2705 lines
653 KiB
Plaintext
2705 lines
653 KiB
Plaintext
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’ü˜ÔC ü˜* ' Utilities for random number generationÁ Ãú üÇJ G Rand provides utilities to generate random numbers, to convert them toÁ ü’K H useful types and distributions, and some randomness-related algorithms.Á Þú Œâ # Quick StartÁ ôú <ø ```Á ü€D A // The prelude import enables methods we use below, specificallyÁ üÅP M // Rng::random, Rng::sample, SliceRandom::shuffle and IndexedRandom::choose.Á Ì– use rand::prelude::*;Á °ú ”´ // Get an RNG:Á ôÇ let mut rng = rand::rng();Á æú üêF C // Try printing a random unicode code point (probably a bad idea)!Á ü±1 . println!("char: '{}'", rng.random::<char>());Á üã8 5 // Try printing a random alphanumeric value instead!Á üœK H println!("alpha: '{}'", rng.sample(rand::distr::Alphanumeric) as char);Á èú üì' $ // Generate and shuffle a sequence:Á ü” 0 - let mut nums: Vec<i32> = (1..100).collect();Á ÜÅ nums.shuffle(&mut rng);Á üá F C // And take a random pick (yes, we didn't need to shuffle first!):Á ü¨
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= : For the user guide and further documentation, please readÁ ü¨ = : [The Rust Rand Book](https://rust-random.github.io/book).Á %https://www.rust-lang.org/favicon.icoÁ„Ä 9https://www.rust-lang.org/logos/rust-logo-128x128-blk.pngÁló #https://rust-random.github.io/rand/Ál„
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’knq”Éh„õ]NQLß?B-0ìïlº ü˜< 9 Generating random samples from probability distributionsÁ Õú üÙL I This module is the home of the [`Distribution`] trait and several of itsÁ ü¦F C implementations. It is the workhorse behind some of the convenientÁ üíJ G functionality of the [`Rng`] trait, e.g. [`Rng::random`] and of courseÁ ¤¸ [`Rng::sample`].Á Íú üÑI F Abstractly, a [probability distribution] describes the probability ofÁ ü›1 . occurrence of each value in its sample space.Á Íú üÑN K More concretely, an implementation of `Distribution<T>` for type `X` is anÁ ü I F algorithm for choosing values from the sample space (a subset of `T`)Á üêM J according to the distribution `X` represents, using an external source ofÁ ü¸: 7 randomness (an RNG supplied to the `sample` function).Á óú ü÷F C A type `X` may implement `Distribution<T>` for multiple types `T`.Á ü¾ I F Any type implementing [`Distribution`] is stateless (i.e. immutable),Á üˆ
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N K but it may have internal parameters set at construction time (for example,Á ü×
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P M [`Uniform`] allows specification of its sample space as a range within `T`).Á ¨ ú ¬ ú ü° ' $ # The Standard Uniform distributionÁ Ø ú üÜ M J The [`StandardUniform`] distribution is important to mention. This is theÁ üª L I distribution used by [`Rng::random`] and represents the "default" way toÁ ü÷ M J produce a random value for many different types, including most primitiveÁ üÅ
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L I types, tuples, arrays, and a few derived types. See the documentation ofÁ ü’) & [`StandardUniform`] for more details.Á ¼ú üÀX U Implementing [`Distribution<T>`] for [`StandardUniform`] for user types `T` makes itÁ ü™M J possible to generate type `T` with [`Rng::random`], and by extension alsoÁ üç! with the [`random`] function.Á ‰ú ü�+ ( ## Other standard uniform distributionsÁ ¹ú ü½J G [`Alphanumeric`] is a simple distribution to sample random letters andÁ üˆT Q numbers of the `char` type; in contrast [`StandardUniform`] may sample any validÁ \Ý `char`.