Implement supports for sampling momentum with quasi-random sequences.

src/hamiltonian.jl

@@ -207,3 +207,21 @@ refresh(
     z.θ,
     ref.α * z.r + sqrt(1 - ref.α^2) * rand(rng, h.metric, h.kinetic, z.θ),
 )
+
+
+
+include("quasi_MC.jl")
+
+"Quasi-random momentum refreshment."
+struct QuasiRandomMomentumRefreshment <: AbstractMomentumRefreshment 
+    quasi_seed::Quasi_MC_seed
+end
+
+function refresh(
+    rng::Union{AbstractRNG,AbstractVector{<:AbstractRNG}},
+    ref::QuasiRandomMomentumRefreshment,
+    h::Hamiltonian,
+    z::PhasePoint,
+) 
+    return phasepoint(h, z.θ, rand(rng, h.metric, h.kinetic, z.θ, ref.quasi_seed))
+end

src/metric.jl

@@ -3,6 +3,9 @@ $(TYPEDEF)
 
 Abstract type for preconditioning metrics. 
 """
+
+include("quasi_MC.jl")
+
 abstract type AbstractMetric end
 
 _string_M⁻¹(mat::AbstractMatrix, n_chars::Int = 32) = _string_M⁻¹(diag(mat), n_chars)
@@ -104,17 +107,27 @@ function _rand(
     rng::Union{AbstractRNG,AbstractVector{<:AbstractRNG}},
     metric::UnitEuclideanMetric{T},
     kinetic::GaussianKinetic,
+    quasi_seed::Union{Nothing, Quasi_MC_seed} = nothing
 ) where {T}
-    r = randn(rng, T, size(metric)...)
+    if isnothing(quasi_seed)
+        r = randn(rng, T, size(metric)...)
+    else
+        r = get_next_vector(quasi_seed)
+    end
     return r
 end
 
 function _rand(
     rng::Union{AbstractRNG,AbstractVector{<:AbstractRNG}},
     metric::DiagEuclideanMetric{T},
     kinetic::GaussianKinetic,
+    quasi_seed::Union{Nothing, Quasi_MC_seed} = nothing
 ) where {T}
-    r = randn(rng, T, size(metric)...)
+    if isnothing(quasi_seed)
+        r = randn(rng, T, size(metric)...)
+    else
+        r = get_next_vector(quasi_seed)
+    end
     r ./= metric.sqrtM⁻¹
     return r
 end
@@ -123,8 +136,13 @@ function _rand(
     rng::Union{AbstractRNG,AbstractVector{<:AbstractRNG}},
     metric::DenseEuclideanMetric{T},
     kinetic::GaussianKinetic,
+    quasi_seed::Union{Nothing, Quasi_MC_seed} = nothing
 ) where {T}
-    r = randn(rng, T, size(metric)...)
+    if isnothing(quasi_seed)
+        r = randn(rng, T, size(metric)...)
+    else
+        r = get_next_vector(quasi_seed)
+    end
     ldiv!(metric.cholM⁻¹, r)
     return r
 end
@@ -153,5 +171,23 @@ Base.rand(
     kinetic::AbstractKinetic,
     θ::AbstractVecOrMat,
 ) = rand(rng, metric, kinetic)
+
+
 Base.rand(metric::AbstractMetric, kinetic::AbstractKinetic, θ::AbstractVecOrMat) =
     rand(metric, kinetic)
+
+
+Base.rand(
+    rng::AbstractRNG,
+    metric::AbstractMetric,
+    kinetic::AbstractKinetic,
+    θ::AbstractVecOrMat,
+    quasi_mc::Quasi_MC_seed
+) = _rand(rng, metric, kinetic, quasi_mc)
+Base.rand(
+    rng::AbstractVector{<:AbstractRNG},
+    metric::AbstractMetric,
+    kinetic::AbstractKinetic,
+    θ::AbstractVecOrMat,
+    quasi_mc::Quasi_MC_seed
+) = _rand(rng, metric, kinetic, quasi_mc)

src/quasi_MC.jl

@@ -0,0 +1,26 @@
+using QuasiMonteCarlo, Distributions
+
+mutable struct Quasi_MC_seed
+    array::AbstractVecOrMat{<:Real}
+    counter::Int
+
+    # Custom constructor with a default value for `counter`
+    function Quasi_MC_seed(array::AbstractVecOrMat{<:Real}, counter::Int = 1)
+        new(array, counter)
+    end
+end
+
+function get_next_vector(q::Quasi_MC_seed; normalized = true)
+    val = q.array[:, q.counter]
+    q.counter += 1
+    if normalized
+        return uniform_to_normal(val)
+    else
+        return val
+    end
+end
+
+function uniform_to_normal(uniform_vector::Vector{Float64})::Vector{Float64}
+    normal_dist = Normal(0, 1)
+    return [quantile(normal_dist, u) for u in uniform_vector]
+end