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-rw-r--r--rand/rand_distr/src/poisson.rs233
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diff --git a/rand/rand_distr/src/poisson.rs b/rand/rand_distr/src/poisson.rs
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-// Copyright 2018 Developers of the Rand project.
-// Copyright 2016-2017 The Rust Project Developers.
-//
-// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
-// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
-// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
-// option. This file may not be copied, modified, or distributed
-// except according to those terms.
-
-//! The Poisson distribution.
-
-use rand::Rng;
-use crate::{Distribution, Cauchy, Standard};
-use crate::utils::Float;
-
-/// The Poisson distribution `Poisson(lambda)`.
-///
-/// This distribution has a density function:
-/// `f(k) = lambda^k * exp(-lambda) / k!` for `k >= 0`.
-///
-/// # Example
-///
-/// ```
-/// use rand_distr::{Poisson, Distribution};
-///
-/// let poi = Poisson::new(2.0).unwrap();
-/// let v: u64 = poi.sample(&mut rand::thread_rng());
-/// println!("{} is from a Poisson(2) distribution", v);
-/// ```
-#[derive(Clone, Copy, Debug)]
-pub struct Poisson<N> {
- lambda: N,
- // precalculated values
- exp_lambda: N,
- log_lambda: N,
- sqrt_2lambda: N,
- magic_val: N,
-}
-
-/// Error type returned from `Poisson::new`.
-#[derive(Clone, Copy, Debug, PartialEq, Eq)]
-pub enum Error {
- /// `lambda <= 0` or `nan`.
- ShapeTooSmall,
-}
-
-impl<N: Float> Poisson<N>
-where Standard: Distribution<N>
-{
- /// Construct a new `Poisson` with the given shape parameter
- /// `lambda`.
- pub fn new(lambda: N) -> Result<Poisson<N>, Error> {
- if !(lambda > N::from(0.0)) {
- return Err(Error::ShapeTooSmall);
- }
- let log_lambda = lambda.ln();
- Ok(Poisson {
- lambda,
- exp_lambda: (-lambda).exp(),
- log_lambda,
- sqrt_2lambda: (N::from(2.0) * lambda).sqrt(),
- magic_val: lambda * log_lambda - (N::from(1.0) + lambda).log_gamma(),
- })
- }
-}
-
-impl<N: Float> Distribution<N> for Poisson<N>
-where Standard: Distribution<N>
-{
- #[inline]
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
- // using the algorithm from Numerical Recipes in C
-
- // for low expected values use the Knuth method
- if self.lambda < N::from(12.0) {
- let mut result = N::from(0.);
- let mut p = N::from(1.0);
- while p > self.exp_lambda {
- p *= rng.gen::<N>();
- result += N::from(1.);
- }
- result - N::from(1.)
- }
- // high expected values - rejection method
- else {
- // we use the Cauchy distribution as the comparison distribution
- // f(x) ~ 1/(1+x^2)
- let cauchy = Cauchy::new(N::from(0.0), N::from(1.0)).unwrap();
- let mut result;
-
- loop {
- let mut comp_dev;
-
- loop {
- // draw from the Cauchy distribution
- comp_dev = rng.sample(cauchy);
- // shift the peak of the comparison ditribution
- result = self.sqrt_2lambda * comp_dev + self.lambda;
- // repeat the drawing until we are in the range of possible values
- if result >= N::from(0.0) {
- break;
- }
- }
- // now the result is a random variable greater than 0 with Cauchy distribution
- // the result should be an integer value
- result = result.floor();
-
- // this is the ratio of the Poisson distribution to the comparison distribution
- // the magic value scales the distribution function to a range of approximately 0-1
- // since it is not exact, we multiply the ratio by 0.9 to avoid ratios greater than 1
