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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 <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);
}
}