# weighted_index.rs - source
Source of the Rust file `/home/key/.cargo/registry/src/github.com-1ecc6299db9ec823/rand-0.8.5/src/distributions/weighted_index.rs`.
Keywords: rust, rustlang, rust-lang

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    // 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.

    //! Weighted index sampling

    use crate::distributions::uniform::{SampleBorrow, SampleUniform, UniformSampler};
    use crate::distributions::Distribution;
    use crate::Rng;
    use core::cmp::PartialOrd;
    use core::fmt;

    // Note that this whole module is only imported if feature="alloc" is enabled.
    use alloc::vec::Vec;

    #[cfg(feature = "serde1")]
    use serde::{Serialize, Deserialize};

    /// A distribution using weighted sampling of discrete items
    ///
    /// 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
    ///
    /// Time complexity of sampling from `WeightedIndex` is `O(log N)` where
    /// `N` is the number of weights. As an alternative,
    /// [`rand_distr::weighted_alias`](https://docs.rs/rand_distr/*/rand_distr/weighted_alias/index.html)
    /// supports `O(1)` sampling, but with much higher initialisation cost.
    ///
    /// 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.
    ///
    /// 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 implementation 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
    /// [`RngCore`]: crate::RngCore
    #[derive(Debug, Clone, PartialEq)]
    #[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
    #[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
    pub struct WeightedIndex<X: SampleUniform + PartialOrd> {
        cumulative_weights: Vec<X>,
        total_weight: 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::InvalidWeight);
            }

            let mut weights = Vec::<X>::with_capacity(iter.size_hint().0);
            for w in iter {
                // Note that `!(w >= x)` is not equivalent to `w < x` for partially
                // ordered types due to NaNs which are equal to nothing.
                if !(w.borrow() >= &zero) {
                    return Err(WeightedError::InvalidWeight);
                }
                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.clone());

            Ok(WeightedIndex {
                cumulative_weights: weights,
                total_weight,
                weight_distribution: distr,
            })
        }

        /// Update a subset of weights, without changing the number of weights.
        ///
        /// `new_weights` must be sorted by the index.
        ///
        /// Using this method instead of `new` might be more efficient if only a small number of
        /// weights is modified. No allocations are performed, unless the weight type `X` uses
        /// allocation internally.
        ///
        /// In case of error, `self` is not modified.
        pub fn update_weights(&mut self, new_weights: &[(usize, &X)]) -> Result<(), WeightedError>
        where X: for<'a> ::core::ops::AddAssign<&'a X>
                + for<'a> ::core::ops::SubAssign<&'a X>
                + Clone
                + Default {
            if new_weights.is_empty() {
                return Ok(());
            }

            let zero = <X as Default>::default();

            let mut total_weight = self.total_weight.clone();

            // Check for errors first, so we don't modify `self` in case something
            // goes wrong.
            let mut prev_i = None;
            for &(i, w) in new_weights {
                if let Some(old_i) = prev_i {
                    if old_i >= i {
                        return Err(WeightedError::InvalidWeight);
                    }
                }
                if !(*w >= zero) {
                    return Err(WeightedError::InvalidWeight);
                }
                if i > self.cumulative_weights.len() {
                    return Err(WeightedError::TooMany);
                }

                let mut old_w = if i < self.cumulative_weights.len() {
                    self.cumulative_weights[i].clone()
                } else {
                    self.total_weight.clone()
                };
                if i > 0 {
                    old_w -= &self.cumulative_weights[i - 1];
                }

                total_weight -= &old_w;
                total_weight += w;
                prev_i = Some(i);
            }
            if total_weight <= zero {
                return Err(WeightedError::AllWeightsZero);
            }

            // Update the weights. Because we checked all the preconditions in the
            // previous loop, this should never panic.
            let mut iter = new_weights.iter();

            let mut prev_weight = zero.clone();
            let mut next_new_weight = iter.next();
            let &(first_new_index, _) = next_new_weight.unwrap();
            let mut cumulative_weight = if first_new_index > 0 {
                self.cumulative_weights[first_new_index - 1].clone()
            } else {
                zero.clone()
            };
            for i in first_new_index..self.cumulative_weights.len() {
                match next_new_weight {
                    Some(&(j, w)) if i == j => {
                        cumulative_weight += w;
                        next_new_weight = iter.next();
                    }
                    _ => {
                        let mut tmp = self.cumulative_weights[i].clone();
                        tmp -= &prev_weight; // We know this is positive.
                        cumulative_weight += &tmp;
                    }
                }
                prev_weight = cumulative_weight.clone();
                core::mem::swap(&mut prev_weight, &mut self.cumulative_weights[i]);
            }

            self.total_weight = total_weight;
            self.weight_distribution = X::Sampler::new(zero, self.total_weight.clone());

            Ok(())
        }
    }

    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()
        }
    }

    #[cfg(test)]
    mod test {
        use super::*;

        #[cfg(feature = "serde1")]
        #[test]
        fn test_weightedindex_serde1() {
            let weighted_index = WeightedIndex::new(&[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]).unwrap();

            let ser_weighted_index = bincode::serialize(&weighted_index).unwrap();
            let de_weighted_index: WeightedIndex<i32> =
                bincode::deserialize(&ser_weighted_index).unwrap();

            assert_eq!(
                de_weighted_index.cumulative_weights,
                weighted_index.cumulative_weights
            );
            assert_eq!(de_weighted_index.total_weight, weighted_index.total_weight);
        }

