| // 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 num_traits::Float; |
| use crate::{uniform::SampleUniform, Distribution, Uniform}; |
| use rand::Rng; |
| |
| /// 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<F: Float + SampleUniform> Distribution<[F; 2]> for UnitCircle { |
| #[inline] |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [F; 2] { |
| let uniform = Uniform::new(F::from(-1.).unwrap(), F::from(1.).unwrap()); |
| 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 < F::from(1.).unwrap() { |
| break; |
| } |
| } |
| let diff = x1 * x1 - x2 * x2; |
| [diff / sum, F::from(2.).unwrap() * x1 * x2 / sum] |
| } |
| } |
| |
| #[cfg(test)] |
| mod tests { |
| use super::UnitCircle; |
| use crate::Distribution; |
| |
| /// 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!( |
| "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); |
| } |
| } |
| } |