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
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
// 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 normal and derived distributions.

use Rng;
use distributions::{ziggurat_tables, Distribution, Open01};
use distributions::utils::ziggurat;

/// Samples floating-point numbers according to the normal distribution
/// `N(0, 1)` (a.k.a. a standard normal, or Gaussian). This is equivalent to
/// `Normal::new(0.0, 1.0)` but faster.
///
/// See `Normal` for the general normal distribution.
///
/// Implemented via the ZIGNOR variant[^1] of the Ziggurat method.
///
/// [^1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to
///       Generate Normal Random Samples*](
///       https://www.doornik.com/research/ziggurat.pdf).
///       Nuffield College, Oxford
///
/// # Example
/// ```
/// use rand::prelude::*;
/// use rand::distributions::StandardNormal;
///
/// let val: f64 = SmallRng::from_entropy().sample(StandardNormal);
/// println!("{}", val);
/// ```
#[derive(Clone, Copy, Debug)]
pub struct StandardNormal;

impl Distribution<f64> for StandardNormal {
    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
        #[inline]
        fn pdf(x: f64) -> f64 {
            (-x*x/2.0).exp()
        }
        #[inline]
        fn zero_case<R: Rng + ?Sized>(rng: &mut R, u: f64) -> f64 {
            // compute a random number in the tail by hand

            // strange initial conditions, because the loop is not
            // do-while, so the condition should be true on the first
            // run, they get overwritten anyway (0 < 1, so these are
            // good).
            let mut x = 1.0f64;
            let mut y = 0.0f64;

            while -2.0 * y < x * x {
                let x_: f64 = rng.sample(Open01);
                let y_: f64 = rng.sample(Open01);

                x = x_.ln() / ziggurat_tables::ZIG_NORM_R;
                y = y_.ln();
            }

            if u < 0.0 { x - ziggurat_tables::ZIG_NORM_R } else { ziggurat_tables::ZIG_NORM_R - x }
        }

        ziggurat(rng, true, // this is symmetric
                 &ziggurat_tables::ZIG_NORM_X,
                 &ziggurat_tables::ZIG_NORM_F,
                 pdf, zero_case)
    }
}

/// The normal distribution `N(mean, std_dev**2)`.
///
/// This uses the ZIGNOR variant of the Ziggurat method, see [`StandardNormal`]
/// for more details.
/// 
/// Note that [`StandardNormal`] is an optimised implementation for mean 0, and
/// standard deviation 1.
///
/// # Example
///
/// ```
/// use rand::distributions::{Normal, Distribution};
///
/// // mean 2, standard deviation 3
/// let normal = Normal::new(2.0, 3.0);
/// let v = normal.sample(&mut rand::thread_rng());
/// println!("{} is from a N(2, 9) distribution", v)
/// ```
///
/// [`StandardNormal`]: crate::distributions::StandardNormal
#[derive(Clone, Copy, Debug)]
pub struct Normal {
    mean: f64,
    std_dev: f64,
}

impl Normal {
    /// Construct a new `Normal` distribution with the given mean and
    /// standard deviation.
    ///
    /// # Panics
    ///
    /// Panics if `std_dev < 0`.
    #[inline]
    pub fn new(mean: f64, std_dev: f64) -> Normal {
        assert!(std_dev >= 0.0, "Normal::new called with `std_dev` < 0");
        Normal {
            mean,
            std_dev
        }
    }
}
impl Distribution<f64> for Normal {
    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
        let n = rng.sample(StandardNormal);
        self.mean + self.std_dev * n
    }
}


/// The log-normal distribution `ln N(mean, std_dev**2)`.
///
/// If `X` is log-normal distributed, then `ln(X)` is `N(mean, std_dev**2)`
/// distributed.
///
/// # Example
///
/// ```
/// use rand::distributions::{LogNormal, Distribution};
///
/// // mean 2, standard deviation 3
/// let log_normal = LogNormal::new(2.0, 3.0);
/// let v = log_normal.sample(&mut rand::thread_rng());
/// println!("{} is from an ln N(2, 9) distribution", v)
/// ```
#[derive(Clone, Copy, Debug)]
pub struct LogNormal {
    norm: Normal
}

impl LogNormal {
    /// Construct a new `LogNormal` distribution with the given mean
    /// and standard deviation.
    ///
    /// # Panics
    ///
    /// Panics if `std_dev < 0`.
    #[inline]
    pub fn new(mean: f64, std_dev: f64) -> LogNormal {
        assert!(std_dev >= 0.0, "LogNormal::new called with `std_dev` < 0");
        LogNormal { norm: Normal::new(mean, std_dev) }
    }
}
impl Distribution<f64> for LogNormal {
    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
        self.norm.sample(rng).exp()
    }
}

#[cfg(test)]
mod tests {
    use distributions::Distribution;
    use super::{Normal, LogNormal};

    #[test]
    fn test_normal() {
        let norm = Normal::new(10.0, 10.0);
        let mut rng = ::test::rng(210);
        for _ in 0..1000 {
            norm.sample(&mut rng);
        }
    }
    #[test]
    #[should_panic]
    fn test_normal_invalid_sd() {
        Normal::new(10.0, -1.0);
    }


    #[test]
    fn test_log_normal() {
        let lnorm = LogNormal::new(10.0, 10.0);
        let mut rng = ::test::rng(211);
        for _ in 0..1000 {
            lnorm.sample(&mut rng);
        }
    }
    #[test]
    #[should_panic]
    fn test_log_normal_invalid_sd() {
        LogNormal::new(10.0, -1.0);
    }
}