Á éú üí\ Y There's also an [`Alphabetic`] distribution which acts similarly to [`Alphanumeric`] butÁ ÜÊ doesn't include digits.Á æú üêN K For floats (`f32`, `f64`), [`StandardUniform`] samples from `[0, 1)`. AlsoÁ ü¹H E provided are [`Open01`] (samples from `(0, 1)`) and [`OpenClosed01`]Á ü‚N K (samples from `(0, 1]`). No option is provided to sample from `[0, 1]`; itÁ üÑN K is suggested to use one of the above half-open ranges since the failure toÁ ü K H sample a value which would have a low chance of being sampled anyway isÁ üì rarely an issue in practice.Á �ú ü‘) & # Parameterized Uniform distributionsÁ »ú ü¿K H The [`Uniform`] distribution provides uniform sampling over a specifiedÁ ü‹H E range on a subset of the types supported by the above distributions.Á Ôú üØ5 2 Implementations support single-value-sampling viaÁ üŽ4 1 [`Rng::random_range(Range)`](Rng::random_range).Á üÃN K Where a fixed (non-`const`) range will be sampled many times, it is likelyÁ ü’; 8 faster to pre-construct a [`Distribution`] object usingÁ üÎB ? [`Uniform::new`], [`Uniform::new_inclusive`] or `From<Range>`.Á ‘ú Ô• # Non-uniform samplingÁ °ú ü´M J Sampling a simple true/false outcome with a given probability has a name:Á ü‚J G the [`Bernoulli`] distribution (this is used by [`Rng::random_bool`]).Á Íú üÑI F For weighted sampling of discrete values see the [`weighted`] module.Á › ú üŸ J G This crate no longer includes other non-uniform distributions; insteadÁ üê G D it is recommended that you use either [`rand_distr`] or [`statrs`].Á ² ú ¶ ú üº V S [probability distribution]: https://en.wikipedia.org/wiki/Probability_distributionÁ ü‘ 7 4 [`rand_distr`]: https://crates.io/crates/rand_distrÁ üÉ / , [`statrs`]: https://crates.io/crates/statrsÁ ìú [`random`]: crate::randomÁ ü˜ 7ãò üÐ /¤ó ,Â
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$Ü ± â ü¿) »À| ¼§ …ª tí ”© ü‚ 7 ü‚J G Construct a new `Bernoulli` with the given probability of success `p`.Á Ñ ú |Ù # PrecisionÁ í ú üõH E For `p = 1.0`, the resulting distribution will always generate true.Á ü I F For `p = 0.0`, the resulting distribution will always generate false.Á � ú ü˜ L I This method is accurate for any input `p` in the range `[0, 1]` which isÁ üé B ? a multiple of 2<sup>-64</sup>. (Note that not all multiples ofÁ ü° ? < 2<sup>-64</sup> in `[0, 1]` can be represented as a `f64`.)Á ‰ Ö¿Ù¿ Ú¿« Û¿ˆ Ü¿ Ý¿Þ¿ˆ ‚†f|Â
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» � üø%X üá!B ? Construct a new `Bernoulli` with the probability of success ofÁ ü¨"D A `numerator`-in-`denominator`. I.e. `new_ratio(2, 3)` will returnÁ üñ"J G a `Bernoulli` with a 2-in-3 chance, or about 67%, of returning `true`.Á À# ú üÈ#E B return `true`. If `numerator == 0` it will always return `false`.Á ü’$I F For `numerator > denominator` and `denominator == 0`, this returns anÁ üà$H E error. Otherwise, for `numerator == denominator`, samples are alwaysÁ ü%8 5 true; for `numerator == 0` samples are always false.ÁTÿ% €
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numeratorÁLŠ& denominatorÁ\š& ´Ý* üÊ)6 3 Returns the probability (`p`) of the distribution.Á …* ú ü�*K H This value may differ slightly from the input due to loss of precision.Á ä* £ £”© æ*
