auto merge of #10859 : huonw/rust/helper-dists, r=cmr
This moves `std::rand::distribitions::{Normal, StandardNormal}` to `...::distributions::normal`, reexporting `Normal` from `distributions` (and similarly for `Exp` and Exp1`), and adds:
- Log-normal
- Chi-squared
- F
- Student T
all of which are implemented in C++11's random library. Tests in 0424b8aded. Note that these are approximately half documentation & half implementation (of which a significant portion is boilerplate `}`'s and so on).
This commit is contained in:
bors
commit
a417dbd1c7
src/libstd/rand/distributions
141
src/libstd/rand/distributions/exponential.rs
Normal file
141
src/libstd/rand/distributions/exponential.rs
Normal file
@ -0,0 +1,141 @@
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// Copyright 2013 The Rust Project Developers. See the COPYRIGHT
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// file at the top-level directory of this distribution and at
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// http://rust-lang.org/COPYRIGHT.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! The exponential distribution.
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use rand::{Rng, Rand};
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use rand::distributions::{ziggurat, ziggurat_tables, Sample, IndependentSample};
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/// A wrapper around an `f64` to generate Exp(1) random numbers.
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///
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/// See `Exp` for the general exponential distribution.Note that this
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// has to be unwrapped before use as an `f64` (using either
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/// `*` or `cast::transmute` is safe).
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///
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/// Implemented via the ZIGNOR variant[1] of the Ziggurat method. The
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/// exact description in the paper was adjusted to use tables for the
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/// exponential distribution rather than normal.
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///
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/// [1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to
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/// Generate Normal Random
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/// Samples*](http://www.doornik.com/research/ziggurat.pdf). Nuffield
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/// College, Oxford
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pub struct Exp1(f64);
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// This could be done via `-rng.gen::<f64>().ln()` but that is slower.
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impl Rand for Exp1 {
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#[inline]
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fn rand<R:Rng>(rng: &mut R) -> Exp1 {
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#[inline]
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fn pdf(x: f64) -> f64 {
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(-x).exp()
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}
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#[inline]
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fn zero_case<R:Rng>(rng: &mut R, _u: f64) -> f64 {
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ziggurat_tables::ZIG_EXP_R - rng.gen::<f64>().ln()
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}
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Exp1(ziggurat(rng, false,
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&ziggurat_tables::ZIG_EXP_X,
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&ziggurat_tables::ZIG_EXP_F,
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pdf, zero_case))
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}
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}
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/// The exponential distribution `Exp(lambda)`.
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///
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/// This distribution has density function: `f(x) = lambda *
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/// exp(-lambda * x)` for `x > 0`.
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///
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/// # Example
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///
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/// ```rust
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/// use std::rand;
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/// use std::rand::distributions::{Exp, IndependentSample};
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///
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/// fn main() {
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/// let exp = Exp::new(2.0);
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/// let v = exp.ind_sample(&mut rand::task_rng());
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/// println!("{} is from a Exp(2) distribution", v);
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/// }
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/// ```
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pub struct Exp {
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/// `lambda` stored as `1/lambda`, since this is what we scale by.
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priv lambda_inverse: f64
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}
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impl Exp {
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/// Construct a new `Exp` with the given shape parameter
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/// `lambda`. Fails if `lambda <= 0`.
