rand_distr/
unit_circle.rs

1// Copyright 2018 Developers of the Rand project.
2//
3// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
4// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
5// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
6// option. This file may not be copied, modified, or distributed
7// except according to those terms.
8
9use num_traits::Float;
10use crate::{uniform::SampleUniform, Distribution, Uniform};
11use rand::Rng;
12
13/// Samples uniformly from the edge of the unit circle in two dimensions.
14///
15/// Implemented via a method by von Neumann[^1].
16///
17///
18/// # Example
19///
20/// ```
21/// use rand_distr::{UnitCircle, Distribution};
22///
23/// let v: [f64; 2] = UnitCircle.sample(&mut rand::thread_rng());
24/// println!("{:?} is from the unit circle.", v)
25/// ```
26///
27/// [^1]: von Neumann, J. (1951) [*Various Techniques Used in Connection with
28///       Random Digits.*](https://mcnp.lanl.gov/pdf_files/nbs_vonneumann.pdf)
29///       NBS Appl. Math. Ser., No. 12. Washington, DC: U.S. Government Printing
30///       Office, pp. 36-38.
31#[derive(Clone, Copy, Debug)]
32#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
33pub struct UnitCircle;
34
35impl<F: Float + SampleUniform> Distribution<[F; 2]> for UnitCircle {
36    #[inline]
37    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [F; 2] {
38        let uniform = Uniform::new(F::from(-1.).unwrap(), F::from(1.).unwrap());
39        let mut x1;
40        let mut x2;
41        let mut sum;
42        loop {
43            x1 = uniform.sample(rng);
44            x2 = uniform.sample(rng);
45            sum = x1 * x1 + x2 * x2;
46            if sum < F::from(1.).unwrap() {
47                break;
48            }
49        }
50        let diff = x1 * x1 - x2 * x2;
51        [diff / sum, F::from(2.).unwrap() * x1 * x2 / sum]
52    }
53}
54
55#[cfg(test)]
56mod tests {
57    use super::UnitCircle;
58    use crate::Distribution;
59
60    #[test]
61    fn norm() {
62        let mut rng = crate::test::rng(1);
63        for _ in 0..1000 {
64            let x: [f64; 2] = UnitCircle.sample(&mut rng);
65            assert_almost_eq!(x[0] * x[0] + x[1] * x[1], 1., 1e-15);
66        }
67    }
68}
rand_distr/unit_circle.rs

rand_distr/
unit_circle.rs
