From 35df837bb42fcd938f921f317d544df8b478104d Mon Sep 17 00:00:00 2001 From: fjosw Date: Mon, 6 Jan 2025 09:47:33 +0000 Subject: [PATCH] Documentation updated --- docs/pyerrors.html | 60 +- docs/pyerrors/correlators.html | 440 ++++---- docs/pyerrors/covobs.html | 38 +- docs/pyerrors/dirac.html | 14 +- docs/pyerrors/fits.html | 182 ++-- docs/pyerrors/input.html | 16 +- docs/pyerrors/input/bdio.html | 44 +- docs/pyerrors/input/dobs.html | 80 +- docs/pyerrors/input/hadrons.html | 82 +- docs/pyerrors/input/json.html | 112 +- docs/pyerrors/input/misc.html | 28 +- docs/pyerrors/input/openQCD.html | 78 +- docs/pyerrors/input/pandas.html | 38 +- docs/pyerrors/input/sfcf.html | 1658 +++++++++++++++--------------- docs/pyerrors/input/utils.html | 18 +- docs/pyerrors/integrate.html | 16 +- docs/pyerrors/linalg.html | 104 +- docs/pyerrors/misc.html | 46 +- docs/pyerrors/mpm.html | 12 +- docs/pyerrors/obs.html | 552 +++++----- docs/pyerrors/roots.html | 20 +- docs/pyerrors/special.html | 271 +++-- docs/search.js | 2 +- 23 files changed, 1983 insertions(+), 1928 deletions(-) diff --git a/docs/pyerrors.html b/docs/pyerrors.html index 9598a9ac..0283701e 100644 --- a/docs/pyerrors.html +++ b/docs/pyerrors.html @@ -167,8 +167,8 @@ conda update -c Basic example
-
import numpy as np
-import pyerrors as pe
+
import numpy as np
+import pyerrors as pe
 
 my_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object
 my_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object
@@ -186,7 +186,7 @@ The samples can either be provided as python list or as numpy array.
 The second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.

 
 

-
import pyerrors as pe
+
import pyerrors as pe
 
 my_obs = pe.Obs([samples], ['ensemble_name'])
 

@@ -202,8 +202,8 @@ The required derivatives $\bar{f}_\alpha$ are evaluated up to machine precision
 
The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.

 
 

-
import numpy as np
-import pyerrors as pe
+
import numpy as np
+import pyerrors as pe
 
 my_obs1 = pe.Obs([samples1], ['ensemble_name'])
 my_obs2 = pe.Obs([samples2], ['ensemble_name'])
@@ -232,7 +232,7 @@ After having arrived at the derived quantity of interest the gamma_method<
 > Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)
 >  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00
 > 1000 samples in 1 ensemble:
->   · Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)
+>   · Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)
 

 

 
@@ -249,7 +249,7 @@ The standard value for the parameter $S$ of this automatic windowing procedure i
 > Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)
 >  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00
 > 1000 samples in 1 ensemble:
->   · Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)
+>   · Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)
 

 

 
@@ -268,7 +268,7 @@ In this case the error estimate is identical to the sample standard error.

 > Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)
 >  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1
 > 1000 samples in 1 ensemble:
->   · Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)
+>   · Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)
@@ -286,8 +286,8 @@ In this case the error estimate is identical to the sample standard error.

my_sum.details() > Result 2.00697958e+00 > 1500 samples in 2 ensembles: -> · Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000) -> · Ensemble 'ensemble2' : 500 configurations (from 1 to 500) +> · Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000) +> · Ensemble 'ensemble2' : 500 configurations (from 1 to 500) @@ -304,8 +304,8 @@ In this case the error estimate is identical to the sample standard error.

> Result 2.00697958e+00 > 1500 samples in 1 ensemble: > · Ensemble 'ensemble1' -> · Replicum 'r01' : 1000 configurations (from 1 to 1000) -> · Replicum 'r02' : 500 configurations (from 1 to 500) +> · Replicum 'r01' : 1000 configurations (from 1 to 1000) +> · Replicum 'r02' : 500 configurations (from 1 to 500) @@ -333,14 +333,14 @@ Passing arguments to the gamma_method still dominates over the dict obs1.details() > Result 9.98319881e-01 > 500 samples in 1 ensemble: -> · Ensemble 'ensemble1' : 500 configurations (from 20 to 519) +> · Ensemble 'ensemble1' : 500 configurations (from 20 to 519) # Observable defined on every second configuration between 5 and 1003 obs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)]) obs2.details() > Result 9.99100712e-01 > 500 samples in 1 ensemble: -> · Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2) +> · Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2) # Observable defined on configurations 2, 9, 28, 29 and 501 obs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]]) @@ -459,7 +459,7 @@ Make sure to check the autocorrelation time with e.g. pyerrors, external input is defined by $M$ mean values, a $M\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.

-
import pyerrors.obs as pe
+
import pyerrors.obs as pe
 
 mpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')
 mpi.gamma_method()
@@ -504,9 +504,9 @@ where the Jacobian is computed for each derived quantity via automatic different
 
Fit functions have to be of the following form

 
 

-
import autograd.numpy as anp
+
import autograd.numpy as anp
 
-def func(a, x):
+def func(a, x):
     return a[1] * anp.exp(-a[0] * x)
 

 

@@ -547,7 +547,7 @@ where the Jacobian is computed for each derived quantity via automatic different
 
For fit functions with multiple independent variables the fit function can be of the form

 
 

-
def func(a, x):
+
def func(a, x):
     (x1, x2) = x
     return a[0] * x1 ** 2 + a[1] * x2
 

@@ -1151,19 +1151,19 @@ The following entries are optional:
 477
 478Julia I/O routines for the json.gz format, compatible with [ADerrors.jl](https://gitlab.ift.uam-csic.es/alberto/aderrors.jl), can be found [here](https://github.com/fjosw/ADjson.jl).
 479'''
-480from .obs import *
-481from .correlators import *
-482from .fits import *
-483from .misc import *
-484from . import dirac as dirac
-485from . import input as input
-486from . import linalg as linalg
-487from . import mpm as mpm
-488from . import roots as roots
-489from . import integrate as integrate
-490from . import special as special
+480from .obs import *
+481from .correlators import *
+482from .fits import *
+483from .misc import *
+484from . import dirac as dirac
+485from . import input as input
+486from . import linalg as linalg
+487from . import mpm as mpm
+488from . import roots as roots
+489from . import integrate as integrate
+490from . import special as special
 491
-492from .version import __version__ as __version__
+492from .version import __version__ as __version__
 

 
 
diff --git a/docs/pyerrors/correlators.html b/docs/pyerrors/correlators.html
index 602f733c..543600bd 100644
--- a/docs/pyerrors/correlators.html
+++ b/docs/pyerrors/correlators.html
@@ -241,20 +241,20 @@
 
                         
 
-                        
   1import warnings
-   2from itertools import permutations
-   3import numpy as np
-   4import autograd.numpy as anp
-   5import matplotlib.pyplot as plt
-   6import scipy.linalg
-   7from .obs import Obs, reweight, correlate, CObs
-   8from .misc import dump_object, _assert_equal_properties
-   9from .fits import least_squares
-  10from .roots import find_root
-  11from . import linalg
+                        
   1import warnings
+   2from itertools import permutations
+   3import numpy as np
+   4import autograd.numpy as anp
+   5import matplotlib.pyplot as plt
+   6import scipy.linalg
+   7from .obs import Obs, reweight, correlate, CObs
+   8from .misc import dump_object, _assert_equal_properties
+   9from .fits import least_squares
+  10from .roots import find_root
+  11from . import linalg
   12
   13
-  14class Corr:
+  14class Corr:
   15    r"""The class for a correlator (time dependent sequence of pe.Obs).
   16
   17    Everything, this class does, can be achieved using lists or arrays of Obs.
@@ -285,7 +285,7 @@
   42
   43    __slots__ = ["content", "N", "T", "tag", "prange"]
   44
-  45    def __init__(self, data_input, padding=[0, 0], prange=None):
+  45    def __init__(self, data_input, padding=[0, 0], prange=None):
   46        """ Initialize a Corr object.
   47
   48        Parameters
@@ -362,7 +362,7 @@
  119        self.T = len(self.content)
  120        self.prange = prange
  121
- 122    def __getitem__(self, idx):
+ 122    def __getitem__(self, idx):
  123        """Return the content of timeslice idx"""
  124        if self.content[idx] is None:
  125            return None
@@ -372,7 +372,7 @@
  129            return self.content[idx]
  130
  131    @property
- 132    def reweighted(self):
+ 132    def reweighted(self):
  133        bool_array = np.array([list(map(lambda x: x.reweighted, o)) for o in [x for x in self.content if x is not None]])
  134        if np.all(bool_array == 1):
  135            return True
@@ -381,7 +381,7 @@
  138        else:
  139            raise Exception("Reweighting status of correlator corrupted.")
  140
- 141    def gamma_method(self, **kwargs):
+ 141    def gamma_method(self, **kwargs):
  142        """Apply the gamma method to the content of the Corr."""
  143        for item in self.content:
  144            if item is not None:
@@ -394,7 +394,7 @@
  151
  152    gm = gamma_method
  153
- 154    def projected(self, vector_l=None, vector_r=None, normalize=False):
+ 154    def projected(self, vector_l=None, vector_r=None, normalize=False):
  155        """We need to project the Correlator with a Vector to get a single value at each timeslice.
  156
  157        The method can use one or two vectors.
@@ -433,7 +433,7 @@
  190            newcontent = [None if (_check_for_none(self, self.content[t]) or vector_l[t] is None or vector_r[t] is None) else np.asarray([vector_l[t].T @ self.content[t] @ vector_r[t]]) for t in range(self.T)]
  191        return Corr(newcontent)
  192
- 193    def item(self, i, j):
+ 193    def item(self, i, j):
  194        """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
  195
  196        Parameters
@@ -448,7 +448,7 @@
  205        newcontent = [None if (item is None) else item[i, j] for item in self.content]
  206        return Corr(newcontent)
  207
- 208    def plottable(self):
+ 208    def plottable(self):
  209        """Outputs the correlator in a plotable format.
  210
  211        Outputs three lists containing the timeslice index, the value on each
@@ -462,7 +462,7 @@
  219
  220        return x_list, y_list, y_err_list
  221
- 222    def symmetric(self):
+ 222    def symmetric(self):
  223        """ Symmetrize the correlator around x0=0."""
  224        if self.N != 1:
  225            raise ValueError('symmetric cannot be safely applied to multi-dimensional correlators.')
@@ -483,7 +483,7 @@
  240            raise ValueError("Corr could not be symmetrized: No redundant values")
  241        return Corr(newcontent, prange=self.prange)
  242
- 243    def anti_symmetric(self):
+ 243    def anti_symmetric(self):
  244        """Anti-symmetrize the correlator around x0=0."""
  245        if self.N != 1:
  246            raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.')
@@ -505,7 +505,7 @@
  262            raise ValueError("Corr could not be symmetrized: No redundant values")
  263        return Corr(newcontent, prange=self.prange)
  264
- 265    def is_matrix_symmetric(self):
+ 265    def is_matrix_symmetric(self):
  266        """Checks whether a correlator matrices is symmetric on every timeslice."""
  267        if self.N == 1:
  268            raise TypeError("Only works for correlator matrices.")
@@ -520,7 +520,7 @@
  277                        return False
  278        return True
  279
- 280    def trace(self):
+ 280    def trace(self):
  281        """Calculates the per-timeslice trace of a correlator matrix."""
  282        if self.N == 1:
  283            raise ValueError("Only works for correlator matrices.")
@@ -532,7 +532,7 @@
  289                newcontent.append(np.trace(self.content[t]))
  290        return Corr(newcontent)
  291
- 292    def matrix_symmetric(self):
+ 292    def matrix_symmetric(self):
  293        """Symmetrizes the correlator matrices on every timeslice."""
  294        if self.N == 1:
  295            raise ValueError("Trying to symmetrize a correlator matrix, that already has N=1.")
@@ -542,7 +542,7 @@
  299            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
  300            return 0.5 * (Corr(transposed) + self)
  301
- 302    def GEVP(self, t0, ts=None, sort="Eigenvalue", vector_obs=False, **kwargs):
+ 302    def GEVP(self, t0, ts=None, sort="Eigenvalue", vector_obs=False, **kwargs):
  303        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
  304
  305        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
@@ -593,7 +593,7 @@
  350        else:
  351            symmetric_corr = self.matrix_symmetric()
  352
- 353        def _get_mat_at_t(t, vector_obs=vector_obs):
+ 353        def _get_mat_at_t(t, vector_obs=vector_obs):
  354            if vector_obs:
  355                return symmetric_corr[t]
  356            else:
@@ -648,7 +648,7 @@
  405        else:
  406            return reordered_vecs
  407
- 408    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue", **kwargs):
+ 408    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue", **kwargs):
  409        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
  410
  411        Parameters
@@ -661,7 +661,7 @@
  418        vec = self.GEVP(t0, ts=ts, sort=sort, **kwargs)[state]
  419        return self.projected(vec)
  420
- 421    def Hankel(self, N, periodic=False):
+ 421    def Hankel(self, N, periodic=False):
  422        """Constructs an NxN Hankel matrix
  423
  424        C(t) c(t+1) ... c(t+n-1)
@@ -685,7 +685,7 @@
  442        for t in range(self.T):
  443            new_content.append(array.copy())
  444
- 445        def wrap(i):
+ 445        def wrap(i):
  446            while i >= self.T:
  447                i -= self.T
  448            return i
@@ -702,7 +702,7 @@
  459
  460        return Corr(new_content)
  461
- 462    def roll(self, dt):
+ 462    def roll(self, dt):
  463        """Periodically shift the correlator by dt timeslices
  464
  465        Parameters
@@ -712,11 +712,11 @@
  469        """
  470        return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0)))
  471
- 472    def reverse(self):
+ 472    def reverse(self):
  473        """Reverse the time ordering of the Corr"""
  474        return Corr(self.content[:: -1])
  475
- 476    def thin(self, spacing=2, offset=0):
+ 476    def thin(self, spacing=2, offset=0):
  477        """Thin out a correlator to suppress correlations
  478
  479        Parameters
@@ -734,7 +734,7 @@
  491                new_content.append(self.content[t])
  492        return Corr(new_content)
  493
- 494    def correlate(self, partner):
+ 494    def correlate(self, partner):
  495        """Correlate the correlator with another correlator or Obs
  496
  497        Parameters
@@ -763,7 +763,7 @@
  520
  521        return Corr(new_content)
  522
- 523    def reweight(self, weight, **kwargs):
+ 523    def reweight(self, weight, **kwargs):
  524        """Reweight the correlator.
  525
  526        Parameters
@@ -786,7 +786,7 @@
  543                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
  544        return Corr(new_content)
  545
- 546    def T_symmetry(self, partner, parity=+1):
+ 546    def T_symmetry(self, partner, parity=+1):
  547        """Return the time symmetry average of the correlator and its partner
  548
  549        Parameters
@@ -816,7 +816,7 @@
  573
  574        return (self + T_partner) / 2
  575
- 576    def deriv(self, variant="symmetric"):
+ 576    def deriv(self, variant="symmetric"):
  577        """Return the first derivative of the correlator with respect to x0.
  578
  579        Parameters
@@ -881,7 +881,7 @@
  638        else:
  639            raise ValueError("Unknown variant.")
  640
- 641    def second_deriv(self, variant="symmetric"):
+ 641    def second_deriv(self, variant="symmetric"):
  642        r"""Return the second derivative of the correlator with respect to x0.
  643
  644        Parameters
@@ -944,7 +944,7 @@
  701        else:
  702            raise ValueError("Unknown variant.")
  703
- 704    def m_eff(self, variant='log', guess=1.0):
+ 704    def m_eff(self, variant='log', guess=1.0):
  705        """Returns the effective mass of the correlator as correlator object
  706
  707        Parameters
@@ -995,7 +995,7 @@
  752            else:
  753                func = anp.sinh
  754
- 755            def root_function(x, d):
+ 755            def root_function(x, d):
  756                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
  757
  758            newcontent = []
@@ -1028,7 +1028,7 @@
  785        else:
  786            raise ValueError('Unknown variant.')
  787
- 788    def fit(self, function, fitrange=None, silent=False, **kwargs):
+ 788    def fit(self, function, fitrange=None, silent=False, **kwargs):
  789        r'''Fits function to the data
  790
  791        Parameters
@@ -1062,7 +1062,7 @@
  819        result = least_squares(xs, ys, function, silent=silent, **kwargs)
  820        return result
  821
- 822    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
+ 822    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
  823        """ Extract a plateau value from a Corr object
  824
  825        Parameters
@@ -1089,7 +1089,7 @@
  846        if auto_gamma:
  847            self.gamma_method()
  848        if method == "fit":
- 849            def const_func(a, t):
+ 849            def const_func(a, t):
  850                return a[0]
  851            return self.fit(const_func, plateau_range)[0]
  852        elif method in ["avg", "average", "mean"]:
@@ -1099,7 +1099,7 @@
  856        else:
  857            raise ValueError("Unsupported plateau method: " + method)
  858
- 859    def set_prange(self, prange):
+ 859    def set_prange(self, prange):
  860        """Sets the attribute prange of the Corr object."""
  861        if not len(prange) == 2:
  862            raise ValueError("prange must be a list or array with two values")
@@ -1111,7 +1111,7 @@
  868        self.prange = prange
  869        return
  870
- 871    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
+ 871    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
  872        """Plots the correlator using the tag of the correlator as label if available.
  873
  874        Parameters
@@ -1236,7 +1236,7 @@
  993            else:
  994                raise TypeError("'save' has to be a string.")
  995
- 996    def spaghetti_plot(self, logscale=True):
+ 996    def spaghetti_plot(self, logscale=True):
  997        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
  998
  999        Parameters
@@ -1265,7 +1265,7 @@
 1022            plt.title(name)
 1023            plt.draw()
 1024
-1025    def dump(self, filename, datatype="json.gz", **kwargs):
+1025    def dump(self, filename, datatype="json.gz", **kwargs):
 1026        """Dumps the Corr into a file of chosen type
 1027        Parameters
 1028        ----------
@@ -1278,7 +1278,7 @@
 1035            specifies a custom path for the file (default '.')
 1036        """
 1037        if datatype == "json.gz":
-1038            from .input.json import dump_to_json
+1038            from .input.json import dump_to_json
 1039            if 'path' in kwargs:
 1040                file_name = kwargs.get('path') + '/' + filename
 1041            else:
@@ -1289,10 +1289,10 @@
 1046        else:
 1047            raise ValueError("Unknown datatype " + str(datatype))
 1048
-1049    def print(self, print_range=None):
+1049    def print(self, print_range=None):
 1050        print(self.__repr__(print_range))
 1051
-1052    def __repr__(self, print_range=None):
+1052    def __repr__(self, print_range=None):
 1053        if print_range is None:
 1054            print_range = [0, None]
 1055
@@ -1317,7 +1317,7 @@
 1074                content_string += '\n'
 1075        return content_string
 1076
-1077    def __str__(self):
+1077    def __str__(self):
 1078        return self.__repr__()
 1079
 1080    # We define the basic operations, that can be performed with correlators.
@@ -1327,14 +1327,14 @@
 1084
 1085    __array_priority__ = 10000
 1086
-1087    def __eq__(self, y):
+1087    def __eq__(self, y):
 1088        if isinstance(y, Corr):
 1089            comp = np.asarray(y.content, dtype=object)
 1090        else:
 1091            comp = np.asarray(y)
 1092        return np.asarray(self.content, dtype=object) == comp
 1093
-1094    def __add__(self, y):
+1094    def __add__(self, y):
 1095        if isinstance(y, Corr):
 1096            if ((self.N != y.N) or (self.T != y.T)):
 1097                raise ValueError("Addition of Corrs with different shape")
@@ -1362,7 +1362,7 @@
 1119        else:
 1120            raise TypeError("Corr + wrong type")
 1121
-1122    def __mul__(self, y):
+1122    def __mul__(self, y):
 1123        if isinstance(y, Corr):
 1124            if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
 1125                raise ValueError("Multiplication of Corr object requires N=N or N=1 and T=T")
@@ -1390,7 +1390,7 @@
 1147        else:
 1148            raise TypeError("Corr * wrong type")
 1149
-1150    def __matmul__(self, y):
+1150    def __matmul__(self, y):
 1151        if isinstance(y, np.ndarray):
 1152            if y.ndim != 2 or y.shape[0] != y.shape[1]:
 1153                raise ValueError("Can only multiply correlators by square matrices.")
@@ -1417,7 +1417,7 @@
 1174        else:
 1175            return NotImplemented
 1176
-1177    def __rmatmul__(self, y):
+1177    def __rmatmul__(self, y):
 1178        if isinstance(y, np.ndarray):
 1179            if y.ndim != 2 or y.shape[0] != y.shape[1]:
 1180                raise ValueError("Can only multiply correlators by square matrices.")
@@ -1433,7 +1433,7 @@
 1190        else:
 1191            return NotImplemented
 1192
-1193    def __truediv__(self, y):
+1193    def __truediv__(self, y):
 1194        if isinstance(y, Corr):
 1195            if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
 1196                raise ValueError("Multiplication of Corr object requires N=N or N=1 and T=T")
@@ -1487,37 +1487,37 @@
 1244        else:
 1245            raise TypeError('Corr / wrong type')
 1246
-1247    def __neg__(self):
+1247    def __neg__(self):
 1248        newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content]
 1249        return Corr(newcontent, prange=self.prange)
 1250
-1251    def __sub__(self, y):
+1251    def __sub__(self, y):
 1252        return self + (-y)
 1253
-1254    def __pow__(self, y):
+1254    def __pow__(self, y):
 1255        if isinstance(y, (Obs, int, float, CObs)):
 1256            newcontent = [None if _check_for_none(self, item) else item**y for item in self.content]
 1257            return Corr(newcontent, prange=self.prange)
 1258        else:
 1259            raise TypeError('Type of exponent not supported')
 1260
-1261    def __abs__(self):
+1261    def __abs__(self):
 1262        newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content]
 1263        return Corr(newcontent, prange=self.prange)
 1264
 1265    # The numpy functions:
-1266    def sqrt(self):
+1266    def sqrt(self):
 1267        return self ** 0.5
 1268
-1269    def log(self):
+1269    def log(self):
 1270        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
 1271        return Corr(newcontent, prange=self.prange)
 1272
-1273    def exp(self):
+1273    def exp(self):
 1274        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
 1275        return Corr(newcontent, prange=self.prange)
 1276
-1277    def _apply_func_to_corr(self, func):
+1277    def _apply_func_to_corr(self, func):
 1278        newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content]
 1279        for t in range(self.T):
 1280            if _check_for_none(self, newcontent[t]):
@@ -1530,58 +1530,58 @@
 1287            raise ValueError('Operation returns undefined correlator')
 1288        return Corr(newcontent)
 1289
-1290    def sin(self):
+1290    def sin(self):
 1291        return self._apply_func_to_corr(np.sin)
 1292
-1293    def cos(self):
+1293    def cos(self):
 1294        return self._apply_func_to_corr(np.cos)
 1295
-1296    def tan(self):
+1296    def tan(self):
 1297        return self._apply_func_to_corr(np.tan)
 1298
-1299    def sinh(self):
+1299    def sinh(self):
 1300        return self._apply_func_to_corr(np.sinh)
 1301
-1302    def cosh(self):
+1302    def cosh(self):
 1303        return self._apply_func_to_corr(np.cosh)
 1304
-1305    def tanh(self):
+1305    def tanh(self):
 1306        return self._apply_func_to_corr(np.tanh)
 1307
-1308    def arcsin(self):
+1308    def arcsin(self):
 1309        return self._apply_func_to_corr(np.arcsin)
 1310
-1311    def arccos(self):
+1311    def arccos(self):
 1312        return self._apply_func_to_corr(np.arccos)
 1313
-1314    def arctan(self):
+1314    def arctan(self):
 1315        return self._apply_func_to_corr(np.arctan)
 1316
-1317    def arcsinh(self):
+1317    def arcsinh(self):
 1318        return self._apply_func_to_corr(np.arcsinh)
 1319
-1320    def arccosh(self):
+1320    def arccosh(self):
 1321        return self._apply_func_to_corr(np.arccosh)
 1322
-1323    def arctanh(self):
+1323    def arctanh(self):
 1324        return self._apply_func_to_corr(np.arctanh)
 1325
 1326    # Right hand side operations (require tweak in main module to work)
-1327    def __radd__(self, y):
+1327    def __radd__(self, y):
 1328        return self + y
 1329
-1330    def __rsub__(self, y):
+1330    def __rsub__(self, y):
 1331        return -self + y
 1332
-1333    def __rmul__(self, y):
+1333    def __rmul__(self, y):
 1334        return self * y
 1335
-1336    def __rtruediv__(self, y):
+1336    def __rtruediv__(self, y):
 1337        return (self / y) ** (-1)
 1338
 1339    @property
-1340    def real(self):
-1341        def return_real(obs_OR_cobs):
+1340    def real(self):
+1341        def return_real(obs_OR_cobs):
 1342            if isinstance(obs_OR_cobs.flatten()[0], CObs):
 1343                return np.vectorize(lambda x: x.real)(obs_OR_cobs)
 1344            else:
@@ -1590,8 +1590,8 @@
 1347        return self._apply_func_to_corr(return_real)
 1348
 1349    @property
-1350    def imag(self):
-1351        def return_imag(obs_OR_cobs):
+1350    def imag(self):
+1351        def return_imag(obs_OR_cobs):
 1352            if isinstance(obs_OR_cobs.flatten()[0], CObs):
 1353                return np.vectorize(lambda x: x.imag)(obs_OR_cobs)
 1354            else:
@@ -1599,7 +1599,7 @@
 1356
 1357        return self._apply_func_to_corr(return_imag)
 1358
-1359    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
+1359    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
 1360        r''' Project large correlation matrix to lowest states
 1361
 1362        This method can be used to reduce the size of an (N x N) correlation matrix
@@ -1657,7 +1657,7 @@
 1414        return Corr(newcontent)
 1415
 1416
-1417def _sort_vectors(vec_set_in, ts):
+1417def _sort_vectors(vec_set_in, ts):
 1418    """Helper function used to find a set of Eigenvectors consistent over all timeslices"""
 1419
 1420    if isinstance(vec_set_in[ts][0][0], Obs):
@@ -1689,12 +1689,12 @@
 1446    return sorted_vec_set
 1447
 1448
-1449def _check_for_none(corr, entry):
+1449def _check_for_none(corr, entry):
 1450    """Checks if entry for correlator corr is None"""
 1451    return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2
 1452
 1453
-1454def _GEVP_solver(Gt, G0, method='eigh', chol_inv=None):
+1454def _GEVP_solver(Gt, G0, method='eigh', chol_inv=None):
 1455    r"""Helper function for solving the GEVP and sorting the eigenvectors.
 1456
 1457    Solves $G(t)v_i=\lambda_i G(t_0)v_i$ and returns the eigenvectors v_i
@@ -1732,10 +1732,10 @@
 1489            cholesky = np.linalg.cholesky
 1490            inv = np.linalg.inv
 1491
-1492            def eigv(x, **kwargs):
+1492            def eigv(x, **kwargs):
 1493                return np.linalg.eigh(x)[1]
 1494
-1495            def matmul(*operands):
+1495            def matmul(*operands):
 1496                return np.linalg.multi_dot(operands)
 1497        N = Gt.shape[0]
 1498        output = [[] for j in range(N)]
@@ -1769,7 +1769,7 @@
 
     

     
-            
  15class Corr:
+            
  15class Corr:
   16    r"""The class for a correlator (time dependent sequence of pe.Obs).
   17
   18    Everything, this class does, can be achieved using lists or arrays of Obs.
@@ -1800,7 +1800,7 @@
   43
   44    __slots__ = ["content", "N", "T", "tag", "prange"]
   45
-  46    def __init__(self, data_input, padding=[0, 0], prange=None):
+  46    def __init__(self, data_input, padding=[0, 0], prange=None):
   47        """ Initialize a Corr object.
   48
   49        Parameters
@@ -1877,7 +1877,7 @@
  120        self.T = len(self.content)
  121        self.prange = prange
  122
- 123    def __getitem__(self, idx):
+ 123    def __getitem__(self, idx):
  124        """Return the content of timeslice idx"""
  125        if self.content[idx] is None:
  126            return None
@@ -1887,7 +1887,7 @@
  130            return self.content[idx]
  131
  132    @property
- 133    def reweighted(self):
+ 133    def reweighted(self):
  134        bool_array = np.array([list(map(lambda x: x.reweighted, o)) for o in [x for x in self.content if x is not None]])
  135        if np.all(bool_array == 1):
  136            return True
@@ -1896,7 +1896,7 @@
  139        else:
  140            raise Exception("Reweighting status of correlator corrupted.")
  141
- 142    def gamma_method(self, **kwargs):
+ 142    def gamma_method(self, **kwargs):
  143        """Apply the gamma method to the content of the Corr."""
  144        for item in self.content:
  145            if item is not None:
@@ -1909,7 +1909,7 @@
  152
  153    gm = gamma_method
  154
- 155    def projected(self, vector_l=None, vector_r=None, normalize=False):
+ 155    def projected(self, vector_l=None, vector_r=None, normalize=False):
  156        """We need to project the Correlator with a Vector to get a single value at each timeslice.
  157
  158        The method can use one or two vectors.
@@ -1948,7 +1948,7 @@
  191            newcontent = [None if (_check_for_none(self, self.content[t]) or vector_l[t] is None or vector_r[t] is None) else np.asarray([vector_l[t].T @ self.content[t] @ vector_r[t]]) for t in range(self.T)]
  192        return Corr(newcontent)
  193
- 194    def item(self, i, j):
+ 194    def item(self, i, j):
  195        """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
  196
  197        Parameters
@@ -1963,7 +1963,7 @@
  206        newcontent = [None if (item is None) else item[i, j] for item in self.content]
  207        return Corr(newcontent)
  208
- 209    def plottable(self):
+ 209    def plottable(self):
  210        """Outputs the correlator in a plotable format.
  211
  212        Outputs three lists containing the timeslice index, the value on each
@@ -1977,7 +1977,7 @@
  220
  221        return x_list, y_list, y_err_list
  222
- 223    def symmetric(self):
+ 223    def symmetric(self):
  224        """ Symmetrize the correlator around x0=0."""
  225        if self.N != 1:
  226            raise ValueError('symmetric cannot be safely applied to multi-dimensional correlators.')
@@ -1998,7 +1998,7 @@
  241            raise ValueError("Corr could not be symmetrized: No redundant values")
  242        return Corr(newcontent, prange=self.prange)
  243
- 244    def anti_symmetric(self):
+ 244    def anti_symmetric(self):
  245        """Anti-symmetrize the correlator around x0=0."""
  246        if self.N != 1:
  247            raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.')
@@ -2020,7 +2020,7 @@
  263            raise ValueError("Corr could not be symmetrized: No redundant values")
  264        return Corr(newcontent, prange=self.prange)
  265
- 266    def is_matrix_symmetric(self):
+ 266    def is_matrix_symmetric(self):
  267        """Checks whether a correlator matrices is symmetric on every timeslice."""
  268        if self.N == 1:
  269            raise TypeError("Only works for correlator matrices.")
@@ -2035,7 +2035,7 @@
  278                        return False
  279        return True
  280
- 281    def trace(self):
+ 281    def trace(self):
  282        """Calculates the per-timeslice trace of a correlator matrix."""
  283        if self.N == 1:
  284            raise ValueError("Only works for correlator matrices.")
@@ -2047,7 +2047,7 @@
  290                newcontent.append(np.trace(self.content[t]))
  291        return Corr(newcontent)
  292
- 293    def matrix_symmetric(self):
+ 293    def matrix_symmetric(self):
  294        """Symmetrizes the correlator matrices on every timeslice."""
  295        if self.N == 1:
  296            raise ValueError("Trying to symmetrize a correlator matrix, that already has N=1.")
@@ -2057,7 +2057,7 @@
  300            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
  301            return 0.5 * (Corr(transposed) + self)
  302
- 303    def GEVP(self, t0, ts=None, sort="Eigenvalue", vector_obs=False, **kwargs):
+ 303    def GEVP(self, t0, ts=None, sort="Eigenvalue", vector_obs=False, **kwargs):
  304        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
  305
  306        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
@@ -2108,7 +2108,7 @@
  351        else:
  352            symmetric_corr = self.matrix_symmetric()
  353
- 354        def _get_mat_at_t(t, vector_obs=vector_obs):
+ 354        def _get_mat_at_t(t, vector_obs=vector_obs):
  355            if vector_obs:
  356                return symmetric_corr[t]
  357            else:
@@ -2163,7 +2163,7 @@
  406        else:
  407            return reordered_vecs
  408
- 409    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue", **kwargs):
+ 409    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue", **kwargs):
  410        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
  411
  412        Parameters
@@ -2176,7 +2176,7 @@
  419        vec = self.GEVP(t0, ts=ts, sort=sort, **kwargs)[state]
  420        return self.projected(vec)
  421
- 422    def Hankel(self, N, periodic=False):
+ 422    def Hankel(self, N, periodic=False):
  423        """Constructs an NxN Hankel matrix
  424
  425        C(t) c(t+1) ... c(t+n-1)
@@ -2200,7 +2200,7 @@
  443        for t in range(self.T):
  444            new_content.append(array.copy())
  445
- 446        def wrap(i):
+ 446        def wrap(i):
  447            while i >= self.T:
  448                i -= self.T
  449            return i
@@ -2217,7 +2217,7 @@
  460
  461        return Corr(new_content)
  462
- 463    def roll(self, dt):
+ 463    def roll(self, dt):
  464        """Periodically shift the correlator by dt timeslices
  465
  466        Parameters
@@ -2227,11 +2227,11 @@
  470        """
  471        return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0)))
  472
- 473    def reverse(self):
+ 473    def reverse(self):
  474        """Reverse the time ordering of the Corr"""
  475        return Corr(self.content[:: -1])
  476
- 477    def thin(self, spacing=2, offset=0):
+ 477    def thin(self, spacing=2, offset=0):
  478        """Thin out a correlator to suppress correlations
  479
  480        Parameters
@@ -2249,7 +2249,7 @@
  492                new_content.append(self.content[t])
  493        return Corr(new_content)
  494
- 495    def correlate(self, partner):
+ 495    def correlate(self, partner):
  496        """Correlate the correlator with another correlator or Obs
  497
  498        Parameters
@@ -2278,7 +2278,7 @@
  521
  522        return Corr(new_content)
  523
- 524    def reweight(self, weight, **kwargs):
+ 524    def reweight(self, weight, **kwargs):
  525        """Reweight the correlator.
  526
  527        Parameters
@@ -2301,7 +2301,7 @@
  544                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
  545        return Corr(new_content)
  546
- 547    def T_symmetry(self, partner, parity=+1):
+ 547    def T_symmetry(self, partner, parity=+1):
  548        """Return the time symmetry average of the correlator and its partner
  549
  550        Parameters
@@ -2331,7 +2331,7 @@
  574
  575        return (self + T_partner) / 2
  576
- 577    def deriv(self, variant="symmetric"):
+ 577    def deriv(self, variant="symmetric"):
  578        """Return the first derivative of the correlator with respect to x0.
  579
  580        Parameters
@@ -2396,7 +2396,7 @@
  639        else:
  640            raise ValueError("Unknown variant.")
  641
- 642    def second_deriv(self, variant="symmetric"):
+ 642    def second_deriv(self, variant="symmetric"):
  643        r"""Return the second derivative of the correlator with respect to x0.
  644
  645        Parameters
@@ -2459,7 +2459,7 @@
  702        else:
  703            raise ValueError("Unknown variant.")
  704
- 705    def m_eff(self, variant='log', guess=1.0):
+ 705    def m_eff(self, variant='log', guess=1.0):
  706        """Returns the effective mass of the correlator as correlator object
  707
  708        Parameters
@@ -2510,7 +2510,7 @@
  753            else:
  754                func = anp.sinh
  755
- 756            def root_function(x, d):
+ 756            def root_function(x, d):
  757                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
  758
  759            newcontent = []
@@ -2543,7 +2543,7 @@
  786        else:
  787            raise ValueError('Unknown variant.')
  788
- 789    def fit(self, function, fitrange=None, silent=False, **kwargs):
+ 789    def fit(self, function, fitrange=None, silent=False, **kwargs):
  790        r'''Fits function to the data
  791
  792        Parameters
@@ -2577,7 +2577,7 @@
  820        result = least_squares(xs, ys, function, silent=silent, **kwargs)
  821        return result
  822
- 823    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
+ 823    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
  824        """ Extract a plateau value from a Corr object
  825
  826        Parameters
@@ -2604,7 +2604,7 @@
  847        if auto_gamma:
  848            self.gamma_method()
  849        if method == "fit":
- 850            def const_func(a, t):
+ 850            def const_func(a, t):
  851                return a[0]
  852            return self.fit(const_func, plateau_range)[0]
  853        elif method in ["avg", "average", "mean"]:
@@ -2614,7 +2614,7 @@
  857        else:
  858            raise ValueError("Unsupported plateau method: " + method)
  859
- 860    def set_prange(self, prange):
+ 860    def set_prange(self, prange):
  861        """Sets the attribute prange of the Corr object."""
  862        if not len(prange) == 2:
  863            raise ValueError("prange must be a list or array with two values")
@@ -2626,7 +2626,7 @@
  869        self.prange = prange
  870        return
  871
- 872    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
+ 872    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
  873        """Plots the correlator using the tag of the correlator as label if available.
  874
  875        Parameters
@@ -2751,7 +2751,7 @@
  994            else:
  995                raise TypeError("'save' has to be a string.")
  996
- 997    def spaghetti_plot(self, logscale=True):
+ 997    def spaghetti_plot(self, logscale=True):
  998        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
  999
 1000        Parameters
@@ -2780,7 +2780,7 @@
 1023            plt.title(name)
 1024            plt.draw()
 1025
-1026    def dump(self, filename, datatype="json.gz", **kwargs):
+1026    def dump(self, filename, datatype="json.gz", **kwargs):
 1027        """Dumps the Corr into a file of chosen type
 1028        Parameters
 1029        ----------
@@ -2793,7 +2793,7 @@
 1036            specifies a custom path for the file (default '.')
 1037        """
 1038        if datatype == "json.gz":
-1039            from .input.json import dump_to_json
+1039            from .input.json import dump_to_json
 1040            if 'path' in kwargs:
 1041                file_name = kwargs.get('path') + '/' + filename
 1042            else:
@@ -2804,10 +2804,10 @@
 1047        else:
 1048            raise ValueError("Unknown datatype " + str(datatype))
 1049
-1050    def print(self, print_range=None):
+1050    def print(self, print_range=None):
 1051        print(self.__repr__(print_range))
 1052
-1053    def __repr__(self, print_range=None):
+1053    def __repr__(self, print_range=None):
 1054        if print_range is None:
 1055            print_range = [0, None]
 1056
@@ -2832,7 +2832,7 @@
 1075                content_string += '\n'
 1076        return content_string
 1077
-1078    def __str__(self):
+1078    def __str__(self):
 1079        return self.__repr__()
 1080
 1081    # We define the basic operations, that can be performed with correlators.
@@ -2842,14 +2842,14 @@
 1085
 1086    __array_priority__ = 10000
 1087
-1088    def __eq__(self, y):
+1088    def __eq__(self, y):
 1089        if isinstance(y, Corr):
 1090            comp = np.asarray(y.content, dtype=object)
 1091        else:
 1092            comp = np.asarray(y)
 1093        return np.asarray(self.content, dtype=object) == comp
 1094
-1095    def __add__(self, y):
+1095    def __add__(self, y):
 1096        if isinstance(y, Corr):
 1097            if ((self.N != y.N) or (self.T != y.T)):
 1098                raise ValueError("Addition of Corrs with different shape")
@@ -2877,7 +2877,7 @@
 1120        else:
 1121            raise TypeError("Corr + wrong type")
 1122
-1123    def __mul__(self, y):
+1123    def __mul__(self, y):
 1124        if isinstance(y, Corr):
 1125            if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
 1126                raise ValueError("Multiplication of Corr object requires N=N or N=1 and T=T")
@@ -2905,7 +2905,7 @@
 1148        else:
 1149            raise TypeError("Corr * wrong type")
 1150
-1151    def __matmul__(self, y):
+1151    def __matmul__(self, y):
 1152        if isinstance(y, np.ndarray):
 1153            if y.ndim != 2 or y.shape[0] != y.shape[1]:
 1154                raise ValueError("Can only multiply correlators by square matrices.")
@@ -2932,7 +2932,7 @@
 1175        else:
 1176            return NotImplemented
 1177
-1178    def __rmatmul__(self, y):
+1178    def __rmatmul__(self, y):
 1179        if isinstance(y, np.ndarray):
 1180            if y.ndim != 2 or y.shape[0] != y.shape[1]:
 1181                raise ValueError("Can only multiply correlators by square matrices.")
@@ -2948,7 +2948,7 @@
 1191        else:
 1192            return NotImplemented
 1193
-1194    def __truediv__(self, y):
+1194    def __truediv__(self, y):
 1195        if isinstance(y, Corr):
 1196            if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
 1197                raise ValueError("Multiplication of Corr object requires N=N or N=1 and T=T")
@@ -3002,37 +3002,37 @@
 1245        else:
 1246            raise TypeError('Corr / wrong type')
 1247
-1248    def __neg__(self):
+1248    def __neg__(self):
 1249        newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content]
 1250        return Corr(newcontent, prange=self.prange)
 1251
-1252    def __sub__(self, y):
+1252    def __sub__(self, y):
 1253        return self + (-y)
 1254
-1255    def __pow__(self, y):
+1255    def __pow__(self, y):
 1256        if isinstance(y, (Obs, int, float, CObs)):
 1257            newcontent = [None if _check_for_none(self, item) else item**y for item in self.content]
 1258            return Corr(newcontent, prange=self.prange)
 1259        else:
 1260            raise TypeError('Type of exponent not supported')
 1261
-1262    def __abs__(self):
+1262    def __abs__(self):
 1263        newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content]
 1264        return Corr(newcontent, prange=self.prange)
 1265
 1266    # The numpy functions:
-1267    def sqrt(self):
+1267    def sqrt(self):
 1268        return self ** 0.5
 1269
-1270    def log(self):
+1270    def log(self):
 1271        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
 1272        return Corr(newcontent, prange=self.prange)
 1273
-1274    def exp(self):
+1274    def exp(self):
 1275        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
 1276        return Corr(newcontent, prange=self.prange)
 1277
-1278    def _apply_func_to_corr(self, func):
+1278    def _apply_func_to_corr(self, func):
 1279        newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content]
 1280        for t in range(self.T):
 1281            if _check_for_none(self, newcontent[t]):
@@ -3045,58 +3045,58 @@
 1288            raise ValueError('Operation returns undefined correlator')
 1289        return Corr(newcontent)
 1290
-1291    def sin(self):
+1291    def sin(self):
 1292        return self._apply_func_to_corr(np.sin)
 1293
-1294    def cos(self):
+1294    def cos(self):
 1295        return self._apply_func_to_corr(np.cos)
 1296
-1297    def tan(self):
+1297    def tan(self):
 1298        return self._apply_func_to_corr(np.tan)
 1299
-1300    def sinh(self):
+1300    def sinh(self):
 1301        return self._apply_func_to_corr(np.sinh)
 1302
-1303    def cosh(self):
+1303    def cosh(self):
 1304        return self._apply_func_to_corr(np.cosh)
 1305
-1306    def tanh(self):
+1306    def tanh(self):
 1307        return self._apply_func_to_corr(np.tanh)
 1308
-1309    def arcsin(self):
+1309    def arcsin(self):
 1310        return self._apply_func_to_corr(np.arcsin)
 1311
-1312    def arccos(self):
+1312    def arccos(self):
 1313        return self._apply_func_to_corr(np.arccos)
 1314
-1315    def arctan(self):
+1315    def arctan(self):
 1316        return self._apply_func_to_corr(np.arctan)
 1317
-1318    def arcsinh(self):
+1318    def arcsinh(self):
 1319        return self._apply_func_to_corr(np.arcsinh)
 1320
-1321    def arccosh(self):
+1321    def arccosh(self):
 1322        return self._apply_func_to_corr(np.arccosh)
 1323
-1324    def arctanh(self):
+1324    def arctanh(self):
 1325        return self._apply_func_to_corr(np.arctanh)
 1326
 1327    # Right hand side operations (require tweak in main module to work)
-1328    def __radd__(self, y):
+1328    def __radd__(self, y):
 1329        return self + y
 1330
-1331    def __rsub__(self, y):
+1331    def __rsub__(self, y):
 1332        return -self + y
 1333
-1334    def __rmul__(self, y):
+1334    def __rmul__(self, y):
 1335        return self * y
 1336
-1337    def __rtruediv__(self, y):
+1337    def __rtruediv__(self, y):
 1338        return (self / y) ** (-1)
 1339
 1340    @property
-1341    def real(self):
-1342        def return_real(obs_OR_cobs):
+1341    def real(self):
+1342        def return_real(obs_OR_cobs):
 1343            if isinstance(obs_OR_cobs.flatten()[0], CObs):
 1344                return np.vectorize(lambda x: x.real)(obs_OR_cobs)
 1345            else:
@@ -3105,8 +3105,8 @@
 1348        return self._apply_func_to_corr(return_real)
 1349
 1350    @property
-1351    def imag(self):
-1352        def return_imag(obs_OR_cobs):
+1351    def imag(self):
+1352        def return_imag(obs_OR_cobs):
 1353            if isinstance(obs_OR_cobs.flatten()[0], CObs):
 1354                return np.vectorize(lambda x: x.imag)(obs_OR_cobs)
 1355            else:
@@ -3114,7 +3114,7 @@
 1357
 1358        return self._apply_func_to_corr(return_imag)
 1359
-1360    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
+1360    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
 1361        r''' Project large correlation matrix to lowest states
 1362
 1363        This method can be used to reduce the size of an (N x N) correlation matrix
@@ -3218,7 +3218,7 @@ the temporal extent of the correlator and N is the dimension of the matrix.

 
     

     
-            
 46    def __init__(self, data_input, padding=[0, 0], prange=None):
+            
 46    def __init__(self, data_input, padding=[0, 0], prange=None):
  47        """ Initialize a Corr object.
  48
  49        Parameters
@@ -3370,7 +3370,7 @@ region identified for this correlator.
     

     
             
132    @property
-133    def reweighted(self):
+133    def reweighted(self):
 134        bool_array = np.array([list(map(lambda x: x.reweighted, o)) for o in [x for x in self.content if x is not None]])
 135        if np.all(bool_array == 1):
 136            return True
@@ -3395,7 +3395,7 @@ region identified for this correlator.
 
     

     
-            
142    def gamma_method(self, **kwargs):
+            
142    def gamma_method(self, **kwargs):
 143        """Apply the gamma method to the content of the Corr."""
 144        for item in self.content:
 145            if item is not None:
@@ -3424,7 +3424,7 @@ region identified for this correlator.
 
     

     
-            
142    def gamma_method(self, **kwargs):
+            
142    def gamma_method(self, **kwargs):
 143        """Apply the gamma method to the content of the Corr."""
 144        for item in self.content:
 145            if item is not None:
@@ -3453,7 +3453,7 @@ region identified for this correlator.
 
     

     
-            
155    def projected(self, vector_l=None, vector_r=None, normalize=False):
+            
155    def projected(self, vector_l=None, vector_r=None, normalize=False):
 156        """We need to project the Correlator with a Vector to get a single value at each timeslice.
 157
 158        The method can use one or two vectors.
@@ -3514,7 +3514,7 @@ By default it will return the lowest source, which usually means unsmeared-unsme
 
     

     
-            
194    def item(self, i, j):
+            
194    def item(self, i, j):
 195        """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
 196
 197        Parameters
@@ -3556,7 +3556,7 @@ Second index to be picked.
 
     

     
-            
209    def plottable(self):
+            
209    def plottable(self):
 210        """Outputs the correlator in a plotable format.
 211
 212        Outputs three lists containing the timeslice index, the value on each
@@ -3591,7 +3591,7 @@ timeslice and the error on each timeslice.

 
     

     
-            
223    def symmetric(self):
+            
223    def symmetric(self):
 224        """ Symmetrize the correlator around x0=0."""
 225        if self.N != 1:
 226            raise ValueError('symmetric cannot be safely applied to multi-dimensional correlators.')
@@ -3630,7 +3630,7 @@ timeslice and the error on each timeslice.

 
     

     
-            
244    def anti_symmetric(self):
+            
244    def anti_symmetric(self):
 245        """Anti-symmetrize the correlator around x0=0."""
 246        if self.N != 1:
 247            raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.')
@@ -3670,7 +3670,7 @@ timeslice and the error on each timeslice.

 
     

     
-            
266    def is_matrix_symmetric(self):
+            
266    def is_matrix_symmetric(self):
 267        """Checks whether a correlator matrices is symmetric on every timeslice."""
 268        if self.N == 1:
 269            raise TypeError("Only works for correlator matrices.")
@@ -3703,7 +3703,7 @@ timeslice and the error on each timeslice.

 
     

     
-            
281    def trace(self):
+            
281    def trace(self):
 282        """Calculates the per-timeslice trace of a correlator matrix."""
 283        if self.N == 1:
 284            raise ValueError("Only works for correlator matrices.")
@@ -3733,7 +3733,7 @@ timeslice and the error on each timeslice.

 
     

     
-            
293    def matrix_symmetric(self):
+            
293    def matrix_symmetric(self):
 294        """Symmetrizes the correlator matrices on every timeslice."""
 295        if self.N == 1:
 296            raise ValueError("Trying to symmetrize a correlator matrix, that already has N=1.")
@@ -3761,7 +3761,7 @@ timeslice and the error on each timeslice.

 
     

     
-            
303    def GEVP(self, t0, ts=None, sort="Eigenvalue", vector_obs=False, **kwargs):
+            
303    def GEVP(self, t0, ts=None, sort="Eigenvalue", vector_obs=False, **kwargs):
 304        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
 305
 306        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
@@ -3812,7 +3812,7 @@ timeslice and the error on each timeslice.

 351        else:
 352            symmetric_corr = self.matrix_symmetric()
 353
-354        def _get_mat_at_t(t, vector_obs=vector_obs):
+354        def _get_mat_at_t(t, vector_obs=vector_obs):
 355            if vector_obs:
 356                return symmetric_corr[t]
 357            else:
@@ -3927,7 +3927,7 @@ Method used to solve the GEVP.
 
     

     
-            
409    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue", **kwargs):
+            
409    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue", **kwargs):
 410        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
 411
 412        Parameters
@@ -3966,7 +3966,7 @@ The state one is interested in ordered by energy. The lowest state is zero.
 
     

     
-            
422    def Hankel(self, N, periodic=False):
+            
422    def Hankel(self, N, periodic=False):
 423        """Constructs an NxN Hankel matrix
 424
 425        C(t) c(t+1) ... c(t+n-1)
@@ -3990,7 +3990,7 @@ The state one is interested in ordered by energy. The lowest state is zero.
 443        for t in range(self.T):
 444            new_content.append(array.copy())
 445
-446        def wrap(i):
+446        def wrap(i):
 447            while i >= self.T:
 448                i -= self.T
 449            return i
@@ -4039,7 +4039,7 @@ determines whether the matrix is extended periodically
 
     

     
-            
463    def roll(self, dt):
+            
463    def roll(self, dt):
 464        """Periodically shift the correlator by dt timeslices
 465
 466        Parameters
@@ -4074,7 +4074,7 @@ number of timeslices
 
     

     
-            
473    def reverse(self):
+            
473    def reverse(self):
 474        """Reverse the time ordering of the Corr"""
 475        return Corr(self.content[:: -1])
 

@@ -4096,7 +4096,7 @@ number of timeslices
 
     

     
-            
477    def thin(self, spacing=2, offset=0):
+            
477    def thin(self, spacing=2, offset=0):
 478        """Thin out a correlator to suppress correlations
 479
 480        Parameters
@@ -4141,7 +4141,7 @@ Offset the equal spacing
 
     

     
-            
495    def correlate(self, partner):
+            
495    def correlate(self, partner):
 496        """Correlate the correlator with another correlator or Obs
 497
 498        Parameters
@@ -4197,7 +4197,7 @@ correlator or a Corr of same length.
 
     

     
-            
524    def reweight(self, weight, **kwargs):
+            
524    def reweight(self, weight, **kwargs):
 525        """Reweight the correlator.
 526
 527        Parameters
@@ -4250,7 +4250,7 @@ on the configurations in obs[i].idl.
 
     

     
-            
547    def T_symmetry(self, partner, parity=+1):
+            
547    def T_symmetry(self, partner, parity=+1):
 548        """Return the time symmetry average of the correlator and its partner
 549
 550        Parameters
@@ -4307,7 +4307,7 @@ Parity quantum number of the correlator, can be +1 or -1
 
     

     
-            
577    def deriv(self, variant="symmetric"):
+            
577    def deriv(self, variant="symmetric"):
 578        """Return the first derivative of the correlator with respect to x0.
 579
 580        Parameters
@@ -4398,7 +4398,7 @@ Available choice: symmetric, forward, backward, improved, log, default: symmetri
 
     

     
-            
642    def second_deriv(self, variant="symmetric"):
+            
642    def second_deriv(self, variant="symmetric"):
 643        r"""Return the second derivative of the correlator with respect to x0.
 644
 645        Parameters
@@ -4495,7 +4495,7 @@ Available choice:
 
     

     
-            
705    def m_eff(self, variant='log', guess=1.0):
+            
705    def m_eff(self, variant='log', guess=1.0):
 706        """Returns the effective mass of the correlator as correlator object
 707
 708        Parameters
@@ -4546,7 +4546,7 @@ Available choice:
 753            else:
 754                func = anp.sinh
 755
-756            def root_function(x, d):
+756            def root_function(x, d):
 757                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
 758
 759            newcontent = []
@@ -4611,7 +4611,7 @@ guess for the root finder, only relevant for the root variant
 
     

     
-            
789    def fit(self, function, fitrange=None, silent=False, **kwargs):
+            
789    def fit(self, function, fitrange=None, silent=False, **kwargs):
 790        r'''Fits function to the data
 791
 792        Parameters
@@ -4677,7 +4677,7 @@ Decides whether output is printed to the standard output.
 
     

     
-            
823    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
+            
823    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
 824        """ Extract a plateau value from a Corr object
 825
 826        Parameters
@@ -4704,7 +4704,7 @@ Decides whether output is printed to the standard output.
 847        if auto_gamma:
 848            self.gamma_method()
 849        if method == "fit":
-850            def const_func(a, t):
+850            def const_func(a, t):
 851                return a[0]
 852            return self.fit(const_func, plateau_range)[0]
 853        elif method in ["avg", "average", "mean"]:
@@ -4746,7 +4746,7 @@ apply gamma_method with default parameters to the Corr. Defaults to None
 
     

     
-            
860    def set_prange(self, prange):
+            
860    def set_prange(self, prange):
 861        """Sets the attribute prange of the Corr object."""
 862        if not len(prange) == 2:
 863            raise ValueError("prange must be a list or array with two values")
@@ -4776,7 +4776,7 @@ apply gamma_method with default parameters to the Corr. Defaults to None
 
     

     
-            
872    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
+            
872    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
 873        """Plots the correlator using the tag of the correlator as label if available.
 874
 875        Parameters
@@ -4949,7 +4949,7 @@ Optional title of the figure.
 
     

     
-            
 997    def spaghetti_plot(self, logscale=True):
+            
 997    def spaghetti_plot(self, logscale=True):
  998        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
  999
 1000        Parameters
@@ -5003,7 +5003,7 @@ Determines whether the scale of the y-axis is logarithmic or standard.
 
     

     
-            
1026    def dump(self, filename, datatype="json.gz", **kwargs):
+            
1026    def dump(self, filename, datatype="json.gz", **kwargs):
 1027        """Dumps the Corr into a file of chosen type
 1028        Parameters
 1029        ----------
@@ -5016,7 +5016,7 @@ Determines whether the scale of the y-axis is logarithmic or standard.
 1036            specifies a custom path for the file (default '.')
 1037        """
 1038        if datatype == "json.gz":
-1039            from .input.json import dump_to_json
+1039            from .input.json import dump_to_json
 1040            if 'path' in kwargs:
 1041                file_name = kwargs.get('path') + '/' + filename
 1042            else:
@@ -5057,7 +5057,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1050    def print(self, print_range=None):
+            
1050    def print(self, print_range=None):
 1051        print(self.__repr__(print_range))
 

 
@@ -5076,7 +5076,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1267    def sqrt(self):
+            
1267    def sqrt(self):
 1268        return self ** 0.5
 

 
@@ -5095,7 +5095,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1270    def log(self):
+            
1270    def log(self):
 1271        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
 1272        return Corr(newcontent, prange=self.prange)
 

@@ -5115,7 +5115,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1274    def exp(self):
+            
1274    def exp(self):
 1275        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
 1276        return Corr(newcontent, prange=self.prange)
 

@@ -5135,7 +5135,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1291    def sin(self):
+            
1291    def sin(self):
 1292        return self._apply_func_to_corr(np.sin)
 

 
@@ -5154,7 +5154,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1294    def cos(self):
+            
1294    def cos(self):
 1295        return self._apply_func_to_corr(np.cos)
 

 
@@ -5173,7 +5173,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1297    def tan(self):
+            
1297    def tan(self):
 1298        return self._apply_func_to_corr(np.tan)
 

 
@@ -5192,7 +5192,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1300    def sinh(self):
+            
1300    def sinh(self):
 1301        return self._apply_func_to_corr(np.sinh)
 

 
@@ -5211,7 +5211,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1303    def cosh(self):
+            
1303    def cosh(self):
 1304        return self._apply_func_to_corr(np.cosh)
 

 
@@ -5230,7 +5230,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1306    def tanh(self):
+            
1306    def tanh(self):
 1307        return self._apply_func_to_corr(np.tanh)
 

 
@@ -5249,7 +5249,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1309    def arcsin(self):
+            
1309    def arcsin(self):
 1310        return self._apply_func_to_corr(np.arcsin)
 

 
@@ -5268,7 +5268,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1312    def arccos(self):
+            
1312    def arccos(self):
 1313        return self._apply_func_to_corr(np.arccos)
 

 
@@ -5287,7 +5287,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1315    def arctan(self):
+            
1315    def arctan(self):
 1316        return self._apply_func_to_corr(np.arctan)
 

 
@@ -5306,7 +5306,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1318    def arcsinh(self):
+            
1318    def arcsinh(self):
 1319        return self._apply_func_to_corr(np.arcsinh)
 

 
@@ -5325,7 +5325,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1321    def arccosh(self):
+            
1321    def arccosh(self):
 1322        return self._apply_func_to_corr(np.arccosh)
 

 
@@ -5344,7 +5344,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1324    def arctanh(self):
+            
1324    def arctanh(self):
 1325        return self._apply_func_to_corr(np.arctanh)
 

 
@@ -5362,8 +5362,8 @@ specifies a custom path for the file (default '.')
     

     
             
1340    @property
-1341    def real(self):
-1342        def return_real(obs_OR_cobs):
+1341    def real(self):
+1342        def return_real(obs_OR_cobs):
 1343            if isinstance(obs_OR_cobs.flatten()[0], CObs):
 1344                return np.vectorize(lambda x: x.real)(obs_OR_cobs)
 1345            else:
@@ -5386,8 +5386,8 @@ specifies a custom path for the file (default '.')
     

     
             
1350    @property
-1351    def imag(self):
-1352        def return_imag(obs_OR_cobs):
+1351    def imag(self):
+1352        def return_imag(obs_OR_cobs):
 1353            if isinstance(obs_OR_cobs.flatten()[0], CObs):
 1354                return np.vectorize(lambda x: x.imag)(obs_OR_cobs)
 1355            else:
@@ -5411,7 +5411,7 @@ specifies a custom path for the file (default '.')
 
