src/distributions/weighted/mod.rs - third_party/rust-mirrors/rand - Git at Google

 // 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
 //!
 //! This module provides two implementations for sampling indices:
 //!
 //! *   [`WeightedIndex`] allows `O(log N)` sampling
 //! *   [`alias_method::WeightedIndex`] allows `O(1)` sampling, but with
 //!      much greater set-up cost
 //!
 //! [`alias_method::WeightedIndex`]: alias_method/struct.WeightedIndex.html

 pub mod alias_method;

 use crate::Rng;
 use crate::distributions::Distribution;
 use crate::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 crate::alloc::vec::Vec;

 /// 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`]: crate::RngCore
 #[derive(Debug, Clone)]
 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 {
             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() + 1 {
                 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::*;

     #[test]
     #[cfg(not(miri))] // 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.into_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);
         }
     }
 }

 /// Error type returned from `WeightedIndex::new`.
 #[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 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,
 }

 impl WeightedError {
     fn msg(&self) -> &str {
         match *self {
             WeightedError::NoItem => "No weights provided.",
             WeightedError::InvalidWeight => "A weight is invalid.",
             WeightedError::AllWeightsZero => "All weights are zero.",
             WeightedError::TooMany => "Too many weights (hit u32::MAX)",
         }
     }
 }

 #[cfg(feature="std")]
 impl ::std::error::Error for WeightedError {
     fn description(&self) -> &str {
         self.msg()
     }
     fn cause(&self) -> Option<&dyn (::std::error::Error)> {
         None
     }
 }

 impl fmt::Display for WeightedError {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         write!(f, "{}", self.msg())
     }
 }
	// 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
	//!
	//! This module provides two implementations for sampling indices:
	//!
	//! * [`WeightedIndex`] allows `O(log N)` sampling
	//! * [`alias_method::WeightedIndex`] allows `O(1)` sampling, but with
	//! much greater set-up cost
	//!
	//! [`alias_method::WeightedIndex`]: alias_method/struct.WeightedIndex.html

	pub mod alias_method;

	use crate::Rng;
	use crate::distributions::Distribution;
	use crate::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 crate::alloc::vec::Vec;

	/// 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`]: crate::RngCore
	#[derive(Debug, Clone)]
	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 {
	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() + 1 {
	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::*;

	#[test]
	#[cfg(not(miri))] // 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.into_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);
	}
	}
	}

	/// Error type returned from `WeightedIndex::new`.
	#[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 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,
	}

	impl WeightedError {
	fn msg(&self) -> &str {
	match *self {
	WeightedError::NoItem => "No weights provided.",
	WeightedError::InvalidWeight => "A weight is invalid.",
	WeightedError::AllWeightsZero => "All weights are zero.",
	WeightedError::TooMany => "Too many weights (hit u32::MAX)",
	}
	}
	}

	#[cfg(feature="std")]
	impl ::std::error::Error for WeightedError {
	fn description(&self) -> &str {
	self.msg()
	}
	fn cause(&self) -> Option<&dyn (::std::error::Error)> {
	None
	}
	}

	impl fmt::Display for WeightedError {
	fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
	write!(f, "{}", self.msg())
	}
	}