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+// Copyright 2018 Developers of the Rand project.
+// Copyright 2016-2017 The Rust Project Developers.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+//! The Cauchy distribution.
+#![allow(deprecated)]
+#![allow(clippy::all)]
+
+use crate::distributions::Distribution;
+use crate::Rng;
+use std::f64::consts::PI;
+
+/// The Cauchy distribution `Cauchy(median, scale)`.
+///
+/// This distribution has a density function:
+/// `f(x) = 1 / (pi * scale * (1 + ((x - median) / scale)^2))`
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct Cauchy {
+ median: f64,
+ scale: f64,
+}
+
+impl Cauchy {
+ /// Construct a new `Cauchy` with the given shape parameters
+ /// `median` the peak location and `scale` the scale factor.
+ /// Panics if `scale <= 0`.
+ pub fn new(median: f64, scale: f64) -> Cauchy {
+ assert!(scale > 0.0, "Cauchy::new called with scale factor <= 0");
+ Cauchy { median, scale }
+ }
+}
+
+impl Distribution<f64> for Cauchy {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ // sample from [0, 1)
+ let x = rng.gen::<f64>();
+ // get standard cauchy random number
+ // note that π/2 is not exactly representable, even if x=0.5 the result is finite
+ let comp_dev = (PI * x).tan();
+ // shift and scale according to parameters
+ let result = self.median + self.scale * comp_dev;
+ result
+ }
+}
+
+#[cfg(test)]
+mod test {
+ use super::Cauchy;
+ use crate::distributions::Distribution;
+
+ fn median(mut numbers: &mut [f64]) -> f64 {
+ sort(&mut numbers);
+ let mid = numbers.len() / 2;
+ numbers[mid]
+ }
+
+ fn sort(numbers: &mut [f64]) {
+ numbers.sort_by(|a, b| a.partial_cmp(b).unwrap());
+ }
+
+ #[test]
+ fn test_cauchy_averages() {
+ // NOTE: given that the variance and mean are undefined,
+ // this test does not have any rigorous statistical meaning.
+ let cauchy = Cauchy::new(10.0, 5.0);
+ let mut rng = crate::test::rng(123);
+ let mut numbers: [f64; 1000] = [0.0; 1000];
+ let mut sum = 0.0;
+ for i in 0..1000 {
+ numbers[i] = cauchy.sample(&mut rng);
+ sum += numbers[i];
+ }
+ let median = median(&mut numbers);
+ println!("Cauchy median: {}", median);
+ assert!((median - 10.0).abs() < 0.4); // not 100% certain, but probable enough
+ let mean = sum / 1000.0;
+ println!("Cauchy mean: {}", mean);
+ // for a Cauchy distribution the mean should not converge
+ assert!((mean - 10.0).abs() > 0.4); // not 100% certain, but probable enough
+ }
+
+ #[test]
+ #[should_panic]
+ fn test_cauchy_invalid_scale_zero() {
+ Cauchy::new(0.0, 0.0);
+ }
+
+ #[test]
+ #[should_panic]
+ fn test_cauchy_invalid_scale_neg() {
+ Cauchy::new(0.0, -10.0);
+ }
+}