pyerrors/pyerrors/mpm.py
2021-11-09 10:27:50 +00:00

58 lines
2.1 KiB
Python

import numpy as np
import scipy.linalg
from .obs import Obs
from .linalg import svd, eig
def matrix_pencil_method(corrs, k=1, p=None, **kwargs):
"""Matrix pencil method to extract k energy levels from data
Implementation of the matrix pencil method based on
eq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
Parameters
----------
data : list
can be a list of Obs for the analysis of a single correlator, or a list of lists
of Obs if several correlators are to analyzed at once.
k : int
Number of states to extract (default 1).
p : int
matrix pencil parameter which filters noise. The optimal value is expected between
len(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is
to len(data)/2 but could possibly suppress more noise (default len(data)//2).
"""
if isinstance(corrs[0], Obs):
data = [corrs]
else:
data = corrs
lengths = [len(d) for d in data]
if lengths.count(lengths[0]) != len(lengths):
raise Exception('All datasets have to have the same length.')
data_sets = len(data)
n_data = len(data[0])
if p is None:
p = max(n_data // 2, k)
if n_data <= p:
raise Exception('The pencil p has to be smaller than the number of data samples.')
if p < k or n_data - p < k:
raise Exception('Cannot extract', k, 'energy levels with p=', p, 'and N-p=', n_data - p)
# Construct the hankel matrices
matrix = []
for n in range(data_sets):
matrix.append(scipy.linalg.hankel(data[n][:n_data - p], data[n][n_data - p - 1:]))
matrix = np.array(matrix)
# Construct y1 and y2
y1 = np.concatenate(matrix[:, :, :p])
y2 = np.concatenate(matrix[:, :, 1:])
# Apply SVD to y2
u, s, vh = svd(y2, **kwargs)
# Construct z from y1 and SVD of y2, setting all singular values beyond the kth to zero
z = np.diag(1. / s[:k]) @ u[:, :k].T @ y1 @ vh.T[:, :k]
# Return the sorted logarithms of the real eigenvalues as Obs
energy_levels = np.log(np.abs(eig(z, **kwargs)))
return sorted(energy_levels, key=lambda x: abs(x.value))