64 lines
2.1 KiB
Rust
64 lines
2.1 KiB
Rust
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// Copyright 2018-2019 Developers of the Rand project.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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use num_traits::Float;
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use crate::{uniform::SampleUniform, Distribution, Uniform};
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use rand::Rng;
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/// Samples uniformly from the surface of the unit sphere in three dimensions.
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///
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/// Implemented via a method by Marsaglia[^1].
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///
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///
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/// # Example
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///
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/// ```
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/// use rand_distr::{UnitSphere, Distribution};
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///
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/// let v: [f64; 3] = UnitSphere.sample(&mut rand::thread_rng());
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/// println!("{:?} is from the unit sphere surface.", v)
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/// ```
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///
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/// [^1]: Marsaglia, George (1972). [*Choosing a Point from the Surface of a
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/// Sphere.*](https://doi.org/10.1214/aoms/1177692644)
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/// Ann. Math. Statist. 43, no. 2, 645--646.
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#[derive(Clone, Copy, Debug)]
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#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
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pub struct UnitSphere;
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impl<F: Float + SampleUniform> Distribution<[F; 3]> for UnitSphere {
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#[inline]
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fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [F; 3] {
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let uniform = Uniform::new(F::from(-1.).unwrap(), F::from(1.).unwrap());
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loop {
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let (x1, x2) = (uniform.sample(rng), uniform.sample(rng));
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let sum = x1 * x1 + x2 * x2;
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if sum >= F::from(1.).unwrap() {
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continue;
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}
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let factor = F::from(2.).unwrap() * (F::one() - sum).sqrt();
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return [x1 * factor, x2 * factor, F::from(1.).unwrap() - F::from(2.).unwrap() * sum];
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}
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}
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}
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#[cfg(test)]
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mod tests {
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use super::UnitSphere;
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use crate::Distribution;
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#[test]
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fn norm() {
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let mut rng = crate::test::rng(1);
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for _ in 0..1000 {
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let x: [f64; 3] = UnitSphere.sample(&mut rng);
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assert_almost_eq!(x[0] * x[0] + x[1] * x[1] + x[2] * x[2], 1., 1e-15);
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}
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}
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}
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