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using Sobol, ArraysOfArrays

function sobolrand(n,k, extraskip::Int=0)
    ω = SobolSeq(k)
    Sobol.skip(ω, n) # recommended in the Sobol.jl README
    for _ in 1:extraskip
        Sobol.next!(ω)
    end
    x = Matrix{Float64}(undef, k, n)

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using LinearAlgebra

# Modify column jᵥ to be orthogonal to column jᵤ
function ortho!(A::AbstractMatrix, jᵥ, jᵤ; startat=1)
    # v ← v - projᵤ(v)
    nrows = size(A,1)
    u_v = 0.0
    u_u = 0.0
    @inbounds for i in startat:nrows
        u_v += A[i,jᵤ] * A[i,jᵥ]

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# Origin:
# https://julialang.zulipchat.com/#narrow/stream/274208-helpdesk-.28published.29/topic/Constraining.20method.20signatures/near/262358928

struct MethodWrapper{F, T <: Tuple, R}
    f::F
end

MethodWrapper(f::F, Ts)  where {F}           = MethodWrapper{F, toTuple(Ts), Any}(f)
MethodWrapper(f::F, (Ts, R)::Pair) where {F} = MethodWrapper{F, toTuple(Ts),   R}(f)
toTuple(::Type{T}) where {T} = Tuple{T}

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using Soss
using ZigZagBoomerang
using MeasureTheory


using Soss: logdensity, xform, ConditionalModel
using ZigZagBoomerang
using ForwardDiff
using ForwardDiff: gradient!
using LinearAlgebra

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using Soss, MeasureTheory, AbstractGPs, Test, SampleChainsDynamicHMC

@testset "Soss" begin
    @testset "GP regression" begin
        k = SqExponentialKernel()
        y = randn(3)
        X = randn(3, 1)
        x = [rand(1) for _ in 1:3]

        gp_regression = Soss.@model X begin

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using Soss, MeasureTheory, Plots

# ℓ: log-posterior density we want to sample
# propose: the Markov kernel for the proposal
# x: current point
mhstep = @model ℓ,propose,x begin
    y ~ propose(x)
    u ~ Uniform()
    accept = log(u) < ℓ(y) - ℓ(x)
    return accept ? y : x

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using PositiveFactorizations
using LinearAlgebra
using StatsFuns
using Random
using OnlineStatsBase
using Statistics
const OSB = OnlineStatsBase

const bessel = OSB.bessel

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using Soss
using ZigZagBoomerang
using Soss: logdensity, xform, ConditionalModel
using ForwardDiff
using ForwardDiff: gradient!
using LinearAlgebra
using SparseArrays
using StructArrays
using TransformVariables
using MeasureTheory

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using MacroTools: @q
using GeneralizedGenerated

struct TypelevelExpr{T}
    expr::Expr
    TypelevelExpr(expr::Expr) = new{to_type(expr)}(expr)
end

@gg function with(nt::NamedTuple{N,T}, ::TypelevelExpr{E}) where {N,T,E}

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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