PoissonRandom.jl: Fast Poisson Random Numbers

PoissonRandom.jl is a component of the SciML ecosystem which allows for fast generation of Poisson random numbers.

Installation

To install PoissonRandom.jl, use the Julia package manager:

using Pkg
Pkg.add("PoissonRandom")

Usage

# Simple Poisson random
pois_rand(λ)

# Using another RNG
using RandomNumbers
rng = Xorshifts.Xoroshiro128Plus()
pois_rand(rng,λ)

Implementation

It mixes two methods. A simple count method and a method from a normal approximation. See this blog post for details.

Benchmark

using RandomNumbers, Distributions, BenchmarkTools, StaticArrays,
      RecursiveArrayTools, Plots, PoissonRandom
labels = ["count_rand","ad_rand","pois_rand","Distributions.jl"]
rng = Xorshifts.Xoroshiro128Plus()

function n_count(rng,λ,n)
  tmp = 0
  for i in 1:n
    tmp += PoissonRandom.count_rand(rng,λ)
  end
end

function n_pois(rng,λ,n)
  tmp = 0
  for i in 1:n
    tmp += pois_rand(rng,λ)
  end
end

function n_ad(rng,λ,n)
  tmp = 0
  for i in 1:n
    tmp += PoissonRandom.ad_rand(rng,λ)
  end
end

function n_dist(λ,n)
  tmp = 0
  for i in 1:n
    tmp += rand(Poisson(λ))
  end
end

function time_λ(rng,λ,n)
  t1 = @elapsed n_count(rng,λ,n)
  t2 = @elapsed n_ad(rng,λ,n)
  t3 = @elapsed n_pois(rng,λ,n)
  t4 = @elapsed n_dist(λ,n)
  @SArray [t1,t2,t3,t4]
end

# Compile
time_λ(rng,5,5000000)
# Run with a bunch of λ
times = VectorOfArray([time_λ(rng,n,5000000) for n in 1:20])'
plot(times,labels = labels, lw = 3)

So this package ends up about 30% or so faster than Distributions.jl (the method at the far edge is λ-independent so that goes on forever).

Contributing

• Please refer to the SciML ColPrac: Contributor's Guide on Collaborative Practices for Community Packages for guidance on PRs, issues, and other matters relating to contributing to SciML.
• There are a few community forums:
  • the #diffeq-bridged channel in the Julia Slack
  • JuliaDiffEq on Gitter
  • on the Julia Discourse forums
  • see also SciML Community page

Reproducibility

Status `~/work/PoissonRandom.jl/PoissonRandom.jl/docs/Project.toml`
  [e30172f5] Documenter v0.27.24
  [e409e4f3] PoissonRandom v0.4.4 `~/work/PoissonRandom.jl/PoissonRandom.jl`

Julia Version 1.8.5
Commit 17cfb8e65ea (2023-01-08 06:45 UTC)
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 2 × Intel(R) Xeon(R) CPU E5-2673 v3 @ 2.40GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-13.0.1 (ORCJIT, haswell)
  Threads: 1 on 2 virtual cores

Status `~/work/PoissonRandom.jl/PoissonRandom.jl/docs/Manifest.toml`
  [a4c015fc] ANSIColoredPrinters v0.0.1
  [ffbed154] DocStringExtensions v0.9.3
  [e30172f5] Documenter v0.27.24
  [b5f81e59] IOCapture v0.2.2
  [682c06a0] JSON v0.21.3
  [69de0a69] Parsers v2.5.8
  [e409e4f3] PoissonRandom v0.4.4 `~/work/PoissonRandom.jl/PoissonRandom.jl`
  [21216c6a] Preferences v1.3.0
  [66db9d55] SnoopPrecompile v1.0.3
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [b77e0a4c] InteractiveUtils
  [76f85450] LibGit2
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [6462fe0b] Sockets
  [fa267f1f] TOML v1.0.0
  [8dfed614] Test
  [4ec0a83e] Unicode