fix weighted computations for non-real arrays

[aplavin]

Update to #649 following suggestion by @nalimilan

[nalimilan]

Thanks. have you tried some benchmarking? dot doesn't seem to be faster anymore on a Julia 1.6, so I wonder whether we could always use broadcast when VERSION >= v"1.6.0" to be able to simplify code later.

julia> using LinearAlgebra, BenchmarkTools

julia> x = rand(10_000);

julia> xm = Vector{Union{Float64, Missing}}(x);

julia> w = rand(10_000);

julia> f(A, w) = sum(Base.Broadcast.instantiate(Base.Broadcast.Broadcasted(*, (A, w))))
f (generic function with 1 method)

julia> @btime dot(x, w);
  2.209 μs (1 allocation: 16 bytes)

julia> @btime f(x, w);
  2.472 μs (1 allocation: 16 bytes)

julia> @btime dot(xm, w);
  20.162 μs (1 allocation: 16 bytes)

julia> @btime f(xm, w);
  23.823 μs (1 allocation: 16 bytes)

[aplavin]

I may try to make it always go through the broadcasting implementation, as you say. But I'm not familiar with how to use the version check so that there is no runtime penalty, could you give an example?

[nalimilan]

Sorry for the late reply. You can just do if VERSION > v"X.Y.Z" (if @static if if not in the global scope).

[aplavin]

Bump without any changes...

The broadcast-based method doesn't work for empty collections:

Expression: wsum(Float64[], Float64[]) === 0.0
ArgumentError: reducing over an empty collection is not allowed

It also doesn't handle multidim arrays, see my comment above. So I didn't add the VERSION >= 1.6 condition as you suggested.

[nalimilan]

Another option that I used at https://github.com/JuliaLang/Statistics.jl/pull/94 is to simply do vec(v)' * w.