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* first example of returns statement in docstring * added a some return statements for pandas API * last return statements in pandas input * added returns to bdio docstrings * few returns statements added to docstring * finished docstrings for hadrons submodule * also finished docstrings for json submodule * finished misc submodule * added returns in docstrings in openqQCD * made some cosmetic chanes to dostrings * added return nad return statement in docstring * linting * Improved docstrings of mpm, fits, roots, misc to have return statements returns added for misc.py returns added for mpm.py reutrns added for fits.py * linting... * Some polishing of docstrings
63 lines
2.2 KiB
Python
63 lines
2.2 KiB
Python
import numpy as np
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import scipy.linalg
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from .obs import Obs
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from .linalg import svd, eig
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def matrix_pencil_method(corrs, k=1, p=None, **kwargs):
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"""Matrix pencil method to extract k energy levels from data
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Implementation of the matrix pencil method based on
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eq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
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Parameters
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----------
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data : list
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can be a list of Obs for the analysis of a single correlator, or a list of lists
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of Obs if several correlators are to analyzed at once.
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k : int
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Number of states to extract (default 1).
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p : int
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matrix pencil parameter which filters noise. The optimal value is expected between
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len(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is
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to len(data)/2 but could possibly suppress more noise (default len(data)//2).
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Returns
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-------
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energy_levels : list[Obs]
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Extracted energy levels
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"""
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if isinstance(corrs[0], Obs):
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data = [corrs]
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else:
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data = corrs
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lengths = [len(d) for d in data]
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if lengths.count(lengths[0]) != len(lengths):
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raise Exception('All datasets have to have the same length.')
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data_sets = len(data)
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n_data = len(data[0])
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if p is None:
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p = max(n_data // 2, k)
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if n_data <= p:
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raise Exception('The pencil p has to be smaller than the number of data samples.')
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if p < k or n_data - p < k:
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raise Exception('Cannot extract', k, 'energy levels with p=', p, 'and N-p=', n_data - p)
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# Construct the hankel matrices
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matrix = []
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for n in range(data_sets):
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matrix.append(scipy.linalg.hankel(data[n][:n_data - p], data[n][n_data - p - 1:]))
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matrix = np.array(matrix)
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# Construct y1 and y2
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y1 = np.concatenate(matrix[:, :, :p])
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y2 = np.concatenate(matrix[:, :, 1:])
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# Apply SVD to y2
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u, s, vh = svd(y2, **kwargs)
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# Construct z from y1 and SVD of y2, setting all singular values beyond the kth to zero
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z = np.diag(1. / s[:k]) @ u[:, :k].T @ y1 @ vh.T[:, :k]
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# Return the sorted logarithms of the real eigenvalues as Obs
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energy_levels = np.log(np.abs(eig(z, **kwargs)))
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return sorted(energy_levels, key=lambda x: abs(x.value))
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