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Diffstat (limited to 'rand/src/distributions/weighted/alias_method.rs')
| -rw-r--r-- | rand/src/distributions/weighted/alias_method.rs | 499 |
1 files changed, 0 insertions, 499 deletions
diff --git a/rand/src/distributions/weighted/alias_method.rs b/rand/src/distributions/weighted/alias_method.rs deleted file mode 100644 index bdd4ba0..0000000 --- a/rand/src/distributions/weighted/alias_method.rs +++ /dev/null @@ -1,499 +0,0 @@ -//! This module contains an implementation of alias method for sampling random -//! indices with probabilities proportional to a collection of weights. - -use super::WeightedError; -#[cfg(not(feature = "std"))] -use crate::alloc::vec::Vec; -#[cfg(not(feature = "std"))] -use crate::alloc::vec; -use core::fmt; -use core::iter::Sum; -use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign}; -use crate::distributions::uniform::SampleUniform; -use crate::distributions::Distribution; -use crate::distributions::Uniform; -use crate::Rng; - -/// A distribution using weighted sampling to pick a discretely selected item. -/// -/// Sampling a [`WeightedIndex<W>`] distribution returns the index of a randomly -/// selected element from the vector used to create the [`WeightedIndex<W>`]. -/// The chance of a given element being picked is proportional to the value of -/// the element. The weights can have any type `W` for which a implementation of -/// [`Weight`] exists. -/// -/// # Performance -/// -/// Given that `n` is the number of items in the vector used to create an -/// [`WeightedIndex<W>`], [`WeightedIndex<W>`] will require `O(n)` amount of -/// memory. More specifically it takes up some constant amount of memory plus -/// the vector used to create it and a [`Vec<u32>`] with capacity `n`. -/// -/// Time complexity for the creation of a [`WeightedIndex<W>`] is `O(n)`. -/// Sampling is `O(1)`, it makes a call to [`Uniform<u32>::sample`] and a call -/// to [`Uniform<W>::sample`]. -/// -/// # Example -/// -/// ``` -/// use rand::distributions::weighted::alias_method::WeightedIndex; -/// use rand::prelude::*; -/// -/// let choices = vec!['a', 'b', 'c']; -/// let weights = vec![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).collect()).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); -/// } -/// ``` -/// -/// [`WeightedIndex<W>`]: crate::distributions::weighted::alias_method::WeightedIndex -/// [`Weight`]: crate::distributions::weighted::alias_method::Weight -/// [`Vec<u32>`]: Vec -/// [`Uniform<u32>::sample`]: Distribution::sample -/// [`Uniform<W>::sample`]: Distribution::sample -pub struct WeightedIndex<W: Weight> { - aliases: Vec<u32>, - no_alias_odds: Vec<W>, - uniform_index: Uniform<u32>, - uniform_within_weight_sum: Uniform<W>, -} - -impl<W: Weight> WeightedIndex<W> { - /// Creates a new [`WeightedIndex`]. - /// - /// Returns an error if: - /// - The vector is empty. - /// - The vector is longer than `u32::MAX`. - /// - For any weight `w`: `w < 0` or `w > max` where `max = W::MAX / - /// weights.len()`. - /// - The sum of weights is zero. - pub fn new(weights: Vec<W>) -> Result<Self, WeightedError> { - let n = weights.len(); - if n == 0 { - return Err(WeightedError::NoItem); - } else if n > ::core::u32::MAX as usize { - return Err(WeightedError::TooMany); - } - let n = n as u32; - - let max_weight_size = W::try_from_u32_lossy(n) - .map(|n| W::MAX / n) - .unwrap_or(W::ZERO); - if !weights - .iter() - .all(|&w| W::ZERO <= w && w <= max_weight_size) - { - return Err(WeightedError::InvalidWeight); - } - - // The sum of weights will represent 100% of no alias odds. - let weight_sum = Weight::sum(weights.as_slice()); - // Prevent floating point overflow due to rounding errors. - let weight_sum = if weight_sum > W::MAX { - W::MAX - } else { - weight_sum - }; - if weight_sum == W::ZERO { - return Err(WeightedError::AllWeightsZero); - } - - // `weight_sum` would have been zero if `try_from_lossy` causes an error here. - let n_converted = W::try_from_u32_lossy(n).unwrap(); - - let mut no_alias_odds = weights; - for odds in no_alias_odds.iter_mut() { - *odds *= n_converted; - // Prevent floating point overflow due to rounding errors. - *odds = if *odds > W::MAX { W::MAX } else { *odds }; - } - - /// This struct is designed to contain three data structures at once, - /// sharing the same memory. More precisely it contains two linked lists - /// and an alias map, which will be the output of this method. To keep - /// the three data structures from getting in each other's way, it must - /// be ensured that a single index is only ever in one of them at the - /// same time. - struct Aliases { - aliases: Vec<u32>, - smalls_head: u32, - bigs_head: u32, - } - - impl Aliases { - fn new(size: u32) -> Self { - Aliases { - aliases: vec![0; size as usize], - smalls_head: ::core::u32::MAX, - bigs_head: ::core::u32::MAX, - } - } - - fn push_small(&mut self, idx: u32) { - self.aliases[idx as usize] = self.smalls_head; - self.smalls_head = idx; - } - - fn push_big(&mut self, idx: u32) { - self.aliases[idx as usize] = self.bigs_head; - self.bigs_head = idx; - } - - fn pop_small(&mut self) -> u32 { - let popped = self.smalls_head; - self.smalls_head = self.aliases[popped as usize]; - popped - } - - fn pop_big(&mut self) -> u32 { - let popped = self.bigs_head; - self.bigs_head = self.aliases[popped as usize]; - popped - } - - fn smalls_is_empty(&self) -> bool { - self.smalls_head == ::core::u32::MAX - } - - fn bigs_is_empty(&self) -> bool { - self.bigs_head == ::core::u32::MAX - } - - fn set_alias(&mut self, idx: u32, alias: u32) { - self.aliases[idx as usize] = alias; - } - } - - let mut aliases = Aliases::new(n); - - // Split indices into those with small weights and those with big weights. - for (index, &odds) in no_alias_odds.iter().enumerate() { - if odds < weight_sum { - aliases.push_small(index as u32); - } else { - aliases.push_big(index as u32); - } - } - - // Build the alias map by finding an alias with big weight for each index with - // small weight. - while !aliases.smalls_is_empty() && !aliases.bigs_is_empty() { - let s = aliases.pop_small(); - let b = aliases.pop_big(); - - aliases.set_alias(s, b); - no_alias_odds[b as usize] = no_alias_odds[b as usize] - - weight_sum - + no_alias_odds[s as usize]; - - if no_alias_odds[b as usize] < weight_sum { - aliases.push_small(b); - } else { - aliases.push_big(b); - } - } - - // The remaining indices should have no alias odds of about 100%. This is due to - // numeric accuracy. Otherwise they would be exactly 100%. - while !aliases.smalls_is_empty() { - no_alias_odds[aliases.pop_small() as usize] = weight_sum; - } - while !aliases.bigs_is_empty() { - no_alias_odds[aliases.pop_big() as usize] = weight_sum; - } - - // Prepare distributions for sampling. Creating them beforehand improves - // sampling performance. - let uniform_index = Uniform::new(0, n); - let uniform_within_weight_sum = Uniform::new(W::ZERO, weight_sum); - - Ok(Self { - aliases: aliases.aliases, - no_alias_odds, - uniform_index, - uniform_within_weight_sum, - }) - } -} - -impl<W: Weight> Distribution<usize> for WeightedIndex<W> { - fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> usize { - let candidate = rng.sample(self.uniform_index); - if rng.sample(&self.uniform_within_weight_sum) < self.no_alias_odds[candidate as usize] { - candidate as usize - } else { - self.aliases[candidate as usize] as usize - } - } -} - -impl<W: Weight> fmt::Debug for WeightedIndex<W> -where - W: fmt::Debug, - Uniform<W>: fmt::Debug, -{ - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - f.debug_struct("WeightedIndex") - .field("aliases", &self.aliases) - .field("no_alias_odds", &self.no_alias_odds) - .field("uniform_index", &self.uniform_index) - .field("uniform_within_weight_sum", &self.uniform_within_weight_sum) - .finish() - } -} - -impl<W: Weight> Clone for WeightedIndex<W> -where - Uniform<W>: Clone, -{ - fn clone(&self) -> Self { - Self { - aliases: self.aliases.clone(), - no_alias_odds: self.no_alias_odds.clone(), - uniform_index: self.uniform_index.clone(), - uniform_within_weight_sum: self.uniform_within_weight_sum.clone(), - } - } -} - -/// Trait that must be implemented for weights, that are used with -/// [`WeightedIndex`]. Currently no guarantees on the correctness of -/// [`WeightedIndex`] are given for custom implementations of this trait. -pub trait Weight: - Sized - + Copy - + SampleUniform - + PartialOrd - + Add<Output = Self> - + AddAssign - + Sub<Output = Self> - + SubAssign - + Mul<Output = Self> - + MulAssign - + Div<Output = Self> - + DivAssign - + Sum -{ - /// Maximum number representable by `Self`. - const MAX: Self; - - /// Element of `Self` equivalent to 0. - const ZERO: Self; - - /// Produce an instance of `Self` from a `u32` value, or return `None` if - /// out of range. Loss of precision (where `Self` is a floating point type) - /// is acceptable. - fn try_from_u32_lossy(n: u32) -> Option<Self>; - - /// Sums all values in slice `values`. - fn sum(values: &[Self]) -> Self { - values.iter().map(|x| *x).sum() - } -} - -macro_rules! impl_weight_for_float { - ($T: ident) => { - impl Weight for $T { - const MAX: Self = ::core::$T::MAX; - const ZERO: Self = 0.0; - - fn try_from_u32_lossy(n: u32) -> Option<Self> { - Some(n as $T) - } - - fn sum(values: &[Self]) -> Self { - pairwise_sum(values) - } - } - }; -} - -/// In comparison to naive accumulation, the pairwise sum algorithm reduces -/// rounding errors when there are many floating point values. -fn pairwise_sum<T: Weight>(values: &[T]) -> T { - if values.len() <= 32 { - values.iter().map(|x| *x).sum() - } else { - let mid = values.len() / 2; - let (a, b) = values.split_at(mid); - pairwise_sum(a) + pairwise_sum(b) - } -} - -macro_rules! impl_weight_for_int { - ($T: ident) => { - impl Weight for $T { - const MAX: Self = ::core::$T::MAX; - const ZERO: Self = 0; - - fn try_from_u32_lossy(n: u32) -> Option<Self> { - let n_converted = n as Self; - if n_converted >= Self::ZERO && n_converted as u32 == n { - Some(n_converted) - } else { - None - } - } - } - }; -} - -impl_weight_for_float!(f64); -impl_weight_for_float!(f32); -impl_weight_for_int!(usize); -#[cfg(not(target_os = "emscripten"))] -impl_weight_for_int!(u128); -impl_weight_for_int!(u64); -impl_weight_for_int!(u32); -impl_weight_for_int!(u16); -impl_weight_for_int!(u8); -impl_weight_for_int!