        #[test]
        fn test_accepting_nan(){
            assert_eq!(
                WeightedIndex::new(&[core::f32::NAN, 0.5]).unwrap_err(),
                WeightedError::InvalidWeight,
            );
            assert_eq!(
                WeightedIndex::new(&[core::f32::NAN]).unwrap_err(),
                WeightedError::InvalidWeight,
            );
            assert_eq!(
                WeightedIndex::new(&[0.5, core::f32::NAN]).unwrap_err(),
                WeightedError::InvalidWeight,
            );

            assert_eq!(
                WeightedIndex::new(&[0.5, 7.0])
                    .unwrap()
                    .update_weights(&[(0, &core::f32::NAN)])
                    .unwrap_err(),
                WeightedError::InvalidWeight,
            )
        }

        #[test]
        #[cfg_attr(miri, ignore)] // Miri is too slow
        fn test_weightedindex() {
            let mut r = crate::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::InvalidWeight
            );
            assert_eq!(
                WeightedIndex::new(&[-10, 20, 1, 30]).unwrap_err(),
                WeightedError::InvalidWeight
            );
            assert_eq!(
                WeightedIndex::new(&[-10]).unwrap_err(),
                WeightedError::InvalidWeight
            );
        }

        #[test]
        fn test_update_weights() {
            let data = [
                (
                    &[10u32, 2, 3, 4][..],
                    &[(1, &100), (2, &4)][..], // positive change
                    &[10, 100, 4, 4][..],
                ),
                (
                    &[1u32, 2, 3, 0, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7][..],
                    &[(2, &1), (5, &1), (13, &100)][..], // negative change and last element
                    &[1u32, 2, 1, 0, 5, 1, 7, 1, 2, 3, 4, 5, 6, 100][..],
                ),
            ];

            for (weights, update, expected_weights) in data.iter() {
                let total_weight = weights.iter().sum::<u32>();
                let mut distr = WeightedIndex::new(weights.to_vec()).unwrap();
                assert_eq!(distr.total_weight, total_weight);

                distr.update_weights(update).unwrap();
                let expected_total_weight = expected_weights.iter().sum::<u32>();
                let expected_distr = WeightedIndex::new(expected_weights.to_vec()).unwrap();
                assert_eq!(distr.total_weight, expected_total_weight);
                assert_eq!(distr.total_weight, expected_distr.total_weight);
                assert_eq!(distr.cumulative_weights, expected_distr.cumulative_weights);
            }
        }

        #[test]
        fn value_stability() {
            fn test_samples<X: SampleUniform + PartialOrd, I>(
                weights: I, buf: &mut [usize], expected: &[usize],
            ) where
                I: IntoIterator,
                I::Item: SampleBorrow<X>,
                X: for<'a> ::core::ops::AddAssign<&'a X> + Clone + Default,
            {
                assert_eq!(buf.len(), expected.len());
                let distr = WeightedIndex::new(weights).unwrap();
                let mut rng = crate::test::rng(701);
                for r in buf.iter_mut() {
                    *r = rng.sample(&distr);
                }
                assert_eq!(buf, expected);
            }

            let mut buf = [0; 10];
            test_samples(&[1i32, 1, 1, 1, 1, 1, 1, 1, 1], &mut buf, &[
                0, 6, 2, 6, 3, 4, 7, 8, 2, 5,
            ]);
            test_samples(&[0.7f32, 0.1, 0.1, 0.1], &mut buf, &[
                0, 0, 0, 1, 0, 0, 2, 3, 0, 0,
            ]);
            test_samples(&[1.0f64, 0.999, 0.998, 0.997], &mut buf, &[
                2, 2, 1, 3, 2, 1, 3, 3, 2, 1,
            ]);
        }

        #[test]
        fn weighted_index_distributions_can_be_compared() {
            assert_eq!(WeightedIndex::new(&[1, 2]), WeightedIndex::new(&[1, 2]));
        }
    }

    /// Error type returned from `WeightedIndex::new`.
    #[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
    #[derive(Debug, Clone, Copy, PartialEq, Eq)]
    pub enum WeightedError {
        /// The provided weight collection contains no items.
        NoItem,

        /// A weight is either less than zero, greater than the supported maximum,
        /// NaN, or otherwise invalid.
        InvalidWeight,

        /// All items in the provided weight collection are zero.
        AllWeightsZero,

        /// Too many weights are provided (length greater than `u32::MAX`)
        TooMany,
    }

    #[cfg(feature = "std")]
    impl std::error::Error for WeightedError {}

    impl fmt::Display for WeightedError {
        fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
            f.write_str(match *self {
                WeightedError::NoItem => "No weights provided in distribution",
                WeightedError::InvalidWeight => "A weight is invalid in distribution",
                WeightedError::AllWeightsZero => "All weights are zero in distribution",
                WeightedError::TooMany => "Too many weights (hit u32::MAX) in distribution",
            })
        }
    }