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±ß$Ï, °6 Õ, +- „� d” !A·Ã÷6 Ê ø �ß4ü úH ù$Ž Œ5 TÃ>¬í-Tˆ Ì� ü•N K Types (distributions) that can be used to create a random instance of `T`.Á äú üèA > It is possible to sample from a distribution through both theÁ üªG D `Distribution` and [`Rng`] traits, via `distr.sample(&mut rng)` andÁ üòO L `rng.sample(distr)`. They also both offer the [`sample_iter`] method, whichÁ üÂ< 9 produces an iterator that samples from the distribution.Á ÿú üƒN K All implementations are expected to be immutable; this has the significantÁ üÒD A advantage of not needing to consider thread safety, and for mostÁ ü—I F distributions efficient state-less sampling algorithms are available.Á áú üåK H Implementations are typically expected to be portable with reproducibleÁ ü± : 7 results when used with a PRNG with fixed seed; see theÁ üì N K [portability chapter](https://rust-random.github.io/book/portability.html)Á ü»
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N K of The Rust Rand Book. In some cases this does not apply, e.g. the `usize`Á üŠ C @ type requires different sampling on 32-bit and 64-bit machines.Á Î ú üÒ . + [`sample_iter`]: Distribution::sample_iterÁ d‹ ! ¥ " ! " Îì ü�  Í짫 ˜ ! ë“* ë“0#%'#%' # ' % 24 üò 4 ü¡ L I Generate a random value of `T`, using `rng` as the source of randomness.Á4õ ¦ § ¦ó“ §£§« !£ $ $ �
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the source of randomness.Á �ú ü¥C @ Note that this function takes `self` by value. This works sinceÁ üíD A `Distribution<T>` is impl'd for `&D` where `D: Distribution<T>`,Á ü¶I F however borrowing is not automatic hence `distr.sample_iter(...)` mayÁ ü„E B need to be replaced with `(&distr).sample_iter(...)` to borrow orÁ üÎC @ `(&*distr).sample_iter(...)` to reborrow an existing reference.Á –ú lž
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# ExampleÁ °ú <¸¨Æ üÄL I use rand::distr::{Distribution, Alphanumeric, Uniform, StandardUniform};Á •ú ô�©È Àú ¼È // Vec of 16 x f32:Á üäO L let v: Vec<f32> = StandardUniform.sample_iter(&mut rng).take(16).collect();Á ¸ú tÀ // String:Á üÓ let s: String = AlphanumericÁ ôø .sample_iter(&mut rng)Á „›
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.take(7)Á Ä° .map(char::from)Á œÍ .collect();Á åú ¤í // Dice-rolling:Á ü†: 7 let die_range = Uniform::new_inclusive(1, 6).unwrap();Á üÅ7 4 let mut roll_die = die_range.sample_iter(&mut rng);Á ü�) & while roll_die.next().unwrap() != 6 {Á ü¯, ) println!("Not a 6; rolling again!");Á ,à }Á <ê¨Æ\ù ó“â• · · ÛT »Ø ¼°6 ½�U KÍ”�
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%󓧫â•$ˆ°6 Ž<> üÛg üÝ" Map sampled values to type `S`Á „ú lŒƒš žú <¦¨Æ ü²- * use rand::distr::{Distribution, Uniform};Á äú üì4 1 let die = Uniform::new_inclusive(1, 6).unwrap();Á ü¥2 / let even_number = die.map(|num| num % 2 == 0);Á üÜ1 . while !even_number.sample(&mut rand::rng()) {Á ü’. + println!("Still odd; rolling again!");Á ,Ň <Ï¨Æ Þ ó“— Ã Ã ÁU ÈØ ÉôU Ê�U >jEf¡E•Ëó“ɦ§«÷¬ !— ( ¤ ) ( ) ! Íìɦ â Íì÷¬ å �"ɦ§« T¢ ɦ÷§˜" ÷¬ « ¿¢,¼
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5÷«ý«ƒ¬$€&üÆ&] • 7 £ 8 ¥ 9 8 7 9 Ù« Ë& ê« Î& û« Ñ& Œ¬|‡' Ÿ¬ Ÿ'´« (* -/ 24 üÐ)e • ; — < ¥ = ¤ > = > < ; í¬ƒ¬˜" ÷¬ ³* Íìí¬ Ø) û« Û) Û§ Þ) Œ¬|’* �"í¬± Tª* Ù« Õ)¦¬? # ? QS VX [] ü¼*34¿* ® ¦¬ ®£÷¬ :£ @ @ ×* : Î솳 Æ* ø†³ É*
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?÷«í¬ƒ¬÷¬†³$Ø*°6 Þ*;= ´, ü§+! Sample or extend a [`String`]Á É+ú üÍ+E B Helper methods to extend a [`String`] or sample a new [`String`].Á »¤Œ™,Ì“, d·, A A ë“ü,† A ë“ ë“ BDBD D B ü.W üÊ,) & Append `len` random chars to `string`Á ø,ú ü€-J G Note: implementations may leave `string` with excess capacity. If thisÁ üÏ-I F is undesirable, consider calling [`String::shrink_to_fit`] after thisÁ \�. method.Ál°. ¯ ° ± ¯ó“ °ý« ±úHúH ß ûHÁ‘4 Ýf‰úM÷ A£ C C Ï. A Îìý« ¾. Ÿ¬ Á.
