computing the weighted mean along dimension dims.

[FerreolS]

I would like to compute weighted mean along a given dimension as it is possible with mean.
The following function implements this feature

function weightedmean_dims(iterable; dims::Union{Colon,Int}=:)
           v = [el.val for el in iterable]
           w = [inv(el.err)^2 for el in iterable]
           invsumw = inv.(sum(w; dims=dims))
           return measurement.(sum(v .* w; dims=dims) .* invsumw, sqrt.(invsumw))
 end

However it is a bit less efficient:

julia> N  = 1_000_000;

julia> m = measurement.(randn(N,5), rand(N,5));

julia> @btime weightedmean(m)
  29.861 ms (8 allocations: 76.30 MiB)
-0.139496023 ± 3.0e-8

julia> @btime weightedmean_dims(m)
  37.372 ms (11 allocations: 114.45 MiB)
-0.139496023 ± 3.0e-8

julia> @btime weightedmean_dims(m; dims=1)
  36.914 ms (22 allocations: 114.45 MiB)
1×5 Matrix{Measurement{Float64}}:
 -0.0789744±3.4e-8  -0.466307±7.2e-8  -0.0655678±5.7e-7  0.720289±3.3e-7  0.0534679±2.9e-7

Any suggestion to improve the performance? before I do a PR (if requested)

[FerreolS]

I found a much faster implementation for both:

function weightedmean_dims(iterable;  dims::Union{Colon,Int}=:)
     _weightedmean_dims(iterable,dims)
end

function _weightedmean_dims(iterable, dims::Int)
    out = mapreduce((a, b) -> map(.+, a, b), iterable, dims=dims, init=(0.0, 0.0)) do el::Measurement
        w = inv(el.err)^2
        el.val * w, w
    end
    invsumw = map(x -> inv(x[2]), out)
    return measurement.(map((x, y) -> y * inv(x[1]), out, invsumw), sqrt.(invsumw))
end

function _weightedmean_dims(iterable, ::Colon)
    out = mapreduce((a, b) -> map(.+, a, b), iterable, init=(0.0, 0.0)) do el::Measurement
        w = inv(el.err)^2
        el.val * w, w
    end
    invsumw = inv(out[2])
    return measurement(out[1] * invsumw, sqrt(invsumw))
end

Thanks to mapreduce it is almost 3 times faster than the original implementation

julia> N  = 1_000_000;

julia> m = measurement.(randn(N,5), rand(N,5));

julia> @btime weightedmean(m)
  29.617 ms (8 allocations: 76.30 MiB)
-0.534119529 ± 7.0e-8

julia> @btime weightedmean_dims(m)
  10.199 ms (2 allocations: 96 bytes)
-0.534119529 ± 7.0e-8

julia> @btime weightedmean_dims(m; dims=1)
  10.294 ms (13 allocations: 864 bytes)
1×5 Matrix{Measurement{Float64}}:
 -5.1e-29±7.2e-8  -3.9e-26±4.6e-7  -7.9e-24±1.3e-6  -2.1e-25±5.7e-7  3.2e-25±5.5e-7

I'll make a PR