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// 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);
}
}
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