gauss_newton_cg
=========================

.. py:module:: jaxns.experimental.solvers.gauss_newton_cg

.. rubric:: :code:`jaxns.experimental.solvers.gauss_newton_cg`


.. rubric:: Module Contents

.. py:data:: DomainType

.. py:data:: ObjectiveRet

.. py:data:: CT

.. py:function:: convert_to_real(x)

   Return a real-valued twin of `x`   and   a merge-back function.


.. py:class:: NewtonDiagnostic

   Bases: :py:obj:`NamedTuple`


   .. py:attribute:: iteration
      :type:  jaxns.internals.types.IntArray


   .. py:attribute:: g_norm
      :type:  jaxns.internals.types.FloatArray


   .. py:attribute:: mu
      :type:  jaxns.internals.types.FloatArray


   .. py:attribute:: damping
      :type:  jaxns.internals.types.FloatArray


   .. py:attribute:: cg_iters
      :type:  jaxns.internals.types.IntArray


   .. py:attribute:: f
      :type:  jaxns.internals.types.FloatArray


   .. py:attribute:: f_prop
      :type:  jaxns.internals.types.FloatArray


   .. py:attribute:: f_quad
      :type:  jaxns.internals.types.FloatArray


   .. py:attribute:: delta_f_pred
      :type:  jaxns.internals.types.FloatArray


   .. py:attribute:: delta_f_actual
      :type:  jaxns.internals.types.FloatArray


   .. py:attribute:: gain_ratio
      :type:  jaxns.internals.types.FloatArray


   .. py:attribute:: accepted
      :type:  jaxns.internals.types.BoolArray


   .. py:attribute:: in_trust_region
      :type:  jaxns.internals.types.BoolArray


   .. py:attribute:: delta_x_norm
      :type:  jaxns.internals.types.FloatArray


   .. py:attribute:: ddelta_x_norm
      :type:  jaxns.internals.types.FloatArray


.. py:function:: newton_cg_solver(obj_fn, x0, args = (), maxiter = 100, maxiter_cg = 100, gtol = 3e-05, p_accept = 0.01, p_lower = 0.25, p_upper = 1.1, mu_init = 1.0, mu_min = 1e-06, mu_in_factor = 5, mu_out_factor = 0.1, approx_hvp = False, verbose = False)

   Trust-region Newton-CG minimiser.

   Identical call signature and adaptive-μ logic as `lm_solver`, but uses a
   scalar objective instead of residuals, and solves
       (H  +  damping·I) δx = -∇f
   by CG with Hessian–vector products.

   :returns: * **x_final** (pytree matching `x0`     (merged back to complex if needed))
             * **diagnostics** (NewtonDiagnostic[...] array with length = `maxiter`)