1 // Copyright 2013 The Rust Project Developers. See the COPYRIGHT
2 // file at the top-level directory of this distribution and at
3 // http://rust-lang.org/COPYRIGHT.
5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
8 // option. This file may not be copied, modified, or distributed
9 // except according to those terms.
11 //! Sampling from random distributions.
13 //! This is a generalization of `Rand` to allow parameters to control the
14 //! exact properties of the generated values, e.g. the mean and standard
15 //! deviation of a normal distribution. The `Sample` trait is the most
16 //! general, and allows for generating values that change some state
17 //! internally. The `IndependentSample` trait is for generating values
18 //! that do not need to record state.
21 use core::marker::PhantomData;
25 pub use self::range::Range;
26 pub use self::gamma::{Gamma, ChiSquared, FisherF, StudentT};
27 pub use self::normal::{Normal, LogNormal};
28 pub use self::exponential::Exp;
35 /// Types that can be used to create a random instance of `Support`.
36 pub trait Sample<Support> {
37 /// Generate a random value of `Support`, using `rng` as the
38 /// source of randomness.
39 fn sample<R: Rng>(&mut self, rng: &mut R) -> Support;
42 /// `Sample`s that do not require keeping track of state.
44 /// Since no state is recorded, each sample is (statistically)
45 /// independent of all others, assuming the `Rng` used has this
47 // FIXME maybe having this separate is overkill (the only reason is to
48 // take &self rather than &mut self)? or maybe this should be the
49 // trait called `Sample` and the other should be `DependentSample`.
50 pub trait IndependentSample<Support>: Sample<Support> {
51 /// Generate a random value.
52 fn ind_sample<R: Rng>(&self, &mut R) -> Support;
55 /// A wrapper for generating types that implement `Rand` via the
56 /// `Sample` & `IndependentSample` traits.
57 pub struct RandSample<Sup> {
58 _marker: PhantomData<Sup>,
61 impl<Sup> RandSample<Sup> {
62 pub fn new() -> RandSample<Sup> {
63 RandSample { _marker: PhantomData }
67 impl<Sup: Rand> Sample<Sup> for RandSample<Sup> {
68 fn sample<R: Rng>(&mut self, rng: &mut R) -> Sup {
73 impl<Sup: Rand> IndependentSample<Sup> for RandSample<Sup> {
74 fn ind_sample<R: Rng>(&self, rng: &mut R) -> Sup {
79 /// A value with a particular weight for use with `WeightedChoice`.
80 pub struct Weighted<T> {
81 /// The numerical weight of this item
83 /// The actual item which is being weighted
87 /// A distribution that selects from a finite collection of weighted items.
89 /// Each item has an associated weight that influences how likely it
90 /// is to be chosen: higher weight is more likely.
92 /// The `Clone` restriction is a limitation of the `Sample` and
93 /// `IndependentSample` traits. Note that `&T` is (cheaply) `Clone` for
94 /// all `T`, as is `usize`, so one can store references or indices into
96 pub struct WeightedChoice<'a, T: 'a> {
97 items: &'a mut [Weighted<T>],
98 weight_range: Range<usize>,
101 impl<'a, T: Clone> WeightedChoice<'a, T> {
102 /// Create a new `WeightedChoice`.
106 /// - the total weight is 0
107 /// - the total weight is larger than a `usize` can contain.
108 pub fn new(items: &'a mut [Weighted<T>]) -> WeightedChoice<'a, T> {
109 // strictly speaking, this is subsumed by the total weight == 0 case
110 assert!(!items.is_empty(),
111 "WeightedChoice::new called with no items");
113 let mut running_total = 0_usize;
115 // we convert the list from individual weights to cumulative
116 // weights so we can binary search. This *could* drop elements
117 // with weight == 0 as an optimisation.