     

     
-            
1360    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
+            
1360    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
 1361        r''' Project large correlation matrix to lowest states
 1362
 1363        This method can be used to reduce the size of an (N x N) correlation matrix
diff --git a/docs/pyerrors/covobs.html b/docs/pyerrors/covobs.html
index 9b20b705..80a4ef5f 100644
--- a/docs/pyerrors/covobs.html
+++ b/docs/pyerrors/covobs.html
@@ -97,12 +97,12 @@
 
                         
 
-                        
  1import numpy as np
+                        
  1import numpy as np
   2
   3
-  4class Covobs:
+  4class Covobs:
   5
-  6    def __init__(self, mean, cov, name, pos=None, grad=None):
+  6    def __init__(self, mean, cov, name, pos=None, grad=None):
   7        """ Initialize Covobs object.
   8
   9        Parameters
@@ -138,12 +138,12 @@
  39            self._set_grad(grad)
  40        self.value = mean
  41
- 42    def errsq(self):
+ 42    def errsq(self):
  43        """ Return the variance (= square of the error) of the Covobs
  44        """
  45        return np.dot(np.transpose(self.grad), np.dot(self.cov, self.grad)).item()
  46
- 47    def _set_cov(self, cov):
+ 47    def _set_cov(self, cov):
  48        """ Set the covariance matrix of the covobs
  49
  50        Parameters
@@ -178,7 +178,7 @@
  79            if ev < 0:
  80                raise Exception('Covariance matrix is not positive-semidefinite!')
  81
- 82    def _set_grad(self, grad):
+ 82    def _set_grad(self, grad):
  83        """ Set the gradient of the covobs
  84
  85        Parameters
@@ -195,11 +195,11 @@
  96            raise Exception('Invalid dimension of grad!')
  97
  98    @property
- 99    def cov(self):
+ 99    def cov(self):
 100        return self._cov
 101
 102    @property
-103    def grad(self):
+103    def grad(self):
 104        return self._grad
 

 
@@ -216,9 +216,9 @@
 
     

     
-            
  5class Covobs:
+            
  5class Covobs:
   6
-  7    def __init__(self, mean, cov, name, pos=None, grad=None):
+  7    def __init__(self, mean, cov, name, pos=None, grad=None):
   8        """ Initialize Covobs object.
   9
  10        Parameters
@@ -254,12 +254,12 @@
  40            self._set_grad(grad)
  41        self.value = mean
  42
- 43    def errsq(self):
+ 43    def errsq(self):
  44        """ Return the variance (= square of the error) of the Covobs
  45        """
  46        return np.dot(np.transpose(self.grad), np.dot(self.cov, self.grad)).item()
  47
- 48    def _set_cov(self, cov):
+ 48    def _set_cov(self, cov):
  49        """ Set the covariance matrix of the covobs
  50
  51        Parameters
@@ -294,7 +294,7 @@
  80            if ev < 0:
  81                raise Exception('Covariance matrix is not positive-semidefinite!')
  82
- 83    def _set_grad(self, grad):
+ 83    def _set_grad(self, grad):
  84        """ Set the gradient of the covobs
  85
  86        Parameters
@@ -311,11 +311,11 @@
  97            raise Exception('Invalid dimension of grad!')
  98
  99    @property
-100    def cov(self):
+100    def cov(self):
 101        return self._cov
 102
 103    @property
-104    def grad(self):
+104    def grad(self):
 105        return self._grad
 

 
@@ -332,7 +332,7 @@
 
     

     
-            
 7    def __init__(self, mean, cov, name, pos=None, grad=None):
+            
 7    def __init__(self, mean, cov, name, pos=None, grad=None):
  8        """ Initialize Covobs object.
  9
 10        Parameters
@@ -424,7 +424,7 @@ Gradient of the Covobs wrt. the means belonging to cov.
 
     

     
-            
43    def errsq(self):
+            
43    def errsq(self):
 44        """ Return the variance (= square of the error) of the Covobs
 45        """
 46        return np.dot(np.transpose(self.grad), np.dot(self.cov, self.grad)).item()
@@ -446,7 +446,7 @@ Gradient of the Covobs wrt. the means belonging to cov.
     

     
             
 99    @property
-100    def cov(self):
+100    def cov(self):
 101        return self._cov
 

 
@@ -464,7 +464,7 @@ Gradient of the Covobs wrt. the means belonging to cov.
     

     
             
103    @property
-104    def grad(self):
+104    def grad(self):
 105        return self._grad
 

 
diff --git a/docs/pyerrors/dirac.html b/docs/pyerrors/dirac.html
index 49b94a06..450c573a 100644
--- a/docs/pyerrors/dirac.html
+++ b/docs/pyerrors/dirac.html
@@ -103,7 +103,7 @@
 
                         
 
-                        
 1import numpy as np
+                        
 1import numpy as np
  2
  3
  4gammaX = np.array(
@@ -127,7 +127,7 @@
 22    dtype=complex)
 23
 24
-25def epsilon_tensor(i, j, k):
+25def epsilon_tensor(i, j, k):
 26    """Rank-3 epsilon tensor
 27
 28    Based on https://codegolf.stackexchange.com/a/160375
@@ -144,7 +144,7 @@
 39    return (i - j) * (j - k) * (k - i) / 2
 40
 41
-42def epsilon_tensor_rank4(i, j, k, o):
+42def epsilon_tensor_rank4(i, j, k, o):
 43    """Rank-4 epsilon tensor
 44
 45    Extension of https://codegolf.stackexchange.com/a/160375
@@ -162,7 +162,7 @@
 57    return (i - j) * (j - k) * (k - i) * (i - o) * (j - o) * (o - k) / 12
 58
 59
-60def Grid_gamma(gamma_tag):
+60def Grid_gamma(gamma_tag):
 61    """Returns gamma matrix in Grid labeling."""
 62    if gamma_tag == 'Identity':
 63        g = identity
@@ -341,7 +341,7 @@
 
     

     
-            
26def epsilon_tensor(i, j, k):
+            
26def epsilon_tensor(i, j, k):
 27    """Rank-3 epsilon tensor
 28
 29    Based on https://codegolf.stackexchange.com/a/160375
@@ -384,7 +384,7 @@ Element (i,j,k) of the epsilon tensor of rank 3
 
     

     
-            
43def epsilon_tensor_rank4(i, j, k, o):
+            
43def epsilon_tensor_rank4(i, j, k, o):
 44    """Rank-4 epsilon tensor
 45
 46    Extension of https://codegolf.stackexchange.com/a/160375
@@ -428,7 +428,7 @@ Element (i,j,k,o) of the epsilon tensor of rank 4
 
     

     
-            
61def Grid_gamma(gamma_tag):
+            
61def Grid_gamma(gamma_tag):
 62    """Returns gamma matrix in Grid labeling."""
 63    if gamma_tag == 'Identity':
 64        g = identity
diff --git a/docs/pyerrors/fits.html b/docs/pyerrors/fits.html
index 21620dbb..63d7aae4 100644
--- a/docs/pyerrors/fits.html
+++ b/docs/pyerrors/fits.html
@@ -109,26 +109,26 @@
 
                         
 
-                        
  1import gc
-  2from collections.abc import Sequence
-  3import warnings
-  4import numpy as np
-  5import autograd.numpy as anp
-  6import scipy.optimize
-  7import scipy.stats
-  8import matplotlib.pyplot as plt
-  9from matplotlib import gridspec
- 10from scipy.odr import ODR, Model, RealData
- 11import iminuit
- 12from autograd import jacobian as auto_jacobian
- 13from autograd import hessian as auto_hessian
- 14from autograd import elementwise_grad as egrad
- 15from numdifftools import Jacobian as num_jacobian
- 16from numdifftools import Hessian as num_hessian
- 17from .obs import Obs, derived_observable, covariance, cov_Obs, invert_corr_cov_cholesky
+                        
  1import gc
+  2from collections.abc import Sequence
+  3import warnings
+  4import numpy as np
+  5import autograd.numpy as anp
+  6import scipy.optimize
+  7import scipy.stats
+  8import matplotlib.pyplot as plt
+  9from matplotlib import gridspec
+ 10from scipy.odr import ODR, Model, RealData
+ 11import iminuit
+ 12from autograd import jacobian as auto_jacobian
+ 13from autograd import hessian as auto_hessian
+ 14from autograd import elementwise_grad as egrad
+ 15from numdifftools import Jacobian as num_jacobian
+ 16from numdifftools import Hessian as num_hessian
+ 17from .obs import Obs, derived_observable, covariance, cov_Obs, invert_corr_cov_cholesky
  18
  19
- 20class Fit_result(Sequence):
+ 20class Fit_result(Sequence):
  21    """Represents fit results.
  22
  23    Attributes
@@ -144,22 +144,22 @@
  33        Hotelling t-squared p-value for correlated fits.
  34    """
  35
- 36    def __init__(self):
+ 36    def __init__(self):
  37        self.fit_parameters = None
  38
- 39    def __getitem__(self, idx):
+ 39    def __getitem__(self, idx):
  40        return self.fit_parameters[idx]
  41
- 42    def __len__(self):
+ 42    def __len__(self):
  43        return len(self.fit_parameters)
  44
- 45    def gamma_method(self, **kwargs):
+ 45    def gamma_method(self, **kwargs):
  46        """Apply the gamma method to all fit parameters"""
  47        [o.gamma_method(**kwargs) for o in self.fit_parameters]
  48
  49    gm = gamma_method
  50
- 51    def __str__(self):
+ 51    def __str__(self):
  52        my_str = 'Goodness of fit:\n'
  53        if hasattr(self, 'chisquare_by_dof'):
  54            my_str += '\u03C7\u00b2/d.o.f. = ' + f'{self.chisquare_by_dof:2.6f}' + '\n'
@@ -176,12 +176,12 @@
  65            my_str += str(i_par) + '\t' + ' ' * int(par >= 0) + str(par).rjust(int(par < 0.0)) + '\n'
  66        return my_str
  67
- 68    def __repr__(self):
+ 68    def __repr__(self):
  69        m = max(map(len, list(self.__dict__.keys()))) + 1
  70        return '\n'.join([key.rjust(m) + ': ' + repr(value) for key, value in sorted(self.__dict__.items())])
  71
  72
- 73def least_squares(x, y, func, priors=None, silent=False, **kwargs):
+ 73def least_squares(x, y, func, priors=None, silent=False, **kwargs):
  74    r'''Performs a non-linear fit to y = func(x).
  75        ```
  76
@@ -455,15 +455,15 @@
 344        x0 = [0.1] * n_parms
 345
 346    if priors is None:
-347        def general_chisqfunc_uncorr(p, ivars, pr):
+347        def general_chisqfunc_uncorr(p, ivars, pr):
 348            model = anp.concatenate([anp.array(funcd[key](p, xd[key])).reshape(-1) for key in key_ls])
 349            return (ivars - model) / dy_f
 350    else:
-351        def general_chisqfunc_uncorr(p, ivars, pr):
+351        def general_chisqfunc_uncorr(p, ivars, pr):
 352            model = anp.concatenate([anp.array(funcd[key](p, xd[key])).reshape(-1) for key in key_ls])
 353            return anp.concatenate(((ivars - model) / dy_f, (p[prior_mask] - pr) / dp_f))
 354
-355    def chisqfunc_uncorr(p):
+355    def chisqfunc_uncorr(p):
 356        return anp.sum(general_chisqfunc_uncorr(p, y_f, p_f) ** 2)
 357
 358    if kwargs.get('correlated_fit') is True:
@@ -481,11 +481,11 @@
 370            inverrdiag = np.diag(1 / np.asarray(dy_f))
 371            chol_inv = invert_corr_cov_cholesky(corr, inverrdiag)
 372
-373        def general_chisqfunc(p, ivars, pr):
+373        def general_chisqfunc(p, ivars, pr):
 374            model = anp.concatenate([anp.array(funcd[key](p, xd[key])).reshape(-1) for key in key_ls])
 375            return anp.concatenate((anp.dot(chol_inv, (ivars - model)), (p[prior_mask] - pr) / dp_f))
 376
-377        def chisqfunc(p):
+377        def chisqfunc(p):
 378            return anp.sum(general_chisqfunc(p, y_f, p_f) ** 2)
 379    else:
 380        general_chisqfunc = general_chisqfunc_uncorr
@@ -519,12 +519,12 @@
 408        if 'tol' in kwargs:
 409            print('tol cannot be set for Levenberg-Marquardt')
 410
-411        def chisqfunc_residuals_uncorr(p):
+411        def chisqfunc_residuals_uncorr(p):
 412            return general_chisqfunc_uncorr(p, y_f, p_f)
 413
 414        fit_result = scipy.optimize.least_squares(chisqfunc_residuals_uncorr, x0, method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
 415        if kwargs.get('correlated_fit') is True:
-416            def chisqfunc_residuals(p):
+416            def chisqfunc_residuals(p):
 417                return general_chisqfunc(p, y_f, p_f)
 418
 419            fit_result = scipy.optimize.least_squares(chisqfunc_residuals, fit_result.x, method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
@@ -551,7 +551,7 @@
 440        print('chisquare/d.o.f.:', output.chisquare_by_dof)
 441        print('fit parameters', fit_result.x)
 442
-443    def prepare_hat_matrix():
+443    def prepare_hat_matrix():
 444        hat_vector = []
 445        for key in key_ls:
 446            if (len(xd[key]) != 0):
@@ -576,11 +576,11 @@
 465    try:
 466        hess = hessian(chisqfunc)(fitp)
 467    except TypeError:
-468        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
+468        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
 469
 470    len_y = len(y_f)
 471
-472    def chisqfunc_compact(d):
+472    def chisqfunc_compact(d):
 473        return anp.sum(general_chisqfunc(d[:n_parms], d[n_parms: n_parms + len_y], d[n_parms + len_y:]) ** 2)
 474
 475    jac_jac_y = hessian(chisqfunc_compact)(np.concatenate((fitp, y_f, p_f)))
@@ -614,7 +614,7 @@
 503    return output
 504
 505
-506def total_least_squares(x, y, func, silent=False, **kwargs):
+506def total_least_squares(x, y, func, silent=False, **kwargs):
 507    r'''Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
 508
 509    Parameters
@@ -742,7 +742,7 @@
 631
 632    m = x_f.size
 633
-634    def odr_chisquare(p):
+634    def odr_chisquare(p):
 635        model = func(p[:n_parms], p[n_parms:].reshape(x_shape))
 636        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((x_f - p[n_parms:].reshape(x_shape)) / dx_f) ** 2)
 637        return chisq
@@ -777,9 +777,9 @@
 666    try:
 667        hess = hessian(odr_chisquare)(np.concatenate((fitp, out.xplus.ravel())))
 668    except TypeError:
-669        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
+669        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
 670
-671    def odr_chisquare_compact_x(d):
+671    def odr_chisquare_compact_x(d):
 672        model = func(d[:n_parms], d[n_parms:n_parms + m].reshape(x_shape))
 673        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((d[n_parms + m:].reshape(x_shape) - d[n_parms:n_parms + m].reshape(x_shape)) / dx_f) ** 2)
 674        return chisq
@@ -792,7 +792,7 @@
 681    except np.linalg.LinAlgError:
 682        raise Exception("Cannot invert hessian matrix.")
 683
-684    def odr_chisquare_compact_y(d):
+684    def odr_chisquare_compact_y(d):
 685        model = func(d[:n_parms], d[n_parms:n_parms + m].reshape(x_shape))
 686        chisq = anp.sum(((d[n_parms + m:] - model) / dy_f) ** 2) + anp.sum(((x_f - d[n_parms:n_parms + m].reshape(x_shape)) / dx_f) ** 2)
 687        return chisq
@@ -818,7 +818,7 @@
 707    return output
 708
 709
-710def fit_lin(x, y, **kwargs):
+710def fit_lin(x, y, **kwargs):
 711    """Performs a linear fit to y = n + m * x and returns two Obs n, m.
 712
 713    Parameters
@@ -835,7 +835,7 @@
 724        LIist of fitted observables.
 725    """
 726
-727    def f(a, x):
+727    def f(a, x):
 728        y = a[0] + a[1] * x
 729        return y
 730
@@ -849,7 +849,7 @@
 738        raise TypeError('Unsupported types for x')
 739
 740
-741def qqplot(x, o_y, func, p, title=""):
+741def qqplot(x, o_y, func, p, title=""):
 742    """Generates a quantile-quantile plot of the fit result which can be used to
 743       check if the residuals of the fit are gaussian distributed.
 744
@@ -879,7 +879,7 @@
 768    plt.draw()
 769
 770
-771def residual_plot(x, y, func, fit_res, title=""):
+771def residual_plot(x, y, func, fit_res, title=""):
 772    """Generates a plot which compares the fit to the data and displays the corresponding residuals
 773
 774    For uncorrelated data the residuals are expected to be distributed ~N(0,1).
@@ -916,7 +916,7 @@
 805    plt.draw()
 806
 807
-808def error_band(x, func, beta):
+808def error_band(x, func, beta):
 809    """Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
 810
 811    Returns
@@ -940,7 +940,7 @@
 829    return err
 830
 831
-832def ks_test(objects=None):
+832def ks_test(objects=None):
 833    """Performs a Kolmogorov–Smirnov test for the p-values of all fit object.
 834
 835    Parameters
@@ -984,7 +984,7 @@
 873    print(scipy.stats.kstest(p_values, 'uniform'))
 874
 875
-876def _extract_val_and_dval(string):
+876def _extract_val_and_dval(string):
 877    split_string = string.split('(')
 878    if '.' in split_string[0] and '.' not in split_string[1][:-1]:
 879        factor = 10 ** -len(split_string[0].partition('.')[2])
@@ -993,7 +993,7 @@
 882    return float(split_string[0]), float(split_string[1][:-1]) * factor
 883
 884
-885def _construct_prior_obs(i_prior, i_n):
+885def _construct_prior_obs(i_prior, i_n):
 886    if isinstance(i_prior, Obs):
 887        return i_prior
 888    elif isinstance(i_prior, str):
@@ -1016,7 +1016,7 @@
 
     

     
-            
21class Fit_result(Sequence):
+            
21class Fit_result(Sequence):
 22    """Represents fit results.
 23
 24    Attributes
@@ -1032,22 +1032,22 @@
 34        Hotelling t-squared p-value for correlated fits.
 35    """
 36
-37    def __init__(self):
+37    def __init__(self):
 38        self.fit_parameters = None
 39
-40    def __getitem__(self, idx):
+40    def __getitem__(self, idx):
 41        return self.fit_parameters[idx]
 42
-43    def __len__(self):
+43    def __len__(self):
 44        return len(self.fit_parameters)
 45
-46    def gamma_method(self, **kwargs):
+46    def gamma_method(self, **kwargs):
 47        """Apply the gamma method to all fit parameters"""
 48        [o.gamma_method(**kwargs) for o in self.fit_parameters]
 49
 50    gm = gamma_method
 51
-52    def __str__(self):
+52    def __str__(self):
 53        my_str = 'Goodness of fit:\n'
 54        if hasattr(self, 'chisquare_by_dof'):
 55            my_str += '\u03C7\u00b2/d.o.f. = ' + f'{self.chisquare_by_dof:2.6f}' + '\n'
@@ -1064,7 +1064,7 @@
 66            my_str += str(i_par) + '\t' + ' ' * int(par >= 0) + str(par).rjust(int(par < 0.0)) + '\n'
 67        return my_str
 68
-69    def __repr__(self):
+69    def __repr__(self):
 70        m = max(map(len, list(self.__dict__.keys()))) + 1
 71        return '\n'.join([key.rjust(m) + ': ' + repr(value) for key, value in sorted(self.__dict__.items())])
 

@@ -1110,7 +1110,7 @@ Hotelling t-squared p-value for correlated fits.
 
     

     
-            
46    def gamma_method(self, **kwargs):
+            
46    def gamma_method(self, **kwargs):
 47        """Apply the gamma method to all fit parameters"""
 48        [o.gamma_method(**kwargs) for o in self.fit_parameters]
 

@@ -1132,7 +1132,7 @@ Hotelling t-squared p-value for correlated fits.
 
     

     
-            
46    def gamma_method(self, **kwargs):
+            
46    def gamma_method(self, **kwargs):
 47        """Apply the gamma method to all fit parameters"""
 48        [o.gamma_method(**kwargs) for o in self.fit_parameters]
 

@@ -1155,7 +1155,7 @@ Hotelling t-squared p-value for correlated fits.
 
     

     
-            
 74def least_squares(x, y, func, priors=None, silent=False, **kwargs):
+            
 74def least_squares(x, y, func, priors=None, silent=False, **kwargs):
  75    r'''Performs a non-linear fit to y = func(x).
  76        ```
  77
@@ -1429,15 +1429,15 @@ Hotelling t-squared p-value for correlated fits.
 345        x0 = [0.1] * n_parms
 346
 347    if priors is None:
-348        def general_chisqfunc_uncorr(p, ivars, pr):
+348        def general_chisqfunc_uncorr(p, ivars, pr):
 349            model = anp.concatenate([anp.array(funcd[key](p, xd[key])).reshape(-1) for key in key_ls])
 350            return (ivars - model) / dy_f
 351    else:
-352        def general_chisqfunc_uncorr(p, ivars, pr):
+352        def general_chisqfunc_uncorr(p, ivars, pr):
 353            model = anp.concatenate([anp.array(funcd[key](p, xd[key])).reshape(-1) for key in key_ls])
 354            return anp.concatenate(((ivars - model) / dy_f, (p[prior_mask] - pr) / dp_f))
 355
-356    def chisqfunc_uncorr(p):
+356    def chisqfunc_uncorr(p):
 357        return anp.sum(general_chisqfunc_uncorr(p, y_f, p_f) ** 2)
 358
 359    if kwargs.get('correlated_fit') is True:
@@ -1455,11 +1455,11 @@ Hotelling t-squared p-value for correlated fits.
 371            inverrdiag = np.diag(1 / np.asarray(dy_f))
 372            chol_inv = invert_corr_cov_cholesky(corr, inverrdiag)
 373
-374        def general_chisqfunc(p, ivars, pr):
+374        def general_chisqfunc(p, ivars, pr):
 375            model = anp.concatenate([anp.array(funcd[key](p, xd[key])).reshape(-1) for key in key_ls])
 376            return anp.concatenate((anp.dot(chol_inv, (ivars - model)), (p[prior_mask] - pr) / dp_f))
 377
-378        def chisqfunc(p):
+378        def chisqfunc(p):
 379            return anp.sum(general_chisqfunc(p, y_f, p_f) ** 2)
 380    else:
 381        general_chisqfunc = general_chisqfunc_uncorr
@@ -1493,12 +1493,12 @@ Hotelling t-squared p-value for correlated fits.
 409        if 'tol' in kwargs:
 410            print('tol cannot be set for Levenberg-Marquardt')
 411
-412        def chisqfunc_residuals_uncorr(p):
+412        def chisqfunc_residuals_uncorr(p):
 413            return general_chisqfunc_uncorr(p, y_f, p_f)
 414
 415        fit_result = scipy.optimize.least_squares(chisqfunc_residuals_uncorr, x0, method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
 416        if kwargs.get('correlated_fit') is True:
-417            def chisqfunc_residuals(p):
+417            def chisqfunc_residuals(p):
 418                return general_chisqfunc(p, y_f, p_f)
 419
 420            fit_result = scipy.optimize.least_squares(chisqfunc_residuals, fit_result.x, method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
@@ -1525,7 +1525,7 @@ Hotelling t-squared p-value for correlated fits.
 441        print('chisquare/d.o.f.:', output.chisquare_by_dof)
 442        print('fit parameters', fit_result.x)
 443
-444    def prepare_hat_matrix():
+444    def prepare_hat_matrix():
 445        hat_vector = []
 446        for key in key_ls:
 447            if (len(xd[key]) != 0):
@@ -1550,11 +1550,11 @@ Hotelling t-squared p-value for correlated fits.
 466    try:
 467        hess = hessian(chisqfunc)(fitp)
 468    except TypeError:
-469        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
+469        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
 470
 471    len_y = len(y_f)
 472
-473    def chisqfunc_compact(d):
+473    def chisqfunc_compact(d):
 474        return anp.sum(general_chisqfunc(d[:n_parms], d[n_parms: n_parms + len_y], d[n_parms + len_y:]) ** 2)
 475
 476    jac_jac_y = hessian(chisqfunc_compact)(np.concatenate((fitp, y_f, p_f)))
@@ -1604,9 +1604,9 @@ list of Obs.
 fit function, has to be of the form

 
 

-
import autograd.numpy as anp
+
import autograd.numpy as anp
 
-def func(a, x):
+def func(a, x):
     return a[0] + a[1] * x + a[2] * anp.sinh(x)
 

 

@@ -1614,7 +1614,7 @@ fit function, has to be of the form

 
For multiple x values func can be of the form

 
 

-
def func(a, x):
+
def func(a, x):
     (x1, x2) = x
     return a[0] * x1 ** 2 + a[1] * x2
 

@@ -1698,10 +1698,10 @@ Parameters and information on the fitted result.
 
 

 
>>> # Example of a correlated (correlated_fit = True, inv_chol_cov_matrix handed over) combined fit, based on a randomly generated data set
->>> import numpy as np
->>> from scipy.stats import norm
->>> from scipy.linalg import cholesky
->>> import pyerrors as pe
+>>> import numpy as np
+>>> from scipy.stats import norm
+>>> from scipy.linalg import cholesky
+>>> import pyerrors as pe
 >>> # generating the random data set
 >>> num_samples = 400
 >>> N = 3
@@ -1734,9 +1734,9 @@ Parameters and information on the fitted result.
 >>>    chol_inv = pe.obs.invert_corr_cov_cholesky(corr, inverrdiag) # gives form of the inverse covariance matrix needed for the combined correlated fit below
 >>> y_dict = {'a': data[:3], 'b': data[3:]}
 >>> # common fit parameter p[0] in combined fit
->>> def fit1(p, x):
+>>> def fit1(p, x):
 >>>    return p[0] + p[1] * x
->>> def fit2(p, x):
+>>> def fit2(p, x):
 >>>    return p[0] + p[2] * x
 >>> fitf_dict = {'a': fit1, 'b':fit2}
 >>> fitp_inv_cov_combined_fit = pe.least_squares(x_dict,y_dict, fitf_dict, correlated_fit = True, inv_chol_cov_matrix = [chol_inv,['a','b']])
@@ -1762,7 +1762,7 @@ Parameters and information on the fitted result.
 
     

     
-            
507def total_least_squares(x, y, func, silent=False, **kwargs):
+            
507def total_least_squares(x, y, func, silent=False, **kwargs):
 508    r'''Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
 509
 510    Parameters
@@ -1890,7 +1890,7 @@ Parameters and information on the fitted result.
 632
 633    m = x_f.size
 634
-635    def odr_chisquare(p):
+635    def odr_chisquare(p):
 636        model = func(p[:n_parms], p[n_parms:].reshape(x_shape))
 637        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((x_f - p[n_parms:].reshape(x_shape)) / dx_f) ** 2)
 638        return chisq
@@ -1925,9 +1925,9 @@ Parameters and information on the fitted result.
 667    try:
 668        hess = hessian(odr_chisquare)(np.concatenate((fitp, out.xplus.ravel())))
 669    except TypeError:
-670        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
+670        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
 671
-672    def odr_chisquare_compact_x(d):
+672    def odr_chisquare_compact_x(d):
 673        model = func(d[:n_parms], d[n_parms:n_parms + m].reshape(x_shape))
 674        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((d[n_parms + m:].reshape(x_shape) - d[n_parms:n_parms + m].reshape(x_shape)) / dx_f) ** 2)
 675        return chisq
@@ -1940,7 +1940,7 @@ Parameters and information on the fitted result.
 682    except np.linalg.LinAlgError:
 683        raise Exception("Cannot invert hessian matrix.")
 684
-685    def odr_chisquare_compact_y(d):
+685    def odr_chisquare_compact_y(d):
 686        model = func(d[:n_parms], d[n_parms:n_parms + m].reshape(x_shape))
 687        chisq = anp.sum(((d[n_parms + m:] - model) / dy_f) ** 2) + anp.sum(((x_f - d[n_parms:n_parms + m].reshape(x_shape)) / dx_f) ** 2)
 688        return chisq
@@ -1980,9 +1980,9 @@ list of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
 func has to be of the form

 
 

-
import autograd.numpy as anp
+
import autograd.numpy as anp
 
-def func(a, x):
+def func(a, x):
     return a[0] + a[1] * x + a[2] * anp.sinh(x)
 

 

@@ -1990,7 +1990,7 @@ func has to be of the form

 
For multiple x values func can be of the form

 
 

-
def func(a, x):
+
def func(a, x):
     (x1, x2) = x
     return a[0] * x1 ** 2 + a[1] * x2
 

@@ -2037,7 +2037,7 @@ Parameters and information on the fitted result.
 
     

     
-            
711def fit_lin(x, y, **kwargs):
+            
711def fit_lin(x, y, **kwargs):
 712    """Performs a linear fit to y = n + m * x and returns two Obs n, m.
 713
 714    Parameters
@@ -2054,7 +2054,7 @@ Parameters and information on the fitted result.
 725        LIist of fitted observables.
 726    """
 727
-728    def f(a, x):
+728    def f(a, x):
 729        y = a[0] + a[1] * x
 730        return y
 731
@@ -2102,7 +2102,7 @@ LIist of fitted observables.
 
     

     
-            
742def qqplot(x, o_y, func, p, title=""):
+            
742def qqplot(x, o_y, func, p, title=""):
 743    """Generates a quantile-quantile plot of the fit result which can be used to
 744       check if the residuals of the fit are gaussian distributed.
 745
@@ -2156,7 +2156,7 @@ LIist of fitted observables.
 
     

     
-            
772def residual_plot(x, y, func, fit_res, title=""):
+            
772def residual_plot(x, y, func, fit_res, title=""):
 773    """Generates a plot which compares the fit to the data and displays the corresponding residuals
 774
 775    For uncorrelated data the residuals are expected to be distributed ~N(0,1).
@@ -2218,7 +2218,7 @@ LIist of fitted observables.
 
     

     
-            
809def error_band(x, func, beta):
+            
809def error_band(x, func, beta):
 810    """Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
 811
 812    Returns
@@ -2266,7 +2266,7 @@ Error band for an array of sample values x
 
     

     
-            
833def ks_test(objects=None):
+            
833def ks_test(objects=None):
 834    """Performs a Kolmogorov–Smirnov test for the p-values of all fit object.
 835
 836    Parameters
diff --git a/docs/pyerrors/input.html b/docs/pyerrors/input.html
index 966d6dfb..3fd783ff 100644
--- a/docs/pyerrors/input.html
+++ b/docs/pyerrors/input.html
@@ -100,14 +100,14 @@ See pyerrors.obs.Obs.export_jackkn
  5For comparison with other analysis workflows `pyerrors` can also generate jackknife samples from an `Obs` object or import jackknife samples into an `Obs` object.
  6See `pyerrors.obs.Obs.export_jackknife` and `pyerrors.obs.import_jackknife` for details.
  7'''
- 8from . import bdio as bdio
- 9from . import dobs as dobs
-10from . import hadrons as hadrons
-11from . import json as json
-12from . import misc as misc
-13from . import openQCD as openQCD
-14from . import pandas as pandas
-15from . import sfcf as sfcf
+ 8from . import bdio as bdio
+ 9from . import dobs as dobs
+10from . import hadrons as hadrons
+11from . import json as json
+12from . import misc as misc
+13from . import openQCD as openQCD
+14from . import pandas as pandas
+15from . import sfcf as sfcf
 

 
 
diff --git a/docs/pyerrors/input/bdio.html b/docs/pyerrors/input/bdio.html
index 2a08f3b0..afaebcd8 100644
--- a/docs/pyerrors/input/bdio.html
+++ b/docs/pyerrors/input/bdio.html
@@ -85,13 +85,13 @@
 
                         
 
-                        
  1import ctypes
-  2import hashlib
-  3import autograd.numpy as np  # Thinly-wrapped numpy
-  4from ..obs import Obs
+                        
  1import ctypes
+  2import hashlib
+  3import autograd.numpy as np  # Thinly-wrapped numpy
+  4from ..obs import Obs
   5
   6
-  7def read_ADerrors(file_path, bdio_path='./libbdio.so', **kwargs):
+  7def read_ADerrors(file_path, bdio_path='./libbdio.so', **kwargs):
   8    """ Extract generic MCMC data from a bdio file
   9
  10    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by
@@ -166,7 +166,7 @@
  79            break
  80        bdio_get_rlen(fbdio)
  81
- 82        def read_c_double():
+ 82        def read_c_double():
  83            d_buf = ctypes.c_double
  84            pd_buf = d_buf()
  85            ppd_buf = ctypes.c_void_p(ctypes.addressof(pd_buf))
@@ -176,7 +176,7 @@
  89        mean = read_c_double()
  90        print('mean', mean)
  91
- 92        def read_c_size_t():
+ 92        def read_c_size_t():
  93            d_buf = ctypes.c_size_t
  94            pd_buf = d_buf()
  95            ppd_buf = ctypes.c_void_p(ctypes.addressof(pd_buf))
@@ -247,7 +247,7 @@
 160    return return_list
 161
 162
-163def write_ADerrors(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):
+163def write_ADerrors(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):
 164    """ Write Obs to a bdio file according to ADerrors conventions
 165
 166    read_mesons requires bdio to be compiled into a shared library. This can be achieved by
@@ -341,12 +341,12 @@
 254
 255        bdio_start_record(0x00, 8, fbdio)
 256
-257        def write_c_double(double):
+257        def write_c_double(double):
 258            pd_buf = ctypes.c_double(double)
 259            ppd_buf = ctypes.c_void_p(ctypes.addressof(pd_buf))
 260            bdio_write_f64(ppd_buf, ctypes.c_size_t(8), ctypes.c_void_p(fbdio))
 261
-262        def write_c_size_t(int32):
+262        def write_c_size_t(int32):
 263            pd_buf = ctypes.c_size_t(int32)
 264            ppd_buf = ctypes.c_void_p(ctypes.addressof(pd_buf))
 265            bdio_write_int32(ppd_buf, ctypes.c_size_t(4), ctypes.c_void_p(fbdio))
@@ -377,15 +377,15 @@
 290    return 0
 291
 292
-293def _get_kwd(string, key):
+293def _get_kwd(string, key):
 294    return (string.split(key, 1)[1]).split(" ", 1)[0]
 295
 296
-297def _get_corr_name(string, key):
+297def _get_corr_name(string, key):
 298    return (string.split(key, 1)[1]).split(' NDIM=', 1)[0]
 299
 300
-301def read_mesons(file_path, bdio_path='./libbdio.so', **kwargs):
+301def read_mesons(file_path, bdio_path='./libbdio.so', **kwargs):
 302    """ Extract mesons data from a bdio file and return it as a dictionary
 303
 304    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
@@ -600,7 +600,7 @@
 513    return result
 514
 515
-516def read_dSdm(file_path, bdio_path='./libbdio.so', **kwargs):
+516def read_dSdm(file_path, bdio_path='./libbdio.so', **kwargs):
 517    """ Extract dSdm data from a bdio file and return it as a dictionary
 518
 519    The dictionary can be accessed with a tuple consisting of (type, kappa)
@@ -794,7 +794,7 @@
 
     

     
-            
  8def read_ADerrors(file_path, bdio_path='./libbdio.so', **kwargs):
+            
  8def read_ADerrors(file_path, bdio_path='./libbdio.so', **kwargs):
   9    """ Extract generic MCMC data from a bdio file
  10
  11    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by
@@ -869,7 +869,7 @@
  80            break
  81        bdio_get_rlen(fbdio)
  82
- 83        def read_c_double():
+ 83        def read_c_double():
  84            d_buf = ctypes.c_double
  85            pd_buf = d_buf()
  86            ppd_buf = ctypes.c_void_p(ctypes.addressof(pd_buf))
@@ -879,7 +879,7 @@
  90        mean = read_c_double()
  91        print('mean', mean)
  92
- 93        def read_c_size_t():
+ 93        def read_c_size_t():
  94            d_buf = ctypes.c_size_t
  95            pd_buf = d_buf()
  96            ppd_buf = ctypes.c_void_p(ctypes.addressof(pd_buf))
@@ -988,7 +988,7 @@ Extracted data
 
     

     
-            
164def write_ADerrors(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):
+            
164def write_ADerrors(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):
 165    """ Write Obs to a bdio file according to ADerrors conventions
 166
 167    read_mesons requires bdio to be compiled into a shared library. This can be achieved by
@@ -1082,12 +1082,12 @@ Extracted data
 255
 256        bdio_start_record(0x00, 8, fbdio)
 257
-258        def write_c_double(double):
+258        def write_c_double(double):
 259            pd_buf = ctypes.c_double(double)
 260            ppd_buf = ctypes.c_void_p(ctypes.addressof(pd_buf))
 261            bdio_write_f64(ppd_buf, ctypes.c_size_t(8), ctypes.c_void_p(fbdio))
 262
-263        def write_c_size_t(int32):
+263        def write_c_size_t(int32):
 264            pd_buf = ctypes.c_size_t(int32)
 265            ppd_buf = ctypes.c_void_p(ctypes.addressof(pd_buf))
 266            bdio_write_int32(ppd_buf, ctypes.c_size_t(4), ctypes.c_void_p(fbdio))
@@ -1156,7 +1156,7 @@ returns 0 is successful
 
     

     
-            
302def read_mesons(file_path, bdio_path='./libbdio.so', **kwargs):
+            
302def read_mesons(file_path, bdio_path='./libbdio.so', **kwargs):
 303    """ Extract mesons data from a bdio file and return it as a dictionary
 304
 305    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
@@ -1421,7 +1421,7 @@ Extracted meson data
 
     

     
-            
517def read_dSdm(file_path, bdio_path='./libbdio.so', **kwargs):
+            
517def read_dSdm(file_path, bdio_path='./libbdio.so', **kwargs):
 518    """ Extract dSdm data from a bdio file and return it as a dictionary
 519
 520    The dictionary can be accessed with a tuple consisting of (type, kappa)
diff --git a/docs/pyerrors/input/dobs.html b/docs/pyerrors/input/dobs.html
index b2a872be..622f2963 100644
--- a/docs/pyerrors/input/dobs.html
+++ b/docs/pyerrors/input/dobs.html
@@ -94,23 +94,23 @@
 
                         
 
-                        
  1from collections import defaultdict
-  2import gzip
-  3import lxml.etree as et
-  4import getpass
-  5import socket
-  6import datetime
-  7import json
-  8import warnings
-  9import numpy as np
- 10from ..obs import Obs
- 11from ..obs import _merge_idx
- 12from ..covobs import Covobs
- 13from .. import version as pyerrorsversion
+                        
  1from collections import defaultdict
+  2import gzip
+  3import lxml.etree as et
+  4import getpass
+  5import socket
+  6import datetime
+  7import json
+  8import warnings
+  9import numpy as np
+ 10from ..obs import Obs
+ 11from ..obs import _merge_idx
+ 12from ..covobs import Covobs
+ 13from .. import version as pyerrorsversion
  14
  15
  16# Based on https://stackoverflow.com/a/10076823
- 17def _etree_to_dict(t):
+ 17def _etree_to_dict(t):
  18    """ Convert the content of an XML file to a python dict"""
  19    d = {t.tag: {} if t.attrib else None}
  20    children = list(t)
@@ -134,7 +134,7 @@
  38    return d
  39
  40
- 41def _dict_to_xmlstring(d):
+ 41def _dict_to_xmlstring(d):
  42    if isinstance(d, dict):
  43        iters = ''
  44        for k in d:
@@ -162,7 +162,7 @@
  66    return iters
  67
  68
- 69def _dict_to_xmlstring_spaces(d, space='  '):
+ 69def _dict_to_xmlstring_spaces(d, space='  '):
  70    s = _dict_to_xmlstring(d)
  71    o = ''
  72    c = 0
@@ -181,7 +181,7 @@
  85    return o
  86
  87
- 88def create_pobs_string(obsl, name, spec='', origin='', symbol=[], enstag=None):
+ 88def create_pobs_string(obsl, name, spec='', origin='', symbol=[], enstag=None):
  89    """Export a list of Obs or structures containing Obs to an xml string
  90    according to the Zeuthen pobs format.
  91
@@ -272,7 +272,7 @@
 176    return rs
 177
 178
-179def write_pobs(obsl, fname, name, spec='', origin='', symbol=[], enstag=None, gz=True):
+179def write_pobs(obsl, fname, name, spec='', origin='', symbol=[], enstag=None, gz=True):
 180    """Export a list of Obs or structures containing Obs to a .xml.gz file
 181    according to the Zeuthen pobs format.
 182
@@ -319,30 +319,30 @@
 223    fp.close()
 224
 225
-226def _import_data(string):
+226def _import_data(string):
 227    return json.loads("[" + ",".join(string.replace(' +', ' ').split()) + "]")
 228
 229
-230def _check(condition):
+230def _check(condition):
 231    if not condition:
 232        raise Exception("XML file format not supported")
 233
 234
-235class _NoTagInDataError(Exception):
+235class _NoTagInDataError(Exception):
 236    """Raised when tag is not in data"""
-237    def __init__(self, tag):
+237    def __init__(self, tag):
 238        self.tag = tag
 239        super().__init__('Tag %s not in data!' % (self.tag))
 240
 241
-242def _find_tag(dat, tag):
+242def _find_tag(dat, tag):
 243    for i in range(len(dat)):
 244        if dat[i].tag == tag:
 245            return i
 246    raise _NoTagInDataError(tag)
 247
 248
-249def _import_array(arr):
+249def _import_array(arr):
 250    name = arr[_find_tag(arr, 'id')].text.strip()
 251    index = _find_tag(arr, 'layout')
 252    try:
@@ -380,12 +380,12 @@
 284        _check(False)
 285
 286
-287def _import_rdata(rd):
+287def _import_rdata(rd):
 288    name, idx, mask, deltas = _import_array(rd)
 289    return deltas, name, idx
 290
 291
-292def _import_cdata(cd):
+292def _import_cdata(cd):
 293    _check(cd[0].tag == "id")
 294    _check(cd[1][0].text.strip() == "cov")
 295    cov = _import_array(cd[1])
@@ -393,7 +393,7 @@
 297    return cd[0].text.strip(), cov, grad
 298
 299
-300def read_pobs(fname, full_output=False, gz=True, separator_insertion=None):
+300def read_pobs(fname, full_output=False, gz=True, separator_insertion=None):
 301    """Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
 302
 303    Tags are not written or recovered automatically.
@@ -493,7 +493,7 @@
 397
 398
 399# this is based on Mattia Bruno's implementation at https://github.com/mbruno46/pyobs/blob/master/pyobs/IO/xml.py
-400def import_dobs_string(content, full_output=False, separator_insertion=True):
+400def import_dobs_string(content, full_output=False, separator_insertion=True):
 401    """Import a list of Obs from a string in the Zeuthen dobs format.
 402
 403    Tags are not written or recovered automatically.
@@ -667,7 +667,7 @@
 571        return res
 572
 573
-574def read_dobs(fname, full_output=False, gz=True, separator_insertion=True):
+574def read_dobs(fname, full_output=False, gz=True, separator_insertion=True):
 575    """Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
 576
 577    Tags are not written or recovered automatically.
@@ -714,7 +714,7 @@
 618    return import_dobs_string(content, full_output, separator_insertion=separator_insertion)
 619
 620
-621def _dobsdict_to_xmlstring(d):
+621def _dobsdict_to_xmlstring(d):
 622    if isinstance(d, dict):
 623        iters = ''
 624        for k in d:
@@ -754,7 +754,7 @@
 658    return iters
 659
 660
-661def _dobsdict_to_xmlstring_spaces(d, space='  '):
+661def _dobsdict_to_xmlstring_spaces(d, space='  '):
 662    s = _dobsdict_to_xmlstring(d)
 663    o = ''
 664    c = 0
@@ -773,7 +773,7 @@
 677    return o
 678
 679
-680def create_dobs_string(obsl, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None):
+680def create_dobs_string(obsl, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None):
 681    """Generate the string for the export of a list of Obs or structures containing Obs
 682    to a .xml.gz file according to the Zeuthen dobs format.
 683
@@ -962,7 +962,7 @@
 866    return rs
 867
 868
-869def write_dobs(obsl, fname, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None, gz=True):
+869def write_dobs(obsl, fname, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None, gz=True):
 870    """Export a list of Obs or structures containing Obs to a .xml.gz file
 871    according to the Zeuthen dobs format.
 872
@@ -1029,7 +1029,7 @@
 
     

     
-            
 89def create_pobs_string(obsl, name, spec='', origin='', symbol=[], enstag=None):
+            
 89def create_pobs_string(obsl, name, spec='', origin='', symbol=[], enstag=None):
  90    """Export a list of Obs or structures containing Obs to an xml string
  91    according to the Zeuthen pobs format.
  92
@@ -1165,7 +1165,7 @@ XML formatted string of the input data
 
     

     
-            
180def write_pobs(obsl, fname, name, spec='', origin='', symbol=[], enstag=None, gz=True):
+            
180def write_pobs(obsl, fname, name, spec='', origin='', symbol=[], enstag=None, gz=True):
 181    """Export a list of Obs or structures containing Obs to a .xml.gz file
 182    according to the Zeuthen pobs format.
 183
@@ -1260,7 +1260,7 @@ If True, the output is a gzipped xml. If False, the output is an xml file.
 
     

     
-            
301def read_pobs(fname, full_output=False, gz=True, separator_insertion=None):
+            
301def read_pobs(fname, full_output=False, gz=True, separator_insertion=None):
 302    """Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
 303
 304    Tags are not written or recovered automatically.
@@ -1403,7 +1403,7 @@ Imported data and meta-data
 
     

     
-            
401def import_dobs_string(content, full_output=False, separator_insertion=True):
+            
401def import_dobs_string(content, full_output=False, separator_insertion=True):
 402    """Import a list of Obs from a string in the Zeuthen dobs format.
 403
 404    Tags are not written or recovered automatically.
@@ -1623,7 +1623,7 @@ Imported data and meta-data
 
     

     
-            
575def read_dobs(fname, full_output=False, gz=True, separator_insertion=True):
+            
575def read_dobs(fname, full_output=False, gz=True, separator_insertion=True):
 576    """Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
 577
 578    Tags are not written or recovered automatically.
@@ -1718,7 +1718,7 @@ Imported data and meta-data
 
     

     
-            
681def create_dobs_string(obsl, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None):
+            
681def create_dobs_string(obsl, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None):
 682    """Generate the string for the export of a list of Obs or structures containing Obs
 683    to a .xml.gz file according to the Zeuthen dobs format.
 684
@@ -1956,7 +1956,7 @@ XML string generated from the data
 
     

     
-            
870def write_dobs(obsl, fname, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None, gz=True):
+            
870def write_dobs(obsl, fname, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None, gz=True):
 871    """Export a list of Obs or structures containing Obs to a .xml.gz file
 872    according to the Zeuthen dobs format.
 873
diff --git a/docs/pyerrors/input/hadrons.html b/docs/pyerrors/input/hadrons.html
index 7512c1f8..fcd3dec1 100644
--- a/docs/pyerrors/input/hadrons.html
+++ b/docs/pyerrors/input/hadrons.html
@@ -103,18 +103,18 @@
 
                         
 
-                        
  1import os
-  2from collections import Counter
-  3import h5py
-  4from pathlib import Path
-  5import numpy as np
-  6from ..obs import Obs, CObs
-  7from ..correlators import Corr
-  8from ..dirac import epsilon_tensor_rank4
-  9from .misc import fit_t0
+                        
  1import os
+  2from collections import Counter
+  3import h5py
+  4from pathlib import Path
+  5import numpy as np
+  6from ..obs import Obs, CObs
+  7from ..correlators import Corr
+  8from ..dirac import epsilon_tensor_rank4
+  9from .misc import fit_t0
  10
  11
- 12def _get_files(path, filestem, idl):
+ 12def _get_files(path, filestem, idl):
  13    ls = os.listdir(path)
  14
  15    # Clean up file list
@@ -123,7 +123,7 @@
  18    if not files:
  19        raise Exception('No files starting with', filestem, 'in folder', path)
  20
- 21    def get_cnfg_number(n):
+ 21    def get_cnfg_number(n):
  22        return int(n.replace(".h5", "")[len(filestem) + 1:])  # From python 3.9 onward the safer 'removesuffix' method can be used.
  23
  24    # Sort according to configuration number
@@ -159,7 +159,7 @@
  54    return filtered_files, idx
  55
  56
- 57def read_hd5(filestem, ens_id, group, attrs=None, idl=None, part="real"):
+ 57def read_hd5(filestem, ens_id, group, attrs=None, idl=None, part="real"):
  58    r'''Read hadrons hdf5 file and extract entry based on attributes.
  59
  60    Parameters
@@ -245,7 +245,7 @@
 140    return corr
 141
 142
-143def read_meson_hd5(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):
+143def read_meson_hd5(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):
 144    r'''Read hadrons meson hdf5 file and extract the meson labeled 'meson'
 145
 146    Parameters
@@ -284,7 +284,7 @@
 179                    part="real")
 180
 181
-182def _extract_real_arrays(path, files, tree, keys):
+182def _extract_real_arrays(path, files, tree, keys):
 183    corr_data = {}
 184    for key in keys:
 185        corr_data[key] = []
@@ -302,7 +302,7 @@
 197    return corr_data
 198
 199
-200def extract_t0_hd5(path, filestem, ens_id, obs='Clover energy density', fit_range=5, idl=None, **kwargs):
+200def extract_t0_hd5(path, filestem, ens_id, obs='Clover energy density', fit_range=5, idl=None, **kwargs):
 201    r'''Read hadrons FlowObservables hdf5 file and extract t0
 202
 203    Parameters
@@ -350,7 +350,7 @@
 245    return fit_t0(t2E_dict, fit_range, plot_fit=kwargs.get('plot_fit'))
 246
 247
-248def read_DistillationContraction_hd5(path, ens_id, diagrams=["direct"], idl=None):
+248def read_DistillationContraction_hd5(path, ens_id, diagrams=["direct"], idl=None):
 249    """Read hadrons DistillationContraction hdf5 files in given directory structure
 250
 251    Parameters
@@ -447,16 +447,16 @@
 342    return res_dict
 343
 344
-345class Npr_matrix(np.ndarray):
+345class Npr_matrix(np.ndarray):
 346
-347    def __new__(cls, input_array, mom_in=None, mom_out=None):
+347    def __new__(cls, input_array, mom_in=None, mom_out=None):
 348        obj = np.asarray(input_array).view(cls)
 349        obj.mom_in = mom_in
 350        obj.mom_out = mom_out
 351        return obj
 352
 353    @property
-354    def g5H(self):
+354    def g5H(self):
 355        """Gamma_5 hermitean conjugate
 356
 357        Uses the fact that the propagator is gamma5 hermitean, so just the
@@ -466,7 +466,7 @@
 361                          mom_in=self.mom_out,
 362                          mom_out=self.mom_in)
 363
-364    def _propagate_mom(self, other, name):
+364    def _propagate_mom(self, other, name):
 365        s_mom = getattr(self, name, None)
 366        o_mom = getattr(other, name, None)
 367        if s_mom is not None and o_mom is not None:
@@ -474,20 +474,20 @@
 369                raise Exception(name + ' does not match.')
 370        return o_mom if o_mom is not None else s_mom
 371
-372    def __matmul__(self, other):
+372    def __matmul__(self, other):
 373        return self.__new__(Npr_matrix,
 374                            super().__matmul__(other),
 375                            self._propagate_mom(other, 'mom_in'),
 376                            self._propagate_mom(other, 'mom_out'))
 377
-378    def __array_finalize__(self, obj):
+378    def __array_finalize__(self, obj):
 379        if obj is None:
 380            return
 381        self.mom_in = getattr(obj, 'mom_in', None)
 382        self.mom_out = getattr(obj, 'mom_out', None)
 383
 384
-385def read_ExternalLeg_hd5(path, filestem, ens_id, idl=None):
+385def read_ExternalLeg_hd5(path, filestem, ens_id, idl=None):
 386    """Read hadrons ExternalLeg hdf5 file and output an array of CObs
 387
 388    Parameters
@@ -532,7 +532,7 @@
 427    return Npr_matrix(matrix, mom_in=mom)
 428
 429
-430def read_Bilinear_hd5(path, filestem, ens_id, idl=None):
+430def read_Bilinear_hd5(path, filestem, ens_id, idl=None):
 431    """Read hadrons Bilinear hdf5 file and output an array of CObs
 432
 433    Parameters
@@ -591,7 +591,7 @@
 486    return result_dict
 487
 488
-489def read_Fourquark_hd5(path, filestem, ens_id, idl=None, vertices=["VA", "AV"]):
+489def read_Fourquark_hd5(path, filestem, ens_id, idl=None, vertices=["VA", "AV"]):
 490    """Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
 491
 492    Parameters
@@ -677,7 +677,7 @@
 572    return result_dict
 573
 574
-575def _get_lorentz_names(name):
+575def _get_lorentz_names(name):
 576    lorentz_index = ['X', 'Y', 'Z', 'T']
 577
 578    res = []
@@ -733,7 +733,7 @@
 
     

     
-            
 58def read_hd5(filestem, ens_id, group, attrs=None, idl=None, part="real"):
+            
 58def read_hd5(filestem, ens_id, group, attrs=None, idl=None, part="real"):
  59    r'''Read hadrons hdf5 file and extract entry based on attributes.
  60
  61    Parameters
@@ -871,7 +871,7 @@ Correlator of the source sink combination in question.
 
     

     
-            
144def read_meson_hd5(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):
+            
144def read_meson_hd5(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):
 145    r'''Read hadrons meson hdf5 file and extract the meson labeled 'meson'
 146
 147    Parameters
@@ -955,7 +955,7 @@ Correlator of the source sink combination in question.
 
     

     
-            
201def extract_t0_hd5(path, filestem, ens_id, obs='Clover energy density', fit_range=5, idl=None, **kwargs):
+            
201def extract_t0_hd5(path, filestem, ens_id, obs='Clover energy density', fit_range=5, idl=None, **kwargs):
 202    r'''Read hadrons FlowObservables hdf5 file and extract t0
 203
 204    Parameters
@@ -1041,7 +1041,7 @@ If true, the fit for the extraction of t0 is shown together with the data.
 
     

     
-            
249def read_DistillationContraction_hd5(path, ens_id, diagrams=["direct"], idl=None):
+            
249def read_DistillationContraction_hd5(path, ens_id, diagrams=["direct"], idl=None):
 250    """Read hadrons DistillationContraction hdf5 files in given directory structure
 251
 252    Parameters
@@ -1175,16 +1175,16 @@ extracted DistillationContration data
 
     

     
-            
346class Npr_matrix(np.ndarray):
+            
346class Npr_matrix(np.ndarray):
 347
-348    def __new__(cls, input_array, mom_in=None, mom_out=None):
+348    def __new__(cls, input_array, mom_in=None, mom_out=None):
 349        obj = np.asarray(input_array).view(cls)
 350        obj.mom_in = mom_in
 351        obj.mom_out = mom_out
 352        return obj
 353
 354    @property
-355    def g5H(self):
+355    def g5H(self):
 356        """Gamma_5 hermitean conjugate
 357
 358        Uses the fact that the propagator is gamma5 hermitean, so just the
@@ -1194,7 +1194,7 @@ extracted DistillationContration data
 362                          mom_in=self.mom_out,
 363                          mom_out=self.mom_in)
 364
-365    def _propagate_mom(self, other, name):
+365    def _propagate_mom(self, other, name):
 366        s_mom = getattr(self, name, None)
 367        o_mom = getattr(other, name, None)
 368        if s_mom is not None and o_mom is not None:
@@ -1202,13 +1202,13 @@ extracted DistillationContration data
 370                raise Exception(name + ' does not match.')
 371        return o_mom if o_mom is not None else s_mom
 372
-373    def __matmul__(self, other):
+373    def __matmul__(self, other):
 374        return self.__new__(Npr_matrix,
 375                            super().__matmul__(other),
 376                            self._propagate_mom(other, 'mom_in'),
 377                            self._propagate_mom(other, 'mom_out'))
 378
-379    def __array_finalize__(self, obj):
+379    def __array_finalize__(self, obj):
 380        if obj is None:
 381            return
 382        self.mom_in = getattr(obj, 'mom_in', None)
@@ -1330,7 +1330,7 @@ ndarray.

 
First mode, buffer is None:

 
 

-
>>> import numpy as np
+
>>> import numpy as np
 >>> np.ndarray(shape=(2,2), dtype=float, order='F')
 array([[0.0e+000, 0.0e+000], # random
        [     nan, 2.5e-323]])
@@ -1359,7 +1359,7 @@ ndarray.

     

     
             
354    @property
-355    def g5H(self):
+355    def g5H(self):
 356        """Gamma_5 hermitean conjugate
 357
 358        Uses the fact that the propagator is gamma5 hermitean, so just the
@@ -1391,7 +1391,7 @@ in and out momenta of the propagator are exchanged.

