Einsum

In linear algebra and mathematical physics, there is a notational convention called Einstein Notation. The python package numpy implements a function called einsum, which is the first hit when googling the term. Several Julia packages exists that implement einsum functionality.

Packages

Tullio.jl

a very flexible einsum macro. It understands many array operations written in index notation – not just matrix multiplication and permutations, but also convolutions, stencils, scatter/gather, and broadcasting.

Einsum.jl

This package exports a single macro @einsum, which implements similar notation to the Einstein summation convention to flexibly specify operations on Julia Arrays, similar to numpy's einsum function (but more flexible!).

OMEinsum.jl

This is a repository for the Google Summer of Code project on Differentiable Tensor Networks. It implements one function that both computer scientists and physicists love, the Einstein summation

Tensorial.jl

Tensorial.jl provides statically sized Tensor type that is compatible with AbstractArray, similar to SArray from StaticArrays.jl. In addition to supporting basic AbstractArray operations, the package offers a tensorial interface and several advanced features:

• Contraction, tensor product (⊗), and a flexible @einsum macro for Einstein summation convention

• A @Symmetry macro to define the tensor symmetries, eliminating unnecessary calculations

• Automatic differentiation via gradient and hessian functions, leveraging ForwardDiff.jl

• Performance comparable to SArray

TensorOperations.jl

TensorCast.jl

ArrayMeta.jl

ArrayMeta.jl exists, but the package is not maintained and registered.

Tortilla.jl

Tortilla.jl was announced in JuliaCon2018, but the package is not public yet.

• For Loops 2.0: Index Notation and the Future of Tensor Compilers | Willow Ahrens | JuliaCon 2018

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