[NDTensors] NamedDimsArrays module

[mtfishman]

This defines a new NamedDimsArrays module, defining a standalone Julia array wrapper type that attaches names to dimensions.

The design is some hybrid of the current ITensor Index system and Julia packages like NamedDims.jl/NamedPlus.jl, DimensionalData.jl, NamedArrays.jl, PyTorch's Named Tensors, etc.

The idea would be to replace the current Tensor type with a NamedDimsArray (or some subtype of AbstractNamedDimsArray), which would have named dimension-aware indexing and tensor operation syntax (i.e. smart addition, contraction, and factorization like ITensors have right now). Then ITensors can be simple opaque mutable wrappers around NamedDimsArrays.

[codecov-commenter]

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[mtfishman]

In that latest I started adding tensor algebra definitions like contract, which are simple wrappers around TensorAlgebra.contract introduced in #1265.

Here is a demonstration of some functionality:

using NDTensors.NamedDimsArrays: align, dimnames, named, unname
using NDTensors.TensorAlgebra: TensorAlgebra

# Named dimensions
i = named(2, "i")
j = named(2, "j")
k = named(2, "k")

# Arrays with named dimensions
na1 = randn(i, j)
na2 = randn(j, k)

@show dimnames(na1) == ("i", "j")

# Indexing
@show na1[j => 2, i => 1] == na1[1, 2]

# Tensor contraction
na_dest = TensorAlgebra.contract(na1, na2)

@show issetequal(dimnames(na_dest), ("i", "k"))
# `unname` removes the names and returns an `Array`
@show unname(na_dest, (i, k)) ≈ unname(na1) * unname(na2)

# Permute dimensions (like `ITensors.permute`)
na1 = align(na1, (j, i))
@show na1[i => 1, j => 2] == na1[2, 1]

So it is very similar to the interface of ITensors.ITensor.

[emstoudenmire]

Interesting to see how short the code for implementing this ended up being. And I can see how it would simplify the ITensor layer on top.