High performance Distributions

When using LowLevelParticleFilters, a number of methods related to distributions are defined for static arrays, making logpdf etc. faster. We also provide a new kind of distribution: TupleProduct <: MultivariateDistribution that behaves similarly to the Product distribution. The TupleProduct however stores the individual distributions in a tuple, has compile-time known length and supports Mixed <: ValueSupport, meaning that it can be a product of both Continuous and Discrete dimensions, something not supported by the standard Product. Example

using BenchmarkTools, LowLevelParticleFilters, Distributions
dt = TupleProduct((Normal(0,2), Normal(0,2), Binomial())) # Mixed value support

A small benchmark

sv = @SVector randn(2)
d = Distributions.Product([Normal(0,2), Normal(0,2)])
dt = TupleProduct((Normal(0,2), Normal(0,2)))
dm = MvNormal(2, 2)
@btime logpdf($d,$(Vector(sv))) # 32.449 ns (1 allocation: 32 bytes)
@btime logpdf($dt,$(Vector(sv))) # 21.141 ns (0 allocations: 0 bytes)
@btime logpdf($dm,$(Vector(sv))) # 48.745 ns (1 allocation: 96 bytes)

@btime logpdf($d,$sv) # 22.651 ns (0 allocations: 0 bytes)
@btime logpdf($dt,$sv) # 0.021 ns (0 allocations: 0 bytes)
@btime logpdf($dm,$sv) # 0.021 ns (0 allocations: 0 bytes)

Without loading LowLevelParticleFilters, the timing for the native distributions are the following

@btime logpdf($d,$sv) # 32.621 ns (1 allocation: 32 bytes)
@btime logpdf($dm,$sv) # 46.415 ns (1 allocation: 96 bytes)