rand_distr/zipf.rs
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// Copyright 2021 Developers of the Rand project.
//
// 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 Zipf distribution.
use crate::{Distribution, Standard};
use core::fmt;
use num_traits::Float;
use rand::Rng;
/// The Zipf (Zipfian) distribution `Zipf(n, s)`.
///
/// The samples follow [Zipf's law](https://en.wikipedia.org/wiki/Zipf%27s_law):
/// The frequency of each sample from a finite set of size `n` is inversely
/// proportional to a power of its frequency rank (with exponent `s`).
///
/// For large `n`, this converges to the [`Zeta`](crate::Zeta) distribution.
///
/// For `s = 0`, this becomes a [`uniform`](crate::Uniform) distribution.
///
/// # Plot
///
/// The following plot illustrates the Zipf distribution for `n = 10` and
/// various values of `s`.
///
/// ![Zipf distribution](https://raw.githubusercontent.com/rust-random/charts/main/charts/zipf.svg)
///
/// # Example
/// ```
/// use rand::prelude::*;
/// use rand_distr::Zipf;
///
/// let val: f64 = rand::rng().sample(Zipf::new(10, 1.5).unwrap());
/// println!("{}", val);
/// ```
///
/// # Implementation details
///
/// Implemented via [rejection sampling](https://en.wikipedia.org/wiki/Rejection_sampling),
/// due to Jason Crease[1].
///
/// [1]: https://jasoncrease.medium.com/rejection-sampling-the-zipf-distribution-6b359792cffa
#[derive(Clone, Copy, Debug, PartialEq)]
pub struct Zipf<F>
where
F: Float,
Standard: Distribution<F>,
{
s: F,
t: F,
q: F,
}
/// Error type returned from [`Zipf::new`].
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum Error {
/// `s < 0` or `nan`.
STooSmall,
/// `n < 1`.
NTooSmall,
}
impl fmt::Display for Error {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
f.write_str(match self {
Error::STooSmall => "s < 0 or is NaN in Zipf distribution",
Error::NTooSmall => "n < 1 in Zipf distribution",
})
}
}
#[cfg(feature = "std")]
impl std::error::Error for Error {}
impl<F> Zipf<F>
where
F: Float,
Standard: Distribution<F>,
{
/// Construct a new `Zipf` distribution for a set with `n` elements and a
/// frequency rank exponent `s`.
///
/// For large `n`, rounding may occur to fit the number into the float type.
#[inline]
pub fn new(n: u64, s: F) -> Result<Zipf<F>, Error> {
if !(s >= F::zero()) {
return Err(Error::STooSmall);
}
if n < 1 {
return Err(Error::NTooSmall);
}
let n = F::from(n).unwrap(); // This does not fail.
let q = if s != F::one() {
// Make sure to calculate the division only once.
F::one() / (F::one() - s)
} else {
// This value is never used.
F::zero()
};
let t = if s != F::one() {
(n.powf(F::one() - s) - s) * q
} else {
F::one() + n.ln()
};
debug_assert!(t > F::zero());
Ok(Zipf { s, t, q })
}
/// Inverse cumulative density function
#[inline]
fn inv_cdf(&self, p: F) -> F {
let one = F::one();
let pt = p * self.t;
if pt <= one {
pt
} else if self.s != one {
(pt * (one - self.s) + self.s).powf(self.q)
} else {
(pt - one).exp()
}
}
}
impl<F> Distribution<F> for Zipf<F>
where
F: Float,
Standard: Distribution<F>,
{
#[inline]
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
let one = F::one();
loop {
let inv_b = self.inv_cdf(rng.sample(Standard));
let x = (inv_b + one).floor();
let mut ratio = x.powf(-self.s);
if x > one {
ratio = ratio * inv_b.powf(self.s)
};
let y = rng.sample(Standard);
if y < ratio {
return x;
}
}
}
}
#[cfg(test)]
mod tests {
use super::*;
fn test_samples<F: Float + fmt::Debug, D: Distribution<F>>(distr: D, zero: F, expected: &[F]) {
let mut rng = crate::test::rng(213);
let mut buf = [zero; 4];
for x in &mut buf {
*x = rng.sample(&distr);
}
assert_eq!(buf, expected);
}
#[test]
#[should_panic]
fn zipf_s_too_small() {
Zipf::new(10, -1.).unwrap();
}
#[test]
#[should_panic]
fn zipf_n_too_small() {
Zipf::new(0, 1.).unwrap();
}
#[test]
#[should_panic]
fn zipf_nan() {
Zipf::new(10, f64::NAN).unwrap();
}
#[test]
fn zipf_sample() {
let d = Zipf::new(10, 0.5).unwrap();
let mut rng = crate::test::rng(2);
for _ in 0..1000 {
let r = d.sample(&mut rng);
assert!(r >= 1.);
}
}
#[test]
fn zipf_sample_s_1() {
let d = Zipf::new(10, 1.).unwrap();
let mut rng = crate::test::rng(2);
for _ in 0..1000 {
let r = d.sample(&mut rng);
assert!(r >= 1.);
}
}
#[test]
fn zipf_sample_s_0() {
let d = Zipf::new(10, 0.).unwrap();
let mut rng = crate::test::rng(2);
for _ in 0..1000 {
let r = d.sample(&mut rng);
assert!(r >= 1.);
}
// TODO: verify that this is a uniform distribution
}
#[test]
fn zipf_sample_large_n() {
let d = Zipf::new(u64::MAX, 1.5).unwrap();
let mut rng = crate::test::rng(2);
for _ in 0..1000 {
let r = d.sample(&mut rng);
assert!(r >= 1.);
}
// TODO: verify that this is a zeta distribution
}
#[test]
fn zipf_value_stability() {
test_samples(Zipf::new(10, 0.5).unwrap(), 0f32, &[10.0, 2.0, 6.0, 7.0]);
test_samples(Zipf::new(10, 2.0).unwrap(), 0f64, &[1.0, 2.0, 3.0, 2.0]);
}
#[test]
fn zipf_distributions_can_be_compared() {
assert_eq!(Zipf::new(1, 2.0), Zipf::new(1, 2.0));
}
}