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