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pub fn new(lambda: f64) -> Exp {
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assert!(lambda > 0.0, "Exp::new called with `lambda` <= 0");
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Exp { lambda_inverse: 1.0 / lambda }
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}
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}
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impl Sample<f64> for Exp {
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fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
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}
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impl IndependentSample<f64> for Exp {
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fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
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(*rng.gen::<Exp1>()) * self.lambda_inverse
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}
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}
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#[cfg(test)]
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mod test {
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use rand::*;
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use super::*;
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use iter::range;
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use option::{Some, None};
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#[test]
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fn test_exp() {
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let mut exp = Exp::new(10.0);
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let mut rng = task_rng();
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for _ in range(0, 1000) {
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assert!(exp.sample(&mut rng) >= 0.0);
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assert!(exp.ind_sample(&mut rng) >= 0.0);
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}
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}
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#[test]
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#[should_fail]
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fn test_exp_invalid_lambda_zero() {
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Exp::new(0.0);
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}
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#[test]
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#[should_fail]
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fn test_exp_invalid_lambda_neg() {
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Exp::new(-10.0);
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}
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}
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#[cfg(test)]
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mod bench {
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use extra::test::BenchHarness;
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use rand::{XorShiftRng, RAND_BENCH_N};
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use super::*;
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use iter::range;
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use option::{Some, None};
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use mem::size_of;
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#[bench]
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fn rand_exp(bh: &mut BenchHarness) {
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let mut rng = XorShiftRng::new();
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let mut exp = Exp::new(2.71828 * 3.14159);
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bh.iter(|| {
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for _ in range(0, RAND_BENCH_N) {
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exp.sample(&mut rng);
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}
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});
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bh.bytes = size_of::<f64>() as u64 * RAND_BENCH_N;
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}
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}
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@ -8,10 +8,11 @@
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! The Gamma distribution.
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//! The Gamma and derived distributions.
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use rand::{Rng, Open01};
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use super::{IndependentSample, Sample, StandardNormal, Exp};
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use super::{IndependentSample, Sample, Exp};
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use super::normal::StandardNormal;
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use num;
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/// The Gamma distribution `Gamma(shape, scale)` distribution.
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@ -168,6 +169,213 @@ impl IndependentSample<f64> for GammaLargeShape {
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}
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}
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/// The chi-squared distribution `χ²(k)`, where `k` is the degrees of
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/// freedom.
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///
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/// For `k > 0` integral, this distribution is the sum of the squares
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/// of `k` independent standard normal random variables. For other
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/// `k`, this uses the equivalent characterisation `χ²(k) = Gamma(k/2,
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/// 2)`.
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///
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/// # Example
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///
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/// ```rust
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/// use std::rand;
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/// use std::rand::distributions::{ChiSquared, IndependentSample};
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///
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/// fn main() {
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/// let chi = ChiSquared::new(11.0);
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/// let v = chi.ind_sample(&mut rand::task_rng());
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/// println!("{} is from a χ²(11) distribution", v)
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/// }
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/// ```
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pub enum ChiSquared {
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// k == 1, Gamma(alpha, ..) is particularly slow for alpha < 1,
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// e.g. when alpha = 1/2 as it would be for this case, so special-
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// casing and using the definition of N(0,1)^2 is faster.
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priv DoFExactlyOne,
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priv DoFAnythingElse(Gamma)
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}
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impl ChiSquared {
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/// Create a new chi-squared distribution with degrees-of-freedom
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/// `k`. Fails if `k < 0`.
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pub fn new(k: f64) -> ChiSquared {
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if k == 1.0 {
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DoFExactlyOne
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} else {
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assert!(k > 0.0, "ChiSquared::new called with `k` < 0");
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DoFAnythingElse(Gamma::new(0.5 * k, 2.0))
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}
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}
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}
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impl Sample<f64> for ChiSquared {
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fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
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}
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impl IndependentSample<f64> for ChiSquared {
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fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
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match *self {
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DoFExactlyOne => {
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// k == 1 => N(0,1)^2
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let norm = *rng.gen::<StandardNormal>();
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norm * norm
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}
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DoFAnythingElse(ref g) => g.ind_sample(rng)
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}
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}
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}
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/// The Fisher F distribution `F(m, n)`.
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///
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/// This distribution is equivalent to the ratio of two normalised
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/// chi-squared distributions, that is, `F(m,n) = (χ²(m)/m) /
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/// (χ²(n)/n)`.
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///
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/// # Example
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///
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/// ```rust
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/// use std::rand;
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/// use std::rand::distributions::{FisherF, IndependentSample};
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///
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/// fn main() {
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/// let f = FisherF::new(2.0, 32.0);
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/// let v = f.ind_sample(&mut rand::task_rng());
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/// println!("{} is from an F(2, 32) distribution", v)
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/// }
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/// ```
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pub struct FisherF {
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priv numer: ChiSquared,
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priv denom: ChiSquared,
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// denom_dof / numer_dof so that this can just be a straight
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// multiplication, rather than a division.