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Bó“ý«$Ð.°6 Ö. stringÁ4ã.‘ ø.=? üƒ1K üŠ// , Generate a [`String`] of `len` random charsÁ ¾/ú üÆ/L I Note: implementations may leave the string with excess capacity. If this
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�L , “L 8´ ”L —L ¡O 8! $¥L 8 ScalarÁ 4ªL ±L , ³L 8´ ´L % ¶L + ÅL ÆL ÍL 8Ý 4ÇL 8 ÛL 8 replaceÁ <ÞL åL ‘M 8 $æL $ êL 8Ö ,ìL & ñL 8¬ ,óL $ øL 8 new_valueÁ LúL & ƒM 8 $…M '‰M 8¸é 4‹M (“M 8 $–M ›M ïM 8 debug_assert_eqÁ |M ¼M ½M ÆM 8Ö ,¾M $ ÃM 7ˆ ÅM % ÇM 8æê LÙM + þM ÿM †N 8Ý 4€N 8 ”N 8 extract_laneÁ d—N £N ¶N 8 $¤N $ ¨N 8Ö ,ªN & ¯N 8¬ ,±N (¸N 8 $»N '¿N 8¸é 4ÁN ÈN —O 8¼ë |ÚN éN êN óN 8Ö ,ëN $ ðN 7ˆ òN % ôN 8 $†O 8 $¬O 8…# \±O 8
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½O , ÁO 8´ ÂO ÅO ÆO % ÍO ¬à 4× lè èL’! P ż„!lµ! ìä Distributions over slicesÁ ,½! Ú ë ì NonZeroUsizeÁd’ ²– Æ Ç¨-t½ Ý Æ ÉìwdÍ � Æ Ê ’²dî ! Æ Ë Òß4© úH Æ Ì¼‡r¬¥bdQSÔà@¬š.Ìð Ë$ Î ¥ Ï Î Ï ÿ“ ùݼÐÑ õ üž1 ü�J G Create a new `Choose` instance which samples uniformly from the slice.Á ßú üç2 / Returns error [`Empty`] if the slice is empty.Á ¥ Ë$
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Ð Ë$§«ž,©üî) ü´5 2 Returns the count of choices in this distributionÁ\õ Ó Óݼ ô ô õ ¨ ÷ ˆÐ mjç�ítoé Í � Í
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Ñ Ë$§«$‚ü¼1 Ë$ Ó ¥ Ô Ó Ô ÿ“ ÅÝ¼Õ # Õ Á üô>4÷ Ô Õ Ôݼ Õâ•Í½ Ò£ Ö Ö – Ò Œ– þ �–T�
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Ø $»± Áü• »À|ƒ ¼ý ß½ üÔ - »¤ŒÀ ̺ 8 Ù Ù Â¾Û B Û üˆ ]l‹ Ú Û Ü Ú¾ Ûý« Ü»¸ Ú£ Ü Ü ± Ú Ž¹ ™ Ÿ¬Tœ
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@ A distribution uniformly sampling numbers within a given range.Á Ü
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ú üàN
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K [`Uniform`] is the standard distribution to sample uniformly from a range;Á ü¯X
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U e.g. `Uniform::new_inclusive(1, 6).unwrap()` can sample integers from 1 to 6, like aÁ üˆH
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E standard die. [`Rng::random_range`] is implemented over [`Uniform`].Á Ñ
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ú œÕ
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# Example usageÁ é
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ú <í
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¨Æ ”õ
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use rand::Rng;Á ìˆ
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use rand::distr::Uniform;Á ¦
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ú ôª
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©È üÉ2
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/ let side = Uniform::new(-10.0, 10.0).unwrap();Á ü
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ú ü€%
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" // sample between 1 and 10 pointsÁ ü¦*
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' for _ in 0..rng.random_range(1..=10) {Á üÑO
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L // sample a point from the square with sides -10 - 10 in two dimensionsÁ ü¡:
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7 let (x, y) = (rng.sample(side), rng.sample(side));Á üÜ(
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% println!("Point: {}, {}", x, y);Á ,…
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/ # Extending `Uniform` to support a custom typeÁ Ê
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ú üÎ K
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H To extend [`Uniform`] to support your own types, write a back-end whichÁ üš
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Q
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N implements the [`UniformSampler`] trait, then implement the [`SampleUniform`]Á üì
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L
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I helper trait to "register" your back-end. See the `MyF32` example below.Á ¹
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ú ü½ P
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M At a minimum, the back-end needs to store any parameters needed for samplingÁ üŽ N