 
     

     
-            
386def read_ExternalLeg_hd5(path, filestem, ens_id, idl=None):
+            
386def read_ExternalLeg_hd5(path, filestem, ens_id, idl=None):
 387    """Read hadrons ExternalLeg hdf5 file and output an array of CObs
 388
 389    Parameters
@@ -1473,7 +1473,7 @@ read Cobs-matrix
 
     

     
-            
431def read_Bilinear_hd5(path, filestem, ens_id, idl=None):
+            
431def read_Bilinear_hd5(path, filestem, ens_id, idl=None):
 432    """Read hadrons Bilinear hdf5 file and output an array of CObs
 433
 434    Parameters
@@ -1569,7 +1569,7 @@ extracted Bilinears
 
     

     
-            
490def read_Fourquark_hd5(path, filestem, ens_id, idl=None, vertices=["VA", "AV"]):
+            
490def read_Fourquark_hd5(path, filestem, ens_id, idl=None, vertices=["VA", "AV"]):
 491    """Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
 492
 493    Parameters
diff --git a/docs/pyerrors/input/json.html b/docs/pyerrors/input/json.html
index f6677161..c6ad22a8 100644
--- a/docs/pyerrors/input/json.html
+++ b/docs/pyerrors/input/json.html
@@ -91,23 +91,23 @@
 
                         
 
-                        
  1import rapidjson as json
-  2import gzip
-  3import getpass
-  4import socket
-  5import datetime
-  6import platform
-  7import warnings
-  8import re
-  9import numpy as np
- 10from ..obs import Obs
- 11from ..covobs import Covobs
- 12from ..correlators import Corr
- 13from ..misc import _assert_equal_properties
- 14from .. import version as pyerrorsversion
+                        
  1import rapidjson as json
+  2import gzip
+  3import getpass
+  4import socket
+  5import datetime
+  6import platform
+  7import warnings
+  8import re
+  9import numpy as np
+ 10from ..obs import Obs
+ 11from ..covobs import Covobs
+ 12from ..correlators import Corr
+ 13from ..misc import _assert_equal_properties
+ 14from .. import version as pyerrorsversion
  15
  16
- 17def create_json_string(ol, description='', indent=1):
+ 17def create_json_string(ol, description='', indent=1):
  18    """Generate the string for the export of a list of Obs or structures containing Obs
  19    to a .json(.gz) file
  20
@@ -129,7 +129,7 @@
  36        String for export to .json(.gz) file
  37    """
  38
- 39    def _gen_data_d_from_list(ol):
+ 39    def _gen_data_d_from_list(ol):
  40        dl = []
  41        No = len(ol)
  42        for name in ol[0].mc_names:
@@ -149,7 +149,7 @@
  56            dl.append(ed)
  57        return dl
  58
- 59    def _gen_cdata_d_from_list(ol):
+ 59    def _gen_cdata_d_from_list(ol):
  60        dl = []
  61        for name in ol[0].cov_names:
  62            ed = {}
@@ -165,7 +165,7 @@
  72            dl.append(ed)
  73        return dl
  74
- 75    def write_Obs_to_dict(o):
+ 75    def write_Obs_to_dict(o):
  76        d = {}
  77        d['type'] = 'Obs'
  78        d['layout'] = '1'
@@ -182,7 +182,7 @@
  89            d['cdata'] = cdata
  90        return d
  91
- 92    def write_List_to_dict(ol):
+ 92    def write_List_to_dict(ol):
  93        _assert_equal_properties(ol)
  94        d = {}
  95        d['type'] = 'List'
@@ -201,7 +201,7 @@
 108            d['cdata'] = cdata
 109        return d
 110
-111    def write_Array_to_dict(oa):
+111    def write_Array_to_dict(oa):
 112        ol = np.ravel(oa)
 113        _assert_equal_properties(ol)
 114        d = {}
@@ -221,7 +221,7 @@
 128            d['cdata'] = cdata
 129        return d
 130
-131    def _nan_Obs_like(obs):
+131    def _nan_Obs_like(obs):
 132        samples = []
 133        names = []
 134        idl = []
@@ -236,7 +236,7 @@
 143        my_obs.reweighted = obs.reweighted
 144        return my_obs
 145
-146    def write_Corr_to_dict(my_corr):
+146    def write_Corr_to_dict(my_corr):
 147        first_not_none = next(i for i, j in enumerate(my_corr.content) if np.all(j))
 148        dummy_array = np.empty((my_corr.N, my_corr.N), dtype=object)
 149        dummy_array[:] = _nan_Obs_like(my_corr.content[first_not_none].ravel()[0])
@@ -281,7 +281,7 @@
 188        else:
 189            raise Exception("Unkown datatype.")
 190
-191    def _jsonifier(obj):
+191    def _jsonifier(obj):
 192        if isinstance(obj, dict):
 193            result = {}
 194            for key in obj:
@@ -309,7 +309,7 @@
 216        return json.dumps(d, indent=indent, ensure_ascii=False, default=_jsonifier, write_mode=json.WM_COMPACT)
 217
 218
-219def dump_to_json(ol, fname, description='', indent=1, gz=True):
+219def dump_to_json(ol, fname, description='', indent=1, gz=True):
 220    """Export a list of Obs or structures containing Obs to a .json(.gz) file.
 221    Dict keys that are not JSON-serializable such as floats are converted to strings.
 222
@@ -351,7 +351,7 @@
 258    fp.close()
 259
 260
-261def _parse_json_dict(json_dict, verbose=True, full_output=False):
+261def _parse_json_dict(json_dict, verbose=True, full_output=False):
 262    """Reconstruct a list of Obs or structures containing Obs from a dict that
 263    was built out of a json string.
 264
@@ -380,7 +380,7 @@
 287        if full_output=True
 288    """
 289
-290    def _gen_obsd_from_datad(d):
+290    def _gen_obsd_from_datad(d):
 291        retd = {}
 292        if d:
 293            retd['names'] = []
@@ -399,7 +399,7 @@
 306                    retd['deltas'].append(np.array([di[1:] for di in rep['deltas']]))
 307        return retd
 308
-309    def _gen_covobsd_from_cdatad(d):
+309    def _gen_covobsd_from_cdatad(d):
 310        retd = {}
 311        for ens in d:
 312            retl = []
@@ -414,7 +414,7 @@
 321            retd[name] = retl
 322        return retd
 323
-324    def get_Obs_from_dict(o):
+324    def get_Obs_from_dict(o):
 325        layouts = o.get('layout', '1').strip()
 326        if layouts != '1':
 327            raise Exception("layout is %s has to be 1 for type Obs." % (layouts), RuntimeWarning)
@@ -438,7 +438,7 @@
 345        ret.tag = o.get('tag', [None])[0]
 346        return ret
 347
-348    def get_List_from_dict(o):
+348    def get_List_from_dict(o):
 349        layouts = o.get('layout', '1').strip()
 350        layout = int(layouts)
 351        values = o['value']
@@ -464,7 +464,7 @@
 371            ret[-1].tag = taglist[i]
 372        return ret
 373
-374    def get_Array_from_dict(o):
+374    def get_Array_from_dict(o):
 375        layouts = o.get('layout', '1').strip()
 376        layout = [int(ls.strip()) for ls in layouts.split(',') if len(ls) > 0]
 377        N = np.prod(layout)
@@ -489,7 +489,7 @@
 396            ret[-1].tag = taglist[i]
 397        return np.reshape(ret, layout)
 398
-399    def get_Corr_from_dict(o):
+399    def get_Corr_from_dict(o):
 400        if isinstance(o.get('tag'), list):  # supports the old way
 401            taglist = o.get('tag')  # This had to be modified to get the taglist from the dictionary
 402            temp_prange = None
@@ -563,7 +563,7 @@
 470        return ol
 471
 472
-473def import_json_string(json_string, verbose=True, full_output=False):
+473def import_json_string(json_string, verbose=True, full_output=False):
 474    """Reconstruct a list of Obs or structures containing Obs from a json string.
 475
 476    The following structures are supported: Obs, list, numpy.ndarray, Corr
@@ -593,7 +593,7 @@
 500    return _parse_json_dict(json.loads(json_string), verbose, full_output)
 501
 502
-503def load_json(fname, verbose=True, gz=True, full_output=False):
+503def load_json(fname, verbose=True, gz=True, full_output=False):
 504    """Import a list of Obs or structures containing Obs from a .json(.gz) file.
 505
 506    The following structures are supported: Obs, list, numpy.ndarray, Corr
@@ -638,7 +638,7 @@
 545    return _parse_json_dict(d, verbose, full_output)
 546
 547
-548def _ol_from_dict(ind, reps='DICTOBS'):
+548def _ol_from_dict(ind, reps='DICTOBS'):
 549    """Convert a dictionary of Obs objects to a list and a dictionary that contains
 550    placeholders instead of the Obs objects.
 551
@@ -659,7 +659,7 @@
 566    ol = []
 567    counter = 0
 568
-569    def dict_replace_obs(d):
+569    def dict_replace_obs(d):
 570        nonlocal ol
 571        nonlocal counter
 572        x = {}
@@ -680,7 +680,7 @@
 587            x[k] = v
 588        return x
 589
-590    def list_replace_obs(li):
+590    def list_replace_obs(li):
 591        nonlocal ol
 592        nonlocal counter
 593        x = []
@@ -701,7 +701,7 @@
 608            x.append(e)
 609        return x
 610
-611    def obslist_replace_obs(li):
+611    def obslist_replace_obs(li):
 612        nonlocal ol
 613        nonlocal counter
 614        il = []
@@ -718,7 +718,7 @@
 625    return ol, nd
 626
 627
-628def dump_dict_to_json(od, fname, description='', indent=1, reps='DICTOBS', gz=True):
+628def dump_dict_to_json(od, fname, description='', indent=1, reps='DICTOBS', gz=True):
 629    """Export a dict of Obs or structures containing Obs to a .json(.gz) file
 630
 631    Parameters
@@ -758,7 +758,7 @@
 665    dump_to_json(ol, fname, description=desc_dict, indent=indent, gz=gz)
 666
 667
-668def _od_from_list_and_dict(ol, ind, reps='DICTOBS'):
+668def _od_from_list_and_dict(ol, ind, reps='DICTOBS'):
 669    """Parse a list of Obs or structures containing Obs and an accompanying
 670    dict, where the structures have been replaced by placeholders to a
 671    dict that contains the structures.
@@ -781,7 +781,7 @@
 688
 689    counter = 0
 690
-691    def dict_replace_string(d):
+691    def dict_replace_string(d):
 692        nonlocal counter
 693        nonlocal ol
 694        x = {}
@@ -797,7 +797,7 @@
 704            x[k] = v
 705        return x
 706
-707    def list_replace_string(li):
+707    def list_replace_string(li):
 708        nonlocal counter
 709        nonlocal ol
 710        x = []
@@ -821,7 +821,7 @@
 728    return nd
 729
 730
-731def load_json_dict(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):
+731def load_json_dict(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):
 732    """Import a dict of Obs or structures containing Obs from a .json(.gz) file.
 733
 734    The following structures are supported: Obs, list, numpy.ndarray, Corr
@@ -875,7 +875,7 @@
 
     

     
-            
 18def create_json_string(ol, description='', indent=1):
+            
 18def create_json_string(ol, description='', indent=1):
  19    """Generate the string for the export of a list of Obs or structures containing Obs
  20    to a .json(.gz) file
  21
@@ -897,7 +897,7 @@
  37        String for export to .json(.gz) file
  38    """
  39
- 40    def _gen_data_d_from_list(ol):
+ 40    def _gen_data_d_from_list(ol):
  41        dl = []
  42        No = len(ol)
  43        for name in ol[0].mc_names:
@@ -917,7 +917,7 @@
  57            dl.append(ed)
  58        return dl
  59
- 60    def _gen_cdata_d_from_list(ol):
+ 60    def _gen_cdata_d_from_list(ol):
  61        dl = []
  62        for name in ol[0].cov_names:
  63            ed = {}
@@ -933,7 +933,7 @@
  73            dl.append(ed)
  74        return dl
  75
- 76    def write_Obs_to_dict(o):
+ 76    def write_Obs_to_dict(o):
  77        d = {}
  78        d['type'] = 'Obs'
  79        d['layout'] = '1'
@@ -950,7 +950,7 @@
  90            d['cdata'] = cdata
  91        return d
  92
- 93    def write_List_to_dict(ol):
+ 93    def write_List_to_dict(ol):
  94        _assert_equal_properties(ol)
  95        d = {}
  96        d['type'] = 'List'
@@ -969,7 +969,7 @@
 109            d['cdata'] = cdata
 110        return d
 111
-112    def write_Array_to_dict(oa):
+112    def write_Array_to_dict(oa):
 113        ol = np.ravel(oa)
 114        _assert_equal_properties(ol)
 115        d = {}
@@ -989,7 +989,7 @@
 129            d['cdata'] = cdata
 130        return d
 131
-132    def _nan_Obs_like(obs):
+132    def _nan_Obs_like(obs):
 133        samples = []
 134        names = []
 135        idl = []
@@ -1004,7 +1004,7 @@
 144        my_obs.reweighted = obs.reweighted
 145        return my_obs
 146
-147    def write_Corr_to_dict(my_corr):
+147    def write_Corr_to_dict(my_corr):
 148        first_not_none = next(i for i, j in enumerate(my_corr.content) if np.all(j))
 149        dummy_array = np.empty((my_corr.N, my_corr.N), dtype=object)
 150        dummy_array[:] = _nan_Obs_like(my_corr.content[first_not_none].ravel()[0])
@@ -1049,7 +1049,7 @@
 189        else:
 190            raise Exception("Unkown datatype.")
 191
-192    def _jsonifier(obj):
+192    def _jsonifier(obj):
 193        if isinstance(obj, dict):
 194            result = {}
 195            for key in obj:
@@ -1116,7 +1116,7 @@ String for export to pyerrors.input.json(.gz) file
 
     

     
-            
220def dump_to_json(ol, fname, description='', indent=1, gz=True):
+            
220def dump_to_json(ol, fname, description='', indent=1, gz=True):
 221    """Export a list of Obs or structures containing Obs to a .json(.gz) file.
 222    Dict keys that are not JSON-serializable such as floats are converted to strings.
 223
@@ -1200,7 +1200,7 @@ If True, the output is a gzipped json. If False, the output is a json file.
 
     

     
-            
474def import_json_string(json_string, verbose=True, full_output=False):
+            
474def import_json_string(json_string, verbose=True, full_output=False):
 475    """Reconstruct a list of Obs or structures containing Obs from a json string.
 476
 477    The following structures are supported: Obs, list, numpy.ndarray, Corr
@@ -1275,7 +1275,7 @@ if full_output=True
 
     

     
-            
504def load_json(fname, verbose=True, gz=True, full_output=False):
+            
504def load_json(fname, verbose=True, gz=True, full_output=False):
 505    """Import a list of Obs or structures containing Obs from a .json(.gz) file.
 506
 507    The following structures are supported: Obs, list, numpy.ndarray, Corr
@@ -1367,7 +1367,7 @@ if full_output=True
 
     

     
-            
629def dump_dict_to_json(od, fname, description='', indent=1, reps='DICTOBS', gz=True):
+            
629def dump_dict_to_json(od, fname, description='', indent=1, reps='DICTOBS', gz=True):
 630    """Export a dict of Obs or structures containing Obs to a .json(.gz) file
 631
 632    Parameters
@@ -1450,7 +1450,7 @@ If True, the output is a gzipped json. If False, the output is a json file.
 
     

     
-            
732def load_json_dict(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):
+            
732def load_json_dict(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):
 733    """Import a dict of Obs or structures containing Obs from a .json(.gz) file.
 734
 735    The following structures are supported: Obs, list, numpy.ndarray, Corr
diff --git a/docs/pyerrors/input/misc.html b/docs/pyerrors/input/misc.html
index 17992f64..125386cf 100644
--- a/docs/pyerrors/input/misc.html
+++ b/docs/pyerrors/input/misc.html
@@ -79,19 +79,19 @@
 
                         
 
-                        
  1import os
-  2import fnmatch
-  3import re
-  4import struct
-  5import warnings
-  6import numpy as np  # Thinly-wrapped numpy
-  7import matplotlib.pyplot as plt
-  8from matplotlib import gridspec
-  9from ..obs import Obs
- 10from ..fits import fit_lin
+                        
  1import os
+  2import fnmatch
+  3import re
+  4import struct
+  5import warnings
+  6import numpy as np  # Thinly-wrapped numpy
+  7import matplotlib.pyplot as plt
+  8from matplotlib import gridspec
+  9from ..obs import Obs
+ 10from ..fits import fit_lin
  11
  12
- 13def fit_t0(t2E_dict, fit_range, plot_fit=False, observable='t0'):
+ 13def fit_t0(t2E_dict, fit_range, plot_fit=False, observable='t0'):
  14    """Compute the root of (flow-based) data based on a dictionary that contains
  15    the necessary information in key-value pairs a la (flow time: observable at flow time).
  16
@@ -178,7 +178,7 @@
  97    return -fit_result[0] / fit_result[1]
  98
  99
-100def read_pbp(path, prefix, **kwargs):
+100def read_pbp(path, prefix, **kwargs):
 101    """Read pbp format from given folder structure.
 102
 103    Parameters
@@ -312,7 +312,7 @@
 
     

     
-            
14def fit_t0(t2E_dict, fit_range, plot_fit=False, observable='t0'):
+            
14def fit_t0(t2E_dict, fit_range, plot_fit=False, observable='t0'):
 15    """Compute the root of (flow-based) data based on a dictionary that contains
 16    the necessary information in key-value pairs a la (flow time: observable at flow time).
 17
@@ -447,7 +447,7 @@ The root of the data series.
 
     

     
-            
101def read_pbp(path, prefix, **kwargs):
+            
101def read_pbp(path, prefix, **kwargs):
 102    """Read pbp format from given folder structure.
 103
 104    Parameters
diff --git a/docs/pyerrors/input/openQCD.html b/docs/pyerrors/input/openQCD.html
index 0a73c540..bb7a26d4 100644
--- a/docs/pyerrors/input/openQCD.html
+++ b/docs/pyerrors/input/openQCD.html
@@ -97,19 +97,19 @@
 
                         
 
-                        
   1import os
-   2import fnmatch
-   3import struct
-   4import warnings
-   5import numpy as np  # Thinly-wrapped numpy
-   6from ..obs import Obs
-   7from ..obs import CObs
-   8from ..correlators import Corr
-   9from .misc import fit_t0
-  10from .utils import sort_names
+                        
   1import os
+   2import fnmatch
+   3import struct
+   4import warnings
+   5import numpy as np  # Thinly-wrapped numpy
+   6from ..obs import Obs
+   7from ..obs import CObs
+   8from ..correlators import Corr
+   9from .misc import fit_t0
+  10from .utils import sort_names
   11
   12
-  13def read_rwms(path, prefix, version='2.0', names=None, **kwargs):
+  13def read_rwms(path, prefix, version='2.0', names=None, **kwargs):
   14    """Read rwms format from given folder structure. Returns a list of length nrw
   15
   16    Parameters
@@ -299,7 +299,7 @@
  200                    r_start_index.append(configlist[-1].index(r_start[rep]))
  201                except ValueError:
  202                    raise Exception('Config %d not in file with range [%d, %d]' % (
- 203                        r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
+ 203                        r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
  204
  205            if r_stop[rep] is None:
  206                r_stop_index.append(len(configlist[-1]) - 1)
@@ -308,7 +308,7 @@
  209                    r_stop_index.append(configlist[-1].index(r_stop[rep]))
  210                except ValueError:
  211                    raise Exception('Config %d not in file with range [%d, %d]' % (
- 212                        r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
+ 212                        r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
  213
  214            for k in range(nrw):
  215                deltas[k].append(tmp_array[k][r_start_index[rep]:r_stop_index[rep] + 1][::r_step])
@@ -328,7 +328,7 @@
  229    return result
  230
  231
- 232def _extract_flowed_energy_density(path, prefix, dtr_read, xmin, spatial_extent, postfix='ms', **kwargs):
+ 232def _extract_flowed_energy_density(path, prefix, dtr_read, xmin, spatial_extent, postfix='ms', **kwargs):
  233    """Extract a dictionary with the flowed Yang-Mills action density from given .ms.dat files.
  234    Returns a dictionary with Obs as values and flow times as keys.
  235
@@ -489,7 +489,7 @@
  390                r_start_index.append(configlist[-1].index(r_start[rep]))
  391            except ValueError:
  392                raise Exception('Config %d not in file with range [%d, %d]' % (
- 393                    r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
+ 393                    r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
  394
  395        if r_stop[rep] is None:
  396            r_stop_index.append(len(configlist[-1]) - 1)
@@ -498,7 +498,7 @@
  399                r_stop_index.append(configlist[-1].index(r_stop[rep]))
  400            except ValueError:
  401                raise Exception('Config %d not in file with range [%d, %d]' % (
- 402                    r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
+ 402                    r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
  403
  404    if np.any([len(np.unique(np.diff(cl))) != 1 for cl in configlist]):
  405        raise Exception('Irregular spaced data in input file!', [len(np.unique(np.diff(cl))) for cl in configlist])
@@ -521,7 +521,7 @@
  422    return E_dict
  423
  424
- 425def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
+ 425def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
  426    """Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
  427
  428    It is assumed that all boundary effects have
@@ -594,7 +594,7 @@
  495    return fit_t0(t2E_dict, fit_range, plot_fit=kwargs.get('plot_fit'))
  496
  497
- 498def extract_w0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
+ 498def extract_w0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
  499    """Extract w0/a from given .ms.dat files. Returns w0 as Obs.
  500
  501    It is assumed that all boundary effects have
@@ -676,7 +676,7 @@
  577    return np.sqrt(fit_t0(tdtt2E_dict, fit_range, plot_fit=kwargs.get('plot_fit'), observable='w0'))
  578
  579
- 580def _parse_array_openQCD2(d, n, size, wa, quadrupel=False):
+ 580def _parse_array_openQCD2(d, n, size, wa, quadrupel=False):
  581    arr = []
  582    if d == 2:
  583        for i in range(n[0]):
@@ -695,7 +695,7 @@
  596    return arr
  597
  598
- 599def _find_files(path, prefix, postfix, ext, known_files=[]):
+ 599def _find_files(path, prefix, postfix, ext, known_files=[]):
  600    found = []
  601    files = []
  602
@@ -735,7 +735,7 @@
  636    return files
  637
  638
- 639def _read_array_openQCD2(fp):
+ 639def _read_array_openQCD2(fp):
  640    t = fp.read(4)
  641    d = struct.unpack('i', t)[0]
  642    t = fp.read(4 * d)
@@ -761,7 +761,7 @@
  662    return {'d': d, 'n': n, 'size': size, 'arr': arr}
  663
  664
- 665def read_qtop(path, prefix, c, dtr_cnfg=1, version="openQCD", **kwargs):
+ 665def read_qtop(path, prefix, c, dtr_cnfg=1, version="openQCD", **kwargs):
  666    """Read the topologial charge based on openQCD gradient flow measurements.
  667
  668    Parameters
@@ -814,7 +814,7 @@
  715    return _read_flow_obs(path, prefix, c, dtr_cnfg=dtr_cnfg, version=version, obspos=0, **kwargs)
  716
  717
- 718def read_gf_coupling(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):
+ 718def read_gf_coupling(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):
  719    """Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
  720
  721    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
@@ -886,7 +886,7 @@
  787    return t * t * (5 / 3 * plaq - 1 / 12 * C2x1) / normdict[L]
  788
  789
- 790def _read_flow_obs(path, prefix, c, dtr_cnfg=1, version="openQCD", obspos=0, sum_t=True, **kwargs):
+ 790def _read_flow_obs(path, prefix, c, dtr_cnfg=1, version="openQCD", obspos=0, sum_t=True, **kwargs):
  791    """Read a flow observable based on openQCD gradient flow measurements.
  792
  793    Parameters
@@ -1094,7 +1094,7 @@
  995                r_start_index.append(configlist[-1].index(r_start[rep]))
  996            except ValueError:
  997                raise Exception('Config %d not in file with range [%d, %d]' % (
- 998                    r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
+ 998                    r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
  999
 1000        if r_stop[rep] is None:
 1001            r_stop_index.append(len(configlist[-1]) - 1)
@@ -1103,7 +1103,7 @@
 1004                r_stop_index.append(configlist[-1].index(r_stop[rep]))
 1005            except ValueError:
 1006                raise Exception('Config %d not in file with range [%d, %d]' % (
-1007                    r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
+1007                    r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
 1008
 1009        if version in ['sfqcd']:
 1010            cstepsize = cmax / ncs
@@ -1158,7 +1158,7 @@
 1059    return result
 1060
 1061
-1062def qtop_projection(qtop, target=0):
+1062def qtop_projection(qtop, target=0):
 1063    """Returns the projection to the topological charge sector defined by target.
 1064
 1065    Parameters
@@ -1184,7 +1184,7 @@
 1085    return reto
 1086
 1087
-1088def read_qtop_sector(path, prefix, c, target=0, **kwargs):
+1088def read_qtop_sector(path, prefix, c, target=0, **kwargs):
 1089    """Constructs reweighting factors to a specified topological sector.
 1090
 1091    Parameters
@@ -1242,7 +1242,7 @@
 1143    return qtop_projection(qtop, target=target)
 1144
 1145
-1146def read_ms5_xsf(path, prefix, qc, corr, sep="r", **kwargs):
+1146def read_ms5_xsf(path, prefix, qc, corr, sep="r", **kwargs):
 1147    """
 1148    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a `Corr` object containing the data.
 1149
@@ -1423,7 +1423,7 @@
 
     

     
-            
 14def read_rwms(path, prefix, version='2.0', names=None, **kwargs):
+            
 14def read_rwms(path, prefix, version='2.0', names=None, **kwargs):
  15    """Read rwms format from given folder structure. Returns a list of length nrw
  16
  17    Parameters
@@ -1613,7 +1613,7 @@
 201                    r_start_index.append(configlist[-1].index(r_start[rep]))
 202                except ValueError:
 203                    raise Exception('Config %d not in file with range [%d, %d]' % (
-204                        r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
+204                        r_start[rep], configlist[-1][0], configlist[-1][-1])) from None
 205
 206            if r_stop[rep] is None:
 207                r_stop_index.append(len(configlist[-1]) - 1)
@@ -1622,7 +1622,7 @@
 210                    r_stop_index.append(configlist[-1].index(r_stop[rep]))
 211                except ValueError:
 212                    raise Exception('Config %d not in file with range [%d, %d]' % (
-213                        r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
+213                        r_stop[rep], configlist[-1][0], configlist[-1][-1])) from None
 214
 215            for k in range(nrw):
 216                deltas[k].append(tmp_array[k][r_start_index[rep]:r_stop_index[rep] + 1][::r_step])
@@ -1696,7 +1696,7 @@ Reweighting factors read
 
     

     
-            
426def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
+            
426def extract_t0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
 427    """Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
 428
 429    It is assumed that all boundary effects have
@@ -1851,7 +1851,7 @@ Extracted t0
 
     

     
-            
499def extract_w0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
+            
499def extract_w0(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, postfix='ms', c=0.3, **kwargs):
 500    """Extract w0/a from given .ms.dat files. Returns w0 as Obs.
 501
 502    It is assumed that all boundary effects have
@@ -2015,7 +2015,7 @@ Extracted w0
 
     

     
-            
666def read_qtop(path, prefix, c, dtr_cnfg=1, version="openQCD", **kwargs):
+            
666def read_qtop(path, prefix, c, dtr_cnfg=1, version="openQCD", **kwargs):
 667    """Read the topologial charge based on openQCD gradient flow measurements.
 668
 669    Parameters
@@ -2135,7 +2135,7 @@ Read topological charge
 
     

     
-            
719def read_gf_coupling(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):
+            
719def read_gf_coupling(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):
 720    """Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
 721
 722    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
@@ -2260,7 +2260,7 @@ postfix of the file to read, e.g. '.gfms.dat' for openQCD-files
 
     

     
-            
1063def qtop_projection(qtop, target=0):
+            
1063def qtop_projection(qtop, target=0):
 1064    """Returns the projection to the topological charge sector defined by target.
 1065
 1066    Parameters
@@ -2319,7 +2319,7 @@ projection to the topological charge sector defined by target
 
     

     
-            
1089def read_qtop_sector(path, prefix, c, target=0, **kwargs):
+            
1089def read_qtop_sector(path, prefix, c, target=0, **kwargs):
 1090    """Constructs reweighting factors to a specified topological sector.
 1091
 1092    Parameters
@@ -2443,7 +2443,7 @@ projection to the topological charge sector defined by target
 
     

     
-            
1147def read_ms5_xsf(path, prefix, qc, corr, sep="r", **kwargs):
+            
1147def read_ms5_xsf(path, prefix, qc, corr, sep="r", **kwargs):
 1148    """
 1149    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a `Corr` object containing the data.
 1150
diff --git a/docs/pyerrors/input/pandas.html b/docs/pyerrors/input/pandas.html
index 58741835..8221e9dd 100644
--- a/docs/pyerrors/input/pandas.html
+++ b/docs/pyerrors/input/pandas.html
@@ -85,17 +85,17 @@
 
                         
 
-                        
  1import warnings
-  2import gzip
-  3import sqlite3
-  4import pandas as pd
-  5from ..obs import Obs
-  6from ..correlators import Corr
-  7from .json import create_json_string, import_json_string
-  8import numpy as np
+                        
  1import warnings
+  2import gzip
+  3import sqlite3
+  4import pandas as pd
+  5from ..obs import Obs
+  6from ..correlators import Corr
+  7from .json import create_json_string, import_json_string
+  8import numpy as np
   9
  10
- 11def to_sql(df, table_name, db, if_exists='fail', gz=True, **kwargs):
+ 11def to_sql(df, table_name, db, if_exists='fail', gz=True, **kwargs):
  12    """Write DataFrame including Obs or Corr valued columns to sqlite database.
  13
  14    Parameters
@@ -121,7 +121,7 @@
  34    con.close()
  35
  36
- 37def read_sql(sql, db, auto_gamma=False, **kwargs):
+ 37def read_sql(sql, db, auto_gamma=False, **kwargs):
  38    """Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
  39
  40    Parameters
@@ -145,7 +145,7 @@
  58    return _deserialize_df(extract_df, auto_gamma=auto_gamma)
  59
  60
- 61def dump_df(df, fname, gz=True):
+ 61def dump_df(df, fname, gz=True):
  62    """Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
  63
  64    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized
@@ -184,7 +184,7 @@
  97        out.to_csv(fname, index=False)
  98
  99
-100def load_df(fname, auto_gamma=False, gz=True):
+100def load_df(fname, auto_gamma=False, gz=True):
 101    """Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
 102
 103    Parameters
@@ -218,7 +218,7 @@
 131    return _deserialize_df(re_import, auto_gamma=auto_gamma)
 132
 133
-134def _serialize_df(df, gz=False):
+134def _serialize_df(df, gz=False):
 135    """Serializes all Obs or Corr valued columns into json strings according to the pyerrors json specification.
 136
 137    Parameters
@@ -239,7 +239,7 @@
 152    return out
 153
 154
-155def _deserialize_df(df, auto_gamma=False):
+155def _deserialize_df(df, auto_gamma=False):
 156    """Deserializes all pyerrors json strings into Obs or Corr objects according to the pyerrors json specification.
 157
 158    Parameters
@@ -275,7 +275,7 @@
 188    return df
 189
 190
-191def _need_to_serialize(col):
+191def _need_to_serialize(col):
 192    serialize = False
 193    i = 0
 194    while i < len(col) and col[i] is None:
@@ -303,7 +303,7 @@
 
     

     
-            
12def to_sql(df, table_name, db, if_exists='fail', gz=True, **kwargs):
+            
12def to_sql(df, table_name, db, if_exists='fail', gz=True, **kwargs):
 13    """Write DataFrame including Obs or Corr valued columns to sqlite database.
 14
 15    Parameters
@@ -367,7 +367,7 @@ If True the json strings are gzipped.
 
     

     
-            
38def read_sql(sql, db, auto_gamma=False, **kwargs):
+            
38def read_sql(sql, db, auto_gamma=False, **kwargs):
 39    """Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
 40
 41    Parameters
@@ -427,7 +427,7 @@ Dataframe with the content of the sqlite database.
 
     

     
-            
62def dump_df(df, fname, gz=True):
+            
62def dump_df(df, fname, gz=True):
 63    """Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
 64
 65    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized
@@ -503,7 +503,7 @@ If True, the output is a gzipped csv file. If False, the output is a csv file.
     
-            
101def load_df(fname, auto_gamma=False, gz=True):
+            
101def load_df(fname, auto_gamma=False, gz=True):
 102    """Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
 103
 104    Parameters
diff --git a/docs/pyerrors/input/sfcf.html b/docs/pyerrors/input/sfcf.html
index 50cb7424..4219c5cd 100644
--- a/docs/pyerrors/input/sfcf.html
+++ b/docs/pyerrors/input/sfcf.html
@@ -82,19 +82,19 @@
 
                         
 
-                        
  1import os
-  2import fnmatch
-  3import re
-  4import numpy as np  # Thinly-wrapped numpy
-  5from ..obs import Obs
-  6from .utils import sort_names, check_idl
-  7import itertools
+                        
  1import os
+  2import fnmatch
+  3import re
+  4import numpy as np  # Thinly-wrapped numpy
+  5from ..obs import Obs
+  6from .utils import sort_names, check_idl
+  7import itertools
   8
   9
  10sep = "/"
  11
  12
- 13def read_sfcf(path, prefix, name, quarks='.*', corr_type="bi", noffset=0, wf=0, wf2=0, version="1.0c", cfg_separator="n", silent=False, **kwargs):
+ 13def read_sfcf(path, prefix, name, quarks='.*', corr_type="bi", noffset=0, wf=0, wf2=0, version="1.0c", cfg_separator="n", silent=False, **kwargs):
  14    """Read sfcf files from given folder structure.
  15
  16    Parameters
@@ -159,7 +159,7 @@
  75    return ret[name][quarks][str(noffset)][str(wf)][str(wf2)]
  76
  77
- 78def read_sfcf_multi(path, prefix, name_list, quarks_list=['.*'], corr_type_list=['bi'], noffset_list=[0], wf_list=[0], wf2_list=[0], version="1.0c", cfg_separator="n", silent=False, keyed_out=False, **kwargs):
+ 78def read_sfcf_multi(path, prefix, name_list, quarks_list=['.*'], corr_type_list=['bi'], noffset_list=[0], wf_list=[0], wf2_list=[0], version="1.0c", cfg_separator="n", silent=False, keyed_out=False, **kwargs):
  79    """Read sfcf files from given folder structure.
  80
  81    Parameters
@@ -211,558 +211,559 @@
 127    check_configs: list[list[int]]
 128        list of list of supposed configs, eg. [range(1,1000)]
 129        for one replicum with 1000 configs
-130
-131    Returns
-132    -------
-133    result: dict[list[Obs]]
-134        dict with one of the following properties:
-135        if keyed_out:
-136            dict[key] = list[Obs]
-137            where key has the form name/quarks/offset/wf/wf2
-138        if not keyed_out:
-139            dict[name][quarks][offset][wf][wf2] = list[Obs]
-140    """
-141
-142    if kwargs.get('im'):
-143        im = 1
-144        part = 'imaginary'
-145    else:
-146        im = 0
-147        part = 'real'
-148
-149    known_versions = ["0.0", "1.0", "2.0", "1.0c", "2.0c", "1.0a", "2.0a"]
-150
-151    if version not in known_versions:
-152        raise Exception("This version is not known!")
-153    if (version[-1] == "c"):
-154        appended = False
-155        compact = True
-156        version = version[:-1]
-157    elif (version[-1] == "a"):
-158        appended = True
-159        compact = False
-160        version = version[:-1]
-161    else:
-162        compact = False
-163        appended = False
-164    ls = []
-165    if "replica" in kwargs:
-166        ls = kwargs.get("replica")
-167    else:
-168        for (dirpath, dirnames, filenames) in os.walk(path):
-169            if not appended:
-170                ls.extend(dirnames)
-171            else:
-172                ls.extend(filenames)
-173            break
-174        if not ls:
-175            raise Exception('Error, directory not found')
-176        # Exclude folders with different names
-177        for exc in ls:
-178            if not fnmatch.fnmatch(exc, prefix + '*'):
-179                ls = list(set(ls) - set([exc]))
-180
-181    if not appended:
-182        ls = sort_names(ls)
-183        replica = len(ls)
-184
-185    else:
-186        replica = len([file.split(".")[-1] for file in ls]) // len(set([file.split(".")[-1] for file in ls]))
-187    if replica == 0:
-188        raise Exception('No replica found in directory')
-189    if not silent:
-190        print('Read', part, 'part of', name_list, 'from', prefix[:-1], ',', replica, 'replica')
-191
-192    if 'names' in kwargs:
-193        new_names = kwargs.get('names')
-194        if len(new_names) != len(set(new_names)):
-195            raise Exception("names are not unique!")
-196        if len(new_names) != replica:
-197            raise Exception('names should have the length', replica)
-198
-199    else:
-200        ens_name = kwargs.get("ens_name")
-201        if not appended:
-202            new_names = _get_rep_names(ls, ens_name)
-203        else:
-204            new_names = _get_appended_rep_names(ls, prefix, name_list[0], ens_name)
-205        new_names = sort_names(new_names)
-206
-207    idl = []
-208
-209    noffset_list = [str(x) for x in noffset_list]
-210    wf_list = [str(x) for x in wf_list]
-211    wf2_list = [str(x) for x in wf2_list]
-212
-213    # setup dict structures
-214    intern = {}
-215    for name, corr_type in zip(name_list, corr_type_list):
-216        intern[name] = {}
-217        b2b, single = _extract_corr_type(corr_type)
-218        intern[name]["b2b"] = b2b
-219        intern[name]["single"] = single
-220        intern[name]["spec"] = {}
-221        for quarks in quarks_list:
-222            intern[name]["spec"][quarks] = {}
-223            for off in noffset_list:
-224                intern[name]["spec"][quarks][off] = {}
-225                for w in wf_list:
-226                    intern[name]["spec"][quarks][off][w] = {}
-227                    if b2b:
-228                        for w2 in wf2_list:
-229                            intern[name]["spec"][quarks][off][w][w2] = {}
-230                            intern[name]["spec"][quarks][off][w][w2]["pattern"] = _make_pattern(version, name, off, w, w2, intern[name]['b2b'], quarks)
-231                    else:
-232                        intern[name]["spec"][quarks][off][w]["0"] = {}
-233                        intern[name]["spec"][quarks][off][w]["0"]["pattern"] = _make_pattern(version, name, off, w, 0, intern[name]['b2b'], quarks)
-234
-235    internal_ret_dict = {}
-236    needed_keys = []
-237    for name, corr_type in zip(name_list, corr_type_list):
-238        b2b, single = _extract_corr_type(corr_type)
-239        if b2b:
-240            needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, wf2_list))
-241        else:
-242            needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, ["0"]))
-243
-244    for key in needed_keys:
-245        internal_ret_dict[key] = []
-246
-247    if not appended:
-248        for i, item in enumerate(ls):
-249            rep_path = path + '/' + item
-250            if "files" in kwargs:
-251                files = kwargs.get("files")
-252                if isinstance(files, list):
-253                    if all(isinstance(f, list) for f in files):
-254                        files = files[i]
-255                    elif all(isinstance(f, str) for f in files):
-256                        files = files
-257                    else:
-258                        raise TypeError("files has to be of type list[list[str]] or list[str]!")
-259                else:
-260                    raise TypeError("files has to be of type list[list[str]] or list[str]!")
-261
-262            else:
-263                files = []
-264            sub_ls = _find_files(rep_path, prefix, compact, files)
-265            rep_idl = []
-266            no_cfg = len(sub_ls)
-267            for cfg in sub_ls:
-268                try:
-269                    if compact:
-270                        rep_idl.append(int(cfg.split(cfg_separator)[-1]))
-271                    else:
-272                        rep_idl.append(int(cfg[3:]))
-273                except Exception:
-274                    raise Exception("Couldn't parse idl from directory, problem with file " + cfg)
-275            rep_idl.sort()
-276            # maybe there is a better way to print the idls
-277            if not silent:
-278                print(item, ':', no_cfg, ' configurations')
-279            idl.append(rep_idl)
-280            # here we have found all the files we need to look into.
-281            if i == 0:
-282                if version != "0.0" and compact:
-283                    file = path + '/' + item + '/' + sub_ls[0]
-284                for name_index, name in enumerate(name_list):
-285                    if version == "0.0" or not compact:
-286                        file = path + '/' + item + '/' + sub_ls[0] + '/' + name
-287                    if corr_type_list[name_index] == 'bi':
-288                        name_keys = _lists2key(quarks_list, noffset_list, wf_list, ["0"])
-289                    else:
-290                        name_keys = _lists2key(quarks_list, noffset_list, wf_list, wf2_list)
-291                    for key in name_keys:
-292                        specs = _key2specs(key)
-293                        quarks = specs[0]
-294                        off = specs[1]
-295                        w = specs[2]
-296                        w2 = specs[3]
-297                        # here, we want to find the place within the file,
-298                        # where the correlator we need is stored.
-299                        # to do so, the pattern needed is put together
-300                        # from the input values
-301                        start_read, T = _find_correlator(file, version, intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["pattern"], intern[name]['b2b'], silent=silent)
-302                        intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["start"] = start_read
-303                        intern[name]["T"] = T
-304                        # preparing the datastructure
-305                        # the correlators get parsed into...
-306                        deltas = []
-307                        for j in range(intern[name]["T"]):
-308                            deltas.append([])
-309                        internal_ret_dict[sep.join([name, key])] = deltas
-310
-311            if compact:
-312                rep_deltas = _read_compact_rep(path, item, sub_ls, intern, needed_keys, im)
-313                for key in needed_keys:
-314                    name = _key2specs(key)[0]
-315                    for t in range(intern[name]["T"]):
-316                        internal_ret_dict[key][t].append(rep_deltas[key][t])
-317            else:
-318                for key in needed_keys:
-319                    rep_data = []
-320                    name = _key2specs(key)[0]
-321                    for subitem in sub_ls:
-322                        cfg_path = path + '/' + item + '/' + subitem
-323                        file_data = _read_o_file(cfg_path, name, needed_keys, intern, version, im)
-324                        rep_data.append(file_data)
-325                    for t in range(intern[name]["T"]):
-326                        internal_ret_dict[key][t].append([])
-327                        for cfg in range(no_cfg):
-328                            internal_ret_dict[key][t][i].append(rep_data[cfg][key][t])
-329    else:
-330        for key in needed_keys:
-331            specs = _key2specs(key)
-332            name = specs[0]
-333            quarks = specs[1]
-334            off = specs[2]
-335            w = specs[3]
-336            w2 = specs[4]
-337            if "files" in kwargs:
-338                if isinstance(kwargs.get("files"), list) and all(isinstance(f, str) for f in kwargs.get("files")):
-339                    name_ls = kwargs.get("files")
-340                else:
-341                    raise TypeError("In append mode, files has to be of type list[str]!")
-342            else:
-343                name_ls = ls
-344                for exc in name_ls:
-345                    if not fnmatch.fnmatch(exc, prefix + '*.' + name):
-346                        name_ls = list(set(name_ls) - set([exc]))
-347            name_ls = sort_names(name_ls)
-348            pattern = intern[name]['spec'][quarks][off][w][w2]['pattern']
-349            deltas = []
-350            for rep, file in enumerate(name_ls):
-351                rep_idl = []
-352                filename = path + '/' + file
-353                T, rep_idl, rep_data = _read_append_rep(filename, pattern, intern[name]['b2b'], cfg_separator, im, intern[name]['single'])
-354                if rep == 0:
-355                    intern[name]['T'] = T
-356                    for t in range(intern[name]['T']):
-357                        deltas.append([])
-358                for t in range(intern[name]['T']):
-359                    deltas[t].append(rep_data[t])
-360                internal_ret_dict[key] = deltas
-361                if name == name_list[0]:
-362                    idl.append(rep_idl)
-363
-364    if kwargs.get("check_configs") is True:
-365        if not silent:
-366            print("Checking for missing configs...")
-367        che = kwargs.get("check_configs")
-368        if not (len(che) == len(idl)):
-369            raise Exception("check_configs has to be the same length as replica!")
-370        for r in range(len(idl)):
-371            if not silent:
-372                print("checking " + new_names[r])
-373            check_idl(idl[r], che[r])
-374        if not silent:
-375            print("Done")
-376
-377    result_dict = {}
-378    if keyed_out:
-379        for key in needed_keys:
-380            name = _key2specs(key)[0]
-381            result = []
-382            for t in range(intern[name]["T"]):
-383                result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
-384            result_dict[key] = result
-385    else:
-386        for name, corr_type in zip(name_list, corr_type_list):
-387            result_dict[name] = {}
-388            for quarks in quarks_list:
-389                result_dict[name][quarks] = {}
-390                for off in noffset_list:
-391                    result_dict[name][quarks][off] = {}
-392                    for w in wf_list:
-393                        result_dict[name][quarks][off][w] = {}
-394                        if corr_type != 'bi':
-395                            for w2 in wf2_list:
-396                                key = _specs2key(name, quarks, off, w, w2)
-397                                result = []
-398                                for t in range(intern[name]["T"]):
-399                                    result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
-400                                result_dict[name][quarks][str(off)][str(w)][str(w2)] = result
-401                        else:
-402                            key = _specs2key(name, quarks, off, w, "0")
-403                            result = []
-404                            for t in range(intern[name]["T"]):
-405                                result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
-406                            result_dict[name][quarks][str(off)][str(w)][str(0)] = result
-407    return result_dict
-408
+130    rep_string: str
+131        Separator of ensemble name and replicum. Example: In "ensAr0", "r" would be the separator string.
+132    Returns
+133    -------
+134    result: dict[list[Obs]]
+135        dict with one of the following properties:
+136        if keyed_out:
+137            dict[key] = list[Obs]
+138            where key has the form name/quarks/offset/wf/wf2
+139        if not keyed_out:
+140            dict[name][quarks][offset][wf][wf2] = list[Obs]
+141    """
+142
+143    if kwargs.get('im'):
+144        im = 1
+145        part = 'imaginary'
+146    else:
+147        im = 0
+148        part = 'real'
+149
+150    known_versions = ["0.0", "1.0", "2.0", "1.0c", "2.0c", "1.0a", "2.0a"]
+151
+152    if version not in known_versions:
+153        raise Exception("This version is not known!")
+154    if (version[-1] == "c"):
+155        appended = False
+156        compact = True
+157        version = version[:-1]
+158    elif (version[-1] == "a"):
+159        appended = True
+160        compact = False
+161        version = version[:-1]
+162    else:
+163        compact = False
+164        appended = False
+165    ls = []
+166    if "replica" in kwargs:
+167        ls = kwargs.get("replica")
+168    else:
+169        for (dirpath, dirnames, filenames) in os.walk(path):
+170            if not appended:
+171                ls.extend(dirnames)
+172            else:
+173                ls.extend(filenames)
+174            break
+175        if not ls:
+176            raise Exception('Error, directory not found')
+177        # Exclude folders with different names
+178        for exc in ls:
+179            if not fnmatch.fnmatch(exc, prefix + '*'):
+180                ls = list(set(ls) - set([exc]))
+181
+182    if not appended:
+183        ls = sort_names(ls)
+184        replica = len(ls)
+185
+186    else:
+187        replica = len([file.split(".")[-1] for file in ls]) // len(set([file.split(".")[-1] for file in ls]))
+188    if replica == 0:
+189        raise Exception('No replica found in directory')
+190    if not silent:
+191        print('Read', part, 'part of', name_list, 'from', prefix[:-1], ',', replica, 'replica')
+192
+193    if 'names' in kwargs:
+194        new_names = kwargs.get('names')
+195        if len(new_names) != len(set(new_names)):
+196            raise Exception("names are not unique!")
+197        if len(new_names) != replica:
+198            raise Exception('names should have the length', replica)
+199
+200    else:
+201        ens_name = kwargs.get("ens_name")
+202        if not appended:
+203            new_names = _get_rep_names(ls, ens_name, rep_sep=(kwargs.get('rep_string', 'r')))
+204        else:
+205            new_names = _get_appended_rep_names(ls, prefix, name_list[0], ens_name, rep_sep=(kwargs.get('rep_string', 'r')))
+206        new_names = sort_names(new_names)
+207
+208    idl = []
+209
+210    noffset_list = [str(x) for x in noffset_list]
+211    wf_list = [str(x) for x in wf_list]
+212    wf2_list = [str(x) for x in wf2_list]
+213
+214    # setup dict structures
+215    intern = {}
+216    for name, corr_type in zip(name_list, corr_type_list):
+217        intern[name] = {}
+218        b2b, single = _extract_corr_type(corr_type)
+219        intern[name]["b2b"] = b2b
+220        intern[name]["single"] = single
+221        intern[name]["spec"] = {}
+222        for quarks in quarks_list:
+223            intern[name]["spec"][quarks] = {}
+224            for off in noffset_list:
+225                intern[name]["spec"][quarks][off] = {}
+226                for w in wf_list:
+227                    intern[name]["spec"][quarks][off][w] = {}
+228                    if b2b:
+229                        for w2 in wf2_list:
+230                            intern[name]["spec"][quarks][off][w][w2] = {}
+231                            intern[name]["spec"][quarks][off][w][w2]["pattern"] = _make_pattern(version, name, off, w, w2, intern[name]['b2b'], quarks)
+232                    else:
+233                        intern[name]["spec"][quarks][off][w]["0"] = {}
+234                        intern[name]["spec"][quarks][off][w]["0"]["pattern"] = _make_pattern(version, name, off, w, 0, intern[name]['b2b'], quarks)
+235
+236    internal_ret_dict = {}
+237    needed_keys = []
+238    for name, corr_type in zip(name_list, corr_type_list):
+239        b2b, single = _extract_corr_type(corr_type)
+240        if b2b:
+241            needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, wf2_list))
+242        else:
+243            needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, ["0"]))
+244
+245    for key in needed_keys:
+246        internal_ret_dict[key] = []
+247
+248    if not appended:
+249        for i, item in enumerate(ls):
+250            rep_path = path + '/' + item
+251            if "files" in kwargs:
+252                files = kwargs.get("files")
+253                if isinstance(files, list):
+254                    if all(isinstance(f, list) for f in files):
+255                        files = files[i]
+256                    elif all(isinstance(f, str) for f in files):
+257                        files = files
+258                    else:
+259                        raise TypeError("files has to be of type list[list[str]] or list[str]!")
+260                else:
+261                    raise TypeError("files has to be of type list[list[str]] or list[str]!")
+262
+263            else:
+264                files = []
+265            sub_ls = _find_files(rep_path, prefix, compact, files)
+266            rep_idl = []
+267            no_cfg = len(sub_ls)
+268            for cfg in sub_ls:
+269                try:
+270                    if compact:
+271                        rep_idl.append(int(cfg.split(cfg_separator)[-1]))
+272                    else:
+273                        rep_idl.append(int(cfg[3:]))
+274                except Exception:
+275                    raise Exception("Couldn't parse idl from directory, problem with file " + cfg)
+276            rep_idl.sort()
+277            # maybe there is a better way to print the idls
+278            if not silent:
+279                print(item, ':', no_cfg, ' configurations')
+280            idl.append(rep_idl)
+281            # here we have found all the files we need to look into.
+282            if i == 0:
+283                if version != "0.0" and compact:
+284                    file = path + '/' + item + '/' + sub_ls[0]
+285                for name_index, name in enumerate(name_list):
+286                    if version == "0.0" or not compact:
+287                        file = path + '/' + item + '/' + sub_ls[0] + '/' + name
+288                    if corr_type_list[name_index] == 'bi':
+289                        name_keys = _lists2key(quarks_list, noffset_list, wf_list, ["0"])
+290                    else:
+291                        name_keys = _lists2key(quarks_list, noffset_list, wf_list, wf2_list)
+292                    for key in name_keys:
+293                        specs = _key2specs(key)
+294                        quarks = specs[0]
+295                        off = specs[1]
+296                        w = specs[2]
+297                        w2 = specs[3]
+298                        # here, we want to find the place within the file,
+299                        # where the correlator we need is stored.
+300                        # to do so, the pattern needed is put together
+301                        # from the input values
+302                        start_read, T = _find_correlator(file, version, intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["pattern"], intern[name]['b2b'], silent=silent)
+303                        intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["start"] = start_read
+304                        intern[name]["T"] = T
+305                        # preparing the datastructure
+306                        # the correlators get parsed into...
+307                        deltas = []
+308                        for j in range(intern[name]["T"]):
+309                            deltas.append([])
+310                        internal_ret_dict[sep.join([name, key])] = deltas
+311
+312            if compact:
+313                rep_deltas = _read_compact_rep(path, item, sub_ls, intern, needed_keys, im)
+314                for key in needed_keys:
+315                    name = _key2specs(key)[0]
+316                    for t in range(intern[name]["T"]):
+317                        internal_ret_dict[key][t].append(rep_deltas[key][t])
+318            else:
+319                for key in needed_keys:
+320                    rep_data = []
+321                    name = _key2specs(key)[0]
+322                    for subitem in sub_ls:
+323                        cfg_path = path + '/' + item + '/' + subitem
+324                        file_data = _read_o_file(cfg_path, name, needed_keys, intern, version, im)
+325                        rep_data.append(file_data)
+326                    for t in range(intern[name]["T"]):
+327                        internal_ret_dict[key][t].append([])
+328                        for cfg in range(no_cfg):
+329                            internal_ret_dict[key][t][i].append(rep_data[cfg][key][t])
+330    else:
+331        for key in needed_keys:
+332            specs = _key2specs(key)
+333            name = specs[0]
+334            quarks = specs[1]
+335            off = specs[2]
+336            w = specs[3]
+337            w2 = specs[4]
+338            if "files" in kwargs:
+339                if isinstance(kwargs.get("files"), list) and all(isinstance(f, str) for f in kwargs.get("files")):
+340                    name_ls = kwargs.get("files")
+341                else:
+342                    raise TypeError("In append mode, files has to be of type list[str]!")
+343            else:
+344                name_ls = ls
+345                for exc in name_ls:
+346                    if not fnmatch.fnmatch(exc, prefix + '*.' + name):
+347                        name_ls = list(set(name_ls) - set([exc]))
+348            name_ls = sort_names(name_ls)
+349            pattern = intern[name]['spec'][quarks][off][w][w2]['pattern']
+350            deltas = []
+351            for rep, file in enumerate(name_ls):
+352                rep_idl = []
+353                filename = path + '/' + file
+354                T, rep_idl, rep_data = _read_append_rep(filename, pattern, intern[name]['b2b'], cfg_separator, im, intern[name]['single'])
+355                if rep == 0:
+356                    intern[name]['T'] = T
+357                    for t in range(intern[name]['T']):
+358                        deltas.append([])
+359                for t in range(intern[name]['T']):
+360                    deltas[t].append(rep_data[t])
+361                internal_ret_dict[key] = deltas
+362                if name == name_list[0]:
+363                    idl.append(rep_idl)
+364
+365    if kwargs.get("check_configs") is True:
+366        if not silent:
+367            print("Checking for missing configs...")
+368        che = kwargs.get("check_configs")
+369        if not (len(che) == len(idl)):
+370            raise Exception("check_configs has to be the same length as replica!")
+371        for r in range(len(idl)):
+372            if not silent:
+373                print("checking " + new_names[r])
+374            check_idl(idl[r], che[r])
+375        if not silent:
+376            print("Done")
+377
+378    result_dict = {}
+379    if keyed_out:
+380        for key in needed_keys:
+381            name = _key2specs(key)[0]
+382            result = []
+383            for t in range(intern[name]["T"]):
+384                result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
+385            result_dict[key] = result
+386    else:
+387        for name, corr_type in zip(name_list, corr_type_list):
+388            result_dict[name] = {}
+389            for quarks in quarks_list:
+390                result_dict[name][quarks] = {}
+391                for off in noffset_list:
+392                    result_dict[name][quarks][off] = {}
+393                    for w in wf_list:
+394                        result_dict[name][quarks][off][w] = {}
+395                        if corr_type != 'bi':
+396                            for w2 in wf2_list:
+397                                key = _specs2key(name, quarks, off, w, w2)
+398                                result = []
+399                                for t in range(intern[name]["T"]):
+400                                    result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
+401                                result_dict[name][quarks][str(off)][str(w)][str(w2)] = result
+402                        else:
+403                            key = _specs2key(name, quarks, off, w, "0")
+404                            result = []
+405                            for t in range(intern[name]["T"]):
+406                                result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
+407                            result_dict[name][quarks][str(off)][str(w)][str(0)] = result
+408    return result_dict
 409
-410def _lists2key(*lists):
-411    keys = []
-412    for tup in itertools.product(*lists):
-413        keys.append(sep.join(tup))
-414    return keys
-415
+410
+411def _lists2key(*lists):
+412    keys = []
+413    for tup in itertools.product(*lists):
+414        keys.append(sep.join(tup))
+415    return keys
 416
-417def _key2specs(key):
-418    return key.split(sep)
-419
+417
+418def _key2specs(key):
+419    return key.split(sep)
 420
-421def _specs2key(*specs):
-422    return sep.join(specs)
-423
+421
+422def _specs2key(*specs):
+423    return sep.join(specs)
 424
-425def _read_o_file(cfg_path, name, needed_keys, intern, version, im):
-426    return_vals = {}
-427    for key in needed_keys:
-428        file = cfg_path + '/' + name
-429        specs = _key2specs(key)
-430        if specs[0] == name:
-431            with open(file) as fp:
-432                lines = fp.readlines()
-433                quarks = specs[1]
-434                off = specs[2]
-435                w = specs[3]
-436                w2 = specs[4]
-437                T = intern[name]["T"]
-438                start_read = intern[name]["spec"][quarks][off][w][w2]["start"]
-439                deltas = []
-440                for line in lines[start_read:start_read + T]:
-441                    floats = list(map(float, line.split()))
-442                    if version == "0.0":
-443                        deltas.append(floats[im - intern[name]["single"]])
-444                    else:
-445                        deltas.append(floats[1 + im - intern[name]["single"]])
-446                return_vals[key] = deltas
-447    return return_vals
-448
+425
+426def _read_o_file(cfg_path, name, needed_keys, intern, version, im):
+427    return_vals = {}
+428    for key in needed_keys:
+429        file = cfg_path + '/' + name
+430        specs = _key2specs(key)
+431        if specs[0] == name:
+432            with open(file) as fp:
+433                lines = fp.readlines()
+434                quarks = specs[1]
+435                off = specs[2]
+436                w = specs[3]
+437                w2 = specs[4]
+438                T = intern[name]["T"]
+439                start_read = intern[name]["spec"][quarks][off][w][w2]["start"]
+440                deltas = []
+441                for line in lines[start_read:start_read + T]:
+442                    floats = list(map(float, line.split()))
+443                    if version == "0.0":
+444                        deltas.append(floats[im - intern[name]["single"]])
+445                    else:
+446                        deltas.append(floats[1 + im - intern[name]["single"]])
+447                return_vals[key] = deltas
+448    return return_vals
 449
-450def _extract_corr_type(corr_type):
-451    if corr_type == 'bb':
-452        b2b = True
-453        single = True
-454    elif corr_type == 'bib':
-455        b2b = True
-456        single = False
-457    else:
-458        b2b = False
-459        single = False
-460    return b2b, single
-461
+450
+451def _extract_corr_type(corr_type):
+452    if corr_type == 'bb':
+453        b2b = True
+454        single = True
+455    elif corr_type == 'bib':
+456        b2b = True
+457        single = False
+458    else:
+459        b2b = False
+460        single = False
+461    return b2b, single
 462
-463def _find_files(rep_path, prefix, compact, files=[]):
-464    sub_ls = []
-465    if not files == []:
-466        files.sort(key=lambda x: int(re.findall(r'\d+', x)[-1]))
-467    else:
-468        for (dirpath, dirnames, filenames) in os.walk(rep_path):
-469            if compact:
-470                sub_ls.extend(filenames)
-471            else:
-472                sub_ls.extend(dirnames)
-473            break
-474        if compact:
-475            for exc in sub_ls:
-476                if not fnmatch.fnmatch(exc, prefix + '*'):
-477                    sub_ls = list(set(sub_ls) - set([exc]))
-478            sub_ls.sort(key=lambda x: int(re.findall(r'\d+', x)[-1]))
-479        else:
-480            for exc in sub_ls:
-481                if not fnmatch.fnmatch(exc, 'cfg*'):
-482                    sub_ls = list(set(sub_ls) - set([exc]))
-483            sub_ls.sort(key=lambda x: int(x[3:]))
-484        files = sub_ls
-485    if len(files) == 0:
-486        raise FileNotFoundError("Did not find files in", rep_path, "with prefix", prefix, "and the given structure.")
-487    return files
-488
+463
+464def _find_files(rep_path, prefix, compact, files=[]):
+465    sub_ls = []
+466    if not files == []:
+467        files.sort(key=lambda x: int(re.findall(r'\d+', x)[-1]))
+468    else:
+469        for (dirpath, dirnames, filenames) in os.walk(rep_path):
+470            if compact:
+471                sub_ls.extend(filenames)
+472            else:
+473                sub_ls.extend(dirnames)
+474            break
+475        if compact:
+476            for exc in sub_ls:
+477                if not fnmatch.fnmatch(exc, prefix + '*'):
+478                    sub_ls = list(set(sub_ls) - set([exc]))
+479            sub_ls.sort(key=lambda x: int(re.findall(r'\d+', x)[-1]))
+480        else:
+481            for exc in sub_ls:
+482                if not fnmatch.fnmatch(exc, 'cfg*'):
+483                    sub_ls = list(set(sub_ls) - set([exc]))
+484            sub_ls.sort(key=lambda x: int(x[3:]))
+485        files = sub_ls
+486    if len(files) == 0:
+487        raise FileNotFoundError("Did not find files in", rep_path, "with prefix", prefix, "and the given structure.")
+488    return files
 489
-490def _make_pattern(version, name, noffset, wf, wf2, b2b, quarks):
-491    if version == "0.0":
-492        pattern = "# " + name + " : offset " + str(noffset) + ", wf " + str(wf)
-493        if b2b:
-494            pattern += ", wf_2 " + str(wf2)
-495        qs = quarks.split(" ")
-496        pattern += " : " + qs[0] + " - " + qs[1]
-497    else:
-498        pattern = 'name      ' + name + '\nquarks    ' + quarks + '\noffset    ' + str(noffset) + '\nwf        ' + str(wf)
-499        if b2b:
-500            pattern += '\nwf_2      ' + str(wf2)
-501    return pattern
-502
+490
+491def _make_pattern(version, name, noffset, wf, wf2, b2b, quarks):
+492    if version == "0.0":
+493        pattern = "# " + name + " : offset " + str(noffset) + ", wf " + str(wf)
+494        if b2b:
+495            pattern += ", wf_2 " + str(wf2)
+496        qs = quarks.split(" ")
+497        pattern += " : " + qs[0] + " - " + qs[1]
+498    else:
+499        pattern = 'name      ' + name + '\nquarks    ' + quarks + '\noffset    ' + str(noffset) + '\nwf        ' + str(wf)
+500        if b2b:
+501            pattern += '\nwf_2      ' + str(wf2)
+502    return pattern
 503
-504def _find_correlator(file_name, version, pattern, b2b, silent=False):
-505    T = 0
-506
-507    with open(file_name, "r") as my_file:
-508
-509        content = my_file.read()
-510        match = re.search(pattern, content)
-511        if match:
-512            if version == "0.0":
-513                start_read = content.count('\n', 0, match.start()) + 1
-514                T = content.count('\n', start_read)
-515            else:
-516                start_read = content.count('\n', 0, match.start()) + 5 + b2b
-517                end_match = re.search(r'\n\s*\n', content[match.start():])
-518                T = content[match.start():].count('\n', 0, end_match.start()) - 4 - b2b
-519            if not T > 0:
-520                raise ValueError("Correlator with pattern\n" + pattern + "\nis empty!")
-521            if not silent:
-522                print(T, 'entries, starting to read in line', start_read)
-523
-524        else:
-525            raise ValueError('Correlator with pattern\n' + pattern + '\nnot found.')
-526
-527    return start_read, T
-528
+504
+505def _find_correlator(file_name, version, pattern, b2b, silent=False):
+506    T = 0
+507
+508    with open(file_name, "r") as my_file:
+509
+510        content = my_file.read()
+511        match = re.search(pattern, content)
+512        if match:
+513            if version == "0.0":
+514                start_read = content.count('\n', 0, match.start()) + 1
+515                T = content.count('\n', start_read)
+516            else:
+517                start_read = content.count('\n', 0, match.start()) + 5 + b2b
+518                end_match = re.search(r'\n\s*\n', content[match.start():])
+519                T = content[match.start():].count('\n', 0, end_match.start()) - 4 - b2b
+520            if not T > 0:
+521                raise ValueError("Correlator with pattern\n" + pattern + "\nis empty!")
+522            if not silent:
+523                print(T, 'entries, starting to read in line', start_read)
+524
+525        else:
+526            raise ValueError('Correlator with pattern\n' + pattern + '\nnot found.')
+527
+528    return start_read, T
 529
-530def _read_compact_file(rep_path, cfg_file, intern, needed_keys, im):
-531    return_vals = {}
-532    with open(rep_path + cfg_file) as fp:
-533        lines = fp.readlines()
-534        for key in needed_keys:
-535            keys = _key2specs(key)
-536            name = keys[0]
-537            quarks = keys[1]
-538            off = keys[2]
-539            w = keys[3]
-540            w2 = keys[4]
-541
-542            T = intern[name]["T"]
-543            start_read = intern[name]["spec"][quarks][off][w][w2]["start"]
-544            # check, if the correlator is in fact
-545            # printed completely
-546            if (start_read + T + 1 > len(lines)):
-547                raise Exception("EOF before end of correlator data! Maybe " + rep_path + cfg_file + " is corrupted?")
-548            corr_lines = lines[start_read - 6: start_read + T]
-549            t_vals = []
-550
-551            if corr_lines[1 - intern[name]["b2b"]].strip() != 'name      ' + name:
-552                raise Exception('Wrong format in file', cfg_file)
-553
-554            for k in range(6, T + 6):
-555                floats = list(map(float, corr_lines[k].split()))
-556                t_vals.append(floats[-2:][im])
-557            return_vals[key] = t_vals
-558    return return_vals
-559
+530
+531def _read_compact_file(rep_path, cfg_file, intern, needed_keys, im):
+532    return_vals = {}
+533    with open(rep_path + cfg_file) as fp:
+534        lines = fp.readlines()
+535        for key in needed_keys:
+536            keys = _key2specs(key)
+537            name = keys[0]
+538            quarks = keys[1]
+539            off = keys[2]
+540            w = keys[3]
+541            w2 = keys[4]
+542
+543            T = intern[name]["T"]
+544            start_read = intern[name]["spec"][quarks][off][w][w2]["start"]
+545            # check, if the correlator is in fact
+546            # printed completely
+547            if (start_read + T + 1 > len(lines)):
+548                raise Exception("EOF before end of correlator data! Maybe " + rep_path + cfg_file + " is corrupted?")
+549            corr_lines = lines[start_read - 6: start_read + T]
+550            t_vals = []
+551
+552            if corr_lines[1 - intern[name]["b2b"]].strip() != 'name      ' + name:
+553                raise Exception('Wrong format in file', cfg_file)
+554
+555            for k in range(6, T + 6):
+556                floats = list(map(float, corr_lines[k].split()))
+557                t_vals.append(floats[-2:][im])
+558            return_vals[key] = t_vals
+559    return return_vals
 560
-561def _read_compact_rep(path, rep, sub_ls, intern, needed_keys, im):
-562    rep_path = path + '/' + rep + '/'
-563    no_cfg = len(sub_ls)
-564
-565    return_vals = {}
-566    for key in needed_keys:
-567        name = _key2specs(key)[0]
-568        deltas = []
-569        for t in range(intern[name]["T"]):
-570            deltas.append(np.zeros(no_cfg))
-571        return_vals[key] = deltas
-572
-573    for cfg in range(no_cfg):
-574        cfg_file = sub_ls[cfg]
-575        cfg_data = _read_compact_file(rep_path, cfg_file, intern, needed_keys, im)
-576        for key in needed_keys:
-577            name = _key2specs(key)[0]
-578            for t in range(intern[name]["T"]):
-579                return_vals[key][t][cfg] = cfg_data[key][t]
-580    return return_vals
-581
+561
+562def _read_compact_rep(path, rep, sub_ls, intern, needed_keys, im):
+563    rep_path = path + '/' + rep + '/'
+564    no_cfg = len(sub_ls)
+565
+566    return_vals = {}
+567    for key in needed_keys:
+568        name = _key2specs(key)[0]
+569        deltas = []
+570        for t in range(intern[name]["T"]):
+571            deltas.append(np.zeros(no_cfg))
+572        return_vals[key] = deltas
+573
+574    for cfg in range(no_cfg):
+575        cfg_file = sub_ls[cfg]
+576        cfg_data = _read_compact_file(rep_path, cfg_file, intern, needed_keys, im)
+577        for key in needed_keys:
+578            name = _key2specs(key)[0]
+579            for t in range(intern[name]["T"]):
+580                return_vals[key][t][cfg] = cfg_data[key][t]
+581    return return_vals
 582
-583def _read_chunk(chunk, gauge_line, cfg_sep, start_read, T, corr_line, b2b, pattern, im, single):
-584    try:
-585        idl = int(chunk[gauge_line].split(cfg_sep)[-1])
-586    except Exception:
-587        raise Exception("Couldn't parse idl from directory, problem with chunk around line ", gauge_line)
-588
-589    found_pat = ""
-590    data = []
-591    for li in chunk[corr_line + 1:corr_line + 6 + b2b]:
-592        found_pat += li
-593    if re.search(pattern, found_pat):
-594        for t, line in enumerate(chunk[start_read:start_read + T]):
-595            floats = list(map(float, line.split()))
-596            data.append(floats[im + 1 - single])
-597    return idl, data
-598
+583
+584def _read_chunk(chunk, gauge_line, cfg_sep, start_read, T, corr_line, b2b, pattern, im, single):
+585    try:
+586        idl = int(chunk[gauge_line].split(cfg_sep)[-1])
+587    except Exception:
+588        raise Exception("Couldn't parse idl from directory, problem with chunk around line ", gauge_line)
+589
+590    found_pat = ""
+591    data = []
+592    for li in chunk[corr_line + 1:corr_line + 6 + b2b]:
+593        found_pat += li
+594    if re.search(pattern, found_pat):
+595        for t, line in enumerate(chunk[start_read:start_read + T]):
+596            floats = list(map(float, line.split()))
+597            data.append(floats[im + 1 - single])
+598    return idl, data
 599
-600def _read_append_rep(filename, pattern, b2b, cfg_separator, im, single):
-601    with open(filename, 'r') as fp:
-602        content = fp.readlines()
-603        data_starts = []
-604        for linenumber, line in enumerate(content):
-605            if "[run]" in line:
-606                data_starts.append(linenumber)
-607        if len(set([data_starts[i] - data_starts[i - 1] for i in range(1, len(data_starts))])) > 1:
-608            raise Exception("Irregularities in file structure found, not all runs have the same output length")
-609        chunk = content[:data_starts[1]]
-610        for linenumber, line in enumerate(chunk):
-611            if line.startswith("gauge_name"):
-612                gauge_line = linenumber
-613            elif line.startswith("[correlator]"):
-614                corr_line = linenumber
-615                found_pat = ""
-616                for li in chunk[corr_line + 1: corr_line + 6 + b2b]:
-617                    found_pat += li
-618                if re.search(pattern, found_pat):
-619                    start_read = corr_line + 7 + b2b
-620                    break
-621                else:
-622                    raise ValueError("Did not find pattern\n", pattern, "\nin\n", filename)
-623        endline = corr_line + 6 + b2b
-624        while not chunk[endline] == "\n":
-625            endline += 1
-626        T = endline - start_read
-627
-628        # all other chunks should follow the same structure
-629        rep_idl = []
-630        rep_data = []
-631
-632        for cnfg in range(len(data_starts)):
-633            start = data_starts[cnfg]
-634            stop = start + data_starts[1]
-635            chunk = content[start:stop]
-636            idl, data = _read_chunk(chunk, gauge_line, cfg_separator, start_read, T, corr_line, b2b, pattern, im, single)
-637            rep_idl.append(idl)
-638            rep_data.append(data)
-639
-640        data = []
-641
-642        for t in range(T):
-643            data.append([])
-644            for c in range(len(rep_data)):
-645                data[t].append(rep_data[c][t])
-646        return T, rep_idl, data
-647
+600
+601def _read_append_rep(filename, pattern, b2b, cfg_separator, im, single):
+602    with open(filename, 'r') as fp:
+603        content = fp.readlines()
+604        data_starts = []
+605        for linenumber, line in enumerate(content):
+606            if "[run]" in line:
+607                data_starts.append(linenumber)
+608        if len(set([data_starts[i] - data_starts[i - 1] for i in range(1, len(data_starts))])) > 1:
+609            raise Exception("Irregularities in file structure found, not all runs have the same output length")
+610        chunk = content[:data_starts[1]]
+611        for linenumber, line in enumerate(chunk):
+612            if line.startswith("gauge_name"):
+613                gauge_line = linenumber
+614            elif line.startswith("[correlator]"):
+615                corr_line = linenumber
+616                found_pat = ""
+617                for li in chunk[corr_line + 1: corr_line + 6 + b2b]:
+618                    found_pat += li
+619                if re.search(pattern, found_pat):
+620                    start_read = corr_line + 7 + b2b
+621                    break
+622                else:
+623                    raise ValueError("Did not find pattern\n", pattern, "\nin\n", filename)
+624        endline = corr_line + 6 + b2b
+625        while not chunk[endline] == "\n":
+626            endline += 1
+627        T = endline - start_read
+628
+629        # all other chunks should follow the same structure
+630        rep_idl = []
+631        rep_data = []
+632
+633        for cnfg in range(len(data_starts)):
+634            start = data_starts[cnfg]
+635            stop = start + data_starts[1]
+636            chunk = content[start:stop]
+637            idl, data = _read_chunk(chunk, gauge_line, cfg_separator, start_read, T, corr_line, b2b, pattern, im, single)
+638            rep_idl.append(idl)
+639            rep_data.append(data)
+640
+641        data = []
+642
+643        for t in range(T):
+644            data.append([])
+645            for c in range(len(rep_data)):
+646                data[t].append(rep_data[c][t])
+647        return T, rep_idl, data
 648
-649def _get_rep_names(ls, ens_name=None):
-650    new_names = []
-651    for entry in ls:
-652        try:
-653            idx = entry.index('r')
-654        except Exception:
-655            raise Exception("Automatic recognition of replicum failed, please enter the key word 'names'.")
-656
-657        if ens_name:
-658            new_names.append('ens_name' + '|' + entry[idx:])
-659        else:
-660            new_names.append(entry[:idx] + '|' + entry[idx:])
-661    return new_names
-662
+649
+650def _get_rep_names(ls, ens_name=None, rep_sep='r'):
+651    new_names = []
+652    for entry in ls:
+653        try:
+654            idx = entry.index(rep_sep)
+655        except Exception:
+656            raise Exception("Automatic recognition of replicum failed, please enter the key word 'names'.")
+657
+658        if ens_name:
+659            new_names.append(ens_name + '|' + entry[idx:])
+660        else:
+661            new_names.append(entry[:idx] + '|' + entry[idx:])
+662    return new_names
 663
-664def _get_appended_rep_names(ls, prefix, name, ens_name=None):
-665    new_names = []
-666    for exc in ls:
-667        if not fnmatch.fnmatch(exc, prefix + '*.' + name):
-668            ls = list(set(ls) - set([exc]))
-669    ls.sort(key=lambda x: int(re.findall(r'\d+', x)[-1]))
-670    for entry in ls:
-671        myentry = entry[:-len(name) - 1]
-672        try:
-673            idx = myentry.index('r')
-674        except Exception:
-675            raise Exception("Automatic recognition of replicum failed, please enter the key word 'names'.")
-676
-677        if ens_name:
-678            new_names.append('ens_name' + '|' + entry[idx:])
-679        else:
-680            new_names.append(myentry[:idx] + '|' + myentry[idx:])
-681    return new_names
+664
+665def _get_appended_rep_names(ls, prefix, name, ens_name=None, rep_sep='r'):
+666    new_names = []
+667    for exc in ls:
+668        if not fnmatch.fnmatch(exc, prefix + '*.' + name):
+669            ls = list(set(ls) - set([exc]))
+670    ls.sort(key=lambda x: int(re.findall(r'\d+', x)[-1]))
+671    for entry in ls:
+672        myentry = entry[:-len(name) - 1]
+673        try:
+674            idx = myentry.index(rep_sep)
+675        except Exception:
+676            raise Exception("Automatic recognition of replicum failed, please enter the key word 'names'.")
+677
+678        if ens_name:
+679            new_names.append(ens_name + '|' + entry[idx:])
+680        else:
+681            new_names.append(myentry[:idx] + '|' + myentry[idx:])
+682    return new_names
 

