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 // 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 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 {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(rng: &mut R) -> StandardNormal { #[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 Open01(x_) = rng.gen::>(); let Open01(y_) = rng.gen::>(); 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 for Normal { fn sample(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } } impl IndependentSample for Normal { fn ind_sample(&self, rng: &mut R) -> f64 { let StandardNormal(n) = rng.gen::(); 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 for LogNormal { fn sample(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } } impl IndependentSample for LogNormal { fn ind_sample(&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); } }