The adjoint of :py:meth:`apply`. Uniform mirror of
   :py:meth:`~t3toolbox.manifold.T3Tangent.apply_transpose`; ``sum_over_probes`` as in
   :py:meth:`probe_transpose`. The bare ``𝒥ᵀ`` (no gauge projector ``Π``).