UT3Frame
========

.. toctree::
   :hidden:

   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.data
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.d
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.N
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.nU
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.nD
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.rL
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.rR
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.stack_shape
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.uniform_structure
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.uniform_variation_shapes
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.up_ranks
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.down_ranks
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.left_ranks
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.right_ranks
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.structure
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.apply_masks
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.orthogonality_residual
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.is_orthogonal
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.minimal_ranks
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.has_minimal_ranks
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.has_numerically_minimal_ranks
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.is_consistent
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.allclose
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.from_t3frame
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.to_t3frame
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.from_ut3
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.to_ut3
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.to_dense
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.reverse
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.orthogonalize
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.random_orthogonal
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.random_orthogonal_like
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.save
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.load
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.supercores
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.contains_jax
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.to_jax
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.to_numpy
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.copy
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.__repr__
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.validate
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.__post_init__
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.unstack
   /autoapi/t3toolbox/uniform_frame_variations_format/UT3Frame.stack

.. py:class:: t3toolbox.uniform_frame_variations_format.UT3Frame

   Frame (orthogonal frame) for the frame-variations representation of uniform Tucker tensor trains.

   Uniform analog of :py:class:`~t3toolbox.frame_variations_format.T3Frame`: four padded supercores
   (``up_tucker``, ``down_tt``, ``left_tt``, ``right_tt``) + the static physical ``shape`` (an int tuple,
   shared across the stack) + a :py:class:`UT3FrameMasks` holder (the four per-stack rank masks).

   .. rubric:: Examples

   >>> import numpy as np
   >>> import t3toolbox.uniform_frame_variations_format as ubcf
   >>> d, N, nU, nD, rL, rR = 3, 6, 4, 5, 3, 2
   >>> up    = np.random.randn(d, nU, N)
   >>> down  = np.random.randn(d, rL, nD, rR)
   >>> left  = np.random.randn(d, rL, nU, rL)
   >>> right = np.random.randn(d, rR, nU, rR)
   >>> shape = (4, 5, 6)                                          # real mode dims (each <= N=6)
   >>> up_mask    = np.arange(nU) < np.array([[2],[3],[4]])       # (d, nU); per-mode up rank
   >>> down_mask  = np.arange(nD) < np.array([[3],[4],[5]])       # (d, nD)
   >>> left_mask  = np.arange(rL) < np.array([[1],[2],[3],[1]])   # (d+1, rL); boundary TT ranks
   >>> right_mask = np.arange(rR) < np.array([[1],[2],[2],[1]])   # (d+1, rR)
   >>> masks = ubcf.UT3FrameMasks(up_mask, down_mask, left_mask, right_mask)
   >>> B = ubcf.UT3Frame(up, down, left, right, shape, masks)
   >>> B.shape
   (4, 5, 6)
   >>> np.asarray(B.up_ranks).tolist()
   [2, 3, 4]
   >>> B.stack_shape
   ()


   .. py:attribute:: up_tucker_supercore
      :type:  t3toolbox.backend.common.NDArray


   .. py:attribute:: down_tt_supercore
      :type:  t3toolbox.backend.common.NDArray


   .. py:attribute:: left_tt_supercore
      :type:  t3toolbox.backend.common.NDArray


   .. py:attribute:: right_tt_supercore
      :type:  t3toolbox.backend.common.NDArray


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


   .. py:attribute:: masks
      :type:  UT3FrameMasks

Methods
-------

.. autoapisummary::

   t3toolbox.uniform_frame_variations_format.UT3Frame.data
   t3toolbox.uniform_frame_variations_format.UT3Frame.d
   t3toolbox.uniform_frame_variations_format.UT3Frame.N
   t3toolbox.uniform_frame_variations_format.UT3Frame.nU
   t3toolbox.uniform_frame_variations_format.UT3Frame.nD
   t3toolbox.uniform_frame_variations_format.UT3Frame.rL
   t3toolbox.uniform_frame_variations_format.UT3Frame.rR
   t3toolbox.uniform_frame_variations_format.UT3Frame.stack_shape
   t3toolbox.uniform_frame_variations_format.UT3Frame.uniform_structure
   t3toolbox.uniform_frame_variations_format.UT3Frame.uniform_variation_shapes
   t3toolbox.uniform_frame_variations_format.UT3Frame.up_ranks
   t3toolbox.uniform_frame_variations_format.UT3Frame.down_ranks
   t3toolbox.uniform_frame_variations_format.UT3Frame.left_ranks
   t3toolbox.uniform_frame_variations_format.UT3Frame.right_ranks
   t3toolbox.uniform_frame_variations_format.UT3Frame.structure
   t3toolbox.uniform_frame_variations_format.UT3Frame.apply_masks
   t3toolbox.uniform_frame_variations_format.UT3Frame.orthogonality_residual
   t3toolbox.uniform_frame_variations_format.UT3Frame.is_orthogonal
   t3toolbox.uniform_frame_variations_format.UT3Frame.minimal_ranks
   t3toolbox.uniform_frame_variations_format.UT3Frame.has_minimal_ranks
   t3toolbox.uniform_frame_variations_format.UT3Frame.has_numerically_minimal_ranks
   t3toolbox.uniform_frame_variations_format.UT3Frame.is_consistent
   t3toolbox.uniform_frame_variations_format.UT3Frame.allclose
   t3toolbox.uniform_frame_variations_format.UT3Frame.from_t3frame
   t3toolbox.uniform_frame_variations_format.UT3Frame.to_t3frame
   t3toolbox.uniform_frame_variations_format.UT3Frame.from_ut3
   t3toolbox.uniform_frame_variations_format.UT3Frame.to_ut3
   t3toolbox.uniform_frame_variations_format.UT3Frame.to_dense
   t3toolbox.uniform_frame_variations_format.UT3Frame.reverse
   t3toolbox.uniform_frame_variations_format.UT3Frame.orthogonalize
   t3toolbox.uniform_frame_variations_format.UT3Frame.random_orthogonal
   t3toolbox.uniform_frame_variations_format.UT3Frame.random_orthogonal_like
   t3toolbox.uniform_frame_variations_format.UT3Frame.save
   t3toolbox.uniform_frame_variations_format.UT3Frame.load
   t3toolbox.uniform_frame_variations_format.UT3Frame.supercores
   t3toolbox.uniform_frame_variations_format.UT3Frame.contains_jax
   t3toolbox.uniform_frame_variations_format.UT3Frame.to_jax
   t3toolbox.uniform_frame_variations_format.UT3Frame.to_numpy
   t3toolbox.uniform_frame_variations_format.UT3Frame.copy
   t3toolbox.uniform_frame_variations_format.UT3Frame.__repr__
   t3toolbox.uniform_frame_variations_format.UT3Frame.validate
   t3toolbox.uniform_frame_variations_format.UT3Frame.__post_init__
   t3toolbox.uniform_frame_variations_format.UT3Frame.unstack
   t3toolbox.uniform_frame_variations_format.UT3Frame.stack