vendor/rand-0.7.3/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 #![allow(clippy::all)]
  11
  12 use crate::distributions::{Distribution, Uniform};
  13 use crate::Rng;
  14
  15 /// Samples uniformly from the surface of the unit sphere in three dimensions.
  16 ///
  17 /// Implemented via a method by Marsaglia[^1].
  18 ///
  19 /// [^1]: Marsaglia, George (1972). [*Choosing a Point from the Surface of a
  20 ///       Sphere.*](https://doi.org/10.1214/aoms/1177692644)
  21 ///       Ann. Math. Statist. 43, no. 2, 645--646.
  22 #[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
  23 #[derive(Clone, Copy, Debug)]
  24 pub struct UnitSphereSurface;
  25
  26 impl UnitSphereSurface {
  27     /// Construct a new `UnitSphereSurface` distribution.
  28     #[inline]
  29     pub fn new() -> UnitSphereSurface {
  30         UnitSphereSurface
  31     }
  32 }
  33
  34 impl Distribution<[f64; 3]> for UnitSphereSurface {
  35     #[inline]
  36     fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [f64; 3] {
  37         let uniform = Uniform::new(-1., 1.);
  38         loop {
  39             let (x1, x2) = (uniform.sample(rng), uniform.sample(rng));
  40             let sum = x1 * x1 + x2 * x2;
  41             if sum >= 1. {
  42                 continue;
  43             }
  44             let factor = 2. * (1.0_f64 - sum).sqrt();
  45             return [x1 * factor, x2 * factor, 1. - 2. * sum];
  46         }
  47     }
  48 }
  49
  50 #[cfg(test)]
  51 mod tests {
  52     use super::UnitSphereSurface;
  53     use crate::distributions::Distribution;
  54
  55     /// Assert that two numbers are almost equal to each other.
  56     ///
  57     /// On panic, this macro will print the values of the expressions with their
  58     /// debug representations.
  59     macro_rules! assert_almost_eq {
  60         ($a:expr, $b:expr, $prec:expr) => {
  61             let diff = ($a - $b).abs();
  62             if diff > $prec {
  63                 panic!(format!(
  64                     "assertion failed: `abs(left - right) = {:.1e} < {:e}`, \
  65                      (left: `{}`, right: `{}`)",
  66                     diff, $prec, $a, $b
  67                 ));
  68             }
  69         };
  70     }
  71
  72     #[test]
  73     fn norm() {
  74         let mut rng = crate::test::rng(1);
  75         let dist = UnitSphereSurface::new();
  76         for _ in 0..1000 {
  77             let x = dist.sample(&mut rng);
  78             assert_almost_eq!(x[0] * x[0] + x[1] * x[1] + x[2] * x[2], 1., 1e-15);
  79         }
  80     }
  81
  82     #[test]
  83     fn value_stability() {
  84         let mut rng = crate::test::rng(2);
  85         let expected = [
  86             [0.03247542860231647, -0.7830477442152738, 0.6211131755296027],
  87             [-0.09978440840914075, 0.9706650829833128, -0.21875184231323952],
  88             [0.2735582468624679, 0.9435374242279655, -0.1868234852870203],
  89         ];
  90         let samples = [
  91             UnitSphereSurface.sample(&mut rng),
  92             UnitSphereSurface.sample(&mut rng),
  93             UnitSphereSurface.sample(&mut rng),
  94         ];
  95         assert_eq!(samples, expected);
  96     }
  97 }