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// 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.
//! Sampling from random distributions.
//!
//! This is a generalization of `Rand` to allow parameters to control the
//! exact properties of the generated values, e.g. the mean and standard
//! deviation of a normal distribution. The `Sample` trait is the most
//! general, and allows for generating values that change some state
//! internally. The `IndependentSample` trait is for generating values
//! that do not need to record state.
use std::marker;
use {Rng, Rand};
pub use self::range::Range;
pub use self::gamma::{Gamma, ChiSquared, FisherF, StudentT};
pub use self::normal::{Normal, LogNormal};
pub use self::exponential::Exp;
pub mod range;
pub mod gamma;
pub mod normal;
pub mod exponential;
/// Types that can be used to create a random instance of `Support`.
pub trait Sample<Support> {
/// Generate a random value of `Support`, using `rng` as the
/// source of randomness.
fn sample<R: Rng>(&mut self, rng: &mut R) -> Support;
}
/// `Sample`s that do not require keeping track of state.
///
/// Since no state is recorded, each sample is (statistically)
/// independent of all others, assuming the `Rng` used has this
/// property.
// FIXME maybe having this separate is overkill (the only reason is to
// take &self rather than &mut self)? or maybe this should be the
// trait called `Sample` and the other should be `DependentSample`.
pub trait IndependentSample<Support>: Sample<Support> {
/// Generate a random value.
fn ind_sample<R: Rng>(&self, &mut R) -> Support;
}
/// A wrapper for generating types that implement `Rand` via the
/// `Sample` & `IndependentSample` traits.
#[derive(Debug)]
pub struct RandSample<Sup> {
_marker: marker::PhantomData<fn() -> Sup>,
}
impl<Sup> Copy for RandSample<Sup> {}
impl<Sup> Clone for RandSample<Sup> {
fn clone(&self) -> Self { *self }
}
impl<Sup: Rand> Sample<Sup> for RandSample<Sup> {
fn sample<R: Rng>(&mut self, rng: &mut R) -> Sup { self.ind_sample(rng) }
}
impl<Sup: Rand> IndependentSample<Sup> for RandSample<Sup> {
fn ind_sample<R: Rng>(&self, rng: &mut R) -> Sup {
rng.gen()
}
}
impl<Sup> RandSample<Sup> {
pub fn new() -> RandSample<Sup> {
RandSample { _marker: marker::PhantomData }
}
}
/// A value with a particular weight for use with `WeightedChoice`.
#[derive(Copy, Clone, Debug)]
pub struct Weighted<T> {
/// The numerical weight of this item
pub weight: u32,
/// The actual item which is being weighted
pub item: T,
}
/// A distribution that selects from a finite collection of weighted items.
///
/// Each item has an associated weight that influences how likely it
/// is to be chosen: higher weight is more likely.
///
/// The `Clone` restriction is a limitation of the `Sample` and
/// `IndependentSample` traits. Note that `&T` is (cheaply) `Clone` for
/// all `T`, as is `u32`, so one can store references or indices into
/// another vector.
///
/// # Example
///
/// ```rust
/// use rand::distributions::{Weighted, WeightedChoice, IndependentSample};
///
/// let mut items = vec!(Weighted { weight: 2, item: 'a' },
/// Weighted { weight: 4, item: 'b' },
/// Weighted { weight: 1, item: 'c' });
/// let wc = WeightedChoice::new(&mut items);
/// let mut rng = rand::thread_rng();
/// for _ in 0..16 {
/// // on average prints 'a' 4 times, 'b' 8 and 'c' twice.
/// println!("{}", wc.ind_sample(&mut rng));
/// }
/// ```
#[derive(Debug)]
pub struct WeightedChoice<'a, T:'a> {
items: &'a mut [Weighted<T>],
weight_range: Range<u32>
}
impl<'a, T: Clone> WeightedChoice<'a, T> {
/// Create a new `WeightedChoice`.