 
 
@@ -790,7 +791,7 @@
 
     

     
-            
14def read_sfcf(path, prefix, name, quarks='.*', corr_type="bi", noffset=0, wf=0, wf2=0, version="1.0c", cfg_separator="n", silent=False, **kwargs):
+            
14def read_sfcf(path, prefix, name, quarks='.*', corr_type="bi", noffset=0, wf=0, wf2=0, version="1.0c", cfg_separator="n", silent=False, **kwargs):
 15    """Read sfcf files from given folder structure.
 16
 17    Parameters
@@ -934,7 +935,7 @@ bb-type correlators have length 1.
 
     

     
-            
 79def read_sfcf_multi(path, prefix, name_list, quarks_list=['.*'], corr_type_list=['bi'], noffset_list=[0], wf_list=[0], wf2_list=[0], version="1.0c", cfg_separator="n", silent=False, keyed_out=False, **kwargs):
+            
 79def read_sfcf_multi(path, prefix, name_list, quarks_list=['.*'], corr_type_list=['bi'], noffset_list=[0], wf_list=[0], wf2_list=[0], version="1.0c", cfg_separator="n", silent=False, keyed_out=False, **kwargs):
  80    """Read sfcf files from given folder structure.
  81
  82    Parameters
@@ -986,284 +987,285 @@ bb-type correlators have length 1.
 128    check_configs: list[list[int]]
 129        list of list of supposed configs, eg. [range(1,1000)]
 130        for one replicum with 1000 configs
-131
-132    Returns
-133    -------
-134    result: dict[list[Obs]]
-135        dict with one of the following properties:
-136        if keyed_out:
-137            dict[key] = list[Obs]
-138            where key has the form name/quarks/offset/wf/wf2
-139        if not keyed_out:
-140            dict[name][quarks][offset][wf][wf2] = list[Obs]
-141    """
-142
-143    if kwargs.get('im'):
-144        im = 1
-145        part = 'imaginary'
-146    else:
-147        im = 0
-148        part = 'real'
-149
-150    known_versions = ["0.0", "1.0", "2.0", "1.0c", "2.0c", "1.0a", "2.0a"]
-151
-152    if version not in known_versions:
-153        raise Exception("This version is not known!")
-154    if (version[-1] == "c"):
-155        appended = False
-156        compact = True
-157        version = version[:-1]
-158    elif (version[-1] == "a"):
-159        appended = True
-160        compact = False
-161        version = version[:-1]
-162    else:
-163        compact = False
-164        appended = False
-165    ls = []
-166    if "replica" in kwargs:
-167        ls = kwargs.get("replica")
-168    else:
-169        for (dirpath, dirnames, filenames) in os.walk(path):
-170            if not appended:
-171                ls.extend(dirnames)
-172            else:
-173                ls.extend(filenames)
-174            break
-175        if not ls:
-176            raise Exception('Error, directory not found')
-177        # Exclude folders with different names
-178        for exc in ls:
-179            if not fnmatch.fnmatch(exc, prefix + '*'):
-180                ls = list(set(ls) - set([exc]))
-181
-182    if not appended:
-183        ls = sort_names(ls)
-184        replica = len(ls)
-185
-186    else:
-187        replica = len([file.split(".")[-1] for file in ls]) // len(set([file.split(".")[-1] for file in ls]))
-188    if replica == 0:
-189        raise Exception('No replica found in directory')
-190    if not silent:
-191        print('Read', part, 'part of', name_list, 'from', prefix[:-1], ',', replica, 'replica')
-192
-193    if 'names' in kwargs:
-194        new_names = kwargs.get('names')
-195        if len(new_names) != len(set(new_names)):
-196            raise Exception("names are not unique!")
-197        if len(new_names) != replica:
-198            raise Exception('names should have the length', replica)
-199
-200    else:
-201        ens_name = kwargs.get("ens_name")
-202        if not appended:
-203            new_names = _get_rep_names(ls, ens_name)
-204        else:
-205            new_names = _get_appended_rep_names(ls, prefix, name_list[0], ens_name)
-206        new_names = sort_names(new_names)
-207
-208    idl = []
-209
-210    noffset_list = [str(x) for x in noffset_list]
-211    wf_list = [str(x) for x in wf_list]
-212    wf2_list = [str(x) for x in wf2_list]
-213
-214    # setup dict structures
-215    intern = {}
-216    for name, corr_type in zip(name_list, corr_type_list):
-217        intern[name] = {}
-218        b2b, single = _extract_corr_type(corr_type)
-219        intern[name]["b2b"] = b2b
-220        intern[name]["single"] = single
-221        intern[name]["spec"] = {}
-222        for quarks in quarks_list:
-223            intern[name]["spec"][quarks] = {}
-224            for off in noffset_list:
-225                intern[name]["spec"][quarks][off] = {}
-226                for w in wf_list:
-227                    intern[name]["spec"][quarks][off][w] = {}
-228                    if b2b:
-229                        for w2 in wf2_list:
-230                            intern[name]["spec"][quarks][off][w][w2] = {}
-231                            intern[name]["spec"][quarks][off][w][w2]["pattern"] = _make_pattern(version, name, off, w, w2, intern[name]['b2b'], quarks)
-232                    else:
-233                        intern[name]["spec"][quarks][off][w]["0"] = {}
-234                        intern[name]["spec"][quarks][off][w]["0"]["pattern"] = _make_pattern(version, name, off, w, 0, intern[name]['b2b'], quarks)
-235
-236    internal_ret_dict = {}
-237    needed_keys = []
-238    for name, corr_type in zip(name_list, corr_type_list):
-239        b2b, single = _extract_corr_type(corr_type)
-240        if b2b:
-241            needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, wf2_list))
-242        else:
-243            needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, ["0"]))
-244
-245    for key in needed_keys:
-246        internal_ret_dict[key] = []
-247
-248    if not appended:
-249        for i, item in enumerate(ls):
-250            rep_path = path + '/' + item
-251            if "files" in kwargs:
-252                files = kwargs.get("files")
-253                if isinstance(files, list):
-254                    if all(isinstance(f, list) for f in files):
-255                        files = files[i]
-256                    elif all(isinstance(f, str) for f in files):
-257                        files = files
-258                    else:
-259                        raise TypeError("files has to be of type list[list[str]] or list[str]!")
-260                else:
-261                    raise TypeError("files has to be of type list[list[str]] or list[str]!")
-262
-263            else:
-264                files = []
-265            sub_ls = _find_files(rep_path, prefix, compact, files)
-266            rep_idl = []
-267            no_cfg = len(sub_ls)
-268            for cfg in sub_ls:
-269                try:
-270                    if compact:
-271                        rep_idl.append(int(cfg.split(cfg_separator)[-1]))
-272                    else:
-273                        rep_idl.append(int(cfg[3:]))
-274                except Exception:
-275                    raise Exception("Couldn't parse idl from directory, problem with file " + cfg)
-276            rep_idl.sort()
-277            # maybe there is a better way to print the idls
-278            if not silent:
-279                print(item, ':', no_cfg, ' configurations')
-280            idl.append(rep_idl)
-281            # here we have found all the files we need to look into.
-282            if i == 0:
-283                if version != "0.0" and compact:
-284                    file = path + '/' + item + '/' + sub_ls[0]
-285                for name_index, name in enumerate(name_list):
-286                    if version == "0.0" or not compact:
-287                        file = path + '/' + item + '/' + sub_ls[0] + '/' + name
-288                    if corr_type_list[name_index] == 'bi':
-289                        name_keys = _lists2key(quarks_list, noffset_list, wf_list, ["0"])
-290                    else:
-291                        name_keys = _lists2key(quarks_list, noffset_list, wf_list, wf2_list)
-292                    for key in name_keys:
-293                        specs = _key2specs(key)
-294                        quarks = specs[0]
-295                        off = specs[1]
-296                        w = specs[2]
-297                        w2 = specs[3]
-298                        # here, we want to find the place within the file,
-299                        # where the correlator we need is stored.
-300                        # to do so, the pattern needed is put together
-301                        # from the input values
-302                        start_read, T = _find_correlator(file, version, intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["pattern"], intern[name]['b2b'], silent=silent)
-303                        intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["start"] = start_read
-304                        intern[name]["T"] = T
-305                        # preparing the datastructure
-306                        # the correlators get parsed into...
-307                        deltas = []
-308                        for j in range(intern[name]["T"]):
-309                            deltas.append([])
-310                        internal_ret_dict[sep.join([name, key])] = deltas
-311
-312            if compact:
-313                rep_deltas = _read_compact_rep(path, item, sub_ls, intern, needed_keys, im)
-314                for key in needed_keys:
-315                    name = _key2specs(key)[0]
-316                    for t in range(intern[name]["T"]):
-317                        internal_ret_dict[key][t].append(rep_deltas[key][t])
-318            else:
-319                for key in needed_keys:
-320                    rep_data = []
-321                    name = _key2specs(key)[0]
-322                    for subitem in sub_ls:
-323                        cfg_path = path + '/' + item + '/' + subitem
-324                        file_data = _read_o_file(cfg_path, name, needed_keys, intern, version, im)
-325                        rep_data.append(file_data)
-326                    for t in range(intern[name]["T"]):
-327                        internal_ret_dict[key][t].append([])
-328                        for cfg in range(no_cfg):
-329                            internal_ret_dict[key][t][i].append(rep_data[cfg][key][t])
-330    else:
-331        for key in needed_keys:
-332            specs = _key2specs(key)
-333            name = specs[0]
-334            quarks = specs[1]
-335            off = specs[2]
-336            w = specs[3]
-337            w2 = specs[4]
-338            if "files" in kwargs:
-339                if isinstance(kwargs.get("files"), list) and all(isinstance(f, str) for f in kwargs.get("files")):
-340                    name_ls = kwargs.get("files")
-341                else:
-342                    raise TypeError("In append mode, files has to be of type list[str]!")
-343            else:
-344                name_ls = ls
-345                for exc in name_ls:
-346                    if not fnmatch.fnmatch(exc, prefix + '*.' + name):
-347                        name_ls = list(set(name_ls) - set([exc]))
-348            name_ls = sort_names(name_ls)
-349            pattern = intern[name]['spec'][quarks][off][w][w2]['pattern']
-350            deltas = []
-351            for rep, file in enumerate(name_ls):
-352                rep_idl = []
-353                filename = path + '/' + file
-354                T, rep_idl, rep_data = _read_append_rep(filename, pattern, intern[name]['b2b'], cfg_separator, im, intern[name]['single'])
-355                if rep == 0:
-356                    intern[name]['T'] = T
-357                    for t in range(intern[name]['T']):
-358                        deltas.append([])
-359                for t in range(intern[name]['T']):
-360                    deltas[t].append(rep_data[t])
-361                internal_ret_dict[key] = deltas
-362                if name == name_list[0]:
-363                    idl.append(rep_idl)
-364
-365    if kwargs.get("check_configs") is True:
-366        if not silent:
-367            print("Checking for missing configs...")
-368        che = kwargs.get("check_configs")
-369        if not (len(che) == len(idl)):
-370            raise Exception("check_configs has to be the same length as replica!")
-371        for r in range(len(idl)):
-372            if not silent:
-373                print("checking " + new_names[r])
-374            check_idl(idl[r], che[r])
-375        if not silent:
-376            print("Done")
-377
-378    result_dict = {}
-379    if keyed_out:
-380        for key in needed_keys:
-381            name = _key2specs(key)[0]
-382            result = []
-383            for t in range(intern[name]["T"]):
-384                result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
-385            result_dict[key] = result
-386    else:
-387        for name, corr_type in zip(name_list, corr_type_list):
-388            result_dict[name] = {}
-389            for quarks in quarks_list:
-390                result_dict[name][quarks] = {}
-391                for off in noffset_list:
-392                    result_dict[name][quarks][off] = {}
-393                    for w in wf_list:
-394                        result_dict[name][quarks][off][w] = {}
-395                        if corr_type != 'bi':
-396                            for w2 in wf2_list:
-397                                key = _specs2key(name, quarks, off, w, w2)
-398                                result = []
-399                                for t in range(intern[name]["T"]):
-400                                    result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
-401                                result_dict[name][quarks][str(off)][str(w)][str(w2)] = result
-402                        else:
-403                            key = _specs2key(name, quarks, off, w, "0")
-404                            result = []
-405                            for t in range(intern[name]["T"]):
-406                                result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
-407                            result_dict[name][quarks][str(off)][str(w)][str(0)] = result
-408    return result_dict
+131    rep_string: str
+132        Separator of ensemble name and replicum. Example: In "ensAr0", "r" would be the separator string.
+133    Returns
+134    -------
+135    result: dict[list[Obs]]
+136        dict with one of the following properties:
+137        if keyed_out:
+138            dict[key] = list[Obs]
+139            where key has the form name/quarks/offset/wf/wf2
+140        if not keyed_out:
+141            dict[name][quarks][offset][wf][wf2] = list[Obs]
+142    """
+143
+144    if kwargs.get('im'):
+145        im = 1
+146        part = 'imaginary'
+147    else:
+148        im = 0
+149        part = 'real'
+150
+151    known_versions = ["0.0", "1.0", "2.0", "1.0c", "2.0c", "1.0a", "2.0a"]
+152
+153    if version not in known_versions:
+154        raise Exception("This version is not known!")
+155    if (version[-1] == "c"):
+156        appended = False
+157        compact = True
+158        version = version[:-1]
+159    elif (version[-1] == "a"):
+160        appended = True
+161        compact = False
+162        version = version[:-1]
+163    else:
+164        compact = False
+165        appended = False
+166    ls = []
+167    if "replica" in kwargs:
+168        ls = kwargs.get("replica")
+169    else:
+170        for (dirpath, dirnames, filenames) in os.walk(path):
+171            if not appended:
+172                ls.extend(dirnames)
+173            else:
+174                ls.extend(filenames)
+175            break
+176        if not ls:
+177            raise Exception('Error, directory not found')
+178        # Exclude folders with different names
+179        for exc in ls:
+180            if not fnmatch.fnmatch(exc, prefix + '*'):
+181                ls = list(set(ls) - set([exc]))
+182
+183    if not appended:
+184        ls = sort_names(ls)
+185        replica = len(ls)
+186
+187    else:
+188        replica = len([file.split(".")[-1] for file in ls]) // len(set([file.split(".")[-1] for file in ls]))
+189    if replica == 0:
+190        raise Exception('No replica found in directory')
+191    if not silent:
+192        print('Read', part, 'part of', name_list, 'from', prefix[:-1], ',', replica, 'replica')
+193
+194    if 'names' in kwargs:
+195        new_names = kwargs.get('names')
+196        if len(new_names) != len(set(new_names)):
+197            raise Exception("names are not unique!")
+198        if len(new_names) != replica:
+199            raise Exception('names should have the length', replica)
+200
+201    else:
+202        ens_name = kwargs.get("ens_name")
+203        if not appended:
+204            new_names = _get_rep_names(ls, ens_name, rep_sep=(kwargs.get('rep_string', 'r')))
+205        else:
+206            new_names = _get_appended_rep_names(ls, prefix, name_list[0], ens_name, rep_sep=(kwargs.get('rep_string', 'r')))
+207        new_names = sort_names(new_names)
+208
+209    idl = []
+210
+211    noffset_list = [str(x) for x in noffset_list]
+212    wf_list = [str(x) for x in wf_list]
+213    wf2_list = [str(x) for x in wf2_list]
+214
+215    # setup dict structures
+216    intern = {}
+217    for name, corr_type in zip(name_list, corr_type_list):
+218        intern[name] = {}
+219        b2b, single = _extract_corr_type(corr_type)
+220        intern[name]["b2b"] = b2b
+221        intern[name]["single"] = single
+222        intern[name]["spec"] = {}
+223        for quarks in quarks_list:
+224            intern[name]["spec"][quarks] = {}
+225            for off in noffset_list:
+226                intern[name]["spec"][quarks][off] = {}
+227                for w in wf_list:
+228                    intern[name]["spec"][quarks][off][w] = {}
+229                    if b2b:
+230                        for w2 in wf2_list:
+231                            intern[name]["spec"][quarks][off][w][w2] = {}
+232                            intern[name]["spec"][quarks][off][w][w2]["pattern"] = _make_pattern(version, name, off, w, w2, intern[name]['b2b'], quarks)
+233                    else:
+234                        intern[name]["spec"][quarks][off][w]["0"] = {}
+235                        intern[name]["spec"][quarks][off][w]["0"]["pattern"] = _make_pattern(version, name, off, w, 0, intern[name]['b2b'], quarks)
+236
+237    internal_ret_dict = {}
+238    needed_keys = []
+239    for name, corr_type in zip(name_list, corr_type_list):
+240        b2b, single = _extract_corr_type(corr_type)
+241        if b2b:
+242            needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, wf2_list))
+243        else:
+244            needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, ["0"]))
+245
+246    for key in needed_keys:
+247        internal_ret_dict[key] = []
+248
+249    if not appended:
+250        for i, item in enumerate(ls):
+251            rep_path = path + '/' + item
+252            if "files" in kwargs:
+253                files = kwargs.get("files")
+254                if isinstance(files, list):
+255                    if all(isinstance(f, list) for f in files):
+256                        files = files[i]
+257                    elif all(isinstance(f, str) for f in files):
+258                        files = files
+259                    else:
+260                        raise TypeError("files has to be of type list[list[str]] or list[str]!")
+261                else:
+262                    raise TypeError("files has to be of type list[list[str]] or list[str]!")
+263
+264            else:
+265                files = []
+266            sub_ls = _find_files(rep_path, prefix, compact, files)
+267            rep_idl = []
+268            no_cfg = len(sub_ls)
+269            for cfg in sub_ls:
+270                try:
+271                    if compact:
+272                        rep_idl.append(int(cfg.split(cfg_separator)[-1]))
+273                    else:
+274                        rep_idl.append(int(cfg[3:]))
+275                except Exception:
+276                    raise Exception("Couldn't parse idl from directory, problem with file " + cfg)
+277            rep_idl.sort()
+278            # maybe there is a better way to print the idls
+279            if not silent:
+280                print(item, ':', no_cfg, ' configurations')
+281            idl.append(rep_idl)
+282            # here we have found all the files we need to look into.
+283            if i == 0:
+284                if version != "0.0" and compact:
+285                    file = path + '/' + item + '/' + sub_ls[0]
+286                for name_index, name in enumerate(name_list):
+287                    if version == "0.0" or not compact:
+288                        file = path + '/' + item + '/' + sub_ls[0] + '/' + name
+289                    if corr_type_list[name_index] == 'bi':
+290                        name_keys = _lists2key(quarks_list, noffset_list, wf_list, ["0"])
+291                    else:
+292                        name_keys = _lists2key(quarks_list, noffset_list, wf_list, wf2_list)
+293                    for key in name_keys:
+294                        specs = _key2specs(key)
+295                        quarks = specs[0]
+296                        off = specs[1]
+297                        w = specs[2]
+298                        w2 = specs[3]
+299                        # here, we want to find the place within the file,
+300                        # where the correlator we need is stored.
+301                        # to do so, the pattern needed is put together
+302                        # from the input values
+303                        start_read, T = _find_correlator(file, version, intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["pattern"], intern[name]['b2b'], silent=silent)
+304                        intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["start"] = start_read
+305                        intern[name]["T"] = T
+306                        # preparing the datastructure
+307                        # the correlators get parsed into...
+308                        deltas = []
+309                        for j in range(intern[name]["T"]):
+310                            deltas.append([])
+311                        internal_ret_dict[sep.join([name, key])] = deltas
+312
+313            if compact:
+314                rep_deltas = _read_compact_rep(path, item, sub_ls, intern, needed_keys, im)
+315                for key in needed_keys:
+316                    name = _key2specs(key)[0]
+317                    for t in range(intern[name]["T"]):
+318                        internal_ret_dict[key][t].append(rep_deltas[key][t])
+319            else:
+320                for key in needed_keys:
+321                    rep_data = []
+322                    name = _key2specs(key)[0]
+323                    for subitem in sub_ls:
+324                        cfg_path = path + '/' + item + '/' + subitem
+325                        file_data = _read_o_file(cfg_path, name, needed_keys, intern, version, im)
+326                        rep_data.append(file_data)
+327                    for t in range(intern[name]["T"]):
+328                        internal_ret_dict[key][t].append([])
+329                        for cfg in range(no_cfg):
+330                            internal_ret_dict[key][t][i].append(rep_data[cfg][key][t])
+331    else:
+332        for key in needed_keys:
+333            specs = _key2specs(key)
+334            name = specs[0]
+335            quarks = specs[1]
+336            off = specs[2]
+337            w = specs[3]
+338            w2 = specs[4]
+339            if "files" in kwargs:
+340                if isinstance(kwargs.get("files"), list) and all(isinstance(f, str) for f in kwargs.get("files")):
+341                    name_ls = kwargs.get("files")
+342                else:
+343                    raise TypeError("In append mode, files has to be of type list[str]!")
+344            else:
+345                name_ls = ls
+346                for exc in name_ls:
+347                    if not fnmatch.fnmatch(exc, prefix + '*.' + name):
+348                        name_ls = list(set(name_ls) - set([exc]))
+349            name_ls = sort_names(name_ls)
+350            pattern = intern[name]['spec'][quarks][off][w][w2]['pattern']
+351            deltas = []
+352            for rep, file in enumerate(name_ls):
+353                rep_idl = []
+354                filename = path + '/' + file
+355                T, rep_idl, rep_data = _read_append_rep(filename, pattern, intern[name]['b2b'], cfg_separator, im, intern[name]['single'])
+356                if rep == 0:
+357                    intern[name]['T'] = T
+358                    for t in range(intern[name]['T']):
+359                        deltas.append([])
+360                for t in range(intern[name]['T']):
+361                    deltas[t].append(rep_data[t])
+362                internal_ret_dict[key] = deltas
+363                if name == name_list[0]:
+364                    idl.append(rep_idl)
+365
+366    if kwargs.get("check_configs") is True:
+367        if not silent:
+368            print("Checking for missing configs...")
+369        che = kwargs.get("check_configs")
+370        if not (len(che) == len(idl)):
+371            raise Exception("check_configs has to be the same length as replica!")
+372        for r in range(len(idl)):
+373            if not silent:
+374                print("checking " + new_names[r])
+375            check_idl(idl[r], che[r])
+376        if not silent:
+377            print("Done")
+378
+379    result_dict = {}
+380    if keyed_out:
+381        for key in needed_keys:
+382            name = _key2specs(key)[0]
+383            result = []
+384            for t in range(intern[name]["T"]):
+385                result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
+386            result_dict[key] = result
+387    else:
+388        for name, corr_type in zip(name_list, corr_type_list):
+389            result_dict[name] = {}
+390            for quarks in quarks_list:
+391                result_dict[name][quarks] = {}
+392                for off in noffset_list:
+393                    result_dict[name][quarks][off] = {}
+394                    for w in wf_list:
+395                        result_dict[name][quarks][off][w] = {}
+396                        if corr_type != 'bi':
+397                            for w2 in wf2_list:
+398                                key = _specs2key(name, quarks, off, w, w2)
+399                                result = []
+400                                for t in range(intern[name]["T"]):
+401                                    result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
+402                                result_dict[name][quarks][str(off)][str(w)][str(w2)] = result
+403                        else:
+404                            key = _specs2key(name, quarks, off, w, "0")
+405                            result = []
+406                            for t in range(intern[name]["T"]):
+407                                result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
+408                            result_dict[name][quarks][str(off)][str(w)][str(0)] = result
+409    return result_dict
 

 
 
@@ -1321,6 +1323,8 @@ for non-compact output format, hand the folders to be read here.
 
  • check_configs (list[list[int]]):
 list of list of supposed configs, eg. [range(1,1000)]
 for one replicum with 1000 configs
    • 
+
  • rep_string (str):
+Separator of ensemble name and replicum. Example: In "ensAr0", "r" would be the separator string.
    • 
 
 
 
    Returns
    
diff --git a/docs/pyerrors/input/utils.html b/docs/pyerrors/input/utils.html
index c43bdbb0..9ef2d497 100644
--- a/docs/pyerrors/input/utils.html
+++ b/docs/pyerrors/input/utils.html
@@ -86,12 +86,12 @@
 
                         
      1"""Utilities for the input"""
   2
-  3import re
-  4import fnmatch
-  5import os
+  3import re
+  4import fnmatch
+  5import os
   6
   7
-  8def sort_names(ll):
+  8def sort_names(ll):
   9    """Sorts a list of names of replika with searches for `r` and `id` in the replikum string.
  10    If this search fails, a fallback method is used,
  11    where the strings are simply compared and the first diffeing numeral is used for differentiation.
@@ -138,7 +138,7 @@
  52    return ll
  53
  54
- 55def check_idl(idl, che):
+ 55def check_idl(idl, che):
  56    """Checks if list of configurations is contained in an idl
  57
  58    Parameters
@@ -168,7 +168,7 @@
  82    return miss_str
  83
  84
- 85def check_params(path, param_hash, prefix, param_prefix="parameters_"):
+ 85def check_params(path, param_hash, prefix, param_prefix="parameters_"):
  86    """
  87    Check if, for sfcf, the parameter hashes at the end of the parameter files are in fact the expected one.
  88
@@ -243,7 +243,7 @@
 
     
    
     
-            
     9def sort_names(ll):
+            
     9def sort_names(ll):
 10    """Sorts a list of names of replika with searches for `r` and `id` in the replikum string.
 11    If this search fails, a fallback method is used,
 12    where the strings are simply compared and the first diffeing numeral is used for differentiation.
@@ -323,7 +323,7 @@ sorted list
 
     
    
     
-            
    56def check_idl(idl, che):
+            
    56def check_idl(idl, che):
 57    """Checks if list of configurations is contained in an idl
 58
 59    Parameters
@@ -386,7 +386,7 @@ string with integers of which idls are missing
 
     
    
     
-            
     86def check_params(path, param_hash, prefix, param_prefix="parameters_"):
+            
     86def check_params(path, param_hash, prefix, param_prefix="parameters_"):
  87    """
  88    Check if, for sfcf, the parameter hashes at the end of the parameter files are in fact the expected one.
  89
diff --git a/docs/pyerrors/integrate.html b/docs/pyerrors/integrate.html
index 3962ac47..02cd8ba7 100644
--- a/docs/pyerrors/integrate.html
+++ b/docs/pyerrors/integrate.html
@@ -76,13 +76,13 @@
 
                         
 
-                        
     1import numpy as np
- 2from .obs import derived_observable, Obs
- 3from autograd import jacobian
- 4from scipy.integrate import quad as squad
+                        
     1import numpy as np
+ 2from .obs import derived_observable, Obs
+ 3from autograd import jacobian
+ 4from scipy.integrate import quad as squad
  5
  6
- 7def quad(func, p, a, b, **kwargs):
+ 7def quad(func, p, a, b, **kwargs):
  8    '''Performs a (one-dimensional) numeric integration of f(p, x) from a to b.
  9
 10    The integration is performed using scipy.integrate.quad().
@@ -178,7 +178,7 @@
 
     
    
     
-            
     8def quad(func, p, a, b, **kwargs):
+            
     8def quad(func, p, a, b, **kwargs):
  9    '''Performs a (one-dimensional) numeric integration of f(p, x) from a to b.
 10
 11    The integration is performed using scipy.integrate.quad().
@@ -275,9 +275,9 @@ The output is the same as for scipy.integrate.quad, the first element being an O
 function to integrate, has to be of the form
    
 
 
    
-
    import autograd.numpy as anp
+
    import autograd.numpy as anp
 
-def func(p, x):
+def func(p, x):
     return p[0] + p[1] * x + p[2] * anp.sinh(x)
 
    
 
    
diff --git a/docs/pyerrors/linalg.html b/docs/pyerrors/linalg.html
index 9a3966d0..d4d856a8 100644
--- a/docs/pyerrors/linalg.html
+++ b/docs/pyerrors/linalg.html
@@ -106,12 +106,12 @@
 
                         
 
-                        
      1import numpy as np
-  2import autograd.numpy as anp  # Thinly-wrapped numpy
-  3from .obs import derived_observable, CObs, Obs, import_jackknife
+                        
      1import numpy as np
+  2import autograd.numpy as anp  # Thinly-wrapped numpy
+  3from .obs import derived_observable, CObs, Obs, import_jackknife
   4
   5
-  6def matmul(*operands):
+  6def matmul(*operands):
   7    """Matrix multiply all operands.
   8
   9    Parameters
@@ -129,7 +129,7 @@
  21            extended_operands.append(tmp[0])
  22            extended_operands.append(tmp[1])
  23
- 24        def multi_dot(operands, part):
+ 24        def multi_dot(operands, part):
  25            stack_r = operands[0]
  26            stack_i = operands[1]
  27            for op_r, op_i in zip(operands[2::2], operands[3::2]):
@@ -144,10 +144,10 @@
  36            else:
  37                return stack_i
  38
- 39        def multi_dot_r(operands):
+ 39        def multi_dot_r(operands):
  40            return multi_dot(operands, 'Real')
  41
- 42        def multi_dot_i(operands):
+ 42        def multi_dot_i(operands):
  43            return multi_dot(operands, 'Imag')
  44
  45        Nr = derived_observable(multi_dot_r, extended_operands, array_mode=True)
@@ -159,7 +159,7 @@
  51
  52        return res
  53    else:
- 54        def multi_dot(operands):
+ 54        def multi_dot(operands):
  55            stack = operands[0]
  56            for op in operands[1:]:
  57                stack = stack @ op
@@ -167,7 +167,7 @@
  59        return derived_observable(multi_dot, operands, array_mode=True)
  60
  61
- 62def jack_matmul(*operands):
+ 62def jack_matmul(*operands):
  63    """Matrix multiply both operands making use of the jackknife approximation.
  64
  65    Parameters
@@ -179,25 +179,25 @@
  71    For large matrices this is considerably faster compared to matmul.
  72    """
  73
- 74    def _exp_to_jack(matrix):
+ 74    def _exp_to_jack(matrix):
  75        base_matrix = np.empty_like(matrix)
  76        for index, entry in np.ndenumerate(matrix):
  77            base_matrix[index] = entry.export_jackknife()
  78        return base_matrix
  79
- 80    def _imp_from_jack(matrix, name, idl):
+ 80    def _imp_from_jack(matrix, name, idl):
  81        base_matrix = np.empty_like(matrix)
  82        for index, entry in np.ndenumerate(matrix):
  83            base_matrix[index] = import_jackknife(entry, name, [idl])
  84        return base_matrix
  85
- 86    def _exp_to_jack_c(matrix):
+ 86    def _exp_to_jack_c(matrix):
  87        base_matrix = np.empty_like(matrix)
  88        for index, entry in np.ndenumerate(matrix):
  89            base_matrix[index] = entry.real.export_jackknife() + 1j * entry.imag.export_jackknife()
  90        return base_matrix
  91
- 92    def _imp_from_jack_c(matrix, name, idl):
+ 92    def _imp_from_jack_c(matrix, name, idl):
  93        base_matrix = np.empty_like(matrix)
  94        for index, entry in np.ndenumerate(matrix):
  95            base_matrix[index] = CObs(import_jackknife(entry.real, name, [idl]),
@@ -228,7 +228,7 @@
 120        return _imp_from_jack(r, name, idl)
 121
 122
-123def einsum(subscripts, *operands):
+123def einsum(subscripts, *operands):
 124    """Wrapper for numpy.einsum
 125
 126    Parameters
@@ -240,25 +240,25 @@
 132        Obs valued.
 133    """
 134
-135    def _exp_to_jack(matrix):
+135    def _exp_to_jack(matrix):
 136        base_matrix = []
 137        for index, entry in np.ndenumerate(matrix):
 138            base_matrix.append(entry.export_jackknife())
 139        return np.asarray(base_matrix).reshape(matrix.shape + base_matrix[0].shape)
 140
-141    def _exp_to_jack_c(matrix):
+141    def _exp_to_jack_c(matrix):
 142        base_matrix = []
 143        for index, entry in np.ndenumerate(matrix):
 144            base_matrix.append(entry.real.export_jackknife() + 1j * entry.imag.export_jackknife())
 145        return np.asarray(base_matrix).reshape(matrix.shape + base_matrix[0].shape)
 146
-147    def _imp_from_jack(matrix, name, idl):
+147    def _imp_from_jack(matrix, name, idl):
 148        base_matrix = np.empty(shape=matrix.shape[:-1], dtype=object)
 149        for index in np.ndindex(matrix.shape[:-1]):
 150            base_matrix[index] = import_jackknife(matrix[index], name, [idl])
 151        return base_matrix
 152
-153    def _imp_from_jack_c(matrix, name, idl):
+153    def _imp_from_jack_c(matrix, name, idl):
 154        base_matrix = np.empty(shape=matrix.shape[:-1], dtype=object)
 155        for index in np.ndindex(matrix.shape[:-1]):
 156            base_matrix[index] = CObs(import_jackknife(matrix[index].real, name, [idl]),
@@ -302,26 +302,26 @@
 194        return result
 195
 196
-197def inv(x):
+197def inv(x):
 198    """Inverse of Obs or CObs valued matrices."""
 199    return _mat_mat_op(anp.linalg.inv, x)
 200
 201
-202def cholesky(x):
+202def cholesky(x):
 203    """Cholesky decomposition of Obs valued matrices."""
 204    if any(isinstance(o, CObs) for o in x.ravel()):
 205        raise Exception("Cholesky decomposition is not implemented for CObs.")
 206    return _mat_mat_op(anp.linalg.cholesky, x)
 207
 208
-209def det(x):
+209def det(x):
 210    """Determinant of Obs valued matrices."""
 211    return _scalar_mat_op(anp.linalg.det, x)
 212
 213
-214def _scalar_mat_op(op, obs, **kwargs):
+214def _scalar_mat_op(op, obs, **kwargs):
 215    """Computes the matrix to scalar operation op to a given matrix of Obs."""
-216    def _mat(x, **kwargs):
+216    def _mat(x, **kwargs):
 217        dim = int(np.sqrt(len(x)))
 218
 219        mat = []
@@ -340,7 +340,7 @@
 232    return derived_observable(_mat, raveled_obs, **kwargs)
 233
 234
-235def _mat_mat_op(op, obs, **kwargs):
+235def _mat_mat_op(op, obs, **kwargs):
 236    """Computes the matrix to matrix operation op to a given matrix of Obs."""
 237    # Use real representation to calculate matrix operations for complex matrices
 238    if any(isinstance(o, CObs) for o in obs.ravel()):
@@ -366,31 +366,31 @@
 258        return derived_observable(lambda x, **kwargs: op(x), [obs], array_mode=True)[0]
 259
 260
-261def eigh(obs, **kwargs):
+261def eigh(obs, **kwargs):
 262    """Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh."""
 263    w = derived_observable(lambda x, **kwargs: anp.linalg.eigh(x)[0], obs)
 264    v = derived_observable(lambda x, **kwargs: anp.linalg.eigh(x)[1], obs)
 265    return w, v
 266
 267
-268def eig(obs, **kwargs):
+268def eig(obs, **kwargs):
 269    """Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig."""
 270    w = derived_observable(lambda x, **kwargs: anp.real(anp.linalg.eig(x)[0]), obs)
 271    return w
 272
 273
-274def eigv(obs, **kwargs):
+274def eigv(obs, **kwargs):
 275    """Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh."""
 276    v = derived_observable(lambda x, **kwargs: anp.linalg.eigh(x)[1], obs)
 277    return v
 278
 279
-280def pinv(obs, **kwargs):
+280def pinv(obs, **kwargs):
 281    """Computes the Moore-Penrose pseudoinverse of a matrix of Obs."""
 282    return derived_observable(lambda x, **kwargs: anp.linalg.pinv(x), obs)
 283
 284
-285def svd(obs, **kwargs):
+285def svd(obs, **kwargs):
 286    """Computes the singular value decomposition of a matrix of Obs."""
 287    u = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[0], obs)
 288    s = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[1], obs)
@@ -411,7 +411,7 @@
 
     
    
     
-            
     7def matmul(*operands):
+            
     7def matmul(*operands):
  8    """Matrix multiply all operands.
  9
 10    Parameters
@@ -429,7 +429,7 @@
 22            extended_operands.append(tmp[0])
 23            extended_operands.append(tmp[1])
 24
-25        def multi_dot(operands, part):
+25        def multi_dot(operands, part):
 26            stack_r = operands[0]
 27            stack_i = operands[1]
 28            for op_r, op_i in zip(operands[2::2], operands[3::2]):
@@ -444,10 +444,10 @@
 37            else:
 38                return stack_i
 39
-40        def multi_dot_r(operands):
+40        def multi_dot_r(operands):
 41            return multi_dot(operands, 'Real')
 42
-43        def multi_dot_i(operands):
+43        def multi_dot_i(operands):
 44            return multi_dot(operands, 'Imag')
 45
 46        Nr = derived_observable(multi_dot_r, extended_operands, array_mode=True)
@@ -459,7 +459,7 @@
 52
 53        return res
 54    else:
-55        def multi_dot(operands):
+55        def multi_dot(operands):
 56            stack = operands[0]
 57            for op in operands[1:]:
 58                stack = stack @ op
@@ -493,7 +493,7 @@ Obs valued.
 
     
    
     
-            
     63def jack_matmul(*operands):
+            
     63def jack_matmul(*operands):
  64    """Matrix multiply both operands making use of the jackknife approximation.
  65
  66    Parameters
@@ -505,25 +505,25 @@ Obs valued.
  72    For large matrices this is considerably faster compared to matmul.
  73    """
  74
- 75    def _exp_to_jack(matrix):
+ 75    def _exp_to_jack(matrix):
  76        base_matrix = np.empty_like(matrix)
  77        for index, entry in np.ndenumerate(matrix):
  78            base_matrix[index] = entry.export_jackknife()
  79        return base_matrix
  80
- 81    def _imp_from_jack(matrix, name, idl):
+ 81    def _imp_from_jack(matrix, name, idl):
  82        base_matrix = np.empty_like(matrix)
  83        for index, entry in np.ndenumerate(matrix):
  84            base_matrix[index] = import_jackknife(entry, name, [idl])
  85        return base_matrix
  86
- 87    def _exp_to_jack_c(matrix):
+ 87    def _exp_to_jack_c(matrix):
  88        base_matrix = np.empty_like(matrix)
  89        for index, entry in np.ndenumerate(matrix):
  90            base_matrix[index] = entry.real.export_jackknife() + 1j * entry.imag.export_jackknife()
  91        return base_matrix
  92
- 93    def _imp_from_jack_c(matrix, name, idl):
+ 93    def _imp_from_jack_c(matrix, name, idl):
  94        base_matrix = np.empty_like(matrix)
  95        for index, entry in np.ndenumerate(matrix):
  96            base_matrix[index] = CObs(import_jackknife(entry.real, name, [idl]),
@@ -580,7 +580,7 @@ Obs valued.
 
     
    
     
-            
    124def einsum(subscripts, *operands):
+            
    124def einsum(subscripts, *operands):
 125    """Wrapper for numpy.einsum
 126
 127    Parameters
@@ -592,25 +592,25 @@ Obs valued.
 133        Obs valued.
 134    """
 135
-136    def _exp_to_jack(matrix):
+136    def _exp_to_jack(matrix):
 137        base_matrix = []
 138        for index, entry in np.ndenumerate(matrix):
 139            base_matrix.append(entry.export_jackknife())
 140        return np.asarray(base_matrix).reshape(matrix.shape + base_matrix[0].shape)
 141
-142    def _exp_to_jack_c(matrix):
+142    def _exp_to_jack_c(matrix):
 143        base_matrix = []
 144        for index, entry in np.ndenumerate(matrix):
 145            base_matrix.append(entry.real.export_jackknife() + 1j * entry.imag.export_jackknife())
 146        return np.asarray(base_matrix).reshape(matrix.shape + base_matrix[0].shape)
 147
-148    def _imp_from_jack(matrix, name, idl):
+148    def _imp_from_jack(matrix, name, idl):
 149        base_matrix = np.empty(shape=matrix.shape[:-1], dtype=object)
 150        for index in np.ndindex(matrix.shape[:-1]):
 151            base_matrix[index] = import_jackknife(matrix[index], name, [idl])
 152        return base_matrix
 153
-154    def _imp_from_jack_c(matrix, name, idl):
+154    def _imp_from_jack_c(matrix, name, idl):
 155        base_matrix = np.empty(shape=matrix.shape[:-1], dtype=object)
 156        for index in np.ndindex(matrix.shape[:-1]):
 157            base_matrix[index] = CObs(import_jackknife(matrix[index].real, name, [idl]),
@@ -681,7 +681,7 @@ Obs valued.
 
     
    
     
-            
    198def inv(x):
+            
    198def inv(x):
 199    """Inverse of Obs or CObs valued matrices."""
 200    return _mat_mat_op(anp.linalg.inv, x)
 
    
@@ -703,7 +703,7 @@ Obs valued.
 
     
    
     
-            
    203def cholesky(x):
+            
    203def cholesky(x):
 204    """Cholesky decomposition of Obs valued matrices."""
 205    if any(isinstance(o, CObs) for o in x.ravel()):
 206        raise Exception("Cholesky decomposition is not implemented for CObs.")
@@ -727,7 +727,7 @@ Obs valued.
 
     
    
     
-            
    210def det(x):
+            
    210def det(x):
 211    """Determinant of Obs valued matrices."""
 212    return _scalar_mat_op(anp.linalg.det, x)
 
    
@@ -749,7 +749,7 @@ Obs valued.
 
     
    
     
-            
    262def eigh(obs, **kwargs):
+            
    262def eigh(obs, **kwargs):
 263    """Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh."""
 264    w = derived_observable(lambda x, **kwargs: anp.linalg.eigh(x)[0], obs)
 265    v = derived_observable(lambda x, **kwargs: anp.linalg.eigh(x)[1], obs)
@@ -773,7 +773,7 @@ Obs valued.
 
     
    
     
-            
    269def eig(obs, **kwargs):
+            
    269def eig(obs, **kwargs):
 270    """Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig."""
 271    w = derived_observable(lambda x, **kwargs: anp.real(anp.linalg.eig(x)[0]), obs)
 272    return w
@@ -796,7 +796,7 @@ Obs valued.
 
     
    
     
-            
    275def eigv(obs, **kwargs):
+            
    275def eigv(obs, **kwargs):
 276    """Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh."""
 277    v = derived_observable(lambda x, **kwargs: anp.linalg.eigh(x)[1], obs)
 278    return v
@@ -819,7 +819,7 @@ Obs valued.
 
     
    
     
-            
    281def pinv(obs, **kwargs):
+            
    281def pinv(obs, **kwargs):
 282    """Computes the Moore-Penrose pseudoinverse of a matrix of Obs."""
 283    return derived_observable(lambda x, **kwargs: anp.linalg.pinv(x), obs)
 
    
@@ -841,7 +841,7 @@ Obs valued.
 
     
    
     
-            
    286def svd(obs, **kwargs):
+            
    286def svd(obs, **kwargs):
 287    """Computes the singular value decomposition of a matrix of Obs."""
 288    u = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[0], obs)
 289    s = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[1], obs)
diff --git a/docs/pyerrors/misc.html b/docs/pyerrors/misc.html
index 3dbc5e50..668a9ac8 100644
--- a/docs/pyerrors/misc.html
+++ b/docs/pyerrors/misc.html
@@ -91,18 +91,18 @@
 
                         
 
-                        
      1import platform
-  2import numpy as np
-  3import scipy
-  4import matplotlib
-  5import matplotlib.pyplot as plt
-  6import pandas as pd
-  7import pickle
-  8from .obs import Obs
-  9from .version import __version__
+                        
      1import platform
+  2import numpy as np
+  3import scipy
+  4import matplotlib
+  5import matplotlib.pyplot as plt
+  6import pandas as pd
+  7import pickle
+  8from .obs import Obs
+  9from .version import __version__
  10
  11
- 12def print_config():
+ 12def print_config():
  13    """Print information about version of python, pyerrors and dependencies."""
  14    config = {"system": platform.system(),
  15              "python": platform.python_version(),
@@ -116,7 +116,7 @@
  23        print(f"{key: <10}\t {value}")
  24
  25
- 26def errorbar(x, y, axes=plt, **kwargs):
+ 26def errorbar(x, y, axes=plt, **kwargs):
  27    """pyerrors wrapper for the errorbars method of matplotlib
  28
  29    Parameters
@@ -147,7 +147,7 @@
  54    axes.errorbar(val["x"], val["y"], xerr=err["x"], yerr=err["y"], **kwargs)
  55
  56
- 57def dump_object(obj, name, **kwargs):
+ 57def dump_object(obj, name, **kwargs):
  58    """Dump object into pickle file.
  59
  60    Parameters
@@ -171,7 +171,7 @@
  78        pickle.dump(obj, fb)
  79
  80
- 81def load_object(path):
+ 81def load_object(path):
  82    """Load object from pickle file.
  83
  84    Parameters
@@ -188,7 +188,7 @@
  95        return pickle.load(file)
  96
  97
- 98def pseudo_Obs(value, dvalue, name, samples=1000):
+ 98def pseudo_Obs(value, dvalue, name, samples=1000):
  99    """Generate an Obs object with given value, dvalue and name for test purposes
 100
 101    Parameters
@@ -225,7 +225,7 @@
 132        return res
 133
 134
-135def gen_correlated_data(means, cov, name, tau=0.5, samples=1000):
+135def gen_correlated_data(means, cov, name, tau=0.5, samples=1000):
 136    """ Generate observables with given covariance and autocorrelation times.
 137
 138    Parameters
@@ -267,7 +267,7 @@
 174    return [Obs([dat], [name]) for dat in corr_data.T]
 175
 176
-177def _assert_equal_properties(ol, otype=Obs):
+177def _assert_equal_properties(ol, otype=Obs):
 178    otype = type(ol[0])
 179    for o in ol[1:]:
 180        if not isinstance(o, otype):
@@ -291,7 +291,7 @@
 
     
    
     
-            
    13def print_config():
+            
    13def print_config():
 14    """Print information about version of python, pyerrors and dependencies."""
 15    config = {"system": platform.system(),
 16              "python": platform.python_version(),
@@ -316,13 +316,13 @@
 
    
             
         def
-        errorbar(	x,	y,	axes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,	**kwargs):
+        errorbar(	x,	y,	axes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,	**kwargs):
 
                 
 
     
    
     
-            
    27def errorbar(x, y, axes=plt, **kwargs):
+            
    27def errorbar(x, y, axes=plt, **kwargs):
 28    """pyerrors wrapper for the errorbars method of matplotlib
 29
 30    Parameters
@@ -381,7 +381,7 @@ The axes to plot on. default is plt.
 
