vendor/rand/src/distributions/cauchy.rs

   1 // Copyright 2018 Developers of the Rand project.
   2 // Copyright 2016-2017 The Rust Project Developers.
   3 //
   4 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
   5 // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
   6 // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
   7 // option. This file may not be copied, modified, or distributed
   8 // except according to those terms.
   9
  10 //! The Cauchy distribution.
  11 #![allow(deprecated)]
  12 #![allow(clippy::all)]
  13
  14 use crate::distributions::Distribution;
  15 use crate::Rng;
  16 use std::f64::consts::PI;
  17
  18 /// The Cauchy distribution `Cauchy(median, scale)`.
  19 ///
  20 /// This distribution has a density function:
  21 /// `f(x) = 1 / (pi * scale * (1 + ((x - median) / scale)^2))`
  22 #[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
  23 #[derive(Clone, Copy, Debug)]
  24 pub struct Cauchy {
  25     median: f64,
  26     scale: f64,
  27 }
  28
  29 impl Cauchy {
  30     /// Construct a new `Cauchy` with the given shape parameters
  31     /// `median` the peak location and `scale` the scale factor.
  32     /// Panics if `scale <= 0`.
  33     pub fn new(median: f64, scale: f64) -> Cauchy {
  34         assert!(scale > 0.0, "Cauchy::new called with scale factor <= 0");
  35         Cauchy { median, scale }
  36     }
  37 }
  38
  39 impl Distribution<f64> for Cauchy {
  40     fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
  41         // sample from [0, 1)
  42         let x = rng.gen::<f64>();
  43         // get standard cauchy random number
  44         // note that π/2 is not exactly representable, even if x=0.5 the result is finite
  45         let comp_dev = (PI * x).tan();
  46         // shift and scale according to parameters
  47         let result = self.median + self.scale * comp_dev;
  48         result
  49     }
  50 }
  51
  52 #[cfg(test)]
  53 mod test {
  54     use super::Cauchy;
  55     use crate::distributions::Distribution;
  56
  57     fn median(mut numbers: &mut [f64]) -> f64 {
  58         sort(&mut numbers);
  59         let mid = numbers.len() / 2;
  60         numbers[mid]
  61     }
  62
  63     fn sort(numbers: &mut [f64]) {
  64         numbers.sort_by(|a, b| a.partial_cmp(b).unwrap());
  65     }
  66
  67     #[test]
  68     fn test_cauchy_averages() {
  69         // NOTE: given that the variance and mean are undefined,
  70         // this test does not have any rigorous statistical meaning.
  71         let cauchy = Cauchy::new(10.0, 5.0);
  72         let mut rng = crate::test::rng(123);
  73         let mut numbers: [f64; 1000] = [0.0; 1000];
  74         let mut sum = 0.0;
  75         for i in 0..1000 {
  76             numbers[i] = cauchy.sample(&mut rng);
  77             sum += numbers[i];
  78         }
  79         let median = median(&mut numbers);
  80         println!("Cauchy median: {}", median);
  81         assert!((median - 10.0).abs() < 0.4); // not 100% certain, but probable enough
  82         let mean = sum / 1000.0;
  83         println!("Cauchy mean: {}", mean);
  84         // for a Cauchy distribution the mean should not converge
  85         assert!((mean - 10.0).abs() > 0.4); // not 100% certain, but probable enough
  86     }
  87
  88     #[test]
  89     #[should_panic]
  90     fn test_cauchy_invalid_scale_zero() {
  91         Cauchy::new(0.0, 0.0);
  92     }
  93
  94     #[test]
  95     #[should_panic]
  96     fn test_cauchy_invalid_scale_neg() {
  97         Cauchy::new(0.0, -10.0);
  98     }
  99 }