///
/// Panics if:
///
/// - `v` is empty
/// - the total weight is 0
/// - the total weight is larger than a `u32` can contain.
pub fn new(items: &'a mut [Weighted<T>]) -> WeightedChoice<'a, T> {
// strictly speaking, this is subsumed by the total weight == 0 case
assert!(!items.is_empty(), "WeightedChoice::new called with no items");
let mut running_total: u32 = 0;
// we convert the list from individual weights to cumulative
// weights so we can binary search. This *could* drop elements
// with weight == 0 as an optimisation.
for item in items.iter_mut() {
running_total = match running_total.checked_add(item.weight) {
Some(n) => n,
None => panic!("WeightedChoice::new called with a total weight \
larger than a u32 can contain")
};
item.weight = running_total;
}
assert!(running_total != 0, "WeightedChoice::new called with a total weight of 0");
WeightedChoice {
items: items,
// we're likely to be generating numbers in this range
// relatively often, so might as well cache it
weight_range: Range::new(0, running_total)
}
}
}
impl<'a, T: Clone> Sample<T> for WeightedChoice<'a, T> {
fn sample<R: Rng>(&mut self, rng: &mut R) -> T { self.ind_sample(rng) }
}
impl<'a, T: Clone> IndependentSample<T> for WeightedChoice<'a, T> {
fn ind_sample<R: Rng>(&self, rng: &mut R) -> T {
// we want to find the first element that has cumulative
// weight > sample_weight, which we do by binary since the
// cumulative weights of self.items are sorted.
// choose a weight in [0, total_weight)
let sample_weight = self.weight_range.ind_sample(rng);
// short circuit when it's the first item
if sample_weight < self.items[0].weight {
return self.items[0].item.clone();
}
let mut idx = 0;
let mut modifier = self.items.len();
// now we know that every possibility has an element to the
// left, so we can just search for the last element that has
// cumulative weight <= sample_weight, then the next one will
// be "it". (Note that this greatest element will never be the
// last element of the vector, since sample_weight is chosen
// in [0, total_weight) and the cumulative weight of the last
// one is exactly the total weight.)
while modifier > 1 {
let i = idx + modifier / 2;
if self.items[i].weight <= sample_weight {
// we're small, so look to the right, but allow this
// exact element still.
idx = i;
// we need the `/ 2` to round up otherwise we'll drop
// the trailing elements when `modifier` is odd.
modifier += 1;
} else {
// otherwise we're too big, so go left. (i.e. do
// nothing)
}
modifier /= 2;
}
return self.items[idx + 1].item.clone();
}
}
mod ziggurat_tables;
/// Sample a random number using the Ziggurat method (specifically the
/// ZIGNOR variant from Doornik 2005). Most of the arguments are
/// directly from the paper:
///
/// * `rng`: source of randomness
/// * `symmetric`: whether this is a symmetric distribution, or one-sided with P(x < 0) = 0.
/// * `X`: the $x_i$ abscissae.
/// * `F`: precomputed values of the PDF at the $x_i$, (i.e. $f(x_i)$)
/// * `F_DIFF`: precomputed values of $f(x_i) - f(x_{i+1})$
/// * `pdf`: the probability density function
/// * `zero_case`: manual sampling from the tail when we chose the
/// bottom box (i.e. i == 0)
// the perf improvement (25-50%) is definitely worth the extra code
// size from force-inlining.
#[inline(always)]
fn ziggurat<R: Rng, P, Z>(
rng: &mut R,
symmetric: bool,
x_tab: ziggurat_tables::ZigTable,
f_tab: ziggurat_tables::ZigTable,
mut pdf: P,
mut zero_case: Z)
-> f64 where P: FnMut(f64) -> f64, Z: FnMut(&mut R, f64) -> f64 {
const SCALE: f64 = (1u64 << 53) as f64;
loop {
// reimplement the f64 generation as an optimisation suggested
// by the Doornik paper: we have a lot of precision-space
// (i.e. there are 11 bits of the 64 of a u64 to use after
// creating a f64), so we might as well reuse some to save
// generating a whole extra random number. (Seems to be 15%
// faster.)
//
// This unfortunately misses out on the benefits of direct
// floating point generation if an RNG like dSMFT is
// used. (That is, such RNGs create floats directly, highly
// efficiently and overload next_f32/f64, so by not calling it
// this may be slower than it would be otherwise.)
// FIXME: investigate/optimise for the above.
let bits: u64 = rng.gen();
let i = (bits & 0xff) as usize;
let f = (bits >> 11) as f64 / SCALE;
// u is either U(-1, 1) or U(0, 1) depending on if this is a
// symmetric distribution or not.
