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//! [k-d trees](https://en.wikipedia.org/wiki/K-d_tree).
use super::{Metric, NearestNeighbors, Neighborhood};
use ordered_float::OrderedFloat;
use std::iter::FromIterator;
/// A point in Cartesian space.
pub trait Cartesian: Metric<[f64]> {
/// Returns the number of dimensions necessary to describe this point.
fn dimensions(&self) -> usize;
/// Returns the value of the `i`th coordinate of this point (`i < self.dimensions()`).
fn coordinate(&self, i: usize) -> f64;
}
/// Blanket [Cartesian] implementation for references.
impl<'a, T: Cartesian> Cartesian for &'a T {
fn dimensions(&self) -> usize {
(*self).dimensions()
}
fn coordinate(&self, i: usize) -> f64 {
(*self).coordinate(i)
}
}
/// Blanket [Metric<[f64]>](Metric) implementation for [Cartesian] references.
impl<'a, T: Cartesian> Metric<[f64]> for &'a T {
type Distance = T::Distance;
fn distance(&self, other: &[f64]) -> Self::Distance {
(*self).distance(other)
}
}
/// Standard cartesian space.
impl Cartesian for [f64] {
fn dimensions(&self) -> usize {
self.len()
}
fn coordinate(&self, i: usize) -> f64 {
self[i]
}
}
/// Marker trait for cartesian metric spaces.
pub trait CartesianMetric<T: ?Sized = Self>:
Cartesian + Metric<T, Distance = <Self as Metric<[f64]>>::Distance>
{
}
/// Blanket [CartesianMetric] implementation for cartesian spaces with compatible metric distance
/// types.
impl<T, U> CartesianMetric<T> for U
where
T: ?Sized,
U: ?Sized + Cartesian + Metric<T, Distance = <U as Metric<[f64]>>::Distance>,
{
}
/// A node in a k-d tree.
#[derive(Debug)]
struct KdNode<T> {
/// The value stored in this node.
item: T,
/// The size of the left subtree.
left_len: usize,
}
impl<T: Cartesian> KdNode<T> {
/// Create a new KdNode.
fn new(item: T) -> Self {
Self { item, left_len: 0 }
}
/// Build a k-d tree recursively.
fn build(slice: &mut [KdNode<T>], i: usize) {
if slice.is_empty() {
return;
}
slice.sort_unstable_by_key(|n| OrderedFloat::from(n.item.coordinate(i)));
let mid = slice.len() / 2;
slice.swap(0, mid);
let (node, children) = slice.split_first_mut().unwrap();
let (left, right) = children.split_at_mut(mid);
node.left_len = left.len();
let j = (i + 1) % node.item.dimensions();
Self::build(left, j);
Self::build(right, j);
}
/// Recursively search for nearest neighbors.
fn recurse<'a, U, N>(
slice: &'a [KdNode<T>],
i: usize,
closest: &mut [f64],
neighborhood: &mut N,
) where
T: 'a,
U: CartesianMetric<&'a T>,
N: Neighborhood<&'a T, U>,
{
let (node, children) = slice.split_first().unwrap();
neighborhood.consider(&node.item);
let target = neighborhood.target();
let ti = target.coordinate(i);
let ni = node.item.coordinate(i);
let j = (i + 1) % node.item.dimensions();
let (left, right) = children.split_at(node.left_len);
let (near, far) = if ti <= ni {
(left, right)
} else {
(right, left)
};
if !near.is_empty() {
Self::recurse(near, j, closest, neighborhood);
}
if !far.is_empty() {
let saved = closest[i];
closest[i] = ni;
if neighborhood.contains_distance(target.distance(closest)) {
Self::recurse(far, j, closest, neighborhood);
}
closest[i] = saved;
}
}
}
/// A [k-d tree](https://en.wikipedia.org/wiki/K-d_tree).
#[derive(Debug)]
pub struct KdTree<T>(Vec<KdNode<T>>);
impl<T: Cartesian> FromIterator<T> for KdTree<T> {
/// Create a new k-d tree from a set of points.
fn from_iter<I: IntoIterator<Item = T>>(items: I) -> Self {
let mut nodes: Vec<_> = items.into_iter().map(KdNode::new).collect();
KdNode::build(nodes.as_mut_slice(), 0);
Self(nodes)
}
}
impl<T, U> NearestNeighbors<T, U> for KdTree<T>
where
T: Cartesian,
U: CartesianMetric<T>,
{
fn search<'a, 'b, N>(&'a self, mut neighborhood: N) -> N
where
T: 'a,
U: 'b,
N: Neighborhood<&'a T, &'b U>,
{
if !self.0.is_empty() {
let target = neighborhood.target();
let dims = target.dimensions();
let mut closest: Vec<_> = (0..dims).map(|i| target.coordinate(i)).collect();
KdNode::recurse(&self.0, 0, &mut closest, &mut neighborhood);
}
neighborhood
}
}
/// An iterator that the moves values out of a k-d tree.
#[derive(Debug)]
pub struct IntoIter<T>(std::vec::IntoIter<KdNode<T>>);
impl<T> Iterator for IntoIter<T> {
type Item = T;
fn next(&mut self) -> Option<T> {
self.0.next().map(|n| n.item)
}
}
impl<T> IntoIterator for KdTree<T> {
type Item = T;
type IntoIter = IntoIter<T>;
fn into_iter(self) -> Self::IntoIter {
IntoIter(self.0.into_iter())
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::metric::tests::{test_nearest_neighbors, Point};
use crate::metric::SquaredDistance;
impl Metric<[f64]> for Point {
type Distance = SquaredDistance;
fn distance(&self, other: &[f64]) -> Self::Distance {
self.0.distance(other)
}
}
impl Cartesian for Point {
fn dimensions(&self) -> usize {
self.0.dimensions()
}
fn coordinate(&self, i: usize) -> f64 {
self.0.coordinate(i)
}
}
#[test]
fn test_kd_tree() {
test_nearest_neighbors(KdTree::from_iter);
}
}
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