eeb94886ad
This commit removes all the old casting/generic traits from `std::num` that are no longer in use by the standard library. This additionally removes the old `strconv` module which has not seen much use in quite a long time. All generic functionality has been supplanted with traits in the `num` crate and the `strconv` module is supplanted with the [rust-strconv crate][rust-strconv]. [rust-strconv]: https://github.com/lifthrasiir/rust-strconv This is a breaking change due to the removal of these deprecated crates, and the alternative crates are listed above. [breaking-change]
353 lines
13 KiB
Rust
353 lines
13 KiB
Rust
// 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 core::prelude::*;
|
|
use core::num::Float;
|
|
use core::marker::PhantomData;
|
|
|
|
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.
|
|
pub struct RandSample<Sup> { _marker: PhantomData<Sup> }
|
|
|
|
impl<Sup> RandSample<Sup> {
|
|
pub fn new() -> RandSample<Sup> {
|
|
RandSample { _marker: PhantomData }
|
|
}
|
|
}
|
|
|
|
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()
|
|
}
|
|
}
|
|
|
|
/// A value with a particular weight for use with `WeightedChoice`.
|
|
pub struct Weighted<T> {
|
|
/// The numerical weight of this item
|
|
pub weight: usize,
|
|
/// 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 `usize`, so one can store references or indices into
|
|
/// another vector.
|
|
pub struct WeightedChoice<'a, T:'a> {
|
|
items: &'a mut [Weighted<T>],
|
|
weight_range: Range<usize>
|
|
}
|
|
|
|
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 `usize` 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 = 0_usize;
|
|
|
|
// 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 &mut *items {
|
|
running_total = match running_total.checked_add(item.weight) {
|
|
Some(n) => n,
|
|
None => panic!("WeightedChoice::new called with a total weight \
|
|
larger than a usize 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 std::prelude::v1::*;
|
|
|
|
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 {
|
|
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] #[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 = (!0) as usize / 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 }]);
|
|
}
|
|
}
|