From 462daaffd5ec720ed80a2e7b1f445a73cabf5833 Mon Sep 17 00:00:00 2001
From: Tavian Barnes <tavianator@tavianator.com>
Date: Sun, 19 Apr 2020 16:59:24 -0400
Subject: metric/approx: Implement approximate nearest neighbor search

---
 src/metric.rs        |   1 +
 src/metric/approx.rs | 131 +++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 132 insertions(+)
 create mode 100644 src/metric/approx.rs

diff --git a/src/metric.rs b/src/metric.rs
index b46c8da..268aefd 100644
--- a/src/metric.rs
+++ b/src/metric.rs
@@ -1,5 +1,6 @@
 //! [Metric spaces](https://en.wikipedia.org/wiki/Metric_space).
 
+pub mod approx;
 pub mod forest;
 pub mod kd;
 pub mod soft;
diff --git a/src/metric/approx.rs b/src/metric/approx.rs
new file mode 100644
index 0000000..c23f9c7
--- /dev/null
+++ b/src/metric/approx.rs
@@ -0,0 +1,131 @@
+//! [Approximate nearest neighbor search](https://en.wikipedia.org/wiki/Nearest_neighbor_search#Approximate_nearest_neighbor).
+
+use super::{Metric, NearestNeighbors, Neighborhood};
+
+/// An approximate [Neighborhood], for approximate nearest neighbor searches.
+#[derive(Debug)]
+struct ApproximateNeighborhood<N> {
+    inner: N,
+    ratio: f64,
+    limit: usize,
+}
+
+impl<N> ApproximateNeighborhood<N> {
+    fn new(inner: N, ratio: f64, limit: usize) -> Self {
+        Self {
+            inner,
+            ratio,
+            limit,
+        }
+    }
+}
+
+impl<T, U, N> Neighborhood<T, U> for ApproximateNeighborhood<N>
+where
+    U: Metric<T>,
+    N: Neighborhood<T, U>,
+{
+    fn target(&self) -> U {
+        self.inner.target()
+    }
+
+    fn contains(&self, distance: f64) -> bool {
+        if self.limit > 0 {
+            self.inner.contains(self.ratio * distance)
+        } else {
+            false
+        }
+    }
+
+    fn contains_distance(&self, distance: U::Distance) -> bool {
+        self.contains(self.ratio * distance.into())
+    }
+
+    fn consider(&mut self, item: T) -> U::Distance {
+        self.limit = self.limit.saturating_sub(1);
+        self.inner.consider(item)
+    }
+}
+
+/// An [approximate nearest neighbor search](https://en.wikipedia.org/wiki/Nearest_neighbor_search#Approximate_nearest_neighbor)
+/// index.
+///
+/// This wrapper converts an exact nearest neighbor search algorithm into an approximate one by
+/// modifying the behavior of [Neighborhood::contains].  The approximation is controlled by two
+/// parameters:
+///
+/// * `ratio`: The [nearest neighbor distance ratio](https://en.wikipedia.org/wiki/Nearest_neighbor_search#Nearest_neighbor_distance_ratio),
+///   which controls how much closer new candidates must be to be considered.  For example, a ratio
+///   of 2.0 means that a neighbor must be less than half of the current threshold away to be
+///   considered.  A ratio of 1.0 means an exact search.
+///
+/// * `limit`: A limit on the number of candidates to consider.  Typical nearest neighbor algorithms
+///   find a close match quickly, so setting a limit bounds the worst-case search time while keeping
+///   good accuracy.
+#[derive(Debug)]
+pub struct ApproximateSearch<T> {
+    inner: T,
+    ratio: f64,
+    limit: usize,
+}
+
+impl<T> ApproximateSearch<T> {
+    /// Create a new ApproximateSearch index.
+    ///
+    /// * `inner`: The [NearestNeighbors] implementation to wrap.
+    /// * `ratio`: The nearest neighbor distance ratio.
+    /// * `limit`: The maximum number of results to consider.
+    pub fn new(inner: T, ratio: f64, limit: usize) -> Self {
+        Self {
+            inner,
+            ratio,
+            limit,
+        }
+    }
+}
+
+impl<T, U, V> NearestNeighbors<T, U> for ApproximateSearch<V>
+where
+    U: Metric<T>,
+    V: NearestNeighbors<T, U>,
+{
+    fn search<'a, 'b, N>(&'a self, neighborhood: N) -> N
+    where
+        T: 'a,
+        U: 'b,
+        N: Neighborhood<&'a T, &'b U>,
+    {
+        self.inner
+            .search(ApproximateNeighborhood::new(
+                neighborhood,
+                self.ratio,
+                self.limit,
+            ))
+            .inner
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    use crate::metric::kd::KdTree;
+    use crate::metric::tests::test_nearest_neighbors;
+    use crate::metric::vp::VpTree;
+
+    use std::iter::FromIterator;
+
+    #[test]
+    fn test_approx_kd_tree() {
+        test_nearest_neighbors(|iter| {
+            ApproximateSearch::new(KdTree::from_iter(iter), 1.0, std::usize::MAX)
+        });
+    }
+
+    #[test]
+    fn test_approx_vp_tree() {
+        test_nearest_neighbors(|iter| {
+            ApproximateSearch::new(VpTree::from_iter(iter), 1.0, std::usize::MAX)
+        });
+    }
+}
-- 
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