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K (e.g. the target range) and implement `new`, `new_inclusive` and `sample`.Á üÝ O
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L Those methods should include an assertion to check the range is valid (i.e.Á ü
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C
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@ `low < high`). The example below merely wraps another back-end.Á ñ
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ú üõ
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M
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J The `new`, `new_inclusive`, `sample_single` and `sample_single_inclusive`Á ôÃ
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functions use arguments ofÁ üâG
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D type `SampleBorrow<X>` to support passing in values by reference orÁ üªI
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F by value. In the implementation of these functions, you can choose toÁ üôT
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Q simply use the reference returned by [`SampleBorrow::borrow`], or you can chooseÁ üÉF
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C to copy or clone the value, whatever is appropriate for your type.Á �
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ú <”
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àÇ ü¶6
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3 use rand::distr::uniform::{Uniform, SampleUniform,Á üí?
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< UniformSampler, UniformFloat, SampleBorrow, Error};Á
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ú ´±
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struct MyF32(f32);Á È
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ú üÌ!
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#[derive(Clone, Copy, Debug)]Á üî+
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( struct UniformMyF32(UniformFloat<f32>);Á š
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ú üž*
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' impl UniformSampler for UniformMyF32 {Á ¼É
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type X = MyF32;Á á
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ú üå@
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= fn new<B1, B2>(low: B1, high: B2) -> Result<Self, Error>Á ü¦4
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1 where B1: SampleBorrow<Self::X> + Sized,Á üÛ3
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0 B2: SampleBorrow<Self::X> + SizedÁ L�
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{Á ü™W
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T UniformFloat::<f32>::new(low.borrow().0, high.borrow().0).map(UniformMyF32)Á Lñ
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}Á üûJ
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G fn new_inclusive<B1, B2>(low: B1, high: B2) -> Result<Self, Error>Á üÆ4
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æ‘ üû3
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Ó“ ü¥C
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@ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {Á üé%
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impl SampleUniform for MyF32 {Á üÆ$
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! type Sampler = UniformMyF32;Á ,ë
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‡ ñ
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ú üõ7
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4 let (low, high) = (MyF32(17.0f32), MyF32(22.0f32));Á ü3
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0 let uniform = Uniform::new(low, high).unwrap();Á üá-
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ú ü›;
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8 [`SampleUniform`]: crate::distr::uniform::SampleUniformÁ ü×=
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: [`UniformSampler`]: crate::distr::uniform::UniformSamplerÁ ü• 5
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2 [`UniformInt`]: crate::distr::uniform::UniformIntÁ üË 9
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6 [`UniformFloat`]: crate::distr::uniform::UniformFloatÁ ü… ?
