linfa_linalg/
norm.rs

1//! Norm of vectors
2
3use ndarray::{prelude::*, Data};
4
5/// Define norm as a metric linear space, treating the whole matrix as one big vector.
6pub trait Norm {
7    type Output;
8
9    /// L-1 norm
10    fn norm_l1(&self) -> Self::Output;
11    /// L-2 norm
12    fn norm_l2(&self) -> Self::Output;
13    /// Maximum norm (L-infinite)
14    fn norm_max(&self) -> Self::Output;
15}
16
17impl<A, S, D> Norm for ArrayBase<S, D>
18where
19    A: NdFloat + std::iter::Sum,
20    S: Data<Elem = A>,
21    D: Dimension,
22{
23    type Output = A;
24
25    fn norm_l1(&self) -> Self::Output {
26        self.iter().map(|x| x.abs()).sum()
27    }
28
29    fn norm_l2(&self) -> Self::Output {
30        self.iter().map(|&x| x * x).sum::<A>().sqrt()
31    }
32
33    fn norm_max(&self) -> Self::Output {
34        self.iter().fold(A::zero(), |f, &val| val.abs().max(f))
35    }
36}
37
38#[cfg(test)]
39mod tests {
40    use approx::assert_abs_diff_eq;
41
42    use super::*;
43
44    #[test]
45    fn norms() {
46        let a = array![[1.0f64, -3.], [2., -8.]];
47        assert_abs_diff_eq!(a.norm_l1(), 14.);
48        assert_abs_diff_eq!(a.norm_l2(), 78.0f64.sqrt());
49        assert_abs_diff_eq!(a.norm_max(), 8.);
50    }
51}
linfa_linalg/norm.rs

linfa_linalg/
norm.rs
