logo
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
// Copyright 2018 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 triangular distribution.

use num_traits::Float;
use crate::{Distribution, Standard};
use rand::Rng;
use core::fmt;

/// The triangular distribution.
///
/// A continuous probability distribution parameterised by a range, and a mode
/// (most likely value) within that range.
///
/// The probability density function is triangular. For a similar distribution
/// with a smooth PDF, see the [`Pert`] distribution.
///
/// # Example
///
/// ```rust
/// use rand_distr::{Triangular, Distribution};
///
/// let d = Triangular::new(0., 5., 2.5).unwrap();
/// let v = d.sample(&mut rand::thread_rng());
/// println!("{} is from a triangular distribution", v);
/// ```
///
/// [`Pert`]: crate::Pert
#[derive(Clone, Copy, Debug, PartialEq)]
#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
pub struct Triangular<F>
where F: Float, Standard: Distribution<F>
{
    min: F,
    max: F,
    mode: F,
}

/// Error type returned from [`Triangular::new`].
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum TriangularError {
    /// `max < min` or `min` or `max` is NaN.
    RangeTooSmall,
    /// `mode < min` or `mode > max` or `mode` is NaN.
    ModeRange,
}

impl fmt::Display for TriangularError {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.write_str(match self {
            TriangularError::RangeTooSmall => {
                "requirement min <= max is not met in triangular distribution"
            }
            TriangularError::ModeRange => "mode is outside [min, max] in triangular distribution",
        })
    }
}

#[cfg(feature = "std")]
#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
impl std::error::Error for TriangularError {}

impl<F> Triangular<F>
where F: Float, Standard: Distribution<F>
{
    /// Set up the Triangular distribution with defined `min`, `max` and `mode`.
    #[inline]
    pub fn new(min: F, max: F, mode: F) -> Result<Triangular<F>, TriangularError> {
        if !(max >= min) {
            return Err(TriangularError::RangeTooSmall);
        }
        if !(mode >= min && max >= mode) {
            return Err(TriangularError::ModeRange);
        }
        Ok(Triangular { min, max, mode })
    }
}

impl<F> Distribution<F> for Triangular<F>
where F: Float, Standard: Distribution<F>
{
    #[inline]
    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
        let f: F = rng.sample(Standard);
        let diff_mode_min = self.mode - self.min;
        let range = self.max - self.min;
        let f_range = f * range;
        if f_range < diff_mode_min {
            self.min + (f_range * diff_mode_min).sqrt()
        } else {
            self.max - ((range - f_range) * (self.max - self.mode)).sqrt()
        }
    }
}

#[cfg(test)]
mod test {
    use super::*;
    use rand::{rngs::mock, Rng};

    #[test]
    fn test_triangular() {
        let mut half_rng = mock::StepRng::new(0x8000_0000_0000_0000, 0);
        assert_eq!(half_rng.gen::<f64>(), 0.5);
        for &(min, max, mode, median) in &[
            (-1., 1., 0., 0.),
            (1., 2., 1., 2. - 0.5f64.sqrt()),
            (5., 25., 25., 5. + 200f64.sqrt()),
            (1e-5, 1e5, 1e-3, 1e5 - 4999999949.5f64.sqrt()),
            (0., 1., 0.9, 0.45f64.sqrt()),
            (-4., -0.5, -2., -4.0 + 3.5f64.sqrt()),
        ] {
            #[cfg(feature = "std")]
            std::println!("{} {} {} {}", min, max, mode, median);
            let distr = Triangular::new(min, max, mode).unwrap();
            // Test correct value at median:
            assert_eq!(distr.sample(&mut half_rng), median);
        }

        for &(min, max, mode) in &[
            (-1., 1., 2.),
            (-1., 1., -2.),
            (2., 1., 1.),
        ] {
            assert!(Triangular::new(min, max, mode).is_err());
        }
    }

    #[test]
    fn triangular_distributions_can_be_compared() {
        assert_eq!(Triangular::new(1.0, 3.0, 2.0), Triangular::new(1.0, 3.0, 2.0));
    }
}