statrs/function/
harmonic.rs

1//! Provides functions for calculating
2//! [harmonic](https://en.wikipedia.org/wiki/Harmonic_number)
3//! numbers
4
5use crate::consts;
6use crate::function::gamma;
7
8/// Computes the `t`-th harmonic number
9///
10/// # Remarks
11///
12/// Returns `1` as a special case when `t == 0`
13pub fn harmonic(t: u64) -> f64 {
14    match t {
15        0 => 1.0,
16        _ => consts::EULER_MASCHERONI + gamma::digamma(t as f64 + 1.0),
17    }
18}
19
20/// Computes the generalized harmonic number of  order `n` of `m`
21/// e.g. `(1 + 1/2^m + 1/3^m + ... + 1/n^m)`
22///
23/// # Remarks
24///
25/// Returns `1` as a special case when `n == 0`
26pub fn gen_harmonic(n: u64, m: f64) -> f64 {
27    match n {
28        0 => 1.0,
29        _ => (0..n).fold(0.0, |acc, x| acc + (x as f64 + 1.0).powf(-m)),
30    }
31}
32
33#[rustfmt::skip]
34#[cfg(test)]
35mod tests {
36    use std::f64;
37
38    #[test]
39    fn test_harmonic() {
40        assert_eq!(super::harmonic(0), 1.0);
41        assert_almost_eq!(super::harmonic(1), 1.0, 1e-14);
42        assert_almost_eq!(super::harmonic(2), 1.5, 1e-14);
43        assert_almost_eq!(super::harmonic(4), 2.083333333333333333333, 1e-14);
44        assert_almost_eq!(super::harmonic(8), 2.717857142857142857143, 1e-14);
45        assert_almost_eq!(super::harmonic(16), 3.380728993228993228993, 1e-14);
46    }
47
48    #[test]
49    fn test_gen_harmonic() {
50        assert_eq!(super::gen_harmonic(0, 0.0), 1.0);
51        assert_eq!(super::gen_harmonic(0, f64::INFINITY), 1.0);
52        assert_eq!(super::gen_harmonic(0, f64::NEG_INFINITY), 1.0);
53        assert_eq!(super::gen_harmonic(1, 0.0), 1.0);
54        assert_eq!(super::gen_harmonic(1, f64::INFINITY), 1.0);
55        assert_eq!(super::gen_harmonic(1, f64::NEG_INFINITY), 1.0);
56        assert_eq!(super::gen_harmonic(2, 1.0), 1.5);
57        assert_eq!(super::gen_harmonic(2, 3.0), 1.125);
58        assert_eq!(super::gen_harmonic(2, f64::INFINITY), 1.0);
59        assert_eq!(super::gen_harmonic(2, f64::NEG_INFINITY), f64::INFINITY);
60        assert_almost_eq!(super::gen_harmonic(4, 1.0), 2.083333333333333333333, 1e-14);
61        assert_eq!(super::gen_harmonic(4, 3.0), 1.177662037037037037037);
62        assert_eq!(super::gen_harmonic(4, f64::INFINITY), 1.0);
63        assert_eq!(super::gen_harmonic(4, f64::NEG_INFINITY), f64::INFINITY);
64    }
65}
statrs/function/harmonic.rs

statrs/function/
harmonic.rs
