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Diffstat (limited to 'rand/rand_distr/src/normal.rs')
| -rw-r--r-- | rand/rand_distr/src/normal.rs | 219 |
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diff --git a/rand/rand_distr/src/normal.rs b/rand/rand_distr/src/normal.rs new file mode 100644 index 0000000..882754f --- /dev/null +++ b/rand/rand_distr/src/normal.rs @@ -0,0 +1,219 @@ +// 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 rand::Rng; +use crate::{ziggurat_tables, Distribution, Open01}; +use crate::utils::{ziggurat, Float}; + +/// 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<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 crate::Distribution; + use super::{Normal, LogNormal}; + + #[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(); + } +} |