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priv dof_ratio: f64,
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}
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impl FisherF {
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/// Create a new `FisherF` distribution, with the given
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/// parameter. Fails if either `m` or `n` are not positive.
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pub fn new(m: f64, n: f64) -> FisherF {
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assert!(m > 0.0, "FisherF::new called with `m < 0`");
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assert!(n > 0.0, "FisherF::new called with `n < 0`");
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FisherF {
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numer: ChiSquared::new(m),
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denom: ChiSquared::new(n),
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dof_ratio: n / m
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}
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}
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}
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impl Sample<f64> for FisherF {
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fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
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}
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impl IndependentSample<f64> for FisherF {
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fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
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self.numer.ind_sample(rng) / self.denom.ind_sample(rng) * self.dof_ratio
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}
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}
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/// The Student t distribution, `t(nu)`, where `nu` is the degrees of
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/// freedom.
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///
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/// # Example
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///
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/// ```rust
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/// use std::rand;
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/// use std::rand::distributions::{StudentT, IndependentSample};
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///
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/// fn main() {
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/// let t = StudentT::new(11.0);
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/// let v = t.ind_sample(&mut rand::task_rng());
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/// println!("{} is from a t(11) distribution", v)
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/// }
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/// ```
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pub struct StudentT {
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priv chi: ChiSquared,
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priv dof: f64
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}
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impl StudentT {
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/// Create a new Student t distribution with `n` degrees of
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/// freedom. Fails if `n <= 0`.
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pub fn new(n: f64) -> StudentT {
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assert!(n > 0.0, "StudentT::new called with `n <= 0`");
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StudentT {
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chi: ChiSquared::new(n),
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dof: n
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}
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}
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}
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impl Sample<f64> for StudentT {
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fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
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}
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impl IndependentSample<f64> for StudentT {
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fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
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let norm = *rng.gen::<StandardNormal>();
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norm * (self.dof / self.chi.ind_sample(rng)).sqrt()
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}
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}
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#[cfg(test)]
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mod test {
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use rand::*;
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use super::*;
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use iter::range;
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use option::{Some, None};
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#[test]
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fn test_chi_squared_one() {
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let mut chi = ChiSquared::new(1.0);
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let mut rng = task_rng();
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for _ in range(0, 1000) {
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chi.sample(&mut rng);
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chi.ind_sample(&mut rng);
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}
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}
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#[test]
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fn test_chi_squared_small() {
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let mut chi = ChiSquared::new(0.5);
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let mut rng = task_rng();
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for _ in range(0, 1000) {
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chi.sample(&mut rng);
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chi.ind_sample(&mut rng);
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}
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}
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#[test]
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fn test_chi_squared_large() {
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let mut chi = ChiSquared::new(30.0);
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let mut rng = task_rng();
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for _ in range(0, 1000) {
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chi.sample(&mut rng);
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chi.ind_sample(&mut rng);
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}
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}
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#[test]
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#[should_fail]
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fn test_log_normal_invalid_dof() {
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ChiSquared::new(-1.0);
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}
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#[test]
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fn test_f() {
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let mut f = FisherF::new(2.0, 32.0);
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let mut rng = task_rng();
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for _ in range(0, 1000) {
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f.sample(&mut rng);
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f.ind_sample(&mut rng);
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}
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}
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#[test]
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fn test_t() {
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let mut t = StudentT::new(11.0);
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let mut rng = task_rng();
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for _ in range(0, 1000) {
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t.sample(&mut rng);
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t.ind_sample(&mut rng);
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}
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}
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}
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#[cfg(test)]
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mod bench {
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use super::*;
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@ -23,14 +23,18 @@ that do not need to record state.
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use iter::range;
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use option::{Some, None};
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use num;
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use rand::{Rng, Rand, Open01};
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use rand::{Rng, Rand};
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use clone::Clone;
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pub use self::range::Range;
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pub use self::gamma::Gamma;
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pub use self::gamma::{Gamma, ChiSquared, FisherF, StudentT};
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pub use self::normal::{Normal, LogNormal};
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pub use self::exponential::Exp;
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pub mod range;
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pub mod gamma;
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pub mod normal;
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pub mod exponential;
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/// Types that can be used to create a random instance of `Support`.
