1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154

// 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();
    }
}