Module smartcore::math::distance::minkowski

A generalization of both the Euclidean distance and the Manhattan distance.

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);

Structs

Minkowski

Defines the Minkowski distance of order p