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use num::{Float, Zero};
use std::iter::Sum;
use std::ops::Mul;
#[inline(always)]
pub fn inner_product<T>(a: &[T], b: &[T]) -> T
where
T: Float + Sum<T> + Mul<T, Output = T>,
{
assert!(a.len() == b.len());
a.iter().zip(b.iter()).map(|(x, y)| (*x) * (*y)).sum()
}
#[inline(always)]
pub fn norm1<T>(a: &[T]) -> T
where
T: Float + Sum<T>,
{
a.iter().map(|x| x.abs()).sum()
}
#[inline(always)]
pub fn norm2<T>(a: &[T]) -> T
where
T: Float + Sum<T> + Mul<T, Output = T>,
{
let norm: T = norm2_squared(a);
norm.sqrt()
}
#[inline(always)]
pub fn norm2_squared_diff<T>(a: &[T], b: &[T]) -> T
where
T: Float + Sum<T> + Mul<T, Output = T> + std::ops::AddAssign,
{
a.iter().zip(b.iter()).fold(T::zero(), |mut sum, (&x, &y)| {
sum += (x - y).powi(2);
sum
})
}
#[inline(always)]
pub fn norm2_squared<T>(a: &[T]) -> T
where
T: Float + Sum<T> + Mul<T, Output = T>,
{
let norm: T = a.iter().map(|x| (*x) * (*x)).sum();
norm
}
#[inline(always)]
pub fn norm_inf<T>(a: &[T]) -> T
where
T: Float + Zero,
{
a.iter()
.fold(T::zero(), |current_max, x| x.abs().max(current_max))
}
#[inline(always)]
pub fn norm_inf_diff<T>(a: &[T], b: &[T]) -> T
where
T: Float + Zero,
{
assert_eq!(a.len(), b.len());
a.iter()
.zip(b.iter())
.fold(T::zero(), |current_max, (x, y)| {
(*x - *y).abs().max(current_max)
})
}
#[cfg(test)]
mod tests {
use crate::*;
#[test]
fn t_inner_product_test() {
assert_eq!(
matrix_operations::inner_product(&vec![1.0, 2.0, 3.0], &vec![1.0, 2.0, 3.0]),
14.0
);
}
#[test]
#[should_panic]
fn t_inner_product_test_panic() {
matrix_operations::inner_product(&vec![2.0, 3.0], &vec![1.0, 2.0, 3.0]);
}
#[test]
fn t_norm1_test() {
assert_eq!(matrix_operations::norm1(&vec![1.0, -2.0, -3.0]), 6.0);
}
#[test]
fn t_norm2_test() {
assert_eq!(matrix_operations::norm2(&vec![3.0, 4.0]), 5.0);
}
#[test]
fn t_norm_inf_test() {
assert_eq!(matrix_operations::norm_inf(&vec![1.0, -2.0, -3.0]), 3.0);
assert_eq!(
matrix_operations::norm_inf(&vec![1.0, -8.0, -3.0, 0.0]),
8.0
);
}
#[test]
fn t_norm_inf_diff() {
let x = [1.0, 2.0, 1.0];
let y = [-4.0, 0.0, 3.0];
let norm_diff = matrix_operations::norm_inf_diff(&x, &y);
assert_eq!(5.0, norm_diff);
assert_eq!(0.0, matrix_operations::norm_inf_diff(&x, &x));
assert_eq!(0.0, matrix_operations::norm_inf_diff(&[], &[]));
}
#[test]
#[should_panic]
fn t_norm_inf_diff_panic() {
let x = [1.0, 2.0, 3.0];
let y = [0.0, 3.0];
let _ = matrix_operations::norm_inf_diff(&x, &y);
}
#[test]
fn t_norm2_squared_diff_test() {
let x = [2.0, 5.0, 7.0, -1.0];
let y = [4.0, 1.0, 0.0, 10.0];
let norm2sq = matrix_operations::norm2_squared_diff(&x, &y);
unit_test_utils::assert_nearly_equal(190., norm2sq, 1e-10, 1e-12, "norm sq diff");
}
}