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-rw-r--r--rand/src/distributions/poisson.rs151
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diff --git a/rand/src/distributions/poisson.rs b/rand/src/distributions/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.
-#![allow(deprecated)]
-
-use crate::Rng;
-use crate::distributions::{Distribution, Cauchy};
-use crate::distributions::utils::log_gamma;
-
-/// The Poisson distribution `Poisson(lambda)`.
-///
-/// This distribution has a density function:
-/// `f(k) = lambda^k * exp(-lambda) / k!` for `k >= 0`.
-#[deprecated(since="0.7.0", note="moved to rand_distr crate")]
-#[derive(Clone, Copy, Debug)]
-pub struct Poisson {
- lambda: f64,
- // precalculated values
- exp_lambda: f64,
- log_lambda: f64,
- sqrt_2lambda: f64,
- magic_val: f64,
-}
-
-impl Poisson {
- /// Construct a new `Poisson` with the given shape parameter
- /// `lambda`. Panics if `lambda <= 0`.
- pub fn new(lambda: f64) -> Poisson {
- assert!(lambda > 0.0, "Poisson::new called with lambda <= 0");
- let log_lambda = lambda.ln();
- Poisson {
- lambda,
- exp_lambda: (-lambda).exp(),
- log_lambda,
- sqrt_2lambda: (2.0 * lambda).sqrt(),
- magic_val: lambda * log_lambda - log_gamma(1.0 + lambda),
- }
- }
-}
-
-impl Distribution<u64> for Poisson {
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
- // using the algorithm from Numerical Recipes in C
-
- // for low expected values use the Knuth method
- if self.lambda < 12.0 {
- let mut result = 0;
- let mut p = 1.0;
- while p > self.exp_lambda {
- p *= rng.gen::<f64>();
- result += 1;
- }
- result - 1
- }
- // high expected values - rejection method
- else {
- let mut int_result: u64;
-
- // we use the Cauchy distribution as the comparison distribution
- // f(x) ~ 1/(1+x^2)
- let cauchy = Cauchy::new(0.0, 1.0);
-
- loop {
- let mut result;
- 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 >= 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();
- int_result = result as u64;
-
- // 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 = 0.9 * (1.0 + comp_dev * comp_dev)
- * (result * self.log_lambda - log_gamma(1.0 + result) - self.magic_val).exp();
-
- // check with uniform random value - if below the threshold, we are within the target distribution
- if rng.gen::<f64>() <= check {
- break;
- }
- }
- int_result
- }
- }
-}
-
-#[cfg(test)]
-mod test {
- use crate::distributions::Distribution;
- use super::Poisson;
-
- #[test]
- #[cfg(not(miri))] // Miri is too slow
- fn test_poisson_10() {
- let poisson = Poisson::new(10.0);
- let mut rng = crate::test::rng(123);
- let mut sum = 0;
- for _ in 0..1000 {
- sum += poisson.sample(&mut rng);
- }
- let avg = (sum as f64) / 1000.0;
- println!("Poisson average: {}", avg);
- assert!((avg - 10.0).abs() < 0.5); // not 100% certain, but probable enough
- }
-
- #[test]
- #[cfg(not(miri))] // Miri doesn't support transcendental functions
- fn test_poisson_15() {
- // Take the 'high expected values' path
- let poisson = Poisson::new(15.0);
- let mut rng = crate::test::rng(123);
- let mut sum = 0;
- for _ in 0..1000 {
- sum += poisson.sample(&mut rng);
- }
- let avg = (sum as f64) / 1000.0;
- println!("Poisson average: {}", avg);
- 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);
- }
-
- #[test]
- #[should_panic]
- fn test_poisson_invalid_lambda_neg() {
- Poisson::new(-10.0);
- }
-}