fdars-core 0.10.0

Functional Data Analysis algorithms in Rust
Documentation 
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//! Covariance accumulation and regularization for GMM components.

use super::CovType;

/// Accumulate full covariance from unit-weighted observations.
pub(super) fn accumulate_full_cov(
    features: &[Vec<f64>],
    indices: &[usize],
    mean: &[f64],
    d: usize,
) -> Vec<f64> {
    let mut cov = vec![0.0; d * d];
    for &i in indices {
        for r in 0..d {
            let dr = features[i][r] - mean[r];
            for s in r..d {
                let val = dr * (features[i][s] - mean[s]);
                cov[r * d + s] += val;
                if r != s {
                    cov[s * d + r] += val;
                }
            }
        }
    }
    cov
}

/// Accumulate diagonal covariance from unit-weighted observations.
pub(super) fn accumulate_diag_cov(
    features: &[Vec<f64>],
    indices: &[usize],
    mean: &[f64],
    d: usize,
) -> Vec<f64> {
    let mut diag = vec![0.0; d];
    for &i in indices {
        for j in 0..d {
            diag[j] += (features[i][j] - mean[j]).powi(2);
        }
    }
    diag
}

/// Accumulate weighted full covariance from all observations.
pub(super) fn accumulate_full_cov_weighted(
    features: &[Vec<f64>],
    resp: &[f64],
    c: usize,
    k: usize,
    mean: &[f64],
    d: usize,
) -> Vec<f64> {
    let mut cov = vec![0.0; d * d];
    for i in 0..features.len() {
        let w = resp[i * k + c];
        for r in 0..d {
            let dr = features[i][r] - mean[r];
            for s in r..d {
                let val = w * dr * (features[i][s] - mean[s]);
                cov[r * d + s] += val;
                if r != s {
                    cov[s * d + r] += val;
                }
            }
        }
    }
    cov
}

/// Accumulate weighted diagonal covariance from all observations.
pub(super) fn accumulate_diag_cov_weighted(
    features: &[Vec<f64>],
    resp: &[f64],
    c: usize,
    k: usize,
    mean: &[f64],
    d: usize,
) -> Vec<f64> {
    let mut diag = vec![0.0; d];
    for i in 0..features.len() {
        let w = resp[i * k + c];
        for j in 0..d {
            diag[j] += w * (features[i][j] - mean[j]).powi(2);
        }
    }
    diag
}

/// Normalize covariance by count and add regularization.
pub(super) fn regularize_cov(cov: &mut [f64], scale: f64, d: usize, reg: f64, is_full: bool) {
    for v in cov.iter_mut() {
        *v /= scale;
    }
    if is_full {
        for j in 0..d {
            cov[j * d + j] += reg;
        }
    } else {
        for v in cov.iter_mut() {
            *v += reg;
        }
    }
}

/// Identity-like regularization covariance (for degenerate components).
pub(super) fn identity_cov(d: usize, reg: f64, cov_type: CovType) -> Vec<f64> {
    match cov_type {
        CovType::Full => {
            let mut cov = vec![0.0; d * d];
            for j in 0..d {
                cov[j * d + j] = reg;
            }
            cov
        }
        CovType::Diagonal => vec![reg; d],
    }
}

/// Compute covariances from hard assignments.
pub(super) fn compute_covariances(
    features: &[Vec<f64>],
    assignments: &[usize],
    means: &[Vec<f64>],
    k: usize,
    d: usize,
    cov_type: CovType,
    reg: f64,
) -> Vec<Vec<f64>> {
    let n = features.len();
    let mut covariances = Vec::with_capacity(k);

    for c in 0..k {
        let members: Vec<usize> = (0..n).filter(|&i| assignments[i] == c).collect();
        let nc = members.len().max(1) as f64;

        let mut cov = match cov_type {
            CovType::Full => accumulate_full_cov(features, &members, &means[c], d),
            CovType::Diagonal => accumulate_diag_cov(features, &members, &means[c], d),
        };
        regularize_cov(&mut cov, nc, d, reg, cov_type == CovType::Full);
        covariances.push(cov);
    }
    covariances
}