156 lines
4.2 KiB
Rust
156 lines
4.2 KiB
Rust
// Copyright 2021 Developers of the Rand project.
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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 Gumbel distribution.
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use crate::{Distribution, OpenClosed01};
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use core::fmt;
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use num_traits::Float;
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use rand::Rng;
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/// Samples floating-point numbers according to the Gumbel distribution
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///
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/// This distribution has density function:
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/// `f(x) = exp(-(z + exp(-z))) / σ`, where `z = (x - μ) / σ`,
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/// `μ` is the location parameter, and `σ` the scale parameter.
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///
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/// # Example
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/// ```
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/// use rand::prelude::*;
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/// use rand_distr::Gumbel;
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///
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/// let val: f64 = thread_rng().sample(Gumbel::new(0.0, 1.0).unwrap());
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/// println!("{}", val);
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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 Gumbel<F>
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where
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F: Float,
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OpenClosed01: Distribution<F>,
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{
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location: F,
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scale: F,
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}
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/// Error type returned from `Gumbel::new`.
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#[derive(Clone, Copy, Debug, PartialEq, Eq)]
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pub enum Error {
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/// location is infinite or NaN
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LocationNotFinite,
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/// scale is not finite positive number
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ScaleNotPositive,
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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::ScaleNotPositive => "scale is not positive and finite in Gumbel distribution",
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Error::LocationNotFinite => "location is not finite in Gumbel 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> Gumbel<F>
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where
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F: Float,
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OpenClosed01: Distribution<F>,
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{
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/// Construct a new `Gumbel` distribution with given `location` and `scale`.
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pub fn new(location: F, scale: F) -> Result<Gumbel<F>, Error> {
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if scale <= F::zero() || scale.is_infinite() || scale.is_nan() {
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return Err(Error::ScaleNotPositive);
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}
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if location.is_infinite() || location.is_nan() {
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return Err(Error::LocationNotFinite);
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}
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Ok(Gumbel { location, scale })
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}
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}
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impl<F> Distribution<F> for Gumbel<F>
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where
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F: Float,
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OpenClosed01: Distribution<F>,
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{
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fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
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let x: F = rng.sample(OpenClosed01);
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self.location - self.scale * (-x.ln()).ln()
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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#[should_panic]
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fn test_zero_scale() {
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Gumbel::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_infinite_scale() {
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Gumbel::new(0.0, core::f64::INFINITY).unwrap();
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}
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#[test]
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#[should_panic]
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fn test_nan_scale() {
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Gumbel::new(0.0, core::f64::NAN).unwrap();
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}
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#[test]
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#[should_panic]
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fn test_infinite_location() {
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Gumbel::new(core::f64::INFINITY, 1.0).unwrap();
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}
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#[test]
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#[should_panic]
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fn test_nan_location() {
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Gumbel::new(core::f64::NAN, 1.0).unwrap();
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}
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#[test]
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fn test_sample_against_cdf() {
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fn neg_log_log(x: f64) -> f64 {
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-(-x.ln()).ln()
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}
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let location = 0.0;
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let scale = 1.0;
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let iterations = 100_000;
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let increment = 1.0 / iterations as f64;
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let probabilities = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9];
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let mut quantiles = [0.0; 9];
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for (i, p) in probabilities.iter().enumerate() {
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quantiles[i] = neg_log_log(*p);
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}
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let mut proportions = [0.0; 9];
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let d = Gumbel::new(location, scale).unwrap();
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let mut rng = crate::test::rng(1);
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for _ in 0..iterations {
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let replicate = d.sample(&mut rng);
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for (i, q) in quantiles.iter().enumerate() {
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if replicate < *q {
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proportions[i] += increment;
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}
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}
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}
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assert!(proportions
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.iter()
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.zip(&probabilities)
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.all(|(p_hat, p)| (p_hat - p).abs() < 0.003))
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}
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}
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