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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 Rng;
-use distributions::{Distribution, Uniform};
-
-/// Samples uniformly from the surface of the unit sphere in three dimensions.
-///
-/// Implemented via a method by Marsaglia[^1].
-///
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{UnitSphereSurface, Distribution};
-///
-/// let sphere = UnitSphereSurface::new();
-/// let v = sphere.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 UnitSphereSurface;
-
-impl UnitSphereSurface {
- /// Construct a new `UnitSphereSurface` distribution.
- #[inline]
- pub fn new() -> UnitSphereSurface {
- UnitSphereSurface
- }
-}
-
-impl Distribution<[f64; 3]> for UnitSphereSurface {
- #[inline]
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [f64; 3] {
- let uniform = Uniform::new(-1., 1.);
- loop {
- let (x1, x2) = (uniform.sample(rng), uniform.sample(rng));
- let sum = x1*x1 + x2*x2;
- if sum >= 1. {
- continue;
- }
- let factor = 2. * (1.0_f64 - sum).sqrt();
- return [x1 * factor, x2 * factor, 1. - 2.*sum];
- }
- }
-}
-
-#[cfg(test)]
-mod tests {
- use distributions::Distribution;
- use super::UnitSphereSurface;
-
- /// 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 = ::test::rng(1);
- let dist = UnitSphereSurface::new();
- for _ in 0..1000 {
- let x = dist.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 = ::test::rng(2);
- let dist = UnitSphereSurface::new();
- assert_eq!(dist.sample(&mut rng),
- [-0.24950027180862533, -0.7552572587896719, 0.6060825747478084]);
- assert_eq!(dist.sample(&mut rng),
- [0.47604534507233487, -0.797200864987207, -0.3712837328763685]);
- assert_eq!(dist.sample(&mut rng),
- [0.9795722330927367, 0.18692349236651176, 0.07414747571708524]);
- }
-}