| // 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 normal and derived distributions. |
| |
| use crate::utils::{ziggurat, Float}; |
| use crate::{ziggurat_tables, Distribution, Open01}; |
| use rand::Rng; |
| use std::{error, fmt}; |
| |
| /// Samples floating-point numbers according to the normal distribution |
| /// `N(0, 1)` (a.k.a. a standard normal, or Gaussian). This is equivalent to |
| /// `Normal::new(0.0, 1.0)` but faster. |
| /// |
| /// See `Normal` for the general normal distribution. |
| /// |
| /// Implemented via the ZIGNOR variant[^1] of the Ziggurat method. |
| /// |
| /// [^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::StandardNormal; |
| /// |
| /// let val: f64 = thread_rng().sample(StandardNormal); |
| /// println!("{}", val); |
| /// ``` |
| #[derive(Clone, Copy, Debug)] |
| pub struct StandardNormal; |
| |
| impl Distribution<f32> for StandardNormal { |
| #[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 |
| } |
| } |
| |
| impl Distribution<f64> for StandardNormal { |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 { |
| #[inline] |
| fn pdf(x: f64) -> f64 { |
| (-x * x / 2.0).exp() |
| } |
| #[inline] |
| fn zero_case<R: Rng + ?Sized>(rng: &mut R, u: f64) -> f64 { |
| // compute a random number in the tail by hand |
| |
| // strange initial conditions, because the loop is not |
| // do-while, so the condition should be true on the first |
| // run, they get overwritten anyway (0 < 1, so these are |
| // good). |
| let mut x = 1.0f64; |
| let mut y = 0.0f64; |
| |
| while -2.0 * y < x * x { |
| let x_: f64 = rng.sample(Open01); |
| let y_: f64 = rng.sample(Open01); |
| |
| x = x_.ln() / ziggurat_tables::ZIG_NORM_R; |
| y = y_.ln(); |
| } |
| |
| if u < 0.0 { |
| x - ziggurat_tables::ZIG_NORM_R |
| } else { |
| ziggurat_tables::ZIG_NORM_R - x |
| } |
| } |
| |
| ziggurat( |
| rng, |
| true, // this is symmetric |
| &ziggurat_tables::ZIG_NORM_X, |
| &ziggurat_tables::ZIG_NORM_F, |
| pdf, |
| zero_case, |
| ) |
| } |
| } |
| |
| /// The normal distribution `N(mean, std_dev**2)`. |
| /// |
| /// This uses the ZIGNOR variant of the Ziggurat method, see [`StandardNormal`] |
| /// for more details. |
| /// |
| /// Note that [`StandardNormal`] is an optimised implementation for mean 0, and |
| /// standard deviation 1. |
| /// |
| /// # Example |
| /// |
| /// ``` |
| /// use rand_distr::{Normal, Distribution}; |
| /// |
| /// // mean 2, standard deviation 3 |
| /// let normal = Normal::new(2.0, 3.0).unwrap(); |
| /// let v = normal.sample(&mut rand::thread_rng()); |
| /// println!("{} is from a N(2, 9) distribution", v) |
| /// ``` |
| /// |
| /// [`StandardNormal`]: crate::StandardNormal |
| #[derive(Clone, Copy, Debug)] |
| pub struct Normal<N> { |
| mean: N, |
| std_dev: N, |
| } |
| |
| /// Error type returned from `Normal::new` and `LogNormal::new`. |
| #[derive(Clone, Copy, Debug, PartialEq, Eq)] |
| pub enum Error { |
| /// `std_dev < 0` or `nan`. |
| StdDevTooSmall, |
| } |
| |
| impl fmt::Display for Error { |
| fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { |
| f.write_str(match self { |
| Error::StdDevTooSmall => "std_dev < 0 or is NaN in normal distribution", |
| }) |
| } |
| } |
| |
| impl error::Error for Error {} |
| |
| impl<N: Float> Normal<N> |
| where StandardNormal: Distribution<N> |
| { |
| /// Construct a new `Normal` distribution with the given mean and |
| /// standard deviation. |
| #[inline] |