118 for item in &mut *items {
119 running_total = match running_total.checked_add(item.weight) {
122 panic!("WeightedChoice::new called with a total weight larger than a usize \
127 item.weight = running_total;
129 assert!(running_total != 0,
130 "WeightedChoice::new called with a total weight of 0");
134 // we're likely to be generating numbers in this range
135 // relatively often, so might as well cache it
136 weight_range: Range::new(0, running_total),
141 impl<'a, T: Clone> Sample<T> for WeightedChoice<'a, T> {
142 fn sample<R: Rng>(&mut self, rng: &mut R) -> T {
147 impl<'a, T: Clone> IndependentSample<T> for WeightedChoice<'a, T> {
148 fn ind_sample<R: Rng>(&self, rng: &mut R) -> T {
149 // we want to find the first element that has cumulative
150 // weight > sample_weight, which we do by binary since the
151 // cumulative weights of self.items are sorted.
153 // choose a weight in [0, total_weight)
154 let sample_weight = self.weight_range.ind_sample(rng);
156 // short circuit when it's the first item
157 if sample_weight < self.items[0].weight {
158 return self.items[0].item.clone();
162 let mut modifier = self.items.len();
164 // now we know that every possibility has an element to the
165 // left, so we can just search for the last element that has
166 // cumulative weight <= sample_weight, then the next one will
167 // be "it". (Note that this greatest element will never be the
168 // last element of the vector, since sample_weight is chosen
169 // in [0, total_weight) and the cumulative weight of the last
170 // one is exactly the total weight.)
172 let i = idx + modifier / 2;
173 if self.items[i].weight <= sample_weight {
174 // we're small, so look to the right, but allow this
175 // exact element still.
177 // we need the `/ 2` to round up otherwise we'll drop
178 // the trailing elements when `modifier` is odd.
181 // otherwise we're too big, so go left. (i.e. do
186 return self.items[idx + 1].item.clone();
192 /// Sample a random number using the Ziggurat method (specifically the
193 /// ZIGNOR variant from Doornik 2005). Most of the arguments are
194 /// directly from the paper:
196 /// * `rng`: source of randomness
197 /// * `symmetric`: whether this is a symmetric distribution, or one-sided with P(x < 0) = 0.
198 /// * `X`: the $x_i$ abscissae.
199 /// * `F`: precomputed values of the PDF at the $x_i$, (i.e. $f(x_i)$)
200 /// * `F_DIFF`: precomputed values of $f(x_i) - f(x_{i+1})$
201 /// * `pdf`: the probability density function
202 /// * `zero_case`: manual sampling from the tail when we chose the
203 /// bottom box (i.e. i == 0)
204 // the perf improvement (25-50%) is definitely worth the extra code
205 // size from force-inlining.
207 fn ziggurat<R: Rng, P, Z>(rng: &mut R,
209 x_tab: ziggurat_tables::ZigTable,
210 f_tab: ziggurat_tables::ZigTable,
214 where P: FnMut(f64) -> f64,
215 Z: FnMut(&mut R, f64) -> f64
217 const SCALE: f64 = (1u64 << 53) as f64;
219 // reimplement the f64 generation as an optimisation suggested
220 // by the Doornik paper: we have a lot of precision-space
221 // (i.e. there are 11 bits of the 64 of a u64 to use after
222 // creating a f64), so we might as well reuse some to save
223 // generating a whole extra random number. (Seems to be 15%
226 // This unfortunately misses out on the benefits of direct
227 // floating point generation if an RNG like dSMFT is
228 // used. (That is, such RNGs create floats directly, highly
229 // efficiently and overload next_f32/f64, so by not calling it
230 // this may be slower than it would be otherwise.)
231 // FIXME: investigate/optimise for the above.
232 let bits: u64 = rng.gen();
233 let i = (bits & 0xff) as usize;
234 let f = (bits >> 11) as f64 / SCALE;
236 // u is either U(-1, 1) or U(0, 1) depending on if this is a
237 // symmetric distribution or not.