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pub trait Sample<Support> {
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@ -246,181 +250,10 @@ fn ziggurat<R:Rng>(
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}
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}
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/// A wrapper around an `f64` to generate N(0, 1) random numbers
|
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/// (a.k.a. a standard normal, or Gaussian).
|
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///
|
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/// See `Normal` for the general normal distribution. That this has to
|
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/// be unwrapped before use as an `f64` (using either `*` or
|
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/// `cast::transmute` is safe).
|
||||
///
|
||||
/// Implemented via the ZIGNOR variant[1] of the Ziggurat method.
|
||||
///
|
||||
/// [1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to
|
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/// Generate Normal Random
|
||||
/// Samples*](http://www.doornik.com/research/ziggurat.pdf). Nuffield
|
||||
/// College, Oxford
|
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pub struct StandardNormal(f64);
|
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|
||||
impl Rand for StandardNormal {
|
||||
fn rand<R:Rng>(rng: &mut R) -> StandardNormal {
|
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#[inline]
|
||||
fn pdf(x: f64) -> f64 {
|
||||
((-x*x/2.0) as f64).exp()
|
||||
}
|
||||
#[inline]
|
||||
fn zero_case<R:Rng>(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 {
|
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let x_ = *rng.gen::<Open01<f64>>();
|
||||
let y_ = *rng.gen::<Open01<f64>>();
|
||||
|
||||
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 }
|
||||
}
|
||||
|
||||
StandardNormal(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.
|
||||
///
|
||||
/// # Example
|
||||
///
|
||||
/// ```
|
||||
/// use std::rand;
|
||||
/// use std::rand::distributions::{Normal, IndependentSample};
|
||||
///
|
||||
/// fn main() {
|
||||
/// let normal = Normal::new(2.0, 3.0);
|
||||
/// let v = normal.ind_sample(rand::task_rng());
|
||||
/// println!("{} is from a N(2, 9) distribution", v)
|
||||
/// }
|
||||
/// ```
|
||||
pub struct Normal {
|
||||
priv mean: f64,
|
||||
priv std_dev: f64
|
||||
}
|
||||
|
||||
impl Normal {
|
||||
/// Construct a new `Normal` distribution with the given mean and
|
||||
/// standard deviation. Fails if `std_dev < 0`.
|
||||
pub fn new(mean: f64, std_dev: f64) -> Normal {
|
||||
assert!(std_dev >= 0.0, "Normal::new called with `std_dev` < 0");
|
||||
Normal {
|
||||
mean: mean,
|
||||
std_dev: std_dev
|
||||
}
|
||||
}
|
||||
}
|
||||
impl Sample<f64> for Normal {
|
||||
fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
|
||||
}
|
||||
impl IndependentSample<f64> for Normal {
|
||||
fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
|
||||
self.mean + self.std_dev * (*rng.gen::<StandardNormal>())
|
||||
}
|
||||
}
|
||||
|
||||
/// A wrapper around an `f64` to generate Exp(1) random numbers.
|
||||
///
|
||||
/// See `Exp` for the general exponential distribution.Note that this
|
||||
// has to be unwrapped before use as an `f64` (using either
|
||||
/// `*` or `cast::transmute` is safe).
|
||||
///
|
||||
/// Implemented via the ZIGNOR variant[1] of the Ziggurat method. The
|
||||
/// exact description in the paper was adjusted to use tables for the
|
||||
/// exponential distribution rather than normal.
|
||||
///
|
||||
/// [1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to
|
||||
/// Generate Normal Random
|
||||
/// Samples*](http://www.doornik.com/research/ziggurat.pdf). Nuffield
|
||||
/// College, Oxford
|
||||
pub struct Exp1(f64);
|
||||
|
||||
// This could be done via `-rng.gen::<f64>().ln()` but that is slower.
