168 lines
5.1 KiB
Rust
168 lines
5.1 KiB
Rust
// Copyright 2018 Developers of the Rand project.
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// Copyright 2016-2017 The Rust Project Developers.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! The Cauchy distribution.
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use num_traits::{Float, FloatConst};
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use crate::{Distribution, Standard};
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use rand::Rng;
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use core::fmt;
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/// The Cauchy distribution `Cauchy(median, scale)`.
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///
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/// This distribution has a density function:
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/// `f(x) = 1 / (pi * scale * (1 + ((x - median) / scale)^2))`
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///
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/// Note that at least for `f32`, results are not fully portable due to minor
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/// differences in the target system's *tan* implementation, `tanf`.
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///
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/// # Example
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///
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/// ```
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/// use rand_distr::{Cauchy, Distribution};
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///
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/// let cau = Cauchy::new(2.0, 5.0).unwrap();
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/// let v = cau.sample(&mut rand::thread_rng());
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/// println!("{} is from a Cauchy(2, 5) distribution", v);
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/// ```
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#[derive(Clone, Copy, Debug)]
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#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
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pub struct Cauchy<F>
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where F: Float + FloatConst, Standard: Distribution<F>
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{
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median: F,
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scale: F,
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}
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/// Error type returned from `Cauchy::new`.
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#[derive(Clone, Copy, Debug, PartialEq, Eq)]
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pub enum Error {
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/// `scale <= 0` or `nan`.
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ScaleTooSmall,
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}
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impl fmt::Display for Error {
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fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
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f.write_str(match self {
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Error::ScaleTooSmall => "scale is not positive in Cauchy distribution",
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})
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}
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}
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#[cfg(feature = "std")]
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#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
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impl std::error::Error for Error {}
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impl<F> Cauchy<F>
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where F: Float + FloatConst, Standard: Distribution<F>
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{
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/// Construct a new `Cauchy` with the given shape parameters
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/// `median` the peak location and `scale` the scale factor.
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pub fn new(median: F, scale: F) -> Result<Cauchy<F>, Error> {
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if !(scale > F::zero()) {
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return Err(Error::ScaleTooSmall);
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}
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Ok(Cauchy { median, scale })
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}
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}
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impl<F> Distribution<F> for Cauchy<F>
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where F: Float + FloatConst, Standard: Distribution<F>
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{
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fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
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// sample from [0, 1)
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let x = Standard.sample(rng);
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// get standard cauchy random number
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// note that π/2 is not exactly representable, even if x=0.5 the result is finite
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let comp_dev = (F::PI() * x).tan();
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// shift and scale according to parameters
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self.median + self.scale * comp_dev
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}
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}
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#[cfg(test)]
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mod test {
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use super::*;
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fn median(numbers: &mut [f64]) -> f64 {
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sort(numbers);
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let mid = numbers.len() / 2;
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numbers[mid]
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}
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fn sort(numbers: &mut [f64]) {
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numbers.sort_by(|a, b| a.partial_cmp(b).unwrap());
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}
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#[test]
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fn test_cauchy_averages() {
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// NOTE: given that the variance and mean are undefined,
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// this test does not have any rigorous statistical meaning.
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let cauchy = Cauchy::new(10.0, 5.0).unwrap();
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let mut rng = crate::test::rng(123);
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let mut numbers: [f64; 1000] = [0.0; 1000];
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let mut sum = 0.0;
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for number in &mut numbers[..] {
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*number = cauchy.sample(&mut rng);
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sum += *number;
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}
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let median = median(&mut numbers);
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#[cfg(feature = "std")]
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std::println!("Cauchy median: {}", median);
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assert!((median - 10.0).abs() < 0.4); // not 100% certain, but probable enough
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let mean = sum / 1000.0;
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#[cfg(feature = "std")]
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std::println!("Cauchy mean: {}", mean);
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// for a Cauchy distribution the mean should not converge
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assert!((mean - 10.0).abs() > 0.4); // not 100% certain, but probable enough
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}
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#[test]
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#[should_panic]
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fn test_cauchy_invalid_scale_zero() {
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Cauchy::new(0.0, 0.0).unwrap();
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}
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#[test]
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#[should_panic]
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fn test_cauchy_invalid_scale_neg() {
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Cauchy::new(0.0, -10.0).unwrap();
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}
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#[test]
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fn value_stability() {
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fn gen_samples<F: Float + FloatConst + core::fmt::Debug>(m: F, s: F, buf: &mut [F])
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where Standard: Distribution<F> {
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let distr = Cauchy::new(m, s).unwrap();
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let mut rng = crate::test::rng(353);
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for x in buf {
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*x = rng.sample(&distr);
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}
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}
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let mut buf = [0.0; 4];
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gen_samples(100f64, 10.0, &mut buf);
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assert_eq!(&buf, &[
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77.93369152808678,
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90.1606912098641,
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125.31516221323625,
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86.10217834773925
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]);
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// Unfortunately this test is not fully portable due to reliance on the
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// system's implementation of tanf (see doc on Cauchy struct).
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let mut buf = [0.0; 4];
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gen_samples(10f32, 7.0, &mut buf);
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let expected = [15.023088, -5.446413, 3.7092876, 3.112482];
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for (a, b) in buf.iter().zip(expected.iter()) {
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assert_almost_eq!(*a, *b, 1e-5);
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}
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}
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}
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