diff --git a/pyerrors/linalg.py b/pyerrors/linalg.py index bc265efa..210f79fa 100644 --- a/pyerrors/linalg.py +++ b/pyerrors/linalg.py @@ -1,6 +1,3 @@ -#!/usr/bin/env python -# coding: utf-8 - import numpy as np from autograd import jacobian import autograd.numpy as anp # Thinly-wrapped numpy diff --git a/pyerrors/misc.py b/pyerrors/misc.py index 7fd0af58..1baa5e53 100644 --- a/pyerrors/misc.py +++ b/pyerrors/misc.py @@ -1,6 +1,3 @@ -#!/usr/bin/env python -# coding: utf-8 - import numpy as np from .obs import Obs diff --git a/pyerrors/mpm.py b/pyerrors/mpm.py index 00ace703..619d3750 100644 --- a/pyerrors/mpm.py +++ b/pyerrors/mpm.py @@ -1,26 +1,26 @@ -#!/usr/bin/env python -# coding: utf-8 - import numpy as np import scipy.linalg from .obs import Obs -from .linalg import svd, eig, pinv +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 + """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 -- 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 -- Number of states to extract (default 1). - p -- 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). + 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] @@ -56,55 +56,3 @@ def matrix_pencil_method(corrs, k=1, p=None, **kwargs): # 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)) - - -def matrix_pencil_method_old(data, p, noise_level=None, verbose=1, **kwargs): - """ Older impleentation of the matrix pencil method with pencil p on given data to - extract energy levels. - - Parameters - ---------- - data -- lists of Obs, where the nth entry is considered to be the correlation function - at x0=n+offset. - p -- matrix pencil parameter which corresponds to the number of energy levels to extract. - higher values for p can help decreasing noise. - noise_level -- If this argument is not None an additional prefiltering via singular - value decomposition is performed in which all singular values below 10^(-noise_level) - times the largest singular value are discarded. This increases the computation time. - verbose -- if larger than zero details about the noise filtering are printed to stdout - (default 1) - - """ - n_data = len(data) - if n_data <= p: - raise Exception('The pencil p has to be smaller than the number of data samples.') - - matrix = scipy.linalg.hankel(data[:n_data - p], data[n_data - p - 1:]) @ np.identity(p + 1) - - if noise_level is not None: - u, s, vh = svd(matrix) - - s_values = np.vectorize(lambda x: x.value)(s) - if verbose > 0: - print('Singular values: ', s_values) - digit = np.argwhere(s_values / s_values[0] < 10.0**(-noise_level)) - if digit.size == 0: - digit = len(s_values) - else: - digit = int(digit[0]) - if verbose > 0: - print('Consider only', digit, 'out of', len(s), 'singular values') - - new_matrix = u[:, :digit] * s[:digit] @ vh[:digit, :] - y1 = new_matrix[:, :-1] - y2 = new_matrix[:, 1:] - else: - y1 = matrix[:, :-1] - y2 = matrix[:, 1:] - - # Moore–Penrose pseudoinverse - pinv_y1 = pinv(y1) - - e = eig((pinv_y1 @ y2), **kwargs) - energy_levels = -np.log(np.abs(e)) - return sorted(energy_levels, key=lambda x: abs(x.value)) diff --git a/pyerrors/obs.py b/pyerrors/obs.py index 794e7287..87f40b58 100644 --- a/pyerrors/obs.py +++ b/pyerrors/obs.py @@ -1,6 +1,3 @@ -#!/usr/bin/env python -# coding: utf-8 - import warnings import pickle import numpy as np