"""Kaczmarz (ART) unfolding method for neutron spectrum reconstruction.
This module provides the core solve_kaczmarz solver and the unfold_kaczmarz
wrapper for use with the Detector class.
"""
import numpy as np
from typing import Dict, Optional, Any, List, Tuple
from ._base_unfolder import run_unfolding, make_solve_wrapper
__all__ = ["solve_kaczmarz", "unfold_kaczmarz"]
[docs]
def solve_kaczmarz(
A: np.ndarray,
b: np.ndarray,
x0: np.ndarray,
max_iterations: int = 1000,
omega: float = 1.0,
tolerance: float = 1e-6,
) -> Tuple[np.ndarray, int, bool]:
"""Solve unfolding problem using Kaczmarz algorithm (ART).
Parameters
----------
A : np.ndarray
Response matrix (m x n).
b : np.ndarray
Measurement vector (m,).
x0 : np.ndarray
Initial guess (n,).
max_iterations : int, optional
Maximum iterations (default: 1000).
omega : float, optional
Relaxation parameter (0 < omega <= 2), default: 1.0.
tolerance : float, optional
Convergence tolerance (default: 1e-6).
Returns
-------
Tuple[np.ndarray, int, bool]
Tuple of (solution, iterations, converged).
"""
import warnings
m, n = A.shape
x = x0.copy()
if omega <= 0 or omega > 2:
warnings.warn(f"omega={omega} outside recommended range (0,2]")
row_norms_sq = np.sum(A * A, axis=1)
converged = False
iterations = 0
x_old = x.copy()
for k in range(max_iterations):
i = k % m
if row_norms_sq[i] > 0:
update = (b[i] - np.dot(A[i], x)) / row_norms_sq[i]
x = x + omega * update * A[i]
x = np.maximum(x, 0)
if (k + 1) % m == 0:
if np.linalg.norm(x - x_old) < tolerance:
converged = True
iterations = k + 1
break
x_old = x.copy()
if not converged:
iterations = max_iterations
return x, iterations, converged
[docs]
def unfold_kaczmarz(
detector_names: List[str],
n_energy_bins: int,
E_MeV: np.ndarray,
sensitivities: Dict[str, np.ndarray],
cc_icrp116: Dict[str, np.ndarray],
save_result_callback,
readings: Dict[str, float],
initial_spectrum: Optional[np.ndarray] = None,
max_iterations: int = 1000,
omega: float = 1.0,
tolerance: float = 1e-6,
calculate_errors: bool = False,
noise_level: float = 0.01,
n_montecarlo: int = 100,
save_result: bool = True,
random_state: Optional[int] = None,
) -> Dict[str, Any]:
"""Unfold neutron spectrum using the Kaczmarz algorithm (ART).
Parameters
----------
detector_names : List[str]
Names of available detectors.
n_energy_bins : int
Number of energy bins.
E_MeV : np.ndarray
Energy grid.
sensitivities : Dict[str, np.ndarray]
Detector sensitivity arrays.
cc_icrp116 : Dict[str, np.ndarray]
ICRP-116 conversion coefficients.
save_result_callback : callable
Callback to save result to history.
readings : Dict[str, float]
Detector readings.
initial_spectrum : Optional[np.ndarray], optional
Initial spectrum guess. If None, zero spectrum is used.
max_iterations : int, optional
Maximum number of iterations, default: 1000.
omega : float, optional
Relaxation parameter (0 < omega <= 2), default: 1.0.
tolerance : float, optional
Convergence tolerance for solution change, default: 1e-6.
calculate_errors : bool, optional
Flag to calculate uncertainty via Monte-Carlo, default: False.
noise_level : float, optional
Noise level for Monte-Carlo uncertainty calculation, default: 0.01.
n_montecarlo : int, optional
Number of Monte-Carlo samples for error estimation, default: 100.
save_result : bool, optional
If True, save result to internal history, default: True.
random_state : int, optional
Random seed for reproducibility.
Returns
-------
Dict[str, Any]
Dictionary containing unfolding results.
"""
x0_default = np.zeros(n_energy_bins)
return run_unfolding(
detector_names=detector_names,
n_energy_bins=n_energy_bins,
E_MeV=E_MeV,
sensitivities=sensitivities,
cc_icrp116=cc_icrp116,
save_result_callback=save_result_callback,
readings=readings,
initial_spectrum=initial_spectrum,
default_initial=x0_default,
solve_func=make_solve_wrapper(
solve_kaczmarz,
max_iterations=max_iterations,
omega=omega,
tolerance=tolerance,
),
solve_kwargs={},
method_name="Kaczmarz",
extra_output={
"tolerance": tolerance,
"omega": omega,
},
calculate_errors=calculate_errors,
noise_level=noise_level,
n_montecarlo=n_montecarlo,
random_state=random_state,
save_result=save_result,
)