shared_geometry
===============


.. py:module:: t3toolbox.shared_geometry

.. autoapi-nested-parse::

   The shared-Tucker-factors (SF-T3) geometry wrapper: ``shared(base, sharing)``.

   Wraps :py:data:`~t3toolbox.manifold.MANIFOLD` / :py:data:`~t3toolbox.manifold.COREWISE` (or their
   uniform twins :py:data:`~t3toolbox.uniform_manifold.UNIFORM_MANIFOLD` /
   :py:data:`~t3toolbox.uniform_manifold.UNIFORM_COREWISE`) so every
   projection lands on the TIED tangent subspace (one Tucker factor per sharing group) and the
   retraction stays on the shared set. One principle, two formulas -- each geometry ties by
   orthogonal projection onto ITS tied subspace in ITS metric on ITS coordinates: the manifold
   geometry's gauged coordinates carry the frame's ``S`` factors, so its post-pass is the
   Gram-weighted (SVD-solved) tilted projection; the corewise coordinates are raw factor copies, so
   its post-pass is the per-group arithmetic mean. Optimizers consume a shared geometry exactly like
   a base one (``t3t.newton_cg(shared_manifold(sharing), 'apply', ww, b, x0)``).



Classes
-------

.. toctree::
   :hidden:

   /autoapi/t3toolbox/shared_geometry/SharedGeometry

.. autoapisummary::

   t3toolbox.shared_geometry.SharedGeometry


Functions
---------

.. toctree::
   :hidden:

   /autoapi/t3toolbox/shared_geometry/shared
   /autoapi/t3toolbox/shared_geometry/shared_manifold
   /autoapi/t3toolbox/shared_geometry/shared_corewise

.. autoapisummary::

   t3toolbox.shared_geometry.shared
   t3toolbox.shared_geometry.shared_manifold
   t3toolbox.shared_geometry.shared_corewise