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use super::Vector;
use crate::{to_i32, Norm};
extern "C" {
// Computes the sum of the absolute values (1-norm or taxicab norm)
// <https://www.netlib.org/lapack/explore-html/de/d05/dasum_8f.html>
fn cblas_dasum(n: i32, x: *const f64, incx: i32) -> f64;
// Computes the Euclidean norm
// <https://www.netlib.org/lapack/explore-html/d6/de0/dnrm2_8f90.html>
fn cblas_dnrm2(n: i32, x: *const f64, incx: i32) -> f64;
// Finds the index of the maximum absolute value
// <https://www.netlib.org/lapack/explore-html/dd/de0/idamax_8f.html>
fn cblas_idamax(n: i32, x: *const f64, incx: i32) -> i32;
}
/// Returns the vector norm
///
/// ```text
/// norm(v) = ‖v‖
/// ```
///
/// # Examples
///
/// ```
/// use russell_lab::{vec_norm, Norm, Vector};
///
/// fn main() {
/// let u = Vector::from(&[2.0, -2.0, 2.0, -2.0, -3.0]);
/// assert_eq!(vec_norm(&u, Norm::One), 11.0);
/// assert_eq!(vec_norm(&u, Norm::Euc), 5.0);
/// assert_eq!(vec_norm(&u, Norm::Max), 3.0);
/// }
/// ```
pub fn vec_norm(v: &Vector, kind: Norm) -> f64 {
let n = to_i32(v.dim());
if n == 0 {
return 0.0;
}
unsafe {
match kind {
Norm::Euc | Norm::Fro => cblas_dnrm2(n, v.as_data().as_ptr(), 1),
Norm::Inf | Norm::Max => {
let idx = cblas_idamax(n, v.as_data().as_ptr(), 1);
f64::abs(v.get(idx as usize))
}
Norm::One => cblas_dasum(n, v.as_data().as_ptr(), 1),
}
}
}
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
#[cfg(test)]
mod tests {
use super::{vec_norm, Vector};
use crate::{approx_eq, Norm};
#[test]
fn vec_norm_works() {
let u0 = Vector::new(0);
assert_eq!(vec_norm(&u0, Norm::Euc), 0.0);
assert_eq!(vec_norm(&u0, Norm::Fro), 0.0);
assert_eq!(vec_norm(&u0, Norm::Inf), 0.0);
assert_eq!(vec_norm(&u0, Norm::Max), 0.0);
assert_eq!(vec_norm(&u0, Norm::One), 0.0);
let u = Vector::from(&[-3.0, 2.0, 1.0, 1.0, 1.0]);
assert_eq!(vec_norm(&u, Norm::Euc), 4.0);
assert_eq!(vec_norm(&u, Norm::Fro), 4.0);
assert_eq!(vec_norm(&u, Norm::Inf), 3.0);
assert_eq!(vec_norm(&u, Norm::Max), 3.0);
assert_eq!(vec_norm(&u, Norm::One), 8.0);
// example from https://netlib.org/lapack/lug/node75.html
let diff = Vector::from(&[-0.1, 1.0, -2.0]);
approx_eq(vec_norm(&diff, Norm::Euc), 2.238, 0.001);
assert_eq!(vec_norm(&diff, Norm::Inf), 2.0);
assert_eq!(vec_norm(&diff, Norm::One), 3.1);
}
}