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// Copyright 2018 Developers of the Rand project.
// Copyright 2013 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 dirichlet distribution.
use rand::Rng;
use crate::{Distribution, Gamma, StandardNormal, Exp1, Open01};
use crate::utils::Float;
/// The dirichelet distribution `Dirichlet(alpha)`.
///
/// The Dirichlet distribution is a family of continuous multivariate
/// probability distributions parameterized by a vector alpha of positive reals.
/// It is a multivariate generalization of the beta distribution.
///
/// # Example
///
/// ```
/// use rand::prelude::*;
/// use rand_distr::Dirichlet;
///
/// let dirichlet = Dirichlet::new(vec![1.0, 2.0, 3.0]).unwrap();
/// let samples = dirichlet.sample(&mut rand::thread_rng());
/// println!("{:?} is from a Dirichlet([1.0, 2.0, 3.0]) distribution", samples);
/// ```
#[derive(Clone, Debug)]
pub struct Dirichlet<N> {
/// Concentration parameters (alpha)
alpha: Vec<N>,
}
/// Error type returned from `Dirchlet::new`.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum Error {
/// `alpha.len() < 2`.
AlphaTooShort,
/// `alpha <= 0.0` or `nan`.
AlphaTooSmall,
/// `size < 2`.
SizeTooSmall,
}
impl<N: Float> Dirichlet<N>
where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
{
/// Construct a new `Dirichlet` with the given alpha parameter `alpha`.
///
/// Requires `alpha.len() >= 2`.
#[inline]
pub fn new<V: Into<Vec<N>>>(alpha: V) -> Result<Dirichlet<N>, Error> {
let a = alpha.into();
if a.len() < 2 {
return Err(Error::AlphaTooShort);
}
for &ai in &a {
if !(ai > N::from(0.0)) {
return Err(Error::AlphaTooSmall);
}
}
Ok(Dirichlet { alpha: a })
}
/// Construct a new `Dirichlet` with the given shape parameter `alpha` and `size`.
///
/// Requires `size >= 2`.
#[inline]
pub fn new_with_size(alpha: N, size: usize) -> Result<Dirichlet<N>, Error> {
if !(alpha > N::from(0.0)) {
return Err(Error::AlphaTooSmall);
}
if size < 2 {
return Err(Error::SizeTooSmall);
}
Ok(Dirichlet {
alpha: vec![alpha; size],
})
}
}
impl<N: Float> Distribution<Vec<N>> for Dirichlet<N>
where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
{
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Vec<N> {
let n = self.alpha.len();
let mut samples = vec![N::from(0.0); n];
let mut sum = N::from(0.0);
for (s, &a) in samples.iter_mut().zip(self.alpha.iter()) {
let g = Gamma::new(a, N::from(1.0)).unwrap();
*s = g.sample(rng);
sum += *s;
}
let invacc = N::from(1.0) / sum;
for s in samples.iter_mut() {
*s *= invacc;
}
samples
}
}
#[cfg(test)]
mod test {
use super::Dirichlet;
use crate::Distribution;
#[test]
fn test_dirichlet() {
let d = Dirichlet::new(vec![1.0, 2.0, 3.0]).unwrap();
let mut rng = crate::test::rng(221);
let samples = d.sample(&mut rng);
let _: Vec<f64> = samples
.into_iter()
.map(|x| {
assert!(x > 0.0);
x
})
.collect();
}
#[test]
fn test_dirichlet_with_param() {
let alpha = 0.5f64;
let size = 2;
let d = Dirichlet::new_with_size(alpha, size).unwrap();
let mut rng = crate::test::rng(221);
let samples = d.sample(&mut rng);
let _: Vec<f64> = samples
.into_iter()
.map(|x| {
assert!(x > 0.0);
x
})
.collect();
}
#[test]
#[should_panic]
fn test_dirichlet_invalid_length() {
Dirichlet::new_with_size(0.5f64, 1).unwrap();
}
#[test]
#[should_panic]
fn test_dirichlet_invalid_alpha() {
Dirichlet::new_with_size(0.0f64, 2).unwrap();
}
}
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