src/librand/distributions/mod.rs

   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.
   4 //
   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.
  10
  11 //! Sampling from random distributions.
  12 //!
  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.
  19
  20 use core::prelude::*;
  21 use core::num::Float;
  22 use core::marker::PhantomData;
  23
  24 use {Rng, Rand};
  25
  26 pub use self::range::Range;
  27 pub use self::gamma::{Gamma, ChiSquared, FisherF, StudentT};
  28 pub use self::normal::{Normal, LogNormal};
  29 pub use self::exponential::Exp;
  30
  31 pub mod range;
  32 pub mod gamma;
  33 pub mod normal;
  34 pub mod exponential;
  35
  36 /// Types that can be used to create a random instance of `Support`.
  37 pub trait Sample<Support> {
  38     /// Generate a random value of `Support`, using `rng` as the
  39     /// source of randomness.
  40     fn sample<R: Rng>(&mut self, rng: &mut R) -> Support;
  41 }
  42
  43 /// `Sample`s that do not require keeping track of state.
  44 ///
  45 /// Since no state is recorded, each sample is (statistically)
  46 /// independent of all others, assuming the `Rng` used has this
  47 /// property.
  48 // FIXME maybe having this separate is overkill (the only reason is to
  49 // take &self rather than &mut self)? or maybe this should be the
  50 // trait called `Sample` and the other should be `DependentSample`.
  51 pub trait IndependentSample<Support>: Sample<Support> {
  52     /// Generate a random value.
  53     fn ind_sample<R: Rng>(&self, &mut R) -> Support;
  54 }
  55
  56 /// A wrapper for generating types that implement `Rand` via the
  57 /// `Sample` & `IndependentSample` traits.
  58 pub struct RandSample<Sup> { _marker: PhantomData<Sup> }
  59
  60 impl<Sup> RandSample<Sup> {
  61     pub fn new() -> RandSample<Sup> {
  62         RandSample { _marker: PhantomData }
  63     }
  64 }
  65
  66 impl<Sup: Rand> Sample<Sup> for RandSample<Sup> {
  67     fn sample<R: Rng>(&mut self, rng: &mut R) -> Sup { self.ind_sample(rng) }
  68 }
  69
  70 impl<Sup: Rand> IndependentSample<Sup> for RandSample<Sup> {
  71     fn ind_sample<R: Rng>(&self, rng: &mut R) -> Sup {
  72         rng.gen()
  73     }
  74 }
  75
  76 /// A value with a particular weight for use with `WeightedChoice`.
  77 pub struct Weighted<T> {
  78     /// The numerical weight of this item
  79     pub weight: usize,
  80     /// The actual item which is being weighted
  81     pub item: T,
  82 }
  83
  84 /// A distribution that selects from a finite collection of weighted items.
  85 ///
  86 /// Each item has an associated weight that influences how likely it
  87 /// is to be chosen: higher weight is more likely.
  88 ///
  89 /// The `Clone` restriction is a limitation of the `Sample` and
  90 /// `IndependentSample` traits. Note that `&T` is (cheaply) `Clone` for
  91 /// all `T`, as is `usize`, so one can store references or indices into
  92 /// another vector.
  93 pub struct WeightedChoice<'a, T:'a> {
  94     items: &'a mut [Weighted<T>],
  95     weight_range: Range<usize>
  96 }
  97
  98 impl<'a, T: Clone> WeightedChoice<'a, T> {
  99     /// Create a new `WeightedChoice`.
 100     ///
 101     /// Panics if:
 102     /// - `v` is empty
 103     /// - the total weight is 0
 104     /// - the total weight is larger than a `usize` can contain.
 105     pub fn new(items: &'a mut [Weighted<T>]) -> WeightedChoice<'a, T> {
 106         // strictly speaking, this is subsumed by the total weight == 0 case
 107         assert!(!items.is_empty(), "WeightedChoice::new called with no items");
 108
 109         let mut running_total = 0_usize;
 110
 111         // we convert the list from individual weights to cumulative
 112         // weights so we can binary search. This *could* drop elements
 113         // with weight == 0 as an optimisation.
 114         for item in &mut *items {
 115             running_total = match running_total.checked_add(item.weight) {
 116                 Some(n) => n,
 117                 None => panic!("WeightedChoice::new called with a total weight \
 118                                larger than a usize can contain")
 119             };
 120
 121             item.weight = running_total;
 122         }
 123         assert!(running_total != 0, "WeightedChoice::new called with a total weight of 0");
 124
 125         WeightedChoice {
 126             items: items,
 127             // we're likely to be generating numbers in this range
 128             // relatively often, so might as well cache it
 129             weight_range: Range::new(0, running_total)
 130         }
 131     }
 132 }
 133
 134 impl<'a, T: Clone> Sample<T> for WeightedChoice<'a, T> {
 135     fn sample<R: Rng>(&mut self, rng: &mut R) -> T { self.ind_sample(rng) }
 136 }
 137
 138 impl<'a, T: Clone> IndependentSample<T> for WeightedChoice<'a, T> {
 139     fn ind_sample<R: Rng>(&self, rng: &mut R) -> T {
 140         // we want to find the first element that has cumulative
 141         // weight > sample_weight, which we do by binary since the
 142         // cumulative weights of self.items are sorted.