     
    
     
-            
    58def dump_object(obj, name, **kwargs):
+            
    58def dump_object(obj, name, **kwargs):
 59    """Dump object into pickle file.
 60
 61    Parameters
@@ -439,7 +439,7 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    82def load_object(path):
+            
    82def load_object(path):
 83    """Load object from pickle file.
 84
 85    Parameters
@@ -487,7 +487,7 @@ Loaded Object
 
     
    
     
-            
     99def pseudo_Obs(value, dvalue, name, samples=1000):
+            
     99def pseudo_Obs(value, dvalue, name, samples=1000):
 100    """Generate an Obs object with given value, dvalue and name for test purposes
 101
 102    Parameters
@@ -561,7 +561,7 @@ Generated Observable
 
     
    
     
-            
    136def gen_correlated_data(means, cov, name, tau=0.5, samples=1000):
+            
    136def gen_correlated_data(means, cov, name, tau=0.5, samples=1000):
 137    """ Generate observables with given covariance and autocorrelation times.
 138
 139    Parameters
diff --git a/docs/pyerrors/mpm.html b/docs/pyerrors/mpm.html
index 1d034251..61928057 100644
--- a/docs/pyerrors/mpm.html
+++ b/docs/pyerrors/mpm.html
@@ -76,13 +76,13 @@
 
                         
 
-                        
     1import numpy as np
- 2import scipy.linalg
- 3from .obs import Obs
- 4from .linalg import svd, eig
+                        
     1import numpy as np
+ 2import scipy.linalg
+ 3from .obs import Obs
+ 4from .linalg import svd, eig
  5
  6
- 7def matrix_pencil_method(corrs, k=1, p=None, **kwargs):
+ 7def matrix_pencil_method(corrs, k=1, p=None, **kwargs):
  8    """Matrix pencil method to extract k energy levels from data
  9
 10    Implementation of the matrix pencil method based on
@@ -154,7 +154,7 @@
 
     
    
     
-            
     8def matrix_pencil_method(corrs, k=1, p=None, **kwargs):
+            
     8def matrix_pencil_method(corrs, k=1, p=None, **kwargs):
  9    """Matrix pencil method to extract k energy levels from data
 10
 11    Implementation of the matrix pencil method based on
diff --git a/docs/pyerrors/obs.html b/docs/pyerrors/obs.html
index cebdb983..5bfeabaf 100644
--- a/docs/pyerrors/obs.html
+++ b/docs/pyerrors/obs.html
@@ -334,24 +334,24 @@
 
                         
 
-                        
       1import warnings
-   2import hashlib
-   3import pickle
-   4import numpy as np
-   5import autograd.numpy as anp  # Thinly-wrapped numpy
-   6import scipy
-   7from autograd import jacobian
-   8import matplotlib.pyplot as plt
-   9from scipy.stats import skew, skewtest, kurtosis, kurtosistest
-  10import numdifftools as nd
-  11from itertools import groupby
-  12from .covobs import Covobs
+                        
       1import warnings
+   2import hashlib
+   3import pickle
+   4import numpy as np
+   5import autograd.numpy as anp  # Thinly-wrapped numpy
+   6import scipy
+   7from autograd import jacobian
+   8import matplotlib.pyplot as plt
+   9from scipy.stats import skew, skewtest, kurtosis, kurtosistest
+  10import numdifftools as nd
+  11from itertools import groupby
+  12from .covobs import Covobs
   13
   14# Improve print output of numpy.ndarrays containing Obs objects.
   15np.set_printoptions(formatter={'object': lambda x: str(x)})
   16
   17
-  18class Obs:
+  18class Obs:
   19    """Class for a general observable.
   20
   21    Instances of Obs are the basic objects of a pyerrors error analysis.
@@ -393,7 +393,7 @@
   57    N_sigma_global = 1.0
   58    N_sigma_dict = {}
   59
-  60    def __init__(self, samples, names, idl=None, **kwargs):
+  60    def __init__(self, samples, names, idl=None, **kwargs):
   61        """ Initialize Obs object.
   62
   63        Parameters
@@ -477,27 +477,27 @@
  141        self.tag = None
  142
  143    @property
- 144    def value(self):
+ 144    def value(self):
  145        return self._value
  146
  147    @property
- 148    def dvalue(self):
+ 148    def dvalue(self):
  149        return self._dvalue
  150
  151    @property
- 152    def e_names(self):
+ 152    def e_names(self):
  153        return sorted(set([o.split('|')[0] for o in self.names]))
  154
  155    @property
- 156    def cov_names(self):
+ 156    def cov_names(self):
  157        return sorted(set([o for o in self.covobs.keys()]))
  158
  159    @property
- 160    def mc_names(self):
+ 160    def mc_names(self):
  161        return sorted(set([o.split('|')[0] for o in self.names if o not in self.cov_names]))
  162
  163    @property
- 164    def e_content(self):
+ 164    def e_content(self):
  165        res = {}
  166        for e, e_name in enumerate(self.e_names):
  167            res[e_name] = sorted(filter(lambda x: x.startswith(e_name + '|'), self.names))
@@ -506,10 +506,10 @@
  170        return res
  171
  172    @property
- 173    def covobs(self):
+ 173    def covobs(self):
  174        return self._covobs
  175
- 176    def gamma_method(self, **kwargs):
+ 176    def gamma_method(self, **kwargs):
  177        """Estimate the error and related properties of the Obs.
  178
  179        Parameters
@@ -553,7 +553,7 @@
  217        else:
  218            fft = True
  219
- 220        def _parse_kwarg(kwarg_name):
+ 220        def _parse_kwarg(kwarg_name):
  221            if kwarg_name in kwargs:
  222                tmp = kwargs.get(kwarg_name)
  223                if isinstance(tmp, (int, float)):
@@ -615,7 +615,7 @@
  279            self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) + 0.5 - self.e_n_tauint[e_name]) / e_N)
  280            self.e_n_dtauint[e_name][0] = 0.0
  281
- 282            def _compute_drho(i):
+ 282            def _compute_drho(i):
  283                tmp = (self.e_rho[e_name][i + 1:w_max]
  284                       + np.concatenate([self.e_rho[e_name][i - 1:None if i - (w_max - 1) // 2 <= 0 else (2 * i - (2 * w_max) // 2):-1],
  285                                         self.e_rho[e_name][1:max(1, w_max - 2 * i)]])
@@ -677,7 +677,7 @@
  341
  342    gm = gamma_method
  343
- 344    def _calc_gamma(self, deltas, idx, shape, w_max, fft, gapsize):
+ 344    def _calc_gamma(self, deltas, idx, shape, w_max, fft, gapsize):
  345        """Calculate Gamma_{AA} from the deltas, which are defined on idx.
  346           idx is assumed to be a contiguous range (possibly with a stepsize != 1)
  347
@@ -713,7 +713,7 @@
  377
  378        return gamma
  379
- 380    def details(self, ens_content=True):
+ 380    def details(self, ens_content=True):
  381        """Output detailed properties of the Obs.
  382
  383        Parameters
@@ -782,7 +782,7 @@
  446                my_string_list.append(my_string)
  447            print('\n'.join(my_string_list))
  448
- 449    def reweight(self, weight):
+ 449    def reweight(self, weight):
  450        """Reweight the obs with given rewighting factors.
  451
  452        Parameters
@@ -797,7 +797,7 @@
  461        """
  462        return reweight(weight, [self])[0]
  463
- 464    def is_zero_within_error(self, sigma=1):
+ 464    def is_zero_within_error(self, sigma=1):
  465        """Checks whether the observable is zero within 'sigma' standard errors.
  466
  467        Parameters
@@ -809,7 +809,7 @@
  473        """
  474        return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue
  475
- 476    def is_zero(self, atol=1e-10):
+ 476    def is_zero(self, atol=1e-10):
  477        """Checks whether the observable is zero within a given tolerance.
  478
  479        Parameters
@@ -819,7 +819,7 @@
  483        """
  484        return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values())
  485
- 486    def plot_tauint(self, save=None):
+ 486    def plot_tauint(self, save=None):
  487        """Plot integrated autocorrelation time for each ensemble.
  488
  489        Parameters
@@ -859,7 +859,7 @@
  523            if save:
  524                fig.savefig(save + "_" + str(e))
  525
- 526    def plot_rho(self, save=None):
+ 526    def plot_rho(self, save=None):
  527        """Plot normalized autocorrelation function time for each ensemble.
  528
  529        Parameters
@@ -890,7 +890,7 @@
  554            if save:
  555                fig.savefig(save + "_" + str(e))
  556
- 557    def plot_rep_dist(self):
+ 557    def plot_rep_dist(self):
  558        """Plot replica distribution for each ensemble with more than one replicum."""
  559        if not hasattr(self, 'e_dvalue'):
  560            raise Exception('Run the gamma method first.')
@@ -912,7 +912,7 @@
  576            plt.title('Replica distribution' + e_name + ' (mean=0, var=1)')
  577            plt.draw()
  578
- 579    def plot_history(self, expand=True):
+ 579    def plot_history(self, expand=True):
  580        """Plot derived Monte Carlo history for each ensemble
  581
  582        Parameters
@@ -944,7 +944,7 @@
  608            plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})')
  609            plt.draw()
  610
- 611    def plot_piechart(self, save=None):
+ 611    def plot_piechart(self, save=None):
  612        """Plot piechart which shows the fractional contribution of each
  613        ensemble to the error and returns a dictionary containing the fractions.
  614
@@ -968,7 +968,7 @@
  632
  633        return dict(zip(labels, sizes))
  634
- 635    def dump(self, filename, datatype="json.gz", description="", **kwargs):
+ 635    def dump(self, filename, datatype="json.gz", description="", **kwargs):
  636        """Dump the Obs to a file 'name' of chosen format.
  637
  638        Parameters
@@ -989,7 +989,7 @@
  653            file_name = filename
  654
  655        if datatype == "json.gz":
- 656            from .input.json import dump_to_json
+ 656            from .input.json import dump_to_json
  657            dump_to_json([self], file_name, description=description)
  658        elif datatype == "pickle":
  659            with open(file_name + '.p', 'wb') as fb:
@@ -997,7 +997,7 @@
  661        else:
  662            raise TypeError("Unknown datatype " + str(datatype))
  663
- 664    def export_jackknife(self):
+ 664    def export_jackknife(self):
  665        """Export jackknife samples from the Obs
  666
  667        Returns
@@ -1023,7 +1023,7 @@
  687        tmp_jacks[1:] = (n * mean - full_data) / (n - 1)
  688        return tmp_jacks
  689
- 690    def export_bootstrap(self, samples=500, random_numbers=None, save_rng=None):
+ 690    def export_bootstrap(self, samples=500, random_numbers=None, save_rng=None):
  691        """Export bootstrap samples from the Obs
  692
  693        Parameters
@@ -1066,16 +1066,16 @@
  730        ret[1:] = proj @ (self.deltas[name] + self.r_values[name])
  731        return ret
  732
- 733    def __float__(self):
+ 733    def __float__(self):
  734        return float(self.value)
  735
- 736    def __repr__(self):
+ 736    def __repr__(self):
  737        return 'Obs[' + str(self) + ']'
  738
- 739    def __str__(self):
+ 739    def __str__(self):
  740        return _format_uncertainty(self.value, self._dvalue)
  741
- 742    def __format__(self, format_type):
+ 742    def __format__(self, format_type):
  743        if format_type == "":
  744            significance = 2
  745        else:
@@ -1088,7 +1088,7 @@
  752                    my_str = char + my_str
  753        return my_str
  754
- 755    def __hash__(self):
+ 755    def __hash__(self):
  756        hash_tuple = (np.array([self.value]).astype(np.float32).data.tobytes(),)
  757        hash_tuple += tuple([o.astype(np.float32).data.tobytes() for o in self.deltas.values()])
  758        hash_tuple += tuple([np.array([o.errsq()]).astype(np.float32).data.tobytes() for o in self.covobs.values()])
@@ -1098,25 +1098,25 @@
  762        return int(m.hexdigest(), 16) & 0xFFFFFFFF
  763
  764    # Overload comparisons
- 765    def __lt__(self, other):
+ 765    def __lt__(self, other):
  766        return self.value < other
  767
- 768    def __le__(self, other):
+ 768    def __le__(self, other):
  769        return self.value <= other
  770
- 771    def __gt__(self, other):
+ 771    def __gt__(self, other):
  772        return self.value > other
  773
- 774    def __ge__(self, other):
+ 774    def __ge__(self, other):
  775        return self.value >= other
  776
- 777    def __eq__(self, other):
+ 777    def __eq__(self, other):
  778        if other is None:
  779            return False
  780        return (self - other).is_zero()
  781
  782    # Overload math operations
- 783    def __add__(self, y):
+ 783    def __add__(self, y):
  784        if isinstance(y, Obs):
  785            return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1])
  786        else:
@@ -1129,10 +1129,10 @@
  793            else:
  794                return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1])
  795
- 796    def __radd__(self, y):
+ 796    def __radd__(self, y):
  797        return self + y
  798
- 799    def __mul__(self, y):
+ 799    def __mul__(self, y):
  800        if isinstance(y, Obs):
  801            return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value])
  802        else:
@@ -1145,10 +1145,10 @@
  809            else:
  810                return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y])
  811
- 812    def __rmul__(self, y):
+ 812    def __rmul__(self, y):
  813        return self * y
  814
- 815    def __sub__(self, y):
+ 815    def __sub__(self, y):
  816        if isinstance(y, Obs):
  817            return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1])
  818        else:
@@ -1159,16 +1159,16 @@
  823            else:
  824                return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1])
  825
- 826    def __rsub__(self, y):
+ 826    def __rsub__(self, y):
  827        return -1 * (self - y)
  828
- 829    def __pos__(self):
+ 829    def __pos__(self):
  830        return self
  831
- 832    def __neg__(self):
+ 832    def __neg__(self):
  833        return -1 * self
  834
- 835    def __truediv__(self, y):
+ 835    def __truediv__(self, y):
  836        if isinstance(y, Obs):
  837            return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2])
  838        else:
@@ -1179,7 +1179,7 @@
  843            else:
  844                return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y])
  845
- 846    def __rtruediv__(self, y):
+ 846    def __rtruediv__(self, y):
  847        if isinstance(y, Obs):
  848            return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2])
  849        else:
@@ -1190,97 +1190,97 @@
  854            else:
  855                return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2])
  856
- 857    def __pow__(self, y):
+ 857    def __pow__(self, y):
  858        if isinstance(y, Obs):
  859            return derived_observable(lambda x, **kwargs: x[0] ** x[1], [self, y], man_grad=[y.value * self.value ** (y.value - 1), self.value ** y.value * np.log(self.value)])
  860        else:
  861            return derived_observable(lambda x, **kwargs: x[0] ** y, [self], man_grad=[y * self.value ** (y - 1)])
  862
- 863    def __rpow__(self, y):
+ 863    def __rpow__(self, y):
  864        return derived_observable(lambda x, **kwargs: y ** x[0], [self], man_grad=[y ** self.value * np.log(y)])
  865
- 866    def __abs__(self):
+ 866    def __abs__(self):
  867        return derived_observable(lambda x: anp.abs(x[0]), [self])
  868
  869    # Overload numpy functions
- 870    def sqrt(self):
+ 870    def sqrt(self):
  871        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
  872
- 873    def log(self):
+ 873    def log(self):
  874        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
  875
- 876    def exp(self):
+ 876    def exp(self):
  877        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
  878
- 879    def sin(self):
+ 879    def sin(self):
  880        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
  881
- 882    def cos(self):
+ 882    def cos(self):
  883        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
  884
- 885    def tan(self):
+ 885    def tan(self):
  886        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
  887
- 888    def arcsin(self):
+ 888    def arcsin(self):
  889        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
  890
- 891    def arccos(self):
+ 891    def arccos(self):
  892        return derived_observable(lambda x: anp.arccos(x[0]), [self])
  893
- 894    def arctan(self):
+ 894    def arctan(self):
  895        return derived_observable(lambda x: anp.arctan(x[0]), [self])
  896
- 897    def sinh(self):
+ 897    def sinh(self):
  898        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
  899
- 900    def cosh(self):
+ 900    def cosh(self):
  901        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
  902
- 903    def tanh(self):
+ 903    def tanh(self):
  904        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
  905
- 906    def arcsinh(self):
+ 906    def arcsinh(self):
  907        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
  908
- 909    def arccosh(self):
+ 909    def arccosh(self):
  910        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
  911
- 912    def arctanh(self):
+ 912    def arctanh(self):
  913        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
  914
  915
- 916class CObs:
+ 916class CObs:
  917    """Class for a complex valued observable."""
  918    __slots__ = ['_real', '_imag', 'tag']
  919
- 920    def __init__(self, real, imag=0.0):
+ 920    def __init__(self, real, imag=0.0):
  921        self._real = real
  922        self._imag = imag
  923        self.tag = None
  924
  925    @property
- 926    def real(self):
+ 926    def real(self):
  927        return self._real
  928
  929    @property
- 930    def imag(self):
+ 930    def imag(self):
  931        return self._imag
  932
- 933    def gamma_method(self, **kwargs):
+ 933    def gamma_method(self, **kwargs):
  934        """Executes the gamma_method for the real and the imaginary part."""
  935        if isinstance(self.real, Obs):
  936            self.real.gamma_method(**kwargs)
  937        if isinstance(self.imag, Obs):
  938            self.imag.gamma_method(**kwargs)
  939
- 940    def is_zero(self):
+ 940    def is_zero(self):
  941        """Checks whether both real and imaginary part are zero within machine precision."""
  942        return self.real == 0.0 and self.imag == 0.0
  943
- 944    def conjugate(self):
+ 944    def conjugate(self):
  945        return CObs(self.real, -self.imag)
  946
- 947    def __add__(self, other):
+ 947    def __add__(self, other):
  948        if isinstance(other, np.ndarray):
  949            return other + self
  950        elif hasattr(other, 'real') and hasattr(other, 'imag'):
@@ -1289,10 +1289,10 @@
  953        else:
  954            return CObs(self.real + other, self.imag)
  955
- 956    def __radd__(self, y):
+ 956    def __radd__(self, y):
  957        return self + y
  958
- 959    def __sub__(self, other):
+ 959    def __sub__(self, other):
  960        if isinstance(other, np.ndarray):
  961            return -1 * (other - self)
  962        elif hasattr(other, 'real') and hasattr(other, 'imag'):
@@ -1300,10 +1300,10 @@
  964        else:
  965            return CObs(self.real - other, self.imag)
  966
- 967    def __rsub__(self, other):
+ 967    def __rsub__(self, other):
  968        return -1 * (self - other)
  969
- 970    def __mul__(self, other):
+ 970    def __mul__(self, other):
  971        if isinstance(other, np.ndarray):
  972            return other * self
  973        elif hasattr(other, 'real') and hasattr(other, 'imag'):
@@ -1322,10 +1322,10 @@
  986        else:
  987            return CObs(self.real * other, self.imag * other)
  988
- 989    def __rmul__(self, other):
+ 989    def __rmul__(self, other):
  990        return self * other
  991
- 992    def __truediv__(self, other):
+ 992    def __truediv__(self, other):
  993        if isinstance(other, np.ndarray):
  994            return 1 / (other / self)
  995        elif hasattr(other, 'real') and hasattr(other, 'imag'):
@@ -1334,32 +1334,32 @@
  998        else:
  999            return CObs(self.real / other, self.imag / other)
 1000
-1001    def __rtruediv__(self, other):
+1001    def __rtruediv__(self, other):
 1002        r = self.real ** 2 + self.imag ** 2
 1003        if hasattr(other, 'real') and hasattr(other, 'imag'):
 1004            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r)
 1005        else:
 1006            return CObs(self.real * other / r, -self.imag * other / r)
 1007
-1008    def __abs__(self):
+1008    def __abs__(self):
 1009        return np.sqrt(self.real**2 + self.imag**2)
 1010
-1011    def __pos__(self):
+1011    def __pos__(self):
 1012        return self
 1013
-1014    def __neg__(self):
+1014    def __neg__(self):
 1015        return -1 * self
 1016
-1017    def __eq__(self, other):
+1017    def __eq__(self, other):
 1018        return self.real == other.real and self.imag == other.imag
 1019
-1020    def __str__(self):
+1020    def __str__(self):
 1021        return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)'
 1022
-1023    def __repr__(self):
+1023    def __repr__(self):
 1024        return 'CObs[' + str(self) + ']'
 1025
-1026    def __format__(self, format_type):
+1026    def __format__(self, format_type):
 1027        if format_type == "":
 1028            significance = 2
 1029            format_type = "2"
@@ -1368,7 +1368,7 @@
 1032        return f"({self.real:{format_type}}{self.imag:+{significance}}j)"
 1033
 1034
-1035def gamma_method(x, **kwargs):
+1035def gamma_method(x, **kwargs):
 1036    """Vectorized version of the gamma_method applicable to lists or arrays of Obs.
 1037
 1038    See docstring of pe.Obs.gamma_method for details.
@@ -1379,7 +1379,7 @@
 1043gm = gamma_method
 1044
 1045
-1046def _format_uncertainty(value, dvalue, significance=2):
+1046def _format_uncertainty(value, dvalue, significance=2):
 1047    """Creates a string of a value and its error in paranthesis notation, e.g., 13.02(45)"""
 1048    if dvalue == 0.0 or (not np.isfinite(dvalue)):
 1049        return str(value)
@@ -1396,7 +1396,7 @@
 1060        return f"{value:.{max(0, int(significance - fexp - 1))}f}({dvalue:2.{max(0, int(significance - fexp - 1))}f})"
 1061
 1062
-1063def _expand_deltas(deltas, idx, shape, gapsize):
+1063def _expand_deltas(deltas, idx, shape, gapsize):
 1064    """Expand deltas defined on idx to a regular range with spacing gapsize between two
 1065       configurations and where holes are filled by 0.
 1066       If idx is of type range, the deltas are not changed if the idx.step == gapsize.
@@ -1422,7 +1422,7 @@
 1086    return ret
 1087
 1088
-1089def _merge_idx(idl):
+1089def _merge_idx(idl):
 1090    """Returns the union of all lists in idl as range or sorted list
 1091
 1092    Parameters
@@ -1445,7 +1445,7 @@
 1109    return idunion
 1110
 1111
-1112def _intersection_idx(idl):
+1112def _intersection_idx(idl):
 1113    """Returns the intersection of all lists in idl as range or sorted list
 1114
 1115    Parameters
@@ -1471,7 +1471,7 @@
 1135    return idinter
 1136
 1137
-1138def _expand_deltas_for_merge(deltas, idx, shape, new_idx, scalefactor):
+1138def _expand_deltas_for_merge(deltas, idx, shape, new_idx, scalefactor):
 1139    """Expand deltas defined on idx to the list of configs that is defined by new_idx.
 1140       New, empty entries are filled by 0. If idx and new_idx are of type range, the smallest
 1141       common divisor of the step sizes is used as new step size.
@@ -1503,7 +1503,7 @@
 1167    return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) * len(new_idx) / len(idx) * scalefactor
 1168
 1169
-1170def derived_observable(func, data, array_mode=False, **kwargs):
+1170def derived_observable(func, data, array_mode=False, **kwargs):
 1171    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
 1172
 1173    Parameters
@@ -1581,7 +1581,7 @@
 1245        new_r_values[name] = func(tmp_values, **kwargs)
 1246        new_idl_d[name] = _merge_idx(idl)
 1247
-1248    def _compute_scalefactor_missing_rep(obs):
+1248    def _compute_scalefactor_missing_rep(obs):
 1249        """
 1250        Computes the scale factor that is to be multiplied with the deltas
 1251        in the case where Obs with different subsets of replica are merged.
@@ -1626,8 +1626,8 @@
 1290
 1291    if array_mode is True:
 1292
-1293        class _Zero_grad():
-1294            def __init__(self, N):
+1293        class _Zero_grad():
+1294            def __init__(self, N):
 1295                self.grad = np.zeros((N, 1))
 1296
 1297        new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x]))
@@ -1693,7 +1693,7 @@
 1357    return final_result
 1358
 1359
-1360def _reduce_deltas(deltas, idx_old, idx_new):
+1360def _reduce_deltas(deltas, idx_old, idx_new):
 1361    """Extract deltas defined on idx_old on all configs of idx_new.
 1362
 1363    Assumes, that idx_old and idx_new are correctly defined idl, i.e., they
@@ -1722,7 +1722,7 @@
 1386    return np.array(deltas)[indices]
 1387
 1388
-1389def reweight(weight, obs, **kwargs):
+1389def reweight(weight, obs, **kwargs):
 1390    """Reweight a list of observables.
 1391
 1392    Parameters
@@ -1764,7 +1764,7 @@
 1428    return result
 1429
 1430
-1431def correlate(obs_a, obs_b):
+1431def correlate(obs_a, obs_b):
 1432    """Correlate two observables.
 1433
 1434    Parameters
@@ -1807,7 +1807,7 @@
 1471    return o
 1472
 1473
-1474def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
+1474def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
 1475    r'''Calculates the error covariance matrix of a set of observables.
 1476
 1477    WARNING: This function should be used with care, especially for observables with support on multiple
@@ -1877,7 +1877,7 @@
 1541    return cov
 1542
 1543
-1544def invert_corr_cov_cholesky(corr, inverrdiag):
+1544def invert_corr_cov_cholesky(corr, inverrdiag):
 1545    """Constructs a lower triangular matrix `chol` via the Cholesky decomposition of the correlation matrix `corr`
 1546       and then returns the inverse covariance matrix `chol_inv` as a lower triangular matrix by solving `chol * x = inverrdiag`.
 1547
@@ -1900,7 +1900,7 @@
 1564    return chol_inv
 1565
 1566
-1567def sort_corr(corr, kl, yd):
+1567def sort_corr(corr, kl, yd):
 1568    """ Reorders a correlation matrix to match the alphabetical order of its underlying y data.
 1569
 1570    The ordering of the input correlation matrix `corr` is given by the list of keys `kl`.
@@ -1963,7 +1963,7 @@
 1627    return corr_sorted
 1628
 1629
-1630def _smooth_eigenvalues(corr, E):
+1630def _smooth_eigenvalues(corr, E):
 1631    """Eigenvalue smoothing as described in hep-lat/9412087
 1632
 1633    corr : np.ndarray
@@ -1980,10 +1980,10 @@
 1644    return vec @ np.diag(vals) @ vec.T
 1645
 1646
-1647def _covariance_element(obs1, obs2):
+1647def _covariance_element(obs1, obs2):
 1648    """Estimates the covariance of two Obs objects, neglecting autocorrelations."""
 1649
-1650    def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx):
+1650    def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx):
 1651        deltas1 = _reduce_deltas(deltas1, idx1, new_idx)
 1652        deltas2 = _reduce_deltas(deltas2, idx2, new_idx)
 1653        return np.sum(deltas1 * deltas2)
@@ -2040,7 +2040,7 @@
 1704    return dvalue
 1705
 1706
-1707def import_jackknife(jacks, name, idl=None):
+1707def import_jackknife(jacks, name, idl=None):
 1708    """Imports jackknife samples and returns an Obs
 1709
 1710    Parameters
@@ -2060,7 +2060,7 @@
 1724    return new_obs
 1725
 1726
-1727def import_bootstrap(boots, name, random_numbers):
+1727def import_bootstrap(boots, name, random_numbers):
 1728    """Imports bootstrap samples and returns an Obs
 1729
 1730    Parameters
@@ -2090,7 +2090,7 @@
 1754    return ret
 1755
 1756
-1757def merge_obs(list_of_obs):
+1757def merge_obs(list_of_obs):
 1758    """Combine all observables in list_of_obs into one new observable
 1759
 1760    Parameters
@@ -2120,7 +2120,7 @@
 1784    return o
 1785
 1786
-1787def cov_Obs(means, cov, name, grad=None):
+1787def cov_Obs(means, cov, name, grad=None):
 1788    """Create an Obs based on mean(s) and a covariance matrix
 1789
 1790    Parameters
@@ -2135,7 +2135,7 @@
 1799        Gradient of the Covobs wrt. the means belonging to cov.
 1800    """
 1801
-1802    def covobs_to_obs(co):
+1802    def covobs_to_obs(co):
 1803        """Make an Obs out of a Covobs
 1804
 1805        Parameters
@@ -2163,7 +2163,7 @@
 1827    return ol
 1828
 1829
-1830def _determine_gap(o, e_content, e_name):
+1830def _determine_gap(o, e_content, e_name):
 1831    gaps = []
 1832    for r_name in e_content[e_name]:
 1833        if isinstance(o.idl[r_name], range):
@@ -2178,7 +2178,7 @@
 1842    return gap
 1843
 1844
-1845def _check_lists_equal(idl):
+1845def _check_lists_equal(idl):
 1846    '''
 1847    Use groupby to efficiently check whether all elements of idl are identical.
 1848    Returns True if all elements are equal, otherwise False.
@@ -2206,7 +2206,7 @@
 
     
    
     
-            
     19class Obs:
+            
     19class Obs:
  20    """Class for a general observable.
  21
  22    Instances of Obs are the basic objects of a pyerrors error analysis.
@@ -2248,7 +2248,7 @@
  58    N_sigma_global = 1.0
  59    N_sigma_dict = {}
  60
- 61    def __init__(self, samples, names, idl=None, **kwargs):
+ 61    def __init__(self, samples, names, idl=None, **kwargs):
  62        """ Initialize Obs object.
  63
  64        Parameters
@@ -2332,27 +2332,27 @@
 142        self.tag = None
 143
 144    @property
-145    def value(self):
+145    def value(self):
 146        return self._value
 147
 148    @property
-149    def dvalue(self):
+149    def dvalue(self):
 150        return self._dvalue
 151
 152    @property
-153    def e_names(self):
+153    def e_names(self):
 154        return sorted(set([o.split('|')[0] for o in self.names]))
 155
 156    @property
-157    def cov_names(self):
+157    def cov_names(self):
 158        return sorted(set([o for o in self.covobs.keys()]))
 159
 160    @property
-161    def mc_names(self):
+161    def mc_names(self):
 162        return sorted(set([o.split('|')[0] for o in self.names if o not in self.cov_names]))
 163
 164    @property
-165    def e_content(self):
+165    def e_content(self):
 166        res = {}
 167        for e, e_name in enumerate(self.e_names):
 168            res[e_name] = sorted(filter(lambda x: x.startswith(e_name + '|'), self.names))
@@ -2361,10 +2361,10 @@
 171        return res
 172
 173    @property
-174    def covobs(self):
+174    def covobs(self):
 175        return self._covobs
 176
-177    def gamma_method(self, **kwargs):
+177    def gamma_method(self, **kwargs):
 178        """Estimate the error and related properties of the Obs.
 179
 180        Parameters
@@ -2408,7 +2408,7 @@
 218        else:
 219            fft = True
 220
-221        def _parse_kwarg(kwarg_name):
+221        def _parse_kwarg(kwarg_name):
 222            if kwarg_name in kwargs:
 223                tmp = kwargs.get(kwarg_name)
 224                if isinstance(tmp, (int, float)):
@@ -2470,7 +2470,7 @@
 280            self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) + 0.5 - self.e_n_tauint[e_name]) / e_N)
 281            self.e_n_dtauint[e_name][0] = 0.0
 282
-283            def _compute_drho(i):
+283            def _compute_drho(i):
 284                tmp = (self.e_rho[e_name][i + 1:w_max]
 285                       + np.concatenate([self.e_rho[e_name][i - 1:None if i - (w_max - 1) // 2 <= 0 else (2 * i - (2 * w_max) // 2):-1],
 286                                         self.e_rho[e_name][1:max(1, w_max - 2 * i)]])
@@ -2532,7 +2532,7 @@
 342
 343    gm = gamma_method
 344
-345    def _calc_gamma(self, deltas, idx, shape, w_max, fft, gapsize):
+345    def _calc_gamma(self, deltas, idx, shape, w_max, fft, gapsize):
 346        """Calculate Gamma_{AA} from the deltas, which are defined on idx.
 347           idx is assumed to be a contiguous range (possibly with a stepsize != 1)
 348
@@ -2568,7 +2568,7 @@
 378
 379        return gamma
 380
-381    def details(self, ens_content=True):
+381    def details(self, ens_content=True):
 382        """Output detailed properties of the Obs.
 383
 384        Parameters
@@ -2637,7 +2637,7 @@
 447                my_string_list.append(my_string)
 448            print('\n'.join(my_string_list))
 449
-450    def reweight(self, weight):
+450    def reweight(self, weight):
 451        """Reweight the obs with given rewighting factors.
 452
 453        Parameters
@@ -2652,7 +2652,7 @@
 462        """
 463        return reweight(weight, [self])[0]
 464
-465    def is_zero_within_error(self, sigma=1):
+465    def is_zero_within_error(self, sigma=1):
 466        """Checks whether the observable is zero within 'sigma' standard errors.
 467
 468        Parameters
@@ -2664,7 +2664,7 @@
 474        """
 475        return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue
 476
-477    def is_zero(self, atol=1e-10):
+477    def is_zero(self, atol=1e-10):
 478        """Checks whether the observable is zero within a given tolerance.
 479
 480        Parameters
@@ -2674,7 +2674,7 @@
 484        """
 485        return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values())
 486
-487    def plot_tauint(self, save=None):
+487    def plot_tauint(self, save=None):
 488        """Plot integrated autocorrelation time for each ensemble.
 489
 490        Parameters
@@ -2714,7 +2714,7 @@
 524            if save:
 525                fig.savefig(save + "_" + str(e))
 526
-527    def plot_rho(self, save=None):
+527    def plot_rho(self, save=None):
 528        """Plot normalized autocorrelation function time for each ensemble.
 529
 530        Parameters
@@ -2745,7 +2745,7 @@
 555            if save:
 556                fig.savefig(save + "_" + str(e))
 557
-558    def plot_rep_dist(self):
+558    def plot_rep_dist(self):
 559        """Plot replica distribution for each ensemble with more than one replicum."""
 560        if not hasattr(self, 'e_dvalue'):
 561            raise Exception('Run the gamma method first.')
@@ -2767,7 +2767,7 @@
 577            plt.title('Replica distribution' + e_name + ' (mean=0, var=1)')
 578            plt.draw()
 579
-580    def plot_history(self, expand=True):
+580    def plot_history(self, expand=True):
 581        """Plot derived Monte Carlo history for each ensemble
 582
 583        Parameters
@@ -2799,7 +2799,7 @@
 609            plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})')
 610            plt.draw()
 611
-612    def plot_piechart(self, save=None):
+612    def plot_piechart(self, save=None):
 613        """Plot piechart which shows the fractional contribution of each
 614        ensemble to the error and returns a dictionary containing the fractions.
 615
@@ -2823,7 +2823,7 @@
 633
 634        return dict(zip(labels, sizes))
 635
-636    def dump(self, filename, datatype="json.gz", description="", **kwargs):
+636    def dump(self, filename, datatype="json.gz", description="", **kwargs):
 637        """Dump the Obs to a file 'name' of chosen format.
 638
 639        Parameters
@@ -2844,7 +2844,7 @@
 654            file_name = filename
 655
 656        if datatype == "json.gz":
-657            from .input.json import dump_to_json
+657            from .input.json import dump_to_json
 658            dump_to_json([self], file_name, description=description)
 659        elif datatype == "pickle":
 660            with open(file_name + '.p', 'wb') as fb:
@@ -2852,7 +2852,7 @@
 662        else:
 663            raise TypeError("Unknown datatype " + str(datatype))
 664
-665    def export_jackknife(self):
+665    def export_jackknife(self):
 666        """Export jackknife samples from the Obs
 667
 668        Returns
@@ -2878,7 +2878,7 @@
 688        tmp_jacks[1:] = (n * mean - full_data) / (n - 1)
 689        return tmp_jacks
 690
-691    def export_bootstrap(self, samples=500, random_numbers=None, save_rng=None):
+691    def export_bootstrap(self, samples=500, random_numbers=None, save_rng=None):
 692        """Export bootstrap samples from the Obs
 693
 694        Parameters
@@ -2921,16 +2921,16 @@
 731        ret[1:] = proj @ (self.deltas[name] + self.r_values[name])
 732        return ret
 733
-734    def __float__(self):
+734    def __float__(self):
 735        return float(self.value)
 736
-737    def __repr__(self):
+737    def __repr__(self):
 738        return 'Obs[' + str(self) + ']'
 739
-740    def __str__(self):
+740    def __str__(self):
 741        return _format_uncertainty(self.value, self._dvalue)
 742
-743    def __format__(self, format_type):
+743    def __format__(self, format_type):
 744        if format_type == "":
 745            significance = 2
 746        else:
@@ -2943,7 +2943,7 @@
 753                    my_str = char + my_str
 754        return my_str
 755
-756    def __hash__(self):
+756    def __hash__(self):
 757        hash_tuple = (np.array([self.value]).astype(np.float32).data.tobytes(),)
 758        hash_tuple += tuple([o.astype(np.float32).data.tobytes() for o in self.deltas.values()])
 759        hash_tuple += tuple([np.array([o.errsq()]).astype(np.float32).data.tobytes() for o in self.covobs.values()])
@@ -2953,25 +2953,25 @@
 763        return int(m.hexdigest(), 16) & 0xFFFFFFFF
 764
 765    # Overload comparisons
-766    def __lt__(self, other):
+766    def __lt__(self, other):
 767        return self.value < other
 768
-769    def __le__(self, other):
+769    def __le__(self, other):
 770        return self.value <= other
 771
-772    def __gt__(self, other):
+772    def __gt__(self, other):
 773        return self.value > other
 774
-775    def __ge__(self, other):
+775    def __ge__(self, other):
 776        return self.value >= other
 777
-778    def __eq__(self, other):
+778    def __eq__(self, other):
 779        if other is None:
 780            return False
 781        return (self - other).is_zero()
 782
 783    # Overload math operations
-784    def __add__(self, y):
+784    def __add__(self, y):
 785        if isinstance(y, Obs):
 786            return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1])
 787        else:
@@ -2984,10 +2984,10 @@
 794            else:
 795                return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1])
 796
-797    def __radd__(self, y):
+797    def __radd__(self, y):
 798        return self + y
 799
-800    def __mul__(self, y):
+800    def __mul__(self, y):
 801        if isinstance(y, Obs):
 802            return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value])
 803        else:
@@ -3000,10 +3000,10 @@
 810            else:
 811                return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y])
 812
-813    def __rmul__(self, y):
+813    def __rmul__(self, y):
 814        return self * y
 815
-816    def __sub__(self, y):
+816    def __sub__(self, y):
 817        if isinstance(y, Obs):
 818            return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1])
 819        else:
@@ -3014,16 +3014,16 @@
 824            else:
 825                return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1])
 826
-827    def __rsub__(self, y):
+827    def __rsub__(self, y):
 828        return -1 * (self - y)
 829
-830    def __pos__(self):
+830    def __pos__(self):
 831        return self
 832
-833    def __neg__(self):
+833    def __neg__(self):
 834        return -1 * self
 835
-836    def __truediv__(self, y):
+836    def __truediv__(self, y):
 837        if isinstance(y, Obs):
 838            return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2])
 839        else:
@@ -3034,7 +3034,7 @@
 844            else:
 845                return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y])
 846
-847    def __rtruediv__(self, y):
+847    def __rtruediv__(self, y):
 848        if isinstance(y, Obs):
 849            return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2])
 850        else:
@@ -3045,62 +3045,62 @@
 855            else:
 856                return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2])
 857
-858    def __pow__(self, y):
+858    def __pow__(self, y):
 859        if isinstance(y, Obs):
 860            return derived_observable(lambda x, **kwargs: x[0] ** x[1], [self, y], man_grad=[y.value * self.value ** (y.value - 1), self.value ** y.value * np.log(self.value)])
 861        else:
 862            return derived_observable(lambda x, **kwargs: x[0] ** y, [self], man_grad=[y * self.value ** (y - 1)])
 863
-864    def __rpow__(self, y):
+864    def __rpow__(self, y):
 865        return derived_observable(lambda x, **kwargs: y ** x[0], [self], man_grad=[y ** self.value * np.log(y)])
 866
-867    def __abs__(self):
+867    def __abs__(self):
 868        return derived_observable(lambda x: anp.abs(x[0]), [self])
 869
 870    # Overload numpy functions
-871    def sqrt(self):
+871    def sqrt(self):
 872        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
 873
-874    def log(self):
+874    def log(self):
 875        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
 876
-877    def exp(self):
+877    def exp(self):
 878        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
 879
-880    def sin(self):
+880    def sin(self):
 881        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
 882
-883    def cos(self):
+883    def cos(self):
 884        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
 885
-886    def tan(self):
+886    def tan(self):
 887        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
 888
-889    def arcsin(self):
+889    def arcsin(self):
 890        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
 891
-892    def arccos(self):
+892    def arccos(self):
 893        return derived_observable(lambda x: anp.arccos(x[0]), [self])
 894
-895    def arctan(self):
+895    def arctan(self):
 896        return derived_observable(lambda x: anp.arctan(x[0]), [self])
 897
-898    def sinh(self):
+898    def sinh(self):
 899        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
 900
-901    def cosh(self):
+901    def cosh(self):
 902        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
 903
-904    def tanh(self):
+904    def tanh(self):
 905        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
 906
-907    def arcsinh(self):
+907    def arcsinh(self):
 908        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
 909
-910    def arccosh(self):
+910    def arccosh(self):
 911        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
 912
-913    def arctanh(self):
+913    def arctanh(self):
 914        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
 
    
 
@@ -3147,7 +3147,7 @@ this overwrites the standard value for that ensemble.
 
     
    
     
-            
     61    def __init__(self, samples, names, idl=None, **kwargs):
+            
     61    def __init__(self, samples, names, idl=None, **kwargs):
  62        """ Initialize Obs object.
  63
  64        Parameters
@@ -3429,7 +3429,7 @@ list of ranges or lists on which the samples are defined
     
    
     
             
    144    @property
-145    def value(self):
+145    def value(self):
 146        return self._value
 
    
 
@@ -3447,7 +3447,7 @@ list of ranges or lists on which the samples are defined
     
    
     
             
    148    @property
-149    def dvalue(self):
+149    def dvalue(self):
 150        return self._dvalue
 
    
 
@@ -3465,7 +3465,7 @@ list of ranges or lists on which the samples are defined
     
    
     
             
    152    @property
-153    def e_names(self):
+153    def e_names(self):
 154        return sorted(set([o.split('|')[0] for o in self.names]))
 
    
 
@@ -3483,7 +3483,7 @@ list of ranges or lists on which the samples are defined
     
    
     
             
    156    @property
-157    def cov_names(self):
+157    def cov_names(self):
 158        return sorted(set([o for o in self.covobs.keys()]))
 
    
 
@@ -3501,7 +3501,7 @@ list of ranges or lists on which the samples are defined
     
    
     
             
    160    @property
-161    def mc_names(self):
+161    def mc_names(self):
 162        return sorted(set([o.split('|')[0] for o in self.names if o not in self.cov_names]))
 
    
 
@@ -3519,7 +3519,7 @@ list of ranges or lists on which the samples are defined
     
    
     
             
    164    @property
-165    def e_content(self):
+165    def e_content(self):
 166        res = {}
 167        for e, e_name in enumerate(self.e_names):
 168            res[e_name] = sorted(filter(lambda x: x.startswith(e_name + '|'), self.names))
@@ -3542,7 +3542,7 @@ list of ranges or lists on which the samples are defined
     
    
     
             
    173    @property
-174    def covobs(self):
+174    def covobs(self):
 175        return self._covobs
 
    
 
@@ -3561,7 +3561,7 @@ list of ranges or lists on which the samples are defined
 
     
    
     
-            
    177    def gamma_method(self, **kwargs):
+            
    177    def gamma_method(self, **kwargs):
 178        """Estimate the error and related properties of the Obs.
 179
 180        Parameters
@@ -3605,7 +3605,7 @@ list of ranges or lists on which the samples are defined
 218        else:
 219            fft = True
 220
-221        def _parse_kwarg(kwarg_name):
+221        def _parse_kwarg(kwarg_name):
 222            if kwarg_name in kwargs:
 223                tmp = kwargs.get(kwarg_name)
 224                if isinstance(tmp, (int, float)):
@@ -3667,7 +3667,7 @@ list of ranges or lists on which the samples are defined
 280            self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) + 0.5 - self.e_n_tauint[e_name]) / e_N)
 281            self.e_n_dtauint[e_name][0] = 0.0
 282
-283            def _compute_drho(i):
+283            def _compute_drho(i):
 284                tmp = (self.e_rho[e_name][i + 1:w_max]
 285                       + np.concatenate([self.e_rho[e_name][i - 1:None if i - (w_max - 1) // 2 <= 0 else (2 * i - (2 * w_max) // 2):-1],
 286                                         self.e_rho[e_name][1:max(1, w_max - 2 * i)]])
@@ -3764,7 +3764,7 @@ of the autocorrelation function (default True)
 
     
    
     
-            
    177    def gamma_method(self, **kwargs):
+            
    177    def gamma_method(self, **kwargs):
 178        """Estimate the error and related properties of the Obs.
 179
 180        Parameters
@@ -3808,7 +3808,7 @@ of the autocorrelation function (default True)
 218        else:
 219            fft = True
 220
-221        def _parse_kwarg(kwarg_name):
+221        def _parse_kwarg(kwarg_name):
 222            if kwarg_name in kwargs:
 223                tmp = kwargs.get(kwarg_name)
 224                if isinstance(tmp, (int, float)):
@@ -3870,7 +3870,7 @@ of the autocorrelation function (default True)
 280            self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) + 0.5 - self.e_n_tauint[e_name]) / e_N)
 281            self.e_n_dtauint[e_name][0] = 0.0
 282
-283            def _compute_drho(i):
+283            def _compute_drho(i):
 284                tmp = (self.e_rho[e_name][i + 1:w_max]
 285                       + np.concatenate([self.e_rho[e_name][i - 1:None if i - (w_max - 1) // 2 <= 0 else (2 * i - (2 * w_max) // 2):-1],
 286                                         self.e_rho[e_name][1:max(1, w_max - 2 * i)]])
@@ -3967,7 +3967,7 @@ of the autocorrelation function (default True)
 
     
    
     
-            
    381    def details(self, ens_content=True):
+            
    381    def details(self, ens_content=True):
 382        """Output detailed properties of the Obs.
 383
 384        Parameters
@@ -4061,7 +4061,7 @@ print details about the ensembles and replica if true.
 
     
    
     
-            
    450    def reweight(self, weight):
+            
    450    def reweight(self, weight):
 451        """Reweight the obs with given rewighting factors.
 452
 453        Parameters
@@ -4106,7 +4106,7 @@ on the configurations in obs[i].idl. Default False.
 
     
    
     
-            
    465    def is_zero_within_error(self, sigma=1):
+            
    465    def is_zero_within_error(self, sigma=1):
 466        """Checks whether the observable is zero within 'sigma' standard errors.
 467
 468        Parameters
@@ -4144,7 +4144,7 @@ Number of standard errors used for the check.
 
     
    
     
-            
    477    def is_zero(self, atol=1e-10):
+            
    477    def is_zero(self, atol=1e-10):
 478        """Checks whether the observable is zero within a given tolerance.
 479
 480        Parameters
@@ -4179,7 +4179,7 @@ Absolute tolerance (for details see numpy documentation).
 
     
    
     
-            
    487    def plot_tauint(self, save=None):
+            
    487    def plot_tauint(self, save=None):
 488        """Plot integrated autocorrelation time for each ensemble.
 489
 490        Parameters
@@ -4244,7 +4244,7 @@ saves the figure to a file named 'save' if.
 
     
    
     
-            
    527    def plot_rho(self, save=None):
+            
    527    def plot_rho(self, save=None):
 528        """Plot normalized autocorrelation function time for each ensemble.
 529
 530        Parameters
@@ -4300,7 +4300,7 @@ saves the figure to a file named 'save' if.
 
     
    
     
-            
    558    def plot_rep_dist(self):
+            
    558    def plot_rep_dist(self):
 559        """Plot replica distribution for each ensemble with more than one replicum."""
 560        if not hasattr(self, 'e_dvalue'):
 561            raise Exception('Run the gamma method first.')
@@ -4340,7 +4340,7 @@ saves the figure to a file named 'save' if.
 
     
    
     
-            
    580    def plot_history(self, expand=True):
+            
    580    def plot_history(self, expand=True):
 581        """Plot derived Monte Carlo history for each ensemble
 582
 583        Parameters
@@ -4397,7 +4397,7 @@ show expanded history for irregular Monte Carlo chains (default: True).
 
     
    
     
-            
    612    def plot_piechart(self, save=None):
+            
    612    def plot_piechart(self, save=None):
 613        """Plot piechart which shows the fractional contribution of each
 614        ensemble to the error and returns a dictionary containing the fractions.
 615
@@ -4447,7 +4447,7 @@ saves the figure to a file named 'save' if.
 
     
    
     
-            
    636    def dump(self, filename, datatype="json.gz", description="", **kwargs):
+            
    636    def dump(self, filename, datatype="json.gz", description="", **kwargs):
 637        """Dump the Obs to a file 'name' of chosen format.
 638
 639        Parameters
@@ -4468,7 +4468,7 @@ saves the figure to a file named 'save' if.
 654            file_name = filename
 655
 656        if datatype == "json.gz":
-657            from .input.json import dump_to_json
+657            from .input.json import dump_to_json
 658            dump_to_json([self], file_name, description=description)
 659        elif datatype == "pickle":
 660            with open(file_name + '.p', 'wb') as fb:
@@ -4508,7 +4508,7 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    665    def export_jackknife(self):
+            
    665    def export_jackknife(self):
 666        """Export jackknife samples from the Obs
 667
 668        Returns
@@ -4563,7 +4563,7 @@ should agree with samples from a full jackknife analysis up to O(1/N).
 
     
    
     
-            
    691    def export_bootstrap(self, samples=500, random_numbers=None, save_rng=None):
+            
    691    def export_bootstrap(self, samples=500, random_numbers=None, save_rng=None):
 692        """Export bootstrap samples from the Obs
 693
 694        Parameters
@@ -4647,7 +4647,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    871    def sqrt(self):
+            
    871    def sqrt(self):
 872        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
 
    
 
@@ -4666,7 +4666,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    874    def log(self):
+            
    874    def log(self):
 875        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
 
    
 
@@ -4685,7 +4685,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    877    def exp(self):
+            
    877    def exp(self):
 878        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
 
    
 
@@ -4704,7 +4704,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    880    def sin(self):
+            
    880    def sin(self):
 881        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
 
    
 
@@ -4723,7 +4723,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    883    def cos(self):
+            
    883    def cos(self):
 884        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
 
    
 
@@ -4742,7 +4742,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    886    def tan(self):
+            
    886    def tan(self):
 887        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
 
    
 
@@ -4761,7 +4761,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    889    def arcsin(self):
+            
    889    def arcsin(self):
 890        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
 
    
 
@@ -4780,7 +4780,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    892    def arccos(self):
+            
    892    def arccos(self):
 893        return derived_observable(lambda x: anp.arccos(x[0]), [self])
 
    
 
@@ -4799,7 +4799,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    895    def arctan(self):
+            
    895    def arctan(self):
 896        return derived_observable(lambda x: anp.arctan(x[0]), [self])
 
    
 
@@ -4818,7 +4818,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    898    def sinh(self):
+            
    898    def sinh(self):
 899        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
 
    
 
@@ -4837,7 +4837,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    901    def cosh(self):
+            
    901    def cosh(self):
 902        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
 
    
 
@@ -4856,7 +4856,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    904    def tanh(self):
+            
    904    def tanh(self):
 905        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
 
    
 
@@ -4875,7 +4875,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    907    def arcsinh(self):
+            
    907    def arcsinh(self):
 908        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
 
    
 
@@ -4894,7 +4894,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    910    def arccosh(self):
+            
    910    def arccosh(self):
 911        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
 
    
 
@@ -4913,7 +4913,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    913    def arctanh(self):
+            
    913    def arctanh(self):
 914        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
 
    
 
@@ -5065,38 +5065,38 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
     917class CObs:
+            
     917class CObs:
  918    """Class for a complex valued observable."""
  919    __slots__ = ['_real', '_imag', 'tag']
  920
- 921    def __init__(self, real, imag=0.0):
+ 921    def __init__(self, real, imag=0.0):
  922        self._real = real
  923        self._imag = imag
  924        self.tag = None
  925
  926    @property
- 927    def real(self):
+ 927    def real(self):
  928        return self._real
  929
  930    @property
- 931    def imag(self):
+ 931    def imag(self):
  932        return self._imag
  933
- 934    def gamma_method(self, **kwargs):
+ 934    def gamma_method(self, **kwargs):
  935        """Executes the gamma_method for the real and the imaginary part."""
  936        if isinstance(self.real, Obs):
  937            self.real.gamma_method(**kwargs)
  938        if isinstance(self.imag, Obs):
  939            self.imag.gamma_method(**kwargs)
  940
- 941    def is_zero(self):
+ 941    def is_zero(self):
  942        """Checks whether both real and imaginary part are zero within machine precision."""
  943        return self.real == 0.0 and self.imag == 0.0
  944
- 945    def conjugate(self):
+ 945    def conjugate(self):
  946        return CObs(self.real, -self.imag)
  947
- 948    def __add__(self, other):
+ 948    def __add__(self, other):
  949        if isinstance(other, np.ndarray):
  950            return other + self
  951        elif hasattr(other, 'real') and hasattr(other, 'imag'):
@@ -5105,10 +5105,10 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
  954        else:
  955            return CObs(self.real + other, self.imag)
  956
- 957    def __radd__(self, y):
+ 957    def __radd__(self, y):
  958        return self + y
  959
- 960    def __sub__(self, other):
+ 960    def __sub__(self, other):
  961        if isinstance(other, np.ndarray):
  962            return -1 * (other - self)
  963        elif hasattr(other, 'real') and hasattr(other, 'imag'):
@@ -5116,10 +5116,10 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
  965        else:
  966            return CObs(self.real - other, self.imag)
  967
- 968    def __rsub__(self, other):
+ 968    def __rsub__(self, other):
  969        return -1 * (self - other)
  970
- 971    def __mul__(self, other):
+ 971    def __mul__(self, other):
  972        if isinstance(other, np.ndarray):
  973            return other * self
  974        elif hasattr(other, 'real') and hasattr(other, 'imag'):
@@ -5138,10 +5138,10 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
  987        else:
  988            return CObs(self.real * other, self.imag * other)
  989
- 990    def __rmul__(self, other):
+ 990    def __rmul__(self, other):
  991        return self * other
  992
- 993    def __truediv__(self, other):
+ 993    def __truediv__(self, other):
  994        if isinstance(other, np.ndarray):
  995            return 1 / (other / self)
  996        elif hasattr(other, 'real') and hasattr(other, 'imag'):
@@ -5150,32 +5150,32 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
  999        else:
 1000            return CObs(self.real / other, self.imag / other)
 1001
-1002    def __rtruediv__(self, other):
+1002    def __rtruediv__(self, other):
 1003        r = self.real ** 2 + self.imag ** 2
 1004        if hasattr(other, 'real') and hasattr(other, 'imag'):
 1005            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r)
 1006        else:
 1007            return CObs(self.real * other / r, -self.imag * other / r)
 1008
-1009    def __abs__(self):
+1009    def __abs__(self):
 1010        return np.sqrt(self.real**2 + self.imag**2)
 1011
-1012    def __pos__(self):
+1012    def __pos__(self):
 1013        return self
 1014
-1015    def __neg__(self):
+1015    def __neg__(self):
 1016        return -1 * self
 1017
-1018    def __eq__(self, other):
+1018    def __eq__(self, other):
 1019        return self.real == other.real and self.imag == other.imag
 1020
-1021    def __str__(self):
+1021    def __str__(self):
 1022        return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)'
 1023
-1024    def __repr__(self):
+1024    def __repr__(self):
 1025        return 'CObs[' + str(self) + ']'
 1026
-1027    def __format__(self, format_type):
+1027    def __format__(self, format_type):
 1028        if format_type == "":
 1029            significance = 2
 1030            format_type = "2"
@@ -5199,7 +5199,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    921    def __init__(self, real, imag=0.0):
+            
    921    def __init__(self, real, imag=0.0):
 922        self._real = real
 923        self._imag = imag
 924        self.tag = None
@@ -5230,7 +5230,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
     
    
     
             
    926    @property
-927    def real(self):
+927    def real(self):
 928        return self._real
 
    
 
@@ -5248,7 +5248,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
     
    
     
             
    930    @property
-931    def imag(self):
+931    def imag(self):
 932        return self._imag
 
    
 
@@ -5267,7 +5267,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    934    def gamma_method(self, **kwargs):
+            
    934    def gamma_method(self, **kwargs):
 935        """Executes the gamma_method for the real and the imaginary part."""
 936        if isinstance(self.real, Obs):
 937            self.real.gamma_method(**kwargs)
@@ -5292,7 +5292,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    941    def is_zero(self):
+            
    941    def is_zero(self):
 942        """Checks whether both real and imaginary part are zero within machine precision."""
 943        return self.real == 0.0 and self.imag == 0.0
 
    
@@ -5314,7 +5314,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    945    def conjugate(self):
+            
    945    def conjugate(self):
 946        return CObs(self.real, -self.imag)
 
    
 
@@ -5334,7 +5334,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    1036def gamma_method(x, **kwargs):
+            
    1036def gamma_method(x, **kwargs):
 1037    """Vectorized version of the gamma_method applicable to lists or arrays of Obs.
 1038
 1039    See docstring of pe.Obs.gamma_method for details.
@@ -5361,7 +5361,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    1036def gamma_method(x, **kwargs):
+            
    1036def gamma_method(x, **kwargs):
 1037    """Vectorized version of the gamma_method applicable to lists or arrays of Obs.
 1038
 1039    See docstring of pe.Obs.gamma_method for details.
@@ -5388,7 +5388,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     
    
     
-            
    1171def derived_observable(func, data, array_mode=False, **kwargs):
+            
    1171def derived_observable(func, data, array_mode=False, **kwargs):
 1172    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
 1173
 1174    Parameters
@@ -5466,7 +5466,7 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 1246        new_r_values[name] = func(tmp_values, **kwargs)
 1247        new_idl_d[name] = _merge_idx(idl)
 1248
-1249    def _compute_scalefactor_missing_rep(obs):
+1249    def _compute_scalefactor_missing_rep(obs):
 1250        """
 1251        Computes the scale factor that is to be multiplied with the deltas
 1252        in the case where Obs with different subsets of replica are merged.
@@ -5511,8 +5511,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 1291
 1292    if array_mode is True:
 1293
-1294        class _Zero_grad():
-1295            def __init__(self, N):
+1294        class _Zero_grad():
+1295            def __init__(self, N):
 1296                self.grad = np.zeros((N, 1))
 1297
 1298        new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x]))
@@ -5622,7 +5622,7 @@ functions. For the ratio of two observables one can e.g. use
    
 
     
    
     
-            
    1390def reweight(weight, obs, **kwargs):
+            
    1390def reweight(weight, obs, **kwargs):
 1391    """Reweight a list of observables.
 1392
 1393    Parameters
@@ -5695,7 +5695,7 @@ on the configurations in obs[i].idl. Default False.
 
     
    
     
-            
    1432def correlate(obs_a, obs_b):
+            
    1432def correlate(obs_a, obs_b):
 1433    """Correlate two observables.
 1434
 1435    Parameters
@@ -5770,7 +5770,7 @@ Currently only works if ensembles are identical (this is not strictly necessary)
 
     
    
     
-            
    1475def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
+            
    1475def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
 1476    r'''Calculates the error covariance matrix of a set of observables.
 1477
 1478    WARNING: This function should be used with care, especially for observables with support on multiple
@@ -5889,7 +5889,7 @@ This construction ensures that the estimated covariance matrix is positive semi-
 
     
    
     
-            
    1545def invert_corr_cov_cholesky(corr, inverrdiag):
+            
    1545def invert_corr_cov_cholesky(corr, inverrdiag):
 1546    """Constructs a lower triangular matrix `chol` via the Cholesky decomposition of the correlation matrix `corr`
 1547       and then returns the inverse covariance matrix `chol_inv` as a lower triangular matrix by solving `chol * x = inverrdiag`.
 1548
@@ -5939,7 +5939,7 @@ diagonal matrix, the entries are the inverse errors of the data points considere
 
     
    
     
-            
    1568def sort_corr(corr, kl, yd):
+            
    1568def sort_corr(corr, kl, yd):
 1569    """ Reorders a correlation matrix to match the alphabetical order of its underlying y data.
 1570
 1571    The ordering of the input correlation matrix `corr` is given by the list of keys `kl`.
@@ -6036,8 +6036,8 @@ of corr. The lists in the dictionary can be lists of Obs.
 
    Example
    
 
 
    
-
    >>> import numpy as np
->>> import pyerrors as pe
+
    >>> import numpy as np
+>>> import pyerrors as pe
 >>> corr = np.array([[1, 0.2, 0.3], [0.2, 1, 0.4], [0.3, 0.4, 1]])
 >>> kl = ['b', 'a']
 >>> yd = {'a': [1, 2], 'b': [3]}
@@ -6063,7 +6063,7 @@ of corr. The lists in the dictionary can be lists of Obs.
 
     
    
     
-            
    1708def import_jackknife(jacks, name, idl=None):
+            
    1708def import_jackknife(jacks, name, idl=None):
 1709    """Imports jackknife samples and returns an Obs
 1710
 1711    Parameters
@@ -6110,7 +6110,7 @@ name of the ensemble the samples are defined on.
 
     
    
     
-            
    1728def import_bootstrap(boots, name, random_numbers):
+            
    1728def import_bootstrap(boots, name, random_numbers):
 1729    """Imports bootstrap samples and returns an Obs
 1730
 1731    Parameters
@@ -6171,7 +6171,7 @@ chain to be reconstructed.
 
     
    
     
-            
    1758def merge_obs(list_of_obs):
+            
    1758def merge_obs(list_of_obs):
 1759    """Combine all observables in list_of_obs into one new observable
 1760
 1761    Parameters
@@ -6229,7 +6229,7 @@ list of the Obs object to be combined
 
     
    
     
-            
    1788def cov_Obs(means, cov, name, grad=None):
+            
    1788def cov_Obs(means, cov, name, grad=None):
 1789    """Create an Obs based on mean(s) and a covariance matrix
 1790
 1791    Parameters
@@ -6244,7 +6244,7 @@ list of the Obs object to be combined
 1800        Gradient of the Covobs wrt. the means belonging to cov.
 1801    """
 1802
-1803    def covobs_to_obs(co):
+1803    def covobs_to_obs(co):
 1804        """Make an Obs out of a Covobs
 1805
 1806        Parameters
diff --git a/docs/pyerrors/roots.html b/docs/pyerrors/roots.html
index 5766c7bc..61335386 100644
--- a/docs/pyerrors/roots.html
+++ b/docs/pyerrors/roots.html
@@ -76,13 +76,13 @@
 
                         
 
-                        
     1import numpy as np
- 2import scipy.optimize
- 3from autograd import jacobian
- 4from .obs import derived_observable
+                        
     1import numpy as np
+ 2import scipy.optimize
+ 3from autograd import jacobian
+ 4from .obs import derived_observable
  5
  6
- 7def find_root(d, func, guess=1.0, **kwargs):
+ 7def find_root(d, func, guess=1.0, **kwargs):
  8    r'''Finds the root of the function func(x, d) where d is an `Obs`.
  9
 10    Parameters
@@ -114,7 +114,7 @@
 36    try:
 37        da = jacobian(lambda u, v: func(v, u))(d_val, root[0])
 38    except TypeError:
-39        raise Exception("It is required to use autograd.numpy instead of numpy within root functions, see the documentation for details.") from None
+39        raise Exception("It is required to use autograd.numpy instead of numpy within root functions, see the documentation for details.") from None
 40    deriv = - da / dx
 41    res = derived_observable(lambda x, **kwargs: (x[0] + np.finfo(np.float64).eps) / (np.array(d).reshape(-1)[0].value + np.finfo(np.float64).eps) * root[0],
 42                             np.array(d).reshape(-1), man_grad=np.array(deriv).reshape(-1))
@@ -134,7 +134,7 @@
 
     
    
     
-            
     8def find_root(d, func, guess=1.0, **kwargs):
+            
     8def find_root(d, func, guess=1.0, **kwargs):
  9    r'''Finds the root of the function func(x, d) where d is an `Obs`.
 10
 11    Parameters
@@ -166,7 +166,7 @@
 37    try:
 38        da = jacobian(lambda u, v: func(v, u))(d_val, root[0])
 39    except TypeError:
-40        raise Exception("It is required to use autograd.numpy instead of numpy within root functions, see the documentation for details.") from None
+40        raise Exception("It is required to use autograd.numpy instead of numpy within root functions, see the documentation for details.") from None
 41    deriv = - da / dx
 42    res = derived_observable(lambda x, **kwargs: (x[0] + np.finfo(np.float64).eps) / (np.array(d).reshape(-1)[0].value + np.finfo(np.float64).eps) * root[0],
 43                             np.array(d).reshape(-1), man_grad=np.array(deriv).reshape(-1))
@@ -186,8 +186,8 @@ Function to be minimized. Any numpy functions have to use the autograd.numpy wra
 Example:
    
 
 
    
-
    import autograd.numpy as anp
-def root_func(x, d):
+
    import autograd.numpy as anp
+def root_func(x, d):
     return anp.exp(-x ** 2) - d
 
    
 
    
diff --git a/docs/pyerrors/special.html b/docs/pyerrors/special.html
index ac8b3a35..4641cd83 100644
--- a/docs/pyerrors/special.html
+++ b/docs/pyerrors/special.html
@@ -166,12 +166,12 @@
 
                         
 
-                        
     1import scipy
- 2import numpy as np
- 3from autograd.extend import primitive, defvjp
- 4from autograd.scipy.special import j0, y0, j1, y1, jn, yn, i0, i1, iv, ive, beta, betainc, betaln
- 5from autograd.scipy.special import polygamma, psi, digamma, gamma, gammaln, gammainc, gammaincc, gammasgn, rgamma, multigammaln
- 6from autograd.scipy.special import erf, erfc, erfinv, erfcinv, logit, expit, logsumexp
+                        
     1import scipy
+ 2import numpy as np
+ 3from autograd.extend import primitive, defvjp
+ 4from autograd.scipy.special import j0, y0, j1, y1, jn, yn, i0, i1, iv, ive, beta, betainc, betaln
+ 5from autograd.scipy.special import polygamma, psi, digamma, gamma, gammaln, gammainc, gammaincc, gammasgn, rgamma, multigammaln
+ 6from autograd.scipy.special import erf, erfc, erfinv, erfcinv, logit, expit, logsumexp
  7
  8
  9__all__ = ["beta", "betainc", "betaln",
@@ -181,7 +181,7 @@
 13
 14
 15@primitive
-16def kn(n, x):
+16def kn(n, x):
 17    """Modified Bessel function of the second kind of integer order n"""
 18    if int(n) != n:
 19        raise TypeError("The order 'n' needs to be an integer.")
@@ -206,7 +206,7 @@
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -262,7 +262,7 @@ value of the beta function  
    
 
    Examples
    
 
 
    
-
    >>> import scipy.special as sc
+
    >>> import scipy.special as sc
 
    
 
    
 
@@ -322,7 +322,7 @@ Eq. 5.12.1. https://dlmf.nist.gov/5.12&
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -390,6 +390,9 @@ without the gamma terms.  One can use the function betabetainc(a, b, x) by
 beta(a, b).
    
