Optimized methods for `mapreduce(f, vcat, xs)` and `mapreduce(f, hcat, xs)`

[oxinabox]

given we had #21672
which makes reduce(vcat and reduce(hcat fast.

I had assumed it also applied to mapreduce of these operations.
But it clearly does not.

julia> @btime reduce(vcat, $datas)
  87.049 μs (2 allocations: 117.27 KiB)

julia> @btime mapreduce(identity, vcat, $datas);
  5.372 ms (10005 allocations: 37.04 MiB)

julia> @btime reduce(vcat, map(identity, $datas));
  93.212 μs (5 allocations: 156.42 KiB)

Right now, if the 2nd arg is vcat or hcat it is faster to call reduce(op, map(f, xs)) than mapreduce(f, op, xs).
And maybe that would be a solid first move to fix this.

[nalimilan]

Should be quite trivial to do indeed by dispatching on ::typeof(identity).

[oxinabox]

That would not be useful.
Identity was just an example.
It needs to be done by dispatching on ::typeof{vcat} and ::typeof{hcat} etc.

julia> const x   = [rand(100) for _ in 1:1000];

julia> @btime mapreduce(z->2z,  vcat, x);
  169.896 ms (2979 allocations: 382.80 MiB)

julia> @btime reduce(vcat, map(z->2z, x));
  124.665 μs (1004 allocations: 1.63 MiB)

julia> @btime mapreduce(z->2z,  hcat, x);
  185.014 ms (3980 allocations: 382.83 MiB)

julia> @btime reduce(hcat, map(z->2z, x));
  125.138 μs (1004 allocations: 1.63 MiB)

Or even say

julia> const y   = [rand(100, 100) for _ in 1:1000];

julia> @btime mapreduce(z->sum(z;dims=2),  hcat, y);
  197.977 ms (9978 allocations: 383.01 MiB)

julia> @btime reduce(hcat, map(z->sum(z; dims=2), y));
  4.590 ms (7004 allocations: 1.81 MiB)

[nalimilan]

Unfortunately, I'm afraid that allowing any f while spcializing on ::typeof(vcat) will introduce ambiguities. I guess one just needs to try it.

[oxinabox]

Seems fine to me.
is this a valid way to check it?

The following matches the signature used by reduce(::typeof{vcat}...

julia> Base.mapreduce(f, op::Union{typeof(vcat),typeof(hcat)}, A::AbstractVector{<:Union{AbstractVector, AbstractMatrix}}) = reduce(op, map(f, A))

julia> using Test

julia> Test.detect_ambiguities(Base)
0-element Array{Tuple{Method,Method},1}

julia> const y   = [rand(100, 100) for _ in 1:1000];

julia> expected = reduce(hcat, map(z->sum(z; dims=2), y));

julia> @test expected == mapreduce(z->sum(z;dims=2),  hcat, y);

julia> methods(mapreduce)
# 5 methods for generic function "mapreduce":
[1] mapreduce(f, op, a::Number) in Base at reduce.jl:324
[2] mapreduce(f, op, itr::Base.SkipMissing{#s623} where #s623<:AbstractArray) in Base at missing.jl:202
[3] mapreduce(f, op::Union{typeof(hcat), typeof(vcat)}, A::AbstractArray{#s3,1} where #s3<:Union{AbstractArray{T,1} where T, AbstractArray{T,2} where T}) in Main at REPL[6]:1
[4] mapreduce(f, op, A::AbstractArray; dims, kw...) in Base at reducedim.jl:304
[5] mapreduce(f, op, itr; kw...) in Base at reduce.jl:205

[nalimilan]

Looks fine. For reduce there's a special SharedArray method but it doesn't seem to exist for mapreduce.

[CameronBieganek]

I just bumped into this. It would definitely be nice to have mapreduce(f, [hv]cat, xs) be optimized.

[mcabbott]

It's not precisely parallel, but many uses of this would be served by #43334. If x and f(x) are vectors then mapreduce(f, hcat, xs) == stack(f, xs).

[stevengj]

Note that we also didn't optimize reduce when there is an init keyword:

julia> v = [rand(1:10, rand(0:10)) for _ in 1:100];

julia> @btime reduce(vcat, $v, init=Int[]);
  23.151 μs (101 allocations: 210.23 KiB)

julia> @btime reduce(vcat, $v);
  962.444 ns (2 allocations: 5.12 KiB)

so clearly we didn't override a low-level enough method.

[mcabbott]

The keyword init could presumably be handled as part of #27188 (i.e. the methods for ::AbstractVector{<:AbstractVecOrMat}}) without needing this PR's extension to mapreduce.

In this case it looks like it's being used to handle the empty case. Possibly #27188 should just allow that, when the type is known:

julia> empty(v)
Vector{Int64}[]

julia> reduce(vcat, empty(v), init=Int[])
Int64[]

julia> reduce(vcat, empty(v))
ERROR: MethodError: reducing over an empty collection is not allowed; consider supplying `init` to the reducer
Stacktrace:
 [1] reduce_empty(op::Base.MappingRF{typeof(eltype), typeof(promote_type)}, #unused#::Type{Vector{Int64}})