Norms & Distances

Both StaticVector and DynamicVector expose a single norm() method: the Euclidean (L2) norm, ‖v‖ = sqrt(v . v), computed as the square root of the vector’s dot product with itself.

#![allow(unused)]
fn main() {
use rustebra::vector::StaticVector;

let v = StaticVector::new([3.0, 4.0]);
assert_eq!(v.norm(), 5.0);
}

There’s no separate distance method. The Euclidean distance between two vectors is just the norm of their difference, and falls out of the existing sub and norm operations:

#![allow(unused)]
fn main() {
use rustebra::vector::StaticVector;

let a = StaticVector::new([1.0, 2.0, 3.0]);
let b = StaticVector::new([4.0, 6.0, 3.0]);

let distance = a.sub(&b).norm();
assert_eq!(distance, 5.0);
}

For DynamicVector, sub returns a Result (two DynamicVectors aren’t guaranteed to match in length at compile time), so the equivalent distance computation is a.sub(&b)?.norm().

Gotchas

• norm() itself never fails or returns a Result — even on DynamicVector — since computing the norm of a single vector has no dimension-mismatch case to report. It’s sub/add/dot between two DynamicVectors that can fail.
• sqrt under the hood is Scalar::sqrt, a fixed-iteration approximation rather than a hardware intrinsic (see Scalars & Numeric Types) — norms of extremely large or small magnitude vectors may lose a little precision relative to f64::sqrt.