1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64

//! Norm of vectors

use ndarray::*;
use num_traits::Zero;

use super::types::*;

/// Define norm as a metric linear space (not as a matrix)
///
/// For operator norms, see opnorm module
pub trait Norm {
    type Output;
    /// rename of `norm_l2`
    fn norm(&self) -> Self::Output {
        self.norm_l2()
    }
    /// L-1 norm
    fn norm_l1(&self) -> Self::Output;
    /// L-2 norm
    fn norm_l2(&self) -> Self::Output;
    /// maximum norm
    fn norm_max(&self) -> Self::Output;
}

impl<A, S, D> Norm for ArrayBase<S, D>
where
    A: Scalar,
    S: Data<Elem = A>,
    D: Dimension,
{
    type Output = A::Real;
    fn norm_l1(&self) -> Self::Output {
        self.iter().map(|x| x.abs()).sum()
    }
    fn norm_l2(&self) -> Self::Output {
        self.iter().map(|x| x.squared()).sum::<A::Real>().sqrt()
    }
    fn norm_max(&self) -> Self::Output {
        self.iter().fold(A::Real::zero(), |f, &val| {
            let v = val.abs();
            if f > v { f } else { v }
        })
    }
}

pub enum NormalizeAxis {
    Row = 0,
    Column = 1,
}

/// normalize in L2 norm
pub fn normalize<A, S>(mut m: ArrayBase<S, Ix2>, axis: NormalizeAxis) -> (ArrayBase<S, Ix2>, Vec<A::Real>)
where
    A: Scalar,
    S: DataMut<Elem = A>,
{
    let mut ms = Vec::new();
    for mut v in m.axis_iter_mut(Axis(axis as usize)) {
        let n = v.norm();
        ms.push(n);
        v.map_inplace(|x| *x = x.div_real(n))
    }
    (m, ms)
}