t3toolbox.tucker_tensor_train
=============================

.. py:module:: t3toolbox.tucker_tensor_train

.. autoapi-nested-parse::

   This module contains type aliases and basic backend for Tucker tensor trains.

   Tucker tensor trains:
   ---------------------

   * :py:type:`TuckerTensorTrain`
       | The cores of a Tucker tensor train with varied ranks
       | (tucker_cores, tt_cores)

   * :py:type:`T3Structure`
       | The structure of a Tucker tensor train.
       | (shape, tucker_ranks, tt_ranks)

   * :py:type:`EdgeWeights`
       | Weights for edges of a Tucker tensor train
       | (tucker_weights, tt_weights)

   * :py:type:`T3Base`
       | Base cores for Tucker tensor trains in base-variation format
       | (up_tucker_cores, left_tt_cores, right_tt_cores, outer_tt_cores)

   * :py:type:`T3Variation`
       | Variation cores for Tucker tensor trains in base-variation format
       | (tucker_variations, tt_variations)

   * :py:type:`BVStructure`
       | The structure of a Tucker tensor train in base-variation format
       | (shape, up_ranks, outer_ranks, left_ranks, right_ranks)

   * :py:type:`BVEdgeWeights`
       | Weights for the edges of a Tucker tensor train in base-variation format
       | (shape_weights, up_weights, outer_weights, left_weights, right_weights)

   Uniform Tucker tensor trains:
   -----------------------------

   * :py:type:`UniformTuckerTensorTrain`
       | Supercores of a uniform Tucker tensor train with uniform ranks
       | (tucker_supercore, tt_supercore)

   * :py:type:`UniformT3Structure`
       | The structure of a uniform Tucker tensor train.
       | (num indices d, index size N, tucker rank nU, TT rank r)

   * :py:type:`UniformEdgeWeights`
       | Weights for the edges of a uniform Tucker tensor train
       | (tucker_weights, tt_weights)

   * :py:type:`UniformT3Base`
       | Base cores for Tucker tensor trains in base-variation format
       | (up_tucker_supercore, left_tt_supercore, right_tt_supercore, outer_tt_supercore)

   * :py:type:`UniformT3Variation`
       | Variation cores for Tucker tensor trains in base-variation format
       | (tucker_variations_supercore, tt_variations_supercore)

   * :py:type:`BVStructure`
       | The structure of a Tucker tensor train in base-variation format
       | (num indices d, index size N, up rank nU, outer rank nO, left rank rL, right rank rR)

   * :py:type:`UniformBVEdgeWeights`
       | Weights for the edges of a Tucker tensor train in base-variation format
       | (shape_weights, up_weights, outer_weights, left_weights, right_weights)






   Other
   =====

   Operations here are defined with respect to the dense N0 x ... x N(d-1) tensors that
   are *represented* by the Tucker tensor train, even though these dense tensors
   are not formed during computations.

   For corewise backend, see :mod:`t3toolbox.corewise`



Classes
-------

.. toctree::
   :hidden:

   /autoapi/t3toolbox/tucker_tensor_train/TuckerTensorTrain

.. autoapisummary::

   t3toolbox.tucker_tensor_train.TuckerTensorTrain


Functions
---------

.. toctree::
   :hidden:

   /autoapi/t3toolbox/tucker_tensor_train/t3_stack
   /autoapi/t3toolbox/tucker_tensor_train/t3_core_shapes
   /autoapi/t3toolbox/tucker_tensor_train/compute_minimal_t3_ranks
   /autoapi/t3toolbox/tucker_tensor_train/t3_zeros
   /autoapi/t3toolbox/tucker_tensor_train/t3_corewise_randn
   /autoapi/t3toolbox/tucker_tensor_train/t3_save
   /autoapi/t3toolbox/tucker_tensor_train/t3_load
   /autoapi/t3toolbox/tucker_tensor_train/t3_to_vector
   /autoapi/t3toolbox/tucker_tensor_train/t3_from_vector
   /autoapi/t3toolbox/tucker_tensor_train/t3_apply
   /autoapi/t3toolbox/tucker_tensor_train/t3_entries
   /autoapi/t3toolbox/tucker_tensor_train/t3_probe
   /autoapi/t3toolbox/tucker_tensor_train/t3_add
   /autoapi/t3toolbox/tucker_tensor_train/t3_sub
   /autoapi/t3toolbox/tucker_tensor_train/t3_inner_product
   /autoapi/t3toolbox/tucker_tensor_train/t3svd_dense
   /autoapi/t3toolbox/tucker_tensor_train/t3svd

.. autoapisummary::

   t3toolbox.tucker_tensor_train.t3_stack
   t3toolbox.tucker_tensor_train.t3_core_shapes
   t3toolbox.tucker_tensor_train.compute_minimal_t3_ranks
   t3toolbox.tucker_tensor_train.t3_zeros
   t3toolbox.tucker_tensor_train.t3_corewise_randn
   t3toolbox.tucker_tensor_train.t3_save
   t3toolbox.tucker_tensor_train.t3_load
   t3toolbox.tucker_tensor_train.t3_to_vector
   t3toolbox.tucker_tensor_train.t3_from_vector
   t3toolbox.tucker_tensor_train.t3_apply
   t3toolbox.tucker_tensor_train.t3_entries
   t3toolbox.tucker_tensor_train.t3_probe
   t3toolbox.tucker_tensor_train.t3_add
   t3toolbox.tucker_tensor_train.t3_sub
   t3toolbox.tucker_tensor_train.t3_inner_product
   t3toolbox.tucker_tensor_train.t3svd_dense
   t3toolbox.tucker_tensor_train.t3svd