- // this doesn't change the resulting distribution, only increases the rate of failed drawings
- let check = N::from(0.9) * (N::from(1.0) + comp_dev * comp_dev)
- * (result * self.log_lambda - (N::from(1.0) + result).log_gamma() - self.magic_val).exp();
-
- // check with uniform random value - if below the threshold, we are within the target distribution
- if rng.gen::<N>() <= check {
- break;
- }
- }
- result
- }
- }
-}
-
-impl<N: Float> Distribution<u64> for Poisson<N>
-where Standard: Distribution<N>
-{
- #[inline]
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
- let result: N = self.sample(rng);
- result.to_u64().unwrap()
- }
-}
-
-#[cfg(test)]
-mod test {
- use crate::Distribution;
- use super::Poisson;
-
- #[test]
- fn test_poisson_10() {
- let poisson = Poisson::new(10.0).unwrap();
- let mut rng = crate::test::rng(123);
- let mut sum_u64 = 0;
- let mut sum_f64 = 0.;
- for _ in 0..1000 {
- let s_u64: u64 = poisson.sample(&mut rng);
- let s_f64: f64 = poisson.sample(&mut rng);
- sum_u64 += s_u64;
- sum_f64 += s_f64;
- }
- let avg_u64 = (sum_u64 as f64) / 1000.0;
- let avg_f64 = sum_f64 / 1000.0;
- println!("Poisson averages: {} (u64) {} (f64)", avg_u64, avg_f64);
- for &avg in &[avg_u64, avg_f64] {
- assert!((avg - 10.0).abs() < 0.5); // not 100% certain, but probable enough
- }
- }
-
- #[test]
- fn test_poisson_15() {
- // Take the 'high expected values' path
- let poisson = Poisson::new(15.0).unwrap();
- let mut rng = crate::test::rng(123);
- let mut sum_u64 = 0;
- let mut sum_f64 = 0.;
- for _ in 0..1000 {
- let s_u64: u64 = poisson.sample(&mut rng);
- let s_f64: f64 = poisson.sample(&mut rng);
- sum_u64 += s_u64;
- sum_f64 += s_f64;
- }
- let avg_u64 = (sum_u64 as f64) / 1000.0;
- let avg_f64 = sum_f64 / 1000.0;
- println!("Poisson average: {} (u64) {} (f64)", avg_u64, avg_f64);
- for &avg in &[avg_u64, avg_f64] {
- assert!((avg - 15.0).abs() < 0.5); // not 100% certain, but probable enough
- }
- }
-
- #[test]
- fn test_poisson_10_f32() {
- let poisson = Poisson::new(10.0f32).unwrap();
- let mut rng = crate::test::rng(123);
- let mut sum_u64 = 0;
- let mut sum_f32 = 0.;
- for _ in 0..1000 {
- let s_u64: u64 = poisson.sample(&mut rng);
- let s_f32: f32 = poisson.sample(&mut rng);
- sum_u64 += s_u64;
- sum_f32 += s_f32;
- }
- let avg_u64 = (sum_u64 as f32) / 1000.0;
- let avg_f32 = sum_f32 / 1000.0;
- println!("Poisson averages: {} (u64) {} (f32)", avg_u64, avg_f32);
- for &avg in &[avg_u64, avg_f32] {
- assert!((avg - 10.0).abs() < 0.5); // not 100% certain, but probable enough
- }
- }
-
- #[test]
- fn test_poisson_15_f32() {
- // Take the 'high expected values' path
- let poisson = Poisson::new(15.0f32).unwrap();
- let mut rng = crate::test::rng(123);
- let mut sum_u64 = 0;
- let mut sum_f32 = 0.;
- for _ in 0..1000 {
- let s_u64: u64 = poisson.sample(&mut rng);
- let s_f32: f32 = poisson.sample(&mut rng);
- sum_u64 += s_u64;
- sum_f32 += s_f32;
- }
- let avg_u64 = (sum_u64 as f32) / 1000.0;
- let avg_f32 = sum_f32 / 1000.0;
- println!("Poisson average: {} (u64) {} (f32)", avg_u64, avg_f32);
- for &avg in &[avg_u64, avg_f32] {
- assert!((avg - 15.0).abs() < 0.5); // not 100% certain, but probable enough
- }
- }
-
- #[test]
- #[should_panic]
- fn test_poisson_invalid_lambda_zero() {
- Poisson::new(0.0).unwrap();
- }
-
- #[test]
- #[should_panic]
- fn test_poisson_invalid_lambda_neg() {
- Poisson::new(-10.0).unwrap();
- }
-}
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