| // Copyright 2018 Developers of the Rand project. |
| // Copyright 2013 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 exponential distribution. |
| |
| use rand::Rng; |
| use crate::{ziggurat_tables, Distribution}; |
| use crate::utils::{ziggurat, Float}; |
| |
| /// Samples floating-point numbers according to the exponential distribution, |
| /// with rate parameter `λ = 1`. This is equivalent to `Exp::new(1.0)` or |
| /// sampling with `-rng.gen::<f64>().ln()`, but faster. |
| /// |
| /// See `Exp` for the general exponential distribution. |
| /// |
| /// Implemented via the ZIGNOR variant[^1] of the Ziggurat method. The exact |
| /// description in the paper was adjusted to use tables for the exponential |
| /// distribution rather than normal. |
| /// |
| /// [^1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to |
| /// Generate Normal Random Samples*]( |
| /// https://www.doornik.com/research/ziggurat.pdf). |
| /// Nuffield College, Oxford |
| /// |
| /// # Example |
| /// ``` |
| /// use rand::prelude::*; |
| /// use rand_distr::Exp1; |
| /// |
| /// let val: f64 = thread_rng().sample(Exp1); |
| /// println!("{}", val); |
| /// ``` |
| #[derive(Clone, Copy, Debug)] |
| pub struct Exp1; |
| |
| impl Distribution<f32> for Exp1 { |
| #[inline] |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f32 { |
| // TODO: use optimal 32-bit implementation |
| let x: f64 = self.sample(rng); |
| x as f32 |
| } |
| } |
| |
| // This could be done via `-rng.gen::<f64>().ln()` but that is slower. |
| impl Distribution<f64> for Exp1 { |
| #[inline] |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 { |
| #[inline] |
| fn pdf(x: f64) -> f64 { |
| (-x).exp() |
| } |
| #[inline] |
| fn zero_case<R: Rng + ?Sized>(rng: &mut R, _u: f64) -> f64 { |
| ziggurat_tables::ZIG_EXP_R - rng.gen::<f64>().ln() |
| } |
| |
| ziggurat(rng, false, |
| &ziggurat_tables::ZIG_EXP_X, |
| &ziggurat_tables::ZIG_EXP_F, |
| pdf, zero_case) |
| } |
| } |
| |
| /// The exponential distribution `Exp(lambda)`. |
| /// |
| /// This distribution has density function: `f(x) = lambda * exp(-lambda * x)` |
| /// for `x > 0`. |
| /// |
| /// Note that [`Exp1`](crate::Exp1) is an optimised implementation for `lambda = 1`. |
| /// |
| /// # Example |
| /// |
| /// ``` |
| /// use rand_distr::{Exp, Distribution}; |
| /// |
| /// let exp = Exp::new(2.0).unwrap(); |
| /// let v = exp.sample(&mut rand::thread_rng()); |
| /// println!("{} is from a Exp(2) distribution", v); |
| /// ``` |
| #[derive(Clone, Copy, Debug)] |
| pub struct Exp<N> { |
| /// `lambda` stored as `1/lambda`, since this is what we scale by. |
| lambda_inverse: N |
| } |
| |
| /// Error type returned from `Exp::new`. |
| #[derive(Clone, Copy, Debug, PartialEq, Eq)] |
| pub enum Error { |
| /// `lambda <= 0` or `nan`. |
| LambdaTooSmall, |
| } |
| |
| impl<N: Float> Exp<N> |
| where Exp1: Distribution<N> |
| { |
| /// Construct a new `Exp` with the given shape parameter |
| /// `lambda`. |
| #[inline] |
| pub fn new(lambda: N) -> Result<Exp<N>, Error> { |
| if !(lambda > N::from(0.0)) { |
| return Err(Error::LambdaTooSmall); |
| } |
| Ok(Exp { lambda_inverse: N::from(1.0) / lambda }) |
| } |
| } |
| |
| impl<N: Float> Distribution<N> for Exp<N> |
| where Exp1: Distribution<N> |
| { |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N { |
| rng.sample(Exp1) * self.lambda_inverse |
| } |
| } |
| |
| #[cfg(test)] |
| mod test { |
| use super::*; |
| |
| #[test] |
| fn test_exp() { |
| let exp = Exp::new(10.0).unwrap(); |
| let mut rng = crate::test::rng(221); |
| for _ in 0..1000 { |
| assert!(exp.sample(&mut rng) >= 0.0); |
| } |
| } |
| #[test] |
| #[should_panic] |
| fn test_exp_invalid_lambda_zero() { |
| Exp::new(0.0).unwrap(); |
| } |
| #[test] |
| #[should_panic] |
| fn test_exp_invalid_lambda_neg() { |
| Exp::new(-10.0).unwrap(); |
| } |
| |
| #[test] |
| fn value_stability() { |
| fn test_samples<N: Float + core::fmt::Debug, D: Distribution<N>> |
| (distr: D, zero: N, expected: &[N]) |
| { |
| let mut rng = crate::test::rng(223); |
| let mut buf = [zero; 4]; |
| for x in &mut buf { |
| *x = rng.sample(&distr); |
| } |
| assert_eq!(buf, expected); |
| } |
| |
| test_samples(Exp1, 0f32, &[1.079617, 1.8325565, 0.04601166, 0.34471703]); |
| test_samples(Exp1, 0f64, &[1.0796170642388276, 1.8325565304274, |
| 0.04601166186842716, 0.3447170217100157]); |
| |
| test_samples(Exp::new(2.0).unwrap(), 0f32, |
| &[0.5398085, 0.91627824, 0.02300583, 0.17235851]); |
| test_samples(Exp::new(1.0).unwrap(), 0f64, &[ |
| 1.0796170642388276, 1.8325565304274, |
| 0.04601166186842716, 0.3447170217100157]); |
| } |
| } |