trainsum -- A Python package for quantics tensor trains

TL;DR

trainsum is a Python package that simplifies tensor train computations for multidimensional data, enabling efficient approximation, arithmetic operations, and applications in various scientific fields.

Contribution

introduces a versatile Python package that facilitates tensor train computations with shape-agnostic approximation and operations, integrating Array API and opt_einsum.

Findings

enables effortless tensor approximation regardless of shape or dimensionality

supports arithmetic operations like addition and Einstein summation on tensor trains

applicable in simulation, data compression, machine learning, and data analysis

Abstract

We present trainsum, a versatile Python package for doing computations with multidimensional quantics tensor trains: https://github.com/fh-igd-iet/trainsum. Using the Array API standard together with opt_einsum, trainsum allows the effortless approximation of tensors or functions by tensor trains independent of their shape or dimensionality. Once approximated, our package can perform normal arithmetic operations with quantics tensor trains, including addition, Einstein summations and element-wise transformations. It can be therefore used for generic computations with applications in simulation, data compression, machine learning and data analysis.