|
||||
impl Rand for Exp1 {
|
||||
#[inline]
|
||||
fn rand<R:Rng>(rng: &mut R) -> Exp1 {
|
||||
#[inline]
|
||||
fn pdf(x: f64) -> f64 {
|
||||
(-x).exp()
|
||||
}
|
||||
#[inline]
|
||||
fn zero_case<R:Rng>(rng: &mut R, _u: f64) -> f64 {
|
||||
ziggurat_tables::ZIG_EXP_R - rng.gen::<f64>().ln()
|
||||
}
|
||||
|
||||
Exp1(ziggurat(rng, false,
|
||||
&ziggurat_tables::ZIG_EXP_X,
|
||||
&ziggurat_tables::ZIG_EXP_F,
|
||||
pdf, zero_case))
|
||||
}
|
||||
}
|
||||
|
||||
/// The exponential distribution `Exp(lambda)`.
|
||||
///
|
||||
/// This distribution has density function: `f(x) = lambda *
|
||||
/// exp(-lambda * x)` for `x > 0`.
|
||||
///
|
||||
/// # Example
|
||||
///
|
||||
/// ```
|
||||
/// use std::rand;
|
||||
/// use std::rand::distributions::{Exp, IndependentSample};
|
||||
///
|
||||
/// fn main() {
|
||||
/// let exp = Exp::new(2.0);
|
||||
/// let v = exp.ind_sample(rand::task_rng());
|
||||
/// println!("{} is from a Exp(2) distribution", v);
|
||||
/// }
|
||||
/// ```
|
||||
pub struct Exp {
|
||||
/// `lambda` stored as `1/lambda`, since this is what we scale by.
|
||||
priv lambda_inverse: f64
|
||||
}
|
||||
|
||||
impl Exp {
|
||||
/// Construct a new `Exp` with the given shape parameter
|
||||
/// `lambda`. Fails if `lambda <= 0`.
|
||||
pub fn new(lambda: f64) -> Exp {
|
||||
assert!(lambda > 0.0, "Exp::new called with `lambda` <= 0");
|
||||
Exp { lambda_inverse: 1.0 / lambda }
|
||||
}
|
||||
}
|
||||
|
||||
impl Sample<f64> for Exp {
|
||||
fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
|
||||
}
|
||||
impl IndependentSample<f64> for Exp {
|
||||
fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
|
||||
(*rng.gen::<Exp1>()) * self.lambda_inverse
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use rand::*;
|
||||
use super::*;
|
||||
use iter::range;
|
||||
use option::{Some, None};
|
||||
|
||||
struct ConstRand(uint);
|
||||
@ -449,42 +282,6 @@ mod tests {
|
||||
assert_eq!(*rand_sample.sample(&mut task_rng()), 0);
|
||||
assert_eq!(*rand_sample.ind_sample(&mut task_rng()), 0);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_normal() {
|
||||
let mut norm = Normal::new(10.0, 10.0);
|
||||
let mut rng = task_rng();
|
||||
for _ in range(0, 1000) {
|
||||
norm.sample(&mut rng);
|
||||
norm.ind_sample(&mut rng);
|
||||
}
|
||||
}
|
||||
#[test]
|
||||
#[should_fail]
|
||||
fn test_normal_invalid_sd() {
|
||||
Normal::new(10.0, -1.0);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_exp() {
|
||||
let mut exp = Exp::new(10.0);
|
||||
let mut rng = task_rng();
|
||||
for _ in range(0, 1000) {
|
||||
assert!(exp.sample(&mut rng) >= 0.0);
|
||||
assert!(exp.ind_sample(&mut rng) >= 0.0);
|
||||
}
|
||||
}
|
||||
#[test]
|
||||
#[should_fail]
|
||||
fn test_exp_invalid_lambda_zero() {
|
||||
Exp::new(0.0);
|
||||
}
|
||||
#[test]
|
||||
#[should_fail]
|
||||
fn test_exp_invalid_lambda_neg() {
|
||||
Exp::new(-10.0);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_weighted_choice() {
|
||||
// this makes assumptions about the internal implementation of
|
||||
@ -556,38 +353,3 @@ mod tests {
|
||||
Weighted { weight: 1, item: 3 }]);
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod bench {
|
||||
use extra::test::BenchHarness;
|
||||
use rand::{XorShiftRng, RAND_BENCH_N};
|
||||
use super::*;
