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9425aed | 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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 | // Spectral + entropy primitives matching resonance-math/lib/entropy.mjs in Rust.
use nalgebra::DMatrix;
use num_complex::Complex64;
const EPSILON: f64 = 1e-14;
/// Shannon entropy H = -Σ p·log₂(p). Matches entropy.mjs:shannonEntropy.
pub fn shannon_entropy(probs: &[f64]) -> f64 {
probs.iter()
.filter(|&&p| p > EPSILON)
.map(|&p| -p * p.log2())
.sum::<f64>()
}
/// Von Neumann entropy S(ρ) = -tr(ρ log₂ ρ) = -Σ λᵢ log₂ λᵢ.
/// Matches entropy.mjs:vonNeumannEntropy but takes density matrix, not pre-computed eigenvalues.
pub fn von_neumann_entropy(rho: &DMatrix<Complex64>) -> f64 {
let res = crate::zheev::zheev(rho).expect("von_neumann_entropy requires Hermitian input");
shannon_entropy(res.eigenvalues.as_slice())
}
/// KL divergence D(p||q) = Σ pᵢ log₂(pᵢ/qᵢ). Matches entropy.mjs:klDivergence.
pub fn kl_divergence(p: &[f64], q: &[f64]) -> f64 {
assert_eq!(p.len(), q.len(), "kl_divergence: length mismatch");
p.iter().zip(q.iter())
.filter(|(&pi, _)| pi > EPSILON)
.map(|(&pi, &qi)| pi * (pi / qi.max(EPSILON)).log2())
.sum()
}
/// Cross-entropy H(p,q) = -Σ pᵢ log₂(qᵢ). Matches entropy.mjs:crossEntropy.
pub fn cross_entropy(p: &[f64], q: &[f64]) -> f64 {
assert_eq!(p.len(), q.len(), "cross_entropy: length mismatch");
-p.iter().zip(q.iter())
.filter(|(&pi, _)| pi > EPSILON)
.map(|(&pi, &qi)| pi * qi.max(EPSILON).log2())
.sum::<f64>()
}
/// Normalize weights to sum to 1. Matches entropy.mjs:normalize.
pub fn normalize(weights: &[f64]) -> Vec<f64> {
let total: f64 = weights.iter().sum();
if total <= EPSILON {
let n = weights.len() as f64;
return vec![1.0 / n; weights.len()];
}
weights.iter().map(|&w| w / total).collect()
}
/// Born rule probabilities: pⱼ = tr(Eⱼ · ρ) for POVM elements {Eⱼ}.
/// Matches measurement_head.f90:measurement_execute.
pub fn born_probabilities(rho: &DMatrix<Complex64>, povms: &[DMatrix<Complex64>]) -> Vec<f64> {
let probs: Vec<f64> = povms.iter()
.map(|e| {
let prod = e * rho;
let tr: f64 = (0..prod.nrows()).map(|i| prod[(i, i)].re).sum();
tr.max(0.0)
})
.collect();
normalize(&probs)
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_shannon_uniform() {
let probs = vec![0.5, 0.5];
let h = shannon_entropy(&probs);
assert!((h - 1.0).abs() < 1e-12, "H = {}", h);
}
#[test]
fn test_kl_self_zero() {
let p = vec![0.3, 0.4, 0.3];
let kl = kl_divergence(&p, &p);
assert!(kl.abs() < 1e-12);
}
#[test]
fn test_normalize_sum() {
let w = vec![1.0, 2.0, 3.0];
let n = normalize(&w);
let s: f64 = n.iter().sum();
assert!((s - 1.0).abs() < 1e-12);
}
#[test]
fn test_born_sums_to_one() {
let n = 2;
let rho = DMatrix::<Complex64>::identity(n, n) * Complex64::new(0.5, 0.0);
let e0 = DMatrix::<Complex64>::identity(n, n) * Complex64::new(0.5, 0.0);
let e1 = DMatrix::<Complex64>::identity(n, n) * Complex64::new(0.5, 0.0);
let probs = born_probabilities(&rho, &[e0, e1]);
let s: f64 = probs.iter().sum();
assert!((s - 1.0).abs() < 1e-10, "sum={}", s);
}
}
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