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// Copyright 2018 Developers of the Rand project.
// Copyright 2013 The Rust Project Developers.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or https://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.
#![allow(deprecated)]
use crate::distributions::utils::ziggurat;
use crate::distributions::{ziggurat_tables, Distribution, Open01};
use crate::Rng;
/// Samples floating-point numbers according to the normal distribution
/// `N(0, 1)` (a.k.a. a standard normal, or Gaussian). This is equivalent to
/// `Normal::new(0.0, 1.0)` but faster.
///
/// 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*](
/// https://www.doornik.com/research/ziggurat.pdf).
/// Nuffield College, Oxford
#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
#[derive(Clone, Copy, Debug)]
pub struct StandardNormal;
impl Distribution<f64> for StandardNormal {
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
#[inline]
fn pdf(x: f64) -> f64 {
(-x * x / 2.0).exp()
}
#[inline]
fn zero_case<R: Rng + ?Sized>(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 x_: f64 = rng.sample(Open01);
let y_: f64 = rng.sample(Open01);
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
}
}
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.
///
/// Note that [`StandardNormal`] is an optimised implementation for mean 0, and
/// standard deviation 1.
///
/// [`StandardNormal`]: crate::distributions::StandardNormal
#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
#[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, std_dev }
}
}
impl Distribution<f64> for Normal {
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
let n = rng.sample(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.
#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
#[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 Distribution<f64> for LogNormal {
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
self.norm.sample(rng).exp()
}
}
#[cfg(test)]
mod tests {
use super::{LogNormal, Normal};
use crate::distributions::Distribution;
#[test]
fn test_normal() {
let norm = Normal::new(10.0, 10.0);
let mut rng = crate::test::rng(210);
for _ in 0..1000 {
norm.sample(&mut rng);
}
}
#[test]
#[should_panic]
fn test_normal_invalid_sd() {
Normal::new(10.0, -1.0);
}
#[test]
fn test_log_normal() {
let lnorm = LogNormal::new(10.0, 10.0);
let mut rng = crate::test::rng(211);
for _ in 0..1000 {
lnorm.sample(&mut rng);
}
}
#[test]
#[should_panic]
fn test_log_normal_invalid_sd() {
LogNormal::new(10.0, -1.0);
}
}