 143
 144         // choose a weight in [0, total_weight)
 145         let sample_weight = self.weight_range.ind_sample(rng);
 146
 147         // short circuit when it's the first item
 148         if sample_weight < self.items[0].weight {
 149             return self.items[0].item.clone();
 150         }
 151
 152         let mut idx = 0;
 153         let mut modifier = self.items.len();
 154
 155         // now we know that every possibility has an element to the
 156         // left, so we can just search for the last element that has
 157         // cumulative weight <= sample_weight, then the next one will
 158         // be "it". (Note that this greatest element will never be the
 159         // last element of the vector, since sample_weight is chosen
 160         // in [0, total_weight) and the cumulative weight of the last
 161         // one is exactly the total weight.)
 162         while modifier > 1 {
 163             let i = idx + modifier / 2;
 164             if self.items[i].weight <= sample_weight {
 165                 // we're small, so look to the right, but allow this
 166                 // exact element still.
 167                 idx = i;
 168                 // we need the `/ 2` to round up otherwise we'll drop
 169                 // the trailing elements when `modifier` is odd.
 170                 modifier += 1;
 171             } else {
 172                 // otherwise we're too big, so go left. (i.e. do
 173                 // nothing)
 174             }
 175             modifier /= 2;
 176         }
 177         return self.items[idx + 1].item.clone();
 178     }
 179 }
 180
 181 mod ziggurat_tables;
 182
 183 /// Sample a random number using the Ziggurat method (specifically the
 184 /// ZIGNOR variant from Doornik 2005). Most of the arguments are
 185 /// directly from the paper:
 186 ///
 187 /// * `rng`: source of randomness
 188 /// * `symmetric`: whether this is a symmetric distribution, or one-sided with P(x < 0) = 0.
 189 /// * `X`: the $x_i$ abscissae.
 190 /// * `F`: precomputed values of the PDF at the $x_i$, (i.e. $f(x_i)$)
 191 /// * `F_DIFF`: precomputed values of $f(x_i) - f(x_{i+1})$
 192 /// * `pdf`: the probability density function
 193 /// * `zero_case`: manual sampling from the tail when we chose the
 194 ///    bottom box (i.e. i == 0)
 195
 196 // the perf improvement (25-50%) is definitely worth the extra code
 197 // size from force-inlining.
 198 #[inline(always)]
 199 fn ziggurat<R: Rng, P, Z>(
 200             rng: &mut R,
 201             symmetric: bool,
 202             x_tab: ziggurat_tables::ZigTable,
 203             f_tab: ziggurat_tables::ZigTable,
 204             mut pdf: P,
 205             mut zero_case: Z)
 206             -> f64 where P: FnMut(f64) -> f64, Z: FnMut(&mut R, f64) -> f64 {
 207     const SCALE: f64 = (1u64 << 53) as f64;
 208     loop {
 209         // reimplement the f64 generation as an optimisation suggested
 210         // by the Doornik paper: we have a lot of precision-space
 211         // (i.e. there are 11 bits of the 64 of a u64 to use after
 212         // creating a f64), so we might as well reuse some to save
 213         // generating a whole extra random number. (Seems to be 15%
 214         // faster.)
 215         //
 216         // This unfortunately misses out on the benefits of direct
 217         // floating point generation if an RNG like dSMFT is
 218         // used. (That is, such RNGs create floats directly, highly
 219         // efficiently and overload next_f32/f64, so by not calling it
 220         // this may be slower than it would be otherwise.)
 221         // FIXME: investigate/optimise for the above.
 222         let bits: u64 = rng.gen();
 223         let i = (bits & 0xff) as usize;
 224         let f = (bits >> 11) as f64 / SCALE;
 225
 226         // u is either U(-1, 1) or U(0, 1) depending on if this is a
 227         // symmetric distribution or not.
