| // 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 rand::Rng; |
| use crate::{Distribution, Standard}; |
| use crate::utils::Float; |
| |
| /// 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)] |
| pub struct Triangular<N> { |
| min: N, |
| max: N, |
| mode: N, |
| } |
| |
| /// 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<N: Float> Triangular<N> |
| where Standard: Distribution<N> |
| { |
| /// Set up the Triangular distribution with defined `min`, `max` and `mode`. |
| #[inline] |
| pub fn new(min: N, max: N, mode: N) -> Result<Triangular<N>, TriangularError> { |
| if !(max >= min) { |
| return Err(TriangularError::RangeTooSmall); |
| } |
| if !(mode >= min && max >= mode) { |
| return Err(TriangularError::ModeRange); |
| } |
| Ok(Triangular { min, max, mode }) |
| } |
| } |
| |
| impl<N: Float> Distribution<N> for Triangular<N> |
| where Standard: Distribution<N> |
| { |
| #[inline] |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N { |
| let f: N = 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 std::f64; |
| use rand::{Rng, rngs::mock}; |
| use super::*; |
| |
| #[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()), |
| ] { |
| 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 value_stability() { |
| let rng = crate::test::rng(860); |
| let distr = Triangular::new(2., 10., 3.).unwrap(); |
| let seq = distr.sample_iter(rng).take(5).collect::<Vec<f64>>(); |
| println!("seq: {:?}", seq); |
| let expected = vec![5.74373257511361, 7.890059162791258, |
| 4.7256280652553455, 2.9474808121184077, 3.058301946314053]; |
| assert!(seq == expected); |
| } |
| } |