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product.jl
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product.jl
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export ProductMeasure
using MappedArrays
using Base: @propagate_inbounds
import Base
using FillArrays
abstract type AbstractProductMeasure <: AbstractMeasure end
struct ProductMeasure{F,S,I} <: AbstractProductMeasure
f::Kernel{F,S}
pars::I
end
# TODO: Test for equality without traversal, probably by first converting to a
# canonical form
function Base.:(==)(a::ProductMeasure, b::ProductMeasure)
all(zip(a.pars, b.pars)) do (aᵢ, bᵢ)
a.f(aᵢ) == b.f(bᵢ)
end
end
Base.size(μ::ProductMeasure) = size(marginals(μ))
Base.length(m::ProductMeasure{T}) where {T} = length(marginals(μ))
basemeasure(d::ProductMeasure) = productmeasure(basekernel(d.f), d.pars)
# TODO: Do we need these methods?
# basemeasure(d::ProductMeasure) = ProductMeasure(basemeasure ∘ d.f, d.pars)
# basemeasure(d::ProductMeasure{typeof(identity)}) = ProductMeasure(identity, map(basemeasure, d.pars))
# basemeasure(d::ProductMeasure{typeof(identity), <:FillArrays.Fill}) = ProductMeasure(identity, map(basemeasure, d.pars))
export marginals
function marginals(d::ProductMeasure{F,S,I}) where {F,S,I}
_marginals(d, isiterable(I))
end
function _marginals(d::ProductMeasure, ::Iterable)
return (d.f(i) for i in d.pars)
end
function _marginals(d::ProductMeasure{F,S,I}, ::NonIterable) where {F,S,I}
error("Type $I is not iterable. Add an `iterate` or `marginals` method to fix.")
end
testvalue(d::ProductMeasure) = map(testvalue, marginals(d))
function Pretty.tile(μ::ProductMeasure{F,S,NamedTuple{N,T}}) where {F,S,N,T}
result = Pretty.literal("Product(")
result *= Pretty.pair_layout(μ.f, μ.pars; sep = ", ")
result *= Pretty.literal(")")
end
function Base.rand(rng::AbstractRNG, ::Type{T}, d::ProductMeasure) where {T}
_rand(rng, T, d, marginals(d))
end
function _rand(rng::AbstractRNG, ::Type{T}, d::ProductMeasure, mar) where {T}
(rand(rng, T, m) for m in mar)
end
###############################################################################
# I <: Tuple
struct TupleProductMeasure{T} <: AbstractProductMeasure
pars::T
end
export ⊗
⊗(μs::AbstractMeasure...) = productmeasure(μs)
marginals(d::TupleProductMeasure{T}) where {F,T<:Tuple} = d.pars
function Pretty.tile(μ::TupleProductMeasure{T}) where {F,T<:Tuple}
mar = marginals(μ)
Pretty.list_layout(Pretty.Layout[Pretty.tile.(mar)...]; sep = " ⊗ ")
end
@inline function logdensity(d::TupleProductMeasure, x::Tuple) where {T<:Tuple}
mapreduce(logdensity, +, d.pars, x)
end
function Base.rand(rng::AbstractRNG, ::Type{T}, d::TupleProductMeasure) where {T}
rand.(d.pars)
end
###############################################################################
# I <: AbstractArray
marginals(d::ProductMeasure{F,S,A}) where {F,S,A<:AbstractArray} = mappedarray(d.f, d.pars)
function marginals(d::ProductMeasure{<:Returns,S,A}) where {F,S,A<:AbstractArray}
Fill(d.f.f.value, size(d.pars))
# mappedarray(d.f.f, d.pars)
end
function logdensity(d::ProductMeasure, x)
mapreduce(logdensity, +, marginals(d), x)
end
function logdensity(d::ProductMeasure{<:Returns}, x)
sum(x -> logdensity(d.f.f.value, x), x)
end
function Pretty.tile(d::ProductMeasure{F,S,A}) where {F,S,A}
result = Pretty.literal("For(")
result *= Pretty.pair_layout(Pretty.tile(d.f), Pretty.tile(d.pars); sep = ", ")
result *= Pretty.literal(")")
end
###############################################################################
# I <: CartesianIndices
function Pretty.tile(d::ProductMeasure{F,S,I}) where {F,S,I<:CartesianIndices}
result = Pretty.literal("For(")
result *= Pretty.pair_layout(Pretty.tile(d.f), Pretty.tile(size(d.pars)); sep = ", ")
result *= Pretty.literal(")")
end
# function Base.rand(rng::AbstractRNG, ::Type{T}, d::ProductMeasure{F,S,I}) where {T,F,I<:CartesianIndices}
# end
###############################################################################
# I <: Base.Generator
export rand!
using Random: rand!, GLOBAL_RNG, AbstractRNG
function logdensity(d::ProductMeasure{F,S,I}, x) where {F,S,I<:Base.Generator}
sum((logdensity(dj, xj) for (dj, xj) in zip(marginals(d), x)))
end
@propagate_inbounds function Random.rand!(
rng::AbstractRNG,
d::ProductMeasure,
x::AbstractArray
)
# TODO: Generalize this
T = Float64
for (j, m) in zip(eachindex(x), marginals(d))
@inbounds x[j] = rand(rng, T, m)
end
return x
end
export rand!
using Random: rand!, GLOBAL_RNG, AbstractRNG
function _rand(rng::AbstractRNG, ::Type{T}, d::ProductMeasure, mar::AbstractArray) where {T}
elT = typeof(rand(rng, T, first(mar)))
sz = size(mar)
x = Array{elT,length(sz)}(undef, sz)
rand!(rng, d, x)
end
# TODO:
# function Base.rand(rng::AbstractRNG, d::ProductMeasure)
# return rand(rng, sampletype(d), d)
# end
# function Base.rand(T::Type, d::ProductMeasure)
# return rand(Random.GLOBAL_RNG, T, d)
# end
# function Base.rand(d::ProductMeasure)
# T = sampletype(d)
# return rand(Random.GLOBAL_RNG, T, d)
# end
function sampletype(d::ProductMeasure{A}) where {T,N,A<:AbstractArray{T,N}}
S = @inbounds sampletype(marginals(d)[1])
Array{S,N}
end
function sampletype(d::ProductMeasure{<:Tuple})
Tuple{sampletype.(marginals(d))...}
end
# function logdensity(μ::ProductMeasure{Aμ}, x::Ax) where {Aμ <: MappedArray, Ax <: AbstractArray}
# μ.data
# end
function ConstructionBase.constructorof(::Type{P}) where {F,S,I,P<:ProductMeasure{F,S,I}}
p -> productmeasure(d.f, p)
end
# function Accessors.set(d::ProductMeasure{N}, ::typeof(params), p) where {N}
# setproperties(d, NamedTuple{N}(p...))
# end
# function Accessors.set(d::ProductMeasure{F,T}, ::typeof(params), p::Tuple) where {F, T<:Tuple}
# set.(marginals(d), params, p)
# end
# function logdensity(μ::ProductMeasure, ν::ProductMeasure, x)
# sum(zip(marginals(μ), marginals(ν), x)) do μ_ν_x
# logdensity(μ_ν_x...)
# end
# end
function kernelfactor(μ::ProductMeasure{F,S,<:Fill}) where {F,S}
k = kernel(first(marginals(μ)))
(p -> k.f(p)^size(μ), k.ops)
end
function kernelfactor(μ::ProductMeasure{F,S,A}) where {F,S,A<:AbstractArray}
(p -> set.(marginals(μ), params, p), μ.pars)
end