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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, "add", "mul", "norm", "mean", Chebyshev interpolation, etc. This 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 format. The program code is organized within a functional paradigm and it is very easy to learn and use.


Current version "0.11.6".

The package can be installed via pip: pip install teneva (it requires the Python programming language of the version >= 3.6). It can be also downloaded from the repository teneva and installed by python install command from the root folder of the project. Required python packages numpy, scipy, numba and matplotlib will be automatically installed during the installation of the main software product.

Documentation and examples

  • See detailed online documentation for a description of each function and numerical examples.
  • See the jupyter notebooks in the ./demo folder 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.


✭ 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      = {2022},
    title     = {Black box approximation in the tensor train format initialized by ANOVA decomposition},
    journal   = {arXiv preprint arXiv:2208.03380},
    doi       = {10.48550/ARXIV.2208.03380},
    url       = {}

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