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Compact implementation of basic operations in the tensor-train (TT) format, including TT-SVD, TT-ALS, TT-ANOVA, TT-CROSS, TT-truncate for approximation of multidimensional arrays and multivariate functions

Project description



This python package, named teneva (tensor evaluation), provides a very compact implementation of basic operations in the tensor-train (TT) format, including TT-SVD, TT-ALS, TT-ANOVA, TT-cross, TT-truncate, Chebyshev interpolation, "add", "mul", "norm", "mean", "sample", etc. Our approach can be used for approximation of multidimensional arrays and multivariate functions, as well as for efficient implementation of various operations of linear algebra in the low rank TT-format. The program code is organized within a functional paradigm and it is very easy to learn and use. Each function has detailed documentation and various usage demos.


Current version "0.14.8".

The package can be installed via pip: pip install teneva (it requires the Python programming language of the version 3.8 or 3.9). It can be also downloaded from the repository teneva and installed by python install command from the root folder of the project.

Documentation, examples and tests

  • See detailed online documentation for a description of each function and various numerical examples for each function.

  • See the jupyter notebooks in the demo folder of the repository teneva with brief description and demonstration of the capabilities of each function from the teneva package, including the basic examples of using the TT-ALS, TT-ANOVA and TT-cross for approximation of the multivariable functions. Note that all examples from this folder are also presented in the online documentation.

  • See file with a description of the changes made for new package versions and file with a description of the rules we use to work on the code (draft!).

  • Run all the tests (based on the unittest framework) from the root of the repository teneva as python test/ (draft!).

Useful links

  • The github repository teneva_jax with the fast jax version of the teneva code.

  • The github repository teneva_bm with benchmarks library for testing multidimensional approximation and optimization methods.

  • The github repository teneva_opti with wrapper for various optimizers adapted to work with benchmarks from teneva_bm.

  • The github repository ttopt with the gradient-free optimization method TTOpt for multivariable functions based on the TT-format and maximal-volume principle (see also NeurIPS-2022 paper).

  • The github repository PROTES with the optimization method PROTES (PRobability Optimizer with TEnsor Sampling) for derivative-free optimization of the multidimensional arrays and discretized multivariate functions based on the TT-format (see also arxiv paper).

  • The github repository Constructive-TT with the method for constructive TT-representation of the tensors given as index interaction functions (see also ICLR-2023 paper).

  • Paper Tensor train decomposition, in which the TT-decomposition is presented and the main its properties are described.

  • Dissertation work Computational tensor methods and their applications (in Russian only), in which the TT-decomposition is proposed and all its properties are described in detail.

  • Dissertation work Tensor methods for multidimensional differential equations (in Russian only), which presents various new algorithms in the TT-format for problems of multidimensional approximation, optimization and solution of differential equations.


✭__🚂 The stars that you give to teneva, motivate us to develop faster and add new interesting features to the code 😃


If you find our approach and/or code useful in your research, please consider citing:

    author    = {Chertkov, Andrei and Ryzhakov, Gleb and Oseledets, Ivan},
    year      = {2023},
    title     = {Black box approximation in the tensor train format initialized by {ANOVA} decomposition},
    journal   = {SIAM Journal on Scientific Computing},
    volume    = {45},
    number    = {4},
    pages     = {A2101-A2118},
    doi       = {10.1137/22M1514088},
    url       = {}
    author    = {Chertkov, Andrei and Ryzhakov, Gleb and Novikov, Georgii and Oseledets, Ivan},
    year      = {2022},
    title     = {Optimization of functions given in the tensor train format},
    journal   = {arXiv preprint arXiv:2209.14808},
    doi       = {10.48550/ARXIV.2209.14808},
    url       = {}

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