84 lines
2.3 KiB
Rust
84 lines
2.3 KiB
Rust
//! # Minkowski Distance
|
||
//!
|
||
//! The Minkowski distance of order _p_ (where _p_ is an integer) is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance.
|
||
//! The Manhattan distance between two points \\(x \in ℝ^n \\) and \\( y \in ℝ^n \\) in n-dimensional space is defined as:
|
||
//!
|
||
//! \\[ d(x, y) = \left(\sum_{i=0}^n \lvert x_i - y_i \rvert^p\right)^{1/p} \\]
|
||
//!
|
||
//! Example:
|
||
//!
|
||
//! ```
|
||
//! use smartcore::math::distance::Distance;
|
||
//! use smartcore::math::distance::minkowski::Minkowski;
|
||
//!
|
||
//! let x = vec![1., 1.];
|
||
//! let y = vec![2., 2.];
|
||
//!
|
||
//! let l1: f64 = Minkowski { p: 1 }.distance(&x, &y);
|
||
//! let l2: f64 = Minkowski { p: 2 }.distance(&x, &y);
|
||
//!
|
||
//! ```
|
||
//! <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_CHTML"></script>
|
||
|
||
use serde::{Deserialize, Serialize};
|
||
|
||
use crate::math::num::RealNumber;
|
||
|
||
use super::Distance;
|
||
|
||
/// Defines the Minkowski distance of order `p`
|
||
#[derive(Serialize, Deserialize, Debug)]
|
||
pub struct Minkowski {
|
||
/// order, integer
|
||
pub p: u16,
|
||
}
|
||
|
||
impl<T: RealNumber> Distance<Vec<T>, T> for Minkowski {
|
||
fn distance(&self, x: &Vec<T>, y: &Vec<T>) -> T {
|
||
if x.len() != y.len() {
|
||
panic!("Input vector sizes are different");
|
||
}
|
||
if self.p < 1 {
|
||
panic!("p must be at least 1");
|
||
}
|
||
|
||
let mut dist = T::zero();
|
||
let p_t = T::from_u16(self.p).unwrap();
|
||
|
||
for i in 0..x.len() {
|
||
let d = (x[i] - y[i]).abs();
|
||
dist = dist + d.powf(p_t);
|
||
}
|
||
|
||
dist.powf(T::one() / p_t)
|
||
}
|
||
}
|
||
|
||
#[cfg(test)]
|
||
mod tests {
|
||
use super::*;
|
||
|
||
#[test]
|
||
fn minkowski_distance() {
|
||
let a = vec![1., 2., 3.];
|
||
let b = vec![4., 5., 6.];
|
||
|
||
let l1: f64 = Minkowski { p: 1 }.distance(&a, &b);
|
||
let l2: f64 = Minkowski { p: 2 }.distance(&a, &b);
|
||
let l3: f64 = Minkowski { p: 3 }.distance(&a, &b);
|
||
|
||
assert!((l1 - 9.0).abs() < 1e-8);
|
||
assert!((l2 - 5.19615242).abs() < 1e-8);
|
||
assert!((l3 - 4.32674871).abs() < 1e-8);
|
||
}
|
||
|
||
#[test]
|
||
#[should_panic(expected = "p must be at least 1")]
|
||
fn minkowski_distance_negative_p() {
|
||
let a = vec![1., 2., 3.];
|
||
let b = vec![4., 5., 6.];
|
||
|
||
let _: f64 = Minkowski { p: 0 }.distance(&a, &b);
|
||
}
|
||
}
|