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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
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! The dirichlet distribution.
#![cfg(feature = "alloc")]
use num_traits::Float;
use crate::{Distribution, Exp1, Gamma, Open01, StandardNormal};
use rand::Rng;
use core::fmt;
use alloc::{boxed::Box, vec, vec::Vec};
/// The Dirichlet 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(&[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);
/// ```
#[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
#[derive(Clone, Debug)]
#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
pub struct Dirichlet<F>
where
F: Float,
StandardNormal: Distribution<F>,
Exp1: Distribution<F>,
Open01: Distribution<F>,
{
/// Concentration parameters (alpha)
alpha: Box<[F]>,
}
/// Error type returned from `Dirchlet::new`.
#[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum Error {
/// `alpha.len() < 2`.
AlphaTooShort,
/// `alpha <= 0.0` or `nan`.
AlphaTooSmall,
/// `size < 2`.
SizeTooSmall,
}
impl fmt::Display for Error {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
f.write_str(match self {
Error::AlphaTooShort | Error::SizeTooSmall => {
"less than 2 dimensions in Dirichlet distribution"
}
Error::AlphaTooSmall => "alpha is not positive in Dirichlet distribution",
})
}
}
#[cfg(feature = "std")]
#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
impl std::error::Error for Error {}
impl<F> Dirichlet<F>
where
F: Float,
StandardNormal: Distribution<F>,
Exp1: Distribution<F>,
Open01: Distribution<F>,
{
/// Construct a new `Dirichlet` with the given alpha parameter `alpha`.
///
/// Requires `alpha.len() >= 2`.
#[inline]
pub fn new(alpha: &[F]) -> Result<Dirichlet<F>, Error> {
if alpha.len() < 2 {
return Err(Error::AlphaTooShort);
}
for &ai in alpha.iter() {
if !(ai > F::zero()) {
return Err(Error::AlphaTooSmall);
}
}
Ok(Dirichlet { alpha: alpha.to_vec().into_boxed_slice() })
}
/// Construct a new `Dirichlet` with the given shape parameter `alpha` and `size`.
///
/// Requires `size >= 2`.
#[inline]
pub fn new_with_size(alpha: F, size: usize) -> Result<Dirichlet<F>, Error> {
if !(alpha > F::zero()) {
return Err(Error::AlphaTooSmall);
}
if size < 2 {
return Err(Error::SizeTooSmall);
}
Ok(Dirichlet {
alpha: vec![alpha; size].into_boxed_slice(),
})
}
}
impl<F> Distribution<Vec<F>> for Dirichlet<F>
where
F: Float,
StandardNormal: Distribution<F>,
Exp1: Distribution<F>,
Open01: Distribution<F>,
{
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Vec<F> {
let n = self.alpha.len();
let mut samples = vec![F::zero(); n];
let mut sum = F::zero();
for (s, &a) in samples.iter_mut().zip(self.alpha.iter()) {
let g = Gamma::new(a, F::one()).unwrap();
*s = g.sample(rng);
sum = sum + (*s);
}
let invacc = F::one() / sum;
for s in samples.iter_mut() {
*s = (*s)*invacc;
}
samples
}
}
#[cfg(test)]
mod test {
use super::*;
#[test]
fn test_dirichlet() {
let d = Dirichlet::new(&[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();
}
}