vendor/rand/src/distributions/unit_sphere.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
   9 #![allow(deprecated)]
  10
  11 use crate::Rng;
  12 use crate::distributions::{Distribution, Uniform};
  13
  14 /// Samples uniformly from the surface of the unit sphere in three dimensions.
  15 ///
  16 /// Implemented via a method by Marsaglia[^1].
  17 ///
  18 /// [^1]: Marsaglia, George (1972). [*Choosing a Point from the Surface of a
  19 ///       Sphere.*](https://doi.org/10.1214/aoms/1177692644)
  20 ///       Ann. Math. Statist. 43, no. 2, 645--646.
  21 #[deprecated(since="0.7.0", note="moved to rand_distr crate")]
  22 #[derive(Clone, Copy, Debug)]
  23 pub struct UnitSphereSurface;
  24
  25 impl UnitSphereSurface {
  26     /// Construct a new `UnitSphereSurface` distribution.
  27     #[inline]
  28     pub fn new() -> UnitSphereSurface {
  29         UnitSphereSurface
  30     }
  31 }
  32
  33 impl Distribution<[f64; 3]> for UnitSphereSurface {
  34     #[inline]
  35     fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [f64; 3] {
  36         let uniform = Uniform::new(-1., 1.);
  37         loop {
  38             let (x1, x2) = (uniform.sample(rng), uniform.sample(rng));
  39             let sum = x1*x1 + x2*x2;
  40             if sum >= 1. {
  41                 continue;
  42             }
  43             let factor = 2. * (1.0_f64 - sum).sqrt();
  44             return [x1 * factor, x2 * factor, 1. - 2.*sum];
  45         }
  46     }
  47 }
  48
  49 #[cfg(test)]
  50 mod tests {
  51     use crate::distributions::Distribution;
  52     use super::UnitSphereSurface;
  53
  54     /// Assert that two numbers are almost equal to each other.
  55     ///
  56     /// On panic, this macro will print the values of the expressions with their
  57     /// debug representations.
  58     macro_rules! assert_almost_eq {
  59         ($a:expr, $b:expr, $prec:expr) => (
  60             let diff = ($a - $b).abs();
  61             if diff > $prec {
  62                 panic!(format!(
  63                     "assertion failed: `abs(left - right) = {:.1e} < {:e}`, \
  64                      (left: `{}`, right: `{}`)",
  65                     diff, $prec, $a, $b));
  66             }
  67         );
  68     }
  69
  70     #[test]
  71     fn norm() {
  72         let mut rng = crate::test::rng(1);
  73         let dist = UnitSphereSurface::new();
  74         for _ in 0..1000 {
  75             let x = dist.sample(&mut rng);
  76             assert_almost_eq!(x[0]*x[0] + x[1]*x[1] + x[2]*x[2], 1., 1e-15);
  77         }
  78     }
  79
  80     #[test]
  81     fn value_stability() {
  82         let mut rng = crate::test::rng(2);
  83         let expected = [
  84                 [0.03247542860231647, -0.7830477442152738, 0.6211131755296027],
  85                 [-0.09978440840914075, 0.9706650829833128, -0.21875184231323952],
  86                 [0.2735582468624679, 0.9435374242279655, -0.1868234852870203],
  87             ];
  88         let samples = [
  89                 UnitSphereSurface.sample(&mut rng),
  90                 UnitSphereSurface.sample(&mut rng),
  91                 UnitSphereSurface.sample(&mut rng),
  92             ];
  93         assert_eq!(samples, expected);
  94     }
  95 }