Views of SArray may use getindex to avoid the SubArray wrapper

[jishnub]

Since SArrays are immutable and support allocation-less vector indexing for certain index types, views of SArrays constructed with such indices do not need to retain the SubArray wrapper and may just return another SArray obtained through indexing. Fixes #892.

After this PR:

julia> s = SMatrix{3,3}(ones(3,3));

julia> sv = @view s[:, :]
3×3 SMatrix{3, 3, Float64, 9} with indices SOneTo(3)×SOneTo(3):
 1.0  1.0  1.0
 1.0  1.0  1.0
 1.0  1.0  1.0

julia> @btime $(Ref(sv))[] + $(Ref(sv))[]
  3.730 ns (0 allocations: 0 bytes)
3×3 SMatrix{3, 3, Float64, 9} with indices SOneTo(3)×SOneTo(3):
 2.0  2.0  2.0
 2.0  2.0  2.0
 2.0  2.0  2.0

[andyferris]

I generally prefer not giving special treatment to SArray - if there were a generic way of doing this (like a trait for immutable arrays) that would be preferable.

On the other hand this is quite practical and seems harmless to merge.

[mateuszbaran]

It looks great now, could you just bump version to 1.2.0? I'll merge and tag a new release.

[jishnub]

Rebased on master and bumped version to 1.2.0

[KristofferC]

This PR caused a difference between using a Matrix and a SMatrix in ForwardDiff as described in JuliaDiff/ForwardDiff.jl#547 (comment). I bisected to this PR with the following script:

using ForwardDiff, LinearAlgebra, StaticArrays


foo2(A) = SVector{4}(norm(r, 2) for r = eachrow(A))

function foo1!(out, x; μ = 0.8 / √2)
    λ = SVector{3}(@view x[1:3])
    K = SMatrix{3,3}(@view x[4:12])

    A_λ = [ 1   0  -1   0 ;
            0   1   0  -1 ;
            μ   μ   μ   μ ]

    out[1:4] = A_λ' * λ + foo2(A_λ' * K)

    out
end

function foo1_s!(out, x; μ = 0.8 / √2)
    λ = SVector{3}(@view x[1:3])
    K = SMatrix{3,3}(@view x[4:12])

    A_λ = @SMatrix [ 1   0  -1   0 ;
                     0   1   0  -1 ;
                     μ   μ   μ   μ ]

    out[1:4] = A_λ' * λ + foo2(A_λ' * K)

    out
end

x = zeros(12);
out = zeros(4);
display(ForwardDiff.jacobian(foo1!, out, x))
display(ForwardDiff.jacobian(foo1_s!, out, x))

nothing

and before this PR they returned the same value, after it, the one with @SMatrix only has NaNs in it.

[mateuszbaran]

The difference is in one check that LinearAlgebra's norm2 does which isn't done by StaticArrays.jl:

https://github.com/JuliaLang/julia/blob/a9a1d80076f98b1e31197c22924acf24bf5da760/stdlib/LinearAlgebra/src/generic.jl#L498

Probably StaticArrays.jl needs to have this check too?

[ferrolho]

Thank you for finding this PR as the breaking changes, @KristofferC. And thank you @mateuszbaran for your reply.

Should I create a new issue to track this?

[KristofferC]

Sounds like a good idea.