using `mean` with distributed Dagger arrays

[Alexander-Barth]

It would be great to have functions from Statistics useable with distributed Dagger arrays. Currenly the function sum does work but the equivalent mean function produces the error below:

using Dagger
using Statistics

sz = (2,2,3)
X = randn(sz)
DX = Distribute(Blocks(sz[1],sz[2],1), X)

# works
@show sum(DX,dims=3) 
# fails
@show mean(DX,dims=3) 

I am using Dagger v0.13.1 in Julia v1.6.2.

By looking at the code of Statistics.jl it seems that a specific implementation of mapreduce(f,g,d::Dagger.Distribute,dims=dims) would be needed. There is already one without the dims parameter. Would a PR be helpful?

Full stack-trace:

ERROR: LoadError: MethodError: no method matching +(::Float64, ::Dagger.GetIndex{Float64, 3})
For element-wise addition, use broadcasting with dot syntax: scalar .+ array
Closest candidates are:
  +(::Any, ::Any, ::Any, ::Any...) at operators.jl:560
  +(::Union{Float16, Float32, Float64}, ::BigFloat) at mpfr.jl:392
  +(::AbstractFloat, ::Bool) at bool.jl:102
  ...
Stacktrace:
  [1] add_sum(x::Float64, y::Dagger.GetIndex{Float64, 3})
    @ Base ./reduce.jl:24
  [2] macro expansion
    @ ./reducedim.jl:270 [inlined]
  [3] macro expansion
    @ ./simdloop.jl:77 [inlined]
  [4] _mapreducedim!(f::Statistics.var"#4#6"{typeof(identity), Dagger.BCast{Base.Broadcast.Broadcasted{Dagger.DaggerBroadcastStyle, Tuple{Base.OneTo{Int64}}, typeof(/), Tuple{Dagger.GetIndex{Float64, 3}, Int64}}, Float64, 1}}, op::typeof(Base.add_sum), R::Array{Float64, 3}, A::Distribute{Float64, 3})
    @ Base ./reducedim.jl:269
  [5] mapreducedim!(f::Function, op::Function, R::Array{Float64, 3}, A::Distribute{Float64, 3})
    @ Base ./reducedim.jl:277
  [6] _mapreduce_dim(f::Function, op::Function, #unused#::Base._InitialValue, A::Distribute{Float64, 3}, dims::Int64)
    @ Base ./reducedim.jl:324
  [7] #mapreduce#672
    @ ./reducedim.jl:310 [inlined]
  [8] #_sum#702
    @ ./reducedim.jl:900 [inlined]
  [9] _sum
    @ ./reducedim.jl:900 [inlined]
 [10] #sum#680
    @ ./reducedim.jl:874 [inlined]
 [11] _mean(f::typeof(identity), A::Distribute{Float64, 3}, dims::Int64)
    @ Statistics /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/Statistics/src/Statistics.jl:177
 [12] #mean#2
    @ /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/Statistics/src/Statistics.jl:164 [inlined]
 [13] top-level scope
    @ show.jl:955
in expression starting at /home/abarth/.julia/dev/NCDatasets/test/test_dagger.jl:46

[jpsamaroo]

Yeah, the lazy nature of the DArray breaks under a lot of regular array operations. Per #226, we'll probably just want to make the DArray eager (like the DTable), potentially by reusing parts of DistributedArrays.jl.