regularization
==============


.. py:module:: t3toolbox.backend.regularization

.. autoapi-nested-parse::

   Backend regularization terms for the fitting objective ``min_x ½‖ω⊙(S(x)−y)‖² + ρ(x)``.

   A ``Regularizer`` is an additive objective term ``ρ(X)`` folded into the local Gauss-Newton model
   (:py:class:`t3toolbox.backend.optimizers.LocalModel`) and ``Problem.objective``, so it composes with
   **every** optimizer, sampling kind, geometry, and representation with no changes to any of them. This
   layer is **check-free** -- a raw-``.data`` user constructs and attaches a regularizer directly, exactly as
   a frontend user does (design record + the razor check: ``dev/regularization_design.md`` §5a).

   The interface is **geometry-agnostic**: each method receives a ``GeometryOps`` and leans only on its
   primitives (``point_norm_sq`` / ``point_tangent`` / ``project`` / ``inner``), so the SAME regularizer
   works on manifold or corewise. Extending to a new regularizer (e.g. the Grasedyck-Kramer inverse-unfolding
   -singular-value weighting) is a new subclass with the same four methods -- ``Problem`` / ``LocalModel`` /
   the optimizers are untouched.



Classes
-------

.. toctree::
   :hidden:

   /autoapi/t3toolbox/backend/regularization/Regularizer
   /autoapi/t3toolbox/backend/regularization/IdentityRegularizer

.. autoapisummary::

   t3toolbox.backend.regularization.Regularizer
   t3toolbox.backend.regularization.IdentityRegularizer