regpy.functionals.ngsolve
=========================

.. py:module:: regpy.functionals.ngsolve

.. autoapi-nested-parse::

   Special NGSolve functionals defined on the `regpy.vecsps.ngsolve.NgsSpace`.



Classes
-------

.. autoapisummary::

   regpy.functionals.ngsolve.NgsL1
   regpy.functionals.ngsolve.NgsTV


Functions
---------

.. autoapisummary::

   regpy.functionals.ngsolve.ngsdivergence


Module Contents
---------------

.. py:class:: NgsL1(domain)

   Bases: :py:obj:`regpy.functionals.Functional`


   Implementation of the :math:`L^1`-norm on a given `NgsSpace`. It is registered under the
   Abstract functional `L1` and should not be called directly but rather used by defining the
   abstract `L1` functional as the `penalty` or `data_fid` when initializing the regularization
   setting by calling `regpy.solvers.RegularizationSetting`.

   :param domain: The underlying `ngsolve` space.
   :type domain: NgsSpace


.. py:class:: NgsTV(domain, h_domain=L2)

   Bases: :py:obj:`regpy.functionals.Functional`


   Implementation of the total variation functional :math:`TV` on a given `NgsSpace`. It is
   registered under the Abstract functional `TV` and should not be called directly but rather
   used by defining the abstract `TV` functional as the `penalty` or `data_fid` when initializing
   the regularization setting by calling `regpy.solvers.RegularizationSetting`.

   :param domain: The underlying `ngsolve` space.
   :type domain: NgsSpace
   :param h_domain: The Hilbert space wrt which the proximal gets computed.
   :type h_domain: HilbertSpace


.. py:function:: ngsdivergence(p, fes)

   Computes the divergence of a vector field 'p' on a FES 'fes'. gradp is a list of ngsolve CoefficientFunctions
   p=(p_x, p_y, p_z, ...). The return value is the coefficient array of the GridFunction holding the divergence.

   :param p: Vector field on a FES 'fes' for which to compute the divergence.
   :type p: vector field
   :param fes: Underlying FES.
   :type fes: ngsolve fes

   :returns: Values of the divergence of the given vector `p`
   :rtype: array