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.
23 use core::num::{Float, Int};
27 pub use self::range::Range;
28 pub use self::gamma::{Gamma, ChiSquared, FisherF, StudentT};
29 pub use self::normal::{Normal, LogNormal};
30 pub use self::exponential::Exp;
37 /// Types that can be used to create a random instance of `Support`.
38 pub trait Sample<Support> {
39 /// Generate a random value of `Support`, using `rng` as the
40 /// source of randomness.
41 fn sample<R: Rng>(&mut self, rng: &mut R) -> Support;
44 /// `Sample`s that do not require keeping track of state.
46 /// Since no state is recorded, each sample is (statistically)
47 /// independent of all others, assuming the `Rng` used has this
49 // FIXME maybe having this separate is overkill (the only reason is to
50 // take &self rather than &mut self)? or maybe this should be the
51 // trait called `Sample` and the other should be `DependentSample`.
52 pub trait IndependentSample<Support>: Sample<Support> {
53 /// Generate a random value.
54 fn ind_sample<R: Rng>(&self, &mut R) -> Support;
57 /// A wrapper for generating types that implement `Rand` via the
58 /// `Sample` & `IndependentSample` traits.
59 pub struct RandSample<Sup>;
61 impl<Sup: Rand> Sample<Sup> for RandSample<Sup> {
62 fn sample<R: Rng>(&mut self, rng: &mut R) -> Sup { self.ind_sample(rng) }
65 impl<Sup: Rand> IndependentSample<Sup> for RandSample<Sup> {
66 fn ind_sample<R: Rng>(&self, rng: &mut R) -> Sup {
71 /// A value with a particular weight for use with `WeightedChoice`.
72 pub struct Weighted<T> {
73 /// The numerical weight of this item
75 /// The actual item which is being weighted
79 /// A distribution that selects from a finite collection of weighted items.
81 /// Each item has an associated weight that influences how likely it
82 /// is to be chosen: higher weight is more likely.
84 /// The `Clone` restriction is a limitation of the `Sample` and
85 /// `IndependentSample` traits. Note that `&T` is (cheaply) `Clone` for
86 /// all `T`, as is `uint`, so one can store references or indices into
93 /// use std::rand::distributions::{Weighted, WeightedChoice, IndependentSample};
95 /// let mut items = vec!(Weighted { weight: 2, item: 'a' },
96 /// Weighted { weight: 4, item: 'b' },
97 /// Weighted { weight: 1, item: 'c' });
98 /// let wc = WeightedChoice::new(items.as_mut_slice());
99 /// let mut rng = rand::thread_rng();
100 /// for _ in range(0u, 16) {
101 /// // on average prints 'a' 4 times, 'b' 8 and 'c' twice.
102 /// println!("{}", wc.ind_sample(&mut rng));
105 pub struct WeightedChoice<'a, T:'a> {
106 items: &'a mut [Weighted<T>],
107 weight_range: Range<uint>
110 impl<'a, T: Clone> WeightedChoice<'a, T> {
111 /// Create a new `WeightedChoice`.
115 /// - the total weight is 0
116 /// - the total weight is larger than a `uint` can contain.
117 pub fn new(items: &'a mut [Weighted<T>]) -> WeightedChoice<'a, T> {
118 // strictly speaking, this is subsumed by the total weight == 0 case
119 assert!(!items.is_empty(), "WeightedChoice::new called with no items");
121 let mut running_total = 0u;
123 // we convert the list from individual weights to cumulative
124 // weights so we can binary search. This *could* drop elements
125 // with weight == 0 as an optimisation.
