`rand` method for "hypercubes", e.g. Sobol sequence

hypercube.jl

using Sobol
using MeasureTheory

abstract type Hypercube{k} end

struct SobolHypercube{k} <: Hypercube{k}
    seq :: SobolSeq{k}
    value :: Vector{Float64}
    index :: Ref{Int}  # start at zero

    function SobolHypercube(k::Int)
        seq = SobolSeq(k)
        value = Sobol.next!(seq)
        return new{k}(seq, value, 0)
    end
end

function Sobol.next!(s::SobolHypercube)
    s.index[] = 0
    Sobol.next!(s.seq, s.value)
end


function rand(ω::SobolHypercube{k}) where {k}
    ω.value[ω.index[] += 1]
end

function rand(ω::Hypercube, d::ParameterizedMeasure)
    Dists.quantile(distproxy(d), rand(ω))
end

function rand(ω::Hypercube, d::ProductMeasure)
    [rand(ω, dj) for dj in d.data]
end


using Colors
using GLMakie

function makeplot()
    ω = SobolHypercube(100)
    x = range(-2,2,length=100)
    d = For(x) do xj Normal(2*xj, 1/(1 + xj^2)) end
    y = rand(ω, d)

    plt = scatter(x,y,markersize=2, color=colorant"rgba(0,0,0,0.1)")
    for j in 1:100
        next!(ω)
        y = rand(ω, d)
        scatter!(x, y, markersize=2, color=colorant"rgba(0,0,0,0.1)")
    end
    plt
end

makeplot()