|
||||
use iter::range;
|
||||
use option::{Some, None};
|
||||
use mem::size_of;
|
||||
|
||||
#[bench]
|
||||
fn rand_normal(bh: &mut BenchHarness) {
|
||||
let mut rng = XorShiftRng::new();
|
||||
let mut normal = Normal::new(-2.71828, 3.14159);
|
||||
|
||||
bh.iter(|| {
|
||||
for _ in range(0, RAND_BENCH_N) {
|
||||
normal.sample(&mut rng);
|
||||
}
|
||||
});
|
||||
bh.bytes = size_of::<f64>() as u64 * RAND_BENCH_N;
|
||||
}
|
||||
#[bench]
|
||||
fn rand_exp(bh: &mut BenchHarness) {
|
||||
let mut rng = XorShiftRng::new();
|
||||
let mut exp = Exp::new(2.71828 * 3.14159);
|
||||
|
||||
bh.iter(|| {
|
||||
for _ in range(0, RAND_BENCH_N) {
|
||||
exp.sample(&mut rng);
|
||||
}
|
||||
});
|
||||
bh.bytes = size_of::<f64>() as u64 * RAND_BENCH_N;
|
||||
}
|
||||
}
|
||||
|
||||
211
src/libstd/rand/distributions/normal.rs
Normal file
211
src/libstd/rand/distributions/normal.rs
Normal file
@ -0,0 +1,211 @@
|
||||
// Copyright 2013 The Rust Project Developers. See the COPYRIGHT
|
||||
// file at the top-level directory of this distribution and at
|
||||
// http://rust-lang.org/COPYRIGHT.
|
||||
//
|
||||
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
|
||||
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
|
||||
// <LICENSE-MIT or http://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 rand::{Rng, Rand, Open01};
|
||||
use rand::distributions::{ziggurat, ziggurat_tables, Sample, IndependentSample};
|
||||
|
||||
/// A wrapper around an `f64` to generate N(0, 1) random numbers
|
||||
/// (a.k.a. a standard normal, or Gaussian).
|
||||
///
|
||||
/// See `Normal` for the general normal distribution. That this has to
|
||||
/// be unwrapped before use as an `f64` (using either `*` or
|
||||
/// `cast::transmute` is safe).
|
||||
///
|
||||
/// Implemented via the ZIGNOR variant[1] of the Ziggurat method.
|
||||
///
|
||||
/// [1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to
|
||||
/// Generate Normal Random
|
||||
/// Samples*](http://www.doornik.com/research/ziggurat.pdf). Nuffield
|
||||
/// College, Oxford
|
||||
pub struct StandardNormal(f64);
|
||||
|
||||
impl Rand for StandardNormal {
|
||||
fn rand<R:Rng>(rng: &mut R) -> StandardNormal {
|
||||
#[inline]
|
||||
fn pdf(x: f64) -> f64 {
|
||||
((-x*x/2.0) as f64).exp()
|
||||
}
|
||||
#[inline]
|
||||
fn zero_case<R:Rng>(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_ = *rng.gen::<Open01<f64>>();
|
||||
let y_ = *rng.gen::<Open01<f64>>();
|
||||
|
||||
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 }
|
||||
}
|
||||
|
||||
StandardNormal(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.
|
||||
///
|
||||
/// # Example
|
||||
///
|
||||
/// ```rust
|
||||
/// use std::rand;
|
||||
/// use std::rand::distributions::{Normal, IndependentSample};
|
||||
///
|
||||
/// fn main() {
|
||||
/// // mean 2, standard deviation 3
|
||||
/// let normal = Normal::new(2.0, 3.0);
|
||||
/// let v = normal.ind_sample(&mut rand::task_rng());
|
||||
/// println!("{} is from a N(2, 9) distribution", v)
|
||||
/// }
|
||||
/// ```
|
||||
pub struct Normal {
|
||||
priv mean: f64,
|
||||
priv std_dev: f64
|
||||
}
|
||||
|
||||
impl Normal {
|
||||
/// Construct a new `Normal` distribution with the given mean and
|
||||
/// standard deviation. Fails if `std_dev < 0`.
