GaussNewtonModel.gn_quadratic
=============================

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

   .. code-block:: python

      def gn_quadratic(
              self,
              p:  t3m.T3Tangent,
      ) -> NDArray:  # pᵀ H p = ‖J p‖², shape C


   The Gauss-Newton quadratic form ``pᵀ H p = ‖J p‖²`` -- ONE forward sweep, NOT a Hessian apply.

   The cheap denominator for Cauchy / line-search step lengths: ``alpha = g.corewise_inner(g) /
   model.gn_quadratic(g)``. Because ``H = JᵀJ``, ``pᵀHp = (Jp)ᵀ(Jp) = ‖Jp‖²``, so this needs only the
   forward :py:meth:`jacobian` -- it avoids the transpose ``𝒥ᵀ`` and the ``H p`` tangent
   materialization that the equivalent ``p.corewise_inner(self.gn_hessian(p))`` would incur. When a
   ``regularizer`` is set this adds its ``⟨p, H_R p⟩`` term, consistent with :py:meth:`gn_hessian`.