/
weighted.rs
438 lines (392 loc) · 15.2 KB
/
weighted.rs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
// Copyright 2018 Developers of the Rand project.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
use Rng;
use distributions::Distribution;
use distributions::uniform::{UniformSampler, SampleUniform, SampleBorrow};
use ::core::cmp::PartialOrd;
use core::fmt;
// Note that this whole module is only imported if feature="alloc" is enabled.
#[cfg(not(feature = "std"))] use alloc::collections::VecDeque;
#[cfg(not(feature="std"))] use alloc::vec::Vec;
#[cfg(feature = "std")] use std::collections::VecDeque;
/// A distribution using weighted sampling to pick a discretely selected
/// item.
///
/// Sampling a `WeightedIndex` distribution returns the index of a randomly
/// selected element from the iterator used when the `WeightedIndex` was
/// created. The chance of a given element being picked is proportional to the
/// value of the element. The weights can use any type `X` for which an
/// implementation of [`Uniform<X>`] exists.
///
/// # Performance
///
/// A `WeightedIndex<X>` contains a `Vec<X>` and a [`Uniform<X>`] and so its
/// size is the sum of the size of those objects, possibly plus some alignment.
///
/// Creating a `WeightedIndex<X>` will allocate enough space to hold `N - 1`
/// weights of type `X`, where `N` is the number of weights. However, since
/// `Vec` doesn't guarantee a particular growth strategy, additional memory
/// might be allocated but not used. Since the `WeightedIndex` object also
/// contains, this might cause additional allocations, though for primitive
/// types, ['Uniform<X>`] doesn't allocate any memory.
///
/// Time complexity of sampling from `WeightedIndex` is `O(log N)` where
/// `N` is the number of weights.
///
/// Sampling from `WeightedIndex` will result in a single call to
/// `Uniform<X>::sample` (method of the [`Distribution`] trait), which typically
/// will request a single value from the underlying [`RngCore`], though the
/// exact number depends on the implementaiton of `Uniform<X>::sample`.
///
/// # Example
///
/// ```
/// use rand::prelude::*;
/// use rand::distributions::WeightedIndex;
///
/// let choices = ['a', 'b', 'c'];
/// let weights = [2, 1, 1];
/// let dist = WeightedIndex::new(&weights).unwrap();
/// let mut rng = thread_rng();
/// for _ in 0..100 {
/// // 50% chance to print 'a', 25% chance to print 'b', 25% chance to print 'c'
/// println!("{}", choices[dist.sample(&mut rng)]);
/// }
///
/// let items = [('a', 0), ('b', 3), ('c', 7)];
/// let dist2 = WeightedIndex::new(items.iter().map(|item| item.1)).unwrap();
/// for _ in 0..100 {
/// // 0% chance to print 'a', 30% chance to print 'b', 70% chance to print 'c'
/// println!("{}", items[dist2.sample(&mut rng)].0);
/// }
/// ```
///
/// [`Uniform<X>`]: crate::distributions::uniform::Uniform
/// [`RngCore`]: rand_core::RngCore
#[derive(Debug, Clone)]
pub struct WeightedIndex<X: SampleUniform + PartialOrd> {
cumulative_weights: Vec<X>,
weight_distribution: X::Sampler,
}
impl<X: SampleUniform + PartialOrd> WeightedIndex<X> {
/// Creates a new a `WeightedIndex` [`Distribution`] using the values
/// in `weights`. The weights can use any type `X` for which an
/// implementation of [`Uniform<X>`] exists.
///
/// Returns an error if the iterator is empty, if any weight is `< 0`, or
/// if its total value is 0.
///
/// [`Uniform<X>`]: crate::distributions::uniform::Uniform
pub fn new<I>(weights: I) -> Result<WeightedIndex<X>, WeightedError>
where I: IntoIterator,
I::Item: SampleBorrow<X>,
X: for<'a> ::core::ops::AddAssign<&'a X> +
Clone +
Default {
let mut iter = weights.into_iter();
let mut total_weight: X = iter.next()
.ok_or(WeightedError::NoItem)?
.borrow()
.clone();
let zero = <X as Default>::default();
if total_weight < zero {
return Err(WeightedError::NegativeWeight);
}
let mut weights = Vec::<X>::with_capacity(iter.size_hint().0);
for w in iter {
if *w.borrow() < zero {
return Err(WeightedError::NegativeWeight);
}
weights.push(total_weight.clone());
total_weight += w.borrow();
}
if total_weight == zero {
return Err(WeightedError::AllWeightsZero);
}
let distr = X::Sampler::new(zero, total_weight);
Ok(WeightedIndex { cumulative_weights: weights, weight_distribution: distr })
}
}
impl<X> Distribution<usize> for WeightedIndex<X> where
X: SampleUniform + PartialOrd {
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> usize {
use ::core::cmp::Ordering;
let chosen_weight = self.weight_distribution.sample(rng);
// Find the first item which has a weight *higher* than the chosen weight.
