Package: teneva
tenevaDescriptionThis python package, namedteneva(tensorevaluation), 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.InstallationCurrent version "0.14.8".The package can be installed via pip:pip install teneva(it requires thePythonprogramming language of the version 3.8 or 3.9). It can be also downloaded from the repositorytenevaand installed bypython setup.py installcommand from the root folder of the project.Documentation, examples and testsSee detailedonline documentationfor a description of each function and various numerical examples for each function.See the jupyter notebooks in thedemofolder of the repositorytenevawith brief description and demonstration of the capabilities of each function from thetenevapackage, 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.Seechangelog.mdfile with a description of the changes made for new package versions andworkflow.mdfile with a description of the rules we use to work on the code (draft!).Run all the tests (based on theunittestframework) from the root of the repositorytenevaaspython test/test.py(draft!).Useful linksThe github repositoryteneva_jaxwith the fastjaxversion of thetenevacode.The github repositoryteneva_bmwith benchmarks library for testing multidimensional approximation and optimization methods.The github repositoryteneva_optiwith wrapper for various optimizers adapted to work with benchmarks fromteneva_bm.The github repositoryttoptwith the gradient-free optimization methodTTOptfor multivariable functions based on the TT-format and maximal-volume principle (see alsoNeurIPS-2022 paper).The github repositoryPROTESwith the optimization methodPROTES(PRobability Optimizer with TEnsor Sampling) for derivative-free optimization of the multidimensional arrays and discretized multivariate functions based on the TT-format (see alsoarxiv paper).The github repositoryConstructive-TTwith the method for constructive TT-representation of the tensors given as index interaction functions (see alsoICLR-2023 paper).PaperTensor train decomposition, in which the TT-decomposition is presented and the main its properties are described.Dissertation workComputational tensor methods and their applications(in Russian only), in which the TT-decomposition is proposed and all its properties are described in detail.Dissertation workTensor 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.AuthorsAndrei ChertkovGleb RyzhakovIvan Oseledets✭__🚂  The stars that you give toteneva, motivate us to develop faster and add new interesting features to the code 😃CitationIf you find our approach and/or code useful in your research, please consider citing:@article{chertkov2023black,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={https://arxiv.org/pdf/2208.03380.pdf}}@article{chertkov2022optimization,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={https://arxiv.org/pdf/2209.14808.pdf}}