Merge branch 'develop' into documentation

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

pyerrors/misc.py

@@ -1,6 +1,3 @@
-#!/usr/bin/env python
-# coding: utf-8
-
 import numpy as np
 from .obs import Obs
 

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))

pyerrors/obs.py

@@ -1,6 +1,3 @@
-#!/usr/bin/env python
-# coding: utf-8
-
 import warnings
 import pickle
 import numpy as np