Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Optimize Cauchy sampling #493

Closed
wants to merge 1 commit into from
Closed
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
59 changes: 44 additions & 15 deletions src/distributions/cauchy.rs
Original file line number Diff line number Diff line change
Expand Up @@ -11,8 +11,7 @@
//! The Cauchy distribution.

use Rng;
use distributions::Distribution;
use std::f64::consts::PI;
use distributions::{Distribution, Open01};

/// The Cauchy distribution `Cauchy(median, scale)`.
///
Expand Down Expand Up @@ -49,13 +48,43 @@ impl Cauchy {

impl Distribution<f64> for Cauchy {
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
// sample from [0, 1)
let x = rng.gen::<f64>();
// 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 = (PI * x).tan();
// shift and scale according to parameters
let result = self.median + self.scale * comp_dev;
// Algorithim from the paper:
// Efficient table-free sampling methods for the exponential, Cauchy, and normal distributions
// by Joachim H. Ahrens and Ulrich Dieter

// ~magic values~
// these are precomputed values for numerically approximating a Cauchy quantile function
let a = 0.6380_6313_6607_7803;
let b = 0.5959_4860_6052_9070;
let q = 0.9339_9629_5760_3656;
let w = 0.2488_7022_8008_3841;
let c = 0.6366_1977_2367_5813;
let d = 0.5972_9975_9353_9963;
let h = 0.0214_9490_0457_0452;
let p = 4.9125_0139_5303_3204;

let mut std_cau: f64;
let mut uni: f64 = rng.sample(Open01);
let mut x = uni - 0.5;
let mut s = w - x*x;
if s > 0.0 {
std_cau = x * ((c / s) + d);
}
else {
// fall back to rejection method
loop {
uni = rng.sample(Open01);
x = uni - 0.5;
s = 0.25 - x*x;
std_cau = x * ((a / s) + b);
let uni1: f64 = rng.sample(Open01);
let test = s*s * ((1.0 + std_cau*std_cau) * (h * uni1 + p) - q) + s;
if test <= 0.5 {
break;
}
}
}
let result = self.median + self.scale * std_cau; // shift and scale according to parameters
result
}
}
Expand All @@ -77,29 +106,29 @@ mod test {

#[test]
fn test_cauchy_median() {
let cauchy = Cauchy::new(10.0, 5.0);
let mut rng = ::test::rng(123);
let cauchy = Cauchy::new(5.0, 10.0);
let mut rng = ::test::rng(321);
let mut numbers: [f64; 1000] = [0.0; 1000];
for i in 0..1000 {
numbers[i] = cauchy.sample(&mut rng);
}
let median = median(&mut numbers);
println!("Cauchy median: {}", median);
assert!((median - 10.0).abs() < 0.5); // not 100% certain, but probable enough
assert!((median - 5.0).abs() < 0.5); // not 100% certain, but probable enough
}

#[test]
fn test_cauchy_mean() {
let cauchy = Cauchy::new(10.0, 5.0);
let mut rng = ::test::rng(123);
let cauchy = Cauchy::new(5.0, 10.0);
let mut rng = ::test::rng(322);
let mut sum = 0.0;
for _ in 0..1000 {
sum += cauchy.sample(&mut rng);
}
let mean = sum / 1000.0;
println!("Cauchy mean: {}", mean);
// for a Cauchy distribution the mean should not converge
assert!((mean - 10.0).abs() > 0.5); // not 100% certain, but probable enough
assert!((mean - 5.0).abs() > 0.5); // not 100% certain, but probable enough
}

#[test]
Expand Down