From d30c8b9dd7524ad34892352617fd81ba4f8d10d6 Mon Sep 17 00:00:00 2001
From: Tavian Barnes <tavianator@tavianator.com>
Date: Wed, 24 Jun 2020 11:03:31 -0400
Subject: lp: Implement general L^p spaces

---
 src/lib.rs |  1 +
 src/lp.rs  | 58 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 59 insertions(+)
 create mode 100644 src/lp.rs

diff --git a/src/lib.rs b/src/lib.rs
index 0bbd835..43d9bf1 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -97,6 +97,7 @@ pub mod euclid;
 pub mod exhaustive;
 pub mod hamming;
 pub mod kd;
+pub mod lp;
 pub mod taxi;
 pub mod vp;
 
diff --git a/src/lp.rs b/src/lp.rs
new file mode 100644
index 0000000..cf65944
--- /dev/null
+++ b/src/lp.rs
@@ -0,0 +1,58 @@
+//! L<sup>p</sup> spaces.
+
+use crate::coords::Coordinates;
+
+use num_traits::real::Real;
+use num_traits::zero;
+
+/// A point in L<sup>1</sup> space.
+pub use crate::taxi::Taxicab as L1;
+
+/// Compute the L<sup>1</sup> distance between two points.
+pub use crate::taxi::taxicab_distance as l1_distance;
+
+/// A point in L<sup>2</sup> space.
+pub use crate::euclid::Euclidean as L2;
+/// An L<sup>2</sup> distance.
+pub use crate::euclid::EuclideanDistance as L2Distance;
+
+/// Compute the L<sup>2</sup> distance between two points.
+pub use crate::euclid::euclidean_distance as l2_distance;
+
+/// A point in L<sup>∞</sup> space.
+pub use crate::chebyshev::Chebyshev as Linf;
+
+/// Compute the L<sup>∞</sup> distance between two points.
+pub use crate::chebyshev::chebyshev_distance as linf_distance;
+
+/// Compute the [L<sup>p</sup> distance] between two points.
+///
+/// [L<sup>p</sup> distance]: https://en.wikipedia.org/wiki/Lp_space
+pub fn lp_distance<T, U>(p: T::Value, x: T, y: U) -> T::Value
+where
+    T: Coordinates,
+    U: Coordinates<Value = T::Value>,
+    T::Value: Real,
+{
+    debug_assert!(x.dims() == y.dims());
+
+    let mut sum: T::Value = zero();
+    for i in 0..x.dims() {
+        sum += (x.coord(i) - y.coord(i)).abs().powf(p);
+    }
+
+    sum.powf(p.recip())
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_lp_distance() {
+        assert_eq!(l1_distance(&[0.0, 0.0], &[3.0, 4.0]), 7.0);
+        assert_eq!(l2_distance(&[0.0, 0.0], &[3.0, 4.0]), 5.0);
+        assert!(lp_distance(3.0, &[0.0, 0.0], &[3.0, 4.0]) < 5.0);
+        assert_eq!(linf_distance(&[0.0, 0.0], &[3.0, 4.0]), 4.0);
+    }
+}
-- 
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