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
  13 use crate::Rng;
  14 use crate::distributions::Distribution;
  15 use std::f64::consts::PI;
  16
  17 /// The Cauchy distribution `Cauchy(median, scale)`.
  18 ///
  19 /// This distribution has a density function:
  20 /// `f(x) = 1 / (pi * scale * (1 + ((x - median) / scale)^2))`
  21 #[deprecated(since="0.7.0", note="moved to rand_distr crate")]
  22 #[derive(Clone, Copy, Debug)]
  23 pub struct Cauchy {
  24     median: f64,
  25     scale: f64
  26 }
  27
  28 impl Cauchy {
  29     /// Construct a new `Cauchy` with the given shape parameters
  30     /// `median` the peak location and `scale` the scale factor.
  31     /// Panics if `scale <= 0`.
  32     pub fn new(median: f64, scale: f64) -> Cauchy {
  33         assert!(scale > 0.0, "Cauchy::new called with scale factor <= 0");
  34         Cauchy {
  35             median,
  36             scale
  37         }
  38     }
  39 }
  40
  41 impl Distribution<f64> for Cauchy {
  42     fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
  43         // sample from [0, 1)
  44         let x = rng.gen::<f64>();
  45         // get standard cauchy random number
  46         // note that π/2 is not exactly representable, even if x=0.5 the result is finite
  47         let comp_dev = (PI * x).tan();
  48         // shift and scale according to parameters
  49         let result = self.median + self.scale * comp_dev;
  50         result
  51     }
  52 }
  53
  54 #[cfg(test)]
  55 mod test {
  56     use crate::distributions::Distribution;
  57     use super::Cauchy;
  58
  59     fn median(mut numbers: &mut [f64]) -> f64 {
  60         sort(&mut numbers);
  61         let mid = numbers.len() / 2;
  62         numbers[mid]
  63     }
  64
  65     fn sort(numbers: &mut [f64]) {
  66         numbers.sort_by(|a, b| a.partial_cmp(b).unwrap());
  67     }
  68
  69     #[test]
  70     #[cfg(not(miri))] // Miri doesn't support transcendental functions
  71     fn test_cauchy_averages() {
  72         // NOTE: given that the variance and mean are undefined,
  73         // this test does not have any rigorous statistical meaning.
  74         let cauchy = Cauchy::new(10.0, 5.0);
  75         let mut rng = crate::test::rng(123);
  76         let mut numbers: [f64; 1000] = [0.0; 1000];
  77         let mut sum = 0.0;
  78         for i in 0..1000 {
  79             numbers[i] = cauchy.sample(&mut rng);
  80             sum += numbers[i];
  81         }
  82         let median = median(&mut numbers);
  83         println!("Cauchy median: {}", median);
  84         assert!((median - 10.0).abs() < 0.4); // not 100% certain, but probable enough
  85         let mean = sum / 1000.0;
  86         println!("Cauchy mean: {}", mean);
  87         // for a Cauchy distribution the mean should not converge
  88         assert!((mean - 10.0).abs() > 0.4); // not 100% certain, but probable enough
  89     }
  90
  91     #[test]
  92     #[should_panic]
  93     fn test_cauchy_invalid_scale_zero() {
  94         Cauchy::new(0.0, 0.0);
  95     }
  96
  97     #[test]
  98     #[should_panic]
  99     fn test_cauchy_invalid_scale_neg() {
 100         Cauchy::new(0.0, -10.0);
 101     }
 102 }