# TensorKit.jl

*A Julia package for large-scale tensor computations, with a hint of category theory.*

## Package summary

TensorKit.jl aims to be a generic package for working with tensors as they appear throughout the physical sciences. TensorKit implements a parametric type `Tensor`

(which is actually a specific case of the type `TensorMap`

) and defines for these types a number of vector space operations (scalar multiplication, addition, norms and inner products), index operations (permutations) and linear algebra operations (multiplication, factorizations). Finally, tensor contractions can be performed using the `@tensor`

macro from TensorOperations.jl.

Currently, most effort is oriented towards tensors as they appear in the context of quantum many body physics and in particular the field of tensor networks. Such tensors often have large dimensions and take on a specific structure when symmetries are present. To deal with generic symmetries, we employ notations and concepts from category theory all the way down to the definition of a tensor.

At the same time, TensorKit.jl focusses on computational efficiency and performance. The underlying storage of a tensor's data can be any `DenseArray`

. Currently, certain operations are already multithreaded, either by distributing the different blocks in case of a structured tensor (i.e. with symmetries) or by using multithreading provided by the package Strided.jl. In the future, we also plan to investigate using `CuArray`

s as underlying storage for the tensors data, so as to leverage GPUs for the different operations defined on tensors.

## Contents of the manual

- Introduction
- Optional introduction to category theory
- Vector spaces
- Sectors, representation spaces and fusion trees
- Tensors and the
`TensorMap`

type - Storage of tensor data
- Constructing tensor maps and accessing tensor data
- Tensor properties
- Reading and writing tensors:
`Dict`

conversion - Vector space and linear algebra operations
- Index manipulations
- Tensor factorizations
- Bosonic tensor contractions and tensor networks
- Fermionic tensor contractions
- Anyonic tensor contractions