self.cumulative_weights.binary_search_by(
|w| if *w <= chosen_weight { Ordering::Less } else { Ordering::Greater }).unwrap_err()
}
}
#[allow(missing_docs)] // todo: add docs
#[derive(Debug, Clone)]
pub struct AliasMethodWeightedIndex {
aliases: Vec<usize>,
no_alias_odds: Vec<f64>,
uniform_index: super::Uniform<usize>,
}
impl AliasMethodWeightedIndex {
#[allow(missing_docs)] // todo: add docs
pub fn new(weights: Vec<f64>) -> Result<Self, AliasMethodWeightedIndexError> {
if weights.is_empty() {
return Err(AliasMethodWeightedIndexError::NoItem);
}
if !weights.iter().all(|&w| w >= 0.0) {
return Err(AliasMethodWeightedIndexError::InvalidWeight);
}
let n = weights.len();
let weight_sum = pairwise_sum_f64(weights.as_slice());
if weight_sum.is_infinite() {
return Err(AliasMethodWeightedIndexError::WeightSumToBig);
}
let weight_scale = n as f64 / weight_sum;
if weight_scale.is_infinite() {
return Err(AliasMethodWeightedIndexError::WeightSumToSmall);
}
let mut no_alias_odds = weights;
for odds in no_alias_odds.iter_mut() {
*odds *= weight_scale;
}
// Split indices into indices with small weights and indices with big weights.
// Instead of two `Vec` with unknown capacity we use a single `VecDeque` with
// known capacity. Front represents smalls and back represents bigs. We also
// need to keep track of the size of each virtual `Vec`.
let mut smalls_bigs = VecDeque::with_capacity(n);
let mut smalls_len = 0_usize;
let mut bigs_len = 0_usize;
for (index, &odds) in no_alias_odds.iter().enumerate() {
if odds < 1.0 {
smalls_bigs.push_front(index);
smalls_len += 1;
} else {
smalls_bigs.push_back(index);
bigs_len += 1;
}
}
let mut aliases = vec![0; n];
while smalls_len > 0 && bigs_len > 0 {
let s = smalls_bigs.pop_front().unwrap();
smalls_len -= 1;
let b = smalls_bigs.pop_back().unwrap();
bigs_len -= 1;
aliases[s] = b;
no_alias_odds[b] = no_alias_odds[s] + no_alias_odds[b] - 1.0;
if no_alias_odds[b] < 1.0 {
smalls_bigs.push_front(b);
smalls_len += 1;
} else {
smalls_bigs.push_back(b);
bigs_len += 1;
}
}
// The remaining indices should have no alias odds of about 1. This is due to
// numeric accuracy. Otherwise they would be exactly 1.
for index in smalls_bigs.into_iter() {
// Because p = 1 we don't need to set an alias. It will never be accessed.
no_alias_odds[index] = 1.0;
}
// Prepare a distribution to sample random indices. Creating it beforehand
// improves sampling performance.
let uniform_index = super::Uniform::new(0, no_alias_odds.len());
Ok(Self {
aliases,
no_alias_odds,
uniform_index,
})
}
}
impl Distribution<usize> for AliasMethodWeightedIndex {
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> usize {
let candidate = rng.sample(self.uniform_index);
if rng.sample::<f64, _>(super::Standard) < self.no_alias_odds[candidate] {
candidate
} else {
self.aliases[candidate]
}
}
}
fn pairwise_sum_f64(values: &[f64]) -> f64 {
if values.len() <= 32 {
values.iter().sum()
} else {
let mid = values.len() / 2;
let (a, b) = values.split_at(mid);
pairwise_sum_f64(a) + pairwise_sum_f64(b)
}
}
#[cfg(test)]
mod test {
use super::*;
#[test]
fn test_weightedindex() {
let mut r = ::test::rng(700);
const N_REPS: u32 = 5000;
let weights = [1u32, 2, 3, 0, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7];
let total_weight = weights.iter().sum::<u32>() as f32;
let verify = |result: [i32; 14]| {
for (i, count) in result.iter().enumerate() {
let exp = (weights[i] * N_REPS) as f32 / total_weight;
let mut err = (*count as f32 - exp).abs();
if err != 0.0 {
err /= exp;
}
assert!(err <= 0.25);
}
};
// WeightedIndex from vec
let mut chosen = [0i32; 14];
let distr = WeightedIndex::new(weights.to_vec()).unwrap();
for _ in 0..N_REPS {
chosen[distr.sample(&mut r)] += 1;
}
verify(chosen);
// WeightedIndex from slice
chosen = [0i32; 14];
let distr = WeightedIndex::new(&weights[..]).unwrap();
for _ in 0..N_REPS {
chosen[distr.sample(&mut r)] += 1;
}
verify(chosen);
// WeightedIndex from iterator
chosen = [0i32; 14];
let distr = WeightedIndex::new(weights.iter()).unwrap();
for _ in 0..N_REPS {
chosen[distr.sample(&mut r)] += 1;
}
verify(chosen);
for _ in 0..5 {
assert_eq!(WeightedIndex::new(&[0, 1]).unwrap().sample(&mut r), 1);
