| // 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); |
| } |
| } |