1 // Copyright 2013 The Rust Project Developers. See the COPYRIGHT
2 // file at the top-level directory of this distribution and at
3 // http://rust-lang.org/COPYRIGHT.
5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
8 // option. This file may not be copied, modified, or distributed
9 // except according to those terms.
11 //! The normal and derived distributions.
15 use {Rng, Rand, Open01};
16 use distributions::{ziggurat, ziggurat_tables, Sample, IndependentSample};
18 /// A wrapper around an `f64` to generate N(0, 1) random numbers
19 /// (a.k.a. a standard normal, or Gaussian).
21 /// See `Normal` for the general normal distribution. That this has to
22 /// be unwrapped before use as an `f64` (using either `*` or
23 /// `mem::transmute` is safe).
25 /// Implemented via the ZIGNOR variant[1] of the Ziggurat method.
27 /// [1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to
28 /// Generate Normal Random
29 /// Samples*](http://www.doornik.com/research/ziggurat.pdf). Nuffield
32 pub struct StandardNormal(pub f64);
34 impl Rand for StandardNormal {
35 fn rand<R:Rng>(rng: &mut R) -> StandardNormal {
37 fn pdf(x: f64) -> f64 {
41 fn zero_case<R:Rng>(rng: &mut R, u: f64) -> f64 {
42 // compute a random number in the tail by hand
44 // strange initial conditions, because the loop is not
45 // do-while, so the condition should be true on the first
46 // run, they get overwritten anyway (0 < 1, so these are
51 while -2.0 * y < x * x {
52 let Open01(x_) = rng.gen::<Open01<f64>>();
53 let Open01(y_) = rng.gen::<Open01<f64>>();
55 x = x_.ln() / ziggurat_tables::ZIG_NORM_R;
59 if u < 0.0 { x - ziggurat_tables::ZIG_NORM_R } else { ziggurat_tables::ZIG_NORM_R - x }
62 StandardNormal(ziggurat(
64 true, // this is symmetric
65 &ziggurat_tables::ZIG_NORM_X,
66 &ziggurat_tables::ZIG_NORM_F,
71 /// The normal distribution `N(mean, std_dev**2)`.
73 /// This uses the ZIGNOR variant of the Ziggurat method, see
74 /// `StandardNormal` for more details.
80 /// use std::rand::distributions::{Normal, IndependentSample};
82 /// // mean 2, standard deviation 3
83 /// let normal = Normal::new(2.0, 3.0);
84 /// let v = normal.ind_sample(&mut rand::thread_rng());
85 /// println!("{} is from a N(2, 9) distribution", v)
94 /// Construct a new `Normal` distribution with the given mean and
95 /// standard deviation.
99 /// Panics if `std_dev < 0`.
100 pub fn new(mean: f64, std_dev: f64) -> Normal {
101 assert!(std_dev >= 0.0, "Normal::new called with `std_dev` < 0");
108 impl Sample<f64> for Normal {
109 fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
111 impl IndependentSample<f64> for Normal {
112 fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
113 let StandardNormal(n) = rng.gen::<StandardNormal>();
114 self.mean + self.std_dev * n
119 /// The log-normal distribution `ln N(mean, std_dev**2)`.
121 /// If `X` is log-normal distributed, then `ln(X)` is `N(mean,
122 /// std_dev**2)` distributed.
128 /// use std::rand::distributions::{LogNormal, IndependentSample};
130 /// // mean 2, standard deviation 3
131 /// let log_normal = LogNormal::new(2.0, 3.0);
132 /// let v = log_normal.ind_sample(&mut rand::thread_rng());
133 /// println!("{} is from an ln N(2, 9) distribution", v)
136 pub struct LogNormal {
141 /// Construct a new `LogNormal` distribution with the given mean
142 /// and standard deviation.
146 /// Panics if `std_dev < 0`.
147 pub fn new(mean: f64, std_dev: f64) -> LogNormal {
148 assert!(std_dev >= 0.0, "LogNormal::new called with `std_dev` < 0");
149 LogNormal { norm: Normal::new(mean, std_dev) }
152 impl Sample<f64> for LogNormal {
153 fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
155 impl IndependentSample<f64> for LogNormal {
156 fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
157 self.norm.ind_sample(rng).exp()
163 use std::prelude::v1::*;
165 use distributions::{Sample, IndependentSample};
166 use super::{Normal, LogNormal};
170 let mut norm = Normal::new(10.0, 10.0);
171 let mut rng = ::test::rng();
172 for _ in range(0u, 1000) {
173 norm.sample(&mut rng);
174 norm.ind_sample(&mut rng);
179 fn test_normal_invalid_sd() {
180 Normal::new(10.0, -1.0);
185 fn test_log_normal() {
186 let mut lnorm = LogNormal::new(10.0, 10.0);
187 let mut rng = ::test::rng();
188 for _ in range(0u, 1000) {
189 lnorm.sample(&mut rng);
190 lnorm.ind_sample(&mut rng);
195 fn test_log_normal_invalid_sd() {
196 LogNormal::new(10.0, -1.0);
203 use std::prelude::v1::*;
204 use self::test::Bencher;
205 use std::mem::size_of;
206 use distributions::{Sample};
210 fn rand_normal(b: &mut Bencher) {
211 let mut rng = ::test::weak_rng();
212 let mut normal = Normal::new(-2.71828, 3.14159);
215 for _ in range(0, ::RAND_BENCH_N) {
216 normal.sample(&mut rng);
219 b.bytes = size_of::<f64>() as u64 * ::RAND_BENCH_N;