|
||||
pub fn new(mean: f64, std_dev: f64) -> Normal {
|
||||
assert!(std_dev >= 0.0, "Normal::new called with `std_dev` < 0");
|
||||
Normal {
|
||||
mean: mean,
|
||||
std_dev: std_dev
|
||||
}
|
||||
}
|
||||
}
|
||||
impl Sample<f64> for Normal {
|
||||
fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
|
||||
}
|
||||
impl IndependentSample<f64> for Normal {
|
||||
fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
|
||||
self.mean + self.std_dev * (*rng.gen::<StandardNormal>())
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/// 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
|
||||
///
|
||||
/// ```rust
|
||||
/// use std::rand;
|
||||
/// use std::rand::distributions::{LogNormal, IndependentSample};
|
||||
///
|
||||
/// fn main() {
|
||||
/// // mean 2, standard deviation 3
|
||||
/// let log_normal = LogNormal::new(2.0, 3.0);
|
||||
/// let v = normal.ind_sample(&mut rand::task_rng());
|
||||
/// println!("{} is from an ln N(2, 9) distribution", v)
|
||||
/// }
|
||||
/// ```
|
||||
pub struct LogNormal {
|
||||
priv norm: Normal
|
||||
}
|
||||
|
||||
impl LogNormal {
|
||||
/// Construct a new `LogNormal` distribution with the given mean
|
||||
/// and standard deviation. Fails if `std_dev < 0`.
|
||||
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 Sample<f64> for LogNormal {
|
||||
fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
|
||||
}
|
||||
impl IndependentSample<f64> for LogNormal {
|
||||
fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
|
||||
self.norm.ind_sample(rng).exp()
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use rand::*;
|
||||
use super::*;
|
||||
use iter::range;
|
||||
use option::{Some, None};
|
||||
|
||||
#[test]
|
||||
fn test_normal() {
|
||||
let mut norm = Normal::new(10.0, 10.0);
|
||||
let mut rng = task_rng();
|
||||
for _ in range(0, 1000) {
|
||||
norm.sample(&mut rng);
|
||||
norm.ind_sample(&mut rng);
|
||||
}
|
||||
}
|
||||
#[test]
|
||||
#[should_fail]
|
||||
fn test_normal_invalid_sd() {
|
||||
Normal::new(10.0, -1.0);
|
||||
}
|
||||
|
||||
|
||||
#[test]
|
||||
fn test_log_normal() {
|
||||
let mut lnorm = LogNormal::new(10.0, 10.0);
|
||||
let mut rng = task_rng();
|
||||
for _ in range(0, 1000) {
|
||||
lnorm.sample(&mut rng);
|
||||
lnorm.ind_sample(&mut rng);
|
||||
}
|
||||
}
|
||||
#[test]
|
||||
#[should_fail]
|
||||
fn test_log_normal_invalid_sd() {
|
||||
LogNormal::new(10.0, -1.0);
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod bench {
|
||||
use extra::test::BenchHarness;
|
||||
use rand::{XorShiftRng, RAND_BENCH_N};
|
||||
use super::*;
|
||||
use iter::range;
|
||||
use option::{Some, None};
|
||||
use mem::size_of;
|
||||
|
||||
#[bench]
|
||||
fn rand_normal(bh: &mut BenchHarness) {
|
||||
let mut rng = XorShiftRng::new();
|
||||
let mut normal = Normal::new(-2.71828, 3.14159);
|
||||
|
||||
bh.iter(|| {
|
||||
for _ in range(0, RAND_BENCH_N) {
|
||||
normal.sample(&mut rng);
|
||||
}
|
||||
});
|
||||
bh.bytes = size_of::<f64>() as u64 * RAND_BENCH_N;
|
||||
}
|
||||
}
|
||||
Loading…
x
Reference in New Issue
Block a user