(isize); -#[cfg(not(target_os = "emscripten"))] -impl_weight_for_int!(i128); -impl_weight_for_int!(i64); -impl_weight_for_int!(i32); -impl_weight_for_int!(i16); -impl_weight_for_int!(i8); - -#[cfg(test)] -mod test { - use super::*; - - #[test] - #[cfg(not(miri))] // Miri is too slow - fn test_weighted_index_f32() { - test_weighted_index(f32::into); - - // Floating point special cases - assert_eq!( - WeightedIndex::new(vec![::core::f32::INFINITY]).unwrap_err(), - WeightedError::InvalidWeight - ); - assert_eq!( - WeightedIndex::new(vec![-0_f32]).unwrap_err(), - WeightedError::AllWeightsZero - ); - assert_eq!( - WeightedIndex::new(vec![-1_f32]).unwrap_err(), - WeightedError::InvalidWeight - ); - assert_eq!( - WeightedIndex::new(vec![-::core::f32::INFINITY]).unwrap_err(), - WeightedError::InvalidWeight - ); - assert_eq!( - WeightedIndex::new(vec![::core::f32::NAN]).unwrap_err(), - WeightedError::InvalidWeight - ); - } - - #[cfg(not(target_os = "emscripten"))] - #[test] - #[cfg(not(miri))] // Miri is too slow - fn test_weighted_index_u128() { - test_weighted_index(|x: u128| x as f64); - } - - #[cfg(all(rustc_1_26, not(target_os = "emscripten")))] - #[test] - #[cfg(not(miri))] // Miri is too slow - fn test_weighted_index_i128() { - test_weighted_index(|x: i128| x as f64); - - // Signed integer special cases - assert_eq!( - WeightedIndex::new(vec![-1_i128]).unwrap_err(), - WeightedError::InvalidWeight - ); - assert_eq!( - WeightedIndex::new(vec![::core::i128::MIN]).unwrap_err(), - WeightedError::InvalidWeight - ); - } - - #[test] - #[cfg(not(miri))] // Miri is too slow - fn test_weighted_index_u8() { - test_weighted_index(u8::into); - } - - #[test] - #[cfg(not(miri))] // Miri is too slow - fn test_weighted_index_i8() { - test_weighted_index(i8::into); - - // Signed integer special cases - assert_eq!( - WeightedIndex::new(vec![-1_i8]).unwrap_err(), - WeightedError::InvalidWeight - ); - assert_eq!( - WeightedIndex::new(vec![::core::i8::MIN]).unwrap_err(), - WeightedError::InvalidWeight - ); - } - - fn test_weighted_index<W: Weight, F: Fn(W) -> f64>(w_to_f64: F) - where - WeightedIndex<W>: fmt::Debug, - { - const NUM_WEIGHTS: u32 = 10; - const ZERO_WEIGHT_INDEX: u32 = 3; - const NUM_SAMPLES: u32 = 15000; - let mut rng = crate::test::rng(0x9c9fa0b0580a7031); - - let weights = { - let mut weights = Vec::with_capacity(NUM_WEIGHTS as usize); - let random_weight_distribution = crate::distributions::Uniform::new_inclusive( - W::ZERO, - W::MAX / W::try_from_u32_lossy(NUM_WEIGHTS).unwrap(), - ); - for _ in 0..NUM_WEIGHTS { - weights.push(rng.sample(&random_weight_distribution)); - } - weights[ZERO_WEIGHT_INDEX as usize] = W::ZERO; - weights - }; - let weight_sum = weights.iter().map(|w| *w).sum::<W>(); - let expected_counts = weights - .iter() - .map(|&w| w_to_f64(w) / w_to_f64(weight_sum) * NUM_SAMPLES as f64) - .collect::<Vec<f64>>(); - let weight_distribution = WeightedIndex::new(weights).unwrap(); - - let mut counts = vec![0; NUM_WEIGHTS as usize]; - for _ in 0..NUM_SAMPLES { - counts[rng.sample(&weight_distribution)] += 1; - } - - assert_eq!(counts[ZERO_WEIGHT_INDEX as usize], 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!( - WeightedIndex::<W>::new(vec![]).unwrap_err(), - WeightedError::NoItem - ); - assert_eq!( - WeightedIndex::new(vec![W::ZERO]).unwrap_err(), - WeightedError::AllWeightsZero - ); - assert_eq!( - WeightedIndex::new(vec![W::MAX, W::MAX]).unwrap_err(), - WeightedError::InvalidWeight - ); - } -} |