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
//! Spectral sanity helpers (feature-gated).
//!
//! These utilities are intentionally lightweight and *do not* change any default behavior.
//! They can be used by callers that already have eigenvalue sequences (e.g. from PCA/covariance).
/// Marchenko–Pastur upper bulk edge \(\lambda_+\) for a sample covariance spectrum.
///
/// `ratio` is \(\gamma = p/n\) (features / samples). `sigma_sq` is the assumed noise variance.
///
/// This uses `rmt::marchenko_pastur_support` and returns only \(\lambda_+\).
#[cfg(feature = "rmt-spectral")]
pub fn mp_lambda_plus(ratio: f64, sigma_sq: f64) -> f64 {
let (_lo, hi) = rmt::marchenko_pastur_support(ratio, sigma_sq);
hi
}
/// Count eigenvalues strictly above the MP bulk edge (optionally with a multiplicative margin).
///
/// Input eigenvalues must be real-valued; order does not matter.
#[cfg(feature = "rmt-spectral")]
pub fn count_mp_outliers(eigenvalues: &[f64], ratio: f64, sigma_sq: f64, margin: f64) -> usize {
let thr = mp_lambda_plus(ratio, sigma_sq) * margin.max(1.0);
eigenvalues
.iter()
.filter(|&&x| x.is_finite() && x > thr)
.count()
}
#[cfg(test)]
mod tests {
#[cfg(feature = "rmt-spectral")]
use super::*;
#[test]
#[cfg(feature = "rmt-spectral")]
fn mp_outlier_count_smoke() {
// Pretend these are covariance eigenvalues: one clear outlier above the bulk.
let evals = vec![0.9, 1.1, 1.0, 3.0];
let ratio = 0.5; // p/n
let sigma_sq = 1.0;
let n = count_mp_outliers(&evals, ratio, sigma_sq, 1.0);
assert!(n >= 1);
}
}