Statistics extension for var and std

[Wu-Chenyang]

Currently, the Statistics extension only extends the mean function. The var and std of a StaticMatrix still returns a regular Matrix.

a = @SMatrix(rand(3,4))
mean(a, dims=2) # 3×1 SMatrix
var(a, dims=2) # 3×1 Matrix
std(a, dims=2) # 3×1 Matrix

I provide a preliminary extension for var and std as follows. Attaching them to the end of StaticArraysStatisticsExt.jl should work.

using Statistics
import Statistics: var, std

@inline var(a::StaticArray;corrected::Bool=true, mean=nothing, dims=:) = begin
    m = isnothing(mean) ? Statistics.mean(a; dims=dims) : mean
    denom = _mean_denom(a, dims) - (corrected ? 1 : 0)
    _reduce(+, (a.-m).^2, dims) / denom
end

@inline std(a::SArray; corrected::Bool=true, mean=nothing, dims=:) = sqrt.(var(a; corrected=corrected, mean=mean, dims=dims))