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Diffstat (limited to 'rand/src/distributions/normal.rs')
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diff --git a/rand/src/distributions/normal.rs b/rand/src/distributions/normal.rs new file mode 100644 index 0000000..280613d --- /dev/null +++ b/rand/src/distributions/normal.rs @@ -0,0 +1,201 @@ +// Copyright 2013 The Rust Project Developers. See the COPYRIGHT +// file at the top-level directory of this distribution and at +// http://rust-lang.org/COPYRIGHT. +// +// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or +// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license +// <LICENSE-MIT or http://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 {Rng, Rand, Open01}; +use distributions::{ziggurat, ziggurat_tables, Sample, IndependentSample}; + +/// A wrapper around an `f64` to generate N(0, 1) random numbers +/// (a.k.a. a standard normal, or Gaussian). +/// +/// 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*](http://www.doornik.com/research/ziggurat.pdf). Nuffield +/// College, Oxford +/// +/// # Example +/// +/// ```rust +/// use rand::distributions::normal::StandardNormal; +/// +/// let StandardNormal(x) = rand::random(); +/// println!("{}", x); +/// ``` +#[derive(Clone, Copy, Debug)] +pub struct StandardNormal(pub f64); + +impl Rand for StandardNormal { + fn rand<R:Rng>(rng: &mut R) -> StandardNormal { + #[inline] + fn pdf(x: f64) -> f64 { + (-x*x/2.0).exp() + } + #[inline] + fn zero_case<R:Rng>(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 Open01(x_) = rng.gen::<Open01<f64>>(); + let Open01(y_) = rng.gen::<Open01<f64>>(); + + 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 } + } + + StandardNormal(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. +/// +/// # Example +/// +/// ```rust +/// use rand::distributions::{Normal, IndependentSample}; +/// +/// // mean 2, standard deviation 3 +/// let normal = Normal::new(2.0, 3.0); +/// let v = normal.ind_sample(&mut rand::thread_rng()); +/// println!("{} is from a N(2, 9) distribution", v) +/// ``` +#[derive(Clone, Copy, Debug)] +pub struct Normal { + mean: f64, + std_dev: f64, +} + +impl Normal { + /// Construct a new `Normal` distribution with the given mean and + /// standard deviation. + /// + /// # Panics + /// + /// Panics if `std_dev < 0`. + #[inline] + pub fn new(mean: f64, std_dev: f64) -> Normal { + assert!(std_dev >= 0.0, "Normal::new called with `std_dev` < 0"); + Normal { + mean: mean, + std_dev: std_dev + } + } +} +impl Sample<f64> for Normal { + fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } +} +impl IndependentSample<f64> for Normal { + fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 { + let StandardNormal(n) = rng.gen::<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 +/// +/// ```rust +/// use rand::distributions::{LogNormal, IndependentSample}; +/// +/// // mean 2, standard deviation 3 +/// let log_normal = LogNormal::new(2.0, 3.0); +/// let v = log_normal.ind_sample(&mut rand::thread_rng()); +/// println!("{} is from an ln N(2, 9) distribution", v) +/// ``` +#[derive(Clone, Copy, Debug)] +pub struct LogNormal { + norm: Normal +} + +impl LogNormal { + /// Construct a new `LogNormal` distribution with the given mean + /// and standard deviation. + /// + /// # Panics + /// + /// Panics if `std_dev < 0`. + #[inline] + pub fn new(mean: f64, std_dev: f64) -> LogNormal { + assert!(std_dev >= 0.0, "LogNormal::new called with `std_dev` < 0"); + LogNormal { norm: Normal::new(mean, std_dev) } + } +} +impl Sample<f64> for LogNormal { + fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } +} +impl IndependentSample<f64> for LogNormal { + fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 { + self.norm.ind_sample(rng).exp() + } +} + +#[cfg(test)] +mod tests { + use distributions::{Sample, IndependentSample}; + use super::{Normal, LogNormal}; + + #[test] + fn test_normal() { + let mut norm = Normal::new(10.0, 10.0); + let mut rng = ::test::rng(); + for _ in 0..1000 { + norm.sample(&mut rng); + norm.ind_sample(&mut rng); + } + } + #[test] + #[should_panic] + fn test_normal_invalid_sd() { + Normal::new(10.0, -1.0); + } + + + #[test] + fn test_log_normal() { + let mut lnorm = LogNormal::new(10.0, 10.0); + let mut rng = ::test::rng(); + for _ in 0..1000 { + lnorm.sample(&mut rng); + lnorm.ind_sample(&mut rng); + } + } + #[test] + #[should_panic] + fn test_log_normal_invalid_sd() { + LogNormal::new(10.0, -1.0); + } +} |