 
+
    This function wraps the ibeta routine from the
+Boost Math C++ library 2.
    
+
 
    References
    
 
 
    Examples
    
@@ -397,7 +400,7 @@ function by multiplying the result of betainc(a, b, x) by
 
    Let \( B(a, b) \) be the beta function.
    
 
 
    
-
    >>> import scipy.special as sc
+
    >>> import scipy.special as sc
 
    
 
    
 
@@ -443,6 +446,10 @@ where \( F \) is the hypergeometric function hyp2f1:
    
 
    NIST Digital Library of Mathematical Functions
 https://dlmf.nist.gov/8.17 ↩
    
 
+
+
  • 
+
    The Boost Developers. "Boost C++ Libraries". https://www.boost.org/. ↩
    
+
    • 
 
 
    
 
    
@@ -462,7 +469,7 @@ where \( F \) is the hypergeometric function hyp2f1:
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -510,8 +517,8 @@ Optional output array for function values
 
    Examples
    
 
 
    
-
    >>> import numpy as np
->>> from scipy.special import betaln, beta
+
    >>> import numpy as np
+>>> from scipy.special import betaln, beta
 
    
 
    
 
@@ -565,7 +572,7 @@ the logarithm of the actual value.
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -614,7 +621,7 @@ Real valued input
 
    Examples
    
 
 
    
-
    >>> from scipy import special
+
    >>> from scipy import special
 >>> x = [2, 3, 25.5]
 >>> special.polygamma(1, x)
 array([ 0.64493407,  0.39493407,  0.03999467])
@@ -639,7 +646,7 @@ Real valued input
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -700,7 +707,7 @@ function should maintain full accuracy around the origin.
    
 
    Examples
    
 
 
    
-
    >>> from scipy.special import psi
+
    >>> from scipy.special import psi
 >>> z = 3 + 4j
 >>> psi(z)
 (1.55035981733341+1.0105022091860445j)
@@ -757,7 +764,7 @@ function should maintain full accuracy around the origin.
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -818,7 +825,7 @@ function should maintain full accuracy around the origin.
    
 
    Examples
    
 
 
    
-
    >>> from scipy.special import psi
+
    >>> from scipy.special import psi
 >>> z = 3 + 4j
 >>> psi(z)
 (1.55035981733341+1.0105022091860445j)
@@ -875,7 +882,7 @@ function should maintain full accuracy around the origin.
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -928,16 +935,41 @@ factorial since \( \Gamma(n + 1) = n! \) for natural numbers
 which, combined with the fact that \( \Gamma(1) = 1 \), implies
 the above identity for \( z = n \).
    
 
+
    The gamma function has poles at non-negative integers and the sign
+of infinity as z approaches each pole depends upon the direction in
+which the pole is approached. For this reason, the consistent thing
+is for gamma(z) to return NaN at negative integers, and to return
+-inf when x = -0.0 and +inf when x = 0.0, using the signbit of zero
+to signify the direction in which the origin is being approached. This
+is for instance what is recommended for the gamma function in annex F
+entry 9.5.4 of the Iso C 99 standard [isoc99]_.
    
+
+
    Prior to SciPy version 1.15, scipy.special.gamma(z) returned +inf
+at each pole. This was fixed in version 1.15, but with the following
+consequence. Expressions where gamma appears in the denominator
+such as
    
+
+
    gamma(u) * gamma(v) / (gamma(w) * gamma(x))
    
+
+
    no longer evaluate to 0 if the numerator is well defined but there is a
+pole in the denominator. Instead such expressions evaluate to NaN. We
+recommend instead using the function rgamma for the reciprocal gamma
+function in such cases. The above expression could for instance be written
+as
    
+
+
    gamma(u) * gamma(v) * (rgamma(w) * rgamma(x))
    
+
 
    References
    
 
 
    .. [dlmf] NIST Digital Library of Mathematical Functions
-          https://dlmf.nist.gov/5.2#E1
    
+          https://dlmf.nist.gov/5.2#E1
+.. [isoc99] https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf
    
 
 
    Examples
    
 
 
    
-
    >>> import numpy as np
->>> from scipy.special import gamma, factorial
+
    >>> import numpy as np
+>>> from scipy.special import gamma, factorial
 
    
 
    
 
@@ -972,7 +1004,7 @@ the above identity for \( z = n \).
    
 
    
 
 
    
-
    >>> import matplotlib.pyplot as plt
+
    >>> import matplotlib.pyplot as plt
 >>> plt.plot(x, y, 'b', alpha=0.6, label='gamma(x)')
 >>> k = np.arange(1, 7)
 >>> plt.plot(k, factorial(k-1), 'k*', alpha=0.6,
@@ -1002,7 +1034,7 @@ the above identity for \( z = n \).
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -1071,8 +1103,8 @@ gammasgn(x) * gamma(x).
    
 
    Examples
    
 
 
    
-
    >>> import numpy as np
->>> import scipy.special as sc
+
    >>> import numpy as np
+>>> import scipy.special as sc
 
    
 
    
 
@@ -1119,7 +1151,7 @@ gammasgn(x) * gamma(x).
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -1188,7 +1220,7 @@ incomplete gamma function.
    
 
    Examples
    
 
 
    
-
    >>> import scipy.special as sc
+
    >>> import scipy.special as sc
 
    
 
    
 
@@ -1228,7 +1260,7 @@ monotonically increases to 1.
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -1297,7 +1329,7 @@ incomplete gamma function.
    
 
    Examples
    
 
 
    
-
    >>> import scipy.special as sc
+
    >>> import scipy.special as sc
 
    
 
    
 
@@ -1338,7 +1370,7 @@ starts at 1 and monotonically decreases to 0.
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -1406,8 +1438,8 @@ np.exp(gammaln(x)).
    
 
    Examples
    
 
 
    
-
    >>> import numpy as np
->>> import scipy.special as sc
+
    >>> import numpy as np
+>>> import scipy.special as sc
 
    
 
    
 
@@ -1454,7 +1486,7 @@ np.exp(gammaln(x)).
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -1513,7 +1545,7 @@ more details.
    
 
    Examples
    
 
 
    
-
    >>> import scipy.special as sc
+
    >>> import scipy.special as sc
 
    
 
    
 
@@ -1559,7 +1591,7 @@ more details.
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -1618,8 +1650,8 @@ probability and mathematical statistics).
    
 
    Examples
    
 
 
    
-
    >>> import numpy as np
->>> from scipy.special import multigammaln, gammaln
+
    >>> import numpy as np
+>>> from scipy.special import multigammaln, gammaln
 >>> a = 23.5
 >>> d = 10
 >>> multigammaln(a, d)
@@ -1652,7 +1684,7 @@ shown above:
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -1686,7 +1718,7 @@ shown above:
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -1754,7 +1786,7 @@ It should not be confused with the spherical Bessel functions (see
 
    Calculate the function at one point:
    
 
 
    
-
    >>> from scipy.special import j0
+
    >>> from scipy.special import j0
 >>> j0(1.)
 0.7651976865579665
 
    
@@ -1763,7 +1795,7 @@ It should not be confused with the spherical Bessel functions (see
 
    Calculate the function at several points:
    
 
 
    
-
    >>> import numpy as np
+
    >>> import numpy as np
 >>> j0(np.array([-2., 0., 4.]))
 array([ 0.22389078,  1.        , -0.39714981])
 
    
@@ -1772,7 +1804,7 @@ It should not be confused with the spherical Bessel functions (see
 
    Plot the function from -20 to 20.
    
 
 
    
-
    >>> import matplotlib.pyplot as plt
+
    >>> import matplotlib.pyplot as plt
 >>> fig, ax = plt.subplots()
 >>> x = np.linspace(-20., 20., 1000)
 >>> y = j0(x)
@@ -1807,7 +1839,7 @@ It should not be confused with the spherical Bessel functions (see
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -1872,7 +1904,7 @@ two rational functions of degree 6/6 and 7/7.
    
 
    Calculate the function at one point:
    
 
 
    
-
    >>> from scipy.special import y0
+
    >>> from scipy.special import y0
 >>> y0(1.)
 0.08825696421567697
 
    
@@ -1881,7 +1913,7 @@ two rational functions of degree 6/6 and 7/7.
    
 
    Calculate at several points:
    
 
 
    
-
    >>> import numpy as np
+
    >>> import numpy as np
 >>> y0(np.array([0.5, 2., 3.]))
 array([-0.44451873,  0.51037567,  0.37685001])
 
    
@@ -1890,7 +1922,7 @@ two rational functions of degree 6/6 and 7/7.
    
 
    Plot the function from 0 to 10.
    
 
 
    
-
    >>> import matplotlib.pyplot as plt
+
    >>> import matplotlib.pyplot as plt
 >>> fig, ax = plt.subplots()
 >>> x = np.linspace(0., 10., 1000)
 >>> y = y0(x)
@@ -1925,7 +1957,7 @@ two rational functions of degree 6/6 and 7/7.
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -1986,7 +2018,7 @@ It should not be confused with the spherical Bessel functions (see
 
    Calculate the function at one point:
    
 
 
    
-
    >>> from scipy.special import j1
+
    >>> from scipy.special import j1
 >>> j1(1.)
 0.44005058574493355
 
    
@@ -1995,7 +2027,7 @@ It should not be confused with the spherical Bessel functions (see
 
    Calculate the function at several points:
    
 
 
    
-
    >>> import numpy as np
+
    >>> import numpy as np
 >>> j1(np.array([-2., 0., 4.]))
 array([-0.57672481,  0.        , -0.06604333])
 
    
@@ -2004,7 +2036,7 @@ It should not be confused with the spherical Bessel functions (see
 
    Plot the function from -20 to 20.
    
 
 
    
-
    >>> import matplotlib.pyplot as plt
+
    >>> import matplotlib.pyplot as plt
 >>> fig, ax = plt.subplots()
 >>> x = np.linspace(-20., 20., 1000)
 >>> y = j1(x)
@@ -2039,7 +2071,7 @@ It should not be confused with the spherical Bessel functions (see
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -2100,7 +2132,7 @@ rational functions of degree 5/5.
    
 
    Calculate the function at one point:
    
 
 
    
-
    >>> from scipy.special import y1
+
    >>> from scipy.special import y1
 >>> y1(1.)
 -0.7812128213002888
 
    
@@ -2109,7 +2141,7 @@ rational functions of degree 5/5.
    
 
    Calculate at several points:
    
 
 
    
-
    >>> import numpy as np
+
    >>> import numpy as np
 >>> y1(np.array([0.5, 2., 3.]))
 array([-1.47147239, -0.10703243,  0.32467442])
 
    
@@ -2118,7 +2150,7 @@ rational functions of degree 5/5.
    
 
    Plot the function from 0 to 10.
    
 
 
    
-
    >>> import matplotlib.pyplot as plt
+
    >>> import matplotlib.pyplot as plt
 >>> fig, ax = plt.subplots()
 >>> x = np.linspace(0., 10., 1000)
 >>> y = y1(x)
@@ -2153,7 +2185,7 @@ rational functions of degree 5/5.
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -2228,7 +2260,7 @@ term is explicitly omitted for v values such that v = floor(v
 
    Evaluate the function of order 0 at one point.
    
 
 
    
-
    >>> from scipy.special import jv
+
    >>> from scipy.special import jv
 >>> jv(0, 1.)
 0.7651976865579666
 
    
@@ -2255,7 +2287,7 @@ providing a list or NumPy array as argument for the v parameter:
    z    .
    
 
 
    
-
    >>> import numpy as np
+
    >>> import numpy as np
 >>> points = np.array([-2., 0., 3.])
 >>> jv(0, points)
 array([ 0.22389078,  1.        , -0.26005195])
@@ -2283,7 +2315,7 @@ To calculate the orders 0 and 1 for an 1D array:
    
 
    Plot the functions of order 0 to 3 from -10 to 10.
    
 
 
    
-
    >>> import matplotlib.pyplot as plt
+
    >>> import matplotlib.pyplot as plt
 >>> fig, ax = plt.subplots()
 >>> x = np.linspace(-10., 10., 1000)
 >>> for i in range(4):
@@ -2320,7 +2352,7 @@ of a Complex Argument and Nonnegative Order",
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -2381,7 +2413,7 @@ the routine for y0 or y1<
 
    Evaluate the function of order 0 at one point.
    
 
 
    
-
    >>> from scipy.special import yn
+
    >>> from scipy.special import yn
 >>> yn(0, 1.)
 0.08825696421567697
 
    
@@ -2408,7 +2440,7 @@ providing a list or NumPy array as argument for the v parameter:
    z    .
    
 
 
    
-
    >>> import numpy as np
+
    >>> import numpy as np
 >>> points = np.array([0.5, 3., 8.])
 >>> yn(0, points)
 array([-0.44451873,  0.37685001,  0.22352149])
@@ -2436,7 +2468,7 @@ To calculate the orders 0 and 1 for an 1D array:
    
 
    Plot the functions of order 0 to 3 from 0 to 10.
    
 
 
    
-
    >>> import matplotlib.pyplot as plt
+
    >>> import matplotlib.pyplot as plt
 >>> fig, ax = plt.subplots()
 >>> x = np.linspace(0., 10., 1000)
 >>> for i in range(4):
@@ -2473,7 +2505,7 @@ To calculate the orders 0 and 1 for an 1D array:
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -2536,7 +2568,7 @@ Chebyshev polynomial expansions are employed in each interval.
    
 
    Calculate the function at one point:
    
 
 
    
-
    >>> from scipy.special import i0
+
    >>> from scipy.special import i0
 >>> i0(1.)
 1.2660658777520082
 
    
@@ -2545,7 +2577,7 @@ Chebyshev polynomial expansions are employed in each interval.
    
 
    Calculate at several points:
    
 
 
    
-
    >>> import numpy as np
+
    >>> import numpy as np
 >>> i0(np.array([-2., 0., 3.5]))
 array([2.2795853 , 1.        , 7.37820343])
 
    
@@ -2554,7 +2586,7 @@ Chebyshev polynomial expansions are employed in each interval.
    
 
    Plot the function from -10 to 10.
    
 
 
    
-
    >>> import matplotlib.pyplot as plt
+
    >>> import matplotlib.pyplot as plt
 >>> fig, ax = plt.subplots()
 >>> x = np.linspace(-10., 10., 1000)
 >>> y = i0(x)
@@ -2589,7 +2621,7 @@ Chebyshev polynomial expansions are employed in each interval.
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -2653,7 +2685,7 @@ Chebyshev polynomial expansions are employed in each interval.
    
 
    Calculate the function at one point:
    
 
 
    
-
    >>> from scipy.special import i1
+
    >>> from scipy.special import i1
 >>> i1(1.)
 0.5651591039924851
 
    
@@ -2662,7 +2694,7 @@ Chebyshev polynomial expansions are employed in each interval.
    
 
    Calculate the function at several points:
    
 
 
    
-
    >>> import numpy as np
+
    >>> import numpy as np
 >>> i1(np.array([-2., 0., 6.]))
 array([-1.59063685,  0.        , 61.34193678])
 
    
@@ -2671,7 +2703,7 @@ Chebyshev polynomial expansions are employed in each interval.
    
 
    Plot the function between -10 and 10.
    
 
 
    
-
    >>> import matplotlib.pyplot as plt
+
    >>> import matplotlib.pyplot as plt
 >>> fig, ax = plt.subplots()
 >>> x = np.linspace(-10., 10., 1000)
 >>> y = i1(x)
@@ -2706,7 +2738,7 @@ Chebyshev polynomial expansions are employed in each interval.
    
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -2786,7 +2818,7 @@ second kind, evaluated using the AMOS routine zbesk.
    
 
    Evaluate the function of order 0 at one point.
    
 
 
    
-
    >>> from scipy.special import iv
+
    >>> from scipy.special import iv
 >>> iv(0, 1.)
 1.2660658777520084
 
    
@@ -2813,7 +2845,7 @@ providing a list or NumPy array as argument for the v parameter:
    z    .
    
 
 
    
-
    >>> import numpy as np
+
    >>> import numpy as np
 >>> points = np.array([-2., 0., 3.])
 >>> iv(0, points)
 array([2.2795853 , 1.        , 4.88079259])
@@ -2841,7 +2873,7 @@ To calculate the orders 0 and 1 for an 1D array:
    
 
    Plot the functions of order 0 to 3 from -5 to 5.
    
 
 
    
-
    >>> import matplotlib.pyplot as plt
+
    >>> import matplotlib.pyplot as plt
 >>> fig, ax = plt.subplots()
 >>> x = np.linspace(-5., 5., 1000)
 >>> for i in range(4):
@@ -2882,7 +2914,7 @@ of a Complex Argument and Nonnegative Order",
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -2969,9 +3001,9 @@ while ive does not due to the exponential scalin
 a finite number.
    
 
 
    
-
    >>> from scipy.special import iv, ive
->>> import numpy as np
->>> import matplotlib.pyplot as plt
+
    >>> from scipy.special import iv, ive
+>>> import numpy as np
+>>> import matplotlib.pyplot as plt
 >>> iv(3, 1000.), ive(3, 1000.)
 (inf, 0.01256056218254712)
 
    
@@ -3049,7 +3081,7 @@ of a Complex Argument and Nonnegative Order",
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -3103,9 +3135,9 @@ The values of the error function at the given points x.
 
    Examples
    
 
 
    
-
    >>> import numpy as np
->>> from scipy import special
->>> import matplotlib.pyplot as plt
+
    >>> import numpy as np
+>>> from scipy import special
+>>> import matplotlib.pyplot as plt
 >>> x = np.linspace(-3, 3)
 >>> plt.plot(x, special.erf(x))
 >>> plt.xlabel('$x$')
@@ -3136,7 +3168,7 @@ The values of the error function at the given points x.
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -3182,9 +3214,9 @@ Optional output array for the function results
 
    Examples
    
 
 
    
-
    >>> import numpy as np
->>> from scipy import special
->>> import matplotlib.pyplot as plt
+
    >>> import numpy as np
+>>> from scipy import special
+>>> import matplotlib.pyplot as plt
 >>> x = np.linspace(-3, 3)
 >>> plt.plot(x, special.erfc(x))
 >>> plt.xlabel('$x$')
@@ -3215,7 +3247,7 @@ Optional output array for the function results
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -3266,12 +3298,19 @@ The inverse of erf of y, element-wise
 erfc:  Complementary error function, 1 - erf(x)
    
 erfcinv:  Inverse of the complementary error function  
    
 
+
    Notes
    
+
+
    This function wraps the erf_inv routine from the
+Boost Math C++ library 1.
    
+
+
    References
    
+
 
    Examples
    
 
 
    
-
    >>> import numpy as np
->>> import matplotlib.pyplot as plt
->>> from scipy.special import erfinv, erf
+
    >>> import numpy as np
+>>> import matplotlib.pyplot as plt
+>>> from scipy.special import erfinv, erf
 
    
 
    
 
@@ -3310,6 +3349,15 @@ The inverse of erf of y, element-wise
 >>> plt.show()
 
    
 
    
+
+
    
+
    
+
      
+
    1. 
+
      The Boost Developers. "Boost C++ Libraries". https://www.boost.org/. ↩
      
+
      2. 
+
    
+
    
 
    
 
 
@@ -3327,7 +3375,7 @@ The inverse of erf of y, element-wise
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -3383,9 +3431,9 @@ The inverse of erfc of y, element-wise
 
    Examples
    
 
 
    
-
    >>> import numpy as np
->>> import matplotlib.pyplot as plt
->>> from scipy.special import erfcinv
+
    >>> import numpy as np
+>>> import matplotlib.pyplot as plt
+>>> from scipy.special import erfcinv
 
    
 
    
 
@@ -3433,7 +3481,7 @@ The inverse of erfc of y, element-wise
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -3451,8 +3499,7 @@ The inverse of erfc of y, element-wise
 
             
    logit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    
 
-
    """
-logit(x, out=None)
    
+
    logit(x, out=None)
    
 
 
    Logit ufunc for ndarrays.
    
 
@@ -3491,8 +3538,8 @@ see ufuncs 
 
    Examples
    
 
 
    
-
    >>> import numpy as np
->>> from scipy.special import logit, expit
+
    >>> import numpy as np
+>>> from scipy.special import logit, expit
 
    
 
    
 
@@ -3513,7 +3560,7 @@ see ufuncs 
 
    Plot logit(x) for x in [0, 1]:
    
 
 
    
-
    >>> import matplotlib.pyplot as plt
+
    >>> import matplotlib.pyplot as plt
 >>> x = np.linspace(0, 1, 501)
 >>> y = logit(x)
 >>> plt.plot(x, y)
@@ -3541,7 +3588,7 @@ see ufuncs 
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -3598,8 +3645,8 @@ see ufuncs 
 
    Examples
    
 
 
    
-
    >>> import numpy as np
->>> from scipy.special import expit, logit
+
    >>> import numpy as np
+>>> from scipy.special import expit, logit
 
    
 
    
 
@@ -3620,7 +3667,7 @@ see ufuncs 
 
    Plot expit(x) for x in [-6, 6]:
    
 
 
    
-
    >>> import matplotlib.pyplot as plt
+
    >>> import matplotlib.pyplot as plt
 >>> x = np.linspace(-6, 6, 121)
 >>> y = expit(x)
 >>> plt.plot(x, y)
@@ -3648,7 +3695,7 @@ see ufuncs 
     
    
     
             
    36    @wraps(f_raw)
-37    def f_wrapped(*args, **kwargs):
+37    def f_wrapped(*args, **kwargs):
 38        boxed_args, trace, node_constructor = find_top_boxed_args(args)
 39        if boxed_args:
 40            argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
@@ -3722,11 +3769,15 @@ If return_sign is False, only one result is returned.
 only handles two arguments. logaddexp.reduce is similar to this
 function, but may be less stable.
    
 
+
    The logarithm is a multivalued function: for each \( x \) there is an
+infinite number of \( z \) such that \( exp(z) = x \). The convention
+is to return the \( z \) whose imaginary part lies in \( (-pi, pi] \).
    
+
 
    Examples
    
 
 
