CorewiseGeometryOps
===================

.. toctree::
   :hidden:

   /autoapi/t3toolbox/backend/geometry/CorewiseGeometryOps.with_sharing
   /autoapi/t3toolbox/backend/geometry/CorewiseGeometryOps.frame
   /autoapi/t3toolbox/backend/geometry/CorewiseGeometryOps.stack_shape
   /autoapi/t3toolbox/backend/geometry/CorewiseGeometryOps.base_point
   /autoapi/t3toolbox/backend/geometry/CorewiseGeometryOps.precompute
   /autoapi/t3toolbox/backend/geometry/CorewiseGeometryOps.project
   /autoapi/t3toolbox/backend/geometry/CorewiseGeometryOps.retract
   /autoapi/t3toolbox/backend/geometry/CorewiseGeometryOps.inner
   /autoapi/t3toolbox/backend/geometry/CorewiseGeometryOps.point_norm_sq
   /autoapi/t3toolbox/backend/geometry/CorewiseGeometryOps.point_tangent

.. py:class:: t3toolbox.backend.geometry.CorewiseGeometryOps

   Bases: :py:obj:`t3toolbox.backend.common.ValueHashedFields`


   The core-parameter Euclidean geometry on raw ``(tucker_cores, tt_cores)`` data -- the check-free
   twin of :py:data:`t3toolbox.manifold.COREWISE`.

   The raw cores ARE the frame (the Section 6.3 substitution ``(P, Q, O) -> G``), there is no gauge, and
   the retraction is additive (``cores += variations``). With a non-empty ``groups`` the projection is
   the per-group arithmetic mean (the corewise coordinates are raw factor copies, so that IS the
   orthogonal projection onto the tied subspace) and the additive retraction preserves tying exactly, so
   ``retract`` only mean-ties its input first -- a bitwise no-op on already-tied input.

   Secondary to the manifold geometry: its Gauss-Newton Hessian is gauge-singular, which first-order and
   quasi-Newton methods tolerate but Newton must truncate around.


   .. py:attribute:: groups
      :type:  t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Tuple[int, ...], ...]
      :value: ()


Methods
-------

.. autoapisummary::

   t3toolbox.backend.geometry.CorewiseGeometryOps.with_sharing
   t3toolbox.backend.geometry.CorewiseGeometryOps.frame
   t3toolbox.backend.geometry.CorewiseGeometryOps.stack_shape
   t3toolbox.backend.geometry.CorewiseGeometryOps.base_point
   t3toolbox.backend.geometry.CorewiseGeometryOps.precompute
   t3toolbox.backend.geometry.CorewiseGeometryOps.project
   t3toolbox.backend.geometry.CorewiseGeometryOps.retract
   t3toolbox.backend.geometry.CorewiseGeometryOps.inner
   t3toolbox.backend.geometry.CorewiseGeometryOps.point_norm_sq
   t3toolbox.backend.geometry.CorewiseGeometryOps.point_tangent