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TensorTrainNumerics.jl

Work in progress

Tensor Train Numerics is a Julia package designed to provide efficient numerical methods for working with tensor trains (TT) and quantized tensor trains (QTT).

Key features

  • Tensor Operations: Support for basic tensor operations such as addition, multiplication, and contraction in tensor train format.
  • Tensor Train Decomposition: Algorithms for decomposing high-dimensional tensors into tensor train format, reducing computational complexity and memory usage.
  • Discrete Operators: Implementation of discrete Laplacians, gradient operators, and shift matrices in tensor train format for solving partial differential equations and other numerical problems.
  • Quantized Tensor Trains: Tools for constructing and manipulating quantized tensor trains, which provide further compression and efficiency for large-scale problems.
  • Iterative Solvers: Integration with iterative solvers for solving linear systems and eigenvalue problems in tensor train format.
  • Visualization: Basic visualization tools for inspecting tensor train structures and their properties.

Getting started

To get started with Tensor Train Numerics, you can install the package using Julia's package manager:

using Pkg
Pkg.add("TensorTrainNumerics")

Acknowledgements

Many of the features are inspired by the work of Mi-Song Dupuy