GaussNewtonModel.jacobian
=========================

.. py:method:: t3toolbox.fitting.GaussNewtonModel.jacobian(p)

   .. code-block:: python

      def jacobian(
              self,
              p:  t3m.T3Tangent,
      ) -> NDArray:  # J p = 𝒥(Π p); apply/entries: shape W+C; probe: len=d, elm_shape=W+C+(Ni,)


   The linearized forward ``J p = 𝒥(Π p)`` (the Gauss-Newton Jacobian-vector product).

   ONE forward sweep -- no transpose ``𝒥ᵀ``, no gauge re-projection of the output, no tangent
   assembly. The general forward primitive: it gives the predicted residual ``r + J p`` (for
   trust-region / line-search predicted reduction) and, via :py:meth:`gn_quadratic`, the Gauss-Newton
   quadratic form. The result lives in the sample space (a scalar per sample for apply / entries; one
   vector per mode for probe).