faasle¹ is a Rust package for evaluating distances (metrics) between multidimensional arrays. It is designed to be simple, fast, and easy to use.

use faasle::{Distance, Euclidean}; use ndarray::{ArrayD, Axis}; let x = ArrayD::from_shape_vec(vec![2, 4], vec![0.0, 3.0, 3.0, 5.0, 11.0, 2.0, 0.0, 9.0]).unwrap(); let y = ArrayD::from_shape_vec(vec![2, 4], vec![9.0, 2.0, 2.0, 1.0, 9.0, 5.0, 4.0, 7.0]).unwrap(); let metric = Euclidean::new(); let distance = metric.evaluate( & x, & y, Axis(1)).unwrap(); assert!(distance.abs_diff_eq( &ArrayD::from_shape_vec(vec![2], vec![9.9498743710662, 5.744562646538029]).unwrap(), 1e-6 ));

Mathematically, a distance metric is a function $d:\mathcal{X}\times\mathcal{X}\rightarrow\mathbb{R}$, where $\mathcal{X}$ is a set, such that they satisfy the following properties:

1. $d(x, y) \geq 0$ for all $x, y \in \mathcal{X}$,
2. $d(x, y) = 0$ if and only if $x = y$,

3. $d(x, y) = d(y, x)$ for all $x, y \in \mathcal{X}$,

4. $d(x, z) \leq d(x, y) + d(y, z)$ for all $x, y, z \in \mathcal{X}$.

The hierarchy of types and their properties are as follows:

@software{faasle2024github, author = {{M}eesum {Q}azalbash}, title = {{faasle}: Rust crate for evaluating distances (metrics).}, url = {https://github.com/Qazalbash/faasle}, version = {0.0.1}, year = {2024} }