/
cauchy.rs
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/
cauchy.rs
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// Copyright 2018 Developers of the Rand project.
// Copyright 2016-2017 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 Cauchy distribution.
use rand::Rng;
use crate::{Distribution, Standard};
use crate::utils::Float;
/// The Cauchy distribution `Cauchy(median, scale)`.
///
/// This distribution has a density function:
/// `f(x) = 1 / (pi * scale * (1 + ((x - median) / scale)^2))`
///
/// # Example
///
/// ```
/// use rand_distr::{Cauchy, Distribution};
///
/// let cau = Cauchy::new(2.0, 5.0).unwrap();
/// let v = cau.sample(&mut rand::thread_rng());
/// println!("{} is from a Cauchy(2, 5) distribution", v);
/// ```
#[derive(Clone, Copy, Debug)]
pub struct Cauchy<N> {
median: N,
scale: N,
}
/// Error type returned from `Cauchy::new`.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum Error {
/// `scale <= 0` or `nan`.
ScaleTooSmall,
}
impl<N: Float> Cauchy<N>
where Standard: Distribution<N>
{
/// Construct a new `Cauchy` with the given shape parameters
/// `median` the peak location and `scale` the scale factor.
pub fn new(median: N, scale: N) -> Result<Cauchy<N>, Error> {
if !(scale > N::from(0.0)) {
return Err(Error::ScaleTooSmall);
}
Ok(Cauchy {
median,
scale
})
}
}
impl<N: Float> Distribution<N> for Cauchy<N>
where Standard: Distribution<N>
{
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
// sample from [0, 1)
let x = Standard.sample(rng);
// get standard cauchy random number
// note that π/2 is not exactly representable, even if x=0.5 the result is finite
let comp_dev = (N::pi() * x).tan();
// shift and scale according to parameters
self.median + self.scale * comp_dev
}
}
#[cfg(test)]
mod test {
use super::*;
fn median(mut numbers: &mut [f64]) -> f64 {
sort(&mut numbers);
let mid = numbers.len() / 2;
numbers[mid]
}
fn sort(numbers: &mut [f64]) {
numbers.sort_by(|a, b| a.partial_cmp(b).unwrap());
}
#[test]
fn test_cauchy_averages() {
// NOTE: given that the variance and mean are undefined,
// this test does not have any rigorous statistical meaning.
let cauchy = Cauchy::new(10.0, 5.0).unwrap();
let mut rng = crate::test::rng(123);
let mut numbers: [f64; 1000] = [0.0; 1000];
let mut sum = 0.0;
for i in 0..1000 {
numbers[i] = cauchy.sample(&mut rng);
sum += numbers[i];
}
let median = median(&mut numbers);
println!("Cauchy median: {}", median);
assert!((median - 10.0).abs() < 0.4); // not 100% certain, but probable enough
let mean = sum / 1000.0;
println!("Cauchy mean: {}", mean);
// for a Cauchy distribution the mean should not converge
assert!((mean - 10.0).abs() > 0.4); // not 100% certain, but probable enough
}
#[test]
#[should_panic]
fn test_cauchy_invalid_scale_zero() {
Cauchy::new(0.0, 0.0).unwrap();
}
#[test]
#[should_panic]
fn test_cauchy_invalid_scale_neg() {
Cauchy::new(0.0, -10.0).unwrap();
}
#[test]
fn value_stability() {
fn test_samples<N: Float + core::fmt::Debug>(m: N, s: N, expected: &[N])
where Standard: Distribution<N> {
let distr = Cauchy::new(m, s).unwrap();
let mut rng = crate::test::rng(353);
let mut buf = [m; 4];
for x in &mut buf {
*x = rng.sample(&distr);
}
assert_eq!(buf, expected);
}
// Warning: in a few cases, results vary slightly between different
// platforms, presumably due to differences in precision of system impls
// of the tan function. We work around this by avoiding these values.
test_samples(100f64, 10.0, &[77.93369152808678, 90.1606912098641,
125.31516221323625, 86.10217834773925]);
test_samples(15f32, 10.0, &[22.175842, -7.066305, 6.0132685, 5.1606884]);
}
}