Extend @SArray (nested cat, 1.7 syntax)

[N5N3]

This PR tries to add support to nested cat, and 1.7 Multidimensional syntax.

julia> @SArray [1 2 ; 3 4 ;;; 5 6 ; 7 8]
2×2×2 SArray{Tuple{2, 2, 2}, Int64, 3, 8} with indices SOneTo(2)×SOneTo(2)×SOneTo(2):
[:, :, 1] =
 1  2
 3  4

[:, :, 2] =
 5  6
 7  8

julia> @SArray [[[1 ; 2] ;; [3 ; 4]] ;;; [[5 ; 6] ;; [7 ; 8]]]
2×2×2 SArray{Tuple{2, 2, 2}, Int64, 3, 8} with indices SOneTo(2)×SOneTo(2)×SOneTo(2):
[:, :, 1] =
 1  3
 2  4

[:, :, 2] =
 5  7
 6  8

Close #974.
Edit: commit histroy has been splitted for easier review.

[N5N3]

Beside the macro extension, most of the convert ambiguities are resolved in this PR. Now with a fresh REPL

julia> using StaticArrays, Test

julia> detect_ambiguities(#=LinearAlgebra, =#StaticArrays)
5-element Vector{Tuple{Method, Method}}:
 ((Scalar)(a::AbstractArray) in StaticArrays at C:\Users\MYJ\.julia\dev\StaticArrays\src\Scalar.jl:10, (::Type{SA})(a::StaticArray) where SA<:StaticArray 
in StaticArrays at C:\Users\MYJ\.julia\dev\StaticArrays\src\convert.jl:16)
 (SHermitianCompact(a::StaticMatrix{N, N, T}) where {N, T} in StaticArrays at C:\Users\MYJ\.julia\dev\StaticArrays\src\SHermitianCompact.jl:82, (::Type{SSC})(a::SSC) where SSC<:SHermitianCompact in StaticArrays at C:\Users\MYJ\.julia\dev\StaticArrays\src\SHermitianCompact.jl:85)
 ((::Type{SSC})(a::AbstractVector) where SSC<:SHermitianCompact in StaticArrays at C:\Users\MYJ\.julia\dev\StaticArrays\src\SHermitianCompact.jl:87, (::Type{SA})(a::StaticArray) where SA<:StaticArray in StaticArrays at C:\Users\MYJ\.julia\dev\StaticArrays\src\convert.jl:16)
 (SHermitianCompact(a::StaticMatrix{N, N, T}) where {N, T} in StaticArrays at C:\Users\MYJ\.julia\dev\StaticArrays\src\SHermitianCompact.jl:82, (::Type{SSC})(a::SHermitianCompact) where SSC<:SHermitianCompact in StaticArrays at C:\Users\MYJ\.julia\dev\StaticArrays\src\SHermitianCompact.jl:84)
 ((Scalar)(a::AbstractArray{T, 0} where T) in StaticArrays at C:\Users\MYJ\.julia\dev\StaticArrays\src\Scalar.jl:11, (::Type{SA})(a::StaticArray) where SA<:StaticArray in StaticArrays at C:\Users\MYJ\.julia\dev\StaticArrays\src\convert.jl:16)

Scalar's ambiguilty could be resolved with

@inline Scalar(a::StaticArray) = ndims(a) === 0 ? Scalar{eltype(a)}((a[],)) : Scalar{typeof(a)}((a,))

But I'm not sure is this the expected behavior.

All test passed locally, so I guess this is ready for review.

Edit: seperated to #1016

[mateuszbaran]

Thank you, this is really great. This will take some time to review though.

[N5N3]

Error seems reproduable on 32bit system. I'll take a look.

[N5N3]

Well, win32 test passed locally with official 1.7.2 (twice). Not sure what happened here.

[mateuszbaran]

Well, win32 test passed locally with official 1.7.2 (twice). Not sure what happened here.

I think the Julia process is just running out of memory.

[N5N3]

Commits for constructor clean has been removed to focus this PR on syntax extension. (SA[1;;1] support has been added.)

[mateuszbaran]

Thanks for this work. I didn't check all details but the code looks good and I only have a few small comments.

[mateuszbaran]

Close #911.

Did you add some tests related to this issue? I can't find it.

[N5N3]

Sorry for the careless. As #1016 has been seperated out, #911 wont be fixed in this PR, as the root cause is a constructor missing:

julia> MMatrix{2,2}((1.0,1,1,1))
ERROR: ArgumentError: Size mismatch in Static Array parameters. Got size Tuple{2, 2}, dimension 2 and length 1.

[mateuszbaran]

This may not be the simplest case but it works for normal arrays but not here:

a = @SArray fill(1, 2,3,2,4,5)
b = @SArray fill(2, 1,1,2,4,5)
c = @SArray fill(3, 1,2,2,4,5)
d = @SArray fill(4, 1,1,1,4,5)
e = @SArray fill(5, 1,1,1,4,5)
f = @SArray fill(6, 1,1,1,4,5)
g = @SArray fill(7, 2,3,1,4,5)
h = @SArray fill(8, 3,3,3,1,2)
i = @SArray fill(9, 3,2,3,3,2)
j = @SArray fill(10, 3,1,3,3,2)

result = @SArray [a; b c ;;; d e f ; g ;;;;; h ;;;; i j]

julia> [a; b c ;;; d e f ; g ;;;;; h ;;;; i j]
3×3×3×4×7 Array{Int64, 5}:
 < content >

julia> @SArray [a; b c ;;; d e f ; g ;;;;; h ;;;; i j]
ERROR: LoadError: DimensionMismatch("mismatch in dimension 2 (expected 1 got 2)")
Stacktrace:
 [1] cat_mismatch(j::Int64, sz::Int64, nsz::Int64)
   @ StaticArrays ~/.julia/dev/StaticArrays/src/SArray.jl:159
 [2] check_cat_size(szs::Vector{Tuple{Int64, Int64}}, catdim::Int64)
   @ StaticArrays ~/.julia/dev/StaticArrays/src/SArray.jl:170
 [3] cat_any(#unused#::Val{2}, #unused#::Val{1}, args::Vector{Any})
   @ StaticArrays ~/.julia/dev/Static

[mateuszbaran]

Ah, right, it can't work without a lot of trouble -- it might be worth documenting somewhere that @SArray and similar assume scalar elements.

[mateuszbaran]

I've tested this and it works well, so I think this can be merged after updating documentation and bumping version.