t3toolbox.tucker_tensor_train

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

Tucker tensor trains:

• TuckerTensorTrain

  The cores of a Tucker tensor train with varied ranks

  (tucker_cores, tt_cores)

• T3Structure

  The structure of a Tucker tensor train.

  (shape, tucker_ranks, tt_ranks)

• EdgeWeights

  Weights for edges of a Tucker tensor train

  (tucker_weights, tt_weights)

• T3Base

  Base cores for Tucker tensor trains in base-variation format

  (up_tucker_cores, left_tt_cores, right_tt_cores, outer_tt_cores)

• T3Variation

  Variation cores for Tucker tensor trains in base-variation format

  (tucker_variations, tt_variations)

• BVStructure

  The structure of a Tucker tensor train in base-variation format

  (shape, up_ranks, outer_ranks, left_ranks, right_ranks)

• 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:

• UniformTuckerTensorTrain

  Supercores of a uniform Tucker tensor train with uniform ranks

  (tucker_supercore, tt_supercore)

• UniformT3Structure

  The structure of a uniform Tucker tensor train.

  (num indices d, index size N, tucker rank nU, TT rank r)

• UniformEdgeWeights

  Weights for the edges of a uniform Tucker tensor train

  (tucker_weights, tt_weights)

• UniformT3Base

  Base cores for Tucker tensor trains in base-variation format

  (up_tucker_supercore, left_tt_supercore, right_tt_supercore, outer_tt_supercore)

• UniformT3Variation

  Variation cores for Tucker tensor trains in base-variation format

  (tucker_variations_supercore, tt_variations_supercore)

• 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)

• 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 t3toolbox.corewise

Classes

TuckerTensorTrain

Tucker tensor train with variable ranks.

Functions

t3_stack(...)	Stacks an array-like structure of TuckerTensorTrains into one stacked TuckerTensorTrain.
t3_core_shapes(...)	Compute the tucker and TT backend shapes for a Tucker tensor train.
compute_minimal_t3_ranks(...)	Find minimal ranks for a generic Tucker tensor train with a given structure.
t3_zeros(, use_jax)	Construct a Tucker tensor train of zeros.
t3_corewise_randn(, use_jax)	Construct a Tucker tensor train with random cores.
t3_save(→ None)	Save a Tucker tensor train to a file.
t3_load(→ TuckerTensorTrain)	Load a Tucker tensor train from a file.
t3_to_vector(→ t3toolbox.backend.common.NDArray)	Converts a TuckerTensorTrain into a 1D vector containing the backend entries.
t3_from_vector() → TuckerTensorTrain)	Constructs a TuckerTensorTrain from a 1D vector containing the backend entries.
t3_apply(→ t3toolbox.backend.common.NDArray)	Contract a Tucker tensor train with vectors in all indices.
t3_entries(→ t3toolbox.backend.common.NDArray)	Compute an entry (or multiple entries) of a Tucker tensor train.
t3_probe(...)	Probe a TuckerTensorTrain.
t3_add(→ TuckerTensorTrain)	Add Tucker tensor trains x and y, yielding a Tucker tensor train x+y with summed ranks.
t3_sub(...)	Subtract Tucker tensor trains, x - y, yielding a Tucker tensor train with summed ranks.
t3_inner_product(x, y[, use_orthogonalization, use_jax])	Compute Hilbert-Schmidt inner product of two Tucker tensor trains.
t3svd_dense(...)	Compute TuckerTensorTrain and edge singular values for dense tensor.
t3svd(...)	Compute (truncated) T3-SVD of TuckerTensorTrain.