    
-
    >>> import numpy as np
->>> from scipy.special import logsumexp
+
    >>> import numpy as np
+>>> from scipy.special import logsumexp
 >>> a = np.arange(10)
 >>> logsumexp(a)
 9.4586297444267107
diff --git a/docs/search.js b/docs/search.js
index 01dc94a6..88de728b 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oWhat is pyerrors?\n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Installation
    \n\n
    Install the most recent release using pip and pypi:
    \n\n
    \n
    python -m pip install pyerrors     # Fresh install\npython -m pip install -U pyerrors  # Update\n
    \n
    \n\n
    Install the most recent release using conda and conda-forge:
    \n\n
    \n
    conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
    \n
    \n\n
    Install the current develop version:
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    \n
    python -m pip install -U --no-deps --force-reinstall git+https://github.com/fjosw/pyerrors.git@develop\n
    \n
    \n\n
    (Also works for any feature branch).
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
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    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The gamma_method is not automatically called after every intermediate step in order to prevent computational overhead.
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
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    Exponential tails
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    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
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    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
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    Multiple ensembles/replica
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    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
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    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
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    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
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    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
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    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
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    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
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    Irregular Monte Carlo chains
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    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
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    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
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    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
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      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
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    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
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    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
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    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
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    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
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    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
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    • Corr.plateau extracts a plateau value from the correlator in a given range.
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    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
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    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
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    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.\nDirect visualizations of the performed fits can be triggered via resplot=True or qqplot=True.
    \n\n
    For all available options including combined fits to multiple datasets see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to as orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice.\nOther dependency (eg. spatial) are not supported.
    \n\n
    The Corr class can also deal with missing measurements or paddings for fixed boundary conditions.\nThe missing entries are represented via the None object.
    \n\n
    Initialization
    \n\n
    A simple correlator can be initialized with a list or a one-dimensional array of Obs or Cobs
    \n\n
    \n
    corr11 = pe.Corr([obs1, obs2])\ncorr11 = pe.Corr(np.array([obs1, obs2]))\n
    \n
    \n\n
    A matrix-valued correlator can either be initialized via a two-dimensional array of Corr objects
    \n\n
    \n
    matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]]))\n
    \n
    \n\n
    or alternatively via a three-dimensional array of Obs or CObs of shape (T, N, N) where T is\nthe temporal extent of the correlator and N is the dimension of the matrix.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion identified for this correlator.
      • \n
    \n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.tag": {"fullname": "pyerrors.correlators.Corr.tag", "modulename": "pyerrors.correlators", "qualname": "Corr.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.content": {"fullname": "pyerrors.correlators.Corr.content", "modulename": "pyerrors.correlators", "qualname": "Corr.content", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.T": {"fullname": "pyerrors.correlators.Corr.T", "modulename": "pyerrors.correlators", "qualname": "Corr.T", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prange": {"fullname": "pyerrors.correlators.Corr.prange", "modulename": "pyerrors.correlators", "qualname": "Corr.prange", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.trace": {"fullname": "pyerrors.correlators.Corr.trace", "modulename": "pyerrors.correlators", "qualname": "Corr.trace", "kind": "function", "doc": "
    Calculates the per-timeslice trace of a correlator matrix.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. (default)
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • None: The GEVP is solved only at ts, no sorting is necessary
        • \n
      • \n
    • vector_obs (bool):\nIf True, uncertainties are propagated in the eigenvector computation (default False).
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    • method (str):\nMethod used to solve the GEVP.\n
        \n
      • \"eigh\": Use scipy.linalg.eigh to solve the GEVP. (default for vector_obs=False)
        • \n
      • \"cholesky\": Use manually implemented solution via the Cholesky decomposition. Automatically chosen if vector_obs==True.
        • \n
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', vector_obs=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • parity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice:\n    - symmetric (default)\n        $$\\tilde{\\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$\n    - big_symmetric\n        $$\\partial^2_0 f(x_0) = \\frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$\n    - improved\n        $$\\partial^2_0 f(x_0) = \\frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$\n    - log\n        $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • fit_key (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tfit_key=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
    \n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.N": {"fullname": "pyerrors.correlators.Corr.N", "modulename": "pyerrors.correlators", "qualname": "Corr.N", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.name": {"fullname": "pyerrors.covobs.Covobs.name", "modulename": "pyerrors.covobs", "qualname": "Covobs.name", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.value": {"fullname": "pyerrors.covobs.Covobs.value", "modulename": "pyerrors.covobs", "qualname": "Covobs.value", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "kind": "variable", "doc": "
    \n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
    \n"}, "pyerrors.dirac.gammaX": {"fullname": "pyerrors.dirac.gammaX", "modulename": "pyerrors.dirac", "qualname": "gammaX", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n       [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaY": {"fullname": "pyerrors.dirac.gammaY", "modulename": "pyerrors.dirac", "qualname": "gammaY", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaZ": {"fullname": "pyerrors.dirac.gammaZ", "modulename": "pyerrors.dirac", "qualname": "gammaZ", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaT": {"fullname": "pyerrors.dirac.gammaT", "modulename": "pyerrors.dirac", "qualname": "gammaT", "kind": "variable", "doc": "
    \n", "default_value": "array([[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n       [1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"}, "pyerrors.dirac.gamma": {"fullname": "pyerrors.dirac.gamma", "modulename": "pyerrors.dirac", "qualname": "gamma", "kind": "variable", "doc": "
    \n", "default_value": "array([[[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n        [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n        [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],\n        [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]]])"}, "pyerrors.dirac.gamma5": {"fullname": "pyerrors.dirac.gamma5", "modulename": "pyerrors.dirac", "qualname": "gamma5", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"}, "pyerrors.dirac.identity": {"fullname": "pyerrors.dirac.identity", "modulename": "pyerrors.dirac", "qualname": "identity", "kind": "variable", "doc": "
    \n", "default_value": "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
      • \n
    \n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
      • \n
    \n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    • chisquare_by_dof (float):\nreduced chisquare.
      • \n
    • p_value (float):\np-value of the fit
      • \n
    • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.fit_parameters": {"fullname": "pyerrors.fits.Fit_result.fit_parameters", "modulename": "pyerrors.fits", "qualname": "Fit_result.fit_parameters", "kind": "variable", "doc": "
    \n"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x).\n    ```
    \n\n
    Parameters
    \n\n
      \n
    • For an uncombined fit:
      • \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n    return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • OR For a combined fit:
      • \n
    • x (dict):\ndict of lists.
      • \n
    • y (dict):\ndict of lists of Obs.
      • \n
    • funcs (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n        \"b\": func_b}
      \n\n
      def func_a(a, x):\n    return a[1] * anp.exp(-a[0] * x)
      \n\n
      def func_b(a, x):\n    return a[2] * anp.exp(-a[0] * x)
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • tol (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm < edm_max)
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
      • \n
    • inv_chol_cov_matrix [array,list], optional: array: shape = (no of y values) X (no of y values)\nlist:   for an uncombined fit: [\"\"]\nfor a combined fit: list of keys belonging to the corr_matrix saved in the array, must be the same as the keys of the y dict in alphabetical order\nIf correlated_fit=True is set as well, can provide an inverse covariance matrix (y errors, dy_f included!) of your own choosing for a correlated fit.\nThe matrix must be a lower triangular matrix constructed from a Cholesky decomposition: The function invert_corr_cov_cholesky(corr, inverrdiag) can be\nused to construct it from a correlation matrix (corr) and the errors dy_f of the data points (inverrdiag = np.diag(1 / np.asarray(dy_f))). For the correct\nordering the correlation matrix (corr) can be sorted via the function sort_corr(corr, kl, yd) where kl is the list of keys and yd the y dict.
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n\n
    Examples
    \n\n
    \n
    >>> # Example of a correlated (correlated_fit = True, inv_chol_cov_matrix handed over) combined fit, based on a randomly generated data set\n>>> import numpy as np\n>>> from scipy.stats import norm\n>>> from scipy.linalg import cholesky\n>>> import pyerrors as pe\n>>> # generating the random data set\n>>> num_samples = 400\n>>> N = 3\n>>> x = np.arange(N)\n>>> x1 = norm.rvs(size=(N, num_samples)) # generate random numbers\n>>> x2 = norm.rvs(size=(N, num_samples)) # generate random numbers\n>>> r = r1 = r2 = np.zeros((N, N))\n>>> y = {}\n>>> for i in range(N):\n>>>    for j in range(N):\n>>>        r[i, j] = np.exp(-0.8 * np.fabs(i - j)) # element in correlation matrix\n>>> errl = np.sqrt([3.4, 2.5, 3.6]) # set y errors\n>>> for i in range(N):\n>>>    for j in range(N):\n>>>        r[i, j] *= errl[i] * errl[j] # element in covariance matrix\n>>> c = cholesky(r, lower=True)\n>>> y = {'a': np.dot(c, x1), 'b': np.dot(c, x2)} # generate y data with the covariance matrix defined\n>>> # random data set has been generated, now the dictionaries and the inverse covariance matrix to be handed over are built\n>>> x_dict = {}\n>>> y_dict = {}\n>>> chol_inv_dict = {}\n>>> data = []\n>>> for key in y.keys():\n>>>    x_dict[key] = x\n>>>    for i in range(N):\n>>>        data.append(pe.Obs([[i + 1 + o for o in y[key][i]]], ['ens'])) # generate y Obs from the y data\n>>>    [o.gamma_method() for o in data]\n>>>    corr = pe.covariance(data, correlation=True)\n>>>    inverrdiag = np.diag(1 / np.asarray([o.dvalue for o in data]))\n>>>    chol_inv = pe.obs.invert_corr_cov_cholesky(corr, inverrdiag) # gives form of the inverse covariance matrix needed for the combined correlated fit below\n>>> y_dict = {'a': data[:3], 'b': data[3:]}\n>>> # common fit parameter p[0] in combined fit\n>>> def fit1(p, x):\n>>>    return p[0] + p[1] * x\n>>> def fit2(p, x):\n>>>    return p[0] + p[2] * x\n>>> fitf_dict = {'a': fit1, 'b':fit2}\n>>> fitp_inv_cov_combined_fit = pe.least_squares(x_dict,y_dict, fitf_dict, correlated_fit = True, inv_chol_cov_matrix = [chol_inv,['a','b']])\nFit with 3 parameters\nMethod: Levenberg-Marquardt\n`ftol` termination condition is satisfied.\nchisquare/d.o.f.: 0.5388013574561786 # random\nfit parameters [1.11897846 0.96361162 0.92325319] # random\n
    \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n    return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy.
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • fit_parameters (list[Obs]):\nLIist of fitted observables.
      • \n
    \n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n\n
    For uncorrelated data the residuals are expected to be distributed ~N(0,1).
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
    Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n\n
    Returns
    \n\n
      \n
    • err (np.array(Obs)):\nError band for an array of sample values x
      • \n
    \n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (List[Obs]):\nExtracted data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • success (int):\nreturns 0 is successful
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (dict):\nExtracted meson data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML formatted string of the input data
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML string generated from the data
      • \n
    \n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_hd5": {"fullname": "pyerrors.input.hadrons.read_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_hd5", "kind": "function", "doc": "
    Read hadrons hdf5 file and extract entry based on attributes.
    \n\n
    Parameters
    \n\n
      \n
    • filestem (str):\nFull namestem of the files to read, including the full path.
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • group (str):\nlabel of the group to be extracted.
      • \n
    • attrs (dict or int):\nDictionary containing the attributes. For example
      \n\n
      \n
      attrs = {"gamma_snk": "Gamma5",\n         "gamma_src": "Gamma5"}\n
      \n
      \n\n
      Alternatively an integer can be specified to identify the sub group.\nThis is discouraged as the order in the file is not guaranteed.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • part (str):\nstring specifying whether to extract the real part ('real'),\nthe imaginary part ('imag') or a complex correlator ('complex').\nDefault 'real'.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr (Corr):\nCorrelator of the source sink combination in question.
      • \n
    \n", "signature": "(filestem, ens_id, group, attrs=None, idl=None, part='real'):", "funcdef": "def"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr (Corr):\nCorrelator of the source sink combination in question.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
    Read hadrons FlowObservables hdf5 file and extract t0
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    \n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (dict):\nextracted DistillationContration data
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array.
    \nzeros:  Create an array, each element of which is zero.
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\").
    \ndtype:  Create a data-type.
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    \n
    >>> import numpy as np\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Npr_matrix):\nread Cobs-matrix
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict[Npr_matrix]):\nextracted Bilinears
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict):\nextracted fourquark matrizes
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • json_string (str):\nString for export to .json(.gz) file
      • \n
    \n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Null
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (Obs / list / Corr):\nRead data
      • \n
    • or
      • \n
    • data (dict):\nRead data and meta-data
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "
    Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).
    \n\n
    It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.
    \n\n
    A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
      • \n
    • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • root (Obs):\nThe root of the data series.
      • \n
    \n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
    Read pbp format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of observables read
      • \n
    \n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • rwms (Obs):\nReweighting factors read
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
    Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • t0 (Obs):\nExtracted t0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "
    Extract w0/a from given .ms.dat files. Returns w0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • w0 (Obs):\nExtracted w0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Obs):\nRead topological charge
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nThe directory to search for the files in.
      • \n
    • prefix (str):\nThe prefix to match the files against.
      • \n
    • qc (str):\nThe quark combination extension to match the files against.
      • \n
    • corr (str):\nThe correlator to extract data for.
      • \n
    • sep (str, optional):\nThe separator to use when parsing the replika names.
      • \n
    • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
      \n\n
        \n
      • names (List[str]): A list of names to use for the replicas.
        • \n
      • files (List[str]): A list of files to read data from.
        • \n
      • idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.
        • \n
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
      • \n
    • or
      • \n
    • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
      • \n
    \n\n
    Raises
    \n\n
      \n
    • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
      • \n
    • IOError: If there is an error reading a file.
      • \n
    • struct.error: If there is an error unpacking binary data.
      • \n
    \n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.sep": {"fullname": "pyerrors.input.sfcf.sep", "modulename": "pyerrors.input.sfcf", "qualname": "sep", "kind": "variable", "doc": "
    \n", "default_value": "'/'"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
    Read sfcf files from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type (str):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.sfcf.read_sfcf_multi": {"fullname": "pyerrors.input.sfcf.read_sfcf_multi", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf_multi", "kind": "function", "doc": "
    Read sfcf files from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks_list (list[str]):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type_list (list[str]):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset_list (list[int]):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf_list (int):\nID of wave function
      • \n
    • wf2_list (list[int]):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list[list[int]]):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (dict[list[Obs]]):\ndict with one of the following properties:\nif keyed_out:\n    dict[key] = list[Obs]\n    where key has the form name/quarks/offset/wf/wf2\nif not keyed_out:\n    dict[name][quarks][offset][wf][wf2] = list[Obs]
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname_list,\tquarks_list=['.*'],\tcorr_type_list=['bi'],\tnoffset_list=[0],\twf_list=[0],\twf2_list=[0],\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\tkeyed_out=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "
    Sorts a list of names of replika with searches for r and id in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • ll (list):\nlist to sort
      • \n
    \n\n
    Returns
    \n\n
      \n
    • ll (list):\nsorted list
      • \n
    \n", "signature": "(ll):", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n\n
    Returns
    \n\n
      \n
    • miss_str (str):\nstring with integers of which idls are missing
      • \n
    \n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.input.utils.check_params": {"fullname": "pyerrors.input.utils.check_params", "modulename": "pyerrors.input.utils", "qualname": "check_params", "kind": "function", "doc": "
    Check if, for sfcf, the parameter hashes at the end of the parameter files are in fact the expected one.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nmeasurement path, same as for sfcf read method
      • \n
    • param_hash (str):\nexpected parameter hash
      • \n
    • prefix (str):\ndata prefix to find the appropriate replicum folders in path
      • \n
    • param_prefix (str):\nprefix of the parameter file. Defaults to 'parameters_'
      • \n
    \n\n
    Returns
    \n\n
      \n
    • nums (dict):\ndictionary of faulty parameter files sorted by the replica paths
      • \n
    \n", "signature": "(path, param_hash, prefix, param_prefix='parameters_'):", "funcdef": "def"}, "pyerrors.integrate": {"fullname": "pyerrors.integrate", "modulename": "pyerrors.integrate", "kind": "module", "doc": "
    \n"}, "pyerrors.integrate.quad": {"fullname": "pyerrors.integrate.quad", "modulename": "pyerrors.integrate", "qualname": "quad", "kind": "function", "doc": "
    Performs a (one-dimensional) numeric integration of f(p, x) from a to b.
    \n\n
    The integration is performed using scipy.integrate.quad().\nAll parameters that can be passed to scipy.integrate.quad may also be passed to this function.\nThe output is the same as for scipy.integrate.quad, the first element being an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\nfunction to integrate, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(p, x):\n    return p[0] + p[1] * x + p[2] * anp.sinh(x)\n
      \n
      \n\n
      where x is the integration variable.
      • \n
    • p (list of floats or Obs):\nparameters of the function func.
      • \n
    • a (float or Obs):\nLower limit of integration (use -numpy.inf for -infinity).
      • \n
    • b (float or Obs):\nUpper limit of integration (use -numpy.inf for -infinity).
      • \n
    • All parameters of scipy.integrate.quad
      • \n
    \n\n
    Returns
    \n\n
      \n
    • y (Obs):\nThe integral of func from a to b.
      • \n
    • abserr (float):\nAn estimate of the absolute error in the result.
      • \n
    • infodict (dict):\nA dictionary containing additional information.\nRun scipy.integrate.quad_explain() for more information.
      • \n
    • message: A convergence message.
      • \n
    • explain: Appended only with 'cos' or 'sin' weighting and infinite\nintegration limits, it contains an explanation of the codes in\ninfodict['ierlst']
      • \n
    \n", "signature": "(func, p, a, b, **kwargs):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eigv": {"fullname": "pyerrors.linalg.eigv", "modulename": "pyerrors.linalg", "qualname": "eigv", "kind": "function", "doc": "
    Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "
    Print information about version of python, pyerrors and dependencies.
    \n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "
    pyerrors wrapper for the errorbars method of matplotlib
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nA list of x-values which can be Obs.
      • \n
    • y (list):\nA list of y-values which can be Obs.
      • \n
    • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
      • \n
    \n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n\n
    Returns
    \n\n
      \n
    • object (Obs):\nLoaded Object
      • \n
    \n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nGenerated Observable
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr_obs (list[Obs]):\nGenerated observable list
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • energy_levels (list[Obs]):\nExtracted energy levels
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "
    \n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "
    \n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "
    \n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "
    Export bootstrap samples from the Obs
    \n\n
    Parameters
    \n\n
      \n
    • samples (int):\nNumber of bootstrap samples to generate.
      • \n
    • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
      • \n
    • save_rng (str):\nSave the random numbers to a file if a path is specified.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).
      • \n
    \n", "signature": "(self, samples=500, random_numbers=None, save_rng=None):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
    \n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.gamma_method": {"fullname": "pyerrors.obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "gamma_method", "kind": "function", "doc": "
    Vectorized version of the gamma_method applicable to lists or arrays of Obs.
    \n\n
    See docstring of pe.Obs.gamma_method for details.
    \n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.gm": {"fullname": "pyerrors.obs.gm", "modulename": "pyerrors.obs", "qualname": "gm", "kind": "function", "doc": "
    Vectorized version of the gamma_method applicable to lists or arrays of Obs.
    \n\n
    See docstring of pe.Obs.gamma_method for details.
    \n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.invert_corr_cov_cholesky": {"fullname": "pyerrors.obs.invert_corr_cov_cholesky", "modulename": "pyerrors.obs", "qualname": "invert_corr_cov_cholesky", "kind": "function", "doc": "
    Constructs a lower triangular matrix chol via the Cholesky decomposition of the correlation matrix corr\n   and then returns the inverse covariance matrix chol_inv as a lower triangular matrix by solving chol * x = inverrdiag.
    \n\n
    Parameters
    \n\n
      \n
    • corr (np.ndarray):\ncorrelation matrix
      • \n
    • inverrdiag (np.ndarray):\ndiagonal matrix, the entries are the inverse errors of the data points considered
      • \n
    \n", "signature": "(corr, inverrdiag):", "funcdef": "def"}, "pyerrors.obs.sort_corr": {"fullname": "pyerrors.obs.sort_corr", "modulename": "pyerrors.obs", "qualname": "sort_corr", "kind": "function", "doc": "
    Reorders a correlation matrix to match the alphabetical order of its underlying y data.
    \n\n
    The ordering of the input correlation matrix corr is given by the list of keys kl.\nThe input dictionary yd (with the same keys kl) must contain the corresponding y data\nthat the correlation matrix is based on.\nThis function sorts the list of keys kl alphabetically and sorts the matrix corr\naccording to this alphabetical order such that the sorted matrix corr_sorted corresponds\nto the y data yd when arranged in an alphabetical order by its keys.
    \n\n
    Parameters
    \n\n
      \n
    • corr (np.ndarray):\nA square correlation matrix constructed using the order of the y data specified by kl.\nThe dimensions of corr should match the total number of y data points in yd combined.
      • \n
    • kl (list of str):\nA list of keys that denotes the order in which the y data from yd was used to build the\ninput correlation matrix corr.
      • \n
    • yd (dict of list):\nA dictionary where each key corresponds to a unique identifier, and its value is a list of\ny data points. The total number of y data points across all keys must match the dimensions\nof corr. The lists in the dictionary can be lists of Obs.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • np.ndarray: A new, sorted correlation matrix that corresponds to the y data from yd when arranged alphabetically by its keys.
      • \n
    \n\n
    Example
    \n\n
    \n
    >>> import numpy as np\n>>> import pyerrors as pe\n>>> corr = np.array([[1, 0.2, 0.3], [0.2, 1, 0.4], [0.3, 0.4, 1]])\n>>> kl = ['b', 'a']\n>>> yd = {'a': [1, 2], 'b': [3]}\n>>> sorted_corr = pe.obs.sort_corr(corr, kl, yd)\n>>> print(sorted_corr)\narray([[1. , 0.3, 0.4],\n       [0.3, 1. , 0.2],\n       [0.4, 0.2, 1. ]])\n
    \n
    \n", "signature": "(corr, kl, yd):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.import_bootstrap": {"fullname": "pyerrors.obs.import_bootstrap", "modulename": "pyerrors.obs", "qualname": "import_bootstrap", "kind": "function", "doc": "
    Imports bootstrap samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • boots (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N bootstrap samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples,\nwhere samples is the number of bootstrap samples and length is the length of the original Monte Carlo\nchain to be reconstructed.
      • \n
    \n", "signature": "(boots, name, random_numbers):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n    return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nObs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.special": {"fullname": "pyerrors.special", "modulename": "pyerrors.special", "kind": "module", "doc": "
    \n"}, "pyerrors.special.beta": {"fullname": "pyerrors.special.beta", "modulename": "pyerrors.special", "qualname": "beta", "kind": "function", "doc": "
    beta(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    beta(a, b, out=None)
    \n\n
    Beta function.
    \n\n
    This function is defined in 1 as
    \n\n
    $$B(a, b) = \\int_0^1 t^{a-1}(1-t)^{b-1}dt\n        = \\frac{\\Gamma(a)\\Gamma(b)}{\\Gamma(a+b)},$$
    \n\n
    where \\( \\Gamma \\) is the gamma function.
    \n\n
    Parameters
    \n\n
      \n
    • a, b (array_like):\nReal-valued arguments
      • \n
    • out (ndarray, optional):\nOptional output array for the function result
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Value of the beta function
      • \n
    \n\n
    See Also
    \n\n
    gamma:  the gamma function
    \nbetainc:   the regularized incomplete beta function
    \nbetaln:  the natural logarithm of the absolute\nvalue of the beta function  
    \n\n
    References
    \n\n
    Examples
    \n\n
    \n
    >>> import scipy.special as sc\n
    \n
    \n\n
    The beta function relates to the gamma function by the\ndefinition given above:
    \n\n
    \n
    >>> sc.beta(2, 3)\n0.08333333333333333\n>>> sc.gamma(2)*sc.gamma(3)/sc.gamma(2 + 3)\n0.08333333333333333\n
    \n
    \n\n
    As this relationship demonstrates, the beta function\nis symmetric:
    \n\n
    \n
    >>> sc.beta(1.7, 2.4)\n0.16567527689031739\n>>> sc.beta(2.4, 1.7)\n0.16567527689031739\n
    \n
    \n\n
    This function satisfies \\( B(1, b) = 1/b \\):
    \n\n
    \n
    >>> sc.beta(1, 4)\n0.25\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      NIST Digital Library of Mathematical Functions,\nEq. 5.12.1. https://dlmf.nist.gov/5.12 ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.betainc": {"fullname": "pyerrors.special.betainc", "modulename": "pyerrors.special", "qualname": "betainc", "kind": "function", "doc": "
    betainc(x1, x2, x3, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    betainc(a, b, x, out=None)
    \n\n
    Regularized incomplete beta function.
    \n\n
    Computes the regularized incomplete beta function, defined as 1:
    \n\n
    $$I_x(a, b) = \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)} \\int_0^x\nt^{a-1}(1-t)^{b-1}dt,$$
    \n\n
    for \\( 0 \\leq x \\leq 1 \\).
    \n\n
    This function is the cumulative distribution function for the beta\ndistribution; its range is [0, 1].
    \n\n
    Parameters
    \n\n
      \n
    • a, b (array_like):\nPositive, real-valued parameters
      • \n
    • x (array_like):\nReal-valued such that \\( 0 \\leq x \\leq 1 \\),\nthe upper limit of integration
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Value of the regularized incomplete beta function
      • \n
    \n\n
    See Also
    \n\n
    beta:  beta function
    \nbetaincinv:  inverse of the regularized incomplete beta function
    \nbetaincc:  complement of the regularized incomplete beta function
    \nscipy.stats.beta:  beta distribution  
    \n\n
    Notes
    \n\n
    The term regularized in the name of this function refers to the\nscaling of the function by the gamma function terms shown in the\nformula.  When not qualified as regularized, the name incomplete\nbeta function often refers to just the integral expression,\nwithout the gamma terms.  One can use the function beta from\nscipy.special to get this \"nonregularized\" incomplete beta\nfunction by multiplying the result of betainc(a, b, x) by\nbeta(a, b).
    \n\n
    References
    \n\n
    Examples
    \n\n
    Let \\( B(a, b) \\) be the beta function.
    \n\n
    \n
    >>> import scipy.special as sc\n
    \n
    \n\n
    The coefficient in terms of gamma is equal to\n\\( 1/B(a, b) \\). Also, when \\( x=1 \\)\nthe integral is equal to \\( B(a, b) \\).\nTherefore, \\( I_{x=1}(a, b) = 1 \\) for any \\( a, b \\).
    \n\n
    \n
    >>> sc.betainc(0.2, 3.5, 1.0)\n1.0\n
    \n
    \n\n
    It satisfies\n\\( I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b)) \\),\nwhere \\( F \\) is the hypergeometric function hyp2f1:
    \n\n
    \n
    >>> a, b, x = 1.4, 3.1, 0.5\n>>> x**a * sc.hyp2f1(a, 1 - b, a + 1, x)/(a * sc.beta(a, b))\n0.8148904036225295\n>>> sc.betainc(a, b, x)\n0.8148904036225296\n
    \n
    \n\n
    This functions satisfies the relationship\n\\( I_x(a, b) = 1 - I_{1-x}(b, a) \\):
    \n\n
    \n
    >>> sc.betainc(2.2, 3.1, 0.4)\n0.49339638807619446\n>>> 1 - sc.betainc(3.1, 2.2, 1 - 0.4)\n0.49339638807619446\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/8.17 ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.betaln": {"fullname": "pyerrors.special.betaln", "modulename": "pyerrors.special", "qualname": "betaln", "kind": "function", "doc": "
    betaln(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    betaln(a, b, out=None)
    \n\n
    Natural logarithm of absolute value of beta function.
    \n\n
    Computes ln(abs(beta(a, b))).
    \n\n
    Parameters
    \n\n
      \n
    • a, b (array_like):\nPositive, real-valued parameters
      • \n
    • out (ndarray, optional):\nOptional output array for function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Value of the betaln function
      • \n
    \n\n
    See Also
    \n\n
    gamma:  the gamma function
    \nbetainc:   the regularized incomplete beta function
    \nbeta:  the beta function  
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.special import betaln, beta\n
    \n
    \n\n
    Verify that, for moderate values of a and b, betaln(a, b)\nis the same as log(beta(a, b)):
    \n\n
    \n
    >>> betaln(3, 4)\n-4.0943445622221\n
    \n
    \n\n
    \n
    >>> np.log(beta(3, 4))\n-4.0943445622221\n
    \n
    \n\n
    In the following beta(a, b) underflows to 0, so we can't compute\nthe logarithm of the actual value.
    \n\n
    \n
    >>> a = 400\n>>> b = 900\n>>> beta(a, b)\n0.0\n
    \n
    \n\n
    We can compute the logarithm of beta(a, b) by using betaln:
    \n\n
    \n
    >>> betaln(a, b)\n-804.3069951764146\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.polygamma": {"fullname": "pyerrors.special.polygamma", "modulename": "pyerrors.special", "qualname": "polygamma", "kind": "function", "doc": "
    Polygamma functions.
    \n\n
    Defined as \\( \\psi^{(n)}(x) \\) where \\( \\psi \\) is the\ndigamma function. See [dlmf]_ for details.
    \n\n
    Parameters
    \n\n
      \n
    • n (array_like):\nThe order of the derivative of the digamma function; must be\nintegral
      • \n
    • x (array_like):\nReal valued input
      • \n
    \n\n
    Returns
    \n\n
      \n
    • ndarray: Function results
      • \n
    \n\n
    See Also
    \n\n
    digamma  
    \n\n
    References
    \n\n
    .. [dlmf] NIST, Digital Library of Mathematical Functions,\n    https://dlmf.nist.gov/5.15
    \n\n
    Examples
    \n\n
    \n
    >>> from scipy import special\n>>> x = [2, 3, 25.5]\n>>> special.polygamma(1, x)\narray([ 0.64493407,  0.39493407,  0.03999467])\n>>> special.polygamma(0, x) == special.psi(x)\narray([ True,  True,  True], dtype=bool)\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.psi": {"fullname": "pyerrors.special.psi", "modulename": "pyerrors.special", "qualname": "psi", "kind": "function", "doc": "
    psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    psi(z, out=None)
    \n\n
    The digamma function.
    \n\n
    The logarithmic derivative of the gamma function evaluated at z.
    \n\n
    Parameters
    \n\n
      \n
    • z (array_like):\nReal or complex argument.
      • \n
    • out (ndarray, optional):\nArray for the computed values of psi.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • digamma (scalar or ndarray):\nComputed values of psi.
      • \n
    \n\n
    Notes
    \n\n
    For large values not close to the negative real axis, psi is\ncomputed using the asymptotic series (5.11.2) from 1. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from 2 is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from 3 is\nused first. Note that psi has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using 4, so the\nfunction should maintain full accuracy around the origin.
    \n\n
    References
    \n\n
    Examples
    \n\n
    \n
    >>> from scipy.special import psi\n>>> z = 3 + 4j\n>>> psi(z)\n(1.55035981733341+1.0105022091860445j)\n
    \n
    \n\n
    Verify psi(z) = psi(z + 1) - 1/z:
    \n\n
    \n
    >>> psi(z + 1) - 1/z\n(1.55035981733341+1.0105022091860445j)\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
      \n
      2. \n\n
    2. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
      \n
      3. \n\n
    3. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
      \n
      4. \n\n
    4. \n
      Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ ↩
      \n
      5. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.digamma": {"fullname": "pyerrors.special.digamma", "modulename": "pyerrors.special", "qualname": "digamma", "kind": "function", "doc": "
    psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    psi(z, out=None)
    \n\n
    The digamma function.
    \n\n
    The logarithmic derivative of the gamma function evaluated at z.
    \n\n
    Parameters
    \n\n
      \n
    • z (array_like):\nReal or complex argument.
      • \n
    • out (ndarray, optional):\nArray for the computed values of psi.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • digamma (scalar or ndarray):\nComputed values of psi.
      • \n
    \n\n
    Notes
    \n\n
    For large values not close to the negative real axis, psi is\ncomputed using the asymptotic series (5.11.2) from 1. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from 2 is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from 3 is\nused first. Note that psi has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using 4, so the\nfunction should maintain full accuracy around the origin.
    \n\n
    References
    \n\n
    Examples
    \n\n
    \n
    >>> from scipy.special import psi\n>>> z = 3 + 4j\n>>> psi(z)\n(1.55035981733341+1.0105022091860445j)\n
    \n
    \n\n
    Verify psi(z) = psi(z + 1) - 1/z:
    \n\n
    \n
    >>> psi(z + 1) - 1/z\n(1.55035981733341+1.0105022091860445j)\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
      \n
      2. \n\n
    2. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
      \n
      3. \n\n
    3. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
      \n
      4. \n\n
    4. \n
      Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ ↩
      \n
      5. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gamma": {"fullname": "pyerrors.special.gamma", "modulename": "pyerrors.special", "qualname": "gamma", "kind": "function", "doc": "
    gamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    gamma(z, out=None)
    \n\n
    gamma function.
    \n\n
    The gamma function is defined as
    \n\n
    $$\\Gamma(z) = \\int_0^\\infty t^{z-1} e^{-t} dt$$
    \n\n
    for \\( \\Re(z) > 0 \\) and is extended to the rest of the complex\nplane by analytic continuation. See [dlmf]_ for more details.
    \n\n
    Parameters
    \n\n
      \n
    • z (array_like):\nReal or complex valued argument
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the gamma function
      • \n
    \n\n
    Notes
    \n\n
    The gamma function is often referred to as the generalized\nfactorial since \\( \\Gamma(n + 1) = n! \\) for natural numbers\n\\( n \\). More generally it satisfies the recurrence relation\n\\( \\Gamma(z + 1) = z \\cdot \\Gamma(z) \\) for complex \\( z \\),\nwhich, combined with the fact that \\( \\Gamma(1) = 1 \\), implies\nthe above identity for \\( z = n \\).
    \n\n
    References
    \n\n
    .. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5.2#E1
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.special import gamma, factorial\n
    \n
    \n\n
    \n
    >>> gamma([0, 0.5, 1, 5])\narray([         inf,   1.77245385,   1.        ,  24.        ])\n
    \n
    \n\n
    \n
    >>> z = 2.5 + 1j\n>>> gamma(z)\n(0.77476210455108352+0.70763120437959293j)\n>>> gamma(z+1), z*gamma(z)  # Recurrence property\n((1.2292740569981171+2.5438401155000685j),\n (1.2292740569981158+2.5438401155000658j))\n
    \n
    \n\n
    \n
    >>> gamma(0.5)**2  # gamma(0.5) = sqrt(pi)\n3.1415926535897927\n
    \n
    \n\n
    Plot gamma(x) for real x
    \n\n
    \n
    >>> x = np.linspace(-3.5, 5.5, 2251)\n>>> y = gamma(x)\n
    \n
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> plt.plot(x, y, 'b', alpha=0.6, label='gamma(x)')\n>>> k = np.arange(1, 7)\n>>> plt.plot(k, factorial(k-1), 'k*', alpha=0.6,\n...          label='(x-1)!, x = 1, 2, ...')\n>>> plt.xlim(-3.5, 5.5)\n>>> plt.ylim(-10, 25)\n>>> plt.grid()\n>>> plt.xlabel('x')\n>>> plt.legend(loc='lower right')\n>>> plt.show()\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammaln": {"fullname": "pyerrors.special.gammaln", "modulename": "pyerrors.special", "qualname": "gammaln", "kind": "function", "doc": "
    gammaln(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    gammaln(x, out=None)
    \n\n
    Logarithm of the absolute value of the gamma function.
    \n\n
    Defined as
    \n\n
    $$\\ln(\\lvert\\Gamma(x)\\rvert)$$
    \n\n
    where \\( \\Gamma \\) is the gamma function. For more details on\nthe gamma function, see [dlmf]_.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nReal argument
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the log of the absolute value of gamma
      • \n
    \n\n
    See Also
    \n\n
    gammasgn:  sign of the gamma function
    \nloggamma:  principal branch of the logarithm of the gamma function  
    \n\n
    Notes
    \n\n
    It is the same function as the Python standard library function\nmath.lgamma().
    \n\n
    When used in conjunction with gammasgn, this function is useful\nfor working in logspace on the real axis without having to deal\nwith complex numbers via the relation exp(gammaln(x)) =\ngammasgn(x) * gamma(x).
    \n\n
    For complex-valued log-gamma, use loggamma instead of gammaln.
    \n\n
    References
    \n\n
    .. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> import scipy.special as sc\n
    \n
    \n\n
    It has two positive zeros.
    \n\n
    \n
    >>> sc.gammaln([1, 2])\narray([0., 0.])\n
    \n
    \n\n
    It has poles at nonpositive integers.
    \n\n
    \n
    >>> sc.gammaln([0, -1, -2, -3, -4])\narray([inf, inf, inf, inf, inf])\n
    \n
    \n\n
    It asymptotically approaches x * log(x) (Stirling's formula).
    \n\n
    \n
    >>> x = np.array([1e10, 1e20, 1e40, 1e80])\n>>> sc.gammaln(x)\narray([2.20258509e+11, 4.50517019e+21, 9.11034037e+41, 1.83206807e+82])\n>>> x * np.log(x)\narray([2.30258509e+11, 4.60517019e+21, 9.21034037e+41, 1.84206807e+82])\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammainc": {"fullname": "pyerrors.special.gammainc", "modulename": "pyerrors.special", "qualname": "gammainc", "kind": "function", "doc": "
    gammainc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    gammainc(a, x, out=None)
    \n\n
    Regularized lower incomplete gamma function.
    \n\n
    It is defined as
    \n\n
    $$P(a, x) = \\frac{1}{\\Gamma(a)} \\int_0^x t^{a - 1}e^{-t} dt$$
    \n\n
    for \\( a > 0 \\) and \\( x \\geq 0 \\). See [dlmf]_ for details.
    \n\n
    Parameters
    \n\n
      \n
    • a (array_like):\nPositive parameter
      • \n
    • x (array_like):\nNonnegative argument
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the lower incomplete gamma function
      • \n
    \n\n
    See Also
    \n\n
    gammaincc:  regularized upper incomplete gamma function
    \ngammaincinv:  inverse of the regularized lower incomplete gamma function
    \ngammainccinv:  inverse of the regularized upper incomplete gamma function  
    \n\n
    Notes
    \n\n
    The function satisfies the relation gammainc(a, x) +\ngammaincc(a, x) = 1 where gammaincc is the regularized upper\nincomplete gamma function.
    \n\n
    The implementation largely follows that of [boost]_.
    \n\n
    References
    \n\n
    .. [dlmf] NIST Digital Library of Mathematical functions\n          https://dlmf.nist.gov/8.2#E4\n.. [boost] Maddock et. al., \"Incomplete Gamma Functions\",\n   https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
    \n\n
    Examples
    \n\n
    \n
    >>> import scipy.special as sc\n
    \n
    \n\n
    It is the CDF of the gamma distribution, so it starts at 0 and\nmonotonically increases to 1.
    \n\n
    \n
    >>> sc.gammainc(0.5, [0, 1, 10, 100])\narray([0.        , 0.84270079, 0.99999226, 1.        ])\n
    \n
    \n\n
    It is equal to one minus the upper incomplete gamma function.
    \n\n
    \n
    >>> a, x = 0.5, 0.4\n>>> sc.gammainc(a, x)\n0.6289066304773024\n>>> 1 - sc.gammaincc(a, x)\n0.6289066304773024\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammaincc": {"fullname": "pyerrors.special.gammaincc", "modulename": "pyerrors.special", "qualname": "gammaincc", "kind": "function", "doc": "
    gammaincc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    gammaincc(a, x, out=None)
    \n\n
    Regularized upper incomplete gamma function.
    \n\n
    It is defined as
    \n\n
    $$Q(a, x) = \\frac{1}{\\Gamma(a)} \\int_x^\\infty t^{a - 1}e^{-t} dt$$
    \n\n
    for \\( a > 0 \\) and \\( x \\geq 0 \\). See [dlmf]_ for details.
    \n\n
    Parameters
    \n\n
      \n
    • a (array_like):\nPositive parameter
      • \n
    • x (array_like):\nNonnegative argument
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the upper incomplete gamma function
      • \n
    \n\n
    See Also
    \n\n
    gammainc:  regularized lower incomplete gamma function
    \ngammaincinv:  inverse of the regularized lower incomplete gamma function
    \ngammainccinv:  inverse of the regularized upper incomplete gamma function  
    \n\n
    Notes
    \n\n
    The function satisfies the relation gammainc(a, x) +\ngammaincc(a, x) = 1 where gammainc is the regularized lower\nincomplete gamma function.
    \n\n
    The implementation largely follows that of [boost]_.
    \n\n
    References
    \n\n
    .. [dlmf] NIST Digital Library of Mathematical functions\n          https://dlmf.nist.gov/8.2#E4\n.. [boost] Maddock et. al., \"Incomplete Gamma Functions\",\n   https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
    \n\n
    Examples
    \n\n
    \n
    >>> import scipy.special as sc\n
    \n
    \n\n
    It is the survival function of the gamma distribution, so it\nstarts at 1 and monotonically decreases to 0.
    \n\n
    \n
    >>> sc.gammaincc(0.5, [0, 1, 10, 100, 1000])\narray([1.00000000e+00, 1.57299207e-01, 7.74421643e-06, 2.08848758e-45,\n       0.00000000e+00])\n
    \n
    \n\n
    It is equal to one minus the lower incomplete gamma function.
    \n\n
    \n
    >>> a, x = 0.5, 0.4\n>>> sc.gammaincc(a, x)\n0.37109336952269756\n>>> 1 - sc.gammainc(a, x)\n0.37109336952269756\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammasgn": {"fullname": "pyerrors.special.gammasgn", "modulename": "pyerrors.special", "qualname": "gammasgn", "kind": "function", "doc": "
    gammasgn(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    gammasgn(x, out=None)
    \n\n
    Sign of the gamma function.
    \n\n
    It is defined as
    \n\n
    $$\\text{gammasgn}(x) =\n\\begin{cases}\n  +1 & \\Gamma(x) > 0 \\\n  -1 & \\Gamma(x) < 0\n\\end{cases}$$
    \n\n
    where \\( \\Gamma \\) is the gamma function; see gamma. This\ndefinition is complete since the gamma function is never zero;\nsee the discussion after [dlmf]_.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nReal argument
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Sign of the gamma function
      • \n
    \n\n
    See Also
    \n\n
    gamma:  the gamma function
    \ngammaln:  log of the absolute value of the gamma function
    \nloggamma:  analytic continuation of the log of the gamma function  
    \n\n
    Notes
    \n\n
    The gamma function can be computed as gammasgn(x) *\nnp.exp(gammaln(x)).
    \n\n
    References
    \n\n
    .. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5.2#E1
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> import scipy.special as sc\n
    \n
    \n\n
    It is 1 for x > 0.
    \n\n
    \n
    >>> sc.gammasgn([1, 2, 3, 4])\narray([1., 1., 1., 1.])\n
    \n
    \n\n
    It alternates between -1 and 1 for negative integers.
    \n\n
    \n
    >>> sc.gammasgn([-0.5, -1.5, -2.5, -3.5])\narray([-1.,  1., -1.,  1.])\n
    \n
    \n\n
    It can be used to compute the gamma function.
    \n\n
    \n
    >>> x = [1.5, 0.5, -0.5, -1.5]\n>>> sc.gammasgn(x) * np.exp(sc.gammaln(x))\narray([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])\n>>> sc.gamma(x)\narray([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.rgamma": {"fullname": "pyerrors.special.rgamma", "modulename": "pyerrors.special", "qualname": "rgamma", "kind": "function", "doc": "
    rgamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    rgamma(z, out=None)
    \n\n
    Reciprocal of the gamma function.
    \n\n
    Defined as \\( 1 / \\Gamma(z) \\), where \\( \\Gamma \\) is the\ngamma function. For more on the gamma function see gamma.
    \n\n
    Parameters
    \n\n
      \n
    • z (array_like):\nReal or complex valued input
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Function results
      • \n
    \n\n
    See Also
    \n\n
    gamma,, gammaln,, loggamma  
    \n\n
    Notes
    \n\n
    The gamma function has no zeros and has simple poles at\nnonpositive integers, so rgamma is an entire function with zeros\nat the nonpositive integers. See the discussion in [dlmf]_ for\nmore details.
    \n\n
    References
    \n\n
    .. [dlmf] Nist, Digital Library of Mathematical functions,\n    https://dlmf.nist.gov/5.2#i
    \n\n
    Examples
    \n\n
    \n
    >>> import scipy.special as sc\n
    \n
    \n\n
    It is the reciprocal of the gamma function.
    \n\n
    \n
    >>> sc.rgamma([1, 2, 3, 4])\narray([1.        , 1.        , 0.5       , 0.16666667])\n>>> 1 / sc.gamma([1, 2, 3, 4])\narray([1.        , 1.        , 0.5       , 0.16666667])\n
    \n
    \n\n
    It is zero at nonpositive integers.
    \n\n
    \n
    >>> sc.rgamma([0, -1, -2, -3])\narray([0., 0., 0., 0.])\n
    \n
    \n\n
    It rapidly underflows to zero along the positive real axis.
    \n\n
    \n
    >>> sc.rgamma([10, 100, 179])\narray([2.75573192e-006, 1.07151029e-156, 0.00000000e+000])\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.multigammaln": {"fullname": "pyerrors.special.multigammaln", "modulename": "pyerrors.special", "qualname": "multigammaln", "kind": "function", "doc": "
    Returns the log of multivariate gamma, also sometimes called the\ngeneralized gamma.
    \n\n
    Parameters
    \n\n
      \n
    • a (ndarray):\nThe multivariate gamma is computed for each item of a.
      • \n
    • d (int):\nThe dimension of the space of integration.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (ndarray):\nThe values of the log multivariate gamma at the given points a.
      • \n
    \n\n
    Notes
    \n\n
    The formal definition of the multivariate gamma of dimension d for a real\na is
    \n\n
    $$\\Gamma_d(a) = \\int_{A>0} e^{-tr(A)} |A|^{a - (d+1)/2} dA$$
    \n\n
    with the condition \\( a > (d-1)/2 \\), and \\( A > 0 \\) being the set of\nall the positive definite matrices of dimension d.  Note that a is a\nscalar: the integrand only is multivariate, the argument is not (the\nfunction is defined over a subset of the real set).
    \n\n
    This can be proven to be equal to the much friendlier equation
    \n\n
    $$\\Gamma_d(a) = \\pi^{d(d-1)/4} \\prod_{i=1}^{d} \\Gamma(a - (i-1)/2).$$
    \n\n
    References
    \n\n
    R. J. Muirhead, Aspects of multivariate statistical theory (Wiley Series in\nprobability and mathematical statistics).
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.special import multigammaln, gammaln\n>>> a = 23.5\n>>> d = 10\n>>> multigammaln(a, d)\n454.1488605074416\n
    \n
    \n\n
    Verify that the result agrees with the logarithm of the equation\nshown above:
    \n\n
    \n
    >>> d*(d-1)/4*np.log(np.pi) + gammaln(a - 0.5*np.arange(0, d)).sum()\n454.1488605074416\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.kn": {"fullname": "pyerrors.special.kn", "modulename": "pyerrors.special", "qualname": "kn", "kind": "function", "doc": "
    Modified Bessel function of the second kind of integer order n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.j0": {"fullname": "pyerrors.special.j0", "modulename": "pyerrors.special", "qualname": "j0", "kind": "function", "doc": "
    j0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    j0(x, out=None)
    \n\n
    Bessel function of the first kind of order 0.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nArgument (float).
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • J (scalar or ndarray):\nValue of the Bessel function of the first kind of order 0 at x.
      • \n
    \n\n
    See Also
    \n\n
    jv:  Bessel function of real order and complex argument.
    \nspherical_jn:  spherical Bessel functions.  
    \n\n
    Notes
    \n\n
    The domain is divided into the intervals [0, 5] and (5, infinity). In the\nfirst interval the following rational approximation is used:
    \n\n
    $$J_0(x) \\approx (w - r_1^2)(w - r_2^2) \\frac{P_3(w)}{Q_8(w)},$$
    \n\n
    where \\( w = x^2 \\) and \\( r_1 \\), \\( r_2 \\) are the zeros of\n\\( J_0 \\), and \\( P_3 \\) and \\( Q_8 \\) are polynomials of degrees 3\nand 8, respectively.
    \n\n
    In the second interval, the Hankel asymptotic expansion is employed with\ntwo rational functions of degree 6/6 and 7/7.
    \n\n
    This function is a wrapper for the Cephes 1 routine j0.\nIt should not be confused with the spherical Bessel functions (see\nspherical_jn).
    \n\n
    References
    \n\n
    Examples
    \n\n
    Calculate the function at one point:
    \n\n
    \n
    >>> from scipy.special import j0\n>>> j0(1.)\n0.7651976865579665\n
    \n
    \n\n
    Calculate the function at several points:
    \n\n
    \n
    >>> import numpy as np\n>>> j0(np.array([-2., 0., 4.]))\narray([ 0.22389078,  1.        , -0.39714981])\n
    \n
    \n\n
    Plot the function from -20 to 20.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-20., 20., 1000)\n>>> y = j0(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.y0": {"fullname": "pyerrors.special.y0", "modulename": "pyerrors.special", "qualname": "y0", "kind": "function", "doc": "
    y0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    y0(x, out=None)
    \n\n
    Bessel function of the second kind of order 0.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nArgument (float).
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Y (scalar or ndarray):\nValue of the Bessel function of the second kind of order 0 at x.
      • \n
    \n\n
    See Also
    \n\n
    j0:  Bessel function of the first kind of order 0
    \nyv:  Bessel function of the first kind  
    \n\n
    Notes
    \n\n
    The domain is divided into the intervals [0, 5] and (5, infinity). In the\nfirst interval a rational approximation \\( R(x) \\) is employed to\ncompute,
    \n\n
    $$Y_0(x) = R(x) + \\frac{2 \\log(x) J_0(x)}{\\pi},$$
    \n\n
    where \\( J_0 \\) is the Bessel function of the first kind of order 0.
    \n\n
    In the second interval, the Hankel asymptotic expansion is employed with\ntwo rational functions of degree 6/6 and 7/7.
    \n\n
    This function is a wrapper for the Cephes 1 routine y0.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Calculate the function at one point:
    \n\n
    \n
    >>> from scipy.special import y0\n>>> y0(1.)\n0.08825696421567697\n
    \n
    \n\n
    Calculate at several points:
    \n\n
    \n
    >>> import numpy as np\n>>> y0(np.array([0.5, 2., 3.]))\narray([-0.44451873,  0.51037567,  0.37685001])\n
    \n
    \n\n
    Plot the function from 0 to 10.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(0., 10., 1000)\n>>> y = y0(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.j1": {"fullname": "pyerrors.special.j1", "modulename": "pyerrors.special", "qualname": "j1", "kind": "function", "doc": "
    j1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    j1(x, out=None)
    \n\n
    Bessel function of the first kind of order 1.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nArgument (float).
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • J (scalar or ndarray):\nValue of the Bessel function of the first kind of order 1 at x.
      • \n
    \n\n
    See Also
    \n\n
    jv:  Bessel function of the first kind
    \nspherical_jn:  spherical Bessel functions.  
    \n\n
    Notes
    \n\n
    The domain is divided into the intervals [0, 8] and (8, infinity). In the\nfirst interval a 24 term Chebyshev expansion is used. In the second, the\nasymptotic trigonometric representation is employed using two rational\nfunctions of degree 5/5.
    \n\n
    This function is a wrapper for the Cephes 1 routine j1.\nIt should not be confused with the spherical Bessel functions (see\nspherical_jn).
    \n\n
    References
    \n\n
    Examples
    \n\n
    Calculate the function at one point:
    \n\n
    \n
    >>> from scipy.special import j1\n>>> j1(1.)\n0.44005058574493355\n
    \n
    \n\n
    Calculate the function at several points:
    \n\n
    \n
    >>> import numpy as np\n>>> j1(np.array([-2., 0., 4.]))\narray([-0.57672481,  0.        , -0.06604333])\n
    \n
    \n\n
    Plot the function from -20 to 20.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-20., 20., 1000)\n>>> y = j1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.y1": {"fullname": "pyerrors.special.y1", "modulename": "pyerrors.special", "qualname": "y1", "kind": "function", "doc": "
    y1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    y1(x, out=None)
    \n\n
    Bessel function of the second kind of order 1.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nArgument (float).
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Y (scalar or ndarray):\nValue of the Bessel function of the second kind of order 1 at x.
      • \n
    \n\n
    See Also
    \n\n
    j1:  Bessel function of the first kind of order 1
    \nyn:  Bessel function of the second kind
    \nyv:  Bessel function of the second kind  
    \n\n
    Notes
    \n\n
    The domain is divided into the intervals [0, 8] and (8, infinity). In the\nfirst interval a 25 term Chebyshev expansion is used, and computing\n\\( J_1 \\) (the Bessel function of the first kind) is required. In the\nsecond, the asymptotic trigonometric representation is employed using two\nrational functions of degree 5/5.
    \n\n
    This function is a wrapper for the Cephes 1 routine y1.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Calculate the function at one point:
    \n\n
    \n
    >>> from scipy.special import y1\n>>> y1(1.)\n-0.7812128213002888\n
    \n
    \n\n
    Calculate at several points:
    \n\n
    \n
    >>> import numpy as np\n>>> y1(np.array([0.5, 2., 3.]))\narray([-1.47147239, -0.10703243,  0.32467442])\n
    \n
    \n\n
    Plot the function from 0 to 10.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(0., 10., 1000)\n>>> y = y1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.jn": {"fullname": "pyerrors.special.jn", "modulename": "pyerrors.special", "qualname": "jn", "kind": "function", "doc": "
    jv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    jv(v, z, out=None)
    \n\n
    Bessel function of the first kind of real order and complex argument.
    \n\n
    Parameters
    \n\n
      \n
    • v (array_like):\nOrder (float).
      • \n
    • z (array_like):\nArgument (float or complex).
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • J (scalar or ndarray):\nValue of the Bessel function, \\( J_v(z) \\).
      • \n
    \n\n
    See Also
    \n\n
    jve:  \\( J_v \\) with leading exponential behavior stripped off.
    \nspherical_jn:  spherical Bessel functions.
    \nj0:  faster version of this function for order 0.
    \nj1:  faster version of this function for order 1.  
    \n\n
    Notes
    \n\n
    For positive v values, the computation is carried out using the AMOS\n1 zbesj routine, which exploits the connection to the modified\nBessel function \\( I_v \\),
    \n\n
    $$J_v(z) = \\exp(v\\pi\\imath/2) I_v(-\\imath z)\\qquad (\\Im z > 0)
    \n\n
    J_v(z) = \\exp(-v\\pi\\imath/2) I_v(\\imath z)\\qquad (\\Im z < 0)$$
    \n\n
    For negative v values the formula,
    \n\n
    $$J_{-v}(z) = J_v(z) \\cos(\\pi v) - Y_v(z) \\sin(\\pi v)$$
    \n\n
    is used, where \\( Y_v(z) \\) is the Bessel function of the second\nkind, computed using the AMOS routine zbesy.  Note that the second\nterm is exactly zero for integer v; to improve accuracy the second\nterm is explicitly omitted for v values such that v = floor(v).
    \n\n
    Not to be confused with the spherical Bessel functions (see spherical_jn).
    \n\n
    References
    \n\n
    Examples
    \n\n
    Evaluate the function of order 0 at one point.
    \n\n
    \n
    >>> from scipy.special import jv\n>>> jv(0, 1.)\n0.7651976865579666\n
    \n
    \n\n
    Evaluate the function at one point for different orders.
    \n\n
    \n
    >>> jv(0, 1.), jv(1, 1.), jv(1.5, 1.)\n(0.7651976865579666, 0.44005058574493355, 0.24029783912342725)\n
    \n
    \n\n
    The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
    \n\n
    \n
    >>> jv([0, 1, 1.5], 1.)\narray([0.76519769, 0.44005059, 0.24029784])\n
    \n
    \n\n
    Evaluate the function at several points for order 0 by providing an\narray for z.
    \n\n
    \n
    >>> import numpy as np\n>>> points = np.array([-2., 0., 3.])\n>>> jv(0, points)\narray([ 0.22389078,  1.        , -0.26005195])\n
    \n
    \n\n
    If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
    \n\n
    \n
    >>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
    \n
    \n\n
    \n
    >>> jv(orders, points)\narray([[ 0.22389078,  1.        , -0.26005195],\n       [-0.57672481,  0.        ,  0.33905896]])\n
    \n
    \n\n
    Plot the functions of order 0 to 3 from -10 to 10.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> for i in range(4):\n...     ax.plot(x, jv(i, x), label=f'$J_{i!r}$')\n>>> ax.legend()\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.yn": {"fullname": "pyerrors.special.yn", "modulename": "pyerrors.special", "qualname": "yn", "kind": "function", "doc": "
    yn(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    yn(n, x, out=None)
    \n\n
    Bessel function of the second kind of integer order and real argument.
    \n\n
    Parameters
    \n\n
      \n
    • n (array_like):\nOrder (integer).
      • \n
    • x (array_like):\nArgument (float).
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Y (scalar or ndarray):\nValue of the Bessel function, \\( Y_n(x) \\).
      • \n
    \n\n
    See Also
    \n\n
    yv:  For real order and real or complex argument.
    \ny0:  faster implementation of this function for order 0
    \ny1:  faster implementation of this function for order 1  
    \n\n
    Notes
    \n\n
    Wrapper for the Cephes 1 routine yn.
    \n\n
    The function is evaluated by forward recurrence on n, starting with\nvalues computed by the Cephes routines y0 and y1. If n = 0 or 1,\nthe routine for y0 or y1 is called directly.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Evaluate the function of order 0 at one point.
    \n\n
    \n
    >>> from scipy.special import yn\n>>> yn(0, 1.)\n0.08825696421567697\n
    \n
    \n\n
    Evaluate the function at one point for different orders.
    \n\n
    \n
    >>> yn(0, 1.), yn(1, 1.), yn(2, 1.)\n(0.08825696421567697, -0.7812128213002888, -1.6506826068162546)\n
    \n
    \n\n
    The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
    \n\n
    \n
    >>> yn([0, 1, 2], 1.)\narray([ 0.08825696, -0.78121282, -1.65068261])\n
    \n
    \n\n
    Evaluate the function at several points for order 0 by providing an\narray for z.
    \n\n
    \n
    >>> import numpy as np\n>>> points = np.array([0.5, 3., 8.])\n>>> yn(0, points)\narray([-0.44451873,  0.37685001,  0.22352149])\n
    \n
    \n\n
    If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
    \n\n
    \n
    >>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
    \n
    \n\n
    \n
    >>> yn(orders, points)\narray([[-0.44451873,  0.37685001,  0.22352149],\n       [-1.47147239,  0.32467442, -0.15806046]])\n
    \n
    \n\n
    Plot the functions of order 0 to 3 from 0 to 10.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(0., 10., 1000)\n>>> for i in range(4):\n...     ax.plot(x, yn(i, x), label=f'$Y_{i!r}$')\n>>> ax.set_ylim(-3, 1)\n>>> ax.legend()\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.i0": {"fullname": "pyerrors.special.i0", "modulename": "pyerrors.special", "qualname": "i0", "kind": "function", "doc": "
    i0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    i0(x, out=None)
    \n\n
    Modified Bessel function of order 0.
    \n\n
    Defined as,
    \n\n
    $$I_0(x) = \\sum_{k=0}^\\infty \\frac{(x^2/4)^k}{(k!)^2} = J_0(\\imath x),$$
    \n\n
    where \\( J_0 \\) is the Bessel function of the first kind of order 0.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nArgument (float)
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • I (scalar or ndarray):\nValue of the modified Bessel function of order 0 at x.
      • \n
    \n\n
    See Also
    \n\n
    iv:  Modified Bessel function of any order
    \ni0e:  Exponentially scaled modified Bessel function of order 0  
    \n\n
    Notes
    \n\n
    The range is partitioned into the two intervals [0, 8] and (8, infinity).\nChebyshev polynomial expansions are employed in each interval.
    \n\n
    This function is a wrapper for the Cephes 1 routine i0.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Calculate the function at one point:
    \n\n
    \n
    >>> from scipy.special import i0\n>>> i0(1.)\n1.2660658777520082\n
    \n
    \n\n
    Calculate at several points:
    \n\n
    \n
    >>> import numpy as np\n>>> i0(np.array([-2., 0., 3.5]))\narray([2.2795853 , 1.        , 7.37820343])\n
    \n
    \n\n
    Plot the function from -10 to 10.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> y = i0(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.i1": {"fullname": "pyerrors.special.i1", "modulename": "pyerrors.special", "qualname": "i1", "kind": "function", "doc": "
    i1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    i1(x, out=None)
    \n\n
    Modified Bessel function of order 1.
    \n\n
    Defined as,
    \n\n
    $$I_1(x) = \\frac{1}{2}x \\sum_{k=0}^\\infty \\frac{(x^2/4)^k}{k! (k + 1)!}\n       = -\\imath J_1(\\imath x),$$
    \n\n
    where \\( J_1 \\) is the Bessel function of the first kind of order 1.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nArgument (float)
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • I (scalar or ndarray):\nValue of the modified Bessel function of order 1 at x.
      • \n
    \n\n
    See Also
    \n\n
    iv:  Modified Bessel function of the first kind
    \ni1e:  Exponentially scaled modified Bessel function of order 1  
    \n\n
    Notes
    \n\n
    The range is partitioned into the two intervals [0, 8] and (8, infinity).\nChebyshev polynomial expansions are employed in each interval.
    \n\n
    This function is a wrapper for the Cephes 1 routine i1.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Calculate the function at one point:
    \n\n
    \n
    >>> from scipy.special import i1\n>>> i1(1.)\n0.5651591039924851\n
    \n
    \n\n
    Calculate the function at several points:
    \n\n
    \n
    >>> import numpy as np\n>>> i1(np.array([-2., 0., 6.]))\narray([-1.59063685,  0.        , 61.34193678])\n
    \n
    \n\n
    Plot the function between -10 and 10.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> y = i1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.iv": {"fullname": "pyerrors.special.iv", "modulename": "pyerrors.special", "qualname": "iv", "kind": "function", "doc": "
    iv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    iv(v, z, out=None)
    \n\n
    Modified Bessel function of the first kind of real order.
    \n\n
    Parameters
    \n\n
      \n
    • v (array_like):\nOrder. If z is of real type and negative, v must be integer\nvalued.
      • \n
    • z (array_like of float or complex):\nArgument.
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the modified Bessel function.
      • \n
    \n\n
    See Also
    \n\n
    ive:  This function with leading exponential behavior stripped off.
    \ni0:  Faster version of this function for order 0.
    \ni1:  Faster version of this function for order 1.  
    \n\n
    Notes
    \n\n
    For real z and \\( v \\in [-50, 50] \\), the evaluation is carried out\nusing Temme's method 1.  For larger orders, uniform asymptotic\nexpansions are applied.
    \n\n
    For complex z and positive v, the AMOS 2 zbesi routine is\ncalled. It uses a power series for small z, the asymptotic expansion\nfor large abs(z), the Miller algorithm normalized by the Wronskian\nand a Neumann series for intermediate magnitudes, and the uniform\nasymptotic expansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large\norders. Backward recurrence is used to generate sequences or reduce\norders when necessary.
    \n\n
    The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,
    \n\n
    $$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$
    \n\n
    (valid when the real part of z is positive).  For negative v, the\nformula
    \n\n
    $$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$
    \n\n
    is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Evaluate the function of order 0 at one point.
    \n\n
    \n
    >>> from scipy.special import iv\n>>> iv(0, 1.)\n1.2660658777520084\n
    \n
    \n\n
    Evaluate the function at one point for different orders.
    \n\n
    \n
    >>> iv(0, 1.), iv(1, 1.), iv(1.5, 1.)\n(1.2660658777520084, 0.565159103992485, 0.2935253263474798)\n
    \n
    \n\n
    The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
    \n\n
    \n
    >>> iv([0, 1, 1.5], 1.)\narray([1.26606588, 0.5651591 , 0.29352533])\n
    \n
    \n\n
    Evaluate the function at several points for order 0 by providing an\narray for z.
    \n\n
    \n
    >>> import numpy as np\n>>> points = np.array([-2., 0., 3.])\n>>> iv(0, points)\narray([2.2795853 , 1.        , 4.88079259])\n
    \n
    \n\n
    If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
    \n\n
    \n
    >>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
    \n
    \n\n
    \n
    >>> iv(orders, points)\narray([[ 2.2795853 ,  1.        ,  4.88079259],\n       [-1.59063685,  0.        ,  3.95337022]])\n
    \n
    \n\n
    Plot the functions of order 0 to 3 from -5 to 5.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, iv(i, x), label=f'$I_{i!r}$')\n>>> ax.legend()\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Temme, Journal of Computational Physics, vol 21, 343 (1976) ↩
      \n
      2. \n\n
    2. \n
      Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
      \n
      3. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.ive": {"fullname": "pyerrors.special.ive", "modulename": "pyerrors.special", "qualname": "ive", "kind": "function", "doc": "
    ive(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    ive(v, z, out=None)
    \n\n
    Exponentially scaled modified Bessel function of the first kind.
    \n\n
    Defined as::
    \n\n
    ive(v, z) = iv(v, z) * exp(-abs(z.real))\n
    \n\n
    For imaginary numbers without a real part, returns the unscaled\nBessel function of the first kind iv.
    \n\n
    Parameters
    \n\n
      \n
    • v (array_like of float):\nOrder.
      • \n
    • z (array_like of float or complex):\nArgument.
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the exponentially scaled modified Bessel function.
      • \n
    \n\n
    See Also
    \n\n
    iv:  Modified Bessel function of the first kind
    \ni0e:  Faster implementation of this function for order 0
    \ni1e:  Faster implementation of this function for order 1  
    \n\n
    Notes
    \n\n
    For positive v, the AMOS 1 zbesi routine is called. It uses a\npower series for small z, the asymptotic expansion for large\nabs(z), the Miller algorithm normalized by the Wronskian and a\nNeumann series for intermediate magnitudes, and the uniform asymptotic\nexpansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large orders.\nBackward recurrence is used to generate sequences or reduce orders when\nnecessary.
    \n\n
    The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,
    \n\n
    $$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$
    \n\n
    (valid when the real part of z is positive).  For negative v, the\nformula
    \n\n
    $$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$
    \n\n
    is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.
    \n\n
    ive is useful for large arguments z: for these, iv easily overflows,\nwhile ive does not due to the exponential scaling.
    \n\n
    References
    \n\n
    Examples
    \n\n
    In the following example iv returns infinity whereas ive still returns\na finite number.
    \n\n
    \n
    >>> from scipy.special import iv, ive\n>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> iv(3, 1000.), ive(3, 1000.)\n(inf, 0.01256056218254712)\n
    \n
    \n\n
    Evaluate the function at one point for different orders by\nproviding a list or NumPy array as argument for the v parameter:
    \n\n
    \n
    >>> ive([0, 1, 1.5], 1.)\narray([0.46575961, 0.20791042, 0.10798193])\n
    \n
    \n\n
    Evaluate the function at several points for order 0 by providing an\narray for z.
    \n\n
    \n
    >>> points = np.array([-2., 0., 3.])\n>>> ive(0, points)\narray([0.30850832, 1.        , 0.24300035])\n
    \n
    \n\n
    Evaluate the function at several points for different orders by\nproviding arrays for both v for z. Both arrays have to be\nbroadcastable to the correct shape. To calculate the orders 0, 1\nand 2 for a 1D array of points:
    \n\n
    \n
    >>> ive([[0], [1], [2]], points)\narray([[ 0.30850832,  1.        ,  0.24300035],\n       [-0.21526929,  0.        ,  0.19682671],\n       [ 0.09323903,  0.        ,  0.11178255]])\n
    \n
    \n\n
    Plot the functions of order 0 to 3 from -5 to 5.
    \n\n
    \n
    >>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, ive(i, x), label=fr'$I_{i!r}(z)\\cdot e^{{-|z|}}$')\n>>> ax.legend()\n>>> ax.set_xlabel(r"$z$")\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erf": {"fullname": "pyerrors.special.erf", "modulename": "pyerrors.special", "qualname": "erf", "kind": "function", "doc": "
    erf(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    erf(z, out=None)
    \n\n
    Returns the error function of complex argument.
    \n\n
    It is defined as 2/sqrt(pi)*integral(exp(-t**2), t=0..z).
    \n\n
    Parameters
    \n\n
      \n
    • x (ndarray):\nInput array.
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (scalar or ndarray):\nThe values of the error function at the given points x.
      • \n
    \n\n
    See Also
    \n\n
    erfc,, erfinv,, erfcinv,, wofz,, erfcx,, erfi  
    \n\n
    Notes
    \n\n
    The cumulative of the unit normal distribution is given by\nPhi(z) = 1/2[1 + erf(z/sqrt(2))].
    \n\n
    References
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy import special\n>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-3, 3)\n>>> plt.plot(x, special.erf(x))\n>>> plt.xlabel('$x$')\n>>> plt.ylabel('$erf(x)$')\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfc": {"fullname": "pyerrors.special.erfc", "modulename": "pyerrors.special", "qualname": "erfc", "kind": "function", "doc": "
    erfc(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    erfc(x, out=None)
    \n\n
    Complementary error function, 1 - erf(x).
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nReal or complex valued argument
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the complementary error function
      • \n
    \n\n
    See Also
    \n\n
    erf,, erfi,, erfcx,, dawsn,, wofz  
    \n\n
    References
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy import special\n>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-3, 3)\n>>> plt.plot(x, special.erfc(x))\n>>> plt.xlabel('$x$')\n>>> plt.ylabel('$erfc(x)$')\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfinv": {"fullname": "pyerrors.special.erfinv", "modulename": "pyerrors.special", "qualname": "erfinv", "kind": "function", "doc": "
    erfinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    erfinv(y, out=None)
    \n\n
    Inverse of the error function.
    \n\n
    Computes the inverse of the error function.
    \n\n
    In the complex domain, there is no unique complex number w satisfying\nerf(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, -1 < x < 1, there is a unique real\nnumber satisfying erf(erfinv(x)) = x.
    \n\n
    Parameters
    \n\n
      \n
    • y (ndarray):\nArgument at which to evaluate. Domain: [-1, 1]
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • erfinv (scalar or ndarray):\nThe inverse of erf of y, element-wise
      • \n
    \n\n
    See Also
    \n\n
    erf:  Error function of a complex argument
    \nerfc:  Complementary error function, 1 - erf(x)
    \nerfcinv:  Inverse of the complementary error function  
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import erfinv, erf\n
    \n
    \n\n
    \n
    >>> erfinv(0.5)\n0.4769362762044699\n
    \n
    \n\n
    \n
    >>> y = np.linspace(-1.0, 1.0, num=9)\n>>> x = erfinv(y)\n>>> x\narray([       -inf, -0.81341985, -0.47693628, -0.22531206,  0.        ,\n        0.22531206,  0.47693628,  0.81341985,         inf])\n
    \n
    \n\n
    Verify that erf(erfinv(y)) is y.
    \n\n
    \n
    >>> erf(x)\narray([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])\n
    \n
    \n\n
    Plot the function:
    \n\n
    \n
    >>> y = np.linspace(-1, 1, 200)\n>>> fig, ax = plt.subplots()\n>>> ax.plot(y, erfinv(y))\n>>> ax.grid(True)\n>>> ax.set_xlabel('y')\n>>> ax.set_title('erfinv(y)')\n>>> plt.show()\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfcinv": {"fullname": "pyerrors.special.erfcinv", "modulename": "pyerrors.special", "qualname": "erfcinv", "kind": "function", "doc": "
    erfcinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    erfcinv(y, out=None)
    \n\n
    Inverse of the complementary error function.
    \n\n
    Computes the inverse of the complementary error function.
    \n\n
    In the complex domain, there is no unique complex number w satisfying\nerfc(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, 0 < x < 2, there is a unique real\nnumber satisfying erfc(erfcinv(x)) = erfcinv(erfc(x)).
    \n\n
    It is related to inverse of the error function by erfcinv(1-x) = erfinv(x)
    \n\n
    Parameters
    \n\n
      \n
    • y (ndarray):\nArgument at which to evaluate. Domain: [0, 2]
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • erfcinv (scalar or ndarray):\nThe inverse of erfc of y, element-wise
      • \n
    \n\n
    See Also
    \n\n
    erf:  Error function of a complex argument
    \nerfc:  Complementary error function, 1 - erf(x)
    \nerfinv:  Inverse of the error function  
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import erfcinv\n
    \n
    \n\n
    \n
    >>> erfcinv(0.5)\n0.4769362762044699\n
    \n
    \n\n
    \n
    >>> y = np.linspace(0.0, 2.0, num=11)\n>>> erfcinv(y)\narray([        inf,  0.9061938 ,  0.59511608,  0.37080716,  0.17914345,\n       -0.        , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,\n              -inf])\n
    \n
    \n\n
    Plot the function:
    \n\n
    \n
    >>> y = np.linspace(0, 2, 200)\n>>> fig, ax = plt.subplots()\n>>> ax.plot(y, erfcinv(y))\n>>> ax.grid(True)\n>>> ax.set_xlabel('y')\n>>> ax.set_title('erfcinv(y)')\n>>> plt.show()\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.logit": {"fullname": "pyerrors.special.logit", "modulename": "pyerrors.special", "qualname": "logit", "kind": "function", "doc": "
    logit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    \"\"\"\nlogit(x, out=None)
    \n\n
    Logit ufunc for ndarrays.
    \n\n
    The logit function is defined as logit(p) = log(p/(1-p)).\nNote that logit(0) = -inf, logit(1) = inf, and logit(p)\nfor p<0 or p>1 yields nan.
    \n\n
    Parameters
    \n\n
      \n
    • x (ndarray):\nThe ndarray to apply logit to element-wise.
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: An ndarray of the same shape as x. Its entries\nare logit of the corresponding entry of x.
      • \n
    \n\n
    See Also
    \n\n
    expit  
    \n\n
    Notes
    \n\n
    As a ufunc logit takes a number of optional\nkeyword arguments. For more information\nsee ufuncs 
    \n\n
    New in version 0.10.0.
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.special import logit, expit\n
    \n
    \n\n
    \n
    >>> logit([0, 0.25, 0.5, 0.75, 1])\narray([       -inf, -1.09861229,  0.        ,  1.09861229,         inf])\n
    \n
    \n\n
    expit is the inverse of logit:
    \n\n
    \n
    >>> expit(logit([0.1, 0.75, 0.999]))\narray([ 0.1  ,  0.75 ,  0.999])\n
    \n
    \n\n
    Plot logit(x) for x in [0, 1]:
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> x = np.linspace(0, 1, 501)\n>>> y = logit(x)\n>>> plt.plot(x, y)\n>>> plt.grid()\n>>> plt.ylim(-6, 6)\n>>> plt.xlabel('x')\n>>> plt.title('logit(x)')\n>>> plt.show()\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.expit": {"fullname": "pyerrors.special.expit", "modulename": "pyerrors.special", "qualname": "expit", "kind": "function", "doc": "
    expit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    expit(x, out=None)
    \n\n
    Expit (a.k.a. logistic sigmoid) ufunc for ndarrays.
    \n\n
    The expit function, also known as the logistic sigmoid function, is\ndefined as expit(x) = 1/(1+exp(-x)).  It is the inverse of the\nlogit function.
    \n\n
    Parameters
    \n\n
      \n
    • x (ndarray):\nThe ndarray to apply expit to element-wise.
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: An ndarray of the same shape as x. Its entries\nare expit of the corresponding entry of x.
      • \n
    \n\n
    See Also
    \n\n
    logit  
    \n\n
    Notes
    \n\n
    As a ufunc expit takes a number of optional\nkeyword arguments. For more information\nsee ufuncs 
    \n\n
    New in version 0.10.0.
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.special import expit, logit\n
    \n
    \n\n
    \n
    >>> expit([-np.inf, -1.5, 0, 1.5, np.inf])\narray([ 0.        ,  0.18242552,  0.5       ,  0.81757448,  1.        ])\n
    \n
    \n\n
    logit is the inverse of expit:
    \n\n
    \n
    >>> logit(expit([-2.5, 0, 3.1, 5.0]))\narray([-2.5,  0. ,  3.1,  5. ])\n
    \n
    \n\n
    Plot expit(x) for x in [-6, 6]:
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-6, 6, 121)\n>>> y = expit(x)\n>>> plt.plot(x, y)\n>>> plt.grid()\n>>> plt.xlim(-6, 6)\n>>> plt.xlabel('x')\n>>> plt.title('expit(x)')\n>>> plt.show()\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.logsumexp": {"fullname": "pyerrors.special.logsumexp", "modulename": "pyerrors.special", "qualname": "logsumexp", "kind": "function", "doc": "
    Compute the log of the sum of exponentials of input elements.
    \n\n
    Parameters
    \n\n
      \n
    • a (array_like):\nInput array.
      • \n
    • axis (None or int or tuple of ints, optional):\nAxis or axes over which the sum is taken. By default axis is None,\nand all elements are summed.
      \n\n
      New in version 0.11.0.
      • \n
    • b (array-like, optional):\nScaling factor for exp(a) must be of the same shape as a or\nbroadcastable to a. These values may be negative in order to\nimplement subtraction.
      \n\n
      New in version 0.12.0.
      • \n
    • keepdims (bool, optional):\nIf this is set to True, the axes which are reduced are left in the\nresult as dimensions with size one. With this option, the result\nwill broadcast correctly against the original array.
      \n\n
      New in version 0.15.0.
      • \n
    • return_sign (bool, optional):\nIf this is set to True, the result will be a pair containing sign\ninformation; if False, results that are negative will be returned\nas NaN. Default is False (no sign information).
      \n\n
      New in version 0.16.0.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (ndarray):\nThe result, np.log(np.sum(np.exp(a))) calculated in a numerically\nmore stable way. If b is given then np.log(np.sum(b*np.exp(a)))\nis returned. If return_sign is True, res contains the log of\nthe absolute value of the argument.
      • \n
    • sgn (ndarray):\nIf return_sign is True, this will be an array of floating-point\nnumbers matching res containing +1, 0, -1 (for real-valued inputs)\nor a complex phase (for complex inputs). This gives the sign of the\nargument of the logarithm in res.\nIf return_sign is False, only one result is returned.
      • \n
    \n\n
    See Also
    \n\n
    numpy.logaddexp,, numpy.logaddexp2  
    \n\n
    Notes
    \n\n
    NumPy has a logaddexp function which is very similar to logsumexp, but\nonly handles two arguments. logaddexp.reduce is similar to this\nfunction, but may be less stable.
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.special import logsumexp\n>>> a = np.arange(10)\n>>> logsumexp(a)\n9.4586297444267107\n>>> np.log(np.sum(np.exp(a)))\n9.4586297444267107\n
    \n
    \n\n
    With weights
    \n\n
    \n
    >>> a = np.arange(10)\n>>> b = np.arange(10, 0, -1)\n>>> logsumexp(a, b=b)\n9.9170178533034665\n>>> np.log(np.sum(b*np.exp(a)))\n9.9170178533034647\n
    \n
    \n\n
    Returning a sign flag
    \n\n
    \n
    >>> logsumexp([1,2],b=[1,-1],return_sign=True)\n(1.5413248546129181, -1.0)\n
    \n
    \n\n
    Notice that logsumexp does not directly support masked arrays. To use it\non a masked array, convert the mask into zero weights:
    \n\n
    \n
