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// Copyright 2018 Developers of the Rand project.
//
// 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.
use rand::Rng;
use crate::{Distribution, Uniform, uniform::SampleUniform};
use crate::utils::Float;
/// Samples uniformly from the edge of the unit circle in two dimensions.
///
/// Implemented via a method by von Neumann[^1].
///
///
/// # Example
///
/// ```
/// use rand_distr::{UnitCircle, Distribution};
///
/// let v: [f64; 2] = UnitCircle.sample(&mut rand::thread_rng());
/// println!("{:?} is from the unit circle.", v)
/// ```
///
/// [^1]: von Neumann, J. (1951) [*Various Techniques Used in Connection with
/// Random Digits.*](https://mcnp.lanl.gov/pdf_files/nbs_vonneumann.pdf)
/// NBS Appl. Math. Ser., No. 12. Washington, DC: U.S. Government Printing
/// Office, pp. 36-38.
#[derive(Clone, Copy, Debug)]
pub struct UnitCircle;
impl<N: Float + SampleUniform> Distribution<[N; 2]> for UnitCircle {
#[inline]
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [N; 2] {
let uniform = Uniform::new(N::from(-1.), N::from(1.));
let mut x1;
let mut x2;
let mut sum;
loop {
x1 = uniform.sample(rng);
x2 = uniform.sample(rng);
sum = x1*x1 + x2*x2;
if sum < N::from(1.) {
break;
}
}
let diff = x1*x1 - x2*x2;
[diff / sum, N::from(2.)*x1*x2 / sum]
}
}
#[cfg(test)]
mod tests {
use crate::Distribution;
use super::UnitCircle;
/// Assert that two numbers are almost equal to each other.
///
/// On panic, this macro will print the values of the expressions with their
/// debug representations.
macro_rules! assert_almost_eq {
($a:expr, $b:expr, $prec:expr) => (
let diff = ($a - $b).abs();
if diff > $prec {
panic!(format!(
"assertion failed: `abs(left - right) = {:.1e} < {:e}`, \
(left: `{}`, right: `{}`)",
diff, $prec, $a, $b));
}
);
}
#[test]
fn norm() {
let mut rng = crate::test::rng(1);
for _ in 0..1000 {
let x: [f64; 2] = UnitCircle.sample(&mut rng);
assert_almost_eq!(x[0]*x[0] + x[1]*x[1], 1., 1e-15);
}
}
#[test]
fn value_stability() {
let mut rng = crate::test::rng(2);
let expected = [
[-0.9965658683520504, -0.08280380447614634],
[-0.9790853270389644, -0.20345004884984505],
[-0.8449189758898707, 0.5348943112253227],
];
let samples: [[f64; 2]; 3] = [
UnitCircle.sample(&mut rng),
UnitCircle.sample(&mut rng),
UnitCircle.sample(&mut rng),
];
assert_eq!(samples, expected);
}
}
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