Problem
=======

.. toctree::
   :hidden:

   /autoapi/t3toolbox/backend/optimizers/Problem.local_model
   /autoapi/t3toolbox/backend/optimizers/Problem.objective

.. py:class:: t3toolbox.backend.optimizers.Problem

   A fixed-rank least-squares fitting problem ``min_x ½‖S(x) - data‖²`` for a sampling op ``S`` on
   geometry ``geom``. **Layout-agnostic**: it holds the operator (``kind``), the geometry, and the FULL
   ``(sample, data)``. ``local_model`` / ``objective`` linearize / evaluate at a point on the full data,
   or on an explicitly-passed minibatch ``(sample, data)`` (e.g. from a ``draw``). The ``Problem`` itself
   owns **no** minibatch-layout logic -- where the sample stack ``W`` lives, how to slice it -- that is
   the ``kind``'s (``kind.take`` for the default flat draw) or the user's ``draw``.


   .. py:attribute:: geom
      :type:  GeometryOps


   .. py:attribute:: kind
      :type:  t3toolbox.backend.common.typ.Any


   .. py:attribute:: sample
      :type:  t3toolbox.backend.common.typ.Any


   .. py:attribute:: data
      :type:  t3toolbox.backend.common.typ.Any


   .. py:attribute:: regularizer
      :type:  t3toolbox.backend.common.typ.Any
      :value: None


Methods
-------

.. autoapisummary::

   t3toolbox.backend.optimizers.Problem.local_model
   t3toolbox.backend.optimizers.Problem.objective