| // Copyright 2018-2019 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 surface of the unit sphere in three dimensions. |
| /// |
| /// Implemented via a method by Marsaglia[^1]. |
| /// |
| /// |
| /// # Example |
| /// |
| /// ``` |
| /// use rand_distr::{UnitSphere, Distribution}; |
| /// |
| /// let v: [f64; 3] = UnitSphere.sample(&mut rand::thread_rng()); |
| /// println!("{:?} is from the unit sphere surface.", v) |
| /// ``` |
| /// |
| /// [^1]: Marsaglia, George (1972). [*Choosing a Point from the Surface of a |
| /// Sphere.*](https://doi.org/10.1214/aoms/1177692644) |
| /// Ann. Math. Statist. 43, no. 2, 645--646. |
| #[derive(Clone, Copy, Debug)] |
| pub struct UnitSphere; |
| |
| impl<N: Float + SampleUniform> Distribution<[N; 3]> for UnitSphere { |
| #[inline] |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [N; 3] { |
| let uniform = Uniform::new(N::from(-1.), N::from(1.)); |
| loop { |
| let (x1, x2) = (uniform.sample(rng), uniform.sample(rng)); |
| let sum = x1*x1 + x2*x2; |
| if sum >= N::from(1.) { |
| continue; |
| } |
| let factor = N::from(2.) * (N::from(1.0) - sum).sqrt(); |
| return [x1 * factor, x2 * factor, N::from(1.) - N::from(2.)*sum]; |
| } |
| } |
| } |
| |
| #[cfg(test)] |
| mod tests { |
| use crate::Distribution; |
| use super::UnitSphere; |
| |
| /// 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; 3] = UnitSphere.sample(&mut rng); |
| assert_almost_eq!(x[0]*x[0] + x[1]*x[1] + x[2]*x[2], 1., 1e-15); |
| } |
| } |
| |
| #[test] |
| fn value_stability() { |
| let mut rng = crate::test::rng(2); |
| let expected = [ |
| [0.03247542860231647, -0.7830477442152738, 0.6211131755296027], |
| [-0.09978440840914075, 0.9706650829833128, -0.21875184231323952], |
| [0.2735582468624679, 0.9435374242279655, -0.1868234852870203], |
| ]; |
| let samples: [[f64; 3]; 3] = [ |
| UnitSphere.sample(&mut rng), |
| UnitSphere.sample(&mut rng), |
| UnitSphere.sample(&mut rng), |
| ]; |
| assert_eq!(samples, expected); |
| } |
| } |