let u = if symmetric {2.0 * f - 1.0} else {f};
let x = u * x_tab[i];
let test_x = if symmetric { x.abs() } else {x};
// algebraically equivalent to |u| < x_tab[i+1]/x_tab[i] (or u < x_tab[i+1]/x_tab[i])
if test_x < x_tab[i + 1] {
return x;
}
if i == 0 {
return zero_case(rng, u);
}
// algebraically equivalent to f1 + DRanU()*(f0 - f1) < 1
if f_tab[i + 1] + (f_tab[i] - f_tab[i + 1]) * rng.gen::<f64>() < pdf(x) {
return x;
}
}
}
#[cfg(test)]
mod tests {
use {Rng, Rand};
use super::{RandSample, WeightedChoice, Weighted, Sample, IndependentSample};
#[derive(PartialEq, Debug)]
struct ConstRand(usize);
impl Rand for ConstRand {
fn rand<R: Rng>(_: &mut R) -> ConstRand {
ConstRand(0)
}
}
// 0, 1, 2, 3, ...
struct CountingRng { i: u32 }
impl Rng for CountingRng {
fn next_u32(&mut self) -> u32 {
self.i += 1;
self.i - 1
}
fn next_u64(&mut self) -> u64 {
self.next_u32() as u64
}
}
#[test]
fn test_rand_sample() {
let mut rand_sample = RandSample::<ConstRand>::new();
assert_eq!(rand_sample.sample(&mut ::test::rng()), ConstRand(0));
assert_eq!(rand_sample.ind_sample(&mut ::test::rng()), ConstRand(0));
}
#[test]
fn test_weighted_choice() {
// this makes assumptions about the internal implementation of
// WeightedChoice, specifically: it doesn't reorder the items,
// it doesn't do weird things to the RNG (so 0 maps to 0, 1 to
// 1, internally; modulo a modulo operation).
macro_rules! t {
($items:expr, $expected:expr) => {{
let mut items = $items;
let wc = WeightedChoice::new(&mut items);
let expected = $expected;
let mut rng = CountingRng { i: 0 };
for &val in expected.iter() {
assert_eq!(wc.ind_sample(&mut rng), val)
}
}}
}
t!(vec!(Weighted { weight: 1, item: 10}), [10]);
// skip some
t!(vec!(Weighted { weight: 0, item: 20},
Weighted { weight: 2, item: 21},
Weighted { weight: 0, item: 22},
Weighted { weight: 1, item: 23}),
[21,21, 23]);
// different weights
t!(vec!(Weighted { weight: 4, item: 30},
Weighted { weight: 3, item: 31}),
[30,30,30,30, 31,31,31]);
// check that we're binary searching
// correctly with some vectors of odd
// length.
t!(vec!(Weighted { weight: 1, item: 40},
Weighted { weight: 1, item: 41},
Weighted { weight: 1, item: 42},
Weighted { weight: 1, item: 43},
Weighted { weight: 1, item: 44}),
[40, 41, 42, 43, 44]);
t!(vec!(Weighted { weight: 1, item: 50},
Weighted { weight: 1, item: 51},
Weighted { weight: 1, item: 52},
Weighted { weight: 1, item: 53},
Weighted { weight: 1, item: 54},
Weighted { weight: 1, item: 55},
Weighted { weight: 1, item: 56}),
[50, 51, 52, 53, 54, 55, 56]);
}
#[test]
fn test_weighted_clone_initialization() {
let initial : Weighted<u32> = Weighted {weight: 1, item: 1};
let clone = initial.clone();
assert_eq!(initial.weight, clone.weight);
assert_eq!(initial.item, clone.item);
}
#[test] #[should_panic]
fn test_weighted_clone_change_weight() {
let initial : Weighted<u32> = Weighted {weight: 1, item: 1};
let mut clone = initial.clone();
clone.weight = 5;
assert_eq!(initial.weight, clone.weight);
}
#[test] #[should_panic]
fn test_weighted_clone_change_item() {
let initial : Weighted<u32> = Weighted {weight: 1, item: 1};
let mut clone = initial.clone();
clone.item = 5;
assert_eq!(initial.item, clone.item);
}
#[test] #[should_panic]
fn test_weighted_choice_no_items() {
WeightedChoice::<isize>::new(&mut []);
}
#[test] #[should_panic]
fn test_weighted_choice_zero_weight() {
WeightedChoice::new(&mut [Weighted { weight: 0, item: 0},
Weighted { weight: 0, item: 1}]);
}
#[test] #[should_panic]
fn test_weighted_choice_weight_overflows() {
let x = ::std::u32::MAX / 2; // x + x + 2 is the overflow
WeightedChoice::new(&mut [Weighted { weight: x, item: 0 },
Weighted { weight: 1, item: 1 },
Weighted { weight: x, item: 2 },
Weighted { weight: 1, item: 3 }]);
}
}