126 for item in items.iter_mut() {
127 running_total = match running_total.checked_add(item.weight) {
129 None => panic!("WeightedChoice::new called with a total weight \
130 larger than a uint can contain")
133 item.weight = running_total;
135 assert!(running_total != 0, "WeightedChoice::new called with a total weight of 0");
139 // we're likely to be generating numbers in this range
140 // relatively often, so might as well cache it
141 weight_range: Range::new(0, running_total)
146 impl<'a, T: Clone> Sample<T> for WeightedChoice<'a, T> {
147 fn sample<R: Rng>(&mut self, rng: &mut R) -> T { self.ind_sample(rng) }
150 impl<'a, T: Clone> IndependentSample<T> for WeightedChoice<'a, T> {
151 fn ind_sample<R: Rng>(&self, rng: &mut R) -> T {
152 // we want to find the first element that has cumulative
153 // weight > sample_weight, which we do by binary since the
154 // cumulative weights of self.items are sorted.
156 // choose a weight in [0, total_weight)
157 let sample_weight = self.weight_range.ind_sample(rng);
159 // short circuit when it's the first item
160 if sample_weight < self.items[0].weight {
161 return self.items[0].item.clone();
165 let mut modifier = self.items.len();
167 // now we know that every possibility has an element to the
168 // left, so we can just search for the last element that has
169 // cumulative weight <= sample_weight, then the next one will
170 // be "it". (Note that this greatest element will never be the
171 // last element of the vector, since sample_weight is chosen
172 // in [0, total_weight) and the cumulative weight of the last
173 // one is exactly the total weight.)
175 let i = idx + modifier / 2;
176 if self.items[i].weight <= sample_weight {
177 // we're small, so look to the right, but allow this
178 // exact element still.
180 // we need the `/ 2` to round up otherwise we'll drop
181 // the trailing elements when `modifier` is odd.
184 // otherwise we're too big, so go left. (i.e. do
189 return self.items[idx + 1].item.clone();
195 /// Sample a random number using the Ziggurat method (specifically the
196 /// ZIGNOR variant from Doornik 2005). Most of the arguments are
197 /// directly from the paper:
199 /// * `rng`: source of randomness
200 /// * `symmetric`: whether this is a symmetric distribution, or one-sided with P(x < 0) = 0.
201 /// * `X`: the $x_i$ abscissae.
202 /// * `F`: precomputed values of the PDF at the $x_i$, (i.e. $f(x_i)$)
203 /// * `F_DIFF`: precomputed values of $f(x_i) - f(x_{i+1})$
204 /// * `pdf`: the probability density function
205 /// * `zero_case`: manual sampling from the tail when we chose the
206 /// bottom box (i.e. i == 0)
208 // the perf improvement (25-50%) is definitely worth the extra code
209 // size from force-inlining.
211 fn ziggurat<R: Rng, P, Z>(
214 x_tab: ziggurat_tables::ZigTable,
215 f_tab: ziggurat_tables::ZigTable,
218 -> f64 where P: FnMut(f64) -> f64, Z: FnMut(&mut R, f64) -> f64 {
219 static SCALE: f64 = (1u64 << 53) as f64;
221 // reimplement the f64 generation as an optimisation suggested
222 // by the Doornik paper: we have a lot of precision-space
223 // (i.e. there are 11 bits of the 64 of a u64 to use after
224 // creating a f64), so we might as well reuse some to save
225 // generating a whole extra random number. (Seems to be 15%
228 // This unfortunately misses out on the benefits of direct
229 // floating point generation if an RNG like dSMFT is
230 // used. (That is, such RNGs create floats directly, highly
231 // efficiently and overload next_f32/f64, so by not calling it
232 // this may be slower than it would be otherwise.)
233 // FIXME: investigate/optimise for the above.
234 let bits: u64 = rng.gen();
235 let i = (bits & 0xff) as uint;
236 let f = (bits >> 11) as f64 / SCALE;
238 // u is either U(-1, 1) or U(0, 1) depending on if this is a
239 // symmetric distribution or not.