 228         let u = if symmetric {2.0 * f - 1.0} else {f};
 229         let x = u * x_tab[i];
 230
 231         let test_x = if symmetric { x.abs() } else {x};
 232
 233         // algebraically equivalent to |u| < x_tab[i+1]/x_tab[i] (or u < x_tab[i+1]/x_tab[i])
 234         if test_x < x_tab[i + 1] {
 235             return x;
 236         }
 237         if i == 0 {
 238             return zero_case(rng, u);
 239         }
 240         // algebraically equivalent to f1 + DRanU()*(f0 - f1) < 1
 241         if f_tab[i + 1] + (f_tab[i] - f_tab[i + 1]) * rng.gen::<f64>() < pdf(x) {
 242             return x;
 243         }
 244     }
 245 }
 246
 247 #[cfg(test)]
 248 mod tests {
 249     use std::prelude::v1::*;
 250
 251     use {Rng, Rand};
 252     use super::{RandSample, WeightedChoice, Weighted, Sample, IndependentSample};
 253
 254     #[derive(PartialEq, Debug)]
 255     struct ConstRand(usize);
 256     impl Rand for ConstRand {
 257         fn rand<R: Rng>(_: &mut R) -> ConstRand {
 258             ConstRand(0)
 259         }
 260     }
 261
 262     // 0, 1, 2, 3, ...
 263     struct CountingRng { i: u32 }
 264     impl Rng for CountingRng {
 265         fn next_u32(&mut self) -> u32 {
 266             self.i += 1;
 267             self.i - 1
 268         }
 269         fn next_u64(&mut self) -> u64 {
 270             self.next_u32() as u64
 271         }
 272     }
 273
 274     #[test]
 275     fn test_rand_sample() {
 276         let mut rand_sample = RandSample::<ConstRand>::new();
 277
 278         assert_eq!(rand_sample.sample(&mut ::test::rng()), ConstRand(0));
 279         assert_eq!(rand_sample.ind_sample(&mut ::test::rng()), ConstRand(0));
 280     }
 281     #[test]
 282     fn test_weighted_choice() {
 283         // this makes assumptions about the internal implementation of
 284         // WeightedChoice, specifically: it doesn't reorder the items,
 285         // it doesn't do weird things to the RNG (so 0 maps to 0, 1 to
 286         // 1, internally; modulo a modulo operation).
 287
 288         macro_rules! t {
 289             ($items:expr, $expected:expr) => {{
 290                 let mut items = $items;
 291                 let wc = WeightedChoice::new(&mut items);
 292                 let expected = $expected;
 293
 294                 let mut rng = CountingRng { i: 0 };
 295
 296                 for &val in &expected {
 297                     assert_eq!(wc.ind_sample(&mut rng), val)
 298                 }
 299             }}
 300         }
 301
 302         t!(vec!(Weighted { weight: 1, item: 10}), [10]);
 303
 304         // skip some
 305         t!(vec!(Weighted { weight: 0, item: 20},
 306                 Weighted { weight: 2, item: 21},
 307                 Weighted { weight: 0, item: 22},
 308                 Weighted { weight: 1, item: 23}),
 309            [21,21, 23]);
 310
 311         // different weights
 312         t!(vec!(Weighted { weight: 4, item: 30},
 313                 Weighted { weight: 3, item: 31}),
 314            [30,30,30,30, 31,31,31]);
 315
 316         // check that we're binary searching
 317         // correctly with some vectors of odd
 318         // length.
 319         t!(vec!(Weighted { weight: 1, item: 40},
 320                 Weighted { weight: 1, item: 41},
 321                 Weighted { weight: 1, item: 42},
 322                 Weighted { weight: 1, item: 43},
 323                 Weighted { weight: 1, item: 44}),
 324            [40, 41, 42, 43, 44]);
 325         t!(vec!(Weighted { weight: 1, item: 50},
 326                 Weighted { weight: 1, item: 51},
 327                 Weighted { weight: 1, item: 52},
 328                 Weighted { weight: 1, item: 53},
 329                 Weighted { weight: 1, item: 54},
 330                 Weighted { weight: 1, item: 55},
 331                 Weighted { weight: 1, item: 56}),
 332            [50, 51, 52, 53, 54, 55, 56]);
 333     }
 334
 335     #[test] #[should_panic]
 336     fn test_weighted_choice_no_items() {
 337         WeightedChoice::<isize>::new(&mut []);
 338     }
 339     #[test] #[should_panic]
 340     fn test_weighted_choice_zero_weight() {
 341         WeightedChoice::new(&mut [Weighted { weight: 0, item: 0},
 342                                   Weighted { weight: 0, item: 1}]);
 343     }
 344     #[test] #[should_panic]
 345     fn test_weighted_choice_weight_overflows() {
 346         let x = (!0) as usize / 2; // x + x + 2 is the overflow
 347         WeightedChoice::new(&mut [Weighted { weight: x, item: 0 },
 348                                   Weighted { weight: 1, item: 1 },
 349                                   Weighted { weight: x, item: 2 },
 350                                   Weighted { weight: 1, item: 3 }]);
 351     }
 352 }