    >>> a = np.ma.array([np.log(2), 2, np.log(3)],\n...                  mask=[False, True, False])\n>>> b = (~a.mask).astype(int)\n>>> logsumexp(a.data, b=b), np.log(5)\n1.6094379124341005, 1.6094379124341005\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
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+    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"pyerrors": {"fullname": "pyerrors", "modulename": "pyerrors", "kind": "module", "doc": "
    What is pyerrors?
    \n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Installation
    \n\n
    Install the most recent release using pip and pypi:
    \n\n
    \n
    python -m pip install pyerrors     # Fresh install\npython -m pip install -U pyerrors  # Update\n
    \n
    \n\n
    Install the most recent release using conda and conda-forge:
    \n\n
    \n
    conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
    \n
    \n\n
    Install the current develop version:
    \n\n
    \n
    python -m pip install -U --no-deps --force-reinstall git+https://github.com/fjosw/pyerrors.git@develop\n
    \n
    \n\n
    (Also works for any feature branch).
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The gamma_method is not automatically called after every intermediate step in order to prevent computational overhead.
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.\nDirect visualizations of the performed fits can be triggered via resplot=True or qqplot=True.
    \n\n
    For all available options including combined fits to multiple datasets see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to as orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice.\nOther dependency (eg. spatial) are not supported.
    \n\n
    The Corr class can also deal with missing measurements or paddings for fixed boundary conditions.\nThe missing entries are represented via the None object.
    \n\n
    Initialization
    \n\n
    A simple correlator can be initialized with a list or a one-dimensional array of Obs or Cobs
    \n\n
    \n
    corr11 = pe.Corr([obs1, obs2])\ncorr11 = pe.Corr(np.array([obs1, obs2]))\n
    \n
    \n\n
    A matrix-valued correlator can either be initialized via a two-dimensional array of Corr objects
    \n\n
    \n
    matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]]))\n
    \n
    \n\n
    or alternatively via a three-dimensional array of Obs or CObs of shape (T, N, N) where T is\nthe temporal extent of the correlator and N is the dimension of the matrix.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion identified for this correlator.
      • \n
    \n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.tag": {"fullname": "pyerrors.correlators.Corr.tag", "modulename": "pyerrors.correlators", "qualname": "Corr.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.content": {"fullname": "pyerrors.correlators.Corr.content", "modulename": "pyerrors.correlators", "qualname": "Corr.content", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.T": {"fullname": "pyerrors.correlators.Corr.T", "modulename": "pyerrors.correlators", "qualname": "Corr.T", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prange": {"fullname": "pyerrors.correlators.Corr.prange", "modulename": "pyerrors.correlators", "qualname": "Corr.prange", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.trace": {"fullname": "pyerrors.correlators.Corr.trace", "modulename": "pyerrors.correlators", "qualname": "Corr.trace", "kind": "function", "doc": "
    Calculates the per-timeslice trace of a correlator matrix.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. (default)
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • None: The GEVP is solved only at ts, no sorting is necessary
        • \n
      • \n
    • vector_obs (bool):\nIf True, uncertainties are propagated in the eigenvector computation (default False).
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    • method (str):\nMethod used to solve the GEVP.\n
        \n
      • \"eigh\": Use scipy.linalg.eigh to solve the GEVP. (default for vector_obs=False)
        • \n
      • \"cholesky\": Use manually implemented solution via the Cholesky decomposition. Automatically chosen if vector_obs==True.
        • \n
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', vector_obs=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • parity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice:\n    - symmetric (default)\n        $$\\tilde{\\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$\n    - big_symmetric\n        $$\\partial^2_0 f(x_0) = \\frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$\n    - improved\n        $$\\partial^2_0 f(x_0) = \\frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$\n    - log\n        $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • fit_key (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tfit_key=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
    \n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.N": {"fullname": "pyerrors.correlators.Corr.N", "modulename": "pyerrors.correlators", "qualname": "Corr.N", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.name": {"fullname": "pyerrors.covobs.Covobs.name", "modulename": "pyerrors.covobs", "qualname": "Covobs.name", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.value": {"fullname": "pyerrors.covobs.Covobs.value", "modulename": "pyerrors.covobs", "qualname": "Covobs.value", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "kind": "variable", "doc": "
    \n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
    \n"}, "pyerrors.dirac.gammaX": {"fullname": "pyerrors.dirac.gammaX", "modulename": "pyerrors.dirac", "qualname": "gammaX", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n       [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaY": {"fullname": "pyerrors.dirac.gammaY", "modulename": "pyerrors.dirac", "qualname": "gammaY", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaZ": {"fullname": "pyerrors.dirac.gammaZ", "modulename": "pyerrors.dirac", "qualname": "gammaZ", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaT": {"fullname": "pyerrors.dirac.gammaT", "modulename": "pyerrors.dirac", "qualname": "gammaT", "kind": "variable", "doc": "
    \n", "default_value": "array([[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n       [1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"}, "pyerrors.dirac.gamma": {"fullname": "pyerrors.dirac.gamma", "modulename": "pyerrors.dirac", "qualname": "gamma", "kind": "variable", "doc": "
    \n", "default_value": "array([[[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n        [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n        [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],\n        [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]]])"}, "pyerrors.dirac.gamma5": {"fullname": "pyerrors.dirac.gamma5", "modulename": "pyerrors.dirac", "qualname": "gamma5", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"}, "pyerrors.dirac.identity": {"fullname": "pyerrors.dirac.identity", "modulename": "pyerrors.dirac", "qualname": "identity", "kind": "variable", "doc": "
    \n", "default_value": "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
      • \n
    \n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
      • \n
    \n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    • chisquare_by_dof (float):\nreduced chisquare.
      • \n
    • p_value (float):\np-value of the fit
      • \n
    • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.fit_parameters": {"fullname": "pyerrors.fits.Fit_result.fit_parameters", "modulename": "pyerrors.fits", "qualname": "Fit_result.fit_parameters", "kind": "variable", "doc": "
    \n"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x).\n    ```
    \n\n
    Parameters
    \n\n
      \n
    • For an uncombined fit:
      • \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n    return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • OR For a combined fit:
      • \n
    • x (dict):\ndict of lists.
      • \n
    • y (dict):\ndict of lists of Obs.
      • \n
    • funcs (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n        \"b\": func_b}
      \n\n
      def func_a(a, x):\n    return a[1] * anp.exp(-a[0] * x)
      \n\n
      def func_b(a, x):\n    return a[2] * anp.exp(-a[0] * x)
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • tol (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm < edm_max)
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
      • \n
    • inv_chol_cov_matrix [array,list], optional: array: shape = (no of y values) X (no of y values)\nlist:   for an uncombined fit: [\"\"]\nfor a combined fit: list of keys belonging to the corr_matrix saved in the array, must be the same as the keys of the y dict in alphabetical order\nIf correlated_fit=True is set as well, can provide an inverse covariance matrix (y errors, dy_f included!) of your own choosing for a correlated fit.\nThe matrix must be a lower triangular matrix constructed from a Cholesky decomposition: The function invert_corr_cov_cholesky(corr, inverrdiag) can be\nused to construct it from a correlation matrix (corr) and the errors dy_f of the data points (inverrdiag = np.diag(1 / np.asarray(dy_f))). For the correct\nordering the correlation matrix (corr) can be sorted via the function sort_corr(corr, kl, yd) where kl is the list of keys and yd the y dict.
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n\n
    Examples
    \n\n
    \n
    >>> # Example of a correlated (correlated_fit = True, inv_chol_cov_matrix handed over) combined fit, based on a randomly generated data set\n>>> import numpy as np\n>>> from scipy.stats import norm\n>>> from scipy.linalg import cholesky\n>>> import pyerrors as pe\n>>> # generating the random data set\n>>> num_samples = 400\n>>> N = 3\n>>> x = np.arange(N)\n>>> x1 = norm.rvs(size=(N, num_samples)) # generate random numbers\n>>> x2 = norm.rvs(size=(N, num_samples)) # generate random numbers\n>>> r = r1 = r2 = np.zeros((N, N))\n>>> y = {}\n>>> for i in range(N):\n>>>    for j in range(N):\n>>>        r[i, j] = np.exp(-0.8 * np.fabs(i - j)) # element in correlation matrix\n>>> errl = np.sqrt([3.4, 2.5, 3.6]) # set y errors\n>>> for i in range(N):\n>>>    for j in range(N):\n>>>        r[i, j] *= errl[i] * errl[j] # element in covariance matrix\n>>> c = cholesky(r, lower=True)\n>>> y = {'a': np.dot(c, x1), 'b': np.dot(c, x2)} # generate y data with the covariance matrix defined\n>>> # random data set has been generated, now the dictionaries and the inverse covariance matrix to be handed over are built\n>>> x_dict = {}\n>>> y_dict = {}\n>>> chol_inv_dict = {}\n>>> data = []\n>>> for key in y.keys():\n>>>    x_dict[key] = x\n>>>    for i in range(N):\n>>>        data.append(pe.Obs([[i + 1 + o for o in y[key][i]]], ['ens'])) # generate y Obs from the y data\n>>>    [o.gamma_method() for o in data]\n>>>    corr = pe.covariance(data, correlation=True)\n>>>    inverrdiag = np.diag(1 / np.asarray([o.dvalue for o in data]))\n>>>    chol_inv = pe.obs.invert_corr_cov_cholesky(corr, inverrdiag) # gives form of the inverse covariance matrix needed for the combined correlated fit below\n>>> y_dict = {'a': data[:3], 'b': data[3:]}\n>>> # common fit parameter p[0] in combined fit\n>>> def fit1(p, x):\n>>>    return p[0] + p[1] * x\n>>> def fit2(p, x):\n>>>    return p[0] + p[2] * x\n>>> fitf_dict = {'a': fit1, 'b':fit2}\n>>> fitp_inv_cov_combined_fit = pe.least_squares(x_dict,y_dict, fitf_dict, correlated_fit = True, inv_chol_cov_matrix = [chol_inv,['a','b']])\nFit with 3 parameters\nMethod: Levenberg-Marquardt\n`ftol` termination condition is satisfied.\nchisquare/d.o.f.: 0.5388013574561786 # random\nfit parameters [1.11897846 0.96361162 0.92325319] # random\n
    \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n    return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy.
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • fit_parameters (list[Obs]):\nLIist of fitted observables.
      • \n
    \n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n\n
    For uncorrelated data the residuals are expected to be distributed ~N(0,1).
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
    Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n\n
    Returns
    \n\n
      \n
    • err (np.array(Obs)):\nError band for an array of sample values x
      • \n
    \n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (List[Obs]):\nExtracted data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • success (int):\nreturns 0 is successful
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (dict):\nExtracted meson data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML formatted string of the input data
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML string generated from the data
      • \n
    \n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_hd5": {"fullname": "pyerrors.input.hadrons.read_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_hd5", "kind": "function", "doc": "
    Read hadrons hdf5 file and extract entry based on attributes.
    \n\n
    Parameters
    \n\n
      \n
    • filestem (str):\nFull namestem of the files to read, including the full path.
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • group (str):\nlabel of the group to be extracted.
      • \n
    • attrs (dict or int):\nDictionary containing the attributes. For example
      \n\n
      \n
      attrs = {"gamma_snk": "Gamma5",\n         "gamma_src": "Gamma5"}\n
      \n
      \n\n
      Alternatively an integer can be specified to identify the sub group.\nThis is discouraged as the order in the file is not guaranteed.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • part (str):\nstring specifying whether to extract the real part ('real'),\nthe imaginary part ('imag') or a complex correlator ('complex').\nDefault 'real'.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr (Corr):\nCorrelator of the source sink combination in question.
      • \n
    \n", "signature": "(filestem, ens_id, group, attrs=None, idl=None, part='real'):", "funcdef": "def"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr (Corr):\nCorrelator of the source sink combination in question.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
    Read hadrons FlowObservables hdf5 file and extract t0
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    \n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (dict):\nextracted DistillationContration data
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array.
    \nzeros:  Create an array, each element of which is zero.
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\").
    \ndtype:  Create a data-type.
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    \n
    >>> import numpy as np\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Npr_matrix):\nread Cobs-matrix
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict[Npr_matrix]):\nextracted Bilinears
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict):\nextracted fourquark matrizes
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • json_string (str):\nString for export to .json(.gz) file
      • \n
    \n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Null
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (Obs / list / Corr):\nRead data
      • \n
    • or
      • \n
    • data (dict):\nRead data and meta-data
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "
    Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).
    \n\n
    It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.
    \n\n
    A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
      • \n
    • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • root (Obs):\nThe root of the data series.
      • \n
    \n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
    Read pbp format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of observables read
      • \n
    \n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • rwms (Obs):\nReweighting factors read
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
    Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • t0 (Obs):\nExtracted t0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "
    Extract w0/a from given .ms.dat files. Returns w0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • w0 (Obs):\nExtracted w0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Obs):\nRead topological charge
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nThe directory to search for the files in.
      • \n
    • prefix (str):\nThe prefix to match the files against.
      • \n
    • qc (str):\nThe quark combination extension to match the files against.
      • \n
    • corr (str):\nThe correlator to extract data for.
      • \n
    • sep (str, optional):\nThe separator to use when parsing the replika names.
      • \n
    • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
      \n\n
        \n
      • names (List[str]): A list of names to use for the replicas.
        • \n
      • files (List[str]): A list of files to read data from.
        • \n
      • idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.
        • \n
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
      • \n
    • or
      • \n
    • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
      • \n
    \n\n
    Raises
    \n\n
      \n
    • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
      • \n
    • IOError: If there is an error reading a file.
      • \n
    • struct.error: If there is an error unpacking binary data.
      • \n
    \n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.sep": {"fullname": "pyerrors.input.sfcf.sep", "modulename": "pyerrors.input.sfcf", "qualname": "sep", "kind": "variable", "doc": "
    \n", "default_value": "'/'"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
    Read sfcf files from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type (str):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.sfcf.read_sfcf_multi": {"fullname": "pyerrors.input.sfcf.read_sfcf_multi", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf_multi", "kind": "function", "doc": "
    Read sfcf files from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks_list (list[str]):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type_list (list[str]):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset_list (list[int]):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf_list (int):\nID of wave function
      • \n
    • wf2_list (list[int]):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list[list[int]]):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    • rep_string (str):\nSeparator of ensemble name and replicum. Example: In \"ensAr0\", \"r\" would be the separator string.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (dict[list[Obs]]):\ndict with one of the following properties:\nif keyed_out:\n    dict[key] = list[Obs]\n    where key has the form name/quarks/offset/wf/wf2\nif not keyed_out:\n    dict[name][quarks][offset][wf][wf2] = list[Obs]
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname_list,\tquarks_list=['.*'],\tcorr_type_list=['bi'],\tnoffset_list=[0],\twf_list=[0],\twf2_list=[0],\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\tkeyed_out=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "
    Sorts a list of names of replika with searches for r and id in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • ll (list):\nlist to sort
      • \n
    \n\n
    Returns
    \n\n
      \n
    • ll (list):\nsorted list
      • \n
    \n", "signature": "(ll):", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n\n
    Returns
    \n\n
      \n
    • miss_str (str):\nstring with integers of which idls are missing
      • \n
    \n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.input.utils.check_params": {"fullname": "pyerrors.input.utils.check_params", "modulename": "pyerrors.input.utils", "qualname": "check_params", "kind": "function", "doc": "
    Check if, for sfcf, the parameter hashes at the end of the parameter files are in fact the expected one.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nmeasurement path, same as for sfcf read method
      • \n
    • param_hash (str):\nexpected parameter hash
      • \n
    • prefix (str):\ndata prefix to find the appropriate replicum folders in path
      • \n
    • param_prefix (str):\nprefix of the parameter file. Defaults to 'parameters_'
      • \n
    \n\n
    Returns
    \n\n
      \n
    • nums (dict):\ndictionary of faulty parameter files sorted by the replica paths
      • \n
    \n", "signature": "(path, param_hash, prefix, param_prefix='parameters_'):", "funcdef": "def"}, "pyerrors.integrate": {"fullname": "pyerrors.integrate", "modulename": "pyerrors.integrate", "kind": "module", "doc": "
    \n"}, "pyerrors.integrate.quad": {"fullname": "pyerrors.integrate.quad", "modulename": "pyerrors.integrate", "qualname": "quad", "kind": "function", "doc": "
    Performs a (one-dimensional) numeric integration of f(p, x) from a to b.
    \n\n
    The integration is performed using scipy.integrate.quad().\nAll parameters that can be passed to scipy.integrate.quad may also be passed to this function.\nThe output is the same as for scipy.integrate.quad, the first element being an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\nfunction to integrate, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(p, x):\n    return p[0] + p[1] * x + p[2] * anp.sinh(x)\n
      \n
      \n\n
      where x is the integration variable.
      • \n
    • p (list of floats or Obs):\nparameters of the function func.
      • \n
    • a (float or Obs):\nLower limit of integration (use -numpy.inf for -infinity).
      • \n
    • b (float or Obs):\nUpper limit of integration (use -numpy.inf for -infinity).
      • \n
    • All parameters of scipy.integrate.quad
      • \n
    \n\n
    Returns
    \n\n
      \n
    • y (Obs):\nThe integral of func from a to b.
      • \n
    • abserr (float):\nAn estimate of the absolute error in the result.
      • \n
    • infodict (dict):\nA dictionary containing additional information.\nRun scipy.integrate.quad_explain() for more information.
      • \n
    • message: A convergence message.
      • \n
    • explain: Appended only with 'cos' or 'sin' weighting and infinite\nintegration limits, it contains an explanation of the codes in\ninfodict['ierlst']
      • \n
    \n", "signature": "(func, p, a, b, **kwargs):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eigv": {"fullname": "pyerrors.linalg.eigv", "modulename": "pyerrors.linalg", "qualname": "eigv", "kind": "function", "doc": "
    Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "
    Print information about version of python, pyerrors and dependencies.
    \n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "
    pyerrors wrapper for the errorbars method of matplotlib
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nA list of x-values which can be Obs.
      • \n
    • y (list):\nA list of y-values which can be Obs.
      • \n
    • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
      • \n
    \n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n\n
    Returns
    \n\n
      \n
    • object (Obs):\nLoaded Object
      • \n
    \n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nGenerated Observable
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr_obs (list[Obs]):\nGenerated observable list
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • energy_levels (list[Obs]):\nExtracted energy levels
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "
    \n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "
    \n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "
    \n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "
    Export bootstrap samples from the Obs
    \n\n
    Parameters
    \n\n
      \n
    • samples (int):\nNumber of bootstrap samples to generate.
      • \n
    • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
      • \n
    • save_rng (str):\nSave the random numbers to a file if a path is specified.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).
      • \n
    \n", "signature": "(self, samples=500, random_numbers=None, save_rng=None):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
    \n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.gamma_method": {"fullname": "pyerrors.obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "gamma_method", "kind": "function", "doc": "
    Vectorized version of the gamma_method applicable to lists or arrays of Obs.
    \n\n
    See docstring of pe.Obs.gamma_method for details.
    \n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.gm": {"fullname": "pyerrors.obs.gm", "modulename": "pyerrors.obs", "qualname": "gm", "kind": "function", "doc": "
    Vectorized version of the gamma_method applicable to lists or arrays of Obs.
    \n\n
    See docstring of pe.Obs.gamma_method for details.
    \n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.invert_corr_cov_cholesky": {"fullname": "pyerrors.obs.invert_corr_cov_cholesky", "modulename": "pyerrors.obs", "qualname": "invert_corr_cov_cholesky", "kind": "function", "doc": "
    Constructs a lower triangular matrix chol via the Cholesky decomposition of the correlation matrix corr\n   and then returns the inverse covariance matrix chol_inv as a lower triangular matrix by solving chol * x = inverrdiag.
    \n\n
    Parameters
    \n\n
      \n
    • corr (np.ndarray):\ncorrelation matrix
      • \n
    • inverrdiag (np.ndarray):\ndiagonal matrix, the entries are the inverse errors of the data points considered
      • \n
    \n", "signature": "(corr, inverrdiag):", "funcdef": "def"}, "pyerrors.obs.sort_corr": {"fullname": "pyerrors.obs.sort_corr", "modulename": "pyerrors.obs", "qualname": "sort_corr", "kind": "function", "doc": "
    Reorders a correlation matrix to match the alphabetical order of its underlying y data.
    \n\n
    The ordering of the input correlation matrix corr is given by the list of keys kl.\nThe input dictionary yd (with the same keys kl) must contain the corresponding y data\nthat the correlation matrix is based on.\nThis function sorts the list of keys kl alphabetically and sorts the matrix corr\naccording to this alphabetical order such that the sorted matrix corr_sorted corresponds\nto the y data yd when arranged in an alphabetical order by its keys.
    \n\n
    Parameters
    \n\n
      \n
    • corr (np.ndarray):\nA square correlation matrix constructed using the order of the y data specified by kl.\nThe dimensions of corr should match the total number of y data points in yd combined.
      • \n
    • kl (list of str):\nA list of keys that denotes the order in which the y data from yd was used to build the\ninput correlation matrix corr.
      • \n
    • yd (dict of list):\nA dictionary where each key corresponds to a unique identifier, and its value is a list of\ny data points. The total number of y data points across all keys must match the dimensions\nof corr. The lists in the dictionary can be lists of Obs.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • np.ndarray: A new, sorted correlation matrix that corresponds to the y data from yd when arranged alphabetically by its keys.
      • \n
    \n\n
    Example
    \n\n
    \n
    >>> import numpy as np\n>>> import pyerrors as pe\n>>> corr = np.array([[1, 0.2, 0.3], [0.2, 1, 0.4], [0.3, 0.4, 1]])\n>>> kl = ['b', 'a']\n>>> yd = {'a': [1, 2], 'b': [3]}\n>>> sorted_corr = pe.obs.sort_corr(corr, kl, yd)\n>>> print(sorted_corr)\narray([[1. , 0.3, 0.4],\n       [0.3, 1. , 0.2],\n       [0.4, 0.2, 1. ]])\n
    \n
    \n", "signature": "(corr, kl, yd):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.import_bootstrap": {"fullname": "pyerrors.obs.import_bootstrap", "modulename": "pyerrors.obs", "qualname": "import_bootstrap", "kind": "function", "doc": "
    Imports bootstrap samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • boots (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N bootstrap samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples,\nwhere samples is the number of bootstrap samples and length is the length of the original Monte Carlo\nchain to be reconstructed.
      • \n
    \n", "signature": "(boots, name, random_numbers):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n    return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nObs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.special": {"fullname": "pyerrors.special", "modulename": "pyerrors.special", "kind": "module", "doc": "
    \n"}, "pyerrors.special.beta": {"fullname": "pyerrors.special.beta", "modulename": "pyerrors.special", "qualname": "beta", "kind": "function", "doc": "
    beta(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    beta(a, b, out=None)
    \n\n
    Beta function.
    \n\n
    This function is defined in 1 as
    \n\n
    $$B(a, b) = \\int_0^1 t^{a-1}(1-t)^{b-1}dt\n        = \\frac{\\Gamma(a)\\Gamma(b)}{\\Gamma(a+b)},$$
    \n\n
    where \\( \\Gamma \\) is the gamma function.
    \n\n
    Parameters
    \n\n
      \n
    • a, b (array_like):\nReal-valued arguments
      • \n
    • out (ndarray, optional):\nOptional output array for the function result
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Value of the beta function
      • \n
    \n\n
    See Also
    \n\n
    gamma:  the gamma function
    \nbetainc:   the regularized incomplete beta function
    \nbetaln:  the natural logarithm of the absolute\nvalue of the beta function  
    \n\n
    References
    \n\n
    Examples
    \n\n
    \n
    >>> import scipy.special as sc\n
    \n
    \n\n
    The beta function relates to the gamma function by the\ndefinition given above:
    \n\n
    \n
    >>> sc.beta(2, 3)\n0.08333333333333333\n>>> sc.gamma(2)*sc.gamma(3)/sc.gamma(2 + 3)\n0.08333333333333333\n
    \n
    \n\n
    As this relationship demonstrates, the beta function\nis symmetric:
    \n\n
    \n
    >>> sc.beta(1.7, 2.4)\n0.16567527689031739\n>>> sc.beta(2.4, 1.7)\n0.16567527689031739\n
    \n
    \n\n
    This function satisfies \\( B(1, b) = 1/b \\):
    \n\n
    \n
    >>> sc.beta(1, 4)\n0.25\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      NIST Digital Library of Mathematical Functions,\nEq. 5.12.1. https://dlmf.nist.gov/5.12 ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.betainc": {"fullname": "pyerrors.special.betainc", "modulename": "pyerrors.special", "qualname": "betainc", "kind": "function", "doc": "
    betainc(x1, x2, x3, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    betainc(a, b, x, out=None)
    \n\n
    Regularized incomplete beta function.
    \n\n
    Computes the regularized incomplete beta function, defined as 1:
    \n\n
    $$I_x(a, b) = \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)} \\int_0^x\nt^{a-1}(1-t)^{b-1}dt,$$
    \n\n
    for \\( 0 \\leq x \\leq 1 \\).
    \n\n
    This function is the cumulative distribution function for the beta\ndistribution; its range is [0, 1].
    \n\n
    Parameters
    \n\n
      \n
    • a, b (array_like):\nPositive, real-valued parameters
      • \n
    • x (array_like):\nReal-valued such that \\( 0 \\leq x \\leq 1 \\),\nthe upper limit of integration
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Value of the regularized incomplete beta function
      • \n
    \n\n
    See Also
    \n\n
    beta:  beta function
    \nbetaincinv:  inverse of the regularized incomplete beta function
    \nbetaincc:  complement of the regularized incomplete beta function
    \nscipy.stats.beta:  beta distribution  
    \n\n
    Notes
    \n\n
    The term regularized in the name of this function refers to the\nscaling of the function by the gamma function terms shown in the\nformula.  When not qualified as regularized, the name incomplete\nbeta function often refers to just the integral expression,\nwithout the gamma terms.  One can use the function beta from\nscipy.special to get this \"nonregularized\" incomplete beta\nfunction by multiplying the result of betainc(a, b, x) by\nbeta(a, b).
    \n\n
    This function wraps the ibeta routine from the\nBoost Math C++ library 2.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Let \\( B(a, b) \\) be the beta function.
    \n\n
    \n
    >>> import scipy.special as sc\n
    \n
    \n\n
    The coefficient in terms of gamma is equal to\n\\( 1/B(a, b) \\). Also, when \\( x=1 \\)\nthe integral is equal to \\( B(a, b) \\).\nTherefore, \\( I_{x=1}(a, b) = 1 \\) for any \\( a, b \\).
    \n\n
    \n
    >>> sc.betainc(0.2, 3.5, 1.0)\n1.0\n
    \n
    \n\n
    It satisfies\n\\( I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b)) \\),\nwhere \\( F \\) is the hypergeometric function hyp2f1:
    \n\n
    \n
    >>> a, b, x = 1.4, 3.1, 0.5\n>>> x**a * sc.hyp2f1(a, 1 - b, a + 1, x)/(a * sc.beta(a, b))\n0.8148904036225295\n>>> sc.betainc(a, b, x)\n0.8148904036225296\n
    \n
    \n\n
    This functions satisfies the relationship\n\\( I_x(a, b) = 1 - I_{1-x}(b, a) \\):
    \n\n
    \n
    >>> sc.betainc(2.2, 3.1, 0.4)\n0.49339638807619446\n>>> 1 - sc.betainc(3.1, 2.2, 1 - 0.4)\n0.49339638807619446\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/8.17 ↩
      \n
      2. \n\n
    2. \n
      The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/. ↩
      \n
      3. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.betaln": {"fullname": "pyerrors.special.betaln", "modulename": "pyerrors.special", "qualname": "betaln", "kind": "function", "doc": "
    betaln(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    betaln(a, b, out=None)
    \n\n
    Natural logarithm of absolute value of beta function.
    \n\n
    Computes ln(abs(beta(a, b))).
    \n\n
    Parameters
    \n\n
      \n
    • a, b (array_like):\nPositive, real-valued parameters
      • \n
    • out (ndarray, optional):\nOptional output array for function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Value of the betaln function
      • \n
    \n\n
    See Also
    \n\n
    gamma:  the gamma function
    \nbetainc:   the regularized incomplete beta function
    \nbeta:  the beta function  
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.special import betaln, beta\n
    \n
    \n\n
    Verify that, for moderate values of a and b, betaln(a, b)\nis the same as log(beta(a, b)):
    \n\n
    \n
    >>> betaln(3, 4)\n-4.0943445622221\n
    \n
    \n\n
    \n
    >>> np.log(beta(3, 4))\n-4.0943445622221\n
    \n
    \n\n
    In the following beta(a, b) underflows to 0, so we can't compute\nthe logarithm of the actual value.
    \n\n
    \n
    >>> a = 400\n>>> b = 900\n>>> beta(a, b)\n0.0\n
    \n
    \n\n
    We can compute the logarithm of beta(a, b) by using betaln:
    \n\n
    \n
    >>> betaln(a, b)\n-804.3069951764146\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.polygamma": {"fullname": "pyerrors.special.polygamma", "modulename": "pyerrors.special", "qualname": "polygamma", "kind": "function", "doc": "
    Polygamma functions.
    \n\n
    Defined as \\( \\psi^{(n)}(x) \\) where \\( \\psi \\) is the\ndigamma function. See [dlmf]_ for details.
    \n\n
    Parameters
    \n\n
      \n
    • n (array_like):\nThe order of the derivative of the digamma function; must be\nintegral
      • \n
    • x (array_like):\nReal valued input
      • \n
    \n\n
    Returns
    \n\n
      \n
    • ndarray: Function results
      • \n
    \n\n
    See Also
    \n\n
    digamma  
    \n\n
    References
    \n\n
    .. [dlmf] NIST, Digital Library of Mathematical Functions,\n    https://dlmf.nist.gov/5.15
    \n\n
    Examples
    \n\n
    \n
    >>> from scipy import special\n>>> x = [2, 3, 25.5]\n>>> special.polygamma(1, x)\narray([ 0.64493407,  0.39493407,  0.03999467])\n>>> special.polygamma(0, x) == special.psi(x)\narray([ True,  True,  True], dtype=bool)\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.psi": {"fullname": "pyerrors.special.psi", "modulename": "pyerrors.special", "qualname": "psi", "kind": "function", "doc": "
    psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    psi(z, out=None)
    \n\n
    The digamma function.
    \n\n
    The logarithmic derivative of the gamma function evaluated at z.
    \n\n
    Parameters
    \n\n
      \n
    • z (array_like):\nReal or complex argument.
      • \n
    • out (ndarray, optional):\nArray for the computed values of psi.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • digamma (scalar or ndarray):\nComputed values of psi.
      • \n
    \n\n
    Notes
    \n\n
    For large values not close to the negative real axis, psi is\ncomputed using the asymptotic series (5.11.2) from 1. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from 2 is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from 3 is\nused first. Note that psi has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using 4, so the\nfunction should maintain full accuracy around the origin.
    \n\n
    References
    \n\n
    Examples
    \n\n
    \n
    >>> from scipy.special import psi\n>>> z = 3 + 4j\n>>> psi(z)\n(1.55035981733341+1.0105022091860445j)\n
    \n
    \n\n
    Verify psi(z) = psi(z + 1) - 1/z:
    \n\n
    \n
    >>> psi(z + 1) - 1/z\n(1.55035981733341+1.0105022091860445j)\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
      \n
      2. \n\n
    2. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
      \n
      3. \n\n
    3. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
      \n
      4. \n\n
    4. \n
      Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ ↩
      \n
      5. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.digamma": {"fullname": "pyerrors.special.digamma", "modulename": "pyerrors.special", "qualname": "digamma", "kind": "function", "doc": "
    psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    psi(z, out=None)
    \n\n
    The digamma function.
    \n\n
    The logarithmic derivative of the gamma function evaluated at z.
    \n\n
    Parameters
    \n\n
      \n
    • z (array_like):\nReal or complex argument.
      • \n
    • out (ndarray, optional):\nArray for the computed values of psi.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • digamma (scalar or ndarray):\nComputed values of psi.
      • \n
    \n\n
    Notes
    \n\n
    For large values not close to the negative real axis, psi is\ncomputed using the asymptotic series (5.11.2) from 1. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from 2 is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from 3 is\nused first. Note that psi has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using 4, so the\nfunction should maintain full accuracy around the origin.
    \n\n
    References
    \n\n
    Examples
    \n\n
    \n
    >>> from scipy.special import psi\n>>> z = 3 + 4j\n>>> psi(z)\n(1.55035981733341+1.0105022091860445j)\n
    \n
    \n\n
    Verify psi(z) = psi(z + 1) - 1/z:
    \n\n
    \n
    >>> psi(z + 1) - 1/z\n(1.55035981733341+1.0105022091860445j)\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
      \n
      2. \n\n
    2. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
      \n
      3. \n\n
    3. \n
      NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
      \n
      4. \n\n
    4. \n
      Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ ↩
      \n
      5. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gamma": {"fullname": "pyerrors.special.gamma", "modulename": "pyerrors.special", "qualname": "gamma", "kind": "function", "doc": "
    gamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    gamma(z, out=None)
    \n\n
    gamma function.
    \n\n
    The gamma function is defined as
    \n\n
    $$\\Gamma(z) = \\int_0^\\infty t^{z-1} e^{-t} dt$$
    \n\n
    for \\( \\Re(z) > 0 \\) and is extended to the rest of the complex\nplane by analytic continuation. See [dlmf]_ for more details.
    \n\n
    Parameters
    \n\n
      \n
    • z (array_like):\nReal or complex valued argument
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the gamma function
      • \n
    \n\n
    Notes
    \n\n
    The gamma function is often referred to as the generalized\nfactorial since \\( \\Gamma(n + 1) = n! \\) for natural numbers\n\\( n \\). More generally it satisfies the recurrence relation\n\\( \\Gamma(z + 1) = z \\cdot \\Gamma(z) \\) for complex \\( z \\),\nwhich, combined with the fact that \\( \\Gamma(1) = 1 \\), implies\nthe above identity for \\( z = n \\).
    \n\n
    The gamma function has poles at non-negative integers and the sign\nof infinity as z approaches each pole depends upon the direction in\nwhich the pole is approached. For this reason, the consistent thing\nis for gamma(z) to return NaN at negative integers, and to return\n-inf when x = -0.0 and +inf when x = 0.0, using the signbit of zero\nto signify the direction in which the origin is being approached. This\nis for instance what is recommended for the gamma function in annex F\nentry 9.5.4 of the Iso C 99 standard [isoc99]_.
    \n\n
    Prior to SciPy version 1.15, scipy.special.gamma(z) returned +inf\nat each pole. This was fixed in version 1.15, but with the following\nconsequence. Expressions where gamma appears in the denominator\nsuch as
    \n\n
    gamma(u) * gamma(v) / (gamma(w) * gamma(x))
    \n\n
    no longer evaluate to 0 if the numerator is well defined but there is a\npole in the denominator. Instead such expressions evaluate to NaN. We\nrecommend instead using the function rgamma for the reciprocal gamma\nfunction in such cases. The above expression could for instance be written\nas
    \n\n
    gamma(u) * gamma(v) * (rgamma(w) * rgamma(x))
    \n\n
    References
    \n\n
    .. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5.2#E1\n.. [isoc99] https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.special import gamma, factorial\n
    \n
    \n\n
    \n
    >>> gamma([0, 0.5, 1, 5])\narray([         inf,   1.77245385,   1.        ,  24.        ])\n
    \n
    \n\n
    \n
    >>> z = 2.5 + 1j\n>>> gamma(z)\n(0.77476210455108352+0.70763120437959293j)\n>>> gamma(z+1), z*gamma(z)  # Recurrence property\n((1.2292740569981171+2.5438401155000685j),\n (1.2292740569981158+2.5438401155000658j))\n
    \n
    \n\n
    \n
    >>> gamma(0.5)**2  # gamma(0.5) = sqrt(pi)\n3.1415926535897927\n
    \n
    \n\n
    Plot gamma(x) for real x
    \n\n
    \n
    >>> x = np.linspace(-3.5, 5.5, 2251)\n>>> y = gamma(x)\n
    \n
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> plt.plot(x, y, 'b', alpha=0.6, label='gamma(x)')\n>>> k = np.arange(1, 7)\n>>> plt.plot(k, factorial(k-1), 'k*', alpha=0.6,\n...          label='(x-1)!, x = 1, 2, ...')\n>>> plt.xlim(-3.5, 5.5)\n>>> plt.ylim(-10, 25)\n>>> plt.grid()\n>>> plt.xlabel('x')\n>>> plt.legend(loc='lower right')\n>>> plt.show()\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammaln": {"fullname": "pyerrors.special.gammaln", "modulename": "pyerrors.special", "qualname": "gammaln", "kind": "function", "doc": "
    gammaln(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    gammaln(x, out=None)
    \n\n
    Logarithm of the absolute value of the gamma function.
    \n\n
    Defined as
    \n\n
    $$\\ln(\\lvert\\Gamma(x)\\rvert)$$
    \n\n
    where \\( \\Gamma \\) is the gamma function. For more details on\nthe gamma function, see [dlmf]_.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nReal argument
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the log of the absolute value of gamma
      • \n
    \n\n
    See Also
    \n\n
    gammasgn:  sign of the gamma function
    \nloggamma:  principal branch of the logarithm of the gamma function  
    \n\n
    Notes
    \n\n
    It is the same function as the Python standard library function\nmath.lgamma().
    \n\n
    When used in conjunction with gammasgn, this function is useful\nfor working in logspace on the real axis without having to deal\nwith complex numbers via the relation exp(gammaln(x)) =\ngammasgn(x) * gamma(x).
    \n\n
    For complex-valued log-gamma, use loggamma instead of gammaln.
    \n\n
    References
    \n\n
    .. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> import scipy.special as sc\n
    \n
    \n\n
    It has two positive zeros.
    \n\n
    \n
    >>> sc.gammaln([1, 2])\narray([0., 0.])\n
    \n
    \n\n
    It has poles at nonpositive integers.
    \n\n
    \n
    >>> sc.gammaln([0, -1, -2, -3, -4])\narray([inf, inf, inf, inf, inf])\n
    \n
    \n\n
    It asymptotically approaches x * log(x) (Stirling's formula).
    \n\n
    \n
    >>> x = np.array([1e10, 1e20, 1e40, 1e80])\n>>> sc.gammaln(x)\narray([2.20258509e+11, 4.50517019e+21, 9.11034037e+41, 1.83206807e+82])\n>>> x * np.log(x)\narray([2.30258509e+11, 4.60517019e+21, 9.21034037e+41, 1.84206807e+82])\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammainc": {"fullname": "pyerrors.special.gammainc", "modulename": "pyerrors.special", "qualname": "gammainc", "kind": "function", "doc": "
    gammainc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    gammainc(a, x, out=None)
    \n\n
    Regularized lower incomplete gamma function.
    \n\n
    It is defined as
    \n\n
    $$P(a, x) = \\frac{1}{\\Gamma(a)} \\int_0^x t^{a - 1}e^{-t} dt$$
    \n\n
    for \\( a > 0 \\) and \\( x \\geq 0 \\). See [dlmf]_ for details.
    \n\n
    Parameters
    \n\n
      \n
    • a (array_like):\nPositive parameter
      • \n
    • x (array_like):\nNonnegative argument
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the lower incomplete gamma function
      • \n
    \n\n
    See Also
    \n\n
    gammaincc:  regularized upper incomplete gamma function
    \ngammaincinv:  inverse of the regularized lower incomplete gamma function
    \ngammainccinv:  inverse of the regularized upper incomplete gamma function  
    \n\n
    Notes
    \n\n
    The function satisfies the relation gammainc(a, x) +\ngammaincc(a, x) = 1 where gammaincc is the regularized upper\nincomplete gamma function.
    \n\n
    The implementation largely follows that of [boost]_.
    \n\n
    References
    \n\n
    .. [dlmf] NIST Digital Library of Mathematical functions\n          https://dlmf.nist.gov/8.2#E4\n.. [boost] Maddock et. al., \"Incomplete Gamma Functions\",\n   https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
    \n\n
    Examples
    \n\n
    \n
    >>> import scipy.special as sc\n
    \n
    \n\n
    It is the CDF of the gamma distribution, so it starts at 0 and\nmonotonically increases to 1.
    \n\n
    \n
    >>> sc.gammainc(0.5, [0, 1, 10, 100])\narray([0.        , 0.84270079, 0.99999226, 1.        ])\n
    \n
    \n\n
    It is equal to one minus the upper incomplete gamma function.
    \n\n
    \n
    >>> a, x = 0.5, 0.4\n>>> sc.gammainc(a, x)\n0.6289066304773024\n>>> 1 - sc.gammaincc(a, x)\n0.6289066304773024\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammaincc": {"fullname": "pyerrors.special.gammaincc", "modulename": "pyerrors.special", "qualname": "gammaincc", "kind": "function", "doc": "
    gammaincc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    gammaincc(a, x, out=None)
    \n\n
    Regularized upper incomplete gamma function.
    \n\n
    It is defined as
    \n\n
    $$Q(a, x) = \\frac{1}{\\Gamma(a)} \\int_x^\\infty t^{a - 1}e^{-t} dt$$
    \n\n
    for \\( a > 0 \\) and \\( x \\geq 0 \\). See [dlmf]_ for details.
    \n\n
    Parameters
    \n\n
      \n
    • a (array_like):\nPositive parameter
      • \n
    • x (array_like):\nNonnegative argument
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the upper incomplete gamma function
      • \n
    \n\n
    See Also
    \n\n
    gammainc:  regularized lower incomplete gamma function
    \ngammaincinv:  inverse of the regularized lower incomplete gamma function
    \ngammainccinv:  inverse of the regularized upper incomplete gamma function  
    \n\n
    Notes
    \n\n
    The function satisfies the relation gammainc(a, x) +\ngammaincc(a, x) = 1 where gammainc is the regularized lower\nincomplete gamma function.
    \n\n
    The implementation largely follows that of [boost]_.
    \n\n
    References
    \n\n
    .. [dlmf] NIST Digital Library of Mathematical functions\n          https://dlmf.nist.gov/8.2#E4\n.. [boost] Maddock et. al., \"Incomplete Gamma Functions\",\n   https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
    \n\n
    Examples
    \n\n
    \n
    >>> import scipy.special as sc\n
    \n
    \n\n
    It is the survival function of the gamma distribution, so it\nstarts at 1 and monotonically decreases to 0.
    \n\n
    \n
    >>> sc.gammaincc(0.5, [0, 1, 10, 100, 1000])\narray([1.00000000e+00, 1.57299207e-01, 7.74421643e-06, 2.08848758e-45,\n       0.00000000e+00])\n
    \n
    \n\n
    It is equal to one minus the lower incomplete gamma function.
    \n\n
    \n
    >>> a, x = 0.5, 0.4\n>>> sc.gammaincc(a, x)\n0.37109336952269756\n>>> 1 - sc.gammainc(a, x)\n0.37109336952269756\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammasgn": {"fullname": "pyerrors.special.gammasgn", "modulename": "pyerrors.special", "qualname": "gammasgn", "kind": "function", "doc": "
    gammasgn(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    gammasgn(x, out=None)
    \n\n
    Sign of the gamma function.
    \n\n
    It is defined as
    \n\n
    $$\\text{gammasgn}(x) =\n\\begin{cases}\n  +1 & \\Gamma(x) > 0 \\\n  -1 & \\Gamma(x) < 0\n\\end{cases}$$
    \n\n
    where \\( \\Gamma \\) is the gamma function; see gamma. This\ndefinition is complete since the gamma function is never zero;\nsee the discussion after [dlmf]_.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nReal argument
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Sign of the gamma function
      • \n
    \n\n
    See Also
    \n\n
    gamma:  the gamma function
    \ngammaln:  log of the absolute value of the gamma function
    \nloggamma:  analytic continuation of the log of the gamma function  
    \n\n
    Notes
    \n\n
    The gamma function can be computed as gammasgn(x) *\nnp.exp(gammaln(x)).
    \n\n
    References
    \n\n
    .. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5.2#E1
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> import scipy.special as sc\n
    \n
    \n\n
    It is 1 for x > 0.
    \n\n
    \n
    >>> sc.gammasgn([1, 2, 3, 4])\narray([1., 1., 1., 1.])\n
    \n
    \n\n
    It alternates between -1 and 1 for negative integers.
    \n\n
    \n
    >>> sc.gammasgn([-0.5, -1.5, -2.5, -3.5])\narray([-1.,  1., -1.,  1.])\n
    \n
    \n\n
    It can be used to compute the gamma function.
    \n\n
    \n
    >>> x = [1.5, 0.5, -0.5, -1.5]\n>>> sc.gammasgn(x) * np.exp(sc.gammaln(x))\narray([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])\n>>> sc.gamma(x)\narray([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.rgamma": {"fullname": "pyerrors.special.rgamma", "modulename": "pyerrors.special", "qualname": "rgamma", "kind": "function", "doc": "
    rgamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    rgamma(z, out=None)
    \n\n
    Reciprocal of the gamma function.
    \n\n
    Defined as \\( 1 / \\Gamma(z) \\), where \\( \\Gamma \\) is the\ngamma function. For more on the gamma function see gamma.
    \n\n
    Parameters
    \n\n
      \n
    • z (array_like):\nReal or complex valued input
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Function results
      • \n
    \n\n
    See Also
    \n\n
    gamma,, gammaln,, loggamma  
    \n\n
    Notes
    \n\n
    The gamma function has no zeros and has simple poles at\nnonpositive integers, so rgamma is an entire function with zeros\nat the nonpositive integers. See the discussion in [dlmf]_ for\nmore details.
    \n\n
    References
    \n\n
    .. [dlmf] Nist, Digital Library of Mathematical functions,\n    https://dlmf.nist.gov/5.2#i
    \n\n
    Examples
    \n\n
    \n
    >>> import scipy.special as sc\n
    \n
    \n\n
    It is the reciprocal of the gamma function.
    \n\n
    \n
    >>> sc.rgamma([1, 2, 3, 4])\narray([1.        , 1.        , 0.5       , 0.16666667])\n>>> 1 / sc.gamma([1, 2, 3, 4])\narray([1.        , 1.        , 0.5       , 0.16666667])\n
    \n
    \n\n
    It is zero at nonpositive integers.
    \n\n
    \n
    >>> sc.rgamma([0, -1, -2, -3])\narray([0., 0., 0., 0.])\n
    \n
    \n\n
    It rapidly underflows to zero along the positive real axis.
    \n\n
    \n
    >>> sc.rgamma([10, 100, 179])\narray([2.75573192e-006, 1.07151029e-156, 0.00000000e+000])\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.multigammaln": {"fullname": "pyerrors.special.multigammaln", "modulename": "pyerrors.special", "qualname": "multigammaln", "kind": "function", "doc": "
    Returns the log of multivariate gamma, also sometimes called the\ngeneralized gamma.
    \n\n
    Parameters
    \n\n
      \n
    • a (ndarray):\nThe multivariate gamma is computed for each item of a.
      • \n
    • d (int):\nThe dimension of the space of integration.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (ndarray):\nThe values of the log multivariate gamma at the given points a.
      • \n
    \n\n
    Notes
    \n\n
    The formal definition of the multivariate gamma of dimension d for a real\na is
    \n\n
    $$\\Gamma_d(a) = \\int_{A>0} e^{-tr(A)} |A|^{a - (d+1)/2} dA$$
    \n\n
    with the condition \\( a > (d-1)/2 \\), and \\( A > 0 \\) being the set of\nall the positive definite matrices of dimension d.  Note that a is a\nscalar: the integrand only is multivariate, the argument is not (the\nfunction is defined over a subset of the real set).
    \n\n
    This can be proven to be equal to the much friendlier equation
    \n\n
    $$\\Gamma_d(a) = \\pi^{d(d-1)/4} \\prod_{i=1}^{d} \\Gamma(a - (i-1)/2).$$
    \n\n
    References
    \n\n
    R. J. Muirhead, Aspects of multivariate statistical theory (Wiley Series in\nprobability and mathematical statistics).
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.special import multigammaln, gammaln\n>>> a = 23.5\n>>> d = 10\n>>> multigammaln(a, d)\n454.1488605074416\n
    \n
    \n\n
    Verify that the result agrees with the logarithm of the equation\nshown above:
    \n\n
    \n
    >>> d*(d-1)/4*np.log(np.pi) + gammaln(a - 0.5*np.arange(0, d)).sum()\n454.1488605074416\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.kn": {"fullname": "pyerrors.special.kn", "modulename": "pyerrors.special", "qualname": "kn", "kind": "function", "doc": "
    Modified Bessel function of the second kind of integer order n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.j0": {"fullname": "pyerrors.special.j0", "modulename": "pyerrors.special", "qualname": "j0", "kind": "function", "doc": "
    j0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    j0(x, out=None)
    \n\n
    Bessel function of the first kind of order 0.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nArgument (float).
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • J (scalar or ndarray):\nValue of the Bessel function of the first kind of order 0 at x.
      • \n
    \n\n
    See Also
    \n\n
    jv:  Bessel function of real order and complex argument.
    \nspherical_jn:  spherical Bessel functions.  
    \n\n
    Notes
    \n\n
    The domain is divided into the intervals [0, 5] and (5, infinity). In the\nfirst interval the following rational approximation is used:
    \n\n
    $$J_0(x) \\approx (w - r_1^2)(w - r_2^2) \\frac{P_3(w)}{Q_8(w)},$$
    \n\n
    where \\( w = x^2 \\) and \\( r_1 \\), \\( r_2 \\) are the zeros of\n\\( J_0 \\), and \\( P_3 \\) and \\( Q_8 \\) are polynomials of degrees 3\nand 8, respectively.
    \n\n
    In the second interval, the Hankel asymptotic expansion is employed with\ntwo rational functions of degree 6/6 and 7/7.
    \n\n
    This function is a wrapper for the Cephes 1 routine j0.\nIt should not be confused with the spherical Bessel functions (see\nspherical_jn).
    \n\n
    References
    \n\n
    Examples
    \n\n
    Calculate the function at one point:
    \n\n
    \n
    >>> from scipy.special import j0\n>>> j0(1.)\n0.7651976865579665\n
    \n
    \n\n
    Calculate the function at several points:
    \n\n
    \n
    >>> import numpy as np\n>>> j0(np.array([-2., 0., 4.]))\narray([ 0.22389078,  1.        , -0.39714981])\n
    \n
    \n\n
    Plot the function from -20 to 20.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-20., 20., 1000)\n>>> y = j0(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.y0": {"fullname": "pyerrors.special.y0", "modulename": "pyerrors.special", "qualname": "y0", "kind": "function", "doc": "
    y0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    y0(x, out=None)
    \n\n
    Bessel function of the second kind of order 0.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nArgument (float).
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Y (scalar or ndarray):\nValue of the Bessel function of the second kind of order 0 at x.
      • \n
    \n\n
    See Also
    \n\n
    j0:  Bessel function of the first kind of order 0
    \nyv:  Bessel function of the first kind  
    \n\n
    Notes
    \n\n
    The domain is divided into the intervals [0, 5] and (5, infinity). In the\nfirst interval a rational approximation \\( R(x) \\) is employed to\ncompute,
    \n\n
    $$Y_0(x) = R(x) + \\frac{2 \\log(x) J_0(x)}{\\pi},$$
    \n\n
    where \\( J_0 \\) is the Bessel function of the first kind of order 0.
    \n\n
    In the second interval, the Hankel asymptotic expansion is employed with\ntwo rational functions of degree 6/6 and 7/7.
    \n\n
    This function is a wrapper for the Cephes 1 routine y0.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Calculate the function at one point:
    \n\n
    \n
    >>> from scipy.special import y0\n>>> y0(1.)\n0.08825696421567697\n
    \n
    \n\n
    Calculate at several points:
    \n\n
    \n
    >>> import numpy as np\n>>> y0(np.array([0.5, 2., 3.]))\narray([-0.44451873,  0.51037567,  0.37685001])\n
    \n
    \n\n
    Plot the function from 0 to 10.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(0., 10., 1000)\n>>> y = y0(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.j1": {"fullname": "pyerrors.special.j1", "modulename": "pyerrors.special", "qualname": "j1", "kind": "function", "doc": "
    j1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    j1(x, out=None)
    \n\n
    Bessel function of the first kind of order 1.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nArgument (float).
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • J (scalar or ndarray):\nValue of the Bessel function of the first kind of order 1 at x.
      • \n
    \n\n
    See Also
    \n\n
    jv:  Bessel function of the first kind
    \nspherical_jn:  spherical Bessel functions.  
    \n\n
    Notes
    \n\n
    The domain is divided into the intervals [0, 8] and (8, infinity). In the\nfirst interval a 24 term Chebyshev expansion is used. In the second, the\nasymptotic trigonometric representation is employed using two rational\nfunctions of degree 5/5.
    \n\n
    This function is a wrapper for the Cephes 1 routine j1.\nIt should not be confused with the spherical Bessel functions (see\nspherical_jn).
    \n\n
    References
    \n\n
    Examples
    \n\n
    Calculate the function at one point:
    \n\n
    \n
    >>> from scipy.special import j1\n>>> j1(1.)\n0.44005058574493355\n
    \n
    \n\n
    Calculate the function at several points:
    \n\n
    \n
    >>> import numpy as np\n>>> j1(np.array([-2., 0., 4.]))\narray([-0.57672481,  0.        , -0.06604333])\n
    \n
    \n\n
    Plot the function from -20 to 20.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-20., 20., 1000)\n>>> y = j1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.y1": {"fullname": "pyerrors.special.y1", "modulename": "pyerrors.special", "qualname": "y1", "kind": "function", "doc": "
    y1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    y1(x, out=None)
    \n\n
    Bessel function of the second kind of order 1.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nArgument (float).
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Y (scalar or ndarray):\nValue of the Bessel function of the second kind of order 1 at x.
      • \n
    \n\n
    See Also
    \n\n
    j1:  Bessel function of the first kind of order 1
    \nyn:  Bessel function of the second kind
    \nyv:  Bessel function of the second kind  
    \n\n
    Notes
    \n\n
    The domain is divided into the intervals [0, 8] and (8, infinity). In the\nfirst interval a 25 term Chebyshev expansion is used, and computing\n\\( J_1 \\) (the Bessel function of the first kind) is required. In the\nsecond, the asymptotic trigonometric representation is employed using two\nrational functions of degree 5/5.
    \n\n
    This function is a wrapper for the Cephes 1 routine y1.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Calculate the function at one point:
    \n\n
    \n
    >>> from scipy.special import y1\n>>> y1(1.)\n-0.7812128213002888\n
    \n
    \n\n
    Calculate at several points:
    \n\n
    \n
    >>> import numpy as np\n>>> y1(np.array([0.5, 2., 3.]))\narray([-1.47147239, -0.10703243,  0.32467442])\n
    \n
    \n\n
    Plot the function from 0 to 10.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(0., 10., 1000)\n>>> y = y1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.jn": {"fullname": "pyerrors.special.jn", "modulename": "pyerrors.special", "qualname": "jn", "kind": "function", "doc": "
    jv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    jv(v, z, out=None)
    \n\n
    Bessel function of the first kind of real order and complex argument.
    \n\n
    Parameters
    \n\n
      \n
    • v (array_like):\nOrder (float).
      • \n
    • z (array_like):\nArgument (float or complex).
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • J (scalar or ndarray):\nValue of the Bessel function, \\( J_v(z) \\).
      • \n
    \n\n
    See Also
    \n\n
    jve:  \\( J_v \\) with leading exponential behavior stripped off.
    \nspherical_jn:  spherical Bessel functions.
    \nj0:  faster version of this function for order 0.
    \nj1:  faster version of this function for order 1.  
    \n\n
    Notes
    \n\n
    For positive v values, the computation is carried out using the AMOS\n1 zbesj routine, which exploits the connection to the modified\nBessel function \\( I_v \\),
    \n\n
    $$J_v(z) = \\exp(v\\pi\\imath/2) I_v(-\\imath z)\\qquad (\\Im z > 0)
    \n\n
    J_v(z) = \\exp(-v\\pi\\imath/2) I_v(\\imath z)\\qquad (\\Im z < 0)$$
    \n\n
    For negative v values the formula,
    \n\n
    $$J_{-v}(z) = J_v(z) \\cos(\\pi v) - Y_v(z) \\sin(\\pi v)$$
    \n\n
    is used, where \\( Y_v(z) \\) is the Bessel function of the second\nkind, computed using the AMOS routine zbesy.  Note that the second\nterm is exactly zero for integer v; to improve accuracy the second\nterm is explicitly omitted for v values such that v = floor(v).
    \n\n
    Not to be confused with the spherical Bessel functions (see spherical_jn).
    \n\n
    References
    \n\n
    Examples
    \n\n
    Evaluate the function of order 0 at one point.
    \n\n
    \n
    >>> from scipy.special import jv\n>>> jv(0, 1.)\n0.7651976865579666\n
    \n
    \n\n
    Evaluate the function at one point for different orders.
    \n\n
    \n
    >>> jv(0, 1.), jv(1, 1.), jv(1.5, 1.)\n(0.7651976865579666, 0.44005058574493355, 0.24029783912342725)\n
    \n
    \n\n
    The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
    \n\n
    \n
    >>> jv([0, 1, 1.5], 1.)\narray([0.76519769, 0.44005059, 0.24029784])\n
    \n
    \n\n
    Evaluate the function at several points for order 0 by providing an\narray for z.
    \n\n
    \n
    >>> import numpy as np\n>>> points = np.array([-2., 0., 3.])\n>>> jv(0, points)\narray([ 0.22389078,  1.        , -0.26005195])\n
    \n
    \n\n
    If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
    \n\n
    \n
    >>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
    \n
    \n\n
    \n
    >>> jv(orders, points)\narray([[ 0.22389078,  1.        , -0.26005195],\n       [-0.57672481,  0.        ,  0.33905896]])\n
    \n
    \n\n
    Plot the functions of order 0 to 3 from -10 to 10.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> for i in range(4):\n...     ax.plot(x, jv(i, x), label=f'$J_{i!r}$')\n>>> ax.legend()\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.yn": {"fullname": "pyerrors.special.yn", "modulename": "pyerrors.special", "qualname": "yn", "kind": "function", "doc": "
    yn(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    yn(n, x, out=None)
    \n\n
    Bessel function of the second kind of integer order and real argument.
    \n\n
    Parameters
    \n\n
      \n
    • n (array_like):\nOrder (integer).
      • \n
    • x (array_like):\nArgument (float).
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Y (scalar or ndarray):\nValue of the Bessel function, \\( Y_n(x) \\).
      • \n
    \n\n
    See Also
    \n\n
    yv:  For real order and real or complex argument.
    \ny0:  faster implementation of this function for order 0
    \ny1:  faster implementation of this function for order 1  
    \n\n
    Notes
    \n\n
    Wrapper for the Cephes 1 routine yn.
    \n\n
    The function is evaluated by forward recurrence on n, starting with\nvalues computed by the Cephes routines y0 and y1. If n = 0 or 1,\nthe routine for y0 or y1 is called directly.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Evaluate the function of order 0 at one point.
    \n\n
    \n
    >>> from scipy.special import yn\n>>> yn(0, 1.)\n0.08825696421567697\n
    \n
    \n\n
    Evaluate the function at one point for different orders.
    \n\n
    \n
    >>> yn(0, 1.), yn(1, 1.), yn(2, 1.)\n(0.08825696421567697, -0.7812128213002888, -1.6506826068162546)\n
    \n
    \n\n
    The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
    \n\n
    \n
    >>> yn([0, 1, 2], 1.)\narray([ 0.08825696, -0.78121282, -1.65068261])\n
    \n
    \n\n
    Evaluate the function at several points for order 0 by providing an\narray for z.
    \n\n
    \n
    >>> import numpy as np\n>>> points = np.array([0.5, 3., 8.])\n>>> yn(0, points)\narray([-0.44451873,  0.37685001,  0.22352149])\n
    \n
    \n\n
    If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
    \n\n
    \n
    >>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
    \n
    \n\n
    \n
    >>> yn(orders, points)\narray([[-0.44451873,  0.37685001,  0.22352149],\n       [-1.47147239,  0.32467442, -0.15806046]])\n
    \n
    \n\n
    Plot the functions of order 0 to 3 from 0 to 10.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(0., 10., 1000)\n>>> for i in range(4):\n...     ax.plot(x, yn(i, x), label=f'$Y_{i!r}$')\n>>> ax.set_ylim(-3, 1)\n>>> ax.legend()\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.i0": {"fullname": "pyerrors.special.i0", "modulename": "pyerrors.special", "qualname": "i0", "kind": "function", "doc": "
    i0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    i0(x, out=None)
    \n\n
    Modified Bessel function of order 0.
    \n\n
    Defined as,
    \n\n
    $$I_0(x) = \\sum_{k=0}^\\infty \\frac{(x^2/4)^k}{(k!)^2} = J_0(\\imath x),$$
    \n\n
    where \\( J_0 \\) is the Bessel function of the first kind of order 0.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nArgument (float)
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • I (scalar or ndarray):\nValue of the modified Bessel function of order 0 at x.
      • \n
    \n\n
    See Also
    \n\n
    iv:  Modified Bessel function of any order
    \ni0e:  Exponentially scaled modified Bessel function of order 0  
    \n\n
    Notes
    \n\n
    The range is partitioned into the two intervals [0, 8] and (8, infinity).\nChebyshev polynomial expansions are employed in each interval.
    \n\n
    This function is a wrapper for the Cephes 1 routine i0.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Calculate the function at one point:
    \n\n
    \n
    >>> from scipy.special import i0\n>>> i0(1.)\n1.2660658777520082\n
    \n
    \n\n
    Calculate at several points:
    \n\n
    \n
    >>> import numpy as np\n>>> i0(np.array([-2., 0., 3.5]))\narray([2.2795853 , 1.        , 7.37820343])\n
    \n
    \n\n
    Plot the function from -10 to 10.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> y = i0(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.i1": {"fullname": "pyerrors.special.i1", "modulename": "pyerrors.special", "qualname": "i1", "kind": "function", "doc": "
    i1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    i1(x, out=None)
    \n\n
    Modified Bessel function of order 1.
    \n\n
    Defined as,
    \n\n
    $$I_1(x) = \\frac{1}{2}x \\sum_{k=0}^\\infty \\frac{(x^2/4)^k}{k! (k + 1)!}\n       = -\\imath J_1(\\imath x),$$
    \n\n
    where \\( J_1 \\) is the Bessel function of the first kind of order 1.
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nArgument (float)
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • I (scalar or ndarray):\nValue of the modified Bessel function of order 1 at x.
      • \n
    \n\n
    See Also
    \n\n
    iv:  Modified Bessel function of the first kind
    \ni1e:  Exponentially scaled modified Bessel function of order 1  
    \n\n
    Notes
    \n\n
    The range is partitioned into the two intervals [0, 8] and (8, infinity).\nChebyshev polynomial expansions are employed in each interval.
    \n\n
    This function is a wrapper for the Cephes 1 routine i1.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Calculate the function at one point:
    \n\n
    \n
    >>> from scipy.special import i1\n>>> i1(1.)\n0.5651591039924851\n
    \n
    \n\n
    Calculate the function at several points:
    \n\n
    \n
    >>> import numpy as np\n>>> i1(np.array([-2., 0., 6.]))\narray([-1.59063685,  0.        , 61.34193678])\n
    \n
    \n\n
    Plot the function between -10 and 10.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> y = i1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.iv": {"fullname": "pyerrors.special.iv", "modulename": "pyerrors.special", "qualname": "iv", "kind": "function", "doc": "
    iv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    iv(v, z, out=None)
    \n\n
    Modified Bessel function of the first kind of real order.
    \n\n
    Parameters
    \n\n
      \n
    • v (array_like):\nOrder. If z is of real type and negative, v must be integer\nvalued.
      • \n
    • z (array_like of float or complex):\nArgument.
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the modified Bessel function.
      • \n
    \n\n
    See Also
    \n\n
    ive:  This function with leading exponential behavior stripped off.
    \ni0:  Faster version of this function for order 0.
    \ni1:  Faster version of this function for order 1.  
    \n\n
    Notes
    \n\n
    For real z and \\( v \\in [-50, 50] \\), the evaluation is carried out\nusing Temme's method 1.  For larger orders, uniform asymptotic\nexpansions are applied.
    \n\n
    For complex z and positive v, the AMOS 2 zbesi routine is\ncalled. It uses a power series for small z, the asymptotic expansion\nfor large abs(z), the Miller algorithm normalized by the Wronskian\nand a Neumann series for intermediate magnitudes, and the uniform\nasymptotic expansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large\norders. Backward recurrence is used to generate sequences or reduce\norders when necessary.
    \n\n
    The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,
    \n\n
    $$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$
    \n\n
    (valid when the real part of z is positive).  For negative v, the\nformula
    \n\n
    $$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$
    \n\n
    is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.
    \n\n
    References
    \n\n
    Examples
    \n\n
    Evaluate the function of order 0 at one point.
    \n\n
    \n
    >>> from scipy.special import iv\n>>> iv(0, 1.)\n1.2660658777520084\n
    \n
    \n\n
    Evaluate the function at one point for different orders.
    \n\n
    \n
    >>> iv(0, 1.), iv(1, 1.), iv(1.5, 1.)\n(1.2660658777520084, 0.565159103992485, 0.2935253263474798)\n
    \n
    \n\n
    The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
    \n\n
    \n
    >>> iv([0, 1, 1.5], 1.)\narray([1.26606588, 0.5651591 , 0.29352533])\n
    \n
    \n\n
    Evaluate the function at several points for order 0 by providing an\narray for z.
    \n\n
    \n
    >>> import numpy as np\n>>> points = np.array([-2., 0., 3.])\n>>> iv(0, points)\narray([2.2795853 , 1.        , 4.88079259])\n
    \n
    \n\n
    If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
    \n\n
    \n
    >>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
    \n
    \n\n
    \n
    >>> iv(orders, points)\narray([[ 2.2795853 ,  1.        ,  4.88079259],\n       [-1.59063685,  0.        ,  3.95337022]])\n
    \n
    \n\n
    Plot the functions of order 0 to 3 from -5 to 5.
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, iv(i, x), label=f'$I_{i!r}$')\n>>> ax.legend()\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Temme, Journal of Computational Physics, vol 21, 343 (1976) ↩
      \n
      2. \n\n
    2. \n
      Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
      \n
      3. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.ive": {"fullname": "pyerrors.special.ive", "modulename": "pyerrors.special", "qualname": "ive", "kind": "function", "doc": "
    ive(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    ive(v, z, out=None)
    \n\n
    Exponentially scaled modified Bessel function of the first kind.
    \n\n
    Defined as::
    \n\n
    ive(v, z) = iv(v, z) * exp(-abs(z.real))\n
    \n\n
    For imaginary numbers without a real part, returns the unscaled\nBessel function of the first kind iv.
    \n\n
    Parameters
    \n\n
      \n
    • v (array_like of float):\nOrder.
      • \n
    • z (array_like of float or complex):\nArgument.
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the exponentially scaled modified Bessel function.
      • \n
    \n\n
    See Also
    \n\n
    iv:  Modified Bessel function of the first kind
    \ni0e:  Faster implementation of this function for order 0
    \ni1e:  Faster implementation of this function for order 1  
    \n\n
    Notes
    \n\n
    For positive v, the AMOS 1 zbesi routine is called. It uses a\npower series for small z, the asymptotic expansion for large\nabs(z), the Miller algorithm normalized by the Wronskian and a\nNeumann series for intermediate magnitudes, and the uniform asymptotic\nexpansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large orders.\nBackward recurrence is used to generate sequences or reduce orders when\nnecessary.
    \n\n
    The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,
    \n\n
    $$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$
    \n\n
    (valid when the real part of z is positive).  For negative v, the\nformula
    \n\n
    $$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$
    \n\n
    is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.
    \n\n
    ive is useful for large arguments z: for these, iv easily overflows,\nwhile ive does not due to the exponential scaling.
    \n\n
    References
    \n\n
    Examples
    \n\n
    In the following example iv returns infinity whereas ive still returns\na finite number.
    \n\n
    \n
    >>> from scipy.special import iv, ive\n>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> iv(3, 1000.), ive(3, 1000.)\n(inf, 0.01256056218254712)\n
    \n
    \n\n
    Evaluate the function at one point for different orders by\nproviding a list or NumPy array as argument for the v parameter:
    \n\n
    \n
    >>> ive([0, 1, 1.5], 1.)\narray([0.46575961, 0.20791042, 0.10798193])\n
    \n
    \n\n
    Evaluate the function at several points for order 0 by providing an\narray for z.
    \n\n
    \n
    >>> points = np.array([-2., 0., 3.])\n>>> ive(0, points)\narray([0.30850832, 1.        , 0.24300035])\n
    \n
    \n\n
    Evaluate the function at several points for different orders by\nproviding arrays for both v for z. Both arrays have to be\nbroadcastable to the correct shape. To calculate the orders 0, 1\nand 2 for a 1D array of points:
    \n\n
    \n
    >>> ive([[0], [1], [2]], points)\narray([[ 0.30850832,  1.        ,  0.24300035],\n       [-0.21526929,  0.        ,  0.19682671],\n       [ 0.09323903,  0.        ,  0.11178255]])\n
    \n
    \n\n
    Plot the functions of order 0 to 3 from -5 to 5.
    \n\n
    \n
    >>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, ive(i, x), label=fr'$I_{i!r}(z)\\cdot e^{{-|z|}}$')\n>>> ax.legend()\n>>> ax.set_xlabel(r"$z$")\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erf": {"fullname": "pyerrors.special.erf", "modulename": "pyerrors.special", "qualname": "erf", "kind": "function", "doc": "
    erf(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    erf(z, out=None)
    \n\n
    Returns the error function of complex argument.
    \n\n
    It is defined as 2/sqrt(pi)*integral(exp(-t**2), t=0..z).
    \n\n
    Parameters
    \n\n
      \n
    • x (ndarray):\nInput array.
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (scalar or ndarray):\nThe values of the error function at the given points x.
      • \n
    \n\n
    See Also
    \n\n
    erfc,, erfinv,, erfcinv,, wofz,, erfcx,, erfi  
    \n\n
    Notes
    \n\n
    The cumulative of the unit normal distribution is given by\nPhi(z) = 1/2[1 + erf(z/sqrt(2))].
    \n\n
    References
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy import special\n>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-3, 3)\n>>> plt.plot(x, special.erf(x))\n>>> plt.xlabel('$x$')\n>>> plt.ylabel('$erf(x)$')\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfc": {"fullname": "pyerrors.special.erfc", "modulename": "pyerrors.special", "qualname": "erfc", "kind": "function", "doc": "
    erfc(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    erfc(x, out=None)
    \n\n
    Complementary error function, 1 - erf(x).
    \n\n
    Parameters
    \n\n
      \n
    • x (array_like):\nReal or complex valued argument
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: Values of the complementary error function
      • \n
    \n\n
    See Also
    \n\n
    erf,, erfi,, erfcx,, dawsn,, wofz  
    \n\n
    References
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy import special\n>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-3, 3)\n>>> plt.plot(x, special.erfc(x))\n>>> plt.xlabel('$x$')\n>>> plt.ylabel('$erfc(x)$')\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfinv": {"fullname": "pyerrors.special.erfinv", "modulename": "pyerrors.special", "qualname": "erfinv", "kind": "function", "doc": "
    erfinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    erfinv(y, out=None)
    \n\n
    Inverse of the error function.
    \n\n
    Computes the inverse of the error function.
    \n\n
    In the complex domain, there is no unique complex number w satisfying\nerf(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, -1 < x < 1, there is a unique real\nnumber satisfying erf(erfinv(x)) = x.
    \n\n
    Parameters
    \n\n
      \n
    • y (ndarray):\nArgument at which to evaluate. Domain: [-1, 1]
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • erfinv (scalar or ndarray):\nThe inverse of erf of y, element-wise
      • \n
    \n\n
    See Also
    \n\n
    erf:  Error function of a complex argument
    \nerfc:  Complementary error function, 1 - erf(x)
    \nerfcinv:  Inverse of the complementary error function  
    \n\n
    Notes
    \n\n
    This function wraps the erf_inv routine from the\nBoost Math C++ library 1.
    \n\n
    References
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import erfinv, erf\n
    \n
    \n\n
    \n
    >>> erfinv(0.5)\n0.4769362762044699\n
    \n
    \n\n
    \n
    >>> y = np.linspace(-1.0, 1.0, num=9)\n>>> x = erfinv(y)\n>>> x\narray([       -inf, -0.81341985, -0.47693628, -0.22531206,  0.        ,\n        0.22531206,  0.47693628,  0.81341985,         inf])\n
    \n
    \n\n
    Verify that erf(erfinv(y)) is y.
    \n\n
    \n
    >>> erf(x)\narray([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])\n
    \n
    \n\n
    Plot the function:
    \n\n
    \n
    >>> y = np.linspace(-1, 1, 200)\n>>> fig, ax = plt.subplots()\n>>> ax.plot(y, erfinv(y))\n>>> ax.grid(True)\n>>> ax.set_xlabel('y')\n>>> ax.set_title('erfinv(y)')\n>>> plt.show()\n
    \n
    \n\n
    \n
    \n
      \n
    1. \n
      The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/. ↩
      \n
      2. \n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfcinv": {"fullname": "pyerrors.special.erfcinv", "modulename": "pyerrors.special", "qualname": "erfcinv", "kind": "function", "doc": "
    erfcinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    erfcinv(y, out=None)
    \n\n
    Inverse of the complementary error function.
    \n\n
    Computes the inverse of the complementary error function.
    \n\n
    In the complex domain, there is no unique complex number w satisfying\nerfc(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, 0 < x < 2, there is a unique real\nnumber satisfying erfc(erfcinv(x)) = erfcinv(erfc(x)).
    \n\n
    It is related to inverse of the error function by erfcinv(1-x) = erfinv(x)
    \n\n
    Parameters
    \n\n
      \n
    • y (ndarray):\nArgument at which to evaluate. Domain: [0, 2]
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • erfcinv (scalar or ndarray):\nThe inverse of erfc of y, element-wise
      • \n
    \n\n
    See Also
    \n\n
    erf:  Error function of a complex argument
    \nerfc:  Complementary error function, 1 - erf(x)
    \nerfinv:  Inverse of the error function  
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import erfcinv\n
    \n
    \n\n
    \n
    >>> erfcinv(0.5)\n0.4769362762044699\n
    \n
    \n\n
    \n
    >>> y = np.linspace(0.0, 2.0, num=11)\n>>> erfcinv(y)\narray([        inf,  0.9061938 ,  0.59511608,  0.37080716,  0.17914345,\n       -0.        , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,\n              -inf])\n
    \n
    \n\n
    Plot the function:
    \n\n
    \n
    >>> y = np.linspace(0, 2, 200)\n>>> fig, ax = plt.subplots()\n>>> ax.plot(y, erfcinv(y))\n>>> ax.grid(True)\n>>> ax.set_xlabel('y')\n>>> ax.set_title('erfcinv(y)')\n>>> plt.show()\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.logit": {"fullname": "pyerrors.special.logit", "modulename": "pyerrors.special", "qualname": "logit", "kind": "function", "doc": "
    logit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    logit(x, out=None)
    \n\n
    Logit ufunc for ndarrays.
    \n\n
    The logit function is defined as logit(p) = log(p/(1-p)).\nNote that logit(0) = -inf, logit(1) = inf, and logit(p)\nfor p<0 or p>1 yields nan.
    \n\n
    Parameters
    \n\n
      \n
    • x (ndarray):\nThe ndarray to apply logit to element-wise.
      • \n
    • out (ndarray, optional):\nOptional output array for the function results
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: An ndarray of the same shape as x. Its entries\nare logit of the corresponding entry of x.
      • \n
    \n\n
    See Also
    \n\n
    expit  
    \n\n
    Notes
    \n\n
    As a ufunc logit takes a number of optional\nkeyword arguments. For more information\nsee ufuncs 
    \n\n
    New in version 0.10.0.
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.special import logit, expit\n
    \n
    \n\n
    \n
    >>> logit([0, 0.25, 0.5, 0.75, 1])\narray([       -inf, -1.09861229,  0.        ,  1.09861229,         inf])\n
    \n
    \n\n
    expit is the inverse of logit:
    \n\n
    \n
    >>> expit(logit([0.1, 0.75, 0.999]))\narray([ 0.1  ,  0.75 ,  0.999])\n
    \n
    \n\n
    Plot logit(x) for x in [0, 1]:
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> x = np.linspace(0, 1, 501)\n>>> y = logit(x)\n>>> plt.plot(x, y)\n>>> plt.grid()\n>>> plt.ylim(-6, 6)\n>>> plt.xlabel('x')\n>>> plt.title('logit(x)')\n>>> plt.show()\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.expit": {"fullname": "pyerrors.special.expit", "modulename": "pyerrors.special", "qualname": "expit", "kind": "function", "doc": "
    expit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
    \n\n
    expit(x, out=None)
    \n\n
    Expit (a.k.a. logistic sigmoid) ufunc for ndarrays.
    \n\n
    The expit function, also known as the logistic sigmoid function, is\ndefined as expit(x) = 1/(1+exp(-x)).  It is the inverse of the\nlogit function.
    \n\n
    Parameters
    \n\n
      \n
    • x (ndarray):\nThe ndarray to apply expit to element-wise.
      • \n
    • out (ndarray, optional):\nOptional output array for the function values
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scalar or ndarray: An ndarray of the same shape as x. Its entries\nare expit of the corresponding entry of x.
      • \n
    \n\n
    See Also
    \n\n
    logit  
    \n\n
    Notes
    \n\n
    As a ufunc expit takes a number of optional\nkeyword arguments. For more information\nsee ufuncs 
    \n\n
    New in version 0.10.0.
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.special import expit, logit\n
    \n
    \n\n
    \n
    >>> expit([-np.inf, -1.5, 0, 1.5, np.inf])\narray([ 0.        ,  0.18242552,  0.5       ,  0.81757448,  1.        ])\n
    \n
    \n\n
    logit is the inverse of expit:
    \n\n
    \n
    >>> logit(expit([-2.5, 0, 3.1, 5.0]))\narray([-2.5,  0. ,  3.1,  5. ])\n
    \n
    \n\n
    Plot expit(x) for x in [-6, 6]:
    \n\n
    \n
    >>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-6, 6, 121)\n>>> y = expit(x)\n>>> plt.plot(x, y)\n>>> plt.grid()\n>>> plt.xlim(-6, 6)\n>>> plt.xlabel('x')\n>>> plt.title('expit(x)')\n>>> plt.show()\n
    \n
    \n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.logsumexp": {"fullname": "pyerrors.special.logsumexp", "modulename": "pyerrors.special", "qualname": "logsumexp", "kind": "function", "doc": "
    Compute the log of the sum of exponentials of input elements.
    \n\n
    Parameters
    \n\n
      \n
    • a (array_like):\nInput array.
      • \n
    • axis (None or int or tuple of ints, optional):\nAxis or axes over which the sum is taken. By default axis is None,\nand all elements are summed.
      \n\n
      New in version 0.11.0.
      • \n
    • b (array-like, optional):\nScaling factor for exp(a) must be of the same shape as a or\nbroadcastable to a. These values may be negative in order to\nimplement subtraction.
      \n\n
      New in version 0.12.0.
      • \n
    • keepdims (bool, optional):\nIf this is set to True, the axes which are reduced are left in the\nresult as dimensions with size one. With this option, the result\nwill broadcast correctly against the original array.
      \n\n
      New in version 0.15.0.
      • \n
    • return_sign (bool, optional):\nIf this is set to True, the result will be a pair containing sign\ninformation; if False, results that are negative will be returned\nas NaN. Default is False (no sign information).
      \n\n
      New in version 0.16.0.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (ndarray):\nThe result, np.log(np.sum(np.exp(a))) calculated in a numerically\nmore stable way. If b is given then np.log(np.sum(b*np.exp(a)))\nis returned. If return_sign is True, res contains the log of\nthe absolute value of the argument.
      • \n
    • sgn (ndarray):\nIf return_sign is True, this will be an array of floating-point\nnumbers matching res containing +1, 0, -1 (for real-valued inputs)\nor a complex phase (for complex inputs). This gives the sign of the\nargument of the logarithm in res.\nIf return_sign is False, only one result is returned.
      • \n
    \n\n
    See Also
    \n\n
    numpy.logaddexp,, numpy.logaddexp2  
    \n\n
    Notes
    \n\n
    NumPy has a logaddexp function which is very similar to logsumexp, but\nonly handles two arguments. logaddexp.reduce is similar to this\nfunction, but may be less stable.
    \n\n
    The logarithm is a multivalued function: for each \\( x \\) there is an\ninfinite number of \\( z \\) such that \\( exp(z) = x \\). The convention\nis to return the \\( z \\) whose imaginary part lies in \\( (-pi, pi] \\).
    \n\n
    Examples
    \n\n
    \n
    >>> import numpy as np\n>>> from scipy.special import logsumexp\n>>> a = np.arange(10)\n>>> logsumexp(a)\n9.4586297444267107\n>>> np.log(np.sum(np.exp(a)))\n9.4586297444267107\n
    \n
    \n\n
    With weights
    \n\n
    \n
    >>> a = np.arange(10)\n>>> b = np.arange(10, 0, -1)\n>>> logsumexp(a, b=b)\n9.9170178533034665\n>>> np.log(np.sum(b*np.exp(a)))\n9.9170178533034647\n
    \n
    \n\n
    Returning a sign flag
    \n\n
    \n
    >>> logsumexp([1,2],b=[1,-1],return_sign=True)\n(1.5413248546129181, -1.0)\n
    \n
    \n\n
    Notice that logsumexp does not directly support masked arrays. To use it\non a masked array, convert the mask into zero weights:
    \n\n
    \n
    >>> a = np.ma.array([np.log(2), 2, np.log(3)],\n...                  mask=[False, True, False])\n>>> b = (~a.mask).astype(int)\n>>> logsumexp(a.data, b=b), np.log(5)\n1.6094379124341005, 1.6094379124341005\n
    \n
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