238 let u = if symmetric {
243 let x = u * x_tab[i];
245 let test_x = if symmetric {
251 // algebraically equivalent to |u| < x_tab[i+1]/x_tab[i] (or u < x_tab[i+1]/x_tab[i])
252 if test_x < x_tab[i + 1] {
256 return zero_case(rng, u);
258 // algebraically equivalent to f1 + DRanU()*(f0 - f1) < 1
259 if f_tab[i + 1] + (f_tab[i] - f_tab[i + 1]) * rng.gen::<f64>() < pdf(x) {
268 use super::{RandSample, WeightedChoice, Weighted, Sample, IndependentSample};
270 #[derive(PartialEq, Debug)]
271 struct ConstRand(usize);
272 impl Rand for ConstRand {
273 fn rand<R: Rng>(_: &mut R) -> ConstRand {
282 impl Rng for CountingRng {
283 fn next_u32(&mut self) -> u32 {
287 fn next_u64(&mut self) -> u64 {
288 self.next_u32() as u64
293 fn test_rand_sample() {
294 let mut rand_sample = RandSample::<ConstRand>::new();
296 assert_eq!(rand_sample.sample(&mut ::test::rng()), ConstRand(0));
297 assert_eq!(rand_sample.ind_sample(&mut ::test::rng()), ConstRand(0));
301 fn test_weighted_choice() {
302 // this makes assumptions about the internal implementation of
303 // WeightedChoice, specifically: it doesn't reorder the items,
304 // it doesn't do weird things to the RNG (so 0 maps to 0, 1 to
305 // 1, internally; modulo a modulo operation).
308 ($items:expr, $expected:expr) => {{
309 let mut items = $items;
310 let wc = WeightedChoice::new(&mut items);
311 let expected = $expected;
313 let mut rng = CountingRng { i: 0 };
315 for &val in &expected {
316 assert_eq!(wc.ind_sample(&mut rng), val)
321 t!(vec!(Weighted { weight: 1, item: 10 }),
325 t!(vec!(Weighted { weight: 0, item: 20 },
326 Weighted { weight: 2, item: 21 },
327 Weighted { weight: 0, item: 22 },
328 Weighted { weight: 1, item: 23 }),
332 t!(vec!(Weighted { weight: 4, item: 30 },
333 Weighted { weight: 3, item: 31 }),
334 [30, 30, 30, 30, 31, 31, 31]);
336 // check that we're binary searching
337 // correctly with some vectors of odd
339 t!(vec!(Weighted { weight: 1, item: 40 },
340 Weighted { weight: 1, item: 41 },
341 Weighted { weight: 1, item: 42 },
342 Weighted { weight: 1, item: 43 },
343 Weighted { weight: 1, item: 44 }),
344 [40, 41, 42, 43, 44]);
345 t!(vec!(Weighted { weight: 1, item: 50 },
346 Weighted { weight: 1, item: 51 },
347 Weighted { weight: 1, item: 52 },
348 Weighted { weight: 1, item: 53 },
349 Weighted { weight: 1, item: 54 },
350 Weighted { weight: 1, item: 55 },
351 Weighted { weight: 1, item: 56 }),
352 [50, 51, 52, 53, 54, 55, 56]);
357 fn test_weighted_choice_no_items() {
358 WeightedChoice::<isize>::new(&mut []);
363 fn test_weighted_choice_zero_weight() {
364 WeightedChoice::new(&mut [Weighted { weight: 0, item: 0 },
365 Weighted { weight: 0, item: 1 }]);
370 fn test_weighted_choice_weight_overflows() {
371 let x = (!0) as usize / 2; // x + x + 2 is the overflow
372 WeightedChoice::new(&mut [Weighted { weight: x, item: 0 },
373 Weighted { weight: 1, item: 1 },
374 Weighted { weight: x, item: 2 },
375 Weighted { weight: 1, item: 3 }]);