LazyStack.jl

This package exports a function lazystack for turning a list of arrays into one AbstractArray. Given several arrays with the same eltype, or an array of such arrays, it returns a lazy Stacked{T,N} view of these:

julia> lazystack([1:2, 3:4, 5:6])
2×3 lazystack(::Vector{UnitRange{Int64}}) with eltype Int64:
 1  3  5
 2  4  6

julia> lazystack([pi^ℯ], [ℯ^pi])
1×2 lazystack(::Tuple{Vector{Float64}, Vector{Float64}}) with eltype Float64:
 22.4592  23.1407

Before v0.1 this function used to be called stack, but that name is now exported by Base (from Julia 1.9). Like this package, Base.stack makes an array with size(result) = (size(inner)..., size(outer)...). However, it always returns a new dense array, not a lazy container. And instead of two vectors (in the above example) it would want a tuple stack(([pi^ℯ], [ℯ^pi])).

Generators such as lazystack([i,2i] for i in 1:5) and arrays of mixed eltype like lazystack([1,2], [3.0, 4.0], [5im, 6im]) used to be be handled here, making a dense array, but are now simply passed through to Base.stack.

When the individual slices aren't backed by an Array, as for instance with CuArrays on a GPU, then again Base.stack is called. This should make one big CuArray, since scalar indexing of individual slices won't work well.

Ragged stack

There is also a version which does not demand that slices have equal size (or equal ndims). For now this is not lazy:

julia> raggedstack([10:10+n for n in 1:3])
4×3 Matrix{Int64}:
 10  10  10
 11  11  11
  0  12  12
  0   0  13

julia> using OffsetArrays

julia> raggedstack(OffsetArray(fill(1.0n, 3), rand(-1:1)) for n in 1:10; fill=NaN)
5×10 OffsetArray(::Matrix{Float64}, 0:4, 1:10) with eltype Float64 with indices 0:4×1:10:
 NaN      2.0  NaN      4.0  NaN      6.0    7.0  NaN      9.0  NaN
   1.0    2.0    3.0    4.0    5.0    6.0    7.0  NaN      9.0   10.0
   1.0    2.0    3.0    4.0    5.0    6.0    7.0    8.0    9.0   10.0
   1.0  NaN      3.0  NaN      5.0  NaN    NaN      8.0  NaN     10.0
 NaN    NaN    NaN    NaN    NaN    NaN    NaN      8.0  NaN    NaN

Other stack-like packages

This one plays well with OffsetArrays.jl, and ChainRules.jl-compatible AD such as Zygote.jl. It's also used internally by TensorCast.jl.

Besides which, there are several other ways to achieve similar things:

• For an array of arrays, you can also use JuliennedArrays.Align. This requires (or enables) you to specify which dimensions of the output belong to the sub-arrays, instead of writing PermutedDimsArray(stack(...), ...).
• There is also RecursiveArrayTools.VectorOfArray which as its name hints only allows a one-dimensional container. (And unlike the package name, nothing is recursive.) Linear indexing retreives a slice, not an element, which is sometimes surprising.
• For a tuple of arrays, LazyArrays.Hcat is at present faster to index than lazystack, but doesn't allow arbitrary dimensions.

And a few more:

• When writing this I missed SplitApplyCombine.combinedimsview, which is very similar to stack, but doesn't handle tuples.
• Newer than this package is StackViews.jl handles both, with StackView(A,B,dims=4) == StackView([A,B],4) creating a 4th dimension; the container is always one-dimensional.
• Flux.stack similarly takes a dimension, but eagerly creates an Array.

The lazy inverse:

• The package ArraysOfArrays.jl solves the opposite problem, of accessing one large array as if it were many slices.

• As does JuliennedArrays.Slices.

• As does PackedVectorsOfVectors, although only 1+1 dimensions. Also has an eager pack method which turns a vector of vectors into view of a single larger matrix.

• Base.eachslice also views one large array as many slices. This was a generator, but JuliaLang#32310 upgrades it to a multi-dimensional indexable container, in Julia 1.9.

• AwkwardArray.jl fits in here somewhere.

Eager:

• After writing this I learned of JuliaLang#31644 which extends reduce(hcat,...) to work on generators. (Not merged yet.)

• Later, JuliaLang#43334 has added a better version of this package's stack_iter method to Base. (Available in Julia 1.9, or in Compat.jl.)

Other flatten-like packages:

• FlexiMaps.flatten is another eager implementation.
• CatViews.jl offers a lazy vcat. But the package is old and I think not so fast.

Experiments: concatenate & flatten

This package also contains a generalisation of reduce(vcat, A) to more dimensions:

julia> mats = [fill(10i+j, i, j) for i in 1:2, j in 3:5];

julia> concatenate(mats)  # block matrix
3×12 Matrix{Int64}:
 13  13  13  14  14  14  14  15  15  15  15  15
 23  23  23  24  24  24  24  25  25  25  25  25
 23  23  23  24  24  24  24  25  25  25  25  25

And an eager version of Iterators.flatten:

julia> flatten([(1,2), [30 40; 50 60], (; z=700)])
7-element Vector{Int64}:
   1
   2
  30
  50
  40
  60
 700

julia> flatten(i -> fill(10i, i), 0:3)
6-element Vector{Int64}:
 10
 20
 20
 30
 30
 30