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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 normal and derived distributions. use crate::utils::ziggurat; use num_traits::Float; use crate::{ziggurat_tables, Distribution, Open01}; use rand::Rng; use core::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 for StandardNormal { #[inline] fn sample(&self, rng: &mut R) -> f32 { // TODO: use optimal 32-bit implementation let x: f64 = self.sample(rng); x as f32 } } impl Distribution for StandardNormal { fn sample(&self, rng: &mut R) -> f64 { #[inline] fn pdf(x: f64) -> f64 { (-x * x / 2.0).exp() } #[inline] fn zero_case(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 where F: Float, StandardNormal: Distribution { mean: F, std_dev: F, } /// 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", }) } } #[cfg(feature = "std")] impl std::error::Error for Error {} impl Normal where F: Float, StandardNormal: Distribution { /// Construct a new `Normal` distribution with the given mean and /// standard deviation. #[inline] pub fn new(mean: F, std_dev: F) -> Result, Error> { if !(std_dev >= F::zero()) { return Err(Error::StdDevTooSmall); } Ok(Normal { mean, std_dev }) } } impl Distribution for Normal where F: Float, StandardNormal: Distribution { fn sample(&self, rng: &mut R) -> F { let n: F = 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 where F: Float, StandardNormal: Distribution { norm: Normal, } impl LogNormal where F: Float, StandardNormal: Distribution { /// Construct a new `LogNormal` distribution with the given mean /// and standard deviation of the logarithm of the distribution. #[inline] pub fn new(mean: F, std_dev: F) -> Result, Error> { if !(std_dev >= F::zero()) { return Err(Error::StdDevTooSmall); } Ok(LogNormal { norm: Normal::new(mean, std_dev).unwrap(), }) } } impl Distribution for LogNormal where F: Float, StandardNormal: Distribution { fn sample(&self, rng: &mut R) -> F { 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(); } }