85 lines
2.4 KiB
Rust
85 lines
2.4 KiB
Rust
//! # Minkowski Distance
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//!
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//! 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.
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//! The Manhattan distance between two points \\(x \in ℝ^n \\) and \\( y \in ℝ^n \\) in n-dimensional space is defined as:
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//!
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//! \\[ d(x, y) = \left(\sum_{i=0}^n \lvert x_i - y_i \rvert^p\right)^{1/p} \\]
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//!
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//! Example:
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//!
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//! ```
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//! use smartcore::math::distance::Distance;
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//! use smartcore::math::distance::minkowski::Minkowski;
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//!
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//! let x = vec![1., 1.];
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//! let y = vec![2., 2.];
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//!
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//! let l1: f64 = Minkowski { p: 1 }.distance(&x, &y);
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//! let l2: f64 = Minkowski { p: 2 }.distance(&x, &y);
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//!
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//! ```
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//! <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
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//! <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
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use serde::{Deserialize, Serialize};
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use crate::math::num::RealNumber;
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use super::Distance;
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/// Defines the Minkowski distance of order `p`
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#[derive(Serialize, Deserialize, Debug)]
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pub struct Minkowski {
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/// order, integer
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pub p: u16,
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}
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impl<T: RealNumber> Distance<Vec<T>, T> for Minkowski {
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fn distance(&self, x: &Vec<T>, y: &Vec<T>) -> T {
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if x.len() != y.len() {
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panic!("Input vector sizes are different");
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}
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if self.p < 1 {
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panic!("p must be at least 1");
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}
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let mut dist = T::zero();
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let p_t = T::from_u16(self.p).unwrap();
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for i in 0..x.len() {
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let d = (x[i] - y[i]).abs();
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dist += d.powf(p_t);
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}
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dist.powf(T::one() / p_t)
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn minkowski_distance() {
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let a = vec![1., 2., 3.];
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let b = vec![4., 5., 6.];
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let l1: f64 = Minkowski { p: 1 }.distance(&a, &b);
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let l2: f64 = Minkowski { p: 2 }.distance(&a, &b);
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let l3: f64 = Minkowski { p: 3 }.distance(&a, &b);
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assert!((l1 - 9.0).abs() < 1e-8);
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assert!((l2 - 5.19615242).abs() < 1e-8);
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assert!((l3 - 4.32674871).abs() < 1e-8);
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}
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#[test]
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#[should_panic(expected = "p must be at least 1")]
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fn minkowski_distance_negative_p() {
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let a = vec![1., 2., 3.];
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let b = vec![4., 5., 6.];
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let _: f64 = Minkowski { p: 0 }.distance(&a, &b);
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}
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}
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