| pub fn new(mean: N, std_dev: N) -> Result<Normal<N>, Error> { |
| if !(std_dev >= N::from(0.0)) { |
| return Err(Error::StdDevTooSmall); |
| } |
| Ok(Normal { mean, std_dev }) |
| } |
| } |
| |
| impl<N: Float> Distribution<N> for Normal<N> |
| where StandardNormal: Distribution<N> |
| { |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N { |
| let n: N = rng.sample(StandardNormal); |
| self.mean + self.std_dev * n |
| } |
| } |
| |
| |
| /// The log-normal distribution `ln N(mean, std_dev**2)`. |
| /// |
| /// If `X` is log-normal distributed, then `ln(X)` is `N(mean, std_dev**2)` |
| /// distributed. |
| /// |
| /// # Example |
| /// |
| /// ``` |
| /// use rand_distr::{LogNormal, Distribution}; |
| /// |
| /// // mean 2, standard deviation 3 |
| /// let log_normal = LogNormal::new(2.0, 3.0).unwrap(); |
| /// let v = log_normal.sample(&mut rand::thread_rng()); |
| /// println!("{} is from an ln N(2, 9) distribution", v) |
| /// ``` |
| #[derive(Clone, Copy, Debug)] |
| pub struct LogNormal<N> { |
| norm: Normal<N>, |
| } |
| |
| impl<N: Float> LogNormal<N> |
| where StandardNormal: Distribution<N> |
| { |
| /// Construct a new `LogNormal` distribution with the given mean |
| /// and standard deviation of the logarithm of the distribution. |
| #[inline] |
| pub fn new(mean: N, std_dev: N) -> Result<LogNormal<N>, Error> { |
| if !(std_dev >= N::from(0.0)) { |
| return Err(Error::StdDevTooSmall); |
| } |
| Ok(LogNormal { |
| norm: Normal::new(mean, std_dev).unwrap(), |
| }) |
| } |
| } |
| |
| impl<N: Float> Distribution<N> for LogNormal<N> |
| where StandardNormal: Distribution<N> |
| { |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N { |
| self.norm.sample(rng).exp() |
| } |
| } |
| |
| #[cfg(test)] |
| mod tests { |
| use super::*; |
| |
| #[test] |
| fn test_normal() { |
| let norm = Normal::new(10.0, 10.0).unwrap(); |
| let mut rng = crate::test::rng(210); |
| for _ in 0..1000 { |
| norm.sample(&mut rng); |
| } |
| } |
| #[test] |
| #[should_panic] |
| fn test_normal_invalid_sd() { |
| Normal::new(10.0, -1.0).unwrap(); |
| } |
| |
| |
| #[test] |
| fn test_log_normal() { |
| let lnorm = LogNormal::new(10.0, 10.0).unwrap(); |
| let mut rng = crate::test::rng(211); |
| for _ in 0..1000 { |
| lnorm.sample(&mut rng); |
| } |
| } |
| #[test] |
| #[should_panic] |
| fn test_log_normal_invalid_sd() { |
| LogNormal::new(10.0, -1.0).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(213); |
| let mut buf = [zero; 4]; |
| for x in &mut buf { |
| *x = rng.sample(&distr); |
| } |
| assert_eq!(buf, expected); |
| } |
| |
| test_samples(StandardNormal, 0f32, &[ |
| -0.11844189, |
| 0.781378, |
| 0.06563994, |
| -1.1932899, |
| ]); |
| test_samples(StandardNormal, 0f64, &[ |
| -0.11844188827977231, |
| 0.7813779637772346, |
| 0.06563993969580051, |
| -1.1932899004186373, |
| ]); |
| |
| test_samples(Normal::new(0.0, 1.0).unwrap(), 0f32, &[ |
| -0.11844189, |
| 0.781378, |
| 0.06563994, |
| -1.1932899, |
| ]); |
| test_samples(Normal::new(2.0, 0.5).unwrap(), 0f64, &[ |
| 1.940779055860114, |
| 2.3906889818886174, |
| 2.0328199698479, |
| 1.4033550497906813, |
| ]); |
| |
| test_samples(LogNormal::new(0.0, 1.0).unwrap(), 0f32, &[ |
| 0.88830346, 2.1844804, 1.0678421, 0.30322206, |
| ]); |
| test_samples(LogNormal::new(2.0, 0.5).unwrap(), 0f64, &[ |
| 6.964174338639032, |
| 10.921015733601452, |
| 7.6355881556915906, |
| 4.068828213584092, |
| ]); |
| } |
| } |