TensorCast.jl

> It's not JUST google and apple, I'm sure they have enough cash and expertise and will to create enough momentum to attract more domain experts in other areas. Maybe, but I'm doubtful. Scientific domain experts flock to languages like Python, Julia, Matlab, R, etc. because they're interactive and allow them to quickly iterate on ideas, query data, produce plots, etc. Swift is not much of an interactive language and is not built around that kind of repl driven experience. > In particular, do you have another example aside from DifferentialEquations.jl ? Sure, here's a smattering of high quality packages made by and for research scientists: https://github.com/JuliaApproximation/ApproxFun.jl https://github.com/BioJulia https://github.com/JuliaDiffEq/ModelingToolkit.jl https://github.com/crstnbr/MonteCarlo.jl https://gith

There are a bunch of packages exploring ideas around labelled dimensions, although we are still far from the vision of caring as little as we do about registers: * https://github.com/JuliaArrays/AxisArrays.jl * https://github.com/davidavdav/NamedArrays.jl * https://github.com/invenia/NamedDims.jl * https://github.com/rafaqz/DimensionalData.jl * https://github.com/ITensor/ITensors.jl While these don't pass dimension labels along in the type, there are also a number of Einsum-like packages which should work on any storage order, and could be taught to interface with such types: * https://github.com/Jutho/TensorOperations.jl * https://github.com/under-Peter/OMEinsum.jl * https://github.com/mcabbott/TensorCast.jl

Julia has some really cool libraries for index notation. I've made extensive use of TensorOperations.jl [1] and TensorCast.jl [2]. I find that the capabilities of these two complement each-other really well since TensorOperations.jl is a bit more restricted in the sort of operations it can do, but it does all sorts of really powerful analysis to find the optimal way of doing a given contraction whereas TensorCast.jl is super flexible, permissive and expressive but doesn't always generate an optimal contraction for big high dimensional contractions. I'm excited to see what comes out of Andreas' summer work on his implementation of Einsum! There's definitely room for more cool ideas in this space. In particular, I think baking in AD functionality is a cool approach. [1] https://github.com/Jutho/TensorOperations.jl [2] https://github.com/mc

I made a thing to audit that you are consistent with your indices [1] as an alternative to explicit named-tensor objects. And found, but have not used, another package in a similar spirit [2]. Although to be honest, simply writing A[n,μ,ν,c] etc. (using different letters for different spaces) makes it pretty easy to visually check that you are getting this right. This is one of the attractions of the notation, even on paper. Unfortunately np.einsum's string notation makes this harder to see, as the indices aren't adjacent to the variable name. [1] https://github.com/mcabbott/TensorCast.jl#checking (Julia) [2] https://github.com/ofnote/tsalib (Python)