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< [`UniformDuration`]: crate::distr::uniform::UniformDurationÁ üÅ I
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F [`SampleBorrow::borrow`]: crate::distr::uniform::SampleBorrow::borrowÁ <Ì! àï“ÛÝ÷€Í Ý Þ ÜfdÖ
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„ï! ìä Weighted (index) samplingÁ ‚ú ü†E B Primarily, this module houses the [`WeightedIndex`] distribution.Á üÌP M See also [`rand_distr::weighted`] for alternative implementations supportingÁ ü�K H potentially-faster sampling or a more easily modifiable tree structure.Á éú üí^ [ [`rand_distr::weighted`]: https://docs.rs/rand_distr/latest/rand_distr/weighted/index.htmlÁ »¤ŒÛ!ÌÕ! D÷! ’ÅÛ
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Error cases:Á üÆ E B - [`Error::InvalidInput`] when the iterator `weights` is empty.Á ü� K H - [`Error::InvalidWeight`] when a weight is not-a-number or negative.Á üà K H - [`Error::InsufficientNonZero`] when the sum of all weights is zero.Á ü° B ? - [`Error::Overflow`] when the sum of all weights overflows.Á ÷ ú üÿ 2 / [`Uniform<X>`]: crate::distr::uniform::UniformÁ ½! šÖ¿Ù¿ Ú¿« Û¿ˆ Ü¿ Ý¿Þ¿ˆ ‚†f|Â
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¶ 8ÿÛ$ˆR üôS< © ¸ ¸ ùØ ùS ŠÙlüS é±TŒT ôÃ,™T ÅÚ¹¼¾ )+ ü¼Xi ü·T8 5 Returns the weight at the given index, if it exists.Á ôT ú üüT; 8 If the index is out of bounds, this will return `None`.Á ¼U ú lÄU ƒš ÖU ú <ÞU ¨Æ üêU- * use rand::distr::weighted::WeightedIndex;Á œV ú ä¤V let weights = [0, 1, 2];Á üÅV5 2 let dist = WeightedIndex::new(&weights).unwrap();Á üÿV( % assert_eq!(dist.weight(0), Some(0));Á ü¬W( % assert_eq!(dist.weight(1), Some(1));Á üÙW( % assert_eq!(dist.weight(2), Some(2));Á ü†X% " assert_eq!(dist.weight(3), None);Á <°X ¨Æ4ÃX † †ÅÚ Û¼Ý¼Þ¼© ß¼ à¼ÛἈ cSñŸ«‡zÙп · ÊX · º œöп ºÐ¿ ü�Y#
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¹Ð¿$ËX Ö,ÑX …Y œ¸Y üµak ü´\X U Returns a lazy-loading iterator containing the current weights of this distribution.Á ‘] ú ü™]V S If this distribution has not been updated since its creation, this will return theÁ üô]) & same weights as were passed to `new`.Á ¢^ ú lª^ ƒš ¼^ ú <Ä^ ¨Æ üÐ^- ÃÏ ‚_ ú äŠ_ let weights = [1, 2, 3];Á ü«_9 6 let mut dist = WeightedIndex::new(&weights).unwrap();Á üé_B ? assert_eq!(dist.weights().collect::<Vec<_>>(), vec![1, 2, 3]);Á ü°`- * dist.update_weights(&[(0, &2)]).unwrap();Á üâ`B ? assert_eq!(dist.weights().collect::<Vec<_>>(), vec![2, 2, 3]);Á <©a ¨Æ<¼a ‡ ‡ÅÚ § § ¯2 ª•1 ’ «Ö ’ ÍðÙûâZ±ç ‡Ð¿ · Äa · ½ œöп ½Ð¿ üüa#
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User-level interface for RNGsÁ ‰
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