assert_eq!(WeightedIndex::new(&[1, 0]).unwrap().sample(&mut r), 0);
assert_eq!(WeightedIndex::new(&[0, 0, 0, 0, 10, 0]).unwrap().sample(&mut r), 4);
}
assert_eq!(WeightedIndex::new(&[10][0..0]).unwrap_err(), WeightedError::NoItem);
assert_eq!(WeightedIndex::new(&[0]).unwrap_err(), WeightedError::AllWeightsZero);
assert_eq!(WeightedIndex::new(&[10, 20, -1, 30]).unwrap_err(), WeightedError::NegativeWeight);
assert_eq!(WeightedIndex::new(&[-10, 20, 1, 30]).unwrap_err(), WeightedError::NegativeWeight);
assert_eq!(WeightedIndex::new(&[-10]).unwrap_err(), WeightedError::NegativeWeight);
}
#[test]
fn test_alias_method_weighted_index() {
const NUM_WEIGHTS: usize = 10;
const ZERO_WEIGHT_INDEX: usize = 3;
const NUM_SAMPLES: u32 = 10000;
let mut rng = ::test::rng(0x9c9fa0b0580a7031);
let weights = {
let mut weights = Vec::with_capacity(NUM_WEIGHTS);
for _ in 0..NUM_WEIGHTS {
weights.push(rng.sample::<f64, _>(::distributions::Standard));
}
weights[ZERO_WEIGHT_INDEX] = 0.0;
weights
};
let weight_sum = weights.iter().sum::<f64>();
let expected_counts = weights
.iter()
.map(|&w| w / weight_sum * NUM_SAMPLES as f64)
.collect::<Vec<f64>>();
let weight_distribution = AliasMethodWeightedIndex::new(weights).unwrap();
let mut counts = vec![0_usize; NUM_WEIGHTS];
for _ in 0..NUM_SAMPLES {
counts[rng.sample(&weight_distribution)] += 1;
}
assert_eq!(counts[ZERO_WEIGHT_INDEX], 0);
for (count, expected_count) in counts.into_iter().zip(expected_counts) {
let difference = (count as f64 - expected_count).abs();
let max_allowed_difference = NUM_SAMPLES as f64 / NUM_WEIGHTS as f64 * 0.1;
assert!(difference <= max_allowed_difference);
}
assert_eq!(
AliasMethodWeightedIndex::new(vec![]).unwrap_err(),
AliasMethodWeightedIndexError::NoItem
);
assert_eq!(
AliasMethodWeightedIndex::new(vec![0.0]).unwrap_err(),
AliasMethodWeightedIndexError::WeightSumToSmall
);
assert_eq!(
AliasMethodWeightedIndex::new(vec![::core::f64::INFINITY]).unwrap_err(),
AliasMethodWeightedIndexError::WeightSumToBig
);
assert_eq!(
AliasMethodWeightedIndex::new(vec![::core::f64::MAX, ::core::f64::MAX]).unwrap_err(),
AliasMethodWeightedIndexError::WeightSumToBig
);
assert_eq!(
AliasMethodWeightedIndex::new(vec![-1.0]).unwrap_err(),
AliasMethodWeightedIndexError::InvalidWeight
);
assert_eq!(
AliasMethodWeightedIndex::new(vec![::core::f64::NAN]).unwrap_err(),
AliasMethodWeightedIndexError::InvalidWeight
);
}
}
/// Error type returned from `WeightedIndex::new`.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum WeightedError {
/// The provided iterator contained no items.
NoItem,
/// A weight lower than zero was used.
NegativeWeight,
/// All items in the provided iterator had a weight of zero.
AllWeightsZero,
}
impl WeightedError {
fn msg(&self) -> &str {
match *self {
WeightedError::NoItem => "No items found",
WeightedError::NegativeWeight => "Item has negative weight",
WeightedError::AllWeightsZero => "All items had weight zero",
}
}
}
#[cfg(feature="std")]
impl ::std::error::Error for WeightedError {
fn description(&self) -> &str {
self.msg()
}
fn cause(&self) -> Option<&::std::error::Error> {
None
}
}
impl fmt::Display for WeightedError {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "{}", self.msg())
}
}
#[allow(missing_docs)] // todo: add docs
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum AliasMethodWeightedIndexError {
NoItem,
InvalidWeight,
WeightSumToSmall,
WeightSumToBig,
}
impl AliasMethodWeightedIndexError {
fn msg(&self) -> &str {
match *self {
AliasMethodWeightedIndexError::NoItem => "No items found.",
AliasMethodWeightedIndexError::InvalidWeight => "An item has an invalid weight.",
AliasMethodWeightedIndexError::WeightSumToSmall => "The sum of weights is to small.",
AliasMethodWeightedIndexError::WeightSumToBig => "The sum of weights is to big.",
}
}
}
impl fmt::Display for AliasMethodWeightedIndexError {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
f.write_str(self.msg())
}
}
#[cfg(feature = "std")]
impl ::std::error::Error for AliasMethodWeightedIndexError {
fn description(&self) -> &str {
self.msg()
}
fn cause(&self) -> Option<&::std::error::Error> {
None
}
}