240 let u = if symmetric {2.0 * f - 1.0} else {f};
241 let x = u * x_tab[i];
243 let test_x = if symmetric { x.abs() } else {x};
245 // algebraically equivalent to |u| < x_tab[i+1]/x_tab[i] (or u < x_tab[i+1]/x_tab[i])
246 if test_x < x_tab[i + 1] {
250 return zero_case(rng, u);
252 // algebraically equivalent to f1 + DRanU()*(f0 - f1) < 1
253 if f_tab[i + 1] + (f_tab[i] - f_tab[i + 1]) * rng.gen() < pdf(x) {
261 use std::prelude::v1::*;
264 use super::{RandSample, WeightedChoice, Weighted, Sample, IndependentSample};
266 #[derive(PartialEq, Show)]
267 struct ConstRand(uint);
268 impl Rand for ConstRand {
269 fn rand<R: Rng>(_: &mut R) -> ConstRand {
275 struct CountingRng { i: u32 }
276 impl Rng for CountingRng {
277 fn next_u32(&mut self) -> u32 {
281 fn next_u64(&mut self) -> u64 {
282 self.next_u32() as u64
287 fn test_rand_sample() {
288 let mut rand_sample = RandSample::<ConstRand>;
290 assert_eq!(rand_sample.sample(&mut ::test::rng()), ConstRand(0));
291 assert_eq!(rand_sample.ind_sample(&mut ::test::rng()), ConstRand(0));
294 fn test_weighted_choice() {
295 // this makes assumptions about the internal implementation of
296 // WeightedChoice, specifically: it doesn't reorder the items,
297 // it doesn't do weird things to the RNG (so 0 maps to 0, 1 to
298 // 1, internally; modulo a modulo operation).
301 ($items:expr, $expected:expr) => {{
302 let mut items = $items;
303 let wc = WeightedChoice::new(items.as_mut_slice());
304 let expected = $expected;
306 let mut rng = CountingRng { i: 0 };
308 for &val in expected.iter() {
309 assert_eq!(wc.ind_sample(&mut rng), val)
314 t!(vec!(Weighted { weight: 1, item: 10i}), [10]);
317 t!(vec!(Weighted { weight: 0, item: 20i},
318 Weighted { weight: 2, item: 21i},
319 Weighted { weight: 0, item: 22i},
320 Weighted { weight: 1, item: 23i}),
324 t!(vec!(Weighted { weight: 4, item: 30i},
325 Weighted { weight: 3, item: 31i}),
326 [30,30,30,30, 31,31,31]);
328 // check that we're binary searching
329 // correctly with some vectors of odd
331 t!(vec!(Weighted { weight: 1, item: 40i},
332 Weighted { weight: 1, item: 41i},
333 Weighted { weight: 1, item: 42i},
334 Weighted { weight: 1, item: 43i},
335 Weighted { weight: 1, item: 44i}),
336 [40, 41, 42, 43, 44]);
337 t!(vec!(Weighted { weight: 1, item: 50i},
338 Weighted { weight: 1, item: 51i},
339 Weighted { weight: 1, item: 52i},
340 Weighted { weight: 1, item: 53i},
341 Weighted { weight: 1, item: 54i},
342 Weighted { weight: 1, item: 55i},
343 Weighted { weight: 1, item: 56i}),
344 [50, 51, 52, 53, 54, 55, 56]);
347 #[test] #[should_fail]
348 fn test_weighted_choice_no_items() {
349 WeightedChoice::<int>::new(&mut []);
351 #[test] #[should_fail]
352 fn test_weighted_choice_zero_weight() {
353 WeightedChoice::new(&mut [Weighted { weight: 0, item: 0i},
354 Weighted { weight: 0, item: 1i}]);
356 #[test] #[should_fail]
357 fn test_weighted_choice_weight_overflows() {
358 let x = (-1) as uint / 2; // x + x + 2 is the overflow
359 WeightedChoice::new(&mut [Weighted { weight: x, item: 0i },
360 Weighted { weight: 1, item: 1i },
361 Weighted { weight: x, item: 2i },
362 Weighted { weight: 1, item: 3i }]);