UniformManifoldGeometryOps
==========================

.. toctree::
   :hidden:

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

.. py:class:: t3toolbox.backend.geometry.UniformManifoldGeometryOps

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


   The uniform **manifold** geometry at a fixed rank -- the raw-supercore twin of
   :py:data:`t3toolbox.uniform_manifold.UNIFORM_MANIFOLD`.

   The uniform layer's optimizer state is a bare ``(tucker_supercore, tt_supercore)`` pair, so the rank
   structure the operations need -- the mode ``shape``, the plain-UT3 ``masks``, and the variation
   ``var_masks`` -- lives here instead, loop-invariant and value-hashed
   (``docs/uniform_backend_jit_recipe.md``: hold the masks as state, trace only the supercores). Build
   it from the point you are about to optimize with :py:meth:`from_point`.

   The uniform layer requires a **minimal-rank** start (:py:func:`~t3toolbox.backend.uniform_fitting.uniform_minimal`):
   from a non-minimal frame the retraction truncates to the realizable rank, which no longer matches the
   fixed masks held here.


   .. py:attribute:: shape
      :type:  t3toolbox.backend.common.typ.Tuple[int, ...]


   .. py:attribute:: masks
      :type:  t3toolbox.backend.common.typ.Tuple


   .. py:attribute:: var_masks
      :type:  t3toolbox.backend.common.typ.Tuple


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



   .. py:property:: n_stack
      :type: int


      ``|C|``, the frame stack rank (0 for a single tensor). The tucker edge mask is
      ``(d,) + C + (n,)``, so the stack is everything between.

Methods
-------

.. autoapisummary::

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