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//! Norm of vectors

use std::ops::*;
use ndarray::*;

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, T> Norm for ArrayBase<S, D>
    where A: Field + Absolute<Output = T>,
          T: RealField,
          S: Data<Elem = A>,
          D: Dimension
{
    type Output = T;
    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::<T>().sqrt()
    }
    fn norm_max(&self) -> Self::Output {
        self.iter().fold(T::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, T>(mut m: ArrayBase<S, Ix2>, axis: NormalizeAxis) -> (ArrayBase<S, Ix2>, Vec<T>)
    where A: Field + Absolute<Output = T> + Div<T, Output = A>,
          S: DataMut<Elem = A>,
          T: RealField
{
    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 / n)
    }
    (m, ms)
}