Improve performance of weighted sum

[nalimilan]

The current code is calling the AbstractArray matrix multiplication fallback, which is slower than BLAS.

Fixes #775.

julia> using BenchmarkTools

julia> using StatsBase

julia> x = rand(1000); w = weights(rand(1000));

# master
julia> @btime wsum(x, w);
  1.029 μs (1 allocation: 16 bytes)

# This PR
julia> @btime wsum(x, w);
  97.572 ns (1 allocation: 16 bytes)

Tests appear to cover all weights types and AbstractVector already.

[rofinn]

Seems like a reasonable extension in this case. Looks like there isn't a test for the UnitWeights dispatch.

[nalimilan]

AFAICT unit weights are tested here, right?

StatsBase.jl/test/weights.jl

Line 479 in 26947bc

@test sum([1.0, 2.0, 3.0], wt) ≈ 6.0

[mschauer]

The CI error seems to be related to sampling?

* wsampling.jl ...
[172](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:172)
┌ Warning: Assignment to `a` in soft scope is ambiguous because a global variable by the same name exists: `a` will be treated as a new local. Disambiguate by using `local a` to suppress this warning or `global a` to assign to the existing global variable.
[173](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:173)
└ @ ~/work/StatsBase.jl/StatsBase.jl/test/wsampling.jl:47
[174](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:174)
ERROR: LoadError: MethodError: no method matching direct_sample!(::UnitRange{Int64}, ::Vector{Float64}, ::Matrix{Int64})
[175](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:175)
Closest candidates are:
[176](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:176)
  direct_sample!(::UnitRange, ::AbstractArray) at ~/work/StatsBase.jl/StatsBase.jl/src/sampling.jl:26
[177](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:177)
  direct_sample!(::AbstractRNG, ::AbstractArray, ::AbstractArray) at ~/work/StatsBase.jl/StatsBase.jl/src/sampling.jl:36
[178](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:178)
  direct_sample!(::AbstractArray, ::AbstractWeights, ::AbstractArray) at ~/work/StatsBase.jl/StatsBase.jl/src/sampling.jl:584
[179](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:179)
  ...
[180](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:180)
Stacktrace:
[181](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:181)
 [1] top-level scope
[182](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:182)
   @ ~/work/StatsBase.jl/StatsBase.jl/test/wsampling.jl:47
[183](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:183)
 [2] include(fname::String)
[184](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:184)
   @ Base.MainInclude ./client.jl:476
[185](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:185)
 [3] top-level scope
[186](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:186)
   @ ~/work/StatsBase.jl/StatsBase.jl/test/runtests.jl:34
[187](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:187)
 [4] include(fname::String)
[188](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:188)
   @ Base.MainInclude ./client.jl:476
[189](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:189)
 [5] top-level scope
[190](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:190)
   @ none:6
[191](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:191)
in expression starting at /home/runner/work/StatsBase.jl/StatsBase.jl/test/wsampling.jl:40
[192](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:192)
in expression starting at /home/runner/work/StatsBase.jl/StatsBase.jl/test/runtests.jl:31
[193](https://github.com/JuliaStats/StatsBase.jl/runs/5703799652?check_suite_focus=true#step:6:193)
ERROR: Package StatsBase errored during testing

[nalimilan]

Yeah these also happen on master: https://github.com/JuliaStats/StatsBase.jl/actions/runs/2044798742

[rofinn]

AFAICT unit weights are tested here, right?

Hmm, codecov says your new dispatch for wsum at line 391 isn't getting hit though :/

[rofinn]

Alright, I figured out why that method wasn't being hit. The specific line you posted calls a sum dispatch which never calls the wsum call.

https://github.com/JuliaStats/StatsBase.jl/blob/nl/wsum/src/weights.jl#L616

The wsum tests in that block all pass an integer and not Colon, so it hits a different dispatch.

https://github.com/JuliaStats/StatsBase.jl/blob/nl/wsum/src/weights.jl#L588

Adding a wsum call with Colon should solve the immediate coverage problem, though I wonder if the number of method overrides for sum and wsum suggestion an organizational/design issue?

[nalimilan]

Indeed. I've added a commit which hopefully simplifies the dispatch logic without breaking anything.

[nalimilan]

Good to go?