1 // Copyright 2016-2017 The Rust Project Developers. See the COPYRIGHT 2 // file at the top-level directory of this distribution and at 3 // https://rust-lang.org/COPYRIGHT. 4 // 5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or 6 // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license 7 // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your 8 // option. This file may not be copied, modified, or distributed 9 // except according to those terms. 10 11 //! The Cauchy distribution. 12 13 use Rng; 14 use 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 /// 22 /// # Example 23 /// 24 /// ``` 25 /// use rand::distributions::{Cauchy, Distribution}; 26 /// 27 /// let cau = Cauchy::new(2.0, 5.0); 28 /// let v = cau.sample(&mut rand::thread_rng()); 29 /// println!("{} is from a Cauchy(2, 5) distribution", v); 30 /// ``` 31 #[derive(Clone, Copy, Debug)] 32 pub struct Cauchy { 33 median: f64, 34 scale: f64 35 } 36 37 impl Cauchy { 38 /// Construct a new `Cauchy` with the given shape parameters 39 /// `median` the peak location and `scale` the scale factor. 40 /// Panics if `scale <= 0`. new(median: f64, scale: f64) -> Cauchy41 pub fn new(median: f64, scale: f64) -> Cauchy { 42 assert!(scale > 0.0, "Cauchy::new called with scale factor <= 0"); 43 Cauchy { 44 median, 45 scale 46 } 47 } 48 } 49 50 impl Distribution<f64> for Cauchy { sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f6451 fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 { 52 // sample from [0, 1) 53 let x = rng.gen::<f64>(); 54 // get standard cauchy random number 55 // note that π/2 is not exactly representable, even if x=0.5 the result is finite 56 let comp_dev = (PI * x).tan(); 57 // shift and scale according to parameters 58 let result = self.median + self.scale * comp_dev; 59 result 60 } 61 } 62 63 #[cfg(test)] 64 mod test { 65 use distributions::Distribution; 66 use super::Cauchy; 67 median(mut numbers: &mut [f64]) -> f6468 fn median(mut numbers: &mut [f64]) -> f64 { 69 sort(&mut numbers); 70 let mid = numbers.len() / 2; 71 numbers[mid] 72 } 73 sort(numbers: &mut [f64])74 fn sort(numbers: &mut [f64]) { 75 numbers.sort_by(|a, b| a.partial_cmp(b).unwrap()); 76 } 77 78 #[test] test_cauchy_median()79 fn test_cauchy_median() { 80 let cauchy = Cauchy::new(10.0, 5.0); 81 let mut rng = ::test::rng(123); 82 let mut numbers: [f64; 1000] = [0.0; 1000]; 83 for i in 0..1000 { 84 numbers[i] = cauchy.sample(&mut rng); 85 } 86 let median = median(&mut numbers); 87 println!("Cauchy median: {}", median); 88 assert!((median - 10.0).abs() < 0.5); // not 100% certain, but probable enough 89 } 90 91 #[test] test_cauchy_mean()92 fn test_cauchy_mean() { 93 let cauchy = Cauchy::new(10.0, 5.0); 94 let mut rng = ::test::rng(123); 95 let mut sum = 0.0; 96 for _ in 0..1000 { 97 sum += cauchy.sample(&mut rng); 98 } 99 let mean = sum / 1000.0; 100 println!("Cauchy mean: {}", mean); 101 // for a Cauchy distribution the mean should not converge 102 assert!((mean - 10.0).abs() > 0.5); // not 100% certain, but probable enough 103 } 104 105 #[test] 106 #[should_panic] test_cauchy_invalid_scale_zero()107 fn test_cauchy_invalid_scale_zero() { 108 Cauchy::new(0.0, 0.0); 109 } 110 111 #[test] 112 #[should_panic] test_cauchy_invalid_scale_neg()113 fn test_cauchy_invalid_scale_neg() { 114 Cauchy::new(0.0, -10.0); 115 } 116 } 117