File size: 1,772 Bytes
c30b460 | 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 | from __future__ import annotations
import numpy as np
def df1(eigenvalues: np.ndarray, value: float) -> float:
eig = np.asarray(eigenvalues, dtype=np.float64)
return float(np.sum(eig / (eig + value)))
def df2(eigenvalues: np.ndarray, value: float, other: float | None = None) -> float:
eig = np.asarray(eigenvalues, dtype=np.float64)
if other is None:
other = value
return float(np.sum(eig**2 / ((eig + value) * (eig + other))))
def solve_kappa(
eigenvalues: np.ndarray,
noise_variance: float,
n_samples: int,
*,
tol: float = 1e-12,
max_iter: int = 200,
) -> float:
"""Solve the Silverstein equation used by the paper for finite spectra."""
eig = np.asarray(eigenvalues, dtype=np.float64)
if np.any(eig < 0):
raise ValueError("eigenvalues must be non-negative")
if noise_variance <= 0:
raise ValueError("noise_variance must be positive")
if n_samples <= 0:
raise ValueError("n_samples must be positive")
gamma = eig.size / float(n_samples)
def residual(kappa: float) -> float:
trace = float(np.mean(eig / (eig + kappa)))
return kappa - noise_variance - gamma * kappa * trace
lo = float(noise_variance)
hi = max(lo * 2.0, lo + 1.0, float(np.max(eig)) + lo)
while residual(hi) <= 0.0:
hi *= 2.0
for _ in range(max_iter):
mid = 0.5 * (lo + hi)
if residual(mid) <= 0.0:
lo = mid
else:
hi = mid
if hi - lo <= tol * max(1.0, hi):
break
return float(0.5 * (lo + hi))
def denoiser_shrinkage(eigenvalues: np.ndarray, noise_variance: float) -> np.ndarray:
eig = np.asarray(eigenvalues, dtype=np.float64)
return eig / (eig + float(noise_variance))
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