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 // Copyright 2018 Developers of the Rand project. // Copyright 2013 The Rust Project Developers. // // Licensed under the Apache License, Version 2.0 or the MIT license // , 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::().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 for Exp1 { #[inline] fn sample(&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::().ln()` but that is slower. impl Distribution for Exp1 { #[inline] fn sample(&self, rng: &mut R) -> f64 { #[inline] fn pdf(x: f64) -> f64 { (-x).exp() } #[inline] fn zero_case(rng: &mut R, _u: f64) -> f64 { ziggurat_tables::ZIG_EXP_R - rng.gen::().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 { /// `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 Exp where Exp1: Distribution { /// Construct a new `Exp` with the given shape parameter /// `lambda`. #[inline] pub fn new(lambda: N) -> Result, Error> { if !(lambda > N::from(0.0)) { return Err(Error::LambdaTooSmall); } Ok(Exp { lambda_inverse: N::from(1.0) / lambda }) } } impl Distribution for Exp where Exp1: Distribution { fn sample(&self, rng: &mut R) -> N { rng.sample(Exp1) * self.lambda_inverse } } #[cfg(test)] mod test